None: 8470276/10000000 ≈ 0.847
├── Some((0, 0)): 11604/21792 ≈ 0.532
  ├── Some((0, 1)): 1619/3017 ≈ 0.537
    ├── Some((1, 0)): 194/357 ≈ 0.543
      ├── Some((0, 2)): 37/63 ≈ 0.587
      ├── Some((0, 3)): 12/31 ≈ 0.387
      ├── Some((0, 4)): 26/49 ≈ 0.531
      ├── Some((0, 5)): 40/66 ≈ 0.606
      ├── Some((0, 6)): 22/44 ≈ 0.500
      ├── Some((0, 7)): 25/48 ≈ 0.521
      └── Some((0, 8)): 31/55 ≈ 0.564
    ├── Some((1, 1)): 201/368 ≈ 0.546
      ├── Some((1, 0)): 30/52 ≈ 0.577
      ├── Some((1, 2)): 25/46 ≈ 0.543
      ├── Some((1, 3)): 10/27 ≈ 0.370
      ├── Some((1, 4)): 27/49 ≈ 0.551
      ├── Some((1, 5)): 12/30 ≈ 0.400
      ├── Some((1, 6)): 45/70 ≈ 0.643
      ├── Some((1, 7)): 38/62 ≈ 0.613
      └── Some((1, 8)): 13/31 ≈ 0.419
    ├── Some((1, 2)): 238/424 ≈ 0.561
      ├── Some((2, 0)): 35/57 ≈ 0.614
      ├── Some((2, 1)): 24/44 ≈ 0.545
      ├── Some((2, 2)): 28/49 ≈ 0.571
      ├── Some((2, 3)): 37/60 ≈ 0.617
      ├── Some((2, 4)): 21/41 ≈ 0.512
      ├── Some((2, 5)): 32/54 ≈ 0.593
      ├── Some((2, 6)): 13/30 ≈ 0.433
      ├── Some((2, 7)): 24/44 ≈ 0.545
      └── Some((2, 8)): 24/44 ≈ 0.545
    ├── Some((1, 3)): 190/351 ≈ 0.541
      ├── Some((3, 0)): 16/33 ≈ 0.485
      ├── Some((3, 1)): 29/48 ≈ 0.604
      ├── Some((3, 2)): 15/32 ≈ 0.469
      ├── Some((3, 3)): 10/25 ≈ 0.400
      ├── Some((3, 4)): 23/41 ≈ 0.561
      ├── Some((3, 5)): 10/25 ≈ 0.400
      ├── Some((3, 6)): 37/58 ≈ 0.638
      ├── Some((3, 7)): 21/39 ≈ 0.538
      └── Some((3, 8)): 29/49 ≈ 0.592
    ├── Some((1, 4)): 93/200 ≈ 0.465
      ├── Some((4, 0)): 9/21 ≈ 0.429
      ├── Some((4, 1)): 9/21 ≈ 0.429
      ├── Some((4, 2)): 20/33 ≈ 0.606
      ├── Some((4, 3)): 5/16 ≈ 0.312
      ├── Some((4, 4)): 12/24 ≈ 0.500
      ├── Some((4, 5)): 11/23 ≈ 0.478
      ├── Some((4, 6)): 7/18 ≈ 0.389
      ├── Some((4, 7)): 4/15 ≈ 0.267
      └── Some((4, 8)): 15/28 ≈ 0.536
    ├── Some((1, 5)): 207/377 ≈ 0.549
      ├── Some((5, 0)): 25/45 ≈ 0.556
      ├── Some((5, 1)): 18/36 ≈ 0.500
      ├── Some((5, 2)): 45/68 ≈ 0.662
      ├── Some((5, 3)): 27/47 ≈ 0.574
      ├── Some((5, 4)): 4/18 ≈ 0.222
      ├── Some((5, 5)): 20/39 ≈ 0.513
      ├── Some((5, 6)): 41/63 ≈ 0.651
      ├── Some((5, 7)): 13/30 ≈ 0.433
      └── Some((5, 8)): 13/30 ≈ 0.433
    ├── Some((1, 6)): 164/311 ≈ 0.527
      ├── Some((6, 0)): 17/33 ≈ 0.515
      ├── Some((6, 1)): 27/45 ≈ 0.600
      ├── Some((6, 2)): 8/22 ≈ 0.364
      ├── Some((6, 3)): 16/32 ≈ 0.500
      ├── Some((6, 4)): 17/33 ≈ 0.515
      ├── Some((6, 5)): 20/37 ≈ 0.541
      ├── Some((6, 6)): 12/27 ≈ 0.444
      ├── Some((6, 7)): 18/35 ≈ 0.514
      └── Some((6, 8)): 28/46 ≈ 0.609
    ├── Some((1, 7)): 144/280 ≈ 0.514
      ├── Some((7, 0)): 19/35 ≈ 0.543
      ├── Some((7, 1)): 13/28 ≈ 0.464
      ├── Some((7, 2)): 19/35 ≈ 0.543
      ├── Some((7, 3)): 11/25 ≈ 0.440
      ├── Some((7, 4)): 23/39 ≈ 0.590
      ├── Some((7, 5)): 12/26 ≈ 0.462
      ├── Some((7, 6)): 30/47 ≈ 0.638
      ├── Some((7, 7)): 13/28 ≈ 0.464
      └── Some((7, 8)): 4/16 ≈ 0.250
    └── Some((1, 8)): 188/348 ≈ 0.540
      ├── Some((8, 0)): 19/37 ≈ 0.514
      ├── Some((8, 1)): 16/33 ≈ 0.485
      ├── Some((8, 2)): 13/29 ≈ 0.448
      ├── Some((8, 3)): 16/33 ≈ 0.485
      ├── Some((8, 4)): 3/16 ≈ 0.188
      ├── Some((8, 5)): 49/71 ≈ 0.690
      ├── Some((8, 6)): 27/46 ≈ 0.587
      ├── Some((8, 7)): 24/43 ≈ 0.558
      └── Some((8, 8)): 21/39 ≈ 0.538
  ├── Some((0, 2)): 910/1782 ≈ 0.511
    ├── Some((2, 0)): 142/260 ≈ 0.546
      ├── Some((0, 1)): 28/46 ≈ 0.609
      ├── Some((0, 3)): 21/38 ≈ 0.553
      ├── Some((0, 4)): 13/28 ≈ 0.464
      ├── Some((0, 5)): 10/25 ≈ 0.400
      ├── Some((0, 6)): 20/37 ≈ 0.541
      ├── Some((0, 7)): 21/38 ≈ 0.553
      └── Some((0, 8)): 29/47 ≈ 0.617
    ├── Some((2, 1)): 158/284 ≈ 0.556
      ├── Some((1, 0)): 19/34 ≈ 0.559
      ├── Some((1, 1)): 11/24 ≈ 0.458
      ├── Some((1, 2)): 16/30 ≈ 0.533
      ├── Some((1, 3)): 7/19 ≈ 0.368
      ├── Some((1, 4)): 33/49 ≈ 0.673
      ├── Some((1, 5)): 4/15 ≈ 0.267
      ├── Some((1, 6)): 17/32 ≈ 0.531
      ├── Some((1, 7)): 13/27 ≈ 0.481
      └── Some((1, 8)): 37/53 ≈ 0.698
    ├── Some((2, 2)): 79/164 ≈ 0.482
      ├── Some((2, 0)): 12/23 ≈ 0.522
      ├── Some((2, 1)): 6/16 ≈ 0.375
      ├── Some((2, 3)): 8/18 ≈ 0.444
      ├── Some((2, 4)): 11/22 ≈ 0.500
      ├── Some((2, 5)): 15/26 ≈ 0.577
      ├── Some((2, 6)): 11/22 ≈ 0.500
      ├── Some((2, 7)): 7/17 ≈ 0.412
      └── Some((2, 8)): 8/19 ≈ 0.421
    ├── Some((2, 3)): 95/189 ≈ 0.503
      ├── Some((3, 0)): 7/17 ≈ 0.412
      ├── Some((3, 1)): 11/22 ≈ 0.500
      ├── Some((3, 2)): 10/21 ≈ 0.476
      ├── Some((3, 3)): 13/24 ≈ 0.542
      ├── Some((3, 4)): 9/19 ≈ 0.474
      ├── Some((3, 5)): 4/13 ≈ 0.308
      ├── Some((3, 6)): 7/17 ≈ 0.412
      ├── Some((3, 7)): 18/29 ≈ 0.621
      └── Some((3, 8)): 15/26 ≈ 0.577
    ├── Some((2, 4)): 74/157 ≈ 0.471
      ├── Some((4, 0)): 2/10 ≈ 0.200
      ├── Some((4, 1)): 13/23 ≈ 0.565
      ├── Some((4, 2)): 10/20 ≈ 0.500
      ├── Some((4, 3)): 3/11 ≈ 0.273
      ├── Some((4, 4)): 5/14 ≈ 0.357
      ├── Some((4, 5)): 3/11 ≈ 0.273
      ├── Some((4, 6)): 8/17 ≈ 0.471
      ├── Some((4, 7)): 15/25 ≈ 0.600
      └── Some((4, 8)): 15/25 ≈ 0.600
    ├── Some((2, 5)): 103/201 ≈ 0.512
      ├── Some((5, 0)): 10/21 ≈ 0.476
      ├── Some((5, 1)): 14/26 ≈ 0.538
      ├── Some((5, 2)): 7/17 ≈ 0.412
      ├── Some((5, 3)): 7/17 ≈ 0.412
      ├── Some((5, 4)): 0/8 ≈ 0.000
      ├── Some((5, 5)): 19/31 ≈ 0.613
      ├── Some((5, 6)): 23/35 ≈ 0.657
      ├── Some((5, 7)): 12/23 ≈ 0.522
      └── Some((5, 8)): 11/22 ≈ 0.500
    ├── Some((2, 6)): 74/157 ≈ 0.471
      ├── Some((6, 0)): 16/26 ≈ 0.615
      ├── Some((6, 1)): 4/13 ≈ 0.308
      ├── Some((6, 2)): 11/20 ≈ 0.550
      ├── Some((6, 3)): 9/18 ≈ 0.500
      ├── Some((6, 4)): 9/18 ≈ 0.500
      ├── Some((6, 5)): 8/17 ≈ 0.471
      ├── Some((6, 6)): 4/13 ≈ 0.308
      ├── Some((6, 7)): 9/18 ≈ 0.500
      └── Some((6, 8)): 4/13 ≈ 0.308
    ├── Some((2, 7)): 83/171 ≈ 0.485
      ├── Some((7, 0)): 9/19 ≈ 0.474
      ├── Some((7, 1)): 10/20 ≈ 0.500
      ├── Some((7, 2)): 12/22 ≈ 0.545
      ├── Some((7, 3)): 9/19 ≈ 0.474
      ├── Some((7, 4)): 19/30 ≈ 0.633
      ├── Some((7, 5)): 8/18 ≈ 0.444
      ├── Some((7, 6)): 5/14 ≈ 0.357
      ├── Some((7, 7)): 6/15 ≈ 0.400
      └── Some((7, 8)): 4/13 ≈ 0.308
    └── Some((2, 8)): 101/198 ≈ 0.510
      ├── Some((8, 0)): 8/18 ≈ 0.444
      ├── Some((8, 1)): 10/21 ≈ 0.476
      ├── Some((8, 2)): 13/24 ≈ 0.542
      ├── Some((8, 3)): 14/25 ≈ 0.560
      ├── Some((8, 4)): 10/21 ≈ 0.476
      ├── Some((8, 5)): 18/29 ≈ 0.621
      ├── Some((8, 6)): 9/20 ≈ 0.450
      ├── Some((8, 7)): 4/14 ≈ 0.286
      └── Some((8, 8)): 14/25 ≈ 0.560
  ├── Some((0, 3)): 1258/2392 ≈ 0.526
    ├── Some((3, 0)): 98/201 ≈ 0.488
      ├── Some((0, 1)): 23/39 ≈ 0.590
      ├── Some((0, 2)): 7/20 ≈ 0.350
      ├── Some((0, 4)): 8/21 ≈ 0.381
      ├── Some((0, 5)): 17/32 ≈ 0.531
      ├── Some((0, 6)): 25/42 ≈ 0.595
      ├── Some((0, 7)): 9/23 ≈ 0.391
      └── Some((0, 8)): 9/23 ≈ 0.391
    ├── Some((3, 1)): 150/282 ≈ 0.532
      ├── Some((1, 0)): 15/30 ≈ 0.500
      ├── Some((1, 1)): 12/26 ≈ 0.462
      ├── Some((1, 2)): 13/27 ≈ 0.481
      ├── Some((1, 3)): 9/22 ≈ 0.409
      ├── Some((1, 4)): 19/34 ≈ 0.559
      ├── Some((1, 5)): 14/28 ≈ 0.500
      ├── Some((1, 6)): 18/33 ≈ 0.545
      ├── Some((1, 7)): 21/36 ≈ 0.583
      └── Some((1, 8)): 29/45 ≈ 0.644
    ├── Some((3, 2)): 122/239 ≈ 0.510
      ├── Some((2, 0)): 15/28 ≈ 0.536
      ├── Some((2, 1)): 16/30 ≈ 0.533
      ├── Some((2, 2)): 10/22 ≈ 0.455
      ├── Some((2, 3)): 10/22 ≈ 0.455
      ├── Some((2, 4)): 11/24 ≈ 0.458
      ├── Some((2, 5)): 10/22 ≈ 0.455
      ├── Some((2, 6)): 13/26 ≈ 0.500
      ├── Some((2, 7)): 10/23 ≈ 0.435
      └── Some((2, 8)): 26/41 ≈ 0.634
    ├── Some((3, 3)): 133/256 ≈ 0.520
      ├── Some((3, 0)): 31/49 ≈ 0.633
      ├── Some((3, 1)): 16/31 ≈ 0.516
      ├── Some((3, 2)): 16/32 ≈ 0.500
      ├── Some((3, 4)): 30/48 ≈ 0.625
      ├── Some((3, 5)): 6/19 ≈ 0.316
      ├── Some((3, 6)): 9/23 ≈ 0.391
      ├── Some((3, 7)): 6/19 ≈ 0.316
      └── Some((3, 8)): 18/34 ≈ 0.529
    ├── Some((3, 4)): 102/208 ≈ 0.490
      ├── Some((4, 0)): 12/24 ≈ 0.500
      ├── Some((4, 1)): 7/18 ≈ 0.389
      ├── Some((4, 2)): 12/24 ≈ 0.500
      ├── Some((4, 3)): 8/19 ≈ 0.421
      ├── Some((4, 4)): 18/31 ≈ 0.581
      ├── Some((4, 5)): 10/21 ≈ 0.476
      ├── Some((4, 6)): 6/17 ≈ 0.353
      ├── Some((4, 7)): 10/21 ≈ 0.476
      └── Some((4, 8)): 19/32 ≈ 0.594
    ├── Some((3, 5)): 181/328 ≈ 0.552
      ├── Some((5, 0)): 39/58 ≈ 0.672
      ├── Some((5, 1)): 12/27 ≈ 0.444
      ├── Some((5, 2)): 28/46 ≈ 0.609
      ├── Some((5, 3)): 18/34 ≈ 0.529
      ├── Some((5, 4)): 25/42 ≈ 0.595
      ├── Some((5, 5)): 9/23 ≈ 0.391
      ├── Some((5, 6)): 19/36 ≈ 0.528
      ├── Some((5, 7)): 12/27 ≈ 0.444
      └── Some((5, 8)): 18/34 ≈ 0.529
    ├── Some((3, 6)): 125/243 ≈ 0.514
      ├── Some((6, 0)): 26/41 ≈ 0.634
      ├── Some((6, 1)): 7/19 ≈ 0.368
      ├── Some((6, 2)): 21/35 ≈ 0.600
      ├── Some((6, 3)): 8/20 ≈ 0.400
      ├── Some((6, 4)): 11/24 ≈ 0.458
      ├── Some((6, 5)): 13/26 ≈ 0.500
      ├── Some((6, 6)): 9/21 ≈ 0.429
      ├── Some((6, 7)): 15/28 ≈ 0.536
      └── Some((6, 8)): 15/28 ≈ 0.536
    ├── Some((3, 7)): 198/354 ≈ 0.559
      ├── Some((7, 0)): 22/39 ≈ 0.564
      ├── Some((7, 1)): 22/39 ≈ 0.564
      ├── Some((7, 2)): 28/46 ≈ 0.609
      ├── Some((7, 3)): 22/40 ≈ 0.550
      ├── Some((7, 4)): 6/20 ≈ 0.300
      ├── Some((7, 5)): 30/49 ≈ 0.612
      ├── Some((7, 6)): 11/26 ≈ 0.423
      ├── Some((7, 7)): 28/46 ≈ 0.609
      └── Some((7, 8)): 29/48 ≈ 0.604
    └── Some((3, 8)): 149/280 ≈ 0.532
      ├── Some((8, 0)): 26/42 ≈ 0.619
      ├── Some((8, 1)): 5/17 ≈ 0.294
      ├── Some((8, 2)): 20/35 ≈ 0.571
      ├── Some((8, 3)): 14/28 ≈ 0.500
      ├── Some((8, 4)): 19/34 ≈ 0.559
      ├── Some((8, 5)): 16/31 ≈ 0.516
      ├── Some((8, 6)): 18/33 ≈ 0.545
      ├── Some((8, 7)): 10/24 ≈ 0.417
      └── Some((8, 8)): 20/35 ≈ 0.571
  ├── Some((0, 4)): 1560/2915 ≈ 0.535
    ├── Some((4, 0)): 219/394 ≈ 0.556
      ├── Some((0, 1)): 35/61 ≈ 0.574
      ├── Some((0, 2)): 22/45 ≈ 0.489
      ├── Some((0, 3)): 36/62 ≈ 0.581
      ├── Some((0, 5)): 39/66 ≈ 0.591
      ├── Some((0, 6)): 29/54 ≈ 0.537
      ├── Some((0, 7)): 14/34 ≈ 0.412
      └── Some((0, 8)): 43/71 ≈ 0.606
    ├── Some((4, 1)): 81/179 ≈ 0.453
      ├── Some((1, 0)): 6/16 ≈ 0.375
      ├── Some((1, 1)): 17/29 ≈ 0.586
      ├── Some((1, 2)): 9/20 ≈ 0.450
      ├── Some((1, 3)): 14/26 ≈ 0.538
      ├── Some((1, 4)): 9/20 ≈ 0.450
      ├── Some((1, 5)): 6/17 ≈ 0.353
      ├── Some((1, 6)): 5/15 ≈ 0.333
      ├── Some((1, 7)): 9/20 ≈ 0.450
      └── Some((1, 8)): 5/15 ≈ 0.333
    ├── Some((4, 2)): 173/324 ≈ 0.534
      ├── Some((2, 0)): 4/17 ≈ 0.235
      ├── Some((2, 1)): 15/31 ≈ 0.484
      ├── Some((2, 2)): 25/43 ≈ 0.581
      ├── Some((2, 3)): 32/51 ≈ 0.627
      ├── Some((2, 4)): 12/27 ≈ 0.444
      ├── Some((2, 5)): 15/31 ≈ 0.484
      ├── Some((2, 6)): 16/32 ≈ 0.500
      ├── Some((2, 7)): 28/47 ≈ 0.596
      └── Some((2, 8)): 26/44 ≈ 0.591
    ├── Some((4, 3)): 238/423 ≈ 0.563
      ├── Some((3, 0)): 44/68 ≈ 0.647
      ├── Some((3, 1)): 17/36 ≈ 0.472
      ├── Some((3, 2)): 23/43 ≈ 0.535
      ├── Some((3, 3)): 30/52 ≈ 0.577
      ├── Some((3, 4)): 28/49 ≈ 0.571
      ├── Some((3, 5)): 24/44 ≈ 0.545
      ├── Some((3, 6)): 8/24 ≈ 0.333
      ├── Some((3, 7)): 23/43 ≈ 0.535
      └── Some((3, 8)): 40/63 ≈ 0.635
    ├── Some((4, 4)): 128/254 ≈ 0.504
      ├── Some((4, 0)): 14/29 ≈ 0.483
      ├── Some((4, 1)): 16/32 ≈ 0.500
      ├── Some((4, 2)): 14/30 ≈ 0.467
      ├── Some((4, 3)): 30/48 ≈ 0.625
      ├── Some((4, 5)): 20/37 ≈ 0.541
      ├── Some((4, 6)): 11/26 ≈ 0.423
      ├── Some((4, 7)): 12/27 ≈ 0.444
      └── Some((4, 8)): 10/24 ≈ 0.417
    ├── Some((4, 5)): 195/358 ≈ 0.545
      ├── Some((5, 0)): 9/24 ≈ 0.375
      ├── Some((5, 1)): 21/39 ≈ 0.538
      ├── Some((5, 2)): 22/40 ≈ 0.550
      ├── Some((5, 3)): 31/51 ≈ 0.608
      ├── Some((5, 4)): 19/37 ≈ 0.514
      ├── Some((5, 5)): 18/36 ≈ 0.500
      ├── Some((5, 6)): 22/40 ≈ 0.550
      ├── Some((5, 7)): 36/56 ≈ 0.643
      └── Some((5, 8)): 17/34 ≈ 0.500
    ├── Some((4, 6)): 113/231 ≈ 0.489
      ├── Some((6, 0)): 13/27 ≈ 0.481
      ├── Some((6, 1)): 11/24 ≈ 0.458
      ├── Some((6, 2)): 7/19 ≈ 0.368
      ├── Some((6, 3)): 10/23 ≈ 0.435
      ├── Some((6, 4)): 12/25 ≈ 0.480
      ├── Some((6, 5)): 12/25 ≈ 0.480
      ├── Some((6, 6)): 8/20 ≈ 0.400
      ├── Some((6, 7)): 8/20 ≈ 0.400
      └── Some((6, 8)): 31/47 ≈ 0.660
    ├── Some((4, 7)): 208/378 ≈ 0.550
      ├── Some((7, 0)): 11/27 ≈ 0.407
      ├── Some((7, 1)): 18/36 ≈ 0.500
      ├── Some((7, 2)): 27/47 ≈ 0.574
      ├── Some((7, 3)): 12/28 ≈ 0.429
      ├── Some((7, 4)): 36/57 ≈ 0.632
      ├── Some((7, 5)): 30/50 ≈ 0.600
      ├── Some((7, 6)): 24/43 ≈ 0.558
      ├── Some((7, 7)): 21/40 ≈ 0.525
      └── Some((7, 8)): 29/49 ≈ 0.592
    └── Some((4, 8)): 205/373 ≈ 0.550
      ├── Some((8, 0)): 17/35 ≈ 0.486
      ├── Some((8, 1)): 17/35 ≈ 0.486
      ├── Some((8, 2)): 16/33 ≈ 0.485
      ├── Some((8, 3)): 32/52 ≈ 0.615
      ├── Some((8, 4)): 12/28 ≈ 0.429
      ├── Some((8, 5)): 26/45 ≈ 0.578
      ├── Some((8, 6)): 42/64 ≈ 0.656
      ├── Some((8, 7)): 18/36 ≈ 0.500
      └── Some((8, 8)): 25/44 ≈ 0.568
  ├── Some((0, 5)): 1247/2373 ≈ 0.525
    ├── Some((5, 0)): 167/308 ≈ 0.542
      ├── Some((0, 1)): 36/59 ≈ 0.610
      ├── Some((0, 2)): 29/50 ≈ 0.580
      ├── Some((0, 3)): 13/31 ≈ 0.419
      ├── Some((0, 4)): 15/33 ≈ 0.455
      ├── Some((0, 6)): 29/51 ≈ 0.569
      ├── Some((0, 7)): 16/34 ≈ 0.471
      └── Some((0, 8)): 28/49 ≈ 0.571
    ├── Some((5, 1)): 170/312 ≈ 0.545
      ├── Some((1, 0)): 8/22 ≈ 0.364
      ├── Some((1, 1)): 23/40 ≈ 0.575
      ├── Some((1, 2)): 10/24 ≈ 0.417
      ├── Some((1, 3)): 25/42 ≈ 0.595
      ├── Some((1, 4)): 13/28 ≈ 0.464
      ├── Some((1, 5)): 15/30 ≈ 0.500
      ├── Some((1, 6)): 29/46 ≈ 0.630
      ├── Some((1, 7)): 31/49 ≈ 0.633
      └── Some((1, 8)): 15/30 ≈ 0.500
    ├── Some((5, 2)): 153/286 ≈ 0.535
      ├── Some((2, 0)): 16/31 ≈ 0.516
      ├── Some((2, 1)): 23/39 ≈ 0.590
      ├── Some((2, 2)): 29/45 ≈ 0.644
      ├── Some((2, 3)): 18/33 ≈ 0.545
      ├── Some((2, 4)): 10/24 ≈ 0.417
      ├── Some((2, 5)): 13/27 ≈ 0.481
      ├── Some((2, 6)): 18/33 ≈ 0.545
      ├── Some((2, 7)): 13/27 ≈ 0.481
      └── Some((2, 8)): 12/26 ≈ 0.462
    ├── Some((5, 3)): 88/186 ≈ 0.473
      ├── Some((3, 0)): 12/23 ≈ 0.522
      ├── Some((3, 1)): 7/18 ≈ 0.389
      ├── Some((3, 2)): 12/23 ≈ 0.522
      ├── Some((3, 3)): 9/20 ≈ 0.450
      ├── Some((3, 4)): 8/19 ≈ 0.421
      ├── Some((3, 5)): 13/24 ≈ 0.542
      ├── Some((3, 6)): 10/21 ≈ 0.476
      ├── Some((3, 7)): 5/15 ≈ 0.333
      └── Some((3, 8)): 11/22 ≈ 0.500
    ├── Some((5, 4)): 203/361 ≈ 0.562
      ├── Some((4, 0)): 18/35 ≈ 0.514
      ├── Some((4, 1)): 30/49 ≈ 0.612
      ├── Some((4, 2)): 23/41 ≈ 0.561
      ├── Some((4, 3)): 16/32 ≈ 0.500
      ├── Some((4, 4)): 35/54 ≈ 0.648
      ├── Some((4, 5)): 21/38 ≈ 0.553
      ├── Some((4, 6)): 18/35 ≈ 0.514
      ├── Some((4, 7)): 9/24 ≈ 0.375
      └── Some((4, 8)): 33/52 ≈ 0.635
    ├── Some((5, 5)): 158/294 ≈ 0.537
      ├── Some((5, 0)): 15/31 ≈ 0.484
      ├── Some((5, 1)): 11/26 ≈ 0.423
      ├── Some((5, 2)): 22/40 ≈ 0.550
      ├── Some((5, 3)): 16/32 ≈ 0.500
      ├── Some((5, 4)): 35/55 ≈ 0.636
      ├── Some((5, 6)): 18/35 ≈ 0.514
      ├── Some((5, 7)): 16/32 ≈ 0.500
      └── Some((5, 8)): 24/42 ≈ 0.571
    ├── Some((5, 6)): 80/173 ≈ 0.462
      ├── Some((6, 0)): 5/15 ≈ 0.333
      ├── Some((6, 1)): 8/18 ≈ 0.444
      ├── Some((6, 2)): 7/17 ≈ 0.412
      ├── Some((6, 3)): 17/29 ≈ 0.586
      ├── Some((6, 4)): 3/12 ≈ 0.250
      ├── Some((6, 5)): 16/27 ≈ 0.593
      ├── Some((6, 6)): 12/23 ≈ 0.522
      ├── Some((6, 7)): 5/15 ≈ 0.333
      └── Some((6, 8)): 6/16 ≈ 0.375
    ├── Some((5, 7)): 142/270 ≈ 0.526
      ├── Some((7, 0)): 11/24 ≈ 0.458
      ├── Some((7, 1)): 15/29 ≈ 0.517
      ├── Some((7, 2)): 16/30 ≈ 0.533
      ├── Some((7, 3)): 12/26 ≈ 0.462
      ├── Some((7, 4)): 8/21 ≈ 0.381
      ├── Some((7, 5)): 24/39 ≈ 0.615
      ├── Some((7, 6)): 27/43 ≈ 0.628
      ├── Some((7, 7)): 10/23 ≈ 0.435
      └── Some((7, 8)): 19/34 ≈ 0.559
    └── Some((5, 8)): 86/182 ≈ 0.473
      ├── Some((8, 0)): 4/14 ≈ 0.286
      ├── Some((8, 1)): 14/25 ≈ 0.560
      ├── Some((8, 2)): 7/17 ≈ 0.412
      ├── Some((8, 3)): 7/17 ≈ 0.412
      ├── Some((8, 4)): 10/21 ≈ 0.476
      ├── Some((8, 5)): 19/31 ≈ 0.613
      ├── Some((8, 6)): 6/16 ≈ 0.375
      ├── Some((8, 7)): 8/19 ≈ 0.421
      └── Some((8, 8)): 10/21 ≈ 0.476
  ├── Some((0, 6)): 1822/3367 ≈ 0.541
    ├── Some((6, 0)): 162/312 ≈ 0.519
      ├── Some((0, 1)): 33/57 ≈ 0.579
      ├── Some((0, 2)): 36/61 ≈ 0.590
      ├── Some((0, 3)): 27/50 ≈ 0.540
      ├── Some((0, 4)): 17/37 ≈ 0.459
      ├── Some((0, 5)): 22/43 ≈ 0.512
      ├── Some((0, 7)): 15/34 ≈ 0.441
      └── Some((0, 8)): 11/29 ≈ 0.379
    ├── Some((6, 1)): 197/366 ≈ 0.538
      ├── Some((1, 0)): 15/33 ≈ 0.455
      ├── Some((1, 1)): 17/35 ≈ 0.486
      ├── Some((1, 2)): 10/26 ≈ 0.385
      ├── Some((1, 3)): 22/41 ≈ 0.537
      ├── Some((1, 4)): 23/42 ≈ 0.548
      ├── Some((1, 5)): 20/39 ≈ 0.513
      ├── Some((1, 6)): 12/29 ≈ 0.414
      ├── Some((1, 7)): 20/39 ≈ 0.513
      └── Some((1, 8)): 57/81 ≈ 0.704
    ├── Some((6, 2)): 235/424 ≈ 0.554
      ├── Some((2, 0)): 29/51 ≈ 0.569
      ├── Some((2, 1)): 30/52 ≈ 0.577
      ├── Some((2, 2)): 23/43 ≈ 0.535
      ├── Some((2, 3)): 32/54 ≈ 0.593
      ├── Some((2, 4)): 33/55 ≈ 0.600
      ├── Some((2, 5)): 21/41 ≈ 0.512
      ├── Some((2, 6)): 24/44 ≈ 0.545
      ├── Some((2, 7)): 19/38 ≈ 0.500
      └── Some((2, 8)): 24/45 ≈ 0.533
    ├── Some((6, 3)): 201/373 ≈ 0.539
      ├── Some((3, 0)): 19/38 ≈ 0.500
      ├── Some((3, 1)): 26/46 ≈ 0.565
      ├── Some((3, 2)): 20/39 ≈ 0.513
      ├── Some((3, 3)): 13/30 ≈ 0.433
      ├── Some((3, 4)): 37/59 ≈ 0.627
      ├── Some((3, 5)): 11/27 ≈ 0.407
      ├── Some((3, 6)): 22/41 ≈ 0.537
      ├── Some((3, 7)): 35/56 ≈ 0.625
      └── Some((3, 8)): 18/36 ≈ 0.500
    ├── Some((6, 4)): 243/437 ≈ 0.556
      ├── Some((4, 0)): 23/44 ≈ 0.523
      ├── Some((4, 1)): 15/34 ≈ 0.441
      ├── Some((4, 2)): 36/59 ≈ 0.610
      ├── Some((4, 3)): 30/52 ≈ 0.577
      ├── Some((4, 4)): 25/46 ≈ 0.543
      ├── Some((4, 5)): 41/65 ≈ 0.631
      ├── Some((4, 6)): 30/52 ≈ 0.577
      ├── Some((4, 7)): 17/36 ≈ 0.472
      └── Some((4, 8)): 26/48 ≈ 0.542
    ├── Some((6, 5)): 204/377 ≈ 0.541
      ├── Some((5, 0)): 32/53 ≈ 0.604
      ├── Some((5, 1)): 14/31 ≈ 0.452
      ├── Some((5, 2)): 22/41 ≈ 0.537
      ├── Some((5, 3)): 12/29 ≈ 0.414
      ├── Some((5, 4)): 21/40 ≈ 0.525
      ├── Some((5, 5)): 22/41 ≈ 0.537
      ├── Some((5, 6)): 18/37 ≈ 0.486
      ├── Some((5, 7)): 24/44 ≈ 0.545
      └── Some((5, 8)): 38/60 ≈ 0.633
    ├── Some((6, 6)): 281/494 ≈ 0.569
      ├── Some((6, 0)): 23/47 ≈ 0.489
      ├── Some((6, 1)): 33/59 ≈ 0.559
      ├── Some((6, 2)): 21/44 ≈ 0.477
      ├── Some((6, 3)): 24/48 ≈ 0.500
      ├── Some((6, 4)): 41/69 ≈ 0.594
      ├── Some((6, 5)): 57/89 ≈ 0.640
      ├── Some((6, 7)): 40/68 ≈ 0.588
      └── Some((6, 8)): 41/69 ≈ 0.594
    ├── Some((6, 7)): 115/238 ≈ 0.483
      ├── Some((7, 0)): 15/29 ≈ 0.517
      ├── Some((7, 1)): 15/29 ≈ 0.517
      ├── Some((7, 2)): 8/21 ≈ 0.381
      ├── Some((7, 3)): 17/31 ≈ 0.548
      ├── Some((7, 4)): 3/14 ≈ 0.214
      ├── Some((7, 5)): 11/24 ≈ 0.458
      ├── Some((7, 6)): 16/30 ≈ 0.533
      ├── Some((7, 7)): 18/33 ≈ 0.545
      └── Some((7, 8)): 12/26 ≈ 0.462
    └── Some((6, 8)): 183/345 ≈ 0.530
      ├── Some((8, 0)): 25/44 ≈ 0.568
      ├── Some((8, 1)): 15/32 ≈ 0.469
      ├── Some((8, 2)): 16/33 ≈ 0.485
      ├── Some((8, 3)): 29/49 ≈ 0.592
      ├── Some((8, 4)): 14/31 ≈ 0.452
      ├── Some((8, 5)): 27/46 ≈ 0.587
      ├── Some((8, 6)): 8/23 ≈ 0.348
      ├── Some((8, 7)): 15/32 ≈ 0.469
      └── Some((8, 8)): 34/54 ≈ 0.630
  ├── Some((0, 7)): 1854/3421 ≈ 0.542
    ├── Some((7, 0)): 250/448 ≈ 0.558
      ├── Some((0, 1)): 15/37 ≈ 0.405
      ├── Some((0, 2)): 69/106 ≈ 0.651
      ├── Some((0, 3)): 54/87 ≈ 0.621
      ├── Some((0, 4)): 29/56 ≈ 0.518
      ├── Some((0, 5)): 39/69 ≈ 0.565
      ├── Some((0, 6)): 20/44 ≈ 0.455
      └── Some((0, 8)): 23/48 ≈ 0.479
    ├── Some((7, 1)): 243/437 ≈ 0.556
      ├── Some((1, 0)): 35/58 ≈ 0.603
      ├── Some((1, 1)): 23/44 ≈ 0.523
      ├── Some((1, 2)): 19/39 ≈ 0.487
      ├── Some((1, 3)): 27/48 ≈ 0.562
      ├── Some((1, 4)): 19/39 ≈ 0.487
      ├── Some((1, 5)): 24/45 ≈ 0.533
      ├── Some((1, 6)): 17/36 ≈ 0.472
      ├── Some((1, 7)): 38/62 ≈ 0.613
      └── Some((1, 8)): 41/65 ≈ 0.631
    ├── Some((7, 2)): 170/325 ≈ 0.523
      ├── Some((2, 0)): 9/24 ≈ 0.375
      ├── Some((2, 1)): 23/41 ≈ 0.561
      ├── Some((2, 2)): 14/30 ≈ 0.467
      ├── Some((2, 3)): 24/42 ≈ 0.571
      ├── Some((2, 4)): 23/41 ≈ 0.561
      ├── Some((2, 5)): 18/35 ≈ 0.514
      ├── Some((2, 6)): 21/39 ≈ 0.538
      ├── Some((2, 7)): 24/43 ≈ 0.558
      └── Some((2, 8)): 13/29 ≈ 0.448
    ├── Some((7, 3)): 260/463 ≈ 0.562
      ├── Some((3, 0)): 31/54 ≈ 0.574
      ├── Some((3, 1)): 34/58 ≈ 0.586
      ├── Some((3, 2)): 41/66 ≈ 0.621
      ├── Some((3, 3)): 19/40 ≈ 0.475
      ├── Some((3, 4)): 22/43 ≈ 0.512
      ├── Some((3, 5)): 48/74 ≈ 0.649
      ├── Some((3, 6)): 22/43 ≈ 0.512
      ├── Some((3, 7)): 22/43 ≈ 0.512
      └── Some((3, 8)): 20/41 ≈ 0.488
    ├── Some((7, 4)): 220/402 ≈ 0.547
      ├── Some((4, 0)): 39/62 ≈ 0.629
      ├── Some((4, 1)): 23/43 ≈ 0.535
      ├── Some((4, 2)): 11/28 ≈ 0.393
      ├── Some((4, 3)): 19/38 ≈ 0.500
      ├── Some((4, 4)): 23/43 ≈ 0.535
      ├── Some((4, 5)): 39/62 ≈ 0.629
      ├── Some((4, 6)): 33/55 ≈ 0.600
      ├── Some((4, 7)): 13/31 ≈ 0.419
      └── Some((4, 8)): 19/39 ≈ 0.487
    ├── Some((7, 5)): 255/455 ≈ 0.560
      ├── Some((5, 0)): 38/62 ≈ 0.613
      ├── Some((5, 1)): 33/56 ≈ 0.589
      ├── Some((5, 2)): 31/54 ≈ 0.574
      ├── Some((5, 3)): 35/59 ≈ 0.593
      ├── Some((5, 4)): 30/53 ≈ 0.566
      ├── Some((5, 5)): 41/66 ≈ 0.621
      ├── Some((5, 6)): 10/27 ≈ 0.370
      ├── Some((5, 7)): 11/29 ≈ 0.379
      └── Some((5, 8)): 26/48 ≈ 0.542
    ├── Some((7, 6)): 156/303 ≈ 0.515
      ├── Some((6, 0)): 20/37 ≈ 0.541
      ├── Some((6, 1)): 3/15 ≈ 0.200
      ├── Some((6, 2)): 31/50 ≈ 0.620
      ├── Some((6, 3)): 12/28 ≈ 0.429
      ├── Some((6, 4)): 34/54 ≈ 0.630
      ├── Some((6, 5)): 8/22 ≈ 0.364
      ├── Some((6, 6)): 11/26 ≈ 0.423
      ├── Some((6, 7)): 31/50 ≈ 0.620
      └── Some((6, 8)): 6/20 ≈ 0.300
    ├── Some((7, 7)): 139/277 ≈ 0.502
      ├── Some((7, 0)): 20/38 ≈ 0.526
      ├── Some((7, 1)): 4/17 ≈ 0.235
      ├── Some((7, 2)): 32/52 ≈ 0.615
      ├── Some((7, 3)): 19/37 ≈ 0.514
      ├── Some((7, 4)): 13/29 ≈ 0.448
      ├── Some((7, 5)): 16/33 ≈ 0.485
      ├── Some((7, 6)): 17/35 ≈ 0.486
      └── Some((7, 8)): 17/35 ≈ 0.486
    └── Some((7, 8)): 160/310 ≈ 0.516
      ├── Some((8, 0)): 20/37 ≈ 0.541
      ├── Some((8, 1)): 7/21 ≈ 0.333
      ├── Some((8, 2)): 10/25 ≈ 0.400
      ├── Some((8, 3)): 24/42 ≈ 0.571
      ├── Some((8, 4)): 10/25 ≈ 0.400
      ├── Some((8, 5)): 26/44 ≈ 0.591
      ├── Some((8, 6)): 21/38 ≈ 0.553
      ├── Some((8, 7)): 23/41 ≈ 0.561
      └── Some((8, 8)): 19/36 ≈ 0.528
  └── Some((0, 8)): 1334/2524 ≈ 0.529
    ├── Some((8, 0)): 79/173 ≈ 0.457
      ├── Some((0, 1)): 6/18 ≈ 0.333
      ├── Some((0, 2)): 11/25 ≈ 0.440
      ├── Some((0, 3)): 18/33 ≈ 0.545
      ├── Some((0, 4)): 30/47 ≈ 0.638
      ├── Some((0, 5)): 5/17 ≈ 0.294
      ├── Some((0, 6)): 2/12 ≈ 0.167
      └── Some((0, 7)): 7/20 ≈ 0.350
    ├── Some((8, 1)): 132/256 ≈ 0.516
      ├── Some((1, 0)): 4/15 ≈ 0.267
      ├── Some((1, 1)): 29/45 ≈ 0.644
      ├── Some((1, 2)): 14/28 ≈ 0.500
      ├── Some((1, 3)): 24/40 ≈ 0.600
      ├── Some((1, 4)): 11/25 ≈ 0.440
      ├── Some((1, 5)): 16/30 ≈ 0.533
      ├── Some((1, 6)): 7/19 ≈ 0.368
      ├── Some((1, 7)): 5/17 ≈ 0.294
      └── Some((1, 8)): 21/36 ≈ 0.583
    ├── Some((8, 2)): 184/335 ≈ 0.549
      ├── Some((2, 0)): 20/37 ≈ 0.541
      ├── Some((2, 1)): 27/45 ≈ 0.600
      ├── Some((2, 2)): 41/61 ≈ 0.672
      ├── Some((2, 3)): 6/19 ≈ 0.316
      ├── Some((2, 4)): 14/30 ≈ 0.467
      ├── Some((2, 5)): 32/51 ≈ 0.627
      ├── Some((2, 6)): 12/27 ≈ 0.444
      ├── Some((2, 7)): 7/21 ≈ 0.333
      └── Some((2, 8)): 25/43 ≈ 0.581
    ├── Some((8, 3)): 137/264 ≈ 0.519
      ├── Some((3, 0)): 36/53 ≈ 0.679
      ├── Some((3, 1)): 6/19 ≈ 0.316
      ├── Some((3, 2)): 9/22 ≈ 0.409
      ├── Some((3, 3)): 16/31 ≈ 0.516
      ├── Some((3, 4)): 31/48 ≈ 0.646
      ├── Some((3, 5)): 12/26 ≈ 0.462
      ├── Some((3, 6)): 9/22 ≈ 0.409
      ├── Some((3, 7)): 1/11 ≈ 0.091
      └── Some((3, 8)): 16/31 ≈ 0.516
    ├── Some((8, 4)): 194/350 ≈ 0.554
      ├── Some((4, 0)): 21/38 ≈ 0.553
      ├── Some((4, 1)): 28/46 ≈ 0.609
      ├── Some((4, 2)): 26/44 ≈ 0.591
      ├── Some((4, 3)): 21/38 ≈ 0.553
      ├── Some((4, 4)): 23/41 ≈ 0.561
      ├── Some((4, 5)): 28/46 ≈ 0.609
      ├── Some((4, 6)): 18/35 ≈ 0.514
      ├── Some((4, 7)): 12/27 ≈ 0.444
      └── Some((4, 8)): 17/34 ≈ 0.500
    ├── Some((8, 5)): 155/291 ≈ 0.533
      ├── Some((5, 0)): 6/19 ≈ 0.316
      ├── Some((5, 1)): 36/54 ≈ 0.667
      ├── Some((5, 2)): 21/37 ≈ 0.568
      ├── Some((5, 3)): 8/21 ≈ 0.381
      ├── Some((5, 4)): 16/31 ≈ 0.516
      ├── Some((5, 5)): 16/31 ≈ 0.516
      ├── Some((5, 6)): 11/25 ≈ 0.440
      ├── Some((5, 7)): 20/36 ≈ 0.556
      └── Some((5, 8)): 20/36 ≈ 0.556
    ├── Some((8, 6)): 136/262 ≈ 0.519
      ├── Some((6, 0)): 1/11 ≈ 0.091
      ├── Some((6, 1)): 16/31 ≈ 0.516
      ├── Some((6, 2)): 28/44 ≈ 0.636
      ├── Some((6, 3)): 1/11 ≈ 0.091
      ├── Some((6, 4)): 14/28 ≈ 0.500
      ├── Some((6, 5)): 25/41 ≈ 0.610
      ├── Some((6, 6)): 16/31 ≈ 0.516
      ├── Some((6, 7)): 21/36 ≈ 0.583
      └── Some((6, 8)): 14/28 ≈ 0.500
    ├── Some((8, 7)): 186/338 ≈ 0.550
      ├── Some((7, 0)): 20/37 ≈ 0.541
      ├── Some((7, 1)): 16/32 ≈ 0.500
      ├── Some((7, 2)): 26/44 ≈ 0.591
      ├── Some((7, 3)): 17/33 ≈ 0.515
      ├── Some((7, 4)): 9/24 ≈ 0.375
      ├── Some((7, 5)): 14/30 ≈ 0.467
      ├── Some((7, 6)): 26/44 ≈ 0.591
      ├── Some((7, 7)): 40/60 ≈ 0.667
      └── Some((7, 8)): 17/33 ≈ 0.515
    └── Some((8, 8)): 131/254 ≈ 0.516
      ├── Some((8, 0)): 11/25 ≈ 0.440
      ├── Some((8, 1)): 18/34 ≈ 0.529
      ├── Some((8, 2)): 12/27 ≈ 0.444
      ├── Some((8, 3)): 5/18 ≈ 0.278
      ├── Some((8, 4)): 18/34 ≈ 0.529
      ├── Some((8, 5)): 35/53 ≈ 0.660
      ├── Some((8, 6)): 14/29 ≈ 0.483
      └── Some((8, 7)): 17/33 ≈ 0.515
├── Some((0, 1)): 11565/21721 ≈ 0.532
  ├── Some((1, 0)): 977/1882 ≈ 0.519
    ├── Some((0, 0)): 134/254 ≈ 0.528
      ├── Some((0, 2)): 25/44 ≈ 0.568
      ├── Some((0, 3)): 10/25 ≈ 0.400
      ├── Some((0, 4)): 24/42 ≈ 0.571
      ├── Some((0, 5)): 7/21 ≈ 0.333
      ├── Some((0, 6)): 26/45 ≈ 0.578
      ├── Some((0, 7)): 22/40 ≈ 0.550
      └── Some((0, 8)): 19/36 ≈ 0.528
    ├── Some((0, 2)): 160/293 ≈ 0.546
      ├── Some((2, 0)): 21/36 ≈ 0.583
      ├── Some((2, 1)): 13/27 ≈ 0.481
      ├── Some((2, 2)): 16/31 ≈ 0.516
      ├── Some((2, 3)): 10/23 ≈ 0.435
      ├── Some((2, 4)): 28/44 ≈ 0.636
      ├── Some((2, 5)): 23/39 ≈ 0.590
      ├── Some((2, 6)): 25/41 ≈ 0.610
      ├── Some((2, 7)): 10/24 ≈ 0.417
      └── Some((2, 8)): 13/27 ≈ 0.481
    ├── Some((0, 3)): 72/157 ≈ 0.459
      ├── Some((3, 0)): 9/19 ≈ 0.474
      ├── Some((3, 1)): 6/15 ≈ 0.400
      ├── Some((3, 2)): 4/13 ≈ 0.308
      ├── Some((3, 3)): 8/18 ≈ 0.444
      ├── Some((3, 4)): 11/21 ≈ 0.524
      ├── Some((3, 5)): 3/12 ≈ 0.250
      ├── Some((3, 6)): 18/28 ≈ 0.643
      ├── Some((3, 7)): 6/15 ≈ 0.400
      └── Some((3, 8)): 6/15 ≈ 0.400
    ├── Some((0, 4)): 104/208 ≈ 0.500
      ├── Some((4, 0)): 11/23 ≈ 0.478
      ├── Some((4, 1)): 15/27 ≈ 0.556
      ├── Some((4, 2)): 16/28 ≈ 0.571
      ├── Some((4, 3)): 20/33 ≈ 0.606
      ├── Some((4, 4)): 18/31 ≈ 0.581
      ├── Some((4, 5)): 13/25 ≈ 0.520
      ├── Some((4, 6)): 1/10 ≈ 0.100
      ├── Some((4, 7)): 5/15 ≈ 0.333
      └── Some((4, 8)): 5/15 ≈ 0.333
    ├── Some((0, 5)): 109/215 ≈ 0.507
      ├── Some((5, 0)): 13/25 ≈ 0.520
      ├── Some((5, 1)): 4/14 ≈ 0.286
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 3)): 14/26 ≈ 0.538
      ├── Some((5, 4)): 22/35 ≈ 0.629
      ├── Some((5, 5)): 15/28 ≈ 0.536
      ├── Some((5, 6)): 23/36 ≈ 0.639
      ├── Some((5, 7)): 6/17 ≈ 0.353
      └── Some((5, 8)): 0/9 ≈ 0.000
    ├── Some((0, 6)): 144/269 ≈ 0.535
      ├── Some((6, 0)): 11/24 ≈ 0.458
      ├── Some((6, 1)): 39/56 ≈ 0.696
      ├── Some((6, 2)): 16/30 ≈ 0.533
      ├── Some((6, 3)): 21/36 ≈ 0.583
      ├── Some((6, 4)): 11/24 ≈ 0.458
      ├── Some((6, 5)): 22/37 ≈ 0.595
      ├── Some((6, 6)): 7/19 ≈ 0.368
      ├── Some((6, 7)): 7/19 ≈ 0.368
      └── Some((6, 8)): 10/23 ≈ 0.435
    ├── Some((0, 7)): 123/237 ≈ 0.519
      ├── Some((7, 0)): 19/33 ≈ 0.576
      ├── Some((7, 1)): 12/25 ≈ 0.480
      ├── Some((7, 2)): 9/21 ≈ 0.429
      ├── Some((7, 3)): 14/27 ≈ 0.519
      ├── Some((7, 4)): 32/46 ≈ 0.696
      ├── Some((7, 5)): 3/13 ≈ 0.231
      ├── Some((7, 6)): 12/25 ≈ 0.480
      ├── Some((7, 7)): 9/21 ≈ 0.429
      └── Some((7, 8)): 12/25 ≈ 0.480
    └── Some((0, 8)): 130/248 ≈ 0.524
      ├── Some((8, 0)): 5/16 ≈ 0.312
      ├── Some((8, 1)): 22/36 ≈ 0.611
      ├── Some((8, 2)): 12/25 ≈ 0.480
      ├── Some((8, 3)): 10/23 ≈ 0.435
      ├── Some((8, 4)): 22/36 ≈ 0.611
      ├── Some((8, 5)): 17/31 ≈ 0.548
      ├── Some((8, 6)): 8/20 ≈ 0.400
      ├── Some((8, 7)): 15/28 ≈ 0.536
      └── Some((8, 8)): 18/32 ≈ 0.562
  ├── Some((1, 1)): 1416/2640 ≈ 0.536
    ├── Some((1, 0)): 124/248 ≈ 0.500
      ├── Some((0, 0)): 10/24 ≈ 0.417
      ├── Some((0, 2)): 10/25 ≈ 0.400
      ├── Some((0, 3)): 24/41 ≈ 0.585
      ├── Some((0, 4)): 9/23 ≈ 0.391
      ├── Some((0, 5)): 8/22 ≈ 0.364
      ├── Some((0, 6)): 18/34 ≈ 0.529
      ├── Some((0, 7)): 16/32 ≈ 0.500
      └── Some((0, 8)): 28/46 ≈ 0.609
    ├── Some((1, 2)): 245/434 ≈ 0.565
      ├── Some((2, 0)): 32/54 ≈ 0.593
      ├── Some((2, 1)): 25/46 ≈ 0.543
      ├── Some((2, 2)): 22/42 ≈ 0.524
      ├── Some((2, 3)): 42/66 ≈ 0.636
      ├── Some((2, 4)): 24/44 ≈ 0.545
      ├── Some((2, 5)): 35/58 ≈ 0.603
      ├── Some((2, 6)): 26/47 ≈ 0.553
      ├── Some((2, 7)): 14/32 ≈ 0.438
      └── Some((2, 8)): 24/44 ≈ 0.545
    ├── Some((1, 3)): 163/309 ≈ 0.528
      ├── Some((3, 0)): 12/27 ≈ 0.444
      ├── Some((3, 1)): 12/27 ≈ 0.444
      ├── Some((3, 2)): 30/48 ≈ 0.625
      ├── Some((3, 3)): 31/49 ≈ 0.633
      ├── Some((3, 4)): 17/33 ≈ 0.515
      ├── Some((3, 5)): 20/37 ≈ 0.541
      ├── Some((3, 6)): 13/28 ≈ 0.464
      ├── Some((3, 7)): 13/28 ≈ 0.464
      └── Some((3, 8)): 15/31 ≈ 0.484
    ├── Some((1, 4)): 175/328 ≈ 0.534
      ├── Some((4, 0)): 28/47 ≈ 0.596
      ├── Some((4, 1)): 15/31 ≈ 0.484
      ├── Some((4, 2)): 39/59 ≈ 0.661
      ├── Some((4, 3)): 20/38 ≈ 0.526
      ├── Some((4, 4)): 16/33 ≈ 0.485
      ├── Some((4, 5)): 7/21 ≈ 0.333
      ├── Some((4, 6)): 8/22 ≈ 0.364
      ├── Some((4, 7)): 12/28 ≈ 0.429
      └── Some((4, 8)): 29/48 ≈ 0.604
    ├── Some((1, 5)): 129/256 ≈ 0.504
      ├── Some((5, 0)): 17/32 ≈ 0.531
      ├── Some((5, 1)): 14/28 ≈ 0.500
      ├── Some((5, 2)): 21/36 ≈ 0.583
      ├── Some((5, 3)): 7/20 ≈ 0.350
      ├── Some((5, 4)): 16/30 ≈ 0.533
      ├── Some((5, 5)): 12/26 ≈ 0.462
      ├── Some((5, 6)): 9/22 ≈ 0.409
      ├── Some((5, 7)): 17/32 ≈ 0.531
      └── Some((5, 8)): 15/29 ≈ 0.517
    ├── Some((1, 6)): 244/432 ≈ 0.565
      ├── Some((6, 0)): 21/41 ≈ 0.512
      ├── Some((6, 1)): 17/36 ≈ 0.472
      ├── Some((6, 2)): 21/41 ≈ 0.512
      ├── Some((6, 3)): 42/65 ≈ 0.646
      ├── Some((6, 4)): 35/57 ≈ 0.614
      ├── Some((6, 5)): 24/44 ≈ 0.545
      ├── Some((6, 6)): 31/53 ≈ 0.585
      ├── Some((6, 7)): 27/48 ≈ 0.562
      └── Some((6, 8)): 25/46 ≈ 0.543
    ├── Some((1, 7)): 192/354 ≈ 0.542
      ├── Some((7, 0)): 23/41 ≈ 0.561
      ├── Some((7, 1)): 11/27 ≈ 0.407
      ├── Some((7, 2)): 24/43 ≈ 0.558
      ├── Some((7, 3)): 19/37 ≈ 0.514
      ├── Some((7, 4)): 20/38 ≈ 0.526
      ├── Some((7, 5)): 16/33 ≈ 0.485
      ├── Some((7, 6)): 16/33 ≈ 0.485
      ├── Some((7, 7)): 34/54 ≈ 0.630
      └── Some((7, 8)): 28/47 ≈ 0.596
    └── Some((1, 8)): 143/278 ≈ 0.514
      ├── Some((8, 0)): 22/38 ≈ 0.579
      ├── Some((8, 1)): 10/24 ≈ 0.417
      ├── Some((8, 2)): 19/35 ≈ 0.543
      ├── Some((8, 3)): 32/50 ≈ 0.640
      ├── Some((8, 4)): 9/23 ≈ 0.391
      ├── Some((8, 5)): 12/26 ≈ 0.462
      ├── Some((8, 6)): 5/17 ≈ 0.294
      ├── Some((8, 7)): 17/32 ≈ 0.531
      └── Some((8, 8)): 17/32 ≈ 0.531
  ├── Some((1, 2)): 1597/2950 ≈ 0.541
    ├── Some((2, 0)): 100/209 ≈ 0.478
      ├── Some((0, 0)): 14/28 ≈ 0.500
      ├── Some((0, 2)): 16/30 ≈ 0.533
      ├── Some((0, 3)): 9/22 ≈ 0.409
      ├── Some((0, 4)): 9/22 ≈ 0.409
      ├── Some((0, 5)): 11/24 ≈ 0.458
      ├── Some((0, 6)): 24/40 ≈ 0.600
      ├── Some((0, 7)): 7/19 ≈ 0.368
      └── Some((0, 8)): 10/23 ≈ 0.435
    ├── Some((2, 1)): 132/259 ≈ 0.510
      ├── Some((1, 0)): 12/27 ≈ 0.444
      ├── Some((1, 1)): 11/26 ≈ 0.423
      ├── Some((1, 3)): 6/19 ≈ 0.316
      ├── Some((1, 4)): 18/35 ≈ 0.514
      ├── Some((1, 5)): 22/39 ≈ 0.564
      ├── Some((1, 6)): 22/39 ≈ 0.564
      ├── Some((1, 7)): 23/40 ≈ 0.575
      └── Some((1, 8)): 17/33 ≈ 0.515
    ├── Some((2, 2)): 211/379 ≈ 0.557
      ├── Some((2, 0)): 28/49 ≈ 0.571
      ├── Some((2, 1)): 31/53 ≈ 0.585
      ├── Some((2, 3)): 19/38 ≈ 0.500
      ├── Some((2, 4)): 29/51 ≈ 0.569
      ├── Some((2, 5)): 42/66 ≈ 0.636
      ├── Some((2, 6)): 20/40 ≈ 0.500
      ├── Some((2, 7)): 19/38 ≈ 0.500
      └── Some((2, 8)): 23/43 ≈ 0.535
    ├── Some((2, 3)): 234/414 ≈ 0.565
      ├── Some((3, 0)): 17/35 ≈ 0.486
      ├── Some((3, 1)): 35/57 ≈ 0.614
      ├── Some((3, 2)): 21/40 ≈ 0.525
      ├── Some((3, 3)): 31/52 ≈ 0.596
      ├── Some((3, 4)): 27/47 ≈ 0.574
      ├── Some((3, 5)): 27/47 ≈ 0.574
      ├── Some((3, 6)): 16/34 ≈ 0.471
      ├── Some((3, 7)): 26/46 ≈ 0.565
      └── Some((3, 8)): 33/55 ≈ 0.600
    ├── Some((2, 4)): 124/246 ≈ 0.504
      ├── Some((4, 0)): 17/31 ≈ 0.548
      ├── Some((4, 1)): 13/27 ≈ 0.481
      ├── Some((4, 2)): 4/15 ≈ 0.267
      ├── Some((4, 3)): 20/35 ≈ 0.571
      ├── Some((4, 4)): 12/25 ≈ 0.480
      ├── Some((4, 5)): 19/33 ≈ 0.576
      ├── Some((4, 6)): 15/29 ≈ 0.517
      ├── Some((4, 7)): 12/25 ≈ 0.480
      └── Some((4, 8)): 12/25 ≈ 0.480
    ├── Some((2, 5)): 138/268 ≈ 0.515
      ├── Some((5, 0)): 12/26 ≈ 0.462
      ├── Some((5, 1)): 23/39 ≈ 0.590
      ├── Some((5, 2)): 5/17 ≈ 0.294
      ├── Some((5, 3)): 15/29 ≈ 0.517
      ├── Some((5, 4)): 18/33 ≈ 0.545
      ├── Some((5, 5)): 15/29 ≈ 0.517
      ├── Some((5, 6)): 22/38 ≈ 0.579
      ├── Some((5, 7)): 23/39 ≈ 0.590
      └── Some((5, 8)): 5/17 ≈ 0.294
    ├── Some((2, 6)): 206/372 ≈ 0.554
      ├── Some((6, 0)): 27/46 ≈ 0.587
      ├── Some((6, 1)): 21/39 ≈ 0.538
      ├── Some((6, 2)): 16/33 ≈ 0.485
      ├── Some((6, 3)): 32/52 ≈ 0.615
      ├── Some((6, 4)): 27/46 ≈ 0.587
      ├── Some((6, 5)): 23/42 ≈ 0.548
      ├── Some((6, 6)): 9/24 ≈ 0.375
      ├── Some((6, 7)): 23/42 ≈ 0.548
      └── Some((6, 8)): 27/47 ≈ 0.574
    ├── Some((2, 7)): 217/388 ≈ 0.559
      ├── Some((7, 0)): 15/32 ≈ 0.469
      ├── Some((7, 1)): 40/62 ≈ 0.645
      ├── Some((7, 2)): 23/42 ≈ 0.548
      ├── Some((7, 3)): 30/50 ≈ 0.600
      ├── Some((7, 4)): 19/37 ≈ 0.514
      ├── Some((7, 5)): 11/27 ≈ 0.407
      ├── Some((7, 6)): 19/37 ≈ 0.514
      ├── Some((7, 7)): 27/47 ≈ 0.574
      └── Some((7, 8)): 32/53 ≈ 0.604
    └── Some((2, 8)): 234/414 ≈ 0.565
      ├── Some((8, 0)): 37/59 ≈ 0.627
      ├── Some((8, 1)): 11/28 ≈ 0.393
      ├── Some((8, 2)): 39/62 ≈ 0.629
      ├── Some((8, 3)): 30/51 ≈ 0.588
      ├── Some((8, 4)): 9/25 ≈ 0.360
      ├── Some((8, 5)): 30/51 ≈ 0.588
      ├── Some((8, 6)): 41/64 ≈ 0.641
      ├── Some((8, 7)): 15/33 ≈ 0.455
      └── Some((8, 8)): 21/40 ≈ 0.525
  ├── Some((1, 3)): 1276/2399 ≈ 0.532
    ├── Some((3, 0)): 134/256 ≈ 0.523
      ├── Some((0, 0)): 15/30 ≈ 0.500
      ├── Some((0, 2)): 15/30 ≈ 0.500
      ├── Some((0, 3)): 14/29 ≈ 0.483
      ├── Some((0, 4)): 13/27 ≈ 0.481
      ├── Some((0, 5)): 25/42 ≈ 0.595
      ├── Some((0, 6)): 28/45 ≈ 0.622
      ├── Some((0, 7)): 11/25 ≈ 0.440
      └── Some((0, 8)): 13/27 ≈ 0.481
    ├── Some((3, 1)): 219/383 ≈ 0.572
      ├── Some((1, 0)): 26/46 ≈ 0.565
      ├── Some((1, 1)): 22/42 ≈ 0.524
      ├── Some((1, 2)): 25/45 ≈ 0.556
      ├── Some((1, 4)): 39/61 ≈ 0.639
      ├── Some((1, 5)): 19/38 ≈ 0.500
      ├── Some((1, 6)): 18/37 ≈ 0.486
      ├── Some((1, 7)): 45/68 ≈ 0.662
      └── Some((1, 8)): 25/45 ≈ 0.556
    ├── Some((3, 2)): 202/358 ≈ 0.564
      ├── Some((2, 0)): 29/47 ≈ 0.617
      ├── Some((2, 1)): 27/45 ≈ 0.600
      ├── Some((2, 2)): 26/44 ≈ 0.591
      ├── Some((2, 3)): 20/37 ≈ 0.541
      ├── Some((2, 4)): 12/27 ≈ 0.444
      ├── Some((2, 5)): 15/31 ≈ 0.484
      ├── Some((2, 6)): 24/42 ≈ 0.571
      ├── Some((2, 7)): 31/50 ≈ 0.620
      └── Some((2, 8)): 17/34 ≈ 0.500
    ├── Some((3, 3)): 174/316 ≈ 0.551
      ├── Some((3, 0)): 22/40 ≈ 0.550
      ├── Some((3, 1)): 9/24 ≈ 0.375
      ├── Some((3, 2)): 19/36 ≈ 0.528
      ├── Some((3, 4)): 23/41 ≈ 0.561
      ├── Some((3, 5)): 17/34 ≈ 0.500
      ├── Some((3, 6)): 41/62 ≈ 0.661
      ├── Some((3, 7)): 18/35 ≈ 0.514
      └── Some((3, 8)): 25/43 ≈ 0.581
    ├── Some((3, 4)): 94/194 ≈ 0.485
      ├── Some((4, 0)): 8/19 ≈ 0.421
      ├── Some((4, 1)): 7/18 ≈ 0.389
      ├── Some((4, 2)): 11/22 ≈ 0.500
      ├── Some((4, 3)): 13/24 ≈ 0.542
      ├── Some((4, 4)): 16/28 ≈ 0.571
      ├── Some((4, 5)): 12/23 ≈ 0.522
      ├── Some((4, 6)): 5/15 ≈ 0.333
      ├── Some((4, 7)): 9/20 ≈ 0.450
      └── Some((4, 8)): 13/24 ≈ 0.542
    ├── Some((3, 5)): 93/192 ≈ 0.484
      ├── Some((5, 0)): 10/21 ≈ 0.476
      ├── Some((5, 1)): 8/19 ≈ 0.421
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 10/21 ≈ 0.476
      ├── Some((5, 4)): 5/15 ≈ 0.333
      ├── Some((5, 5)): 14/26 ≈ 0.538
      ├── Some((5, 6)): 7/18 ≈ 0.389
      ├── Some((5, 7)): 21/33 ≈ 0.636
      └── Some((5, 8)): 6/16 ≈ 0.375
    ├── Some((3, 6)): 158/292 ≈ 0.541
      ├── Some((6, 0)): 23/39 ≈ 0.590
      ├── Some((6, 1)): 13/27 ≈ 0.481
      ├── Some((6, 2)): 19/34 ≈ 0.559
      ├── Some((6, 3)): 6/19 ≈ 0.316
      ├── Some((6, 4)): 16/31 ≈ 0.516
      ├── Some((6, 5)): 8/21 ≈ 0.381
      ├── Some((6, 6)): 35/52 ≈ 0.673
      ├── Some((6, 7)): 17/32 ≈ 0.531
      └── Some((6, 8)): 20/36 ≈ 0.556
    ├── Some((3, 7)): 79/170 ≈ 0.465
      ├── Some((7, 0)): 13/24 ≈ 0.542
      ├── Some((7, 1)): 8/18 ≈ 0.444
      ├── Some((7, 2)): 4/13 ≈ 0.308
      ├── Some((7, 3)): 12/22 ≈ 0.545
      ├── Some((7, 4)): 16/27 ≈ 0.593
      ├── Some((7, 5)): 8/18 ≈ 0.444
      ├── Some((7, 6)): 7/17 ≈ 0.412
      ├── Some((7, 7)): 7/17 ≈ 0.412
      └── Some((7, 8)): 4/13 ≈ 0.308
    └── Some((3, 8)): 122/237 ≈ 0.515
      ├── Some((8, 0)): 7/19 ≈ 0.368
      ├── Some((8, 1)): 16/29 ≈ 0.552
      ├── Some((8, 2)): 10/22 ≈ 0.455
      ├── Some((8, 3)): 10/22 ≈ 0.455
      ├── Some((8, 4)): 14/27 ≈ 0.519
      ├── Some((8, 5)): 21/35 ≈ 0.600
      ├── Some((8, 6)): 25/39 ≈ 0.641
      ├── Some((8, 7)): 11/23 ≈ 0.478
      └── Some((8, 8)): 8/20 ≈ 0.400
  ├── Some((1, 4)): 1316/2468 ≈ 0.533
    ├── Some((4, 0)): 230/400 ≈ 0.575
      ├── Some((0, 0)): 29/51 ≈ 0.569
      ├── Some((0, 2)): 12/29 ≈ 0.414
      ├── Some((0, 3)): 21/41 ≈ 0.512
      ├── Some((0, 4)): 45/69 ≈ 0.652
      ├── Some((0, 5)): 47/71 ≈ 0.662
      ├── Some((0, 6)): 34/57 ≈ 0.596
      ├── Some((0, 7)): 15/33 ≈ 0.455
      └── Some((0, 8)): 27/48 ≈ 0.562
    ├── Some((4, 1)): 121/236 ≈ 0.513
      ├── Some((1, 0)): 26/42 ≈ 0.619
      ├── Some((1, 1)): 15/29 ≈ 0.517
      ├── Some((1, 2)): 6/18 ≈ 0.333
      ├── Some((1, 3)): 12/26 ≈ 0.462
      ├── Some((1, 5)): 17/32 ≈ 0.531
      ├── Some((1, 6)): 7/20 ≈ 0.350
      ├── Some((1, 7)): 23/39 ≈ 0.590
      └── Some((1, 8)): 15/29 ≈ 0.517
    ├── Some((4, 2)): 196/349 ≈ 0.562
      ├── Some((2, 0)): 28/46 ≈ 0.609
      ├── Some((2, 1)): 23/40 ≈ 0.575
      ├── Some((2, 2)): 29/47 ≈ 0.617
      ├── Some((2, 3)): 14/30 ≈ 0.467
      ├── Some((2, 4)): 19/36 ≈ 0.528
      ├── Some((2, 5)): 22/39 ≈ 0.564
      ├── Some((2, 6)): 13/28 ≈ 0.464
      ├── Some((2, 7)): 24/41 ≈ 0.585
      └── Some((2, 8)): 24/41 ≈ 0.585
    ├── Some((4, 3)): 105/211 ≈ 0.498
      ├── Some((3, 0)): 13/25 ≈ 0.520
      ├── Some((3, 1)): 11/23 ≈ 0.478
      ├── Some((3, 2)): 16/28 ≈ 0.571
      ├── Some((3, 3)): 7/18 ≈ 0.389
      ├── Some((3, 4)): 10/21 ≈ 0.476
      ├── Some((3, 5)): 11/23 ≈ 0.478
      ├── Some((3, 6)): 7/18 ≈ 0.389
      ├── Some((3, 7)): 16/28 ≈ 0.571
      └── Some((3, 8)): 14/26 ≈ 0.538
    ├── Some((4, 4)): 170/311 ≈ 0.547
      ├── Some((4, 0)): 31/51 ≈ 0.608
      ├── Some((4, 1)): 30/49 ≈ 0.612
      ├── Some((4, 2)): 19/36 ≈ 0.528
      ├── Some((4, 3)): 11/26 ≈ 0.423
      ├── Some((4, 5)): 21/39 ≈ 0.538
      ├── Some((4, 6)): 19/36 ≈ 0.528
      ├── Some((4, 7)): 11/26 ≈ 0.423
      └── Some((4, 8)): 28/47 ≈ 0.596
    ├── Some((4, 5)): 120/235 ≈ 0.511
      ├── Some((5, 0)): 17/30 ≈ 0.567
      ├── Some((5, 1)): 10/22 ≈ 0.455
      ├── Some((5, 2)): 15/28 ≈ 0.536
      ├── Some((5, 3)): 8/20 ≈ 0.400
      ├── Some((5, 4)): 14/27 ≈ 0.519
      ├── Some((5, 5)): 11/24 ≈ 0.458
      ├── Some((5, 6)): 21/35 ≈ 0.600
      ├── Some((5, 7)): 3/13 ≈ 0.231
      └── Some((5, 8)): 21/35 ≈ 0.600
    ├── Some((4, 6)): 111/221 ≈ 0.502
      ├── Some((6, 0)): 10/22 ≈ 0.455
      ├── Some((6, 1)): 6/17 ≈ 0.353
      ├── Some((6, 2)): 22/36 ≈ 0.611
      ├── Some((6, 3)): 19/32 ≈ 0.594
      ├── Some((6, 4)): 7/19 ≈ 0.368
      ├── Some((6, 5)): 9/21 ≈ 0.429
      ├── Some((6, 6)): 26/40 ≈ 0.650
      ├── Some((6, 7)): 6/17 ≈ 0.353
      └── Some((6, 8)): 5/16 ≈ 0.312
    ├── Some((4, 7)): 114/225 ≈ 0.507
      ├── Some((7, 0)): 12/24 ≈ 0.500
      ├── Some((7, 1)): 20/34 ≈ 0.588
      ├── Some((7, 2)): 1/10 ≈ 0.100
      ├── Some((7, 3)): 12/25 ≈ 0.480
      ├── Some((7, 4)): 18/31 ≈ 0.581
      ├── Some((7, 5)): 17/30 ≈ 0.567
      ├── Some((7, 6)): 14/27 ≈ 0.519
      ├── Some((7, 7)): 11/23 ≈ 0.478
      └── Some((7, 8)): 8/20 ≈ 0.400
    └── Some((4, 8)): 149/279 ≈ 0.534
      ├── Some((8, 0)): 21/36 ≈ 0.583
      ├── Some((8, 1)): 19/34 ≈ 0.559
      ├── Some((8, 2)): 5/17 ≈ 0.294
      ├── Some((8, 3)): 19/34 ≈ 0.559
      ├── Some((8, 4)): 12/26 ≈ 0.462
      ├── Some((8, 5)): 13/27 ≈ 0.481
      ├── Some((8, 6)): 25/41 ≈ 0.610
      ├── Some((8, 7)): 21/36 ≈ 0.583
      └── Some((8, 8)): 13/27 ≈ 0.481
  ├── Some((1, 5)): 883/1717 ≈ 0.514
    ├── Some((5, 0)): 77/159 ≈ 0.484
      ├── Some((0, 0)): 18/29 ≈ 0.621
      ├── Some((0, 2)): 7/17 ≈ 0.412
      ├── Some((0, 3)): 9/19 ≈ 0.474
      ├── Some((0, 4)): 12/23 ≈ 0.522
      ├── Some((0, 5)): 17/28 ≈ 0.607
      ├── Some((0, 6)): 5/14 ≈ 0.357
      ├── Some((0, 7)): 3/12 ≈ 0.250
      └── Some((0, 8)): 6/16 ≈ 0.375
    ├── Some((5, 1)): 56/126 ≈ 0.444
      ├── Some((1, 0)): 7/16 ≈ 0.438
      ├── Some((1, 1)): 15/25 ≈ 0.600
      ├── Some((1, 2)): 1/8 ≈ 0.125
      ├── Some((1, 3)): 11/20 ≈ 0.550
      ├── Some((1, 4)): 3/11 ≈ 0.273
      ├── Some((1, 6)): 4/12 ≈ 0.333
      ├── Some((1, 7)): 3/11 ≈ 0.273
      └── Some((1, 8)): 12/22 ≈ 0.545
    ├── Some((5, 2)): 94/185 ≈ 0.508
      ├── Some((2, 0)): 19/30 ≈ 0.633
      ├── Some((2, 1)): 9/19 ≈ 0.474
      ├── Some((2, 2)): 19/30 ≈ 0.633
      ├── Some((2, 3)): 10/20 ≈ 0.500
      ├── Some((2, 4)): 10/20 ≈ 0.500
      ├── Some((2, 5)): 12/22 ≈ 0.545
      ├── Some((2, 6)): 6/16 ≈ 0.375
      ├── Some((2, 7)): 1/9 ≈ 0.111
      └── Some((2, 8)): 8/18 ≈ 0.444
    ├── Some((5, 3)): 68/145 ≈ 0.469
      ├── Some((3, 0)): 10/19 ≈ 0.526
      ├── Some((3, 1)): 6/14 ≈ 0.429
      ├── Some((3, 2)): 4/12 ≈ 0.333
      ├── Some((3, 3)): 12/21 ≈ 0.571
      ├── Some((3, 4)): 3/11 ≈ 0.273
      ├── Some((3, 5)): 9/18 ≈ 0.500
      ├── Some((3, 6)): 13/22 ≈ 0.591
      ├── Some((3, 7)): 7/16 ≈ 0.438
      └── Some((3, 8)): 3/11 ≈ 0.273
    ├── Some((5, 4)): 107/205 ≈ 0.522
      ├── Some((4, 0)): 17/29 ≈ 0.586
      ├── Some((4, 1)): 7/17 ≈ 0.412
      ├── Some((4, 2)): 14/25 ≈ 0.560
      ├── Some((4, 3)): 16/27 ≈ 0.593
      ├── Some((4, 4)): 14/25 ≈ 0.560
      ├── Some((4, 5)): 7/17 ≈ 0.412
      ├── Some((4, 6)): 14/25 ≈ 0.560
      ├── Some((4, 7)): 2/11 ≈ 0.182
      └── Some((4, 8)): 16/28 ≈ 0.571
    ├── Some((5, 5)): 108/206 ≈ 0.524
      ├── Some((5, 0)): 8/19 ≈ 0.421
      ├── Some((5, 1)): 12/24 ≈ 0.500
      ├── Some((5, 2)): 21/34 ≈ 0.618
      ├── Some((5, 3)): 30/44 ≈ 0.682
      ├── Some((5, 4)): 9/21 ≈ 0.429
      ├── Some((5, 6)): 8/19 ≈ 0.421
      ├── Some((5, 7)): 10/22 ≈ 0.455
      └── Some((5, 8)): 10/22 ≈ 0.455
    ├── Some((5, 6)): 160/283 ≈ 0.565
      ├── Some((6, 0)): 23/37 ≈ 0.622
      ├── Some((6, 1)): 23/37 ≈ 0.622
      ├── Some((6, 2)): 13/26 ≈ 0.500
      ├── Some((6, 3)): 16/30 ≈ 0.533
      ├── Some((6, 4)): 20/34 ≈ 0.588
      ├── Some((6, 5)): 13/26 ≈ 0.500
      ├── Some((6, 6)): 20/34 ≈ 0.588
      ├── Some((6, 7)): 15/28 ≈ 0.536
      └── Some((6, 8)): 16/30 ≈ 0.533
    ├── Some((5, 7)): 85/172 ≈ 0.494
      ├── Some((7, 0)): 9/19 ≈ 0.474
      ├── Some((7, 1)): 14/24 ≈ 0.583
      ├── Some((7, 2)): 7/16 ≈ 0.438
      ├── Some((7, 3)): 2/10 ≈ 0.200
      ├── Some((7, 4)): 13/23 ≈ 0.565
      ├── Some((7, 5)): 15/25 ≈ 0.600
      ├── Some((7, 6)): 6/15 ≈ 0.400
      ├── Some((7, 7)): 11/21 ≈ 0.524
      └── Some((7, 8)): 8/18 ≈ 0.444
    └── Some((5, 8)): 127/235 ≈ 0.540
      ├── Some((8, 0)): 15/27 ≈ 0.556
      ├── Some((8, 1)): 10/22 ≈ 0.455
      ├── Some((8, 2)): 20/33 ≈ 0.606
      ├── Some((8, 3)): 11/23 ≈ 0.478
      ├── Some((8, 4)): 17/29 ≈ 0.586
      ├── Some((8, 5)): 18/30 ≈ 0.600
      ├── Some((8, 6)): 11/23 ≈ 0.478
      ├── Some((8, 7)): 9/20 ≈ 0.450
      └── Some((8, 8)): 15/27 ≈ 0.556
  ├── Some((1, 6)): 1516/2812 ≈ 0.539
    ├── Some((6, 0)): 127/249 ≈ 0.510
      ├── Some((0, 0)): 24/41 ≈ 0.585
      ├── Some((0, 2)): 6/19 ≈ 0.316
      ├── Some((0, 3)): 8/22 ≈ 0.364
      ├── Some((0, 4)): 7/20 ≈ 0.350
      ├── Some((0, 5)): 18/34 ≈ 0.529
      ├── Some((0, 6)): 17/33 ≈ 0.515
      ├── Some((0, 7)): 11/25 ≈ 0.440
      └── Some((0, 8)): 36/54 ≈ 0.667
    ├── Some((6, 1)): 131/255 ≈ 0.514
      ├── Some((1, 0)): 6/19 ≈ 0.316
      ├── Some((1, 1)): 22/38 ≈ 0.579
      ├── Some((1, 2)): 31/49 ≈ 0.633
      ├── Some((1, 3)): 13/28 ≈ 0.464
      ├── Some((1, 4)): 13/28 ≈ 0.464
      ├── Some((1, 5)): 13/28 ≈ 0.464
      ├── Some((1, 7)): 14/29 ≈ 0.483
      └── Some((1, 8)): 19/35 ≈ 0.543
    ├── Some((6, 2)): 139/268 ≈ 0.519
      ├── Some((2, 0)): 33/50 ≈ 0.660
      ├── Some((2, 1)): 6/18 ≈ 0.333
      ├── Some((2, 2)): 14/28 ≈ 0.500
      ├── Some((2, 3)): 15/29 ≈ 0.517
      ├── Some((2, 4)): 25/41 ≈ 0.610
      ├── Some((2, 5)): 12/26 ≈ 0.462
      ├── Some((2, 6)): 7/20 ≈ 0.350
      ├── Some((2, 7)): 10/23 ≈ 0.435
      └── Some((2, 8)): 17/32 ≈ 0.531
    ├── Some((6, 3)): 223/395 ≈ 0.565
      ├── Some((3, 0)): 24/43 ≈ 0.558
      ├── Some((3, 1)): 19/37 ≈ 0.514
      ├── Some((3, 2)): 51/74 ≈ 0.689
      ├── Some((3, 3)): 31/52 ≈ 0.596
      ├── Some((3, 4)): 13/30 ≈ 0.433
      ├── Some((3, 5)): 8/23 ≈ 0.348
      ├── Some((3, 6)): 38/60 ≈ 0.633
      ├── Some((3, 7)): 20/38 ≈ 0.526
      └── Some((3, 8)): 19/37 ≈ 0.514
    ├── Some((6, 4)): 151/286 ≈ 0.528
      ├── Some((4, 0)): 29/46 ≈ 0.630
      ├── Some((4, 1)): 15/30 ≈ 0.500
      ├── Some((4, 2)): 16/31 ≈ 0.516
      ├── Some((4, 3)): 19/34 ≈ 0.559
      ├── Some((4, 4)): 15/30 ≈ 0.500
      ├── Some((4, 5)): 13/27 ≈ 0.481
      ├── Some((4, 6)): 11/25 ≈ 0.440
      ├── Some((4, 7)): 25/41 ≈ 0.610
      └── Some((4, 8)): 8/21 ≈ 0.381
    ├── Some((6, 5)): 200/360 ≈ 0.556
      ├── Some((5, 0)): 34/54 ≈ 0.630
      ├── Some((5, 1)): 30/49 ≈ 0.612
      ├── Some((5, 2)): 17/34 ≈ 0.500
      ├── Some((5, 3)): 9/24 ≈ 0.375
      ├── Some((5, 4)): 25/43 ≈ 0.581
      ├── Some((5, 5)): 16/33 ≈ 0.485
      ├── Some((5, 6)): 25/43 ≈ 0.581
      ├── Some((5, 7)): 27/46 ≈ 0.587
      └── Some((5, 8)): 16/33 ≈ 0.485
    ├── Some((6, 6)): 220/390 ≈ 0.564
      ├── Some((6, 0)): 25/46 ≈ 0.543
      ├── Some((6, 1)): 34/57 ≈ 0.596
      ├── Some((6, 2)): 16/35 ≈ 0.457
      ├── Some((6, 3)): 38/61 ≈ 0.623
      ├── Some((6, 4)): 27/48 ≈ 0.562
      ├── Some((6, 5)): 29/51 ≈ 0.569
      ├── Some((6, 7)): 32/54 ≈ 0.593
      └── Some((6, 8)): 18/37 ≈ 0.486
    ├── Some((6, 7)): 161/302 ≈ 0.533
      ├── Some((7, 0)): 10/24 ≈ 0.417
      ├── Some((7, 1)): 12/27 ≈ 0.444
      ├── Some((7, 2)): 22/39 ≈ 0.564
      ├── Some((7, 3)): 17/33 ≈ 0.515
      ├── Some((7, 4)): 16/31 ≈ 0.516
      ├── Some((7, 5)): 22/39 ≈ 0.564
      ├── Some((7, 6)): 16/31 ≈ 0.516
      ├── Some((7, 7)): 16/31 ≈ 0.516
      └── Some((7, 8)): 29/46 ≈ 0.630
    └── Some((6, 8)): 164/306 ≈ 0.536
      ├── Some((8, 0)): 23/40 ≈ 0.575
      ├── Some((8, 1)): 9/23 ≈ 0.391
      ├── Some((8, 2)): 22/39 ≈ 0.564
      ├── Some((8, 3)): 11/25 ≈ 0.440
      ├── Some((8, 4)): 23/40 ≈ 0.575
      ├── Some((8, 5)): 15/30 ≈ 0.500
      ├── Some((8, 6)): 16/31 ≈ 0.516
      ├── Some((8, 7)): 26/43 ≈ 0.605
      └── Some((8, 8)): 18/34 ≈ 0.529
  ├── Some((1, 7)): 1390/2596 ≈ 0.535
    ├── Some((7, 0)): 142/270 ≈ 0.526
      ├── Some((0, 0)): 25/42 ≈ 0.595
      ├── Some((0, 2)): 14/29 ≈ 0.483
      ├── Some((0, 3)): 30/48 ≈ 0.625
      ├── Some((0, 4)): 16/32 ≈ 0.500
      ├── Some((0, 5)): 22/39 ≈ 0.564
      ├── Some((0, 6)): 10/24 ≈ 0.417
      ├── Some((0, 7)): 7/21 ≈ 0.333
      └── Some((0, 8)): 18/34 ≈ 0.529
    ├── Some((7, 1)): 143/271 ≈ 0.528
      ├── Some((1, 0)): 16/32 ≈ 0.500
      ├── Some((1, 1)): 34/53 ≈ 0.642
      ├── Some((1, 2)): 7/20 ≈ 0.350
      ├── Some((1, 3)): 18/34 ≈ 0.529
      ├── Some((1, 4)): 23/40 ≈ 0.575
      ├── Some((1, 5)): 9/23 ≈ 0.391
      ├── Some((1, 6)): 23/40 ≈ 0.575
      └── Some((1, 8)): 13/28 ≈ 0.464
    ├── Some((7, 2)): 160/297 ≈ 0.539
      ├── Some((2, 0)): 14/29 ≈ 0.483
      ├── Some((2, 1)): 18/33 ≈ 0.545
      ├── Some((2, 2)): 21/37 ≈ 0.568
      ├── Some((2, 3)): 13/28 ≈ 0.464
      ├── Some((2, 4)): 22/38 ≈ 0.579
      ├── Some((2, 5)): 30/47 ≈ 0.638
      ├── Some((2, 6)): 19/35 ≈ 0.543
      ├── Some((2, 7)): 5/17 ≈ 0.294
      └── Some((2, 8)): 17/32 ≈ 0.531
    ├── Some((7, 3)): 161/299 ≈ 0.538
      ├── Some((3, 0)): 8/21 ≈ 0.381
      ├── Some((3, 1)): 12/27 ≈ 0.444
      ├── Some((3, 2)): 15/30 ≈ 0.500
      ├── Some((3, 3)): 22/38 ≈ 0.579
      ├── Some((3, 4)): 18/34 ≈ 0.529
      ├── Some((3, 5)): 5/17 ≈ 0.294
      ├── Some((3, 6)): 19/35 ≈ 0.543
      ├── Some((3, 7)): 33/51 ≈ 0.647
      └── Some((3, 8)): 28/45 ≈ 0.622
    ├── Some((7, 4)): 137/262 ≈ 0.523
      ├── Some((4, 0)): 14/28 ≈ 0.500
      ├── Some((4, 1)): 14/28 ≈ 0.500
      ├── Some((4, 2)): 15/29 ≈ 0.517
      ├── Some((4, 3)): 8/20 ≈ 0.400
      ├── Some((4, 4)): 25/40 ≈ 0.625
      ├── Some((4, 5)): 11/24 ≈ 0.458
      ├── Some((4, 6)): 17/31 ≈ 0.548
      ├── Some((4, 7)): 18/32 ≈ 0.562
      └── Some((4, 8)): 15/29 ≈ 0.517
    ├── Some((7, 5)): 148/279 ≈ 0.530
      ├── Some((5, 0)): 16/31 ≈ 0.516
      ├── Some((5, 1)): 3/14 ≈ 0.214
      ├── Some((5, 2)): 13/27 ≈ 0.481
      ├── Some((5, 3)): 23/39 ≈ 0.590
      ├── Some((5, 4)): 9/22 ≈ 0.409
      ├── Some((5, 5)): 19/34 ≈ 0.559
      ├── Some((5, 6)): 27/43 ≈ 0.628
      ├── Some((5, 7)): 14/29 ≈ 0.483
      └── Some((5, 8)): 23/39 ≈ 0.590
    ├── Some((7, 6)): 96/198 ≈ 0.485
      ├── Some((6, 0)): 11/22 ≈ 0.500
      ├── Some((6, 1)): 13/25 ≈ 0.520
      ├── Some((6, 2)): 11/22 ≈ 0.500
      ├── Some((6, 3)): 3/13 ≈ 0.231
      ├── Some((6, 4)): 14/26 ≈ 0.538
      ├── Some((6, 5)): 12/24 ≈ 0.500
      ├── Some((6, 6)): 14/26 ≈ 0.538
      ├── Some((6, 7)): 12/24 ≈ 0.500
      └── Some((6, 8)): 5/15 ≈ 0.333
    ├── Some((7, 7)): 224/393 ≈ 0.570
      ├── Some((7, 0)): 12/29 ≈ 0.414
      ├── Some((7, 1)): 35/58 ≈ 0.603
      ├── Some((7, 2)): 23/43 ≈ 0.535
      ├── Some((7, 3)): 44/68 ≈ 0.647
      ├── Some((7, 4)): 36/59 ≈ 0.610
      ├── Some((7, 5)): 23/43 ≈ 0.535
      ├── Some((7, 6)): 24/44 ≈ 0.545
      └── Some((7, 8)): 27/48 ≈ 0.562
    └── Some((7, 8)): 179/326 ≈ 0.549
      ├── Some((8, 0)): 30/48 ≈ 0.625
      ├── Some((8, 1)): 13/28 ≈ 0.464
      ├── Some((8, 2)): 18/34 ≈ 0.529
      ├── Some((8, 3)): 18/34 ≈ 0.529
      ├── Some((8, 4)): 20/36 ≈ 0.556
      ├── Some((8, 5)): 19/35 ≈ 0.543
      ├── Some((8, 6)): 24/41 ≈ 0.585
      ├── Some((8, 7)): 21/38 ≈ 0.553
      └── Some((8, 8)): 15/31 ≈ 0.484
  └── Some((1, 8)): 1193/2256 ≈ 0.529
    ├── Some((8, 0)): 163/297 ≈ 0.549
      ├── Some((0, 0)): 36/55 ≈ 0.655
      ├── Some((0, 2)): 30/48 ≈ 0.625
      ├── Some((0, 3)): 19/36 ≈ 0.528
      ├── Some((0, 4)): 15/31 ≈ 0.484
      ├── Some((0, 5)): 12/27 ≈ 0.444
      ├── Some((0, 6)): 14/29 ≈ 0.483
      ├── Some((0, 7)): 18/34 ≈ 0.529
      └── Some((0, 8)): 19/36 ≈ 0.528
    ├── Some((8, 1)): 129/245 ≈ 0.527
      ├── Some((1, 0)): 17/32 ≈ 0.531
      ├── Some((1, 1)): 16/30 ≈ 0.533
      ├── Some((1, 2)): 11/25 ≈ 0.440
      ├── Some((1, 3)): 16/30 ≈ 0.533
      ├── Some((1, 4)): 26/42 ≈ 0.619
      ├── Some((1, 5)): 7/19 ≈ 0.368
      ├── Some((1, 6)): 20/35 ≈ 0.571
      └── Some((1, 7)): 16/31 ≈ 0.516
    ├── Some((8, 2)): 104/207 ≈ 0.502
      ├── Some((2, 0)): 17/29 ≈ 0.586
      ├── Some((2, 1)): 10/21 ≈ 0.476
      ├── Some((2, 2)): 9/20 ≈ 0.450
      ├── Some((2, 3)): 7/18 ≈ 0.389
      ├── Some((2, 4)): 8/19 ≈ 0.421
      ├── Some((2, 5)): 13/25 ≈ 0.520
      ├── Some((2, 6)): 11/23 ≈ 0.478
      ├── Some((2, 7)): 3/13 ≈ 0.231
      └── Some((2, 8)): 25/38 ≈ 0.658
    ├── Some((8, 3)): 127/242 ≈ 0.525
      ├── Some((3, 0)): 17/30 ≈ 0.567
      ├── Some((3, 1)): 15/28 ≈ 0.536
      ├── Some((3, 2)): 10/22 ≈ 0.455
      ├── Some((3, 3)): 22/36 ≈ 0.611
      ├── Some((3, 4)): 19/32 ≈ 0.594
      ├── Some((3, 5)): 11/23 ≈ 0.478
      ├── Some((3, 6)): 14/27 ≈ 0.519
      ├── Some((3, 7)): 5/16 ≈ 0.312
      └── Some((3, 8)): 14/27 ≈ 0.519
    ├── Some((8, 4)): 156/286 ≈ 0.545
      ├── Some((4, 0)): 25/41 ≈ 0.610
      ├── Some((4, 1)): 8/21 ≈ 0.381
      ├── Some((4, 2)): 24/39 ≈ 0.615
      ├── Some((4, 3)): 30/46 ≈ 0.652
      ├── Some((4, 4)): 12/26 ≈ 0.462
      ├── Some((4, 5)): 18/33 ≈ 0.545
      ├── Some((4, 6)): 8/21 ≈ 0.381
      ├── Some((4, 7)): 14/28 ≈ 0.500
      └── Some((4, 8)): 16/30 ≈ 0.533
    ├── Some((8, 5)): 153/282 ≈ 0.543
      ├── Some((5, 0)): 6/18 ≈ 0.333
      ├── Some((5, 1)): 37/54 ≈ 0.685
      ├── Some((5, 2)): 16/30 ≈ 0.533
      ├── Some((5, 3)): 8/21 ≈ 0.381
      ├── Some((5, 4)): 18/33 ≈ 0.545
      ├── Some((5, 5)): 16/30 ≈ 0.533
      ├── Some((5, 6)): 16/30 ≈ 0.533
      ├── Some((5, 7)): 16/30 ≈ 0.533
      └── Some((5, 8)): 20/35 ≈ 0.571
    ├── Some((8, 6)): 114/223 ≈ 0.511
      ├── Some((6, 0)): 14/26 ≈ 0.538
      ├── Some((6, 1)): 18/31 ≈ 0.581
      ├── Some((6, 2)): 15/28 ≈ 0.536
      ├── Some((6, 3)): 4/14 ≈ 0.286
      ├── Some((6, 4)): 20/33 ≈ 0.606
      ├── Some((6, 5)): 16/29 ≈ 0.552
      ├── Some((6, 6)): 10/22 ≈ 0.455
      ├── Some((6, 7)): 10/22 ≈ 0.455
      └── Some((6, 8)): 6/17 ≈ 0.353
    ├── Some((8, 7)): 150/277 ≈ 0.542
      ├── Some((7, 0)): 17/32 ≈ 0.531
      ├── Some((7, 1)): 15/29 ≈ 0.517
      ├── Some((7, 2)): 14/28 ≈ 0.500
      ├── Some((7, 3)): 10/23 ≈ 0.435
      ├── Some((7, 4)): 18/33 ≈ 0.545
      ├── Some((7, 5)): 13/27 ≈ 0.481
      ├── Some((7, 6)): 24/39 ≈ 0.615
      ├── Some((7, 7)): 4/15 ≈ 0.267
      └── Some((7, 8)): 34/50 ≈ 0.680
    └── Some((8, 8)): 97/196 ≈ 0.495
      ├── Some((8, 0)): 5/16 ≈ 0.312
      ├── Some((8, 1)): 16/29 ≈ 0.552
      ├── Some((8, 2)): 17/30 ≈ 0.567
      ├── Some((8, 3)): 10/22 ≈ 0.455
      ├── Some((8, 4)): 14/27 ≈ 0.519
      ├── Some((8, 5)): 22/36 ≈ 0.611
      ├── Some((8, 6)): 7/19 ≈ 0.368
      └── Some((8, 7)): 5/16 ≈ 0.312
├── Some((0, 2)): 7751/14787 ≈ 0.524
  ├── Some((2, 0)): 741/1437 ≈ 0.516
    ├── Some((0, 0)): 90/176 ≈ 0.511
      ├── Some((0, 1)): 11/23 ≈ 0.478
      ├── Some((0, 3)): 8/20 ≈ 0.400
      ├── Some((0, 4)): 20/33 ≈ 0.606
      ├── Some((0, 5)): 21/34 ≈ 0.618
      ├── Some((0, 6)): 4/14 ≈ 0.286
      ├── Some((0, 7)): 9/21 ≈ 0.429
      └── Some((0, 8)): 17/30 ≈ 0.567
    ├── Some((0, 1)): 73/150 ≈ 0.487
      ├── Some((1, 0)): 8/16 ≈ 0.500
      ├── Some((1, 1)): 7/15 ≈ 0.467
      ├── Some((1, 2)): 10/19 ≈ 0.526
      ├── Some((1, 3)): 2/10 ≈ 0.200
      ├── Some((1, 4)): 4/12 ≈ 0.333
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 11/20 ≈ 0.550
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 13/22 ≈ 0.591
    ├── Some((0, 3)): 88/173 ≈ 0.509
      ├── Some((3, 0)): 12/22 ≈ 0.545
      ├── Some((3, 1)): 11/21 ≈ 0.524
      ├── Some((3, 2)): 2/10 ≈ 0.200
      ├── Some((3, 3)): 4/13 ≈ 0.308
      ├── Some((3, 4)): 6/15 ≈ 0.400
      ├── Some((3, 5)): 18/28 ≈ 0.643
      ├── Some((3, 6)): 17/27 ≈ 0.630
      ├── Some((3, 7)): 9/18 ≈ 0.500
      └── Some((3, 8)): 9/18 ≈ 0.500
    ├── Some((0, 4)): 107/201 ≈ 0.532
      ├── Some((4, 0)): 7/17 ≈ 0.412
      ├── Some((4, 1)): 10/20 ≈ 0.500
      ├── Some((4, 2)): 20/31 ≈ 0.645
      ├── Some((4, 3)): 13/23 ≈ 0.565
      ├── Some((4, 4)): 13/23 ≈ 0.565
      ├── Some((4, 5)): 15/26 ≈ 0.577
      ├── Some((4, 6)): 8/18 ≈ 0.444
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 13/24 ≈ 0.542
    ├── Some((0, 5)): 78/158 ≈ 0.494
      ├── Some((5, 0)): 3/11 ≈ 0.273
      ├── Some((5, 1)): 6/15 ≈ 0.400
      ├── Some((5, 2)): 17/26 ≈ 0.654
      ├── Some((5, 3)): 17/26 ≈ 0.654
      ├── Some((5, 4)): 9/18 ≈ 0.500
      ├── Some((5, 5)): 7/16 ≈ 0.438
      ├── Some((5, 6)): 7/16 ≈ 0.438
      ├── Some((5, 7)): 4/12 ≈ 0.333
      └── Some((5, 8)): 8/17 ≈ 0.471
    ├── Some((0, 6)): 130/235 ≈ 0.553
      ├── Some((6, 0)): 8/19 ≈ 0.421
      ├── Some((6, 1)): 7/18 ≈ 0.389
      ├── Some((6, 2)): 19/31 ≈ 0.613
      ├── Some((6, 3)): 13/25 ≈ 0.520
      ├── Some((6, 4)): 28/41 ≈ 0.683
      ├── Some((6, 5)): 2/11 ≈ 0.182
      ├── Some((6, 6)): 27/40 ≈ 0.675
      ├── Some((6, 7)): 6/17 ≈ 0.353
      └── Some((6, 8)): 20/32 ≈ 0.625
    ├── Some((0, 7)): 101/193 ≈ 0.523
      ├── Some((7, 0)): 21/32 ≈ 0.656
      ├── Some((7, 1)): 2/11 ≈ 0.182
      ├── Some((7, 2)): 3/12 ≈ 0.250
      ├── Some((7, 3)): 5/15 ≈ 0.333
      ├── Some((7, 4)): 14/25 ≈ 0.560
      ├── Some((7, 5)): 4/13 ≈ 0.308
      ├── Some((7, 6)): 27/39 ≈ 0.692
      ├── Some((7, 7)): 5/15 ≈ 0.333
      └── Some((7, 8)): 19/30 ≈ 0.633
    └── Some((0, 8)): 73/150 ≈ 0.487
      ├── Some((8, 0)): 5/13 ≈ 0.385
      ├── Some((8, 1)): 9/18 ≈ 0.500
      ├── Some((8, 2)): 8/17 ≈ 0.471
      ├── Some((8, 3)): 16/25 ≈ 0.640
      ├── Some((8, 4)): 8/17 ≈ 0.471
      ├── Some((8, 5)): 0/7 ≈ 0.000
      ├── Some((8, 6)): 7/16 ≈ 0.438
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 13/22 ≈ 0.591
  ├── Some((2, 1)): 1238/2288 ≈ 0.541
    ├── Some((1, 0)): 93/188 ≈ 0.495
      ├── Some((0, 0)): 10/22 ≈ 0.455
      ├── Some((0, 1)): 15/27 ≈ 0.556
      ├── Some((0, 3)): 13/25 ≈ 0.520
      ├── Some((0, 4)): 6/17 ≈ 0.353
      ├── Some((0, 5)): 5/15 ≈ 0.333
      ├── Some((0, 6)): 13/25 ≈ 0.520
      ├── Some((0, 7)): 13/25 ≈ 0.520
      └── Some((0, 8)): 18/31 ≈ 0.581
    ├── Some((1, 1)): 172/307 ≈ 0.560
      ├── Some((1, 0)): 17/33 ≈ 0.515
      ├── Some((1, 2)): 9/23 ≈ 0.391
      ├── Some((1, 3)): 25/43 ≈ 0.581
      ├── Some((1, 4)): 28/46 ≈ 0.609
      ├── Some((1, 5)): 17/33 ≈ 0.515
      ├── Some((1, 6)): 26/44 ≈ 0.591
      ├── Some((1, 7)): 25/43 ≈ 0.581
      └── Some((1, 8)): 24/41 ≈ 0.585
    ├── Some((1, 2)): 91/185 ≈ 0.492
      ├── Some((2, 0)): 11/23 ≈ 0.478
      ├── Some((2, 2)): 10/21 ≈ 0.476
      ├── Some((2, 3)): 11/23 ≈ 0.478
      ├── Some((2, 4)): 10/21 ≈ 0.476
      ├── Some((2, 5)): 10/21 ≈ 0.476
      ├── Some((2, 6)): 21/34 ≈ 0.618
      ├── Some((2, 7)): 10/22 ≈ 0.455
      └── Some((2, 8)): 8/19 ≈ 0.421
    ├── Some((1, 3)): 283/467 ≈ 0.606
      ├── Some((3, 0)): 24/43 ≈ 0.558
      ├── Some((3, 1)): 35/56 ≈ 0.625
      ├── Some((3, 2)): 30/50 ≈ 0.600
      ├── Some((3, 3)): 31/51 ≈ 0.608
      ├── Some((3, 4)): 24/43 ≈ 0.558
      ├── Some((3, 5)): 26/46 ≈ 0.565
      ├── Some((3, 6)): 39/60 ≈ 0.650
      ├── Some((3, 7)): 34/55 ≈ 0.618
      └── Some((3, 8)): 40/62 ≈ 0.645
    ├── Some((1, 4)): 114/220 ≈ 0.518
      ├── Some((4, 0)): 12/24 ≈ 0.500
      ├── Some((4, 1)): 19/32 ≈ 0.594
      ├── Some((4, 2)): 13/25 ≈ 0.520
      ├── Some((4, 3)): 13/25 ≈ 0.520
      ├── Some((4, 4)): 18/30 ≈ 0.600
      ├── Some((4, 5)): 7/18 ≈ 0.389
      ├── Some((4, 6)): 11/23 ≈ 0.478
      ├── Some((4, 7)): 15/27 ≈ 0.556
      └── Some((4, 8)): 5/15 ≈ 0.333
    ├── Some((1, 5)): 162/292 ≈ 0.555
      ├── Some((5, 0)): 22/37 ≈ 0.595
      ├── Some((5, 1)): 15/29 ≈ 0.517
      ├── Some((5, 2)): 13/27 ≈ 0.481
      ├── Some((5, 3)): 31/47 ≈ 0.660
      ├── Some((5, 4)): 9/22 ≈ 0.409
      ├── Some((5, 5)): 5/17 ≈ 0.294
      ├── Some((5, 6)): 25/40 ≈ 0.625
      ├── Some((5, 7)): 20/35 ≈ 0.571
      └── Some((5, 8)): 22/37 ≈ 0.595
    ├── Some((1, 6)): 143/264 ≈ 0.542
      ├── Some((6, 0)): 9/21 ≈ 0.429
      ├── Some((6, 1)): 13/26 ≈ 0.500
      ├── Some((6, 2)): 18/32 ≈ 0.562
      ├── Some((6, 3)): 13/26 ≈ 0.500
      ├── Some((6, 4)): 16/30 ≈ 0.533
      ├── Some((6, 5)): 20/34 ≈ 0.588
      ├── Some((6, 6)): 22/36 ≈ 0.611
      ├── Some((6, 7)): 16/30 ≈ 0.533
      └── Some((6, 8)): 15/28 ≈ 0.536
    ├── Some((1, 7)): 63/141 ≈ 0.447
      ├── Some((7, 0)): 5/14 ≈ 0.357
      ├── Some((7, 1)): 9/18 ≈ 0.500
      ├── Some((7, 2)): 7/16 ≈ 0.438
      ├── Some((7, 3)): 4/12 ≈ 0.333
      ├── Some((7, 4)): 11/20 ≈ 0.550
      ├── Some((7, 5)): 4/12 ≈ 0.333
      ├── Some((7, 6)): 11/20 ≈ 0.550
      ├── Some((7, 7)): 2/10 ≈ 0.200
      └── Some((7, 8)): 9/18 ≈ 0.500
    └── Some((1, 8)): 116/223 ≈ 0.520
      ├── Some((8, 0)): 19/32 ≈ 0.594
      ├── Some((8, 1)): 13/25 ≈ 0.520
      ├── Some((8, 2)): 9/20 ≈ 0.450
      ├── Some((8, 3)): 14/26 ≈ 0.538
      ├── Some((8, 4)): 9/20 ≈ 0.450
      ├── Some((8, 5)): 14/26 ≈ 0.538
      ├── Some((8, 6)): 5/16 ≈ 0.312
      ├── Some((8, 7)): 14/26 ≈ 0.538
      └── Some((8, 8)): 18/31 ≈ 0.581
  ├── Some((2, 2)): 1128/2102 ≈ 0.537
    ├── Some((2, 0)): 174/313 ≈ 0.556
      ├── Some((0, 0)): 23/41 ≈ 0.561
      ├── Some((0, 1)): 13/29 ≈ 0.448
      ├── Some((0, 3)): 19/36 ≈ 0.528
      ├── Some((0, 4)): 21/38 ≈ 0.553
      ├── Some((0, 5)): 27/45 ≈ 0.600
      ├── Some((0, 6)): 17/33 ≈ 0.515
      ├── Some((0, 7)): 29/47 ≈ 0.617
      └── Some((0, 8)): 25/43 ≈ 0.581
    ├── Some((2, 1)): 187/332 ≈ 0.563
      ├── Some((1, 0)): 21/37 ≈ 0.568
      ├── Some((1, 1)): 21/37 ≈ 0.568
      ├── Some((1, 2)): 17/33 ≈ 0.515
      ├── Some((1, 3)): 36/54 ≈ 0.667
      ├── Some((1, 4)): 11/25 ≈ 0.440
      ├── Some((1, 5)): 29/46 ≈ 0.630
      ├── Some((1, 6)): 24/41 ≈ 0.585
      ├── Some((1, 7)): 17/33 ≈ 0.515
      └── Some((1, 8)): 11/25 ≈ 0.440
    ├── Some((2, 3)): 176/316 ≈ 0.557
      ├── Some((3, 0)): 20/36 ≈ 0.556
      ├── Some((3, 1)): 15/30 ≈ 0.500
      ├── Some((3, 2)): 46/65 ≈ 0.708
      ├── Some((3, 3)): 17/32 ≈ 0.531
      ├── Some((3, 4)): 28/45 ≈ 0.622
      ├── Some((3, 5)): 15/30 ≈ 0.500
      ├── Some((3, 6)): 10/24 ≈ 0.417
      ├── Some((3, 7)): 17/33 ≈ 0.515
      └── Some((3, 8)): 7/20 ≈ 0.350
    ├── Some((2, 4)): 85/177 ≈ 0.480
      ├── Some((4, 0)): 11/21 ≈ 0.524
      ├── Some((4, 1)): 4/13 ≈ 0.308
      ├── Some((4, 2)): 10/20 ≈ 0.500
      ├── Some((4, 3)): 11/22 ≈ 0.500
      ├── Some((4, 4)): 6/16 ≈ 0.375
      ├── Some((4, 5)): 14/25 ≈ 0.560
      ├── Some((4, 6)): 12/23 ≈ 0.522
      ├── Some((4, 7)): 10/20 ≈ 0.500
      └── Some((4, 8)): 6/16 ≈ 0.375
    ├── Some((2, 5)): 145/269 ≈ 0.539
      ├── Some((5, 0)): 12/25 ≈ 0.480
      ├── Some((5, 1)): 21/36 ≈ 0.583
      ├── Some((5, 2)): 23/38 ≈ 0.605
      ├── Some((5, 3)): 25/40 ≈ 0.625
      ├── Some((5, 4)): 25/40 ≈ 0.625
      ├── Some((5, 5)): 16/30 ≈ 0.533
      ├── Some((5, 6)): 4/15 ≈ 0.267
      ├── Some((5, 7)): 8/20 ≈ 0.400
      └── Some((5, 8)): 11/24 ≈ 0.458
    ├── Some((2, 6)): 144/268 ≈ 0.537
      ├── Some((6, 0)): 23/38 ≈ 0.605
      ├── Some((6, 1)): 6/18 ≈ 0.333
      ├── Some((6, 2)): 22/37 ≈ 0.595
      ├── Some((6, 3)): 12/25 ≈ 0.480
      ├── Some((6, 4)): 20/35 ≈ 0.571
      ├── Some((6, 5)): 13/26 ≈ 0.500
      ├── Some((6, 6)): 19/33 ≈ 0.576
      ├── Some((6, 7)): 12/25 ≈ 0.480
      └── Some((6, 8)): 16/30 ≈ 0.533
    ├── Some((2, 7)): 123/236 ≈ 0.521
      ├── Some((7, 0)): 23/37 ≈ 0.622
      ├── Some((7, 1)): 9/21 ≈ 0.429
      ├── Some((7, 2)): 18/31 ≈ 0.581
      ├── Some((7, 3)): 16/29 ≈ 0.552
      ├── Some((7, 4)): 18/32 ≈ 0.562
      ├── Some((7, 5)): 17/30 ≈ 0.567
      ├── Some((7, 6)): 6/17 ≈ 0.353
      ├── Some((7, 7)): 10/22 ≈ 0.455
      └── Some((7, 8)): 5/16 ≈ 0.312
    └── Some((2, 8)): 93/190 ≈ 0.489
      ├── Some((8, 0)): 5/15 ≈ 0.333
      ├── Some((8, 1)): 8/18 ≈ 0.444
      ├── Some((8, 2)): 8/19 ≈ 0.421
      ├── Some((8, 3)): 18/30 ≈ 0.600
      ├── Some((8, 4)): 5/15 ≈ 0.333
      ├── Some((8, 5)): 25/37 ≈ 0.676
      ├── Some((8, 6)): 7/17 ≈ 0.412
      ├── Some((8, 7)): 7/17 ≈ 0.412
      └── Some((8, 8)): 10/21 ≈ 0.476
  ├── Some((2, 3)): 805/1548 ≈ 0.520
    ├── Some((3, 0)): 111/204 ≈ 0.544
      ├── Some((0, 0)): 13/25 ≈ 0.520
      ├── Some((0, 1)): 16/28 ≈ 0.571
      ├── Some((0, 3)): 10/21 ≈ 0.476
      ├── Some((0, 4)): 18/30 ≈ 0.600
      ├── Some((0, 5)): 12/23 ≈ 0.522
      ├── Some((0, 6)): 12/23 ≈ 0.522
      ├── Some((0, 7)): 16/28 ≈ 0.571
      └── Some((0, 8)): 13/25 ≈ 0.520
    ├── Some((3, 1)): 123/222 ≈ 0.554
      ├── Some((1, 0)): 6/16 ≈ 0.375
      ├── Some((1, 1)): 21/32 ≈ 0.656
      ├── Some((1, 2)): 7/17 ≈ 0.412
      ├── Some((1, 3)): 13/24 ≈ 0.542
      ├── Some((1, 4)): 14/25 ≈ 0.560
      ├── Some((1, 5)): 13/24 ≈ 0.542
      ├── Some((1, 6)): 16/27 ≈ 0.593
      ├── Some((1, 7)): 12/23 ≈ 0.522
      └── Some((1, 8)): 21/33 ≈ 0.636
    ├── Some((3, 2)): 93/178 ≈ 0.522
      ├── Some((2, 0)): 17/29 ≈ 0.586
      ├── Some((2, 1)): 10/21 ≈ 0.476
      ├── Some((2, 2)): 6/16 ≈ 0.375
      ├── Some((2, 4)): 8/18 ≈ 0.444
      ├── Some((2, 5)): 5/15 ≈ 0.333
      ├── Some((2, 6)): 5/15 ≈ 0.333
      ├── Some((2, 7)): 5/15 ≈ 0.333
      └── Some((2, 8)): 36/48 ≈ 0.750
    ├── Some((3, 3)): 47/108 ≈ 0.435
      ├── Some((3, 0)): 4/11 ≈ 0.364
      ├── Some((3, 1)): 7/15 ≈ 0.467
      ├── Some((3, 2)): 4/11 ≈ 0.364
      ├── Some((3, 4)): 9/17 ≈ 0.529
      ├── Some((3, 5)): 12/20 ≈ 0.600
      ├── Some((3, 6)): 2/9 ≈ 0.222
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 4/11 ≈ 0.364
    ├── Some((3, 4)): 121/219 ≈ 0.553
      ├── Some((4, 0)): 16/27 ≈ 0.593
      ├── Some((4, 1)): 11/22 ≈ 0.500
      ├── Some((4, 2)): 22/34 ≈ 0.647
      ├── Some((4, 3)): 17/28 ≈ 0.607
      ├── Some((4, 4)): 9/19 ≈ 0.474
      ├── Some((4, 5)): 11/22 ≈ 0.500
      ├── Some((4, 6)): 5/15 ≈ 0.333
      ├── Some((4, 7)): 10/21 ≈ 0.476
      └── Some((4, 8)): 19/30 ≈ 0.633
    ├── Some((3, 5)): 53/118 ≈ 0.449
      ├── Some((5, 0)): 2/9 ≈ 0.222
      ├── Some((5, 1)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 8/15 ≈ 0.533
      ├── Some((5, 4)): 2/9 ≈ 0.222
      ├── Some((5, 5)): 15/22 ≈ 0.682
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((3, 6)): 109/202 ≈ 0.540
      ├── Some((6, 0)): 3/12 ≈ 0.250
      ├── Some((6, 1)): 21/32 ≈ 0.656
      ├── Some((6, 2)): 11/21 ≈ 0.524
      ├── Some((6, 3)): 11/22 ≈ 0.500
      ├── Some((6, 4)): 5/15 ≈ 0.333
      ├── Some((6, 5)): 23/34 ≈ 0.676
      ├── Some((6, 6)): 8/18 ≈ 0.444
      ├── Some((6, 7)): 20/31 ≈ 0.645
      └── Some((6, 8)): 6/16 ≈ 0.375
    ├── Some((3, 7)): 47/108 ≈ 0.435
      ├── Some((7, 0)): 2/8 ≈ 0.250
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 4/11 ≈ 0.364
      ├── Some((7, 3)): 6/13 ≈ 0.462
      ├── Some((7, 4)): 3/9 ≈ 0.333
      ├── Some((7, 5)): 10/17 ≈ 0.588
      ├── Some((7, 6)): 5/12 ≈ 0.417
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 9/16 ≈ 0.562
    └── Some((3, 8)): 100/188 ≈ 0.532
      ├── Some((8, 0)): 6/15 ≈ 0.400
      ├── Some((8, 1)): 3/12 ≈ 0.250
      ├── Some((8, 2)): 11/21 ≈ 0.524
      ├── Some((8, 3)): 8/17 ≈ 0.471
      ├── Some((8, 4)): 14/24 ≈ 0.583
      ├── Some((8, 5)): 12/22 ≈ 0.545
      ├── Some((8, 6)): 11/21 ≈ 0.524
      ├── Some((8, 7)): 25/35 ≈ 0.714
      └── Some((8, 8)): 10/20 ≈ 0.500
  ├── Some((2, 4)): 833/1596 ≈ 0.522
    ├── Some((4, 0)): 57/124 ≈ 0.460
      ├── Some((0, 0)): 8/16 ≈ 0.500
      ├── Some((0, 1)): 6/14 ≈ 0.429
      ├── Some((0, 3)): 8/16 ≈ 0.500
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 12/21 ≈ 0.571
      ├── Some((0, 6)): 10/19 ≈ 0.526
      ├── Some((0, 7)): 4/12 ≈ 0.333
      └── Some((0, 8)): 4/12 ≈ 0.333
    ├── Some((4, 1)): 71/146 ≈ 0.486
      ├── Some((1, 0)): 4/12 ≈ 0.333
      ├── Some((1, 1)): 1/8 ≈ 0.125
      ├── Some((1, 2)): 13/22 ≈ 0.591
      ├── Some((1, 3)): 11/20 ≈ 0.550
      ├── Some((1, 4)): 13/22 ≈ 0.591
      ├── Some((1, 5)): 7/15 ≈ 0.467
      ├── Some((1, 6)): 9/18 ≈ 0.500
      ├── Some((1, 7)): 4/12 ≈ 0.333
      └── Some((1, 8)): 8/16 ≈ 0.500
    ├── Some((4, 2)): 110/203 ≈ 0.542
      ├── Some((2, 0)): 15/27 ≈ 0.556
      ├── Some((2, 1)): 12/23 ≈ 0.522
      ├── Some((2, 2)): 12/23 ≈ 0.522
      ├── Some((2, 3)): 12/23 ≈ 0.522
      ├── Some((2, 5)): 9/20 ≈ 0.450
      ├── Some((2, 6)): 15/27 ≈ 0.556
      ├── Some((2, 7)): 10/21 ≈ 0.476
      └── Some((2, 8)): 25/38 ≈ 0.658
    ├── Some((4, 3)): 85/167 ≈ 0.509
      ├── Some((3, 0)): 8/17 ≈ 0.471
      ├── Some((3, 1)): 7/16 ≈ 0.438
      ├── Some((3, 2)): 10/19 ≈ 0.526
      ├── Some((3, 3)): 1/9 ≈ 0.111
      ├── Some((3, 4)): 6/15 ≈ 0.400
      ├── Some((3, 5)): 15/24 ≈ 0.625
      ├── Some((3, 6)): 10/19 ≈ 0.526
      ├── Some((3, 7)): 20/30 ≈ 0.667
      └── Some((3, 8)): 8/17 ≈ 0.471
    ├── Some((4, 4)): 116/212 ≈ 0.547
      ├── Some((4, 0)): 24/37 ≈ 0.649
      ├── Some((4, 1)): 20/33 ≈ 0.606
      ├── Some((4, 2)): 6/17 ≈ 0.353
      ├── Some((4, 3)): 14/26 ≈ 0.538
      ├── Some((4, 5)): 12/24 ≈ 0.500
      ├── Some((4, 6)): 7/18 ≈ 0.389
      ├── Some((4, 7)): 9/20 ≈ 0.450
      └── Some((4, 8)): 23/36 ≈ 0.639
    ├── Some((4, 5)): 62/132 ≈ 0.470
      ├── Some((5, 0)): 11/19 ≈ 0.579
      ├── Some((5, 1)): 12/20 ≈ 0.600
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 3/10 ≈ 0.300
      ├── Some((5, 4)): 6/14 ≈ 0.429
      ├── Some((5, 5)): 8/16 ≈ 0.500
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 3/10 ≈ 0.300
      └── Some((5, 8)): 9/17 ≈ 0.529
    ├── Some((4, 6)): 130/233 ≈ 0.558
      ├── Some((6, 0)): 15/27 ≈ 0.556
      ├── Some((6, 1)): 13/24 ≈ 0.542
      ├── Some((6, 2)): 27/39 ≈ 0.692
      ├── Some((6, 3)): 17/29 ≈ 0.586
      ├── Some((6, 4)): 10/21 ≈ 0.476
      ├── Some((6, 5)): 11/22 ≈ 0.500
      ├── Some((6, 6)): 11/22 ≈ 0.500
      ├── Some((6, 7)): 14/26 ≈ 0.538
      └── Some((6, 8)): 11/22 ≈ 0.500
    ├── Some((4, 7)): 121/219 ≈ 0.553
      ├── Some((7, 0)): 13/24 ≈ 0.542
      ├── Some((7, 1)): 16/27 ≈ 0.593
      ├── Some((7, 2)): 8/18 ≈ 0.444
      ├── Some((7, 3)): 8/18 ≈ 0.444
      ├── Some((7, 4)): 17/28 ≈ 0.607
      ├── Some((7, 5)): 7/17 ≈ 0.412
      ├── Some((7, 6)): 25/37 ≈ 0.676
      ├── Some((7, 7)): 14/25 ≈ 0.560
      └── Some((7, 8)): 13/24 ≈ 0.542
    └── Some((4, 8)): 80/159 ≈ 0.503
      ├── Some((8, 0)): 8/17 ≈ 0.471
      ├── Some((8, 1)): 4/12 ≈ 0.333
      ├── Some((8, 2)): 13/22 ≈ 0.591
      ├── Some((8, 3)): 6/14 ≈ 0.429
      ├── Some((8, 4)): 10/19 ≈ 0.526
      ├── Some((8, 5)): 8/17 ≈ 0.471
      ├── Some((8, 6)): 13/22 ≈ 0.591
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 12/21 ≈ 0.571
  ├── Some((2, 5)): 1026/1928 ≈ 0.532
    ├── Some((5, 0)): 106/203 ≈ 0.522
      ├── Some((0, 0)): 11/23 ≈ 0.478
      ├── Some((0, 1)): 17/30 ≈ 0.567
      ├── Some((0, 3)): 12/24 ≈ 0.500
      ├── Some((0, 4)): 13/25 ≈ 0.520
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 9/20 ≈ 0.450
      ├── Some((0, 7)): 20/33 ≈ 0.606
      └── Some((0, 8)): 11/23 ≈ 0.478
    ├── Some((5, 1)): 43/105 ≈ 0.410
      ├── Some((1, 0)): 4/11 ≈ 0.364
      ├── Some((1, 1)): 6/13 ≈ 0.462
      ├── Some((1, 2)): 4/11 ≈ 0.364
      ├── Some((1, 3)): 6/13 ≈ 0.462
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 5/12 ≈ 0.417
      ├── Some((1, 6)): 2/8 ≈ 0.250
      ├── Some((1, 7)): 3/10 ≈ 0.300
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((5, 2)): 144/259 ≈ 0.556
      ├── Some((2, 0)): 19/34 ≈ 0.559
      ├── Some((2, 1)): 23/38 ≈ 0.605
      ├── Some((2, 2)): 24/39 ≈ 0.615
      ├── Some((2, 3)): 14/28 ≈ 0.500
      ├── Some((2, 4)): 17/32 ≈ 0.531
      ├── Some((2, 6)): 24/39 ≈ 0.615
      ├── Some((2, 7)): 16/30 ≈ 0.533
      └── Some((2, 8)): 6/18 ≈ 0.333
    ├── Some((5, 3)): 144/259 ≈ 0.556
      ├── Some((3, 0)): 29/43 ≈ 0.674
      ├── Some((3, 1)): 10/22 ≈ 0.455
      ├── Some((3, 2)): 14/27 ≈ 0.519
      ├── Some((3, 3)): 18/31 ≈ 0.581
      ├── Some((3, 4)): 24/38 ≈ 0.632
      ├── Some((3, 5)): 11/23 ≈ 0.478
      ├── Some((3, 6)): 22/36 ≈ 0.611
      ├── Some((3, 7)): 10/22 ≈ 0.455
      └── Some((3, 8)): 5/16 ≈ 0.312
    ├── Some((5, 4)): 138/251 ≈ 0.550
      ├── Some((4, 0)): 17/30 ≈ 0.567
      ├── Some((4, 1)): 18/31 ≈ 0.581
      ├── Some((4, 2)): 9/21 ≈ 0.429
      ├── Some((4, 3)): 5/16 ≈ 0.312
      ├── Some((4, 4)): 20/33 ≈ 0.606
      ├── Some((4, 5)): 12/24 ≈ 0.500
      ├── Some((4, 6)): 12/24 ≈ 0.500
      ├── Some((4, 7)): 22/35 ≈ 0.629
      └── Some((4, 8)): 23/36 ≈ 0.639
    ├── Some((5, 5)): 122/227 ≈ 0.537
      ├── Some((5, 0)): 5/16 ≈ 0.312
      ├── Some((5, 1)): 19/33 ≈ 0.576
      ├── Some((5, 2)): 28/43 ≈ 0.651
      ├── Some((5, 3)): 16/29 ≈ 0.552
      ├── Some((5, 4)): 15/28 ≈ 0.536
      ├── Some((5, 6)): 6/17 ≈ 0.353
      ├── Some((5, 7)): 19/33 ≈ 0.576
      └── Some((5, 8)): 14/27 ≈ 0.519
    ├── Some((5, 6)): 122/227 ≈ 0.537
      ├── Some((6, 0)): 6/17 ≈ 0.353
      ├── Some((6, 1)): 13/25 ≈ 0.520
      ├── Some((6, 2)): 5/15 ≈ 0.333
      ├── Some((6, 3)): 17/29 ≈ 0.586
      ├── Some((6, 4)): 15/27 ≈ 0.556
      ├── Some((6, 5)): 18/31 ≈ 0.581
      ├── Some((6, 6)): 27/40 ≈ 0.675
      ├── Some((6, 7)): 16/28 ≈ 0.571
      └── Some((6, 8)): 4/14 ≈ 0.286
    ├── Some((5, 7)): 140/254 ≈ 0.551
      ├── Some((7, 0)): 20/33 ≈ 0.606
      ├── Some((7, 1)): 21/35 ≈ 0.600
      ├── Some((7, 2)): 6/17 ≈ 0.353
      ├── Some((7, 3)): 11/23 ≈ 0.478
      ├── Some((7, 4)): 21/35 ≈ 0.600
      ├── Some((7, 5)): 2/12 ≈ 0.167
      ├── Some((7, 6)): 32/46 ≈ 0.696
      ├── Some((7, 7)): 12/24 ≈ 0.500
      └── Some((7, 8)): 15/28 ≈ 0.536
    └── Some((5, 8)): 66/142 ≈ 0.465
      ├── Some((8, 0)): 2/10 ≈ 0.200
      ├── Some((8, 1)): 20/30 ≈ 0.667
      ├── Some((8, 2)): 1/8 ≈ 0.125
      ├── Some((8, 3)): 1/8 ≈ 0.125
      ├── Some((8, 4)): 4/12 ≈ 0.333
      ├── Some((8, 5)): 9/18 ≈ 0.500
      ├── Some((8, 6)): 9/18 ≈ 0.500
      ├── Some((8, 7)): 8/17 ≈ 0.471
      └── Some((8, 8)): 11/20 ≈ 0.550
  ├── Some((2, 6)): 669/1312 ≈ 0.510
    ├── Some((6, 0)): 62/128 ≈ 0.484
      ├── Some((0, 0)): 13/22 ≈ 0.591
      ├── Some((0, 1)): 5/13 ≈ 0.385
      ├── Some((0, 3)): 2/9 ≈ 0.222
      ├── Some((0, 4)): 17/26 ≈ 0.654
      ├── Some((0, 5)): 6/14 ≈ 0.429
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 6/14 ≈ 0.429
      └── Some((0, 8)): 9/17 ≈ 0.529
    ├── Some((6, 1)): 60/125 ≈ 0.480
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 14/22 ≈ 0.636
      ├── Some((1, 2)): 4/11 ≈ 0.364
      ├── Some((1, 3)): 10/18 ≈ 0.556
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 3/10 ≈ 0.300
      └── Some((1, 8)): 2/9 ≈ 0.222
    ├── Some((6, 2)): 49/108 ≈ 0.454
      ├── Some((2, 0)): 11/19 ≈ 0.579
      ├── Some((2, 1)): 5/12 ≈ 0.417
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 2/9 ≈ 0.222
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 7/15 ≈ 0.467
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((6, 3)): 65/132 ≈ 0.492
      ├── Some((3, 0)): 10/18 ≈ 0.556
      ├── Some((3, 1)): 4/11 ≈ 0.364
      ├── Some((3, 2)): 2/9 ≈ 0.222
      ├── Some((3, 3)): 10/18 ≈ 0.556
      ├── Some((3, 4)): 7/14 ≈ 0.500
      ├── Some((3, 5)): 4/11 ≈ 0.364
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 12/20 ≈ 0.600
      └── Some((3, 8)): 8/15 ≈ 0.533
    ├── Some((6, 4)): 75/147 ≈ 0.510
      ├── Some((4, 0)): 21/29 ≈ 0.724
      ├── Some((4, 1)): 13/21 ≈ 0.619
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 7/15 ≈ 0.467
      ├── Some((4, 4)): 8/16 ≈ 0.500
      ├── Some((4, 5)): 10/18 ≈ 0.556
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 3/11 ≈ 0.273
      └── Some((4, 8)): 1/8 ≈ 0.125
    ├── Some((6, 5)): 82/157 ≈ 0.522
      ├── Some((5, 0)): 2/9 ≈ 0.222
      ├── Some((5, 1)): 11/19 ≈ 0.579
      ├── Some((5, 2)): 12/21 ≈ 0.571
      ├── Some((5, 3)): 14/23 ≈ 0.609
      ├── Some((5, 4)): 6/14 ≈ 0.429
      ├── Some((5, 5)): 11/19 ≈ 0.579
      ├── Some((5, 6)): 9/17 ≈ 0.529
      ├── Some((5, 7)): 12/21 ≈ 0.571
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((6, 6)): 57/120 ≈ 0.475
      ├── Some((6, 0)): 4/12 ≈ 0.333
      ├── Some((6, 1)): 9/17 ≈ 0.529
      ├── Some((6, 2)): 5/13 ≈ 0.385
      ├── Some((6, 3)): 4/12 ≈ 0.333
      ├── Some((6, 4)): 13/21 ≈ 0.619
      ├── Some((6, 5)): 8/16 ≈ 0.500
      ├── Some((6, 7)): 2/9 ≈ 0.222
      └── Some((6, 8)): 11/19 ≈ 0.579
    ├── Some((6, 7)): 103/188 ≈ 0.548
      ├── Some((7, 0)): 12/21 ≈ 0.571
      ├── Some((7, 1)): 15/25 ≈ 0.600
      ├── Some((7, 2)): 10/19 ≈ 0.526
      ├── Some((7, 3)): 17/27 ≈ 0.630
      ├── Some((7, 4)): 16/26 ≈ 0.615
      ├── Some((7, 5)): 4/13 ≈ 0.308
      ├── Some((7, 6)): 7/16 ≈ 0.438
      ├── Some((7, 7)): 8/17 ≈ 0.471
      └── Some((7, 8)): 13/23 ≈ 0.565
    └── Some((6, 8)): 116/206 ≈ 0.563
      ├── Some((8, 0)): 12/22 ≈ 0.545
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 16/26 ≈ 0.615
      ├── Some((8, 3)): 8/18 ≈ 0.444
      ├── Some((8, 4)): 15/25 ≈ 0.600
      ├── Some((8, 5)): 14/24 ≈ 0.583
      ├── Some((8, 6)): 9/19 ≈ 0.474
      ├── Some((8, 7)): 18/29 ≈ 0.621
      └── Some((8, 8)): 17/27 ≈ 0.630
  ├── Some((2, 7)): 740/1436 ≈ 0.515
    ├── Some((7, 0)): 89/170 ≈ 0.524
      ├── Some((0, 0)): 13/23 ≈ 0.565
      ├── Some((0, 1)): 7/17 ≈ 0.412
      ├── Some((0, 3)): 19/30 ≈ 0.633
      ├── Some((0, 4)): 11/21 ≈ 0.524
      ├── Some((0, 5)): 13/24 ≈ 0.542
      ├── Some((0, 6)): 18/29 ≈ 0.621
      ├── Some((0, 7)): 3/12 ≈ 0.250
      └── Some((0, 8)): 4/13 ≈ 0.308
    ├── Some((7, 1)): 49/110 ≈ 0.445
      ├── Some((1, 0)): 9/16 ≈ 0.562
      ├── Some((1, 1)): 11/18 ≈ 0.611
      ├── Some((1, 2)): 1/7 ≈ 0.143
      ├── Some((1, 3)): 8/15 ≈ 0.533
      ├── Some((1, 4)): 0/6 ≈ 0.000
      ├── Some((1, 5)): 4/11 ≈ 0.364
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 2/9 ≈ 0.222
    ├── Some((7, 2)): 136/238 ≈ 0.571
      ├── Some((2, 0)): 10/22 ≈ 0.455
      ├── Some((2, 1)): 18/31 ≈ 0.581
      ├── Some((2, 2)): 22/35 ≈ 0.629
      ├── Some((2, 3)): 23/36 ≈ 0.639
      ├── Some((2, 4)): 15/28 ≈ 0.536
      ├── Some((2, 5)): 10/22 ≈ 0.455
      ├── Some((2, 6)): 25/38 ≈ 0.658
      └── Some((2, 8)): 13/25 ≈ 0.520
    ├── Some((7, 3)): 68/139 ≈ 0.489
      ├── Some((3, 0)): 0/7 ≈ 0.000
      ├── Some((3, 1)): 9/17 ≈ 0.529
      ├── Some((3, 2)): 20/28 ≈ 0.714
      ├── Some((3, 3)): 12/20 ≈ 0.600
      ├── Some((3, 4)): 7/15 ≈ 0.467
      ├── Some((3, 5)): 6/14 ≈ 0.429
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 3/11 ≈ 0.273
      └── Some((3, 8)): 5/13 ≈ 0.385
    ├── Some((7, 4)): 68/139 ≈ 0.489
      ├── Some((4, 0)): 5/13 ≈ 0.385
      ├── Some((4, 1)): 15/23 ≈ 0.652
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 12/20 ≈ 0.600
      ├── Some((4, 5)): 4/11 ≈ 0.364
      ├── Some((4, 6)): 10/18 ≈ 0.556
      ├── Some((4, 7)): 4/12 ≈ 0.333
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((7, 5)): 90/172 ≈ 0.523
      ├── Some((5, 0)): 9/18 ≈ 0.500
      ├── Some((5, 1)): 13/23 ≈ 0.565
      ├── Some((5, 2)): 11/20 ≈ 0.550
      ├── Some((5, 3)): 7/16 ≈ 0.438
      ├── Some((5, 4)): 25/35 ≈ 0.714
      ├── Some((5, 5)): 9/18 ≈ 0.500
      ├── Some((5, 6)): 6/15 ≈ 0.400
      ├── Some((5, 7)): 6/15 ≈ 0.400
      └── Some((5, 8)): 3/11 ≈ 0.273
    ├── Some((7, 6)): 59/126 ≈ 0.468
      ├── Some((6, 0)): 5/12 ≈ 0.417
      ├── Some((6, 1)): 8/16 ≈ 0.500
      ├── Some((6, 2)): 12/20 ≈ 0.600
      ├── Some((6, 3)): 8/16 ≈ 0.500
      ├── Some((6, 4)): 4/11 ≈ 0.364
      ├── Some((6, 5)): 7/15 ≈ 0.467
      ├── Some((6, 6)): 4/11 ≈ 0.364
      ├── Some((6, 7)): 5/12 ≈ 0.417
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((7, 7)): 45/104 ≈ 0.433
      ├── Some((7, 0)): 9/17 ≈ 0.529
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 7/14 ≈ 0.500
      ├── Some((7, 3)): 1/8 ≈ 0.125
      ├── Some((7, 4)): 5/12 ≈ 0.417
      ├── Some((7, 5)): 3/10 ≈ 0.300
      ├── Some((7, 6)): 4/11 ≈ 0.364
      └── Some((7, 8)): 13/21 ≈ 0.619
    └── Some((7, 8)): 135/237 ≈ 0.570
      ├── Some((8, 0)): 13/24 ≈ 0.542
      ├── Some((8, 1)): 19/30 ≈ 0.633
      ├── Some((8, 2)): 19/31 ≈ 0.613
      ├── Some((8, 3)): 11/22 ≈ 0.500
      ├── Some((8, 4)): 16/27 ≈ 0.593
      ├── Some((8, 5)): 10/21 ≈ 0.476
      ├── Some((8, 6)): 11/22 ≈ 0.500
      ├── Some((8, 7)): 22/34 ≈ 0.647
      └── Some((8, 8)): 14/25 ≈ 0.560
  └── Some((2, 8)): 570/1139 ≈ 0.500
    ├── Some((8, 0)): 87/161 ≈ 0.540
      ├── Some((0, 0)): 11/20 ≈ 0.550
      ├── Some((0, 1)): 10/19 ≈ 0.526
      ├── Some((0, 3)): 7/16 ≈ 0.438
      ├── Some((0, 4)): 12/21 ≈ 0.571
      ├── Some((0, 5)): 10/19 ≈ 0.526
      ├── Some((0, 6)): 7/16 ≈ 0.438
      ├── Some((0, 7)): 20/30 ≈ 0.667
      └── Some((0, 8)): 10/19 ≈ 0.526
    ├── Some((8, 1)): 37/87 ≈ 0.425
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 4/9 ≈ 0.444
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 4/9 ≈ 0.444
      ├── Some((1, 4)): 7/12 ≈ 0.583
      ├── Some((1, 5)): 4/10 ≈ 0.400
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((8, 2)): 36/86 ≈ 0.419
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 7/14 ≈ 0.500
      ├── Some((2, 2)): 1/7 ≈ 0.143
      ├── Some((2, 3)): 10/17 ≈ 0.588
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 0/6 ≈ 0.000
      └── Some((2, 7)): 4/10 ≈ 0.400
    ├── Some((8, 3)): 81/153 ≈ 0.529
      ├── Some((3, 0)): 2/9 ≈ 0.222
      ├── Some((3, 1)): 8/16 ≈ 0.500
      ├── Some((3, 2)): 4/12 ≈ 0.333
      ├── Some((3, 3)): 4/12 ≈ 0.333
      ├── Some((3, 4)): 11/19 ≈ 0.579
      ├── Some((3, 5)): 12/20 ≈ 0.600
      ├── Some((3, 6)): 12/20 ≈ 0.600
      ├── Some((3, 7)): 10/18 ≈ 0.556
      └── Some((3, 8)): 18/26 ≈ 0.692
    ├── Some((8, 4)): 58/119 ≈ 0.487
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 11/18 ≈ 0.611
      ├── Some((4, 2)): 1/7 ≈ 0.143
      ├── Some((4, 3)): 4/10 ≈ 0.400
      ├── Some((4, 4)): 4/11 ≈ 0.364
      ├── Some((4, 5)): 5/12 ≈ 0.417
      ├── Some((4, 6)): 10/17 ≈ 0.588
      ├── Some((4, 7)): 9/16 ≈ 0.562
      └── Some((4, 8)): 5/12 ≈ 0.417
    ├── Some((8, 5)): 46/101 ≈ 0.455
      ├── Some((5, 0)): 2/8 ≈ 0.250
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 7/13 ≈ 0.538
      ├── Some((5, 5)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 7/14 ≈ 0.500
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 4/10 ≈ 0.400
    ├── Some((8, 6)): 84/157 ≈ 0.535
      ├── Some((6, 0)): 9/17 ≈ 0.529
      ├── Some((6, 1)): 10/18 ≈ 0.556
      ├── Some((6, 2)): 5/13 ≈ 0.385
      ├── Some((6, 3)): 1/8 ≈ 0.125
      ├── Some((6, 4)): 10/18 ≈ 0.556
      ├── Some((6, 5)): 8/16 ≈ 0.500
      ├── Some((6, 6)): 20/28 ≈ 0.714
      ├── Some((6, 7)): 11/20 ≈ 0.550
      └── Some((6, 8)): 10/18 ≈ 0.556
    ├── Some((8, 7)): 84/157 ≈ 0.535
      ├── Some((7, 0)): 7/15 ≈ 0.467
      ├── Some((7, 1)): 15/24 ≈ 0.625
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 5/13 ≈ 0.385
      ├── Some((7, 4)): 17/25 ≈ 0.680
      ├── Some((7, 5)): 1/8 ≈ 0.125
      ├── Some((7, 6)): 7/15 ≈ 0.467
      ├── Some((7, 7)): 7/15 ≈ 0.467
      └── Some((7, 8)): 16/25 ≈ 0.640
    └── Some((8, 8)): 57/117 ≈ 0.487
      ├── Some((8, 0)): 3/10 ≈ 0.300
      ├── Some((8, 1)): 3/10 ≈ 0.300
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 3/10 ≈ 0.300
      ├── Some((8, 4)): 21/29 ≈ 0.724
      ├── Some((8, 5)): 0/6 ≈ 0.000
      ├── Some((8, 6)): 12/20 ≈ 0.600
      └── Some((8, 7)): 7/15 ≈ 0.467
├── Some((0, 3)): 7032/13473 ≈ 0.522
  ├── Some((3, 0)): 918/1734 ≈ 0.529
    ├── Some((0, 0)): 74/155 ≈ 0.477
      ├── Some((0, 1)): 7/18 ≈ 0.389
      ├── Some((0, 2)): 15/28 ≈ 0.536
      ├── Some((0, 4)): 5/15 ≈ 0.333
      ├── Some((0, 5)): 10/22 ≈ 0.455
      ├── Some((0, 6)): 14/26 ≈ 0.538
      ├── Some((0, 7)): 19/32 ≈ 0.594
      └── Some((0, 8)): 3/13 ≈ 0.231
    ├── Some((0, 1)): 120/225 ≈ 0.533
      ├── Some((1, 0)): 5/15 ≈ 0.333
      ├── Some((1, 1)): 12/24 ≈ 0.500
      ├── Some((1, 2)): 24/37 ≈ 0.649
      ├── Some((1, 3)): 7/18 ≈ 0.389
      ├── Some((1, 4)): 19/32 ≈ 0.594
      ├── Some((1, 5)): 18/30 ≈ 0.600
      ├── Some((1, 6)): 19/32 ≈ 0.594
      ├── Some((1, 7)): 5/15 ≈ 0.333
      └── Some((1, 8)): 10/21 ≈ 0.476
    ├── Some((0, 2)): 101/197 ≈ 0.513
      ├── Some((2, 0)): 8/18 ≈ 0.444
      ├── Some((2, 1)): 16/27 ≈ 0.593
      ├── Some((2, 2)): 11/22 ≈ 0.500
      ├── Some((2, 3)): 7/17 ≈ 0.412
      ├── Some((2, 4)): 15/26 ≈ 0.577
      ├── Some((2, 5)): 7/17 ≈ 0.412
      ├── Some((2, 6)): 7/17 ≈ 0.412
      ├── Some((2, 7)): 12/23 ≈ 0.522
      └── Some((2, 8)): 17/29 ≈ 0.586
    ├── Some((0, 4)): 153/274 ≈ 0.558
      ├── Some((4, 0)): 23/37 ≈ 0.622
      ├── Some((4, 1)): 14/27 ≈ 0.519
      ├── Some((4, 2)): 18/32 ≈ 0.562
      ├── Some((4, 3)): 20/34 ≈ 0.588
      ├── Some((4, 4)): 17/31 ≈ 0.548
      ├── Some((4, 5)): 9/21 ≈ 0.429
      ├── Some((4, 6)): 6/17 ≈ 0.353
      ├── Some((4, 7)): 21/35 ≈ 0.600
      └── Some((4, 8)): 25/39 ≈ 0.641
    ├── Some((0, 5)): 62/136 ≈ 0.456
      ├── Some((5, 0)): 2/9 ≈ 0.222
      ├── Some((5, 1)): 14/23 ≈ 0.609
      ├── Some((5, 2)): 12/21 ≈ 0.571
      ├── Some((5, 3)): 3/11 ≈ 0.273
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 6/14 ≈ 0.429
      ├── Some((5, 6)): 8/17 ≈ 0.471
      ├── Some((5, 7)): 5/13 ≈ 0.385
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((0, 6)): 119/224 ≈ 0.531
      ├── Some((6, 0)): 10/21 ≈ 0.476
      ├── Some((6, 1)): 10/21 ≈ 0.476
      ├── Some((6, 2)): 19/31 ≈ 0.613
      ├── Some((6, 3)): 12/24 ≈ 0.500
      ├── Some((6, 4)): 13/25 ≈ 0.520
      ├── Some((6, 5)): 15/27 ≈ 0.556
      ├── Some((6, 6)): 26/39 ≈ 0.667
      ├── Some((6, 7)): 10/21 ≈ 0.476
      └── Some((6, 8)): 4/14 ≈ 0.286
    ├── Some((0, 7)): 121/226 ≈ 0.535
      ├── Some((7, 0)): 15/27 ≈ 0.556
      ├── Some((7, 1)): 13/25 ≈ 0.520
      ├── Some((7, 2)): 20/32 ≈ 0.625
      ├── Some((7, 3)): 7/18 ≈ 0.389
      ├── Some((7, 4)): 22/35 ≈ 0.629
      ├── Some((7, 5)): 5/15 ≈ 0.333
      ├── Some((7, 6)): 20/32 ≈ 0.625
      ├── Some((7, 7)): 9/20 ≈ 0.450
      └── Some((7, 8)): 10/21 ≈ 0.476
    └── Some((0, 8)): 168/296 ≈ 0.568
      ├── Some((8, 0)): 15/29 ≈ 0.517
      ├── Some((8, 1)): 12/25 ≈ 0.480
      ├── Some((8, 2)): 20/35 ≈ 0.571
      ├── Some((8, 3)): 23/38 ≈ 0.605
      ├── Some((8, 4)): 29/44 ≈ 0.659
      ├── Some((8, 5)): 10/23 ≈ 0.435
      ├── Some((8, 6)): 23/38 ≈ 0.605
      ├── Some((8, 7)): 26/41 ≈ 0.634
      └── Some((8, 8)): 9/22 ≈ 0.409
  ├── Some((3, 1)): 861/1637 ≈ 0.526
    ├── Some((1, 0)): 102/191 ≈ 0.534
      ├── Some((0, 0)): 14/25 ≈ 0.560
      ├── Some((0, 1)): 21/33 ≈ 0.636
      ├── Some((0, 2)): 22/34 ≈ 0.647
      ├── Some((0, 4)): 11/22 ≈ 0.500
      ├── Some((0, 5)): 14/25 ≈ 0.560
      ├── Some((0, 6)): 4/14 ≈ 0.286
      ├── Some((0, 7)): 5/15 ≈ 0.333
      └── Some((0, 8)): 11/22 ≈ 0.500
    ├── Some((1, 1)): 106/197 ≈ 0.538
      ├── Some((1, 0)): 24/36 ≈ 0.667
      ├── Some((1, 2)): 9/20 ≈ 0.450
      ├── Some((1, 3)): 13/25 ≈ 0.520
      ├── Some((1, 4)): 11/22 ≈ 0.500
      ├── Some((1, 5)): 9/20 ≈ 0.450
      ├── Some((1, 6)): 18/30 ≈ 0.600
      ├── Some((1, 7)): 12/23 ≈ 0.522
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((1, 2)): 83/163 ≈ 0.509
      ├── Some((2, 0)): 8/17 ≈ 0.471
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 11/20 ≈ 0.550
      ├── Some((2, 3)): 12/21 ≈ 0.571
      ├── Some((2, 4)): 2/10 ≈ 0.200
      ├── Some((2, 5)): 19/28 ≈ 0.679
      ├── Some((2, 6)): 8/17 ≈ 0.471
      ├── Some((2, 7)): 5/13 ≈ 0.385
      └── Some((2, 8)): 10/19 ≈ 0.526
    ├── Some((1, 3)): 105/196 ≈ 0.536
      ├── Some((3, 0)): 12/23 ≈ 0.522
      ├── Some((3, 2)): 16/28 ≈ 0.571
      ├── Some((3, 3)): 19/31 ≈ 0.613
      ├── Some((3, 4)): 17/29 ≈ 0.586
      ├── Some((3, 5)): 13/24 ≈ 0.542
      ├── Some((3, 6)): 10/21 ≈ 0.476
      ├── Some((3, 7)): 15/27 ≈ 0.556
      └── Some((3, 8)): 3/12 ≈ 0.250
    ├── Some((1, 4)): 69/142 ≈ 0.486
      ├── Some((4, 0)): 6/14 ≈ 0.429
      ├── Some((4, 1)): 7/15 ≈ 0.467
      ├── Some((4, 2)): 0/7 ≈ 0.000
      ├── Some((4, 3)): 6/14 ≈ 0.429
      ├── Some((4, 4)): 5/13 ≈ 0.385
      ├── Some((4, 5)): 6/14 ≈ 0.429
      ├── Some((4, 6)): 12/20 ≈ 0.600
      ├── Some((4, 7)): 18/27 ≈ 0.667
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((1, 5)): 75/151 ≈ 0.497
      ├── Some((5, 0)): 4/12 ≈ 0.333
      ├── Some((5, 1)): 7/16 ≈ 0.438
      ├── Some((5, 2)): 13/22 ≈ 0.591
      ├── Some((5, 3)): 12/21 ≈ 0.571
      ├── Some((5, 4)): 17/26 ≈ 0.654
      ├── Some((5, 5)): 1/8 ≈ 0.125
      ├── Some((5, 6)): 3/11 ≈ 0.273
      ├── Some((5, 7)): 11/20 ≈ 0.550
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((1, 6)): 109/202 ≈ 0.540
      ├── Some((6, 0)): 21/32 ≈ 0.656
      ├── Some((6, 1)): 19/30 ≈ 0.633
      ├── Some((6, 2)): 9/19 ≈ 0.474
      ├── Some((6, 3)): 16/26 ≈ 0.615
      ├── Some((6, 4)): 7/17 ≈ 0.412
      ├── Some((6, 5)): 9/19 ≈ 0.474
      ├── Some((6, 6)): 10/20 ≈ 0.500
      ├── Some((6, 7)): 8/18 ≈ 0.444
      └── Some((6, 8)): 10/20 ≈ 0.500
    ├── Some((1, 7)): 111/205 ≈ 0.541
      ├── Some((7, 0)): 10/20 ≈ 0.500
      ├── Some((7, 1)): 16/27 ≈ 0.593
      ├── Some((7, 2)): 8/18 ≈ 0.444
      ├── Some((7, 3)): 20/31 ≈ 0.645
      ├── Some((7, 4)): 9/19 ≈ 0.474
      ├── Some((7, 5)): 9/19 ≈ 0.474
      ├── Some((7, 6)): 10/20 ≈ 0.500
      ├── Some((7, 7)): 20/31 ≈ 0.645
      └── Some((7, 8)): 9/19 ≈ 0.474
    └── Some((1, 8)): 100/189 ≈ 0.529
      ├── Some((8, 0)): 15/25 ≈ 0.600
      ├── Some((8, 1)): 13/23 ≈ 0.565
      ├── Some((8, 2)): 16/27 ≈ 0.593
      ├── Some((8, 3)): 3/12 ≈ 0.250
      ├── Some((8, 4)): 6/15 ≈ 0.400
      ├── Some((8, 5)): 15/25 ≈ 0.600
      ├── Some((8, 6)): 23/34 ≈ 0.676
      ├── Some((8, 7)): 1/9 ≈ 0.111
      └── Some((8, 8)): 8/18 ≈ 0.444
  ├── Some((3, 2)): 597/1180 ≈ 0.506
    ├── Some((2, 0)): 31/78 ≈ 0.397
      ├── Some((0, 0)): 1/6 ≈ 0.167
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 6/12 ≈ 0.500
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((2, 1)): 91/167 ≈ 0.545
      ├── Some((1, 0)): 6/14 ≈ 0.429
      ├── Some((1, 1)): 7/15 ≈ 0.467
      ├── Some((1, 2)): 6/14 ≈ 0.429
      ├── Some((1, 3)): 13/21 ≈ 0.619
      ├── Some((1, 4)): 13/22 ≈ 0.591
      ├── Some((1, 5)): 14/23 ≈ 0.609
      ├── Some((1, 6)): 9/17 ≈ 0.529
      ├── Some((1, 7)): 8/16 ≈ 0.500
      └── Some((1, 8)): 15/24 ≈ 0.625
    ├── Some((2, 2)): 96/175 ≈ 0.549
      ├── Some((2, 0)): 15/25 ≈ 0.600
      ├── Some((2, 1)): 18/28 ≈ 0.643
      ├── Some((2, 3)): 8/18 ≈ 0.444
      ├── Some((2, 4)): 10/20 ≈ 0.500
      ├── Some((2, 5)): 6/15 ≈ 0.400
      ├── Some((2, 6)): 14/24 ≈ 0.583
      ├── Some((2, 7)): 5/14 ≈ 0.357
      └── Some((2, 8)): 19/30 ≈ 0.633
    ├── Some((2, 3)): 75/144 ≈ 0.521
      ├── Some((3, 0)): 8/16 ≈ 0.500
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 3)): 9/18 ≈ 0.500
      ├── Some((3, 4)): 12/21 ≈ 0.571
      ├── Some((3, 5)): 3/11 ≈ 0.273
      ├── Some((3, 6)): 12/21 ≈ 0.571
      ├── Some((3, 7)): 8/17 ≈ 0.471
      └── Some((3, 8)): 17/26 ≈ 0.654
    ├── Some((2, 4)): 85/159 ≈ 0.535
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 10/18 ≈ 0.556
      ├── Some((4, 2)): 8/16 ≈ 0.500
      ├── Some((4, 3)): 6/14 ≈ 0.429
      ├── Some((4, 4)): 16/25 ≈ 0.640
      ├── Some((4, 5)): 15/24 ≈ 0.625
      ├── Some((4, 6)): 6/14 ≈ 0.429
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((2, 5)): 32/79 ≈ 0.405
      ├── Some((5, 0)): 5/10 ≈ 0.500
      ├── Some((5, 1)): 1/6 ≈ 0.167
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 1/6 ≈ 0.167
      ├── Some((5, 4)): 0/5 ≈ 0.000
      ├── Some((5, 5)): 9/14 ≈ 0.643
      ├── Some((5, 6)): 0/5 ≈ 0.000
      ├── Some((5, 7)): 9/14 ≈ 0.643
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((2, 6)): 76/146 ≈ 0.521
      ├── Some((6, 0)): 12/20 ≈ 0.600
      ├── Some((6, 1)): 4/11 ≈ 0.364
      ├── Some((6, 2)): 13/21 ≈ 0.619
      ├── Some((6, 3)): 11/19 ≈ 0.579
      ├── Some((6, 4)): 12/20 ≈ 0.600
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 9/17 ≈ 0.529
      ├── Some((6, 7)): 6/14 ≈ 0.429
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((2, 7)): 56/116 ≈ 0.483
      ├── Some((7, 0)): 10/17 ≈ 0.588
      ├── Some((7, 1)): 1/7 ≈ 0.143
      ├── Some((7, 2)): 7/14 ≈ 0.500
      ├── Some((7, 3)): 3/9 ≈ 0.333
      ├── Some((7, 4)): 3/9 ≈ 0.333
      ├── Some((7, 5)): 8/15 ≈ 0.533
      ├── Some((7, 6)): 6/13 ≈ 0.462
      ├── Some((7, 7)): 7/14 ≈ 0.500
      └── Some((7, 8)): 11/17 ≈ 0.647
    └── Some((2, 8)): 55/115 ≈ 0.478
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 11/18 ≈ 0.611
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 3/9 ≈ 0.333
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 3/9 ≈ 0.333
      ├── Some((8, 7)): 10/17 ≈ 0.588
      └── Some((8, 8)): 7/14 ≈ 0.500
  ├── Some((3, 3)): 573/1138 ≈ 0.504
    ├── Some((3, 0)): 133/232 ≈ 0.573
      ├── Some((0, 0)): 5/16 ≈ 0.312
      ├── Some((0, 1)): 16/28 ≈ 0.571
      ├── Some((0, 2)): 16/28 ≈ 0.571
      ├── Some((0, 4)): 11/23 ≈ 0.478
      ├── Some((0, 5)): 17/30 ≈ 0.567
      ├── Some((0, 6)): 22/35 ≈ 0.629
      ├── Some((0, 7)): 29/42 ≈ 0.690
      └── Some((0, 8)): 16/29 ≈ 0.552
    ├── Some((3, 1)): 84/162 ≈ 0.519
      ├── Some((1, 0)): 15/24 ≈ 0.625
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 2)): 8/17 ≈ 0.471
      ├── Some((1, 3)): 8/17 ≈ 0.471
      ├── Some((1, 4)): 16/25 ≈ 0.640
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 4/12 ≈ 0.333
      ├── Some((1, 7)): 3/11 ≈ 0.273
      └── Some((1, 8)): 6/14 ≈ 0.429
    ├── Some((3, 2)): 103/189 ≈ 0.545
      ├── Some((2, 0)): 15/25 ≈ 0.600
      ├── Some((2, 1)): 16/26 ≈ 0.615
      ├── Some((2, 2)): 9/18 ≈ 0.500
      ├── Some((2, 3)): 7/16 ≈ 0.438
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 12/21 ≈ 0.571
      ├── Some((2, 6)): 13/23 ≈ 0.565
      ├── Some((2, 7)): 5/14 ≈ 0.357
      └── Some((2, 8)): 20/30 ≈ 0.667
    ├── Some((3, 4)): 53/115 ≈ 0.461
      ├── Some((4, 0)): 3/10 ≈ 0.300
      ├── Some((4, 1)): 1/7 ≈ 0.143
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 12/19 ≈ 0.632
      ├── Some((4, 4)): 8/15 ≈ 0.533
      ├── Some((4, 5)): 8/15 ≈ 0.533
      ├── Some((4, 6)): 5/12 ≈ 0.417
      ├── Some((4, 7)): 9/16 ≈ 0.562
      └── Some((4, 8)): 2/8 ≈ 0.250
    ├── Some((3, 5)): 49/109 ≈ 0.450
      ├── Some((5, 0)): 1/7 ≈ 0.143
      ├── Some((5, 1)): 1/7 ≈ 0.143
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 3)): 2/8 ≈ 0.250
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 14/20 ≈ 0.700
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((3, 6)): 55/118 ≈ 0.466
      ├── Some((6, 0)): 2/9 ≈ 0.222
      ├── Some((6, 1)): 5/12 ≈ 0.417
      ├── Some((6, 2)): 3/10 ≈ 0.300
      ├── Some((6, 3)): 6/13 ≈ 0.462
      ├── Some((6, 4)): 12/19 ≈ 0.632
      ├── Some((6, 5)): 5/12 ≈ 0.417
      ├── Some((6, 6)): 11/18 ≈ 0.611
      ├── Some((6, 7)): 4/11 ≈ 0.364
      └── Some((6, 8)): 6/13 ≈ 0.462
    ├── Some((3, 7)): 52/113 ≈ 0.460
      ├── Some((7, 0)): 4/10 ≈ 0.400
      ├── Some((7, 1)): 1/7 ≈ 0.143
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 5/12 ≈ 0.417
      ├── Some((7, 4)): 13/20 ≈ 0.650
      ├── Some((7, 5)): 8/15 ≈ 0.533
      ├── Some((7, 6)): 9/16 ≈ 0.562
      ├── Some((7, 7)): 5/12 ≈ 0.417
      └── Some((7, 8)): 4/11 ≈ 0.364
    └── Some((3, 8)): 43/99 ≈ 0.434
      ├── Some((8, 0)): 3/9 ≈ 0.333
      ├── Some((8, 1)): 2/8 ≈ 0.250
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 10/16 ≈ 0.625
      ├── Some((8, 4)): 6/12 ≈ 0.500
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((3, 4)): 996/1867 ≈ 0.533
    ├── Some((4, 0)): 109/205 ≈ 0.532
      ├── Some((0, 0)): 21/34 ≈ 0.618
      ├── Some((0, 1)): 10/21 ≈ 0.476
      ├── Some((0, 2)): 11/23 ≈ 0.478
      ├── Some((0, 4)): 14/26 ≈ 0.538
      ├── Some((0, 5)): 9/20 ≈ 0.450
      ├── Some((0, 6)): 17/29 ≈ 0.586
      ├── Some((0, 7)): 17/29 ≈ 0.586
      └── Some((0, 8)): 10/22 ≈ 0.455
    ├── Some((4, 1)): 129/235 ≈ 0.549
      ├── Some((1, 0)): 9/20 ≈ 0.450
      ├── Some((1, 1)): 13/25 ≈ 0.520
      ├── Some((1, 2)): 20/33 ≈ 0.606
      ├── Some((1, 3)): 7/18 ≈ 0.389
      ├── Some((1, 4)): 1/10 ≈ 0.100
      ├── Some((1, 5)): 27/40 ≈ 0.675
      ├── Some((1, 6)): 30/43 ≈ 0.698
      ├── Some((1, 7)): 17/29 ≈ 0.586
      └── Some((1, 8)): 5/16 ≈ 0.312
    ├── Some((4, 2)): 130/236 ≈ 0.551
      ├── Some((2, 0)): 4/14 ≈ 0.286
      ├── Some((2, 1)): 11/23 ≈ 0.478
      ├── Some((2, 2)): 10/21 ≈ 0.476
      ├── Some((2, 3)): 23/36 ≈ 0.639
      ├── Some((2, 4)): 15/27 ≈ 0.556
      ├── Some((2, 5)): 10/21 ≈ 0.476
      ├── Some((2, 6)): 17/29 ≈ 0.586
      ├── Some((2, 7)): 15/27 ≈ 0.556
      └── Some((2, 8)): 24/37 ≈ 0.649
    ├── Some((4, 3)): 71/148 ≈ 0.480
      ├── Some((3, 0)): 8/18 ≈ 0.444
      ├── Some((3, 1)): 2/10 ≈ 0.200
      ├── Some((3, 2)): 6/15 ≈ 0.400
      ├── Some((3, 3)): 7/16 ≈ 0.438
      ├── Some((3, 5)): 4/13 ≈ 0.308
      ├── Some((3, 6)): 12/22 ≈ 0.545
      ├── Some((3, 7)): 13/23 ≈ 0.565
      └── Some((3, 8)): 19/30 ≈ 0.633
    ├── Some((4, 4)): 75/154 ≈ 0.487
      ├── Some((4, 0)): 9/19 ≈ 0.474
      ├── Some((4, 1)): 12/22 ≈ 0.545
      ├── Some((4, 2)): 7/16 ≈ 0.438
      ├── Some((4, 3)): 10/20 ≈ 0.500
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 9/19 ≈ 0.474
      ├── Some((4, 7)): 7/16 ≈ 0.438
      └── Some((4, 8)): 12/22 ≈ 0.545
    ├── Some((4, 5)): 102/195 ≈ 0.523
      ├── Some((5, 0)): 10/20 ≈ 0.500
      ├── Some((5, 1)): 16/27 ≈ 0.593
      ├── Some((5, 2)): 5/15 ≈ 0.333
      ├── Some((5, 3)): 7/17 ≈ 0.412
      ├── Some((5, 4)): 14/25 ≈ 0.560
      ├── Some((5, 5)): 11/21 ≈ 0.524
      ├── Some((5, 6)): 20/31 ≈ 0.645
      ├── Some((5, 7)): 11/21 ≈ 0.524
      └── Some((5, 8)): 7/17 ≈ 0.412
    ├── Some((4, 6)): 128/233 ≈ 0.549
      ├── Some((6, 0)): 18/30 ≈ 0.600
      ├── Some((6, 1)): 16/28 ≈ 0.571
      ├── Some((6, 2)): 17/29 ≈ 0.586
      ├── Some((6, 3)): 15/27 ≈ 0.556
      ├── Some((6, 4)): 9/20 ≈ 0.450
      ├── Some((6, 5)): 6/17 ≈ 0.353
      ├── Some((6, 6)): 19/31 ≈ 0.613
      ├── Some((6, 7)): 17/29 ≈ 0.586
      └── Some((6, 8)): 10/21 ≈ 0.476
    ├── Some((4, 7)): 126/231 ≈ 0.545
      ├── Some((7, 0)): 12/23 ≈ 0.522
      ├── Some((7, 1)): 18/30 ≈ 0.600
      ├── Some((7, 2)): 4/14 ≈ 0.286
      ├── Some((7, 3)): 14/26 ≈ 0.538
      ├── Some((7, 4)): 12/24 ≈ 0.500
      ├── Some((7, 5)): 20/32 ≈ 0.625
      ├── Some((7, 6)): 8/19 ≈ 0.421
      ├── Some((7, 7)): 15/27 ≈ 0.556
      └── Some((7, 8)): 23/35 ≈ 0.657
    └── Some((4, 8)): 125/229 ≈ 0.546
      ├── Some((8, 0)): 15/27 ≈ 0.556
      ├── Some((8, 1)): 9/20 ≈ 0.450
      ├── Some((8, 2)): 19/31 ≈ 0.613
      ├── Some((8, 3)): 4/14 ≈ 0.286
      ├── Some((8, 4)): 24/36 ≈ 0.667
      ├── Some((8, 5)): 17/29 ≈ 0.586
      ├── Some((8, 6)): 9/20 ≈ 0.450
      ├── Some((8, 7)): 18/30 ≈ 0.600
      └── Some((8, 8)): 10/21 ≈ 0.476
  ├── Some((3, 5)): 377/792 ≈ 0.476
    ├── Some((5, 0)): 34/76 ≈ 0.447
      ├── Some((0, 0)): 3/8 ≈ 0.375
      ├── Some((0, 1)): 3/8 ≈ 0.375
      ├── Some((0, 2)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 7/12 ≈ 0.583
      ├── Some((0, 6)): 10/15 ≈ 0.667
      ├── Some((0, 7)): 1/6 ≈ 0.167
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((5, 1)): 28/67 ≈ 0.418
      ├── Some((1, 0)): 3/7 ≈ 0.429
      ├── Some((1, 1)): 1/5 ≈ 0.200
      ├── Some((1, 2)): 4/8 ≈ 0.500
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 2/6 ≈ 0.333
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 6/10 ≈ 0.600
      └── Some((1, 8)): 4/8 ≈ 0.500
    ├── Some((5, 2)): 43/90 ≈ 0.478
      ├── Some((2, 0)): 6/11 ≈ 0.545
      ├── Some((2, 1)): 8/13 ≈ 0.615
      ├── Some((2, 2)): 8/13 ≈ 0.615
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 1/6 ≈ 0.167
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 6/12 ≈ 0.500
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((5, 3)): 47/96 ≈ 0.490
      ├── Some((3, 0)): 1/7 ≈ 0.143
      ├── Some((3, 1)): 6/12 ≈ 0.500
      ├── Some((3, 2)): 1/7 ≈ 0.143
      ├── Some((3, 3)): 10/16 ≈ 0.625
      ├── Some((3, 4)): 8/14 ≈ 0.571
      ├── Some((3, 6)): 2/8 ≈ 0.250
      ├── Some((3, 7)): 7/13 ≈ 0.538
      └── Some((3, 8)): 12/18 ≈ 0.667
    ├── Some((5, 4)): 55/107 ≈ 0.514
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 10/16 ≈ 0.625
      ├── Some((4, 2)): 10/16 ≈ 0.625
      ├── Some((4, 3)): 7/13 ≈ 0.538
      ├── Some((4, 4)): 1/6 ≈ 0.167
      ├── Some((4, 5)): 1/6 ≈ 0.167
      ├── Some((4, 6)): 9/15 ≈ 0.600
      ├── Some((4, 7)): 8/14 ≈ 0.571
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((5, 5)): 49/98 ≈ 0.500
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 2/8 ≈ 0.250
      ├── Some((5, 2)): 8/14 ≈ 0.571
      ├── Some((5, 3)): 2/8 ≈ 0.250
      ├── Some((5, 4)): 10/16 ≈ 0.625
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 6/12 ≈ 0.500
      └── Some((5, 8)): 10/16 ≈ 0.625
    ├── Some((5, 6)): 46/94 ≈ 0.489
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 8/13 ≈ 0.615
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 13/18 ≈ 0.722
    ├── Some((5, 7)): 41/87 ≈ 0.471
      ├── Some((7, 0)): 2/7 ≈ 0.286
      ├── Some((7, 1)): 6/11 ≈ 0.545
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 3)): 5/10 ≈ 0.500
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 11/16 ≈ 0.688
      ├── Some((7, 6)): 6/11 ≈ 0.545
      ├── Some((7, 7)): 1/6 ≈ 0.167
      └── Some((7, 8)): 5/10 ≈ 0.500
    └── Some((5, 8)): 34/76 ≈ 0.447
      ├── Some((8, 0)): 0/4 ≈ 0.000
      ├── Some((8, 1)): 9/13 ≈ 0.692
      ├── Some((8, 2)): 1/6 ≈ 0.167
      ├── Some((8, 3)): 5/10 ≈ 0.500
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 3/8 ≈ 0.375
      └── Some((8, 8)): 6/10 ≈ 0.600
  ├── Some((3, 6)): 995/1865 ≈ 0.534
    ├── Some((6, 0)): 77/157 ≈ 0.490
      ├── Some((0, 0)): 14/24 ≈ 0.583
      ├── Some((0, 1)): 4/13 ≈ 0.308
      ├── Some((0, 2)): 11/21 ≈ 0.524
      ├── Some((0, 4)): 7/17 ≈ 0.412
      ├── Some((0, 5)): 7/17 ≈ 0.412
      ├── Some((0, 6)): 9/19 ≈ 0.474
      ├── Some((0, 7)): 6/15 ≈ 0.400
      └── Some((0, 8)): 19/30 ≈ 0.633
    ├── Some((6, 1)): 125/229 ≈ 0.546
      ├── Some((1, 0)): 21/33 ≈ 0.636
      ├── Some((1, 1)): 6/16 ≈ 0.375
      ├── Some((1, 2)): 12/24 ≈ 0.500
      ├── Some((1, 3)): 17/29 ≈ 0.586
      ├── Some((1, 4)): 29/42 ≈ 0.690
      ├── Some((1, 5)): 15/27 ≈ 0.556
      ├── Some((1, 6)): 9/20 ≈ 0.450
      ├── Some((1, 7)): 2/11 ≈ 0.182
      └── Some((1, 8)): 14/26 ≈ 0.538
    ├── Some((6, 2)): 148/262 ≈ 0.565
      ├── Some((2, 0)): 10/22 ≈ 0.455
      ├── Some((2, 1)): 31/45 ≈ 0.689
      ├── Some((2, 2)): 15/28 ≈ 0.536
      ├── Some((2, 3)): 6/17 ≈ 0.353
      ├── Some((2, 4)): 14/27 ≈ 0.519
      ├── Some((2, 5)): 11/23 ≈ 0.478
      ├── Some((2, 6)): 17/30 ≈ 0.567
      ├── Some((2, 7)): 33/47 ≈ 0.702
      └── Some((2, 8)): 10/22 ≈ 0.455
    ├── Some((6, 3)): 122/224 ≈ 0.545
      ├── Some((3, 0)): 21/34 ≈ 0.618
      ├── Some((3, 1)): 11/23 ≈ 0.478
      ├── Some((3, 2)): 19/32 ≈ 0.594
      ├── Some((3, 3)): 13/25 ≈ 0.520
      ├── Some((3, 4)): 19/32 ≈ 0.594
      ├── Some((3, 5)): 8/20 ≈ 0.400
      ├── Some((3, 7)): 18/31 ≈ 0.581
      └── Some((3, 8)): 13/26 ≈ 0.500
    ├── Some((6, 4)): 115/214 ≈ 0.537
      ├── Some((4, 0)): 8/19 ≈ 0.421
      ├── Some((4, 1)): 27/39 ≈ 0.692
      ├── Some((4, 2)): 15/27 ≈ 0.556
      ├── Some((4, 3)): 7/17 ≈ 0.412
      ├── Some((4, 4)): 12/23 ≈ 0.522
      ├── Some((4, 5)): 3/12 ≈ 0.250
      ├── Some((4, 6)): 13/24 ≈ 0.542
      ├── Some((4, 7)): 18/30 ≈ 0.600
      └── Some((4, 8)): 11/22 ≈ 0.500
    ├── Some((6, 5)): 107/202 ≈ 0.530
      ├── Some((5, 0)): 12/23 ≈ 0.522
      ├── Some((5, 1)): 7/17 ≈ 0.412
      ├── Some((5, 2)): 9/19 ≈ 0.474
      ├── Some((5, 3)): 16/27 ≈ 0.593
      ├── Some((5, 4)): 14/25 ≈ 0.560
      ├── Some((5, 5)): 20/31 ≈ 0.645
      ├── Some((5, 6)): 15/26 ≈ 0.577
      ├── Some((5, 7)): 3/12 ≈ 0.250
      └── Some((5, 8)): 10/21 ≈ 0.476
    ├── Some((6, 6)): 121/223 ≈ 0.543
      ├── Some((6, 0)): 27/41 ≈ 0.659
      ├── Some((6, 1)): 10/22 ≈ 0.455
      ├── Some((6, 2)): 10/22 ≈ 0.455
      ├── Some((6, 3)): 12/24 ≈ 0.500
      ├── Some((6, 4)): 21/35 ≈ 0.600
      ├── Some((6, 5)): 5/16 ≈ 0.312
      ├── Some((6, 7)): 22/36 ≈ 0.611
      └── Some((6, 8)): 13/26 ≈ 0.500
    ├── Some((6, 7)): 95/185 ≈ 0.514
      ├── Some((7, 0)): 12/22 ≈ 0.545
      ├── Some((7, 1)): 15/26 ≈ 0.577
      ├── Some((7, 2)): 11/21 ≈ 0.524
      ├── Some((7, 3)): 12/22 ≈ 0.545
      ├── Some((7, 4)): 12/22 ≈ 0.545
      ├── Some((7, 5)): 7/17 ≈ 0.412
      ├── Some((7, 6)): 10/20 ≈ 0.500
      ├── Some((7, 7)): 5/14 ≈ 0.357
      └── Some((7, 8)): 10/20 ≈ 0.500
    └── Some((6, 8)): 84/168 ≈ 0.500
      ├── Some((8, 0)): 8/17 ≈ 0.471
      ├── Some((8, 1)): 12/22 ≈ 0.545
      ├── Some((8, 2)): 6/15 ≈ 0.400
      ├── Some((8, 3)): 8/17 ≈ 0.471
      ├── Some((8, 4)): 13/23 ≈ 0.565
      ├── Some((8, 5)): 9/18 ≈ 0.500
      ├── Some((8, 6)): 8/17 ≈ 0.471
      ├── Some((8, 7)): 9/18 ≈ 0.500
      └── Some((8, 8)): 11/20 ≈ 0.550
  ├── Some((3, 7)): 803/1537 ≈ 0.522
    ├── Some((7, 0)): 59/126 ≈ 0.468
      ├── Some((0, 0)): 9/17 ≈ 0.529
      ├── Some((0, 1)): 11/20 ≈ 0.550
      ├── Some((0, 2)): 12/21 ≈ 0.571
      ├── Some((0, 4)): 7/15 ≈ 0.467
      ├── Some((0, 5)): 5/13 ≈ 0.385
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 7/15 ≈ 0.467
      └── Some((0, 8)): 4/12 ≈ 0.333
    ├── Some((7, 1)): 109/200 ≈ 0.545
      ├── Some((1, 0)): 7/17 ≈ 0.412
      ├── Some((1, 1)): 13/23 ≈ 0.565
      ├── Some((1, 2)): 17/28 ≈ 0.607
      ├── Some((1, 3)): 8/18 ≈ 0.444
      ├── Some((1, 4)): 15/25 ≈ 0.600
      ├── Some((1, 5)): 20/31 ≈ 0.645
      ├── Some((1, 6)): 15/25 ≈ 0.600
      ├── Some((1, 7)): 11/21 ≈ 0.524
      └── Some((1, 8)): 2/11 ≈ 0.182
    ├── Some((7, 2)): 84/164 ≈ 0.512
      ├── Some((2, 0)): 9/18 ≈ 0.500
      ├── Some((2, 1)): 16/25 ≈ 0.640
      ├── Some((2, 2)): 8/17 ≈ 0.471
      ├── Some((2, 3)): 14/23 ≈ 0.609
      ├── Some((2, 4)): 10/19 ≈ 0.526
      ├── Some((2, 5)): 1/9 ≈ 0.111
      ├── Some((2, 6)): 10/19 ≈ 0.526
      ├── Some((2, 7)): 13/22 ≈ 0.591
      └── Some((2, 8)): 3/11 ≈ 0.273
    ├── Some((7, 3)): 125/223 ≈ 0.561
      ├── Some((3, 0)): 31/44 ≈ 0.705
      ├── Some((3, 1)): 8/19 ≈ 0.421
      ├── Some((3, 2)): 11/23 ≈ 0.478
      ├── Some((3, 3)): 23/36 ≈ 0.639
      ├── Some((3, 4)): 18/31 ≈ 0.581
      ├── Some((3, 5)): 12/24 ≈ 0.500
      ├── Some((3, 6)): 16/28 ≈ 0.571
      └── Some((3, 8)): 6/17 ≈ 0.353
    ├── Some((7, 4)): 99/186 ≈ 0.532
      ├── Some((4, 0)): 6/15 ≈ 0.400
      ├── Some((4, 1)): 16/26 ≈ 0.615
      ├── Some((4, 2)): 7/16 ≈ 0.438
      ├── Some((4, 3)): 21/31 ≈ 0.677
      ├── Some((4, 4)): 13/23 ≈ 0.565
      ├── Some((4, 5)): 11/21 ≈ 0.524
      ├── Some((4, 6)): 5/14 ≈ 0.357
      ├── Some((4, 7)): 17/27 ≈ 0.630
      └── Some((4, 8)): 3/12 ≈ 0.250
    ├── Some((7, 5)): 49/110 ≈ 0.445
      ├── Some((5, 0)): 10/17 ≈ 0.588
      ├── Some((5, 1)): 7/14 ≈ 0.500
      ├── Some((5, 2)): 2/8 ≈ 0.250
      ├── Some((5, 3)): 8/15 ≈ 0.533
      ├── Some((5, 4)): 9/16 ≈ 0.562
      ├── Some((5, 5)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 2/8 ≈ 0.250
      ├── Some((5, 7)): 1/7 ≈ 0.143
      └── Some((5, 8)): 3/10 ≈ 0.300
    ├── Some((7, 6)): 114/207 ≈ 0.551
      ├── Some((6, 0)): 8/18 ≈ 0.444
      ├── Some((6, 1)): 15/26 ≈ 0.577
      ├── Some((6, 2)): 10/20 ≈ 0.500
      ├── Some((6, 3)): 6/16 ≈ 0.375
      ├── Some((6, 4)): 12/22 ≈ 0.545
      ├── Some((6, 5)): 17/28 ≈ 0.607
      ├── Some((6, 6)): 12/22 ≈ 0.545
      ├── Some((6, 7)): 12/22 ≈ 0.545
      └── Some((6, 8)): 21/32 ≈ 0.656
    ├── Some((7, 7)): 82/161 ≈ 0.509
      ├── Some((7, 0)): 15/25 ≈ 0.600
      ├── Some((7, 1)): 16/27 ≈ 0.593
      ├── Some((7, 2)): 7/17 ≈ 0.412
      ├── Some((7, 3)): 19/30 ≈ 0.633
      ├── Some((7, 4)): 0/7 ≈ 0.000
      ├── Some((7, 5)): 9/19 ≈ 0.474
      ├── Some((7, 6)): 10/20 ≈ 0.500
      └── Some((7, 8)): 6/15 ≈ 0.400
    └── Some((7, 8)): 81/159 ≈ 0.509
      ├── Some((8, 0)): 12/21 ≈ 0.571
      ├── Some((8, 1)): 4/12 ≈ 0.333
      ├── Some((8, 2)): 10/19 ≈ 0.526
      ├── Some((8, 3)): 9/18 ≈ 0.500
      ├── Some((8, 4)): 6/14 ≈ 0.429
      ├── Some((8, 5)): 3/11 ≈ 0.273
      ├── Some((8, 6)): 23/32 ≈ 0.719
      ├── Some((8, 7)): 7/15 ≈ 0.467
      └── Some((8, 8)): 7/16 ≈ 0.438
  └── Some((3, 8)): 911/1722 ≈ 0.529
    ├── Some((8, 0)): 130/234 ≈ 0.556
      ├── Some((0, 0)): 22/36 ≈ 0.611
      ├── Some((0, 1)): 16/29 ≈ 0.552
      ├── Some((0, 2)): 10/22 ≈ 0.455
      ├── Some((0, 4)): 19/32 ≈ 0.594
      ├── Some((0, 5)): 6/17 ≈ 0.353
      ├── Some((0, 6)): 21/35 ≈ 0.600
      ├── Some((0, 7)): 11/23 ≈ 0.478
      └── Some((0, 8)): 25/39 ≈ 0.641
    ├── Some((8, 1)): 40/98 ≈ 0.408
      ├── Some((1, 0)): 9/16 ≈ 0.562
      ├── Some((1, 1)): 1/7 ≈ 0.143
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 6/13 ≈ 0.462
      ├── Some((1, 4)): 1/7 ≈ 0.143
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((8, 2)): 124/225 ≈ 0.551
      ├── Some((2, 0)): 7/18 ≈ 0.389
      ├── Some((2, 1)): 17/29 ≈ 0.586
      ├── Some((2, 2)): 11/22 ≈ 0.500
      ├── Some((2, 3)): 9/20 ≈ 0.450
      ├── Some((2, 4)): 13/24 ≈ 0.542
      ├── Some((2, 5)): 9/20 ≈ 0.450
      ├── Some((2, 6)): 30/42 ≈ 0.714
      ├── Some((2, 7)): 3/13 ≈ 0.231
      └── Some((2, 8)): 24/36 ≈ 0.667
    ├── Some((8, 3)): 63/134 ≈ 0.470
      ├── Some((3, 0)): 8/17 ≈ 0.471
      ├── Some((3, 1)): 8/17 ≈ 0.471
      ├── Some((3, 2)): 1/9 ≈ 0.111
      ├── Some((3, 3)): 4/13 ≈ 0.308
      ├── Some((3, 4)): 10/19 ≈ 0.526
      ├── Some((3, 5)): 6/15 ≈ 0.400
      ├── Some((3, 6)): 1/9 ≈ 0.111
      └── Some((3, 7)): 24/34 ≈ 0.706
    ├── Some((8, 4)): 87/171 ≈ 0.509
      ├── Some((4, 0)): 8/17 ≈ 0.471
      ├── Some((4, 1)): 14/24 ≈ 0.583
      ├── Some((4, 2)): 11/21 ≈ 0.524
      ├── Some((4, 3)): 4/13 ≈ 0.308
      ├── Some((4, 4)): 3/11 ≈ 0.273
      ├── Some((4, 5)): 17/27 ≈ 0.630
      ├── Some((4, 6)): 12/22 ≈ 0.545
      ├── Some((4, 7)): 7/16 ≈ 0.438
      └── Some((4, 8)): 10/19 ≈ 0.526
    ├── Some((8, 5)): 111/207 ≈ 0.536
      ├── Some((5, 0)): 15/26 ≈ 0.577
      ├── Some((5, 1)): 11/22 ≈ 0.500
      ├── Some((5, 2)): 10/20 ≈ 0.500
      ├── Some((5, 3)): 10/21 ≈ 0.476
      ├── Some((5, 4)): 6/16 ≈ 0.375
      ├── Some((5, 5)): 22/33 ≈ 0.667
      ├── Some((5, 6)): 12/23 ≈ 0.522
      ├── Some((5, 7)): 8/18 ≈ 0.444
      └── Some((5, 8)): 16/27 ≈ 0.593
    ├── Some((8, 6)): 129/233 ≈ 0.554
      ├── Some((6, 0)): 15/27 ≈ 0.556
      ├── Some((6, 1)): 6/16 ≈ 0.375
      ├── Some((6, 2)): 22/34 ≈ 0.647
      ├── Some((6, 3)): 18/30 ≈ 0.600
      ├── Some((6, 4)): 12/24 ≈ 0.500
      ├── Some((6, 5)): 6/16 ≈ 0.375
      ├── Some((6, 6)): 21/33 ≈ 0.636
      ├── Some((6, 7)): 10/21 ≈ 0.476
      └── Some((6, 8)): 19/31 ≈ 0.613
    ├── Some((8, 7)): 125/227 ≈ 0.551
      ├── Some((7, 0)): 25/37 ≈ 0.676
      ├── Some((7, 1)): 17/29 ≈ 0.586
      ├── Some((7, 2)): 12/23 ≈ 0.522
      ├── Some((7, 3)): 15/27 ≈ 0.556
      ├── Some((7, 4)): 11/22 ≈ 0.500
      ├── Some((7, 5)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 21/33 ≈ 0.636
      ├── Some((7, 7)): 8/19 ≈ 0.421
      └── Some((7, 8)): 5/15 ≈ 0.333
    └── Some((8, 8)): 101/192 ≈ 0.526
      ├── Some((8, 0)): 2/11 ≈ 0.182
      ├── Some((8, 1)): 17/29 ≈ 0.586
      ├── Some((8, 2)): 17/29 ≈ 0.586
      ├── Some((8, 3)): 6/17 ≈ 0.353
      ├── Some((8, 4)): 6/17 ≈ 0.353
      ├── Some((8, 5)): 25/38 ≈ 0.658
      ├── Some((8, 6)): 11/22 ≈ 0.500
      └── Some((8, 7)): 16/28 ≈ 0.571
├── Some((0, 4)): 11223/21101 ≈ 0.532
  ├── Some((4, 0)): 1513/2804 ≈ 0.540
    ├── Some((0, 0)): 228/410 ≈ 0.556
      ├── Some((0, 1)): 31/57 ≈ 0.544
      ├── Some((0, 2)): 44/73 ≈ 0.603
      ├── Some((0, 3)): 46/75 ≈ 0.613
      ├── Some((0, 5)): 37/64 ≈ 0.578
      ├── Some((0, 6)): 29/54 ≈ 0.537
      ├── Some((0, 7)): 26/51 ≈ 0.510
      └── Some((0, 8)): 14/35 ≈ 0.400
    ├── Some((0, 1)): 163/311 ≈ 0.524
      ├── Some((1, 0)): 23/40 ≈ 0.575
      ├── Some((1, 1)): 9/23 ≈ 0.391
      ├── Some((1, 2)): 18/35 ≈ 0.514
      ├── Some((1, 3)): 22/39 ≈ 0.564
      ├── Some((1, 4)): 11/26 ≈ 0.423
      ├── Some((1, 5)): 16/32 ≈ 0.500
      ├── Some((1, 6)): 26/44 ≈ 0.591
      ├── Some((1, 7)): 24/42 ≈ 0.571
      └── Some((1, 8)): 13/29 ≈ 0.448
    ├── Some((0, 2)): 262/462 ≈ 0.567
      ├── Some((2, 0)): 47/73 ≈ 0.644
      ├── Some((2, 1)): 39/63 ≈ 0.619
      ├── Some((2, 2)): 32/55 ≈ 0.582
      ├── Some((2, 3)): 28/50 ≈ 0.560
      ├── Some((2, 4)): 22/43 ≈ 0.512
      ├── Some((2, 5)): 30/53 ≈ 0.566
      ├── Some((2, 6)): 34/57 ≈ 0.596
      ├── Some((2, 7)): 12/30 ≈ 0.400
      └── Some((2, 8)): 17/37 ≈ 0.459
    ├── Some((0, 3)): 196/362 ≈ 0.541
      ├── Some((3, 0)): 17/34 ≈ 0.500
      ├── Some((3, 1)): 29/49 ≈ 0.592
      ├── Some((3, 2)): 33/53 ≈ 0.623
      ├── Some((3, 3)): 27/46 ≈ 0.587
      ├── Some((3, 4)): 10/26 ≈ 0.385
      ├── Some((3, 5)): 28/48 ≈ 0.583
      ├── Some((3, 6)): 22/41 ≈ 0.537
      ├── Some((3, 7)): 14/31 ≈ 0.452
      └── Some((3, 8)): 16/33 ≈ 0.485
    ├── Some((0, 5)): 133/264 ≈ 0.504
      ├── Some((5, 0)): 7/20 ≈ 0.350
      ├── Some((5, 1)): 27/44 ≈ 0.614
      ├── Some((5, 2)): 7/20 ≈ 0.350
      ├── Some((5, 3)): 11/25 ≈ 0.440
      ├── Some((5, 4)): 24/40 ≈ 0.600
      ├── Some((5, 5)): 12/26 ≈ 0.462
      ├── Some((5, 6)): 23/39 ≈ 0.590
      ├── Some((5, 7)): 7/20 ≈ 0.350
      └── Some((5, 8)): 14/29 ≈ 0.483
    ├── Some((0, 6)): 230/413 ≈ 0.557
      ├── Some((6, 0)): 28/49 ≈ 0.571
      ├── Some((6, 1)): 27/48 ≈ 0.562
      ├── Some((6, 2)): 31/52 ≈ 0.596
      ├── Some((6, 3)): 26/47 ≈ 0.553
      ├── Some((6, 4)): 24/44 ≈ 0.545
      ├── Some((6, 5)): 18/37 ≈ 0.486
      ├── Some((6, 6)): 17/35 ≈ 0.486
      ├── Some((6, 7)): 35/57 ≈ 0.614
      └── Some((6, 8)): 23/43 ≈ 0.535
    ├── Some((0, 7)): 177/333 ≈ 0.532
      ├── Some((7, 0)): 44/65 ≈ 0.677
      ├── Some((7, 1)): 31/50 ≈ 0.620
      ├── Some((7, 2)): 19/36 ≈ 0.528
      ├── Some((7, 3)): 11/26 ≈ 0.423
      ├── Some((7, 4)): 17/34 ≈ 0.500
      ├── Some((7, 5)): 11/27 ≈ 0.407
      ├── Some((7, 6)): 15/32 ≈ 0.469
      ├── Some((7, 7)): 9/24 ≈ 0.375
      └── Some((7, 8)): 20/38 ≈ 0.526
    └── Some((0, 8)): 123/248 ≈ 0.496
      ├── Some((8, 0)): 26/42 ≈ 0.619
      ├── Some((8, 1)): 15/29 ≈ 0.517
      ├── Some((8, 2)): 11/24 ≈ 0.458
      ├── Some((8, 3)): 12/26 ≈ 0.462
      ├── Some((8, 4)): 8/21 ≈ 0.381
      ├── Some((8, 5)): 10/23 ≈ 0.435
      ├── Some((8, 6)): 8/21 ≈ 0.381
      ├── Some((8, 7)): 15/29 ≈ 0.517
      └── Some((8, 8)): 17/32 ≈ 0.531
  ├── Some((4, 1)): 1241/2337 ≈ 0.531
    ├── Some((1, 0)): 110/217 ≈ 0.507
      ├── Some((0, 0)): 14/27 ≈ 0.519
      ├── Some((0, 1)): 16/30 ≈ 0.533
      ├── Some((0, 2)): 11/24 ≈ 0.458
      ├── Some((0, 3)): 17/31 ≈ 0.548
      ├── Some((0, 5)): 10/23 ≈ 0.435
      ├── Some((0, 6)): 12/25 ≈ 0.480
      ├── Some((0, 7)): 22/36 ≈ 0.611
      └── Some((0, 8)): 8/20 ≈ 0.400
    ├── Some((1, 1)): 185/330 ≈ 0.561
      ├── Some((1, 0)): 27/46 ≈ 0.587
      ├── Some((1, 2)): 22/40 ≈ 0.550
      ├── Some((1, 3)): 14/30 ≈ 0.467
      ├── Some((1, 4)): 16/33 ≈ 0.485
      ├── Some((1, 5)): 28/47 ≈ 0.596
      ├── Some((1, 6)): 30/50 ≈ 0.600
      ├── Some((1, 7)): 18/35 ≈ 0.514
      └── Some((1, 8)): 29/48 ≈ 0.604
    ├── Some((1, 2)): 132/251 ≈ 0.526
      ├── Some((2, 0)): 5/16 ≈ 0.312
      ├── Some((2, 1)): 27/42 ≈ 0.643
      ├── Some((2, 2)): 7/19 ≈ 0.368
      ├── Some((2, 3)): 22/36 ≈ 0.611
      ├── Some((2, 4)): 23/38 ≈ 0.605
      ├── Some((2, 5)): 11/24 ≈ 0.458
      ├── Some((2, 6)): 11/24 ≈ 0.458
      ├── Some((2, 7)): 9/21 ≈ 0.429
      └── Some((2, 8)): 16/30 ≈ 0.533
    ├── Some((1, 3)): 182/326 ≈ 0.558
      ├── Some((3, 0)): 16/31 ≈ 0.516
      ├── Some((3, 1)): 24/41 ≈ 0.585
      ├── Some((3, 2)): 11/25 ≈ 0.440
      ├── Some((3, 3)): 24/41 ≈ 0.585
      ├── Some((3, 4)): 36/54 ≈ 0.667
      ├── Some((3, 5)): 17/33 ≈ 0.515
      ├── Some((3, 6)): 13/28 ≈ 0.464
      ├── Some((3, 7)): 10/24 ≈ 0.417
      └── Some((3, 8)): 30/48 ≈ 0.625
    ├── Some((1, 4)): 147/274 ≈ 0.536
      ├── Some((4, 0)): 26/43 ≈ 0.605
      ├── Some((4, 2)): 17/33 ≈ 0.515
      ├── Some((4, 3)): 27/44 ≈ 0.614
      ├── Some((4, 4)): 17/33 ≈ 0.515
      ├── Some((4, 5)): 6/19 ≈ 0.316
      ├── Some((4, 6)): 11/26 ≈ 0.423
      ├── Some((4, 7)): 14/29 ≈ 0.483
      └── Some((4, 8)): 28/46 ≈ 0.609
    ├── Some((1, 5)): 116/226 ≈ 0.513
      ├── Some((5, 0)): 7/18 ≈ 0.389
      ├── Some((5, 1)): 9/21 ≈ 0.429
      ├── Some((5, 2)): 19/32 ≈ 0.594
      ├── Some((5, 3)): 15/28 ≈ 0.536
      ├── Some((5, 4)): 8/19 ≈ 0.421
      ├── Some((5, 5)): 16/29 ≈ 0.552
      ├── Some((5, 6)): 13/25 ≈ 0.520
      ├── Some((5, 7)): 17/30 ≈ 0.567
      └── Some((5, 8)): 11/23 ≈ 0.478
    ├── Some((1, 6)): 141/265 ≈ 0.532
      ├── Some((6, 0)): 15/29 ≈ 0.517
      ├── Some((6, 1)): 21/35 ≈ 0.600
      ├── Some((6, 2)): 22/37 ≈ 0.595
      ├── Some((6, 3)): 6/18 ≈ 0.333
      ├── Some((6, 4)): 16/30 ≈ 0.533
      ├── Some((6, 5)): 11/24 ≈ 0.458
      ├── Some((6, 6)): 8/20 ≈ 0.400
      ├── Some((6, 7)): 18/32 ≈ 0.562
      └── Some((6, 8)): 24/39 ≈ 0.615
    ├── Some((1, 7)): 116/227 ≈ 0.511
      ├── Some((7, 0)): 13/25 ≈ 0.520
      ├── Some((7, 1)): 20/33 ≈ 0.606
      ├── Some((7, 2)): 6/17 ≈ 0.353
      ├── Some((7, 3)): 13/25 ≈ 0.520
      ├── Some((7, 4)): 16/29 ≈ 0.552
      ├── Some((7, 5)): 8/20 ≈ 0.400
      ├── Some((7, 6)): 10/22 ≈ 0.455
      ├── Some((7, 7)): 16/29 ≈ 0.552
      └── Some((7, 8)): 13/26 ≈ 0.500
    └── Some((1, 8)): 112/220 ≈ 0.509
      ├── Some((8, 0)): 10/22 ≈ 0.455
      ├── Some((8, 1)): 4/14 ≈ 0.286
      ├── Some((8, 2)): 7/18 ≈ 0.389
      ├── Some((8, 3)): 23/36 ≈ 0.639
      ├── Some((8, 4)): 19/32 ≈ 0.594
      ├── Some((8, 5)): 5/16 ≈ 0.312
      ├── Some((8, 6)): 9/21 ≈ 0.429
      ├── Some((8, 7)): 10/22 ≈ 0.455
      └── Some((8, 8)): 25/38 ≈ 0.658
  ├── Some((4, 2)): 1294/2428 ≈ 0.533
    ├── Some((2, 0)): 125/242 ≈ 0.517
      ├── Some((0, 0)): 14/29 ≈ 0.483
      ├── Some((0, 1)): 11/25 ≈ 0.440
      ├── Some((0, 2)): 6/18 ≈ 0.333
      ├── Some((0, 3)): 14/29 ≈ 0.483
      ├── Some((0, 5)): 9/22 ≈ 0.409
      ├── Some((0, 6)): 11/25 ≈ 0.440
      ├── Some((0, 7)): 37/54 ≈ 0.685
      └── Some((0, 8)): 23/39 ≈ 0.590
    ├── Some((2, 1)): 118/232 ≈ 0.509
      ├── Some((1, 0)): 7/19 ≈ 0.368
      ├── Some((1, 1)): 18/32 ≈ 0.562
      ├── Some((1, 2)): 22/36 ≈ 0.611
      ├── Some((1, 3)): 12/25 ≈ 0.480
      ├── Some((1, 4)): 22/36 ≈ 0.611
      ├── Some((1, 5)): 17/30 ≈ 0.567
      ├── Some((1, 6)): 11/24 ≈ 0.458
      ├── Some((1, 7)): 5/16 ≈ 0.312
      └── Some((1, 8)): 3/13 ≈ 0.231
    ├── Some((2, 2)): 79/170 ≈ 0.465
      ├── Some((2, 0)): 7/18 ≈ 0.389
      ├── Some((2, 1)): 23/36 ≈ 0.639
      ├── Some((2, 3)): 7/18 ≈ 0.389
      ├── Some((2, 4)): 4/14 ≈ 0.286
      ├── Some((2, 5)): 10/22 ≈ 0.455
      ├── Some((2, 6)): 3/13 ≈ 0.231
      ├── Some((2, 7)): 19/32 ≈ 0.594
      └── Some((2, 8)): 5/16 ≈ 0.312
    ├── Some((2, 3)): 131/252 ≈ 0.520
      ├── Some((3, 0)): 17/31 ≈ 0.548
      ├── Some((3, 1)): 8/20 ≈ 0.400
      ├── Some((3, 2)): 12/25 ≈ 0.480
      ├── Some((3, 3)): 20/34 ≈ 0.588
      ├── Some((3, 4)): 11/24 ≈ 0.458
      ├── Some((3, 5)): 18/32 ≈ 0.562
      ├── Some((3, 6)): 17/31 ≈ 0.548
      ├── Some((3, 7)): 7/19 ≈ 0.368
      └── Some((3, 8)): 20/35 ≈ 0.571
    ├── Some((2, 4)): 211/371 ≈ 0.569
      ├── Some((4, 0)): 26/47 ≈ 0.553
      ├── Some((4, 1)): 66/92 ≈ 0.717
      ├── Some((4, 3)): 15/33 ≈ 0.455
      ├── Some((4, 4)): 5/19 ≈ 0.263
      ├── Some((4, 5)): 22/42 ≈ 0.524
      ├── Some((4, 6)): 17/36 ≈ 0.472
      ├── Some((4, 7)): 45/69 ≈ 0.652
      └── Some((4, 8)): 14/32 ≈ 0.438
    ├── Some((2, 5)): 219/383 ≈ 0.572
      ├── Some((5, 0)): 39/60 ≈ 0.650
      ├── Some((5, 1)): 30/49 ≈ 0.612
      ├── Some((5, 2)): 10/25 ≈ 0.400
      ├── Some((5, 3)): 29/48 ≈ 0.604
      ├── Some((5, 4)): 29/48 ≈ 0.604
      ├── Some((5, 5)): 5/19 ≈ 0.263
      ├── Some((5, 6)): 26/45 ≈ 0.578
      ├── Some((5, 7)): 28/47 ≈ 0.596
      └── Some((5, 8)): 23/41 ≈ 0.561
    ├── Some((2, 6)): 170/310 ≈ 0.548
      ├── Some((6, 0)): 14/29 ≈ 0.483
      ├── Some((6, 1)): 33/51 ≈ 0.647
      ├── Some((6, 2)): 12/27 ≈ 0.444
      ├── Some((6, 3)): 31/48 ≈ 0.646
      ├── Some((6, 4)): 16/31 ≈ 0.516
      ├── Some((6, 5)): 16/31 ≈ 0.516
      ├── Some((6, 6)): 23/39 ≈ 0.590
      ├── Some((6, 7)): 11/25 ≈ 0.440
      └── Some((6, 8)): 13/28 ≈ 0.464
    ├── Some((2, 7)): 161/297 ≈ 0.542
      ├── Some((7, 0)): 15/30 ≈ 0.500
      ├── Some((7, 1)): 20/36 ≈ 0.556
      ├── Some((7, 2)): 16/31 ≈ 0.516
      ├── Some((7, 3)): 22/38 ≈ 0.579
      ├── Some((7, 4)): 19/34 ≈ 0.559
      ├── Some((7, 5)): 24/40 ≈ 0.600
      ├── Some((7, 6)): 8/21 ≈ 0.381
      ├── Some((7, 7)): 18/33 ≈ 0.545
      └── Some((7, 8)): 18/33 ≈ 0.545
    └── Some((2, 8)): 79/170 ≈ 0.465
      ├── Some((8, 0)): 5/14 ≈ 0.357
      ├── Some((8, 1)): 8/18 ≈ 0.444
      ├── Some((8, 2)): 19/30 ≈ 0.633
      ├── Some((8, 3)): 13/24 ≈ 0.542
      ├── Some((8, 4)): 8/18 ≈ 0.444
      ├── Some((8, 5)): 6/16 ≈ 0.375
      ├── Some((8, 6)): 7/17 ≈ 0.412
      ├── Some((8, 7)): 3/12 ≈ 0.250
      └── Some((8, 8)): 10/20 ≈ 0.500
  ├── Some((4, 3)): 1119/2126 ≈ 0.526
    ├── Some((3, 0)): 122/233 ≈ 0.524
      ├── Some((0, 0)): 20/35 ≈ 0.571
      ├── Some((0, 1)): 18/32 ≈ 0.562
      ├── Some((0, 2)): 8/21 ≈ 0.381
      ├── Some((0, 3)): 11/24 ≈ 0.458
      ├── Some((0, 5)): 10/23 ≈ 0.435
      ├── Some((0, 6)): 15/29 ≈ 0.517
      ├── Some((0, 7)): 24/39 ≈ 0.615
      └── Some((0, 8)): 15/29 ≈ 0.517
    ├── Some((3, 1)): 169/303 ≈ 0.558
      ├── Some((1, 0)): 22/38 ≈ 0.579
      ├── Some((1, 1)): 12/26 ≈ 0.462
      ├── Some((1, 2)): 22/38 ≈ 0.579
      ├── Some((1, 3)): 14/28 ≈ 0.500
      ├── Some((1, 4)): 15/29 ≈ 0.517
      ├── Some((1, 5)): 27/43 ≈ 0.628
      ├── Some((1, 6)): 26/42 ≈ 0.619
      ├── Some((1, 7)): 20/35 ≈ 0.571
      └── Some((1, 8)): 10/23 ≈ 0.435
    ├── Some((3, 2)): 96/193 ≈ 0.497
      ├── Some((2, 0)): 7/17 ≈ 0.412
      ├── Some((2, 1)): 4/14 ≈ 0.286
      ├── Some((2, 2)): 11/22 ≈ 0.500
      ├── Some((2, 3)): 7/17 ≈ 0.412
      ├── Some((2, 4)): 15/26 ≈ 0.577
      ├── Some((2, 5)): 15/27 ≈ 0.556
      ├── Some((2, 6)): 8/19 ≈ 0.421
      ├── Some((2, 7)): 21/33 ≈ 0.636
      └── Some((2, 8)): 7/17 ≈ 0.412
    ├── Some((3, 3)): 131/246 ≈ 0.533
      ├── Some((3, 0)): 10/23 ≈ 0.435
      ├── Some((3, 1)): 20/35 ≈ 0.571
      ├── Some((3, 2)): 14/28 ≈ 0.500
      ├── Some((3, 4)): 17/31 ≈ 0.548
      ├── Some((3, 5)): 18/33 ≈ 0.545
      ├── Some((3, 6)): 9/22 ≈ 0.409
      ├── Some((3, 7)): 19/34 ≈ 0.559
      └── Some((3, 8)): 24/39 ≈ 0.615
    ├── Some((3, 4)): 93/189 ≈ 0.492
      ├── Some((4, 0)): 12/24 ≈ 0.500
      ├── Some((4, 1)): 10/22 ≈ 0.455
      ├── Some((4, 2)): 11/23 ≈ 0.478
      ├── Some((4, 4)): 14/26 ≈ 0.538
      ├── Some((4, 5)): 15/28 ≈ 0.536
      ├── Some((4, 6)): 8/19 ≈ 0.421
      ├── Some((4, 7)): 10/22 ≈ 0.455
      └── Some((4, 8)): 12/24 ≈ 0.500
    ├── Some((3, 5)): 137/255 ≈ 0.537
      ├── Some((5, 0)): 14/27 ≈ 0.519
      ├── Some((5, 1)): 21/35 ≈ 0.600
      ├── Some((5, 2)): 13/26 ≈ 0.500
      ├── Some((5, 3)): 11/23 ≈ 0.478
      ├── Some((5, 4)): 16/29 ≈ 0.552
      ├── Some((5, 5)): 18/31 ≈ 0.581
      ├── Some((5, 6)): 18/32 ≈ 0.562
      ├── Some((5, 7)): 17/30 ≈ 0.567
      └── Some((5, 8)): 9/21 ≈ 0.429
    ├── Some((3, 6)): 124/236 ≈ 0.525
      ├── Some((6, 0)): 15/28 ≈ 0.536
      ├── Some((6, 1)): 14/27 ≈ 0.519
      ├── Some((6, 2)): 20/34 ≈ 0.588
      ├── Some((6, 3)): 24/38 ≈ 0.632
      ├── Some((6, 4)): 18/31 ≈ 0.581
      ├── Some((6, 5)): 18/31 ≈ 0.581
      ├── Some((6, 6)): 10/22 ≈ 0.455
      ├── Some((6, 7)): 2/12 ≈ 0.167
      └── Some((6, 8)): 2/12 ≈ 0.167
    ├── Some((3, 7)): 115/222 ≈ 0.518
      ├── Some((7, 0)): 10/21 ≈ 0.476
      ├── Some((7, 1)): 13/25 ≈ 0.520
      ├── Some((7, 2)): 3/13 ≈ 0.231
      ├── Some((7, 3)): 21/34 ≈ 0.618
      ├── Some((7, 4)): 10/22 ≈ 0.455
      ├── Some((7, 5)): 18/30 ≈ 0.600
      ├── Some((7, 6)): 16/28 ≈ 0.571
      ├── Some((7, 7)): 14/26 ≈ 0.538
      └── Some((7, 8)): 10/22 ≈ 0.455
    └── Some((3, 8)): 132/248 ≈ 0.532
      ├── Some((8, 0)): 3/13 ≈ 0.231
      ├── Some((8, 1)): 13/26 ≈ 0.500
      ├── Some((8, 2)): 17/30 ≈ 0.567
      ├── Some((8, 3)): 9/21 ≈ 0.429
      ├── Some((8, 4)): 11/23 ≈ 0.478
      ├── Some((8, 5)): 22/36 ≈ 0.611
      ├── Some((8, 6)): 14/27 ≈ 0.519
      ├── Some((8, 7)): 25/39 ≈ 0.641
      └── Some((8, 8)): 18/32 ≈ 0.562
  ├── Some((4, 4)): 708/1408 ≈ 0.503
    ├── Some((4, 0)): 110/209 ≈ 0.526
      ├── Some((0, 0)): 13/26 ≈ 0.500
      ├── Some((0, 1)): 3/13 ≈ 0.231
      ├── Some((0, 2)): 11/23 ≈ 0.478
      ├── Some((0, 3)): 16/29 ≈ 0.552
      ├── Some((0, 5)): 10/22 ≈ 0.455
      ├── Some((0, 6)): 17/30 ≈ 0.567
      ├── Some((0, 7)): 18/31 ≈ 0.581
      └── Some((0, 8)): 21/34 ≈ 0.618
    ├── Some((4, 1)): 72/151 ≈ 0.477
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 1)): 10/19 ≈ 0.526
      ├── Some((1, 2)): 6/15 ≈ 0.400
      ├── Some((1, 3)): 2/10 ≈ 0.200
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 3/11 ≈ 0.273
      ├── Some((1, 7)): 6/15 ≈ 0.400
      └── Some((1, 8)): 13/22 ≈ 0.591
    ├── Some((4, 2)): 41/102 ≈ 0.402
      ├── Some((2, 0)): 2/8 ≈ 0.250
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 0/6 ≈ 0.000
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 8/15 ≈ 0.533
      ├── Some((2, 6)): 2/8 ≈ 0.250
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 9/16 ≈ 0.562
    ├── Some((4, 3)): 89/177 ≈ 0.503
      ├── Some((3, 0)): 9/19 ≈ 0.474
      ├── Some((3, 1)): 3/12 ≈ 0.250
      ├── Some((3, 2)): 14/24 ≈ 0.583
      ├── Some((3, 3)): 10/20 ≈ 0.500
      ├── Some((3, 4)): 7/17 ≈ 0.412
      ├── Some((3, 5)): 6/15 ≈ 0.400
      ├── Some((3, 6)): 10/20 ≈ 0.500
      ├── Some((3, 7)): 14/24 ≈ 0.583
      └── Some((3, 8)): 15/25 ≈ 0.600
    ├── Some((4, 5)): 91/180 ≈ 0.506
      ├── Some((5, 0)): 4/13 ≈ 0.308
      ├── Some((5, 1)): 8/18 ≈ 0.444
      ├── Some((5, 2)): 6/15 ≈ 0.400
      ├── Some((5, 3)): 13/23 ≈ 0.565
      ├── Some((5, 4)): 12/22 ≈ 0.545
      ├── Some((5, 5)): 13/23 ≈ 0.565
      ├── Some((5, 6)): 8/18 ≈ 0.444
      ├── Some((5, 7)): 19/29 ≈ 0.655
      └── Some((5, 8)): 8/18 ≈ 0.444
    ├── Some((4, 6)): 143/258 ≈ 0.554
      ├── Some((6, 0)): 29/43 ≈ 0.674
      ├── Some((6, 1)): 8/20 ≈ 0.400
      ├── Some((6, 2)): 23/37 ≈ 0.622
      ├── Some((6, 3)): 6/17 ≈ 0.353
      ├── Some((6, 4)): 30/44 ≈ 0.682
      ├── Some((6, 5)): 15/28 ≈ 0.536
      ├── Some((6, 6)): 9/21 ≈ 0.429
      ├── Some((6, 7)): 13/25 ≈ 0.520
      └── Some((6, 8)): 10/22 ≈ 0.455
    ├── Some((4, 7)): 59/131 ≈ 0.450
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 10/18 ≈ 0.556
      ├── Some((7, 2)): 4/12 ≈ 0.333
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 3/11 ≈ 0.273
      ├── Some((7, 5)): 11/19 ≈ 0.579
      ├── Some((7, 6)): 4/12 ≈ 0.333
      ├── Some((7, 7)): 3/11 ≈ 0.273
      └── Some((7, 8)): 4/12 ≈ 0.333
    └── Some((4, 8)): 103/199 ≈ 0.518
      ├── Some((8, 0)): 12/23 ≈ 0.522
      ├── Some((8, 1)): 10/21 ≈ 0.476
      ├── Some((8, 2)): 17/28 ≈ 0.607
      ├── Some((8, 3)): 8/18 ≈ 0.444
      ├── Some((8, 4)): 6/16 ≈ 0.375
      ├── Some((8, 5)): 7/17 ≈ 0.412
      ├── Some((8, 6)): 6/16 ≈ 0.375
      ├── Some((8, 7)): 23/35 ≈ 0.657
      └── Some((8, 8)): 13/24 ≈ 0.542
  ├── Some((4, 5)): 1301/2440 ≈ 0.533
    ├── Some((5, 0)): 113/223 ≈ 0.507
      ├── Some((0, 0)): 23/38 ≈ 0.605
      ├── Some((0, 1)): 15/29 ≈ 0.517
      ├── Some((0, 2)): 18/33 ≈ 0.545
      ├── Some((0, 3)): 16/30 ≈ 0.533
      ├── Some((0, 5)): 2/13 ≈ 0.154
      ├── Some((0, 6)): 8/21 ≈ 0.381
      ├── Some((0, 7)): 14/28 ≈ 0.500
      └── Some((0, 8)): 16/30 ≈ 0.533
    ├── Some((5, 1)): 139/263 ≈ 0.529
      ├── Some((1, 0)): 18/33 ≈ 0.545
      ├── Some((1, 1)): 17/31 ≈ 0.548
      ├── Some((1, 2)): 11/24 ≈ 0.458
      ├── Some((1, 3)): 26/41 ≈ 0.634
      ├── Some((1, 4)): 21/36 ≈ 0.583
      ├── Some((1, 5)): 4/15 ≈ 0.267
      ├── Some((1, 6)): 24/39 ≈ 0.615
      ├── Some((1, 7)): 6/18 ≈ 0.333
      └── Some((1, 8)): 12/25 ≈ 0.480
    ├── Some((5, 2)): 115/227 ≈ 0.507
      ├── Some((2, 0)): 10/22 ≈ 0.455
      ├── Some((2, 1)): 13/26 ≈ 0.500
      ├── Some((2, 2)): 20/33 ≈ 0.606
      ├── Some((2, 3)): 12/24 ≈ 0.500
      ├── Some((2, 4)): 23/37 ≈ 0.622
      ├── Some((2, 5)): 13/26 ≈ 0.500
      ├── Some((2, 6)): 12/24 ≈ 0.500
      ├── Some((2, 7)): 6/17 ≈ 0.353
      └── Some((2, 8)): 6/17 ≈ 0.353
    ├── Some((5, 3)): 183/329 ≈ 0.556
      ├── Some((3, 0)): 21/38 ≈ 0.553
      ├── Some((3, 1)): 19/35 ≈ 0.543
      ├── Some((3, 2)): 28/45 ≈ 0.622
      ├── Some((3, 3)): 19/35 ≈ 0.543
      ├── Some((3, 4)): 24/41 ≈ 0.585
      ├── Some((3, 5)): 13/28 ≈ 0.464
      ├── Some((3, 6)): 14/29 ≈ 0.483
      ├── Some((3, 7)): 16/32 ≈ 0.500
      └── Some((3, 8)): 28/45 ≈ 0.622
    ├── Some((5, 4)): 128/247 ≈ 0.518
      ├── Some((4, 0)): 16/31 ≈ 0.516
      ├── Some((4, 1)): 25/41 ≈ 0.610
      ├── Some((4, 2)): 20/36 ≈ 0.556
      ├── Some((4, 3)): 12/26 ≈ 0.462
      ├── Some((4, 4)): 16/31 ≈ 0.516
      ├── Some((4, 6)): 21/37 ≈ 0.568
      ├── Some((4, 7)): 13/27 ≈ 0.481
      └── Some((4, 8)): 5/17 ≈ 0.294
    ├── Some((5, 5)): 193/344 ≈ 0.561
      ├── Some((5, 0)): 34/55 ≈ 0.618
      ├── Some((5, 1)): 35/56 ≈ 0.625
      ├── Some((5, 2)): 49/72 ≈ 0.681
      ├── Some((5, 3)): 10/26 ≈ 0.385
      ├── Some((5, 4)): 19/37 ≈ 0.514
      ├── Some((5, 6)): 10/26 ≈ 0.385
      ├── Some((5, 7)): 29/49 ≈ 0.592
      └── Some((5, 8)): 7/22 ≈ 0.318
    ├── Some((5, 6)): 158/292 ≈ 0.541
      ├── Some((6, 0)): 5/17 ≈ 0.294
      ├── Some((6, 1)): 29/46 ≈ 0.630
      ├── Some((6, 2)): 12/26 ≈ 0.462
      ├── Some((6, 3)): 24/40 ≈ 0.600
      ├── Some((6, 4)): 27/43 ≈ 0.628
      ├── Some((6, 5)): 18/33 ≈ 0.545
      ├── Some((6, 6)): 10/24 ≈ 0.417
      ├── Some((6, 7)): 24/40 ≈ 0.600
      └── Some((6, 8)): 9/22 ≈ 0.409
    ├── Some((5, 7)): 98/200 ≈ 0.490
      ├── Some((7, 0)): 2/11 ≈ 0.182
      ├── Some((7, 1)): 10/21 ≈ 0.476
      ├── Some((7, 2)): 8/19 ≈ 0.421
      ├── Some((7, 3)): 16/28 ≈ 0.571
      ├── Some((7, 4)): 12/24 ≈ 0.500
      ├── Some((7, 5)): 10/22 ≈ 0.455
      ├── Some((7, 6)): 14/26 ≈ 0.538
      ├── Some((7, 7)): 9/20 ≈ 0.450
      └── Some((7, 8)): 16/28 ≈ 0.571
    └── Some((5, 8)): 173/314 ≈ 0.551
      ├── Some((8, 0)): 26/43 ≈ 0.605
      ├── Some((8, 1)): 8/22 ≈ 0.364
      ├── Some((8, 2)): 35/53 ≈ 0.660
      ├── Some((8, 3)): 19/35 ≈ 0.543
      ├── Some((8, 4)): 21/37 ≈ 0.568
      ├── Some((8, 5)): 21/37 ≈ 0.568
      ├── Some((8, 6)): 3/15 ≈ 0.200
      ├── Some((8, 7)): 19/35 ≈ 0.543
      └── Some((8, 8)): 20/36 ≈ 0.556
  ├── Some((4, 6)): 853/1663 ≈ 0.513
    ├── Some((6, 0)): 122/227 ≈ 0.537
      ├── Some((0, 0)): 6/18 ≈ 0.333
      ├── Some((0, 1)): 24/38 ≈ 0.632
      ├── Some((0, 2)): 19/33 ≈ 0.576
      ├── Some((0, 3)): 8/20 ≈ 0.400
      ├── Some((0, 5)): 24/38 ≈ 0.632
      ├── Some((0, 6)): 9/21 ≈ 0.429
      ├── Some((0, 7)): 13/26 ≈ 0.500
      └── Some((0, 8)): 18/32 ≈ 0.562
    ├── Some((6, 1)): 97/189 ≈ 0.513
      ├── Some((1, 0)): 11/21 ≈ 0.524
      ├── Some((1, 1)): 4/13 ≈ 0.308
      ├── Some((1, 2)): 18/29 ≈ 0.621
      ├── Some((1, 3)): 6/16 ≈ 0.375
      ├── Some((1, 4)): 5/14 ≈ 0.357
      ├── Some((1, 5)): 15/26 ≈ 0.577
      ├── Some((1, 6)): 9/19 ≈ 0.474
      ├── Some((1, 7)): 14/24 ≈ 0.583
      └── Some((1, 8)): 15/26 ≈ 0.577
    ├── Some((6, 2)): 119/222 ≈ 0.536
      ├── Some((2, 0)): 23/35 ≈ 0.657
      ├── Some((2, 1)): 14/26 ≈ 0.538
      ├── Some((2, 2)): 9/20 ≈ 0.450
      ├── Some((2, 3)): 22/34 ≈ 0.647
      ├── Some((2, 4)): 7/18 ≈ 0.389
      ├── Some((2, 5)): 14/26 ≈ 0.538
      ├── Some((2, 6)): 12/24 ≈ 0.500
      ├── Some((2, 7)): 15/27 ≈ 0.556
      └── Some((2, 8)): 2/11 ≈ 0.182
    ├── Some((6, 3)): 44/107 ≈ 0.411
      ├── Some((3, 0)): 10/18 ≈ 0.556
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 1/7 ≈ 0.143
      ├── Some((3, 3)): 1/8 ≈ 0.125
      ├── Some((3, 4)): 6/13 ≈ 0.462
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 1/8 ≈ 0.125
    ├── Some((6, 4)): 57/128 ≈ 0.445
      ├── Some((4, 0)): 5/14 ≈ 0.357
      ├── Some((4, 1)): 12/21 ≈ 0.571
      ├── Some((4, 2)): 3/11 ≈ 0.273
      ├── Some((4, 3)): 2/10 ≈ 0.200
      ├── Some((4, 4)): 12/21 ≈ 0.571
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 7)): 12/22 ≈ 0.545
      └── Some((4, 8)): 3/11 ≈ 0.273
    ├── Some((6, 5)): 45/108 ≈ 0.417
      ├── Some((5, 0)): 0/6 ≈ 0.000
      ├── Some((5, 1)): 9/16 ≈ 0.562
      ├── Some((5, 2)): 3/10 ≈ 0.300
      ├── Some((5, 3)): 1/7 ≈ 0.143
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 5)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 5/12 ≈ 0.417
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((6, 6)): 128/235 ≈ 0.545
      ├── Some((6, 0)): 19/33 ≈ 0.576
      ├── Some((6, 1)): 13/26 ≈ 0.500
      ├── Some((6, 2)): 21/35 ≈ 0.600
      ├── Some((6, 3)): 4/15 ≈ 0.267
      ├── Some((6, 4)): 17/31 ≈ 0.548
      ├── Some((6, 5)): 14/27 ≈ 0.519
      ├── Some((6, 7)): 23/37 ≈ 0.622
      └── Some((6, 8)): 16/30 ≈ 0.533
    ├── Some((6, 7)): 89/177 ≈ 0.503
      ├── Some((7, 0)): 14/25 ≈ 0.560
      ├── Some((7, 1)): 16/27 ≈ 0.593
      ├── Some((7, 2)): 20/31 ≈ 0.645
      ├── Some((7, 3)): 4/13 ≈ 0.308
      ├── Some((7, 4)): 2/10 ≈ 0.200
      ├── Some((7, 5)): 7/17 ≈ 0.412
      ├── Some((7, 6)): 13/23 ≈ 0.565
      ├── Some((7, 7)): 1/9 ≈ 0.111
      └── Some((7, 8)): 11/21 ≈ 0.524
    └── Some((6, 8)): 151/269 ≈ 0.561
      ├── Some((8, 0)): 18/31 ≈ 0.581
      ├── Some((8, 1)): 19/33 ≈ 0.576
      ├── Some((8, 2)): 16/29 ≈ 0.552
      ├── Some((8, 3)): 10/22 ≈ 0.455
      ├── Some((8, 4)): 23/37 ≈ 0.622
      ├── Some((8, 5)): 15/28 ≈ 0.536
      ├── Some((8, 6)): 11/23 ≈ 0.478
      ├── Some((8, 7)): 24/38 ≈ 0.632
      └── Some((8, 8)): 14/27 ≈ 0.519
  ├── Some((4, 7)): 1747/3203 ≈ 0.545
    ├── Some((7, 0)): 213/385 ≈ 0.553
      ├── Some((0, 0)): 25/46 ≈ 0.543
      ├── Some((0, 1)): 36/60 ≈ 0.600
      ├── Some((0, 2)): 30/53 ≈ 0.566
      ├── Some((0, 3)): 9/26 ≈ 0.346
      ├── Some((0, 5)): 38/62 ≈ 0.613
      ├── Some((0, 6)): 34/57 ≈ 0.596
      ├── Some((0, 7)): 12/30 ≈ 0.400
      └── Some((0, 8)): 28/50 ≈ 0.560
    ├── Some((7, 1)): 235/418 ≈ 0.562
      ├── Some((1, 0)): 42/65 ≈ 0.646
      ├── Some((1, 1)): 41/64 ≈ 0.641
      ├── Some((1, 2)): 21/41 ≈ 0.512
      ├── Some((1, 3)): 14/32 ≈ 0.438
      ├── Some((1, 4)): 19/38 ≈ 0.500
      ├── Some((1, 5)): 41/64 ≈ 0.641
      ├── Some((1, 6)): 17/36 ≈ 0.472
      ├── Some((1, 7)): 23/43 ≈ 0.535
      └── Some((1, 8)): 16/34 ≈ 0.471
    ├── Some((7, 2)): 205/373 ≈ 0.550
      ├── Some((2, 0)): 29/49 ≈ 0.592
      ├── Some((2, 1)): 45/67 ≈ 0.672
      ├── Some((2, 2)): 11/27 ≈ 0.407
      ├── Some((2, 3)): 11/27 ≈ 0.407
      ├── Some((2, 4)): 13/30 ≈ 0.433
      ├── Some((2, 5)): 31/51 ≈ 0.608
      ├── Some((2, 6)): 20/38 ≈ 0.526
      ├── Some((2, 7)): 18/36 ≈ 0.500
      └── Some((2, 8)): 27/47 ≈ 0.574
    ├── Some((7, 3)): 173/324 ≈ 0.534
      ├── Some((3, 0)): 34/53 ≈ 0.642
      ├── Some((3, 1)): 24/42 ≈ 0.571
      ├── Some((3, 2)): 7/21 ≈ 0.333
      ├── Some((3, 3)): 7/21 ≈ 0.333
      ├── Some((3, 4)): 16/32 ≈ 0.500
      ├── Some((3, 5)): 37/57 ≈ 0.649
      ├── Some((3, 6)): 14/30 ≈ 0.467
      ├── Some((3, 7)): 7/21 ≈ 0.333
      └── Some((3, 8)): 27/46 ≈ 0.587
    ├── Some((7, 4)): 243/430 ≈ 0.565
      ├── Some((4, 0)): 44/70 ≈ 0.629
      ├── Some((4, 1)): 31/55 ≈ 0.564
      ├── Some((4, 2)): 33/57 ≈ 0.579
      ├── Some((4, 3)): 30/53 ≈ 0.566
      ├── Some((4, 4)): 17/37 ≈ 0.459
      ├── Some((4, 5)): 36/61 ≈ 0.590
      ├── Some((4, 6)): 22/44 ≈ 0.500
      └── Some((4, 8)): 29/52 ≈ 0.558
    ├── Some((7, 5)): 169/318 ≈ 0.531
      ├── Some((5, 0)): 29/48 ≈ 0.604
      ├── Some((5, 1)): 23/41 ≈ 0.561
      ├── Some((5, 2)): 17/33 ≈ 0.515
      ├── Some((5, 3)): 15/31 ≈ 0.484
      ├── Some((5, 4)): 16/32 ≈ 0.500
      ├── Some((5, 5)): 16/32 ≈ 0.500
      ├── Some((5, 6)): 27/45 ≈ 0.600
      ├── Some((5, 7)): 17/33 ≈ 0.515
      └── Some((5, 8)): 8/22 ≈ 0.364
    ├── Some((7, 6)): 114/232 ≈ 0.491
      ├── Some((6, 0)): 14/28 ≈ 0.500
      ├── Some((6, 1)): 7/19 ≈ 0.368
      ├── Some((6, 2)): 5/17 ≈ 0.294
      ├── Some((6, 3)): 8/20 ≈ 0.400
      ├── Some((6, 4)): 19/33 ≈ 0.576
      ├── Some((6, 5)): 13/26 ≈ 0.500
      ├── Some((6, 6)): 33/49 ≈ 0.673
      ├── Some((6, 7)): 2/12 ≈ 0.167
      └── Some((6, 8)): 13/27 ≈ 0.481
    ├── Some((7, 7)): 151/290 ≈ 0.521
      ├── Some((7, 0)): 32/52 ≈ 0.615
      ├── Some((7, 1)): 9/24 ≈ 0.375
      ├── Some((7, 2)): 13/29 ≈ 0.448
      ├── Some((7, 3)): 10/25 ≈ 0.400
      ├── Some((7, 4)): 22/40 ≈ 0.550
      ├── Some((7, 5)): 16/33 ≈ 0.485
      ├── Some((7, 6)): 34/54 ≈ 0.630
      └── Some((7, 8)): 15/32 ≈ 0.469
    └── Some((7, 8)): 244/432 ≈ 0.565
      ├── Some((8, 0)): 49/74 ≈ 0.662
      ├── Some((8, 1)): 17/36 ≈ 0.472
      ├── Some((8, 2)): 23/43 ≈ 0.535
      ├── Some((8, 3)): 43/67 ≈ 0.642
      ├── Some((8, 4)): 17/36 ≈ 0.472
      ├── Some((8, 5)): 35/57 ≈ 0.614
      ├── Some((8, 6)): 23/43 ≈ 0.535
      ├── Some((8, 7)): 19/38 ≈ 0.500
      └── Some((8, 8)): 18/37 ≈ 0.486
  └── Some((4, 8)): 1447/2691 ≈ 0.538
    ├── Some((8, 0)): 145/275 ≈ 0.527
      ├── Some((0, 0)): 29/47 ≈ 0.617
      ├── Some((0, 1)): 27/45 ≈ 0.600
      ├── Some((0, 2)): 14/30 ≈ 0.467
      ├── Some((0, 3)): 24/41 ≈ 0.585
      ├── Some((0, 5)): 9/23 ≈ 0.391
      ├── Some((0, 6)): 17/33 ≈ 0.515
      ├── Some((0, 7)): 12/27 ≈ 0.444
      └── Some((0, 8)): 13/28 ≈ 0.464
    ├── Some((8, 1)): 146/277 ≈ 0.527
      ├── Some((1, 0)): 36/53 ≈ 0.679
      ├── Some((1, 1)): 16/31 ≈ 0.516
      ├── Some((1, 2)): 17/32 ≈ 0.531
      ├── Some((1, 3)): 15/29 ≈ 0.517
      ├── Some((1, 4)): 13/27 ≈ 0.481
      ├── Some((1, 5)): 8/21 ≈ 0.381
      ├── Some((1, 6)): 8/21 ≈ 0.381
      ├── Some((1, 7)): 20/35 ≈ 0.571
      └── Some((1, 8)): 13/27 ≈ 0.481
    ├── Some((8, 2)): 178/326 ≈ 0.546
      ├── Some((2, 0)): 24/41 ≈ 0.585
      ├── Some((2, 1)): 25/42 ≈ 0.595
      ├── Some((2, 2)): 25/42 ≈ 0.595
      ├── Some((2, 3)): 19/35 ≈ 0.543
      ├── Some((2, 4)): 15/31 ≈ 0.484
      ├── Some((2, 5)): 24/41 ≈ 0.585
      ├── Some((2, 6)): 12/27 ≈ 0.444
      ├── Some((2, 7)): 19/36 ≈ 0.528
      └── Some((2, 8)): 14/30 ≈ 0.467
    ├── Some((8, 3)): 146/277 ≈ 0.527
      ├── Some((3, 0)): 23/39 ≈ 0.590
      ├── Some((3, 1)): 18/33 ≈ 0.545
      ├── Some((3, 2)): 4/16 ≈ 0.250
      ├── Some((3, 3)): 14/28 ≈ 0.500
      ├── Some((3, 4)): 7/20 ≈ 0.350
      ├── Some((3, 5)): 17/32 ≈ 0.531
      ├── Some((3, 6)): 33/49 ≈ 0.673
      ├── Some((3, 7)): 14/28 ≈ 0.500
      └── Some((3, 8)): 16/31 ≈ 0.516
    ├── Some((8, 4)): 137/263 ≈ 0.521
      ├── Some((4, 0)): 18/34 ≈ 0.529
      ├── Some((4, 1)): 16/32 ≈ 0.500
      ├── Some((4, 2)): 15/31 ≈ 0.484
      ├── Some((4, 3)): 30/48 ≈ 0.625
      ├── Some((4, 4)): 23/40 ≈ 0.575
      ├── Some((4, 5)): 18/34 ≈ 0.529
      ├── Some((4, 6)): 12/27 ≈ 0.444
      └── Some((4, 7)): 4/16 ≈ 0.250
    ├── Some((8, 5)): 210/373 ≈ 0.563
      ├── Some((5, 0)): 20/38 ≈ 0.526
      ├── Some((5, 1)): 23/41 ≈ 0.561
      ├── Some((5, 2)): 27/46 ≈ 0.587
      ├── Some((5, 3)): 28/47 ≈ 0.596
      ├── Some((5, 4)): 34/54 ≈ 0.630
      ├── Some((5, 5)): 28/47 ≈ 0.596
      ├── Some((5, 6)): 18/36 ≈ 0.500
      ├── Some((5, 7)): 4/17 ≈ 0.235
      └── Some((5, 8)): 27/46 ≈ 0.587
    ├── Some((8, 6)): 224/394 ≈ 0.569
      ├── Some((6, 0)): 30/50 ≈ 0.600
      ├── Some((6, 1)): 37/58 ≈ 0.638
      ├── Some((6, 2)): 17/34 ≈ 0.500
      ├── Some((6, 3)): 24/43 ≈ 0.558
      ├── Some((6, 4)): 25/44 ≈ 0.568
      ├── Some((6, 5)): 17/34 ≈ 0.500
      ├── Some((6, 6)): 27/46 ≈ 0.587
      ├── Some((6, 7)): 28/47 ≈ 0.596
      └── Some((6, 8)): 19/37 ≈ 0.514
    ├── Some((8, 7)): 128/249 ≈ 0.514
      ├── Some((7, 0)): 22/36 ≈ 0.611
      ├── Some((7, 1)): 17/31 ≈ 0.548
      ├── Some((7, 2)): 15/29 ≈ 0.517
      ├── Some((7, 3)): 14/27 ≈ 0.519
      ├── Some((7, 4)): 12/25 ≈ 0.480
      ├── Some((7, 5)): 11/24 ≈ 0.458
      ├── Some((7, 6)): 10/23 ≈ 0.435
      ├── Some((7, 7)): 16/30 ≈ 0.533
      └── Some((7, 8)): 10/23 ≈ 0.435
    └── Some((8, 8)): 132/256 ≈ 0.516
      ├── Some((8, 0)): 21/37 ≈ 0.568
      ├── Some((8, 1)): 26/43 ≈ 0.605
      ├── Some((8, 2)): 6/19 ≈ 0.316
      ├── Some((8, 3)): 16/32 ≈ 0.500
      ├── Some((8, 4)): 18/34 ≈ 0.529
      ├── Some((8, 5)): 20/36 ≈ 0.556
      ├── Some((8, 6)): 15/30 ≈ 0.500
      └── Some((8, 7)): 10/24 ≈ 0.417
├── Some((0, 5)): 7046/13499 ≈ 0.522
  ├── Some((5, 0)): 993/1862 ≈ 0.533
    ├── Some((0, 0)): 157/282 ≈ 0.557
      ├── Some((0, 1)): 20/37 ≈ 0.541
      ├── Some((0, 2)): 23/41 ≈ 0.561
      ├── Some((0, 3)): 15/31 ≈ 0.484
      ├── Some((0, 4)): 31/50 ≈ 0.620
      ├── Some((0, 6)): 22/40 ≈ 0.550
      ├── Some((0, 7)): 25/43 ≈ 0.581
      └── Some((0, 8)): 21/39 ≈ 0.538
    ├── Some((0, 1)): 62/138 ≈ 0.449
      ├── Some((1, 0)): 6/14 ≈ 0.429
      ├── Some((1, 1)): 8/17 ≈ 0.471
      ├── Some((1, 2)): 5/13 ≈ 0.385
      ├── Some((1, 3)): 12/21 ≈ 0.571
      ├── Some((1, 4)): 8/17 ≈ 0.471
      ├── Some((1, 5)): 2/9 ≈ 0.222
      ├── Some((1, 6)): 3/11 ≈ 0.273
      ├── Some((1, 7)): 13/22 ≈ 0.591
      └── Some((1, 8)): 5/13 ≈ 0.385
    ├── Some((0, 2)): 151/274 ≈ 0.551
      ├── Some((2, 0)): 19/33 ≈ 0.576
      ├── Some((2, 1)): 19/33 ≈ 0.576
      ├── Some((2, 2)): 18/32 ≈ 0.562
      ├── Some((2, 3)): 30/45 ≈ 0.667
      ├── Some((2, 4)): 14/27 ≈ 0.519
      ├── Some((2, 5)): 14/28 ≈ 0.500
      ├── Some((2, 6)): 20/34 ≈ 0.588
      ├── Some((2, 7)): 7/19 ≈ 0.368
      └── Some((2, 8)): 9/22 ≈ 0.409
    ├── Some((0, 3)): 106/206 ≈ 0.515
      ├── Some((3, 0)): 12/23 ≈ 0.522
      ├── Some((3, 1)): 14/25 ≈ 0.560
      ├── Some((3, 2)): 14/26 ≈ 0.538
      ├── Some((3, 3)): 23/35 ≈ 0.657
      ├── Some((3, 4)): 4/14 ≈ 0.286
      ├── Some((3, 5)): 8/19 ≈ 0.421
      ├── Some((3, 6)): 12/23 ≈ 0.522
      ├── Some((3, 7)): 7/17 ≈ 0.412
      └── Some((3, 8)): 12/23 ≈ 0.522
    ├── Some((0, 4)): 131/244 ≈ 0.537
      ├── Some((4, 0)): 16/29 ≈ 0.552
      ├── Some((4, 1)): 28/42 ≈ 0.667
      ├── Some((4, 2)): 7/18 ≈ 0.389
      ├── Some((4, 3)): 24/38 ≈ 0.632
      ├── Some((4, 4)): 15/28 ≈ 0.536
      ├── Some((4, 5)): 11/23 ≈ 0.478
      ├── Some((4, 6)): 11/23 ≈ 0.478
      ├── Some((4, 7)): 11/23 ≈ 0.478
      └── Some((4, 8)): 7/19 ≈ 0.368
    ├── Some((0, 6)): 78/163 ≈ 0.479
      ├── Some((6, 0)): 10/20 ≈ 0.500
      ├── Some((6, 1)): 12/22 ≈ 0.545
      ├── Some((6, 2)): 8/17 ≈ 0.471
      ├── Some((6, 3)): 5/14 ≈ 0.357
      ├── Some((6, 4)): 15/25 ≈ 0.600
      ├── Some((6, 5)): 15/25 ≈ 0.600
      ├── Some((6, 6)): 6/15 ≈ 0.400
      ├── Some((6, 7)): 3/11 ≈ 0.273
      └── Some((6, 8)): 4/13 ≈ 0.308
    ├── Some((0, 7)): 150/272 ≈ 0.551
      ├── Some((7, 0)): 20/34 ≈ 0.588
      ├── Some((7, 1)): 14/27 ≈ 0.519
      ├── Some((7, 2)): 7/19 ≈ 0.368
      ├── Some((7, 3)): 5/16 ≈ 0.312
      ├── Some((7, 4)): 18/32 ≈ 0.562
      ├── Some((7, 5)): 18/32 ≈ 0.562
      ├── Some((7, 6)): 34/49 ≈ 0.694
      ├── Some((7, 7)): 23/38 ≈ 0.605
      └── Some((7, 8)): 11/24 ≈ 0.458
    └── Some((0, 8)): 157/282 ≈ 0.557
      ├── Some((8, 0)): 16/30 ≈ 0.533
      ├── Some((8, 1)): 16/30 ≈ 0.533
      ├── Some((8, 2)): 22/36 ≈ 0.611
      ├── Some((8, 3)): 12/25 ≈ 0.480
      ├── Some((8, 4)): 13/26 ≈ 0.500
      ├── Some((8, 5)): 19/33 ≈ 0.576
      ├── Some((8, 6)): 6/18 ≈ 0.333
      ├── Some((8, 7)): 24/39 ≈ 0.615
      └── Some((8, 8)): 29/44 ≈ 0.659
  ├── Some((5, 1)): 743/1433 ≈ 0.518
    ├── Some((1, 0)): 89/169 ≈ 0.527
      ├── Some((0, 0)): 8/18 ≈ 0.444
      ├── Some((0, 1)): 19/29 ≈ 0.655
      ├── Some((0, 2)): 13/23 ≈ 0.565
      ├── Some((0, 3)): 3/12 ≈ 0.250
      ├── Some((0, 4)): 12/22 ≈ 0.545
      ├── Some((0, 6)): 8/18 ≈ 0.444
      ├── Some((0, 7)): 15/25 ≈ 0.600
      └── Some((0, 8)): 11/21 ≈ 0.524
    ├── Some((1, 1)): 103/190 ≈ 0.542
      ├── Some((1, 0)): 8/18 ≈ 0.444
      ├── Some((1, 2)): 14/25 ≈ 0.560
      ├── Some((1, 3)): 11/22 ≈ 0.500
      ├── Some((1, 4)): 14/25 ≈ 0.560
      ├── Some((1, 5)): 14/25 ≈ 0.560
      ├── Some((1, 6)): 8/18 ≈ 0.444
      ├── Some((1, 7)): 17/28 ≈ 0.607
      └── Some((1, 8)): 17/28 ≈ 0.607
    ├── Some((1, 2)): 39/94 ≈ 0.415
      ├── Some((2, 0)): 1/7 ≈ 0.143
      ├── Some((2, 1)): 6/12 ≈ 0.500
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 7/13 ≈ 0.538
      ├── Some((2, 4)): 2/8 ≈ 0.250
      ├── Some((2, 5)): 1/7 ≈ 0.143
      ├── Some((2, 6)): 2/8 ≈ 0.250
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 6/12 ≈ 0.500
    ├── Some((1, 3)): 118/211 ≈ 0.559
      ├── Some((3, 0)): 3/12 ≈ 0.250
      ├── Some((3, 1)): 12/22 ≈ 0.545
      ├── Some((3, 2)): 26/37 ≈ 0.703
      ├── Some((3, 3)): 10/20 ≈ 0.500
      ├── Some((3, 4)): 7/17 ≈ 0.412
      ├── Some((3, 5)): 12/23 ≈ 0.522
      ├── Some((3, 6)): 24/35 ≈ 0.686
      ├── Some((3, 7)): 12/23 ≈ 0.522
      └── Some((3, 8)): 11/21 ≈ 0.524
    ├── Some((1, 4)): 78/153 ≈ 0.510
      ├── Some((4, 0)): 4/12 ≈ 0.333
      ├── Some((4, 1)): 7/15 ≈ 0.467
      ├── Some((4, 2)): 5/13 ≈ 0.385
      ├── Some((4, 3)): 18/27 ≈ 0.667
      ├── Some((4, 4)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 12/21 ≈ 0.571
      ├── Some((4, 6)): 2/9 ≈ 0.222
      ├── Some((4, 7)): 14/23 ≈ 0.609
      └── Some((4, 8)): 9/18 ≈ 0.500
    ├── Some((1, 5)): 51/112 ≈ 0.455
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 7/15 ≈ 0.467
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 8/16 ≈ 0.500
      ├── Some((5, 7)): 3/10 ≈ 0.300
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((1, 6)): 122/217 ≈ 0.562
      ├── Some((6, 0)): 23/34 ≈ 0.676
      ├── Some((6, 1)): 11/21 ≈ 0.524
      ├── Some((6, 2)): 11/21 ≈ 0.524
      ├── Some((6, 3)): 14/25 ≈ 0.560
      ├── Some((6, 4)): 6/16 ≈ 0.375
      ├── Some((6, 5)): 17/28 ≈ 0.607
      ├── Some((6, 6)): 11/22 ≈ 0.500
      ├── Some((6, 7)): 10/20 ≈ 0.500
      └── Some((6, 8)): 18/29 ≈ 0.621
    ├── Some((1, 7)): 71/143 ≈ 0.497
      ├── Some((7, 0)): 14/23 ≈ 0.609
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 2/9 ≈ 0.222
      ├── Some((7, 3)): 11/19 ≈ 0.579
      ├── Some((7, 4)): 13/21 ≈ 0.619
      ├── Some((7, 5)): 6/14 ≈ 0.429
      ├── Some((7, 6)): 5/13 ≈ 0.385
      ├── Some((7, 7)): 7/15 ≈ 0.467
      └── Some((7, 8)): 5/13 ≈ 0.385
    └── Some((1, 8)): 71/143 ≈ 0.497
      ├── Some((8, 0)): 10/18 ≈ 0.556
      ├── Some((8, 1)): 10/18 ≈ 0.556
      ├── Some((8, 2)): 4/12 ≈ 0.333
      ├── Some((8, 3)): 5/13 ≈ 0.385
      ├── Some((8, 4)): 8/16 ≈ 0.500
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 9/17 ≈ 0.529
      ├── Some((8, 7)): 12/20 ≈ 0.600
      └── Some((8, 8)): 5/13 ≈ 0.385
  ├── Some((5, 2)): 953/1794 ≈ 0.531
    ├── Some((2, 0)): 151/266 ≈ 0.568
      ├── Some((0, 0)): 8/21 ≈ 0.381
      ├── Some((0, 1)): 0/9 ≈ 0.000
      ├── Some((0, 2)): 25/41 ≈ 0.610
      ├── Some((0, 3)): 24/40 ≈ 0.600
      ├── Some((0, 4)): 22/37 ≈ 0.595
      ├── Some((0, 6)): 32/48 ≈ 0.667
      ├── Some((0, 7)): 17/32 ≈ 0.531
      └── Some((0, 8)): 22/37 ≈ 0.595
    ├── Some((2, 1)): 76/155 ≈ 0.490
      ├── Some((1, 0)): 5/13 ≈ 0.385
      ├── Some((1, 1)): 6/15 ≈ 0.400
      ├── Some((1, 2)): 8/17 ≈ 0.471
      ├── Some((1, 3)): 16/25 ≈ 0.640
      ├── Some((1, 4)): 12/21 ≈ 0.571
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 5/13 ≈ 0.385
      ├── Some((1, 7)): 5/13 ≈ 0.385
      └── Some((1, 8)): 7/16 ≈ 0.438
    ├── Some((2, 2)): 125/228 ≈ 0.548
      ├── Some((2, 0)): 17/30 ≈ 0.567
      ├── Some((2, 1)): 7/19 ≈ 0.368
      ├── Some((2, 3)): 7/19 ≈ 0.368
      ├── Some((2, 4)): 17/30 ≈ 0.567
      ├── Some((2, 5)): 18/31 ≈ 0.581
      ├── Some((2, 6)): 17/30 ≈ 0.567
      ├── Some((2, 7)): 18/31 ≈ 0.581
      └── Some((2, 8)): 23/37 ≈ 0.622
    ├── Some((2, 3)): 110/206 ≈ 0.534
      ├── Some((3, 0)): 10/20 ≈ 0.500
      ├── Some((3, 1)): 14/25 ≈ 0.560
      ├── Some((3, 2)): 17/28 ≈ 0.607
      ├── Some((3, 3)): 17/28 ≈ 0.607
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 5/14 ≈ 0.357
      ├── Some((3, 6)): 12/23 ≈ 0.522
      ├── Some((3, 7)): 13/24 ≈ 0.542
      └── Some((3, 8)): 14/25 ≈ 0.560
    ├── Some((2, 4)): 65/138 ≈ 0.471
      ├── Some((4, 0)): 5/13 ≈ 0.385
      ├── Some((4, 1)): 8/16 ≈ 0.500
      ├── Some((4, 2)): 9/17 ≈ 0.529
      ├── Some((4, 3)): 7/15 ≈ 0.467
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 5/13 ≈ 0.385
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 11/19 ≈ 0.579
    ├── Some((2, 5)): 70/146 ≈ 0.479
      ├── Some((5, 0)): 5/14 ≈ 0.357
      ├── Some((5, 1)): 7/16 ≈ 0.438
      ├── Some((5, 3)): 7/16 ≈ 0.438
      ├── Some((5, 4)): 5/14 ≈ 0.357
      ├── Some((5, 5)): 9/19 ≈ 0.474
      ├── Some((5, 6)): 23/34 ≈ 0.676
      ├── Some((5, 7)): 7/16 ≈ 0.438
      └── Some((5, 8)): 7/16 ≈ 0.438
    ├── Some((2, 6)): 125/228 ≈ 0.548
      ├── Some((6, 0)): 10/21 ≈ 0.476
      ├── Some((6, 1)): 10/21 ≈ 0.476
      ├── Some((6, 2)): 8/19 ≈ 0.421
      ├── Some((6, 3)): 14/26 ≈ 0.538
      ├── Some((6, 4)): 17/29 ≈ 0.586
      ├── Some((6, 5)): 27/39 ≈ 0.692
      ├── Some((6, 6)): 9/20 ≈ 0.450
      ├── Some((6, 7)): 20/32 ≈ 0.625
      └── Some((6, 8)): 9/20 ≈ 0.450
    ├── Some((2, 7)): 113/210 ≈ 0.538
      ├── Some((7, 0)): 14/25 ≈ 0.560
      ├── Some((7, 1)): 6/16 ≈ 0.375
      ├── Some((7, 2)): 17/28 ≈ 0.607
      ├── Some((7, 3)): 15/26 ≈ 0.577
      ├── Some((7, 4)): 13/24 ≈ 0.542
      ├── Some((7, 5)): 18/29 ≈ 0.621
      ├── Some((7, 6)): 9/20 ≈ 0.450
      ├── Some((7, 7)): 6/16 ≈ 0.375
      └── Some((7, 8)): 14/25 ≈ 0.560
    └── Some((2, 8)): 117/216 ≈ 0.542
      ├── Some((8, 0)): 22/34 ≈ 0.647
      ├── Some((8, 1)): 14/25 ≈ 0.560
      ├── Some((8, 2)): 17/29 ≈ 0.586
      ├── Some((8, 3)): 5/15 ≈ 0.333
      ├── Some((8, 4)): 7/17 ≈ 0.412
      ├── Some((8, 5)): 3/12 ≈ 0.250
      ├── Some((8, 6)): 12/23 ≈ 0.522
      ├── Some((8, 7)): 17/29 ≈ 0.586
      └── Some((8, 8)): 19/31 ≈ 0.613
  ├── Some((5, 3)): 608/1199 ≈ 0.507
    ├── Some((3, 0)): 104/186 ≈ 0.559
      ├── Some((0, 0)): 11/21 ≈ 0.524
      ├── Some((0, 1)): 14/24 ≈ 0.583
      ├── Some((0, 2)): 12/22 ≈ 0.545
      ├── Some((0, 3)): 19/30 ≈ 0.633
      ├── Some((0, 4)): 13/23 ≈ 0.565
      ├── Some((0, 6)): 14/25 ≈ 0.560
      ├── Some((0, 7)): 17/28 ≈ 0.607
      └── Some((0, 8)): 3/12 ≈ 0.250
    ├── Some((3, 1)): 77/147 ≈ 0.524
      ├── Some((1, 0)): 3/10 ≈ 0.300
      ├── Some((1, 1)): 18/26 ≈ 0.692
      ├── Some((1, 2)): 8/16 ≈ 0.500
      ├── Some((1, 3)): 7/15 ≈ 0.467
      ├── Some((1, 4)): 2/9 ≈ 0.222
      ├── Some((1, 5)): 10/18 ≈ 0.556
      ├── Some((1, 6)): 9/17 ≈ 0.529
      ├── Some((1, 7)): 5/13 ≈ 0.385
      └── Some((1, 8)): 14/22 ≈ 0.636
    ├── Some((3, 2)): 69/136 ≈ 0.507
      ├── Some((2, 0)): 7/15 ≈ 0.467
      ├── Some((2, 1)): 16/24 ≈ 0.667
      ├── Some((2, 2)): 2/9 ≈ 0.222
      ├── Some((2, 3)): 3/10 ≈ 0.300
      ├── Some((2, 4)): 4/11 ≈ 0.364
      ├── Some((2, 5)): 3/10 ≈ 0.300
      ├── Some((2, 6)): 15/23 ≈ 0.652
      ├── Some((2, 7)): 12/20 ≈ 0.600
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((3, 3)): 73/142 ≈ 0.514
      ├── Some((3, 0)): 15/24 ≈ 0.625
      ├── Some((3, 1)): 10/19 ≈ 0.526
      ├── Some((3, 2)): 7/16 ≈ 0.438
      ├── Some((3, 4)): 3/11 ≈ 0.273
      ├── Some((3, 5)): 14/23 ≈ 0.609
      ├── Some((3, 6)): 11/20 ≈ 0.550
      ├── Some((3, 7)): 11/20 ≈ 0.550
      └── Some((3, 8)): 1/8 ≈ 0.125
    ├── Some((3, 4)): 93/170 ≈ 0.547
      ├── Some((4, 0)): 13/22 ≈ 0.591
      ├── Some((4, 1)): 13/22 ≈ 0.591
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 10/18 ≈ 0.556
      ├── Some((4, 4)): 8/16 ≈ 0.500
      ├── Some((4, 5)): 11/20 ≈ 0.550
      ├── Some((4, 6)): 17/26 ≈ 0.654
      ├── Some((4, 7)): 6/14 ≈ 0.429
      └── Some((4, 8)): 8/16 ≈ 0.500
    ├── Some((3, 5)): 62/125 ≈ 0.496
      ├── Some((5, 0)): 2/9 ≈ 0.222
      ├── Some((5, 1)): 11/19 ≈ 0.579
      ├── Some((5, 2)): 15/23 ≈ 0.652
      ├── Some((5, 4)): 3/10 ≈ 0.300
      ├── Some((5, 5)): 3/11 ≈ 0.273
      ├── Some((5, 6)): 14/22 ≈ 0.636
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((3, 6)): 40/92 ≈ 0.435
      ├── Some((6, 0)): 11/16 ≈ 0.688
      ├── Some((6, 1)): 2/8 ≈ 0.250
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 1/6 ≈ 0.167
      ├── Some((6, 4)): 2/8 ≈ 0.250
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 8/14 ≈ 0.571
      └── Some((6, 8)): 2/8 ≈ 0.250
    ├── Some((3, 7)): 37/88 ≈ 0.420
      ├── Some((7, 0)): 5/11 ≈ 0.455
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 6/12 ≈ 0.500
      ├── Some((7, 7)): 6/12 ≈ 0.500
      └── Some((7, 8)): 1/6 ≈ 0.167
    └── Some((3, 8)): 53/112 ≈ 0.473
      ├── Some((8, 0)): 10/16 ≈ 0.625
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 7/14 ≈ 0.500
      ├── Some((8, 5)): 9/16 ≈ 0.562
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 2/8 ≈ 0.250
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((5, 4)): 881/1670 ≈ 0.528
    ├── Some((4, 0)): 100/189 ≈ 0.529
      ├── Some((0, 0)): 11/22 ≈ 0.500
      ├── Some((0, 1)): 9/20 ≈ 0.450
      ├── Some((0, 2)): 12/23 ≈ 0.522
      ├── Some((0, 3)): 11/22 ≈ 0.500
      ├── Some((0, 4)): 21/33 ≈ 0.636
      ├── Some((0, 6)): 13/24 ≈ 0.542
      ├── Some((0, 7)): 12/23 ≈ 0.522
      └── Some((0, 8)): 10/21 ≈ 0.476
    ├── Some((4, 1)): 147/257 ≈ 0.572
      ├── Some((1, 0)): 25/38 ≈ 0.658
      ├── Some((1, 1)): 18/31 ≈ 0.581
      ├── Some((1, 2)): 24/37 ≈ 0.649
      ├── Some((1, 3)): 21/34 ≈ 0.618
      ├── Some((1, 4)): 25/38 ≈ 0.658
      ├── Some((1, 5)): 16/28 ≈ 0.571
      ├── Some((1, 6)): 4/14 ≈ 0.286
      ├── Some((1, 7)): 5/16 ≈ 0.312
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((4, 2)): 99/187 ≈ 0.529
      ├── Some((2, 0)): 9/19 ≈ 0.474
      ├── Some((2, 1)): 14/24 ≈ 0.583
      ├── Some((2, 2)): 10/20 ≈ 0.500
      ├── Some((2, 3)): 3/12 ≈ 0.250
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 16/26 ≈ 0.615
      ├── Some((2, 6)): 15/25 ≈ 0.600
      ├── Some((2, 7)): 4/13 ≈ 0.308
      └── Some((2, 8)): 21/32 ≈ 0.656
    ├── Some((4, 3)): 88/171 ≈ 0.515
      ├── Some((3, 0)): 6/15 ≈ 0.400
      ├── Some((3, 1)): 10/19 ≈ 0.526
      ├── Some((3, 2)): 12/21 ≈ 0.571
      ├── Some((3, 3)): 18/28 ≈ 0.643
      ├── Some((3, 4)): 14/24 ≈ 0.583
      ├── Some((3, 5)): 8/17 ≈ 0.471
      ├── Some((3, 6)): 8/17 ≈ 0.471
      ├── Some((3, 7)): 8/17 ≈ 0.471
      └── Some((3, 8)): 4/12 ≈ 0.333
    ├── Some((4, 4)): 109/202 ≈ 0.540
      ├── Some((4, 0)): 7/18 ≈ 0.389
      ├── Some((4, 1)): 31/44 ≈ 0.705
      ├── Some((4, 2)): 13/25 ≈ 0.520
      ├── Some((4, 3)): 14/26 ≈ 0.538
      ├── Some((4, 5)): 4/14 ≈ 0.286
      ├── Some((4, 6)): 7/18 ≈ 0.389
      ├── Some((4, 7)): 18/30 ≈ 0.600
      └── Some((4, 8)): 14/26 ≈ 0.538
    ├── Some((4, 5)): 90/174 ≈ 0.517
      ├── Some((5, 0)): 18/29 ≈ 0.621
      ├── Some((5, 1)): 11/22 ≈ 0.500
      ├── Some((5, 2)): 7/17 ≈ 0.412
      ├── Some((5, 3)): 3/12 ≈ 0.250
      ├── Some((5, 5)): 12/23 ≈ 0.522
      ├── Some((5, 6)): 10/20 ≈ 0.500
      ├── Some((5, 7)): 15/26 ≈ 0.577
      └── Some((5, 8)): 13/24 ≈ 0.542
    ├── Some((4, 6)): 95/181 ≈ 0.525
      ├── Some((6, 0)): 10/20 ≈ 0.500
      ├── Some((6, 1)): 16/26 ≈ 0.615
      ├── Some((6, 2)): 11/21 ≈ 0.524
      ├── Some((6, 3)): 9/18 ≈ 0.500
      ├── Some((6, 4)): 15/25 ≈ 0.600
      ├── Some((6, 5)): 7/16 ≈ 0.438
      ├── Some((6, 6)): 5/14 ≈ 0.357
      ├── Some((6, 7)): 8/17 ≈ 0.471
      └── Some((6, 8)): 13/23 ≈ 0.565
    ├── Some((4, 7)): 69/143 ≈ 0.483
      ├── Some((7, 0)): 1/8 ≈ 0.125
      ├── Some((7, 1)): 16/25 ≈ 0.640
      ├── Some((7, 2)): 4/12 ≈ 0.333
      ├── Some((7, 3)): 6/14 ≈ 0.429
      ├── Some((7, 4)): 6/14 ≈ 0.429
      ├── Some((7, 5)): 11/20 ≈ 0.550
      ├── Some((7, 6)): 6/14 ≈ 0.429
      ├── Some((7, 7)): 10/19 ≈ 0.526
      └── Some((7, 8)): 8/16 ≈ 0.500
    └── Some((4, 8)): 84/165 ≈ 0.509
      ├── Some((8, 0)): 8/17 ≈ 0.471
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 4/12 ≈ 0.333
      ├── Some((8, 4)): 13/22 ≈ 0.591
      ├── Some((8, 5)): 15/24 ≈ 0.625
      ├── Some((8, 6)): 15/24 ≈ 0.625
      ├── Some((8, 7)): 6/15 ≈ 0.400
      └── Some((8, 8)): 8/17 ≈ 0.471
  ├── Some((5, 5)): 1158/2142 ≈ 0.541
    ├── Some((5, 0)): 136/255 ≈ 0.533
      ├── Some((0, 0)): 8/21 ≈ 0.381
      ├── Some((0, 1)): 22/38 ≈ 0.579
      ├── Some((0, 2)): 25/41 ≈ 0.610
      ├── Some((0, 3)): 10/24 ≈ 0.417
      ├── Some((0, 4)): 11/25 ≈ 0.440
      ├── Some((0, 6)): 26/42 ≈ 0.619
      ├── Some((0, 7)): 15/30 ≈ 0.500
      └── Some((0, 8)): 18/33 ≈ 0.545
    ├── Some((5, 1)): 183/325 ≈ 0.563
      ├── Some((1, 0)): 33/51 ≈ 0.647
      ├── Some((1, 1)): 14/29 ≈ 0.483
      ├── Some((1, 2)): 6/19 ≈ 0.316
      ├── Some((1, 3)): 15/30 ≈ 0.500
      ├── Some((1, 4)): 31/48 ≈ 0.646
      ├── Some((1, 5)): 11/25 ≈ 0.440
      ├── Some((1, 6)): 25/42 ≈ 0.595
      ├── Some((1, 7)): 27/44 ≈ 0.614
      └── Some((1, 8)): 20/36 ≈ 0.556
    ├── Some((5, 2)): 91/187 ≈ 0.487
      ├── Some((2, 0)): 8/18 ≈ 0.444
      ├── Some((2, 1)): 5/15 ≈ 0.333
      ├── Some((2, 2)): 6/16 ≈ 0.375
      ├── Some((2, 3)): 18/30 ≈ 0.600
      ├── Some((2, 4)): 10/21 ≈ 0.476
      ├── Some((2, 5)): 17/28 ≈ 0.607
      ├── Some((2, 6)): 4/14 ≈ 0.286
      ├── Some((2, 7)): 17/28 ≈ 0.607
      └── Some((2, 8)): 6/16 ≈ 0.375
    ├── Some((5, 3)): 224/385 ≈ 0.582
      ├── Some((3, 0)): 33/52 ≈ 0.635
      ├── Some((3, 1)): 12/27 ≈ 0.444
      ├── Some((3, 2)): 36/55 ≈ 0.655
      ├── Some((3, 3)): 30/49 ≈ 0.612
      ├── Some((3, 4)): 29/48 ≈ 0.604
      ├── Some((3, 5)): 12/28 ≈ 0.429
      ├── Some((3, 6)): 13/29 ≈ 0.448
      ├── Some((3, 7)): 20/37 ≈ 0.541
      └── Some((3, 8)): 39/59 ≈ 0.661
    ├── Some((5, 4)): 169/305 ≈ 0.554
      ├── Some((4, 0)): 8/21 ≈ 0.381
      ├── Some((4, 1)): 20/35 ≈ 0.571
      ├── Some((4, 2)): 36/53 ≈ 0.679
      ├── Some((4, 3)): 12/26 ≈ 0.462
      ├── Some((4, 4)): 26/42 ≈ 0.619
      ├── Some((4, 5)): 15/30 ≈ 0.500
      ├── Some((4, 6)): 20/36 ≈ 0.556
      ├── Some((4, 7)): 15/30 ≈ 0.500
      └── Some((4, 8)): 16/31 ≈ 0.516
    ├── Some((5, 6)): 101/202 ≈ 0.500
      ├── Some((6, 0)): 3/13 ≈ 0.231
      ├── Some((6, 1)): 20/32 ≈ 0.625
      ├── Some((6, 2)): 13/24 ≈ 0.542
      ├── Some((6, 3)): 15/27 ≈ 0.556
      ├── Some((6, 4)): 5/15 ≈ 0.333
      ├── Some((6, 5)): 9/20 ≈ 0.450
      ├── Some((6, 6)): 18/30 ≈ 0.600
      ├── Some((6, 7)): 7/18 ≈ 0.389
      └── Some((6, 8)): 11/22 ≈ 0.500
    ├── Some((5, 7)): 145/269 ≈ 0.539
      ├── Some((7, 0)): 25/40 ≈ 0.625
      ├── Some((7, 1)): 7/19 ≈ 0.368
      ├── Some((7, 2)): 17/31 ≈ 0.548
      ├── Some((7, 3)): 17/31 ≈ 0.548
      ├── Some((7, 4)): 23/38 ≈ 0.605
      ├── Some((7, 5)): 14/28 ≈ 0.500
      ├── Some((7, 6)): 12/25 ≈ 0.480
      ├── Some((7, 7)): 10/23 ≈ 0.435
      └── Some((7, 8)): 19/33 ≈ 0.576
    └── Some((5, 8)): 108/213 ≈ 0.507
      ├── Some((8, 0)): 14/26 ≈ 0.538
      ├── Some((8, 1)): 11/23 ≈ 0.478
      ├── Some((8, 2)): 14/26 ≈ 0.538
      ├── Some((8, 3)): 4/14 ≈ 0.286
      ├── Some((8, 4)): 17/29 ≈ 0.586
      ├── Some((8, 5)): 11/23 ≈ 0.478
      ├── Some((8, 6)): 10/21 ≈ 0.476
      ├── Some((8, 7)): 13/25 ≈ 0.520
      └── Some((8, 8)): 13/25 ≈ 0.520
  ├── Some((5, 6)): 524/1052 ≈ 0.498
    ├── Some((6, 0)): 35/83 ≈ 0.422
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 1/6 ≈ 0.167
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 12/18 ≈ 0.667
      ├── Some((0, 6)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 1/7 ≈ 0.143
    ├── Some((6, 1)): 62/123 ≈ 0.504
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 1)): 8/15 ≈ 0.533
      ├── Some((1, 2)): 11/18 ≈ 0.611
      ├── Some((1, 3)): 6/13 ≈ 0.462
      ├── Some((1, 4)): 14/20 ≈ 0.700
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 1/7 ≈ 0.143
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 7/14 ≈ 0.500
    ├── Some((6, 2)): 96/172 ≈ 0.558
      ├── Some((2, 0)): 18/27 ≈ 0.667
      ├── Some((2, 1)): 13/22 ≈ 0.591
      ├── Some((2, 2)): 6/14 ≈ 0.429
      ├── Some((2, 3)): 12/21 ≈ 0.571
      ├── Some((2, 4)): 16/25 ≈ 0.640
      ├── Some((2, 5)): 7/15 ≈ 0.467
      ├── Some((2, 6)): 4/12 ≈ 0.333
      ├── Some((2, 7)): 10/18 ≈ 0.556
      └── Some((2, 8)): 9/17 ≈ 0.529
    ├── Some((6, 3)): 57/116 ≈ 0.491
      ├── Some((3, 0)): 6/13 ≈ 0.462
      ├── Some((3, 1)): 10/16 ≈ 0.625
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 4/10 ≈ 0.400
      ├── Some((3, 4)): 3/9 ≈ 0.333
      ├── Some((3, 5)): 10/17 ≈ 0.588
      ├── Some((3, 6)): 9/16 ≈ 0.562
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 9/16 ≈ 0.562
    ├── Some((6, 4)): 30/75 ≈ 0.400
      ├── Some((4, 0)): 6/11 ≈ 0.545
      ├── Some((4, 1)): 1/6 ≈ 0.167
      ├── Some((4, 2)): 7/12 ≈ 0.583
      ├── Some((4, 3)): 2/7 ≈ 0.286
      ├── Some((4, 4)): 0/4 ≈ 0.000
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 7/12 ≈ 0.583
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((6, 5)): 56/114 ≈ 0.491
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 1/7 ≈ 0.143
      ├── Some((5, 4)): 4/11 ≈ 0.364
      ├── Some((5, 5)): 10/18 ≈ 0.556
      ├── Some((5, 7)): 15/22 ≈ 0.682
      └── Some((5, 8)): 4/11 ≈ 0.364
    ├── Some((6, 6)): 62/123 ≈ 0.504
      ├── Some((6, 0)): 14/22 ≈ 0.636
      ├── Some((6, 1)): 13/21 ≈ 0.619
      ├── Some((6, 2)): 8/16 ≈ 0.500
      ├── Some((6, 3)): 10/18 ≈ 0.556
      ├── Some((6, 4)): 0/6 ≈ 0.000
      ├── Some((6, 5)): 6/13 ≈ 0.462
      ├── Some((6, 7)): 2/9 ≈ 0.222
      └── Some((6, 8)): 9/17 ≈ 0.529
    ├── Some((6, 7)): 96/172 ≈ 0.558
      ├── Some((7, 0)): 11/19 ≈ 0.579
      ├── Some((7, 1)): 9/17 ≈ 0.529
      ├── Some((7, 2)): 12/21 ≈ 0.571
      ├── Some((7, 3)): 12/21 ≈ 0.571
      ├── Some((7, 4)): 10/18 ≈ 0.556
      ├── Some((7, 5)): 9/17 ≈ 0.529
      ├── Some((7, 6)): 9/17 ≈ 0.529
      ├── Some((7, 7)): 11/20 ≈ 0.550
      └── Some((7, 8)): 12/21 ≈ 0.571
    └── Some((6, 8)): 29/73 ≈ 0.397
      ├── Some((8, 0)): 0/4 ≈ 0.000
      ├── Some((8, 1)): 4/9 ≈ 0.444
      ├── Some((8, 2)): 4/9 ≈ 0.444
      ├── Some((8, 3)): 1/6 ≈ 0.167
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 6/10 ≈ 0.600
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 5/10 ≈ 0.500
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((5, 7)): 578/1147 ≈ 0.504
    ├── Some((7, 0)): 37/87 ≈ 0.425
      ├── Some((0, 0)): 6/12 ≈ 0.500
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 1/7 ≈ 0.143
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 6/13 ≈ 0.462
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((7, 1)): 79/149 ≈ 0.530
      ├── Some((1, 0)): 11/19 ≈ 0.579
      ├── Some((1, 1)): 11/19 ≈ 0.579
      ├── Some((1, 2)): 8/16 ≈ 0.500
      ├── Some((1, 3)): 4/11 ≈ 0.364
      ├── Some((1, 4)): 15/23 ≈ 0.652
      ├── Some((1, 5)): 13/21 ≈ 0.619
      ├── Some((1, 6)): 2/9 ≈ 0.222
      ├── Some((1, 7)): 8/16 ≈ 0.500
      └── Some((1, 8)): 7/14 ≈ 0.500
    ├── Some((7, 2)): 41/93 ≈ 0.441
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 6/12 ≈ 0.500
      ├── Some((2, 2)): 10/15 ≈ 0.667
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 7/13 ≈ 0.538
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 0/5 ≈ 0.000
    ├── Some((7, 3)): 89/164 ≈ 0.543
      ├── Some((3, 0)): 9/17 ≈ 0.529
      ├── Some((3, 1)): 14/23 ≈ 0.609
      ├── Some((3, 2)): 9/17 ≈ 0.529
      ├── Some((3, 3)): 14/23 ≈ 0.609
      ├── Some((3, 4)): 20/29 ≈ 0.690
      ├── Some((3, 5)): 6/14 ≈ 0.429
      ├── Some((3, 6)): 7/15 ≈ 0.467
      ├── Some((3, 7)): 2/10 ≈ 0.200
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((7, 4)): 58/119 ≈ 0.487
      ├── Some((4, 0)): 3/10 ≈ 0.300
      ├── Some((4, 1)): 1/7 ≈ 0.143
      ├── Some((4, 2)): 13/20 ≈ 0.650
      ├── Some((4, 3)): 2/9 ≈ 0.222
      ├── Some((4, 4)): 8/15 ≈ 0.533
      ├── Some((4, 5)): 8/15 ≈ 0.533
      ├── Some((4, 6)): 1/7 ≈ 0.143
      ├── Some((4, 7)): 3/10 ≈ 0.300
      └── Some((4, 8)): 18/25 ≈ 0.720
    ├── Some((7, 5)): 58/119 ≈ 0.487
      ├── Some((5, 0)): 4/11 ≈ 0.364
      ├── Some((5, 1)): 11/19 ≈ 0.579
      ├── Some((5, 2)): 3/10 ≈ 0.300
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 13/21 ≈ 0.619
      ├── Some((5, 5)): 5/13 ≈ 0.385
      ├── Some((5, 6)): 11/19 ≈ 0.579
      └── Some((5, 8)): 3/10 ≈ 0.300
    ├── Some((7, 6)): 69/135 ≈ 0.511
      ├── Some((6, 0)): 2/9 ≈ 0.222
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 3)): 13/21 ≈ 0.619
      ├── Some((6, 4)): 14/22 ≈ 0.636
      ├── Some((6, 5)): 13/21 ≈ 0.619
      ├── Some((6, 6)): 6/13 ≈ 0.462
      ├── Some((6, 7)): 4/11 ≈ 0.364
      └── Some((6, 8)): 2/9 ≈ 0.222
    ├── Some((7, 7)): 115/201 ≈ 0.572
      ├── Some((7, 0)): 30/42 ≈ 0.714
      ├── Some((7, 1)): 25/37 ≈ 0.676
      ├── Some((7, 2)): 16/27 ≈ 0.593
      ├── Some((7, 3)): 3/12 ≈ 0.250
      ├── Some((7, 4)): 15/26 ≈ 0.577
      ├── Some((7, 5)): 12/23 ≈ 0.522
      ├── Some((7, 6)): 4/13 ≈ 0.308
      └── Some((7, 8)): 9/20 ≈ 0.450
    └── Some((7, 8)): 32/79 ≈ 0.405
      ├── Some((8, 0)): 1/6 ≈ 0.167
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 4/9 ≈ 0.444
      ├── Some((8, 3)): 7/12 ≈ 0.583
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 0/5 ≈ 0.000
  └── Some((5, 8)): 608/1199 ≈ 0.507
    ├── Some((8, 0)): 40/92 ≈ 0.435
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 2/8 ≈ 0.250
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 8/15 ≈ 0.533
      └── Some((0, 8)): 4/10 ≈ 0.400
    ├── Some((8, 1)): 54/114 ≈ 0.474
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 6/13 ≈ 0.462
      ├── Some((1, 2)): 9/16 ≈ 0.562
      ├── Some((1, 3)): 1/7 ≈ 0.143
      ├── Some((1, 4)): 10/16 ≈ 0.625
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 8/15 ≈ 0.533
    ├── Some((8, 2)): 108/192 ≈ 0.562
      ├── Some((2, 0)): 12/22 ≈ 0.545
      ├── Some((2, 1)): 4/13 ≈ 0.308
      ├── Some((2, 2)): 7/16 ≈ 0.438
      ├── Some((2, 3)): 10/19 ≈ 0.526
      ├── Some((2, 4)): 19/29 ≈ 0.655
      ├── Some((2, 5)): 3/11 ≈ 0.273
      ├── Some((2, 6)): 22/32 ≈ 0.688
      ├── Some((2, 7)): 8/17 ≈ 0.471
      └── Some((2, 8)): 22/32 ≈ 0.688
    ├── Some((8, 3)): 63/127 ≈ 0.496
      ├── Some((3, 0)): 4/11 ≈ 0.364
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 6/13 ≈ 0.462
      ├── Some((3, 3)): 5/12 ≈ 0.417
      ├── Some((3, 4)): 18/25 ≈ 0.720
      ├── Some((3, 5)): 8/15 ≈ 0.533
      ├── Some((3, 6)): 3/10 ≈ 0.300
      ├── Some((3, 7)): 5/12 ≈ 0.417
      └── Some((3, 8)): 9/16 ≈ 0.562
    ├── Some((8, 4)): 60/123 ≈ 0.488
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 3/10 ≈ 0.300
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 5/12 ≈ 0.417
      ├── Some((4, 4)): 9/16 ≈ 0.562
      ├── Some((4, 5)): 10/17 ≈ 0.588
      ├── Some((4, 6)): 6/13 ≈ 0.462
      ├── Some((4, 7)): 14/21 ≈ 0.667
      └── Some((4, 8)): 3/10 ≈ 0.300
    ├── Some((8, 5)): 79/150 ≈ 0.527
      ├── Some((5, 0)): 7/15 ≈ 0.467
      ├── Some((5, 1)): 8/17 ≈ 0.471
      ├── Some((5, 2)): 8/17 ≈ 0.471
      ├── Some((5, 3)): 11/20 ≈ 0.550
      ├── Some((5, 4)): 15/24 ≈ 0.625
      ├── Some((5, 5)): 19/28 ≈ 0.679
      ├── Some((5, 6)): 3/11 ≈ 0.273
      └── Some((5, 7)): 8/17 ≈ 0.471
    ├── Some((8, 6)): 79/150 ≈ 0.527
      ├── Some((6, 0)): 9/17 ≈ 0.529
      ├── Some((6, 1)): 7/15 ≈ 0.467
      ├── Some((6, 2)): 8/16 ≈ 0.500
      ├── Some((6, 3)): 3/10 ≈ 0.300
      ├── Some((6, 4)): 10/18 ≈ 0.556
      ├── Some((6, 5)): 15/23 ≈ 0.652
      ├── Some((6, 6)): 7/15 ≈ 0.467
      ├── Some((6, 7)): 8/16 ≈ 0.500
      └── Some((6, 8)): 11/19 ≈ 0.579
    ├── Some((8, 7)): 30/77 ≈ 0.390
      ├── Some((7, 0)): 2/7 ≈ 0.286
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 4/9 ≈ 0.444
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 4)): 5/11 ≈ 0.455
      ├── Some((7, 5)): 3/8 ≈ 0.375
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((8, 8)): 95/173 ≈ 0.549
      ├── Some((8, 0)): 15/25 ≈ 0.600
      ├── Some((8, 1)): 19/29 ≈ 0.655
      ├── Some((8, 2)): 7/16 ≈ 0.438
      ├── Some((8, 3)): 6/15 ≈ 0.400
      ├── Some((8, 4)): 15/25 ≈ 0.600
      ├── Some((8, 5)): 13/23 ≈ 0.565
      ├── Some((8, 6)): 10/20 ≈ 0.500
      └── Some((8, 7)): 9/19 ≈ 0.474
├── Some((0, 6)): 5944/11479 ≈ 0.518
  ├── Some((6, 0)): 338/714 ≈ 0.473
    ├── Some((0, 0)): 50/100 ≈ 0.500
      ├── Some((0, 1)): 5/12 ≈ 0.417
      ├── Some((0, 2)): 9/16 ≈ 0.562
      ├── Some((0, 3)): 5/12 ≈ 0.417
      ├── Some((0, 4)): 14/21 ≈ 0.667
      ├── Some((0, 5)): 1/7 ≈ 0.143
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 11/19 ≈ 0.579
    ├── Some((0, 1)): 56/109 ≈ 0.514
      ├── Some((1, 0)): 10/16 ≈ 0.625
      ├── Some((1, 1)): 0/5 ≈ 0.000
      ├── Some((1, 2)): 8/14 ≈ 0.571
      ├── Some((1, 3)): 9/15 ≈ 0.600
      ├── Some((1, 4)): 8/14 ≈ 0.571
      ├── Some((1, 5)): 6/12 ≈ 0.500
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 6/12 ≈ 0.500
    ├── Some((0, 2)): 32/74 ≈ 0.432
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 5/9 ≈ 0.556
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 4/8 ≈ 0.500
      ├── Some((2, 6)): 4/9 ≈ 0.444
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 6/10 ≈ 0.600
    ├── Some((0, 3)): 44/92 ≈ 0.478
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 8/13 ≈ 0.615
      ├── Some((3, 2)): 9/14 ≈ 0.643
      ├── Some((3, 3)): 8/13 ≈ 0.615
      ├── Some((3, 4)): 6/12 ≈ 0.500
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 1/6 ≈ 0.167
      ├── Some((3, 7)): 1/6 ≈ 0.167
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((0, 4)): 42/89 ≈ 0.472
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 4/9 ≈ 0.444
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 5/11 ≈ 0.455
      ├── Some((4, 5)): 7/12 ≈ 0.583
      ├── Some((4, 6)): 6/11 ≈ 0.545
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 4/9 ≈ 0.444
    ├── Some((0, 5)): 42/89 ≈ 0.472
      ├── Some((5, 0)): 4/9 ≈ 0.444
      ├── Some((5, 1)): 8/13 ≈ 0.615
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 2/7 ≈ 0.286
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 2/7 ≈ 0.286
      ├── Some((5, 7)): 9/14 ≈ 0.643
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((0, 7)): 42/89 ≈ 0.472
      ├── Some((7, 0)): 3/8 ≈ 0.375
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 2)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 7/12 ≈ 0.583
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 5/10 ≈ 0.500
      ├── Some((7, 6)): 8/13 ≈ 0.615
      ├── Some((7, 7)): 0/5 ≈ 0.000
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((0, 8)): 30/71 ≈ 0.423
      ├── Some((8, 0)): 0/4 ≈ 0.000
      ├── Some((8, 1)): 7/11 ≈ 0.636
      ├── Some((8, 2)): 4/9 ≈ 0.444
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 5/10 ≈ 0.500
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 1/5 ≈ 0.200
      ├── Some((8, 7)): 4/9 ≈ 0.444
      └── Some((8, 8)): 5/10 ≈ 0.500
  ├── Some((6, 1)): 830/1568 ≈ 0.529
    ├── Some((1, 0)): 130/229 ≈ 0.568
      ├── Some((0, 0)): 15/27 ≈ 0.556
      ├── Some((0, 1)): 29/43 ≈ 0.674
      ├── Some((0, 2)): 6/17 ≈ 0.353
      ├── Some((0, 3)): 15/27 ≈ 0.556
      ├── Some((0, 4)): 15/27 ≈ 0.556
      ├── Some((0, 5)): 7/18 ≈ 0.389
      ├── Some((0, 7)): 25/38 ≈ 0.658
      └── Some((0, 8)): 18/31 ≈ 0.581
    ├── Some((1, 1)): 98/183 ≈ 0.536
      ├── Some((1, 0)): 10/20 ≈ 0.500
      ├── Some((1, 2)): 13/24 ≈ 0.542
      ├── Some((1, 3)): 14/25 ≈ 0.560
      ├── Some((1, 4)): 10/21 ≈ 0.476
      ├── Some((1, 5)): 7/17 ≈ 0.412
      ├── Some((1, 6)): 16/27 ≈ 0.593
      ├── Some((1, 7)): 18/29 ≈ 0.621
      └── Some((1, 8)): 9/19 ≈ 0.474
    ├── Some((1, 2)): 86/165 ≈ 0.521
      ├── Some((2, 0)): 8/16 ≈ 0.500
      ├── Some((2, 1)): 12/21 ≈ 0.571
      ├── Some((2, 2)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 9/18 ≈ 0.500
      ├── Some((2, 4)): 9/18 ≈ 0.500
      ├── Some((2, 5)): 11/20 ≈ 0.550
      ├── Some((2, 6)): 7/15 ≈ 0.467
      ├── Some((2, 7)): 14/23 ≈ 0.609
      └── Some((2, 8)): 9/18 ≈ 0.500
    ├── Some((1, 3)): 65/134 ≈ 0.485
      ├── Some((3, 0)): 6/14 ≈ 0.429
      ├── Some((3, 1)): 13/21 ≈ 0.619
      ├── Some((3, 2)): 1/8 ≈ 0.125
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 6/14 ≈ 0.429
      ├── Some((3, 5)): 2/9 ≈ 0.222
      ├── Some((3, 6)): 3/10 ≈ 0.300
      ├── Some((3, 7)): 18/26 ≈ 0.692
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((1, 4)): 99/184 ≈ 0.538
      ├── Some((4, 0)): 7/16 ≈ 0.438
      ├── Some((4, 1)): 4/13 ≈ 0.308
      ├── Some((4, 2)): 14/24 ≈ 0.583
      ├── Some((4, 3)): 11/20 ≈ 0.550
      ├── Some((4, 4)): 11/20 ≈ 0.550
      ├── Some((4, 5)): 11/21 ≈ 0.524
      ├── Some((4, 6)): 8/17 ≈ 0.471
      ├── Some((4, 7)): 17/27 ≈ 0.630
      └── Some((4, 8)): 15/25 ≈ 0.600
    ├── Some((1, 5)): 97/182 ≈ 0.533
      ├── Some((5, 0)): 8/17 ≈ 0.471
      ├── Some((5, 1)): 6/15 ≈ 0.400
      ├── Some((5, 2)): 15/25 ≈ 0.600
      ├── Some((5, 3)): 16/26 ≈ 0.615
      ├── Some((5, 4)): 8/17 ≈ 0.471
      ├── Some((5, 5)): 4/13 ≈ 0.308
      ├── Some((5, 6)): 12/21 ≈ 0.571
      ├── Some((5, 7)): 8/17 ≈ 0.471
      └── Some((5, 8)): 20/30 ≈ 0.667
    ├── Some((1, 6)): 98/183 ≈ 0.536
      ├── Some((6, 0)): 2/11 ≈ 0.182
      ├── Some((6, 2)): 20/31 ≈ 0.645
      ├── Some((6, 3)): 10/20 ≈ 0.500
      ├── Some((6, 4)): 14/25 ≈ 0.560
      ├── Some((6, 5)): 10/20 ≈ 0.500
      ├── Some((6, 6)): 13/24 ≈ 0.542
      ├── Some((6, 7)): 10/21 ≈ 0.476
      └── Some((6, 8)): 19/30 ≈ 0.633
    ├── Some((1, 7)): 109/199 ≈ 0.548
      ├── Some((7, 0)): 12/22 ≈ 0.545
      ├── Some((7, 1)): 11/21 ≈ 0.524
      ├── Some((7, 2)): 20/31 ≈ 0.645
      ├── Some((7, 3)): 17/28 ≈ 0.607
      ├── Some((7, 4)): 2/11 ≈ 0.182
      ├── Some((7, 5)): 13/23 ≈ 0.565
      ├── Some((7, 6)): 6/15 ≈ 0.400
      ├── Some((7, 7)): 12/22 ≈ 0.545
      └── Some((7, 8)): 15/25 ≈ 0.600
    └── Some((1, 8)): 48/108 ≈ 0.444
      ├── Some((8, 0)): 2/8 ≈ 0.250
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 5/12 ≈ 0.417
      ├── Some((8, 3)): 9/16 ≈ 0.562
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 10/17 ≈ 0.588
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 5/12 ≈ 0.417
  ├── Some((6, 2)): 698/1342 ≈ 0.520
    ├── Some((2, 0)): 91/169 ≈ 0.538
      ├── Some((0, 0)): 6/15 ≈ 0.400
      ├── Some((0, 1)): 6/15 ≈ 0.400
      ├── Some((0, 2)): 9/19 ≈ 0.474
      ├── Some((0, 3)): 14/24 ≈ 0.583
      ├── Some((0, 4)): 16/26 ≈ 0.615
      ├── Some((0, 5)): 14/24 ≈ 0.583
      ├── Some((0, 7)): 20/30 ≈ 0.667
      └── Some((0, 8)): 6/15 ≈ 0.400
    ├── Some((2, 1)): 93/172 ≈ 0.541
      ├── Some((1, 0)): 14/23 ≈ 0.609
      ├── Some((1, 1)): 12/21 ≈ 0.571
      ├── Some((1, 2)): 8/17 ≈ 0.471
      ├── Some((1, 3)): 2/10 ≈ 0.200
      ├── Some((1, 4)): 10/19 ≈ 0.526
      ├── Some((1, 5)): 11/20 ≈ 0.550
      ├── Some((1, 6)): 12/21 ≈ 0.571
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 17/26 ≈ 0.654
    ├── Some((2, 2)): 86/162 ≈ 0.531
      ├── Some((2, 0)): 13/23 ≈ 0.565
      ├── Some((2, 1)): 15/25 ≈ 0.600
      ├── Some((2, 3)): 11/21 ≈ 0.524
      ├── Some((2, 4)): 20/30 ≈ 0.667
      ├── Some((2, 5)): 3/11 ≈ 0.273
      ├── Some((2, 6)): 12/22 ≈ 0.545
      ├── Some((2, 7)): 1/9 ≈ 0.111
      └── Some((2, 8)): 10/20 ≈ 0.500
    ├── Some((2, 3)): 62/126 ≈ 0.492
      ├── Some((3, 0)): 4/11 ≈ 0.364
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 7/14 ≈ 0.500
      ├── Some((3, 3)): 4/11 ≈ 0.364
      ├── Some((3, 4)): 10/17 ≈ 0.588
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 13/20 ≈ 0.650
    ├── Some((2, 4)): 92/170 ≈ 0.541
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 9/18 ≈ 0.500
      ├── Some((4, 2)): 12/21 ≈ 0.571
      ├── Some((4, 3)): 3/11 ≈ 0.273
      ├── Some((4, 4)): 11/20 ≈ 0.550
      ├── Some((4, 5)): 15/24 ≈ 0.625
      ├── Some((4, 6)): 19/28 ≈ 0.679
      ├── Some((4, 7)): 6/14 ≈ 0.429
      └── Some((4, 8)): 9/18 ≈ 0.500
    ├── Some((2, 5)): 80/153 ≈ 0.523
      ├── Some((5, 0)): 16/24 ≈ 0.667
      ├── Some((5, 1)): 7/15 ≈ 0.467
      ├── Some((5, 2)): 4/12 ≈ 0.333
      ├── Some((5, 3)): 4/12 ≈ 0.333
      ├── Some((5, 4)): 8/16 ≈ 0.500
      ├── Some((5, 5)): 6/14 ≈ 0.429
      ├── Some((5, 6)): 12/20 ≈ 0.600
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 15/23 ≈ 0.652
    ├── Some((2, 6)): 87/163 ≈ 0.534
      ├── Some((6, 0)): 15/25 ≈ 0.600
      ├── Some((6, 1)): 10/19 ≈ 0.526
      ├── Some((6, 3)): 7/16 ≈ 0.438
      ├── Some((6, 4)): 7/16 ≈ 0.438
      ├── Some((6, 5)): 7/16 ≈ 0.438
      ├── Some((6, 6)): 14/24 ≈ 0.583
      ├── Some((6, 7)): 13/22 ≈ 0.591
      └── Some((6, 8)): 14/24 ≈ 0.583
    ├── Some((2, 7)): 46/102 ≈ 0.451
      ├── Some((7, 0)): 2/8 ≈ 0.250
      ├── Some((7, 1)): 11/17 ≈ 0.647
      ├── Some((7, 2)): 4/10 ≈ 0.400
      ├── Some((7, 3)): 9/16 ≈ 0.562
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 0/6 ≈ 0.000
      ├── Some((7, 6)): 0/6 ≈ 0.000
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 11/18 ≈ 0.611
    └── Some((2, 8)): 60/124 ≈ 0.484
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 3/10 ≈ 0.300
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 12/20 ≈ 0.600
      ├── Some((8, 4)): 14/22 ≈ 0.636
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 8/15 ≈ 0.533
      ├── Some((8, 7)): 0/6 ≈ 0.000
      └── Some((8, 8)): 3/10 ≈ 0.300
  ├── Some((6, 3)): 877/1647 ≈ 0.532
    ├── Some((3, 0)): 105/194 ≈ 0.541
      ├── Some((0, 0)): 15/26 ≈ 0.577
      ├── Some((0, 1)): 10/21 ≈ 0.476
      ├── Some((0, 2)): 12/23 ≈ 0.522
      ├── Some((0, 3)): 24/36 ≈ 0.667
      ├── Some((0, 4)): 12/23 ≈ 0.522
      ├── Some((0, 5)): 14/25 ≈ 0.560
      ├── Some((0, 7)): 15/27 ≈ 0.556
      └── Some((0, 8)): 3/12 ≈ 0.250
    ├── Some((3, 1)): 130/230 ≈ 0.565
      ├── Some((1, 0)): 16/27 ≈ 0.593
      ├── Some((1, 1)): 9/20 ≈ 0.450
      ├── Some((1, 2)): 12/23 ≈ 0.522
      ├── Some((1, 3)): 5/15 ≈ 0.333
      ├── Some((1, 4)): 15/26 ≈ 0.577
      ├── Some((1, 5)): 12/23 ≈ 0.522
      ├── Some((1, 6)): 18/29 ≈ 0.621
      ├── Some((1, 7)): 26/38 ≈ 0.684
      └── Some((1, 8)): 17/28 ≈ 0.607
    ├── Some((3, 2)): 73/147 ≈ 0.497
      ├── Some((2, 0)): 8/16 ≈ 0.500
      ├── Some((2, 1)): 9/17 ≈ 0.529
      ├── Some((2, 2)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 10/19 ≈ 0.526
      ├── Some((2, 4)): 1/8 ≈ 0.125
      ├── Some((2, 5)): 11/20 ≈ 0.550
      ├── Some((2, 6)): 4/12 ≈ 0.333
      ├── Some((2, 7)): 14/23 ≈ 0.609
      └── Some((2, 8)): 8/16 ≈ 0.500
    ├── Some((3, 3)): 108/199 ≈ 0.543
      ├── Some((3, 0)): 12/23 ≈ 0.522
      ├── Some((3, 1)): 10/21 ≈ 0.476
      ├── Some((3, 2)): 16/28 ≈ 0.571
      ├── Some((3, 4)): 25/37 ≈ 0.676
      ├── Some((3, 5)): 3/13 ≈ 0.231
      ├── Some((3, 6)): 16/28 ≈ 0.571
      ├── Some((3, 7)): 14/26 ≈ 0.538
      └── Some((3, 8)): 11/22 ≈ 0.500
    ├── Some((3, 4)): 92/175 ≈ 0.526
      ├── Some((4, 0)): 3/11 ≈ 0.273
      ├── Some((4, 1)): 28/38 ≈ 0.737
      ├── Some((4, 2)): 13/23 ≈ 0.565
      ├── Some((4, 3)): 12/21 ≈ 0.571
      ├── Some((4, 4)): 6/15 ≈ 0.400
      ├── Some((4, 5)): 7/16 ≈ 0.438
      ├── Some((4, 6)): 6/15 ≈ 0.400
      ├── Some((4, 7)): 9/18 ≈ 0.500
      └── Some((4, 8)): 8/17 ≈ 0.471
    ├── Some((3, 5)): 62/131 ≈ 0.473
      ├── Some((5, 0)): 13/21 ≈ 0.619
      ├── Some((5, 1)): 10/18 ≈ 0.556
      ├── Some((5, 2)): 6/14 ≈ 0.429
      ├── Some((5, 3)): 6/14 ≈ 0.429
      ├── Some((5, 4)): 10/18 ≈ 0.556
      ├── Some((5, 5)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 3/10 ≈ 0.300
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((3, 6)): 88/169 ≈ 0.521
      ├── Some((6, 0)): 15/26 ≈ 0.577
      ├── Some((6, 1)): 14/25 ≈ 0.560
      ├── Some((6, 2)): 10/20 ≈ 0.500
      ├── Some((6, 4)): 19/30 ≈ 0.633
      ├── Some((6, 5)): 8/18 ≈ 0.444
      ├── Some((6, 6)): 5/14 ≈ 0.357
      ├── Some((6, 7)): 5/14 ≈ 0.357
      └── Some((6, 8)): 11/21 ≈ 0.524
    ├── Some((3, 7)): 125/223 ≈ 0.561
      ├── Some((7, 0)): 13/24 ≈ 0.542
      ├── Some((7, 1)): 18/29 ≈ 0.621
      ├── Some((7, 2)): 16/27 ≈ 0.593
      ├── Some((7, 3)): 8/18 ≈ 0.444
      ├── Some((7, 4)): 15/26 ≈ 0.577
      ├── Some((7, 5)): 19/30 ≈ 0.633
      ├── Some((7, 6)): 4/14 ≈ 0.286
      ├── Some((7, 7)): 20/32 ≈ 0.625
      └── Some((7, 8)): 11/22 ≈ 0.500
    └── Some((3, 8)): 94/178 ≈ 0.528
      ├── Some((8, 0)): 14/24 ≈ 0.583
      ├── Some((8, 1)): 5/14 ≈ 0.357
      ├── Some((8, 2)): 3/11 ≈ 0.273
      ├── Some((8, 3)): 10/19 ≈ 0.526
      ├── Some((8, 4)): 6/15 ≈ 0.400
      ├── Some((8, 5)): 9/18 ≈ 0.500
      ├── Some((8, 6)): 11/21 ≈ 0.524
      ├── Some((8, 7)): 19/29 ≈ 0.655
      └── Some((8, 8)): 16/26 ≈ 0.615
  ├── Some((6, 4)): 576/1132 ≈ 0.509
    ├── Some((4, 0)): 36/84 ≈ 0.429
      ├── Some((0, 0)): 4/10 ≈ 0.400
      ├── Some((0, 1)): 9/15 ≈ 0.600
      ├── Some((0, 2)): 2/7 ≈ 0.286
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 2/8 ≈ 0.250
      └── Some((0, 8)): 9/15 ≈ 0.600
    ├── Some((4, 1)): 63/125 ≈ 0.504
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 13/20 ≈ 0.650
      ├── Some((1, 2)): 5/12 ≈ 0.417
      ├── Some((1, 3)): 5/12 ≈ 0.417
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 8/15 ≈ 0.533
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((4, 2)): 52/108 ≈ 0.481
      ├── Some((2, 0)): 3/9 ≈ 0.333
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 13/19 ≈ 0.684
      ├── Some((2, 4)): 8/15 ≈ 0.533
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 10/16 ≈ 0.625
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 3/9 ≈ 0.333
    ├── Some((4, 3)): 86/158 ≈ 0.544
      ├── Some((3, 0)): 4/12 ≈ 0.333
      ├── Some((3, 1)): 9/17 ≈ 0.529
      ├── Some((3, 2)): 7/15 ≈ 0.467
      ├── Some((3, 3)): 6/14 ≈ 0.429
      ├── Some((3, 4)): 21/29 ≈ 0.724
      ├── Some((3, 5)): 13/21 ≈ 0.619
      ├── Some((3, 6)): 7/15 ≈ 0.467
      ├── Some((3, 7)): 11/19 ≈ 0.579
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((4, 4)): 62/123 ≈ 0.504
      ├── Some((4, 0)): 6/13 ≈ 0.462
      ├── Some((4, 1)): 11/19 ≈ 0.579
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 6/14 ≈ 0.429
      ├── Some((4, 6)): 3/10 ≈ 0.300
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 11/19 ≈ 0.579
    ├── Some((4, 5)): 84/155 ≈ 0.542
      ├── Some((5, 0)): 6/14 ≈ 0.429
      ├── Some((5, 1)): 3/10 ≈ 0.300
      ├── Some((5, 2)): 3/10 ≈ 0.300
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 13/21 ≈ 0.619
      ├── Some((5, 5)): 23/31 ≈ 0.742
      ├── Some((5, 6)): 18/26 ≈ 0.692
      ├── Some((5, 7)): 7/15 ≈ 0.467
      └── Some((5, 8)): 4/12 ≈ 0.333
    ├── Some((4, 6)): 62/123 ≈ 0.504
      ├── Some((6, 0)): 4/11 ≈ 0.364
      ├── Some((6, 1)): 13/21 ≈ 0.619
      ├── Some((6, 2)): 12/20 ≈ 0.600
      ├── Some((6, 3)): 11/19 ≈ 0.579
      ├── Some((6, 5)): 5/13 ≈ 0.385
      ├── Some((6, 6)): 3/10 ≈ 0.300
      ├── Some((6, 7)): 1/8 ≈ 0.125
      └── Some((6, 8)): 12/20 ≈ 0.600
    ├── Some((4, 7)): 46/100 ≈ 0.460
      ├── Some((7, 0)): 1/7 ≈ 0.143
      ├── Some((7, 1)): 3/9 ≈ 0.333
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 6/12 ≈ 0.500
      ├── Some((7, 4)): 5/11 ≈ 0.455
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 9/15 ≈ 0.600
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 8/14 ≈ 0.571
    └── Some((4, 8)): 84/155 ≈ 0.542
      ├── Some((8, 0)): 6/14 ≈ 0.429
      ├── Some((8, 1)): 8/16 ≈ 0.500
      ├── Some((8, 2)): 18/26 ≈ 0.692
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 11/19 ≈ 0.579
      ├── Some((8, 5)): 11/19 ≈ 0.579
      ├── Some((8, 6)): 12/20 ≈ 0.600
      ├── Some((8, 7)): 3/10 ≈ 0.300
      └── Some((8, 8)): 7/15 ≈ 0.467
  ├── Some((6, 5)): 484/972 ≈ 0.498
    ├── Some((5, 0)): 76/140 ≈ 0.543
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 13/21 ≈ 0.619
      ├── Some((0, 2)): 16/24 ≈ 0.667
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 8/16 ≈ 0.500
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 7)): 6/13 ≈ 0.462
      └── Some((0, 8)): 8/16 ≈ 0.500
    ├── Some((5, 1)): 49/101 ≈ 0.485
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 3/9 ≈ 0.333
      ├── Some((1, 2)): 1/6 ≈ 0.167
      ├── Some((1, 3)): 8/14 ≈ 0.571
      ├── Some((1, 4)): 7/13 ≈ 0.538
      ├── Some((1, 5)): 9/15 ≈ 0.600
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 1/6 ≈ 0.167
      └── Some((1, 8)): 10/16 ≈ 0.625
    ├── Some((5, 2)): 65/125 ≈ 0.520
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 9/16 ≈ 0.562
      ├── Some((2, 3)): 3/9 ≈ 0.333
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 14/20 ≈ 0.700
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 11/17 ≈ 0.647
    ├── Some((5, 3)): 34/79 ≈ 0.430
      ├── Some((3, 0)): 9/13 ≈ 0.692
      ├── Some((3, 1)): 0/5 ≈ 0.000
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 5/10 ≈ 0.500
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 6/11 ≈ 0.545
      ├── Some((3, 6)): 0/5 ≈ 0.000
      ├── Some((3, 7)): 6/11 ≈ 0.545
      └── Some((3, 8)): 1/6 ≈ 0.167
    ├── Some((5, 4)): 39/87 ≈ 0.448
      ├── Some((4, 0)): 8/13 ≈ 0.615
      ├── Some((4, 1)): 13/18 ≈ 0.722
      ├── Some((4, 2)): 2/7 ≈ 0.286
      ├── Some((4, 3)): 0/5 ≈ 0.000
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((5, 5)): 45/95 ≈ 0.474
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 1/7 ≈ 0.143
      ├── Some((5, 4)): 14/20 ≈ 0.700
      ├── Some((5, 6)): 11/18 ≈ 0.611
      ├── Some((5, 7)): 3/9 ≈ 0.333
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((5, 6)): 53/107 ≈ 0.495
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 8/15 ≈ 0.533
      ├── Some((6, 2)): 10/17 ≈ 0.588
      ├── Some((6, 3)): 1/7 ≈ 0.143
      ├── Some((6, 4)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 11/18 ≈ 0.611
      ├── Some((6, 7)): 10/17 ≈ 0.588
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((5, 7)): 62/120 ≈ 0.517
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 5/12 ≈ 0.417
      ├── Some((7, 3)): 6/13 ≈ 0.462
      ├── Some((7, 4)): 13/19 ≈ 0.684
      ├── Some((7, 5)): 17/23 ≈ 0.739
      ├── Some((7, 6)): 4/11 ≈ 0.364
      ├── Some((7, 7)): 6/13 ≈ 0.462
      └── Some((7, 8)): 3/9 ≈ 0.333
    └── Some((5, 8)): 60/117 ≈ 0.513
      ├── Some((8, 0)): 6/12 ≈ 0.500
      ├── Some((8, 1)): 10/16 ≈ 0.625
      ├── Some((8, 2)): 18/24 ≈ 0.750
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 3/9 ≈ 0.333
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 3/9 ≈ 0.333
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((6, 6)): 593/1161 ≈ 0.511
    ├── Some((6, 0)): 40/94 ≈ 0.426
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 0/6 ≈ 0.000
      ├── Some((0, 2)): 11/18 ≈ 0.611
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 0/6 ≈ 0.000
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 3/10 ≈ 0.300
      └── Some((0, 8)): 13/20 ≈ 0.650
    ├── Some((6, 1)): 91/171 ≈ 0.532
      ├── Some((1, 0)): 15/24 ≈ 0.625
      ├── Some((1, 1)): 6/15 ≈ 0.400
      ├── Some((1, 2)): 4/12 ≈ 0.333
      ├── Some((1, 3)): 14/23 ≈ 0.609
      ├── Some((1, 4)): 7/16 ≈ 0.438
      ├── Some((1, 5)): 11/20 ≈ 0.550
      ├── Some((1, 6)): 11/20 ≈ 0.550
      ├── Some((1, 7)): 11/20 ≈ 0.550
      └── Some((1, 8)): 11/20 ≈ 0.550
    ├── Some((6, 2)): 57/120 ≈ 0.475
      ├── Some((2, 0)): 2/9 ≈ 0.222
      ├── Some((2, 1)): 15/22 ≈ 0.682
      ├── Some((2, 2)): 10/17 ≈ 0.588
      ├── Some((2, 3)): 1/7 ≈ 0.143
      ├── Some((2, 4)): 3/10 ≈ 0.300
      ├── Some((2, 5)): 9/16 ≈ 0.562
      ├── Some((2, 6)): 7/14 ≈ 0.500
      ├── Some((2, 7)): 8/15 ≈ 0.533
      └── Some((2, 8)): 2/9 ≈ 0.222
    ├── Some((6, 3)): 93/174 ≈ 0.534
      ├── Some((3, 0)): 15/24 ≈ 0.625
      ├── Some((3, 1)): 8/17 ≈ 0.471
      ├── Some((3, 2)): 7/16 ≈ 0.438
      ├── Some((3, 3)): 11/20 ≈ 0.550
      ├── Some((3, 4)): 13/22 ≈ 0.591
      ├── Some((3, 5)): 8/17 ≈ 0.471
      ├── Some((3, 6)): 10/19 ≈ 0.526
      ├── Some((3, 7)): 8/17 ≈ 0.471
      └── Some((3, 8)): 12/21 ≈ 0.571
    ├── Some((6, 4)): 142/243 ≈ 0.584
      ├── Some((4, 0)): 18/29 ≈ 0.621
      ├── Some((4, 1)): 15/26 ≈ 0.577
      ├── Some((4, 2)): 13/24 ≈ 0.542
      ├── Some((4, 3)): 19/30 ≈ 0.633
      ├── Some((4, 4)): 11/22 ≈ 0.500
      ├── Some((4, 5)): 25/37 ≈ 0.676
      ├── Some((4, 6)): 12/23 ≈ 0.522
      ├── Some((4, 7)): 14/25 ≈ 0.560
      └── Some((4, 8)): 15/26 ≈ 0.577
    ├── Some((6, 5)): 60/125 ≈ 0.480
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 2/9 ≈ 0.222
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 9/16 ≈ 0.562
      ├── Some((5, 5)): 11/19 ≈ 0.579
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 8/15 ≈ 0.533
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((6, 7)): 54/116 ≈ 0.466
      ├── Some((7, 0)): 9/16 ≈ 0.562
      ├── Some((7, 1)): 7/14 ≈ 0.500
      ├── Some((7, 2)): 9/16 ≈ 0.562
      ├── Some((7, 3)): 1/7 ≈ 0.143
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 12/19 ≈ 0.632
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 2/9 ≈ 0.222
    └── Some((6, 8)): 55/117 ≈ 0.470
      ├── Some((8, 0)): 9/16 ≈ 0.562
      ├── Some((8, 1)): 1/7 ≈ 0.143
      ├── Some((8, 2)): 5/12 ≈ 0.417
      ├── Some((8, 3)): 11/18 ≈ 0.611
      ├── Some((8, 4)): 9/16 ≈ 0.562
      ├── Some((8, 5)): 9/16 ≈ 0.562
      ├── Some((8, 6)): 1/7 ≈ 0.143
      ├── Some((8, 7)): 4/11 ≈ 0.364
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((6, 7)): 804/1523 ≈ 0.528
    ├── Some((7, 0)): 82/159 ≈ 0.516
      ├── Some((0, 0)): 4/13 ≈ 0.308
      ├── Some((0, 1)): 8/18 ≈ 0.444
      ├── Some((0, 2)): 19/29 ≈ 0.655
      ├── Some((0, 3)): 14/24 ≈ 0.583
      ├── Some((0, 4)): 14/24 ≈ 0.583
      ├── Some((0, 5)): 1/9 ≈ 0.111
      ├── Some((0, 7)): 5/14 ≈ 0.357
      └── Some((0, 8)): 17/27 ≈ 0.630
    ├── Some((7, 1)): 143/246 ≈ 0.581
      ├── Some((1, 0)): 20/32 ≈ 0.625
      ├── Some((1, 1)): 14/25 ≈ 0.560
      ├── Some((1, 2)): 13/24 ≈ 0.542
      ├── Some((1, 3)): 9/20 ≈ 0.450
      ├── Some((1, 4)): 36/48 ≈ 0.750
      ├── Some((1, 5)): 10/21 ≈ 0.476
      ├── Some((1, 6)): 12/23 ≈ 0.522
      ├── Some((1, 7)): 15/27 ≈ 0.556
      └── Some((1, 8)): 14/25 ≈ 0.560
    ├── Some((7, 2)): 102/188 ≈ 0.543
      ├── Some((2, 0)): 7/16 ≈ 0.438
      ├── Some((2, 1)): 9/18 ≈ 0.500
      ├── Some((2, 2)): 23/33 ≈ 0.697
      ├── Some((2, 3)): 10/20 ≈ 0.500
      ├── Some((2, 4)): 10/20 ≈ 0.500
      ├── Some((2, 5)): 21/31 ≈ 0.677
      ├── Some((2, 6)): 7/16 ≈ 0.438
      ├── Some((2, 7)): 4/13 ≈ 0.308
      └── Some((2, 8)): 10/20 ≈ 0.500
    ├── Some((7, 3)): 86/165 ≈ 0.521
      ├── Some((3, 0)): 8/17 ≈ 0.471
      ├── Some((3, 1)): 6/14 ≈ 0.429
      ├── Some((3, 2)): 8/17 ≈ 0.471
      ├── Some((3, 3)): 12/21 ≈ 0.571
      ├── Some((3, 4)): 8/17 ≈ 0.471
      ├── Some((3, 5)): 7/16 ≈ 0.438
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 21/30 ≈ 0.700
      └── Some((3, 8)): 10/19 ≈ 0.526
    ├── Some((7, 4)): 63/131 ≈ 0.481
      ├── Some((4, 0)): 2/9 ≈ 0.222
      ├── Some((4, 1)): 10/18 ≈ 0.556
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 15/23 ≈ 0.652
      ├── Some((4, 4)): 0/6 ≈ 0.000
      ├── Some((4, 5)): 4/12 ≈ 0.333
      ├── Some((4, 6)): 8/16 ≈ 0.500
      ├── Some((4, 7)): 14/22 ≈ 0.636
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((7, 5)): 72/144 ≈ 0.500
      ├── Some((5, 0)): 13/21 ≈ 0.619
      ├── Some((5, 1)): 10/18 ≈ 0.556
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 6/14 ≈ 0.429
      ├── Some((5, 5)): 12/20 ≈ 0.600
      ├── Some((5, 6)): 1/8 ≈ 0.125
      ├── Some((5, 7)): 7/15 ≈ 0.467
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((7, 6)): 82/159 ≈ 0.516
      ├── Some((6, 0)): 16/26 ≈ 0.615
      ├── Some((6, 1)): 12/22 ≈ 0.545
      ├── Some((6, 2)): 7/17 ≈ 0.412
      ├── Some((6, 3)): 3/12 ≈ 0.250
      ├── Some((6, 4)): 8/18 ≈ 0.444
      ├── Some((6, 5)): 16/26 ≈ 0.615
      ├── Some((6, 6)): 17/27 ≈ 0.630
      └── Some((6, 8)): 2/10 ≈ 0.200
    ├── Some((7, 7)): 92/173 ≈ 0.532
      ├── Some((7, 0)): 10/20 ≈ 0.500
      ├── Some((7, 1)): 4/13 ≈ 0.308
      ├── Some((7, 2)): 12/22 ≈ 0.545
      ├── Some((7, 3)): 12/22 ≈ 0.545
      ├── Some((7, 4)): 22/33 ≈ 0.667
      ├── Some((7, 5)): 9/19 ≈ 0.474
      ├── Some((7, 6)): 17/28 ≈ 0.607
      └── Some((7, 8)): 6/15 ≈ 0.400
    └── Some((7, 8)): 81/157 ≈ 0.516
      ├── Some((8, 0)): 4/12 ≈ 0.333
      ├── Some((8, 1)): 7/15 ≈ 0.467
      ├── Some((8, 2)): 18/27 ≈ 0.667
      ├── Some((8, 3)): 10/18 ≈ 0.556
      ├── Some((8, 4)): 10/19 ≈ 0.526
      ├── Some((8, 5)): 8/16 ≈ 0.500
      ├── Some((8, 6)): 5/13 ≈ 0.385
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 13/22 ≈ 0.591
  └── Some((6, 8)): 743/1419 ≈ 0.524
    ├── Some((8, 0)): 58/122 ≈ 0.475
      ├── Some((0, 0)): 8/16 ≈ 0.500
      ├── Some((0, 1)): 6/14 ≈ 0.429
      ├── Some((0, 2)): 6/14 ≈ 0.429
      ├── Some((0, 3)): 7/15 ≈ 0.467
      ├── Some((0, 4)): 4/11 ≈ 0.364
      ├── Some((0, 5)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 15/23 ≈ 0.652
      └── Some((0, 8)): 8/16 ≈ 0.500
    ├── Some((8, 1)): 97/179 ≈ 0.542
      ├── Some((1, 0)): 7/16 ≈ 0.438
      ├── Some((1, 1)): 13/22 ≈ 0.591
      ├── Some((1, 2)): 0/7 ≈ 0.000
      ├── Some((1, 3)): 22/32 ≈ 0.688
      ├── Some((1, 4)): 7/16 ≈ 0.438
      ├── Some((1, 5)): 6/15 ≈ 0.400
      ├── Some((1, 6)): 10/19 ≈ 0.526
      ├── Some((1, 7)): 14/23 ≈ 0.609
      └── Some((1, 8)): 18/28 ≈ 0.643
    ├── Some((8, 2)): 128/224 ≈ 0.571
      ├── Some((2, 0)): 10/20 ≈ 0.500
      ├── Some((2, 1)): 11/21 ≈ 0.524
      ├── Some((2, 2)): 12/22 ≈ 0.545
      ├── Some((2, 3)): 12/23 ≈ 0.522
      ├── Some((2, 4)): 19/30 ≈ 0.633
      ├── Some((2, 5)): 17/28 ≈ 0.607
      ├── Some((2, 6)): 10/20 ≈ 0.500
      ├── Some((2, 7)): 17/28 ≈ 0.607
      └── Some((2, 8)): 20/31 ≈ 0.645
    ├── Some((8, 3)): 45/102 ≈ 0.441
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 2/8 ≈ 0.250
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 6/12 ≈ 0.500
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((8, 4)): 117/208 ≈ 0.562
      ├── Some((4, 0)): 16/26 ≈ 0.615
      ├── Some((4, 1)): 15/25 ≈ 0.600
      ├── Some((4, 2)): 12/22 ≈ 0.545
      ├── Some((4, 3)): 17/27 ≈ 0.630
      ├── Some((4, 4)): 8/18 ≈ 0.444
      ├── Some((4, 5)): 15/25 ≈ 0.600
      ├── Some((4, 6)): 7/17 ≈ 0.412
      ├── Some((4, 7)): 19/30 ≈ 0.633
      └── Some((4, 8)): 7/17 ≈ 0.412
    ├── Some((8, 5)): 53/114 ≈ 0.465
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 7/14 ≈ 0.500
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 5/12 ≈ 0.417
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 3/9 ≈ 0.333
      ├── Some((5, 6)): 7/14 ≈ 0.500
      ├── Some((5, 7)): 3/9 ≈ 0.333
      └── Some((5, 8)): 4/11 ≈ 0.364
    ├── Some((8, 6)): 103/188 ≈ 0.548
      ├── Some((6, 0)): 4/13 ≈ 0.308
      ├── Some((6, 1)): 12/23 ≈ 0.522
      ├── Some((6, 2)): 17/28 ≈ 0.607
      ├── Some((6, 3)): 10/20 ≈ 0.500
      ├── Some((6, 4)): 24/35 ≈ 0.686
      ├── Some((6, 5)): 13/24 ≈ 0.542
      ├── Some((6, 6)): 14/25 ≈ 0.560
      └── Some((6, 7)): 9/19 ≈ 0.474
    ├── Some((8, 7)): 77/150 ≈ 0.513
      ├── Some((7, 0)): 4/12 ≈ 0.333
      ├── Some((7, 1)): 4/12 ≈ 0.333
      ├── Some((7, 2)): 18/26 ≈ 0.692
      ├── Some((7, 3)): 2/9 ≈ 0.222
      ├── Some((7, 4)): 5/13 ≈ 0.385
      ├── Some((7, 5)): 13/22 ≈ 0.591
      ├── Some((7, 6)): 18/26 ≈ 0.692
      ├── Some((7, 7)): 7/15 ≈ 0.467
      └── Some((7, 8)): 6/14 ≈ 0.429
    └── Some((8, 8)): 64/131 ≈ 0.489
      ├── Some((8, 0)): 9/17 ≈ 0.529
      ├── Some((8, 1)): 8/16 ≈ 0.500
      ├── Some((8, 2)): 6/14 ≈ 0.429
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 14/23 ≈ 0.609
      ├── Some((8, 6)): 5/13 ≈ 0.385
      └── Some((8, 7)): 10/19 ≈ 0.526
├── Some((0, 7)): 9286/17584 ≈ 0.528
  ├── Some((7, 0)): 1099/2076 ≈ 0.529
    ├── Some((0, 0)): 131/250 ≈ 0.524
      ├── Some((0, 1)): 16/32 ≈ 0.500
      ├── Some((0, 2)): 17/34 ≈ 0.500
      ├── Some((0, 3)): 21/38 ≈ 0.553
      ├── Some((0, 4)): 21/39 ≈ 0.538
      ├── Some((0, 5)): 27/46 ≈ 0.587
      ├── Some((0, 6)): 5/18 ≈ 0.278
      └── Some((0, 8)): 24/42 ≈ 0.571
    ├── Some((0, 1)): 103/207 ≈ 0.498
      ├── Some((1, 0)): 12/24 ≈ 0.500
      ├── Some((1, 1)): 18/31 ≈ 0.581
      ├── Some((1, 2)): 5/15 ≈ 0.333
      ├── Some((1, 3)): 13/25 ≈ 0.520
      ├── Some((1, 4)): 14/26 ≈ 0.538
      ├── Some((1, 5)): 12/24 ≈ 0.500
      ├── Some((1, 6)): 14/26 ≈ 0.538
      ├── Some((1, 7)): 9/20 ≈ 0.450
      └── Some((1, 8)): 5/15 ≈ 0.333
    ├── Some((0, 2)): 154/285 ≈ 0.540
      ├── Some((2, 0)): 10/23 ≈ 0.435
      ├── Some((2, 1)): 16/30 ≈ 0.533
      ├── Some((2, 2)): 13/27 ≈ 0.481
      ├── Some((2, 3)): 16/30 ≈ 0.533
      ├── Some((2, 4)): 28/44 ≈ 0.636
      ├── Some((2, 5)): 16/31 ≈ 0.516
      ├── Some((2, 6)): 16/31 ≈ 0.516
      ├── Some((2, 7)): 20/35 ≈ 0.571
      └── Some((2, 8)): 18/33 ≈ 0.545
    ├── Some((0, 3)): 150/279 ≈ 0.538
      ├── Some((3, 0)): 28/44 ≈ 0.636
      ├── Some((3, 1)): 14/28 ≈ 0.500
      ├── Some((3, 2)): 10/23 ≈ 0.435
      ├── Some((3, 3)): 28/44 ≈ 0.636
      ├── Some((3, 4)): 9/22 ≈ 0.409
      ├── Some((3, 5)): 21/36 ≈ 0.583
      ├── Some((3, 6)): 18/33 ≈ 0.545
      ├── Some((3, 7)): 14/28 ≈ 0.500
      └── Some((3, 8)): 7/20 ≈ 0.350
    ├── Some((0, 4)): 120/233 ≈ 0.515
      ├── Some((4, 0)): 25/39 ≈ 0.641
      ├── Some((4, 1)): 14/27 ≈ 0.519
      ├── Some((4, 2)): 14/27 ≈ 0.519
      ├── Some((4, 3)): 21/35 ≈ 0.600
      ├── Some((4, 4)): 7/18 ≈ 0.389
      ├── Some((4, 5)): 11/23 ≈ 0.478
      ├── Some((4, 6)): 9/21 ≈ 0.429
      ├── Some((4, 7)): 5/16 ≈ 0.312
      └── Some((4, 8)): 13/26 ≈ 0.500
    ├── Some((0, 5)): 146/272 ≈ 0.537
      ├── Some((5, 0)): 13/27 ≈ 0.481
      ├── Some((5, 1)): 17/31 ≈ 0.548
      ├── Some((5, 2)): 7/19 ≈ 0.368
      ├── Some((5, 3)): 36/52 ≈ 0.692
      ├── Some((5, 4)): 22/37 ≈ 0.595
      ├── Some((5, 5)): 7/19 ≈ 0.368
      ├── Some((5, 6)): 14/28 ≈ 0.500
      ├── Some((5, 7)): 17/32 ≈ 0.531
      └── Some((5, 8)): 12/26 ≈ 0.462
    ├── Some((0, 6)): 144/269 ≈ 0.535
      ├── Some((6, 0)): 6/18 ≈ 0.333
      ├── Some((6, 1)): 16/30 ≈ 0.533
      ├── Some((6, 2)): 24/39 ≈ 0.615
      ├── Some((6, 3)): 15/29 ≈ 0.517
      ├── Some((6, 4)): 14/28 ≈ 0.500
      ├── Some((6, 5)): 31/47 ≈ 0.660
      ├── Some((6, 6)): 21/36 ≈ 0.583
      ├── Some((6, 7)): 5/17 ≈ 0.294
      └── Some((6, 8)): 11/24 ≈ 0.458
    └── Some((0, 8)): 151/280 ≈ 0.539
      ├── Some((8, 0)): 20/35 ≈ 0.571
      ├── Some((8, 1)): 6/18 ≈ 0.333
      ├── Some((8, 2)): 5/17 ≈ 0.294
      ├── Some((8, 3)): 22/37 ≈ 0.595
      ├── Some((8, 4)): 20/35 ≈ 0.571
      ├── Some((8, 5)): 26/42 ≈ 0.619
      ├── Some((8, 6)): 17/32 ≈ 0.531
      ├── Some((8, 7)): 21/36 ≈ 0.583
      └── Some((8, 8)): 13/27 ≈ 0.481
  ├── Some((7, 1)): 1223/2289 ≈ 0.534
    ├── Some((1, 0)): 181/322 ≈ 0.562
      ├── Some((0, 0)): 19/36 ≈ 0.528
      ├── Some((0, 1)): 25/43 ≈ 0.581
      ├── Some((0, 2)): 30/49 ≈ 0.612
      ├── Some((0, 3)): 14/30 ≈ 0.467
      ├── Some((0, 4)): 22/40 ≈ 0.550
      ├── Some((0, 5)): 18/35 ≈ 0.514
      ├── Some((0, 6)): 16/32 ≈ 0.500
      └── Some((0, 8)): 36/56 ≈ 0.643
    ├── Some((1, 1)): 254/429 ≈ 0.592
      ├── Some((1, 0)): 44/68 ≈ 0.647
      ├── Some((1, 2)): 31/53 ≈ 0.585
      ├── Some((1, 3)): 15/33 ≈ 0.455
      ├── Some((1, 4)): 22/42 ≈ 0.524
      ├── Some((1, 5)): 41/65 ≈ 0.631
      ├── Some((1, 6)): 18/37 ≈ 0.486
      ├── Some((1, 7)): 36/59 ≈ 0.610
      └── Some((1, 8)): 46/71 ≈ 0.648
    ├── Some((1, 2)): 91/187 ≈ 0.487
      ├── Some((2, 0)): 14/26 ≈ 0.538
      ├── Some((2, 1)): 2/11 ≈ 0.182
      ├── Some((2, 2)): 6/16 ≈ 0.375
      ├── Some((2, 3)): 22/34 ≈ 0.647
      ├── Some((2, 4)): 13/24 ≈ 0.542
      ├── Some((2, 5)): 2/11 ≈ 0.182
      ├── Some((2, 6)): 6/16 ≈ 0.375
      ├── Some((2, 7)): 16/28 ≈ 0.571
      └── Some((2, 8)): 9/20 ≈ 0.450
    ├── Some((1, 3)): 92/188 ≈ 0.489
      ├── Some((3, 0)): 17/28 ≈ 0.607
      ├── Some((3, 1)): 12/23 ≈ 0.522
      ├── Some((3, 2)): 11/22 ≈ 0.500
      ├── Some((3, 3)): 11/22 ≈ 0.500
      ├── Some((3, 4)): 17/28 ≈ 0.607
      ├── Some((3, 5)): 7/17 ≈ 0.412
      ├── Some((3, 6)): 7/17 ≈ 0.412
      ├── Some((3, 7)): 4/14 ≈ 0.286
      └── Some((3, 8)): 6/16 ≈ 0.375
    ├── Some((1, 4)): 83/174 ≈ 0.477
      ├── Some((4, 0)): 8/18 ≈ 0.444
      ├── Some((4, 1)): 16/27 ≈ 0.593
      ├── Some((4, 2)): 5/14 ≈ 0.357
      ├── Some((4, 3)): 3/12 ≈ 0.250
      ├── Some((4, 4)): 4/13 ≈ 0.308
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 5/15 ≈ 0.333
      ├── Some((4, 7)): 20/31 ≈ 0.645
      └── Some((4, 8)): 13/24 ≈ 0.542
    ├── Some((1, 5)): 134/252 ≈ 0.532
      ├── Some((5, 0)): 8/20 ≈ 0.400
      ├── Some((5, 1)): 8/20 ≈ 0.400
      ├── Some((5, 2)): 16/29 ≈ 0.552
      ├── Some((5, 3)): 14/27 ≈ 0.519
      ├── Some((5, 4)): 23/37 ≈ 0.622
      ├── Some((5, 5)): 7/19 ≈ 0.368
      ├── Some((5, 6)): 16/29 ≈ 0.552
      ├── Some((5, 7)): 18/32 ≈ 0.562
      └── Some((5, 8)): 24/38 ≈ 0.632
    ├── Some((1, 6)): 152/279 ≈ 0.545
      ├── Some((6, 0)): 32/48 ≈ 0.667
      ├── Some((6, 1)): 24/39 ≈ 0.615
      ├── Some((6, 2)): 17/31 ≈ 0.548
      ├── Some((6, 3)): 10/23 ≈ 0.435
      ├── Some((6, 4)): 23/38 ≈ 0.605
      ├── Some((6, 5)): 4/15 ≈ 0.267
      ├── Some((6, 6)): 8/21 ≈ 0.381
      ├── Some((6, 7)): 15/29 ≈ 0.517
      └── Some((6, 8)): 19/34 ≈ 0.559
    ├── Some((1, 7)): 113/221 ≈ 0.511
      ├── Some((7, 0)): 8/20 ≈ 0.400
      ├── Some((7, 2)): 7/19 ≈ 0.368
      ├── Some((7, 3)): 30/46 ≈ 0.652
      ├── Some((7, 4)): 15/29 ≈ 0.517
      ├── Some((7, 5)): 11/24 ≈ 0.458
      ├── Some((7, 6)): 27/43 ≈ 0.628
      ├── Some((7, 7)): 3/14 ≈ 0.214
      └── Some((7, 8)): 12/25 ≈ 0.480
    └── Some((1, 8)): 123/236 ≈ 0.521
      ├── Some((8, 0)): 8/20 ≈ 0.400
      ├── Some((8, 1)): 11/23 ≈ 0.478
      ├── Some((8, 2)): 12/24 ≈ 0.500
      ├── Some((8, 3)): 16/29 ≈ 0.552
      ├── Some((8, 4)): 14/27 ≈ 0.519
      ├── Some((8, 5)): 19/32 ≈ 0.594
      ├── Some((8, 6)): 10/22 ≈ 0.455
      ├── Some((8, 7)): 13/25 ≈ 0.520
      └── Some((8, 8)): 20/33 ≈ 0.606
  ├── Some((7, 2)): 1284/2394 ≈ 0.536
    ├── Some((2, 0)): 116/226 ≈ 0.513
      ├── Some((0, 0)): 25/40 ≈ 0.625
      ├── Some((0, 1)): 18/33 ≈ 0.545
      ├── Some((0, 2)): 6/18 ≈ 0.333
      ├── Some((0, 3)): 11/24 ≈ 0.458
      ├── Some((0, 4)): 8/21 ≈ 0.381
      ├── Some((0, 5)): 19/34 ≈ 0.559
      ├── Some((0, 6)): 16/30 ≈ 0.533
      └── Some((0, 8)): 12/25 ≈ 0.480
    ├── Some((2, 1)): 164/299 ≈ 0.548
      ├── Some((1, 0)): 19/34 ≈ 0.559
      ├── Some((1, 1)): 12/26 ≈ 0.462
      ├── Some((1, 2)): 32/49 ≈ 0.653
      ├── Some((1, 3)): 19/34 ≈ 0.559
      ├── Some((1, 4)): 7/20 ≈ 0.350
      ├── Some((1, 5)): 10/24 ≈ 0.417
      ├── Some((1, 6)): 29/45 ≈ 0.644
      ├── Some((1, 7)): 25/41 ≈ 0.610
      └── Some((1, 8)): 11/25 ≈ 0.440
    ├── Some((2, 2)): 196/346 ≈ 0.566
      ├── Some((2, 0)): 22/41 ≈ 0.537
      ├── Some((2, 1)): 35/56 ≈ 0.625
      ├── Some((2, 3)): 9/24 ≈ 0.375
      ├── Some((2, 4)): 55/79 ≈ 0.696
      ├── Some((2, 5)): 12/28 ≈ 0.429
      ├── Some((2, 6)): 25/44 ≈ 0.568
      ├── Some((2, 7)): 19/37 ≈ 0.514
      └── Some((2, 8)): 18/36 ≈ 0.500
    ├── Some((2, 3)): 107/212 ≈ 0.505
      ├── Some((3, 0)): 3/13 ≈ 0.231
      ├── Some((3, 1)): 7/18 ≈ 0.389
      ├── Some((3, 2)): 18/30 ≈ 0.600
      ├── Some((3, 3)): 12/24 ≈ 0.500
      ├── Some((3, 4)): 14/26 ≈ 0.538
      ├── Some((3, 5)): 15/27 ≈ 0.556
      ├── Some((3, 6)): 13/25 ≈ 0.520
      ├── Some((3, 7)): 6/17 ≈ 0.353
      └── Some((3, 8)): 18/31 ≈ 0.581
    ├── Some((2, 4)): 157/288 ≈ 0.545
      ├── Some((4, 0)): 19/34 ≈ 0.559
      ├── Some((4, 1)): 7/20 ≈ 0.350
      ├── Some((4, 2)): 22/37 ≈ 0.595
      ├── Some((4, 3)): 13/27 ≈ 0.481
      ├── Some((4, 4)): 31/47 ≈ 0.660
      ├── Some((4, 5)): 29/45 ≈ 0.644
      ├── Some((4, 6)): 12/26 ≈ 0.462
      ├── Some((4, 7)): 14/28 ≈ 0.500
      └── Some((4, 8)): 10/23 ≈ 0.435
    ├── Some((2, 5)): 183/327 ≈ 0.560
      ├── Some((5, 0)): 14/29 ≈ 0.483
      ├── Some((5, 1)): 17/33 ≈ 0.515
      ├── Some((5, 2)): 28/45 ≈ 0.622
      ├── Some((5, 3)): 13/28 ≈ 0.464
      ├── Some((5, 4)): 40/58 ≈ 0.690
      ├── Some((5, 5)): 22/38 ≈ 0.579
      ├── Some((5, 6)): 14/29 ≈ 0.483
      ├── Some((5, 7)): 20/36 ≈ 0.556
      └── Some((5, 8)): 15/30 ≈ 0.500
    ├── Some((2, 6)): 141/264 ≈ 0.534
      ├── Some((6, 0)): 16/30 ≈ 0.533
      ├── Some((6, 1)): 17/31 ≈ 0.548
      ├── Some((6, 2)): 19/33 ≈ 0.576
      ├── Some((6, 3)): 26/41 ≈ 0.634
      ├── Some((6, 4)): 2/12 ≈ 0.167
      ├── Some((6, 5)): 21/36 ≈ 0.583
      ├── Some((6, 6)): 10/23 ≈ 0.435
      ├── Some((6, 7)): 14/28 ≈ 0.500
      └── Some((6, 8)): 15/29 ≈ 0.517
    ├── Some((2, 7)): 67/150 ≈ 0.447
      ├── Some((7, 0)): 6/16 ≈ 0.375
      ├── Some((7, 1)): 9/20 ≈ 0.450
      ├── Some((7, 3)): 0/8 ≈ 0.000
      ├── Some((7, 4)): 12/23 ≈ 0.522
      ├── Some((7, 5)): 4/14 ≈ 0.286
      ├── Some((7, 6)): 11/22 ≈ 0.500
      ├── Some((7, 7)): 14/25 ≈ 0.560
      └── Some((7, 8)): 10/21 ≈ 0.476
    └── Some((2, 8)): 152/281 ≈ 0.541
      ├── Some((8, 0)): 6/18 ≈ 0.333
      ├── Some((8, 1)): 18/33 ≈ 0.545
      ├── Some((8, 2)): 22/37 ≈ 0.595
      ├── Some((8, 3)): 25/41 ≈ 0.610
      ├── Some((8, 4)): 10/23 ≈ 0.435
      ├── Some((8, 5)): 16/31 ≈ 0.516
      ├── Some((8, 6)): 10/23 ≈ 0.435
      ├── Some((8, 7)): 21/36 ≈ 0.583
      └── Some((8, 8)): 23/38 ≈ 0.605
  ├── Some((7, 3)): 739/1451 ≈ 0.509
    ├── Some((3, 0)): 93/178 ≈ 0.522
      ├── Some((0, 0)): 12/23 ≈ 0.522
      ├── Some((0, 1)): 4/13 ≈ 0.308
      ├── Some((0, 2)): 21/32 ≈ 0.656
      ├── Some((0, 3)): 6/16 ≈ 0.375
      ├── Some((0, 4)): 10/20 ≈ 0.500
      ├── Some((0, 5)): 12/23 ≈ 0.522
      ├── Some((0, 6)): 12/23 ≈ 0.522
      └── Some((0, 8)): 16/27 ≈ 0.593
    ├── Some((3, 1)): 74/149 ≈ 0.497
      ├── Some((1, 0)): 6/14 ≈ 0.429
      ├── Some((1, 1)): 3/11 ≈ 0.273
      ├── Some((1, 2)): 13/22 ≈ 0.591
      ├── Some((1, 3)): 7/15 ≈ 0.467
      ├── Some((1, 4)): 7/15 ≈ 0.467
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 9/18 ≈ 0.500
      ├── Some((1, 7)): 8/16 ≈ 0.500
      └── Some((1, 8)): 8/16 ≈ 0.500
    ├── Some((3, 2)): 104/194 ≈ 0.536
      ├── Some((2, 0)): 17/28 ≈ 0.607
      ├── Some((2, 1)): 4/13 ≈ 0.308
      ├── Some((2, 2)): 14/24 ≈ 0.583
      ├── Some((2, 3)): 14/24 ≈ 0.583
      ├── Some((2, 4)): 3/12 ≈ 0.250
      ├── Some((2, 5)): 13/23 ≈ 0.565
      ├── Some((2, 6)): 9/19 ≈ 0.474
      ├── Some((2, 7)): 11/21 ≈ 0.524
      └── Some((2, 8)): 18/29 ≈ 0.621
    ├── Some((3, 3)): 68/140 ≈ 0.486
      ├── Some((3, 0)): 8/17 ≈ 0.471
      ├── Some((3, 1)): 12/21 ≈ 0.571
      ├── Some((3, 2)): 3/11 ≈ 0.273
      ├── Some((3, 4)): 19/28 ≈ 0.679
      ├── Some((3, 5)): 7/16 ≈ 0.438
      ├── Some((3, 6)): 8/17 ≈ 0.471
      ├── Some((3, 7)): 5/14 ≈ 0.357
      └── Some((3, 8)): 6/15 ≈ 0.400
    ├── Some((3, 4)): 67/139 ≈ 0.482
      ├── Some((4, 0)): 1/8 ≈ 0.125
      ├── Some((4, 1)): 14/22 ≈ 0.636
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 12/20 ≈ 0.600
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 10/18 ≈ 0.556
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 4/12 ≈ 0.333
      └── Some((4, 8)): 7/15 ≈ 0.467
    ├── Some((3, 5)): 76/152 ≈ 0.500
      ├── Some((5, 0)): 9/17 ≈ 0.529
      ├── Some((5, 1)): 10/19 ≈ 0.526
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 3/11 ≈ 0.273
      ├── Some((5, 5)): 3/11 ≈ 0.273
      ├── Some((5, 6)): 23/32 ≈ 0.719
      ├── Some((5, 7)): 4/12 ≈ 0.333
      └── Some((5, 8)): 10/19 ≈ 0.526
    ├── Some((3, 6)): 116/211 ≈ 0.550
      ├── Some((6, 0)): 19/30 ≈ 0.633
      ├── Some((6, 1)): 11/21 ≈ 0.524
      ├── Some((6, 2)): 7/17 ≈ 0.412
      ├── Some((6, 3)): 22/33 ≈ 0.667
      ├── Some((6, 4)): 11/21 ≈ 0.524
      ├── Some((6, 5)): 7/17 ≈ 0.412
      ├── Some((6, 6)): 10/20 ≈ 0.500
      ├── Some((6, 7)): 17/28 ≈ 0.607
      └── Some((6, 8)): 12/23 ≈ 0.522
    ├── Some((3, 7)): 79/157 ≈ 0.503
      ├── Some((7, 0)): 11/21 ≈ 0.524
      ├── Some((7, 1)): 14/24 ≈ 0.583
      ├── Some((7, 2)): 2/10 ≈ 0.200
      ├── Some((7, 4)): 10/20 ≈ 0.500
      ├── Some((7, 5)): 16/27 ≈ 0.593
      ├── Some((7, 6)): 8/18 ≈ 0.444
      ├── Some((7, 7)): 4/13 ≈ 0.308
      └── Some((7, 8)): 13/23 ≈ 0.565
    └── Some((3, 8)): 61/130 ≈ 0.469
      ├── Some((8, 0)): 7/15 ≈ 0.467
      ├── Some((8, 1)): 14/22 ≈ 0.636
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 4/11 ≈ 0.364
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 4/11 ≈ 0.364
      ├── Some((8, 6)): 11/19 ≈ 0.579
      ├── Some((8, 7)): 5/13 ≈ 0.385
      └── Some((8, 8)): 3/10 ≈ 0.300
  ├── Some((7, 4)): 1778/3233 ≈ 0.550
    ├── Some((4, 0)): 266/463 ≈ 0.575
      ├── Some((0, 0)): 31/55 ≈ 0.564
      ├── Some((0, 1)): 20/42 ≈ 0.476
      ├── Some((0, 2)): 38/64 ≈ 0.594
      ├── Some((0, 3)): 24/47 ≈ 0.511
      ├── Some((0, 4)): 45/72 ≈ 0.625
      ├── Some((0, 5)): 64/94 ≈ 0.681
      ├── Some((0, 6)): 18/39 ≈ 0.462
      └── Some((0, 8)): 26/49 ≈ 0.531
    ├── Some((4, 1)): 128/253 ≈ 0.506
      ├── Some((1, 0)): 26/42 ≈ 0.619
      ├── Some((1, 1)): 4/15 ≈ 0.267
      ├── Some((1, 2)): 14/28 ≈ 0.500
      ├── Some((1, 3)): 9/22 ≈ 0.409
      ├── Some((1, 4)): 18/33 ≈ 0.545
      ├── Some((1, 5)): 8/21 ≈ 0.381
      ├── Some((1, 6)): 25/41 ≈ 0.610
      ├── Some((1, 7)): 11/24 ≈ 0.458
      └── Some((1, 8)): 12/26 ≈ 0.462
    ├── Some((4, 2)): 160/303 ≈ 0.528
      ├── Some((2, 0)): 23/40 ≈ 0.575
      ├── Some((2, 1)): 13/28 ≈ 0.464
      ├── Some((2, 2)): 5/18 ≈ 0.278
      ├── Some((2, 3)): 29/47 ≈ 0.617
      ├── Some((2, 4)): 13/28 ≈ 0.464
      ├── Some((2, 5)): 18/34 ≈ 0.529
      ├── Some((2, 6)): 9/23 ≈ 0.391
      ├── Some((2, 7)): 16/32 ≈ 0.500
      └── Some((2, 8)): 33/52 ≈ 0.635
    ├── Some((4, 3)): 233/413 ≈ 0.564
      ├── Some((3, 0)): 14/32 ≈ 0.438
      ├── Some((3, 1)): 29/50 ≈ 0.580
      ├── Some((3, 2)): 25/45 ≈ 0.556
      ├── Some((3, 3)): 33/54 ≈ 0.611
      ├── Some((3, 4)): 20/39 ≈ 0.513
      ├── Some((3, 5)): 34/56 ≈ 0.607
      ├── Some((3, 6)): 33/54 ≈ 0.611
      ├── Some((3, 7)): 22/41 ≈ 0.537
      └── Some((3, 8)): 22/41 ≈ 0.537
    ├── Some((4, 4)): 276/477 ≈ 0.579
      ├── Some((4, 0)): 29/53 ≈ 0.547
      ├── Some((4, 1)): 21/43 ≈ 0.488
      ├── Some((4, 2)): 20/42 ≈ 0.476
      ├── Some((4, 3)): 38/64 ≈ 0.594
      ├── Some((4, 5)): 52/81 ≈ 0.642
      ├── Some((4, 6)): 34/59 ≈ 0.576
      ├── Some((4, 7)): 62/92 ≈ 0.674
      └── Some((4, 8)): 20/42 ≈ 0.476
    ├── Some((4, 5)): 119/239 ≈ 0.498
      ├── Some((5, 0)): 22/37 ≈ 0.595
      ├── Some((5, 1)): 18/32 ≈ 0.562
      ├── Some((5, 2)): 17/31 ≈ 0.548
      ├── Some((5, 3)): 10/23 ≈ 0.435
      ├── Some((5, 4)): 3/14 ≈ 0.214
      ├── Some((5, 5)): 11/24 ≈ 0.458
      ├── Some((5, 6)): 17/31 ≈ 0.548
      ├── Some((5, 7)): 8/21 ≈ 0.381
      └── Some((5, 8)): 12/25 ≈ 0.480
    ├── Some((4, 6)): 210/379 ≈ 0.554
      ├── Some((6, 0)): 14/31 ≈ 0.452
      ├── Some((6, 1)): 23/42 ≈ 0.548
      ├── Some((6, 2)): 16/33 ≈ 0.485
      ├── Some((6, 3)): 8/23 ≈ 0.348
      ├── Some((6, 4)): 29/49 ≈ 0.592
      ├── Some((6, 5)): 50/73 ≈ 0.685
      ├── Some((6, 6)): 31/51 ≈ 0.608
      ├── Some((6, 7)): 16/34 ≈ 0.471
      └── Some((6, 8)): 23/42 ≈ 0.548
    ├── Some((4, 7)): 203/368 ≈ 0.552
      ├── Some((7, 0)): 22/42 ≈ 0.524
      ├── Some((7, 1)): 29/51 ≈ 0.569
      ├── Some((7, 2)): 26/47 ≈ 0.553
      ├── Some((7, 3)): 24/44 ≈ 0.545
      ├── Some((7, 5)): 33/55 ≈ 0.600
      ├── Some((7, 6)): 28/49 ≈ 0.571
      ├── Some((7, 7)): 24/44 ≈ 0.545
      └── Some((7, 8)): 16/35 ≈ 0.457
    └── Some((4, 8)): 182/337 ≈ 0.540
      ├── Some((8, 0)): 16/32 ≈ 0.500
      ├── Some((8, 1)): 30/49 ≈ 0.612
      ├── Some((8, 2)): 23/41 ≈ 0.561
      ├── Some((8, 3)): 21/38 ≈ 0.553
      ├── Some((8, 4)): 14/30 ≈ 0.467
      ├── Some((8, 5)): 15/31 ≈ 0.484
      ├── Some((8, 6)): 22/40 ≈ 0.550
      ├── Some((8, 7)): 24/42 ≈ 0.571
      └── Some((8, 8)): 16/33 ≈ 0.485
  ├── Some((7, 5)): 595/1198 ≈ 0.497
    ├── Some((5, 0)): 43/98 ≈ 0.439
      ├── Some((0, 0)): 3/9 ≈ 0.333
      ├── Some((0, 1)): 3/10 ≈ 0.300
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 5/12 ≈ 0.417
      ├── Some((0, 4)): 3/10 ≈ 0.300
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 12/19 ≈ 0.632
      └── Some((0, 8)): 5/12 ≈ 0.417
    ├── Some((5, 1)): 47/105 ≈ 0.448
      ├── Some((1, 0)): 3/9 ≈ 0.333
      ├── Some((1, 1)): 12/18 ≈ 0.667
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 1/7 ≈ 0.143
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 5/12 ≈ 0.417
    ├── Some((5, 2)): 65/132 ≈ 0.492
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 8/16 ≈ 0.500
      ├── Some((2, 2)): 8/16 ≈ 0.500
      ├── Some((2, 3)): 4/11 ≈ 0.364
      ├── Some((2, 4)): 11/19 ≈ 0.579
      ├── Some((2, 5)): 7/14 ≈ 0.500
      ├── Some((2, 6)): 7/15 ≈ 0.467
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((5, 3)): 104/189 ≈ 0.550
      ├── Some((3, 0)): 17/27 ≈ 0.630
      ├── Some((3, 1)): 11/20 ≈ 0.550
      ├── Some((3, 2)): 9/18 ≈ 0.500
      ├── Some((3, 3)): 17/27 ≈ 0.630
      ├── Some((3, 4)): 10/19 ≈ 0.526
      ├── Some((3, 5)): 10/19 ≈ 0.526
      ├── Some((3, 6)): 14/24 ≈ 0.583
      ├── Some((3, 7)): 6/15 ≈ 0.400
      └── Some((3, 8)): 10/19 ≈ 0.526
    ├── Some((5, 4)): 56/118 ≈ 0.475
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 6/13 ≈ 0.462
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 4)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 9/16 ≈ 0.562
      ├── Some((4, 7)): 3/9 ≈ 0.333
      └── Some((4, 8)): 8/15 ≈ 0.533
    ├── Some((5, 5)): 60/124 ≈ 0.484
      ├── Some((5, 0)): 5/13 ≈ 0.385
      ├── Some((5, 1)): 12/20 ≈ 0.600
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 6/14 ≈ 0.429
      ├── Some((5, 4)): 6/14 ≈ 0.429
      ├── Some((5, 6)): 4/12 ≈ 0.333
      ├── Some((5, 7)): 13/21 ≈ 0.619
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((5, 6)): 87/164 ≈ 0.530
      ├── Some((6, 0)): 9/17 ≈ 0.529
      ├── Some((6, 1)): 12/21 ≈ 0.571
      ├── Some((6, 2)): 16/25 ≈ 0.640
      ├── Some((6, 3)): 7/15 ≈ 0.467
      ├── Some((6, 4)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 8/16 ≈ 0.500
      ├── Some((6, 6)): 11/20 ≈ 0.550
      ├── Some((6, 7)): 10/19 ≈ 0.526
      └── Some((6, 8)): 3/11 ≈ 0.273
    ├── Some((5, 7)): 70/139 ≈ 0.504
      ├── Some((7, 0)): 14/23 ≈ 0.609
      ├── Some((7, 1)): 9/18 ≈ 0.500
      ├── Some((7, 2)): 11/20 ≈ 0.550
      ├── Some((7, 3)): 6/14 ≈ 0.429
      ├── Some((7, 4)): 10/19 ≈ 0.526
      ├── Some((7, 6)): 8/16 ≈ 0.500
      ├── Some((7, 7)): 6/14 ≈ 0.429
      └── Some((7, 8)): 6/14 ≈ 0.429
    └── Some((5, 8)): 62/128 ≈ 0.484
      ├── Some((8, 0)): 3/10 ≈ 0.300
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 11/19 ≈ 0.579
      ├── Some((8, 3)): 14/21 ≈ 0.667
      ├── Some((8, 4)): 10/18 ≈ 0.556
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 4/11 ≈ 0.364
      └── Some((8, 8)): 4/11 ≈ 0.364
  ├── Some((7, 6)): 1050/1992 ≈ 0.527
    ├── Some((6, 0)): 69/149 ≈ 0.463
      ├── Some((0, 0)): 5/14 ≈ 0.357
      ├── Some((0, 1)): 14/25 ≈ 0.560
      ├── Some((0, 2)): 10/20 ≈ 0.500
      ├── Some((0, 3)): 10/20 ≈ 0.500
      ├── Some((0, 4)): 5/15 ≈ 0.333
      ├── Some((0, 5)): 14/25 ≈ 0.560
      ├── Some((0, 6)): 8/18 ≈ 0.444
      └── Some((0, 8)): 2/11 ≈ 0.182
    ├── Some((6, 1)): 42/106 ≈ 0.396
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 1)): 2/9 ≈ 0.222
      ├── Some((1, 2)): 2/9 ≈ 0.222
      ├── Some((1, 3)): 6/13 ≈ 0.462
      ├── Some((1, 4)): 9/16 ≈ 0.562
      ├── Some((1, 5)): 5/12 ≈ 0.417
      ├── Some((1, 6)): 2/9 ≈ 0.222
      ├── Some((1, 7)): 4/11 ≈ 0.364
      └── Some((1, 8)): 7/14 ≈ 0.500
    ├── Some((6, 2)): 85/174 ≈ 0.489
      ├── Some((2, 0)): 14/25 ≈ 0.560
      ├── Some((2, 1)): 2/10 ≈ 0.200
      ├── Some((2, 2)): 13/23 ≈ 0.565
      ├── Some((2, 3)): 13/23 ≈ 0.565
      ├── Some((2, 4)): 13/23 ≈ 0.565
      ├── Some((2, 5)): 8/18 ≈ 0.444
      ├── Some((2, 6)): 10/20 ≈ 0.500
      ├── Some((2, 7)): 9/19 ≈ 0.474
      └── Some((2, 8)): 3/12 ≈ 0.250
    ├── Some((6, 3)): 95/190 ≈ 0.500
      ├── Some((3, 0)): 1/10 ≈ 0.100
      ├── Some((3, 1)): 2/11 ≈ 0.182
      ├── Some((3, 2)): 14/25 ≈ 0.560
      ├── Some((3, 3)): 17/29 ≈ 0.586
      ├── Some((3, 4)): 18/30 ≈ 0.600
      ├── Some((3, 5)): 14/25 ≈ 0.560
      ├── Some((3, 6)): 6/16 ≈ 0.375
      ├── Some((3, 7)): 7/17 ≈ 0.412
      └── Some((3, 8)): 15/26 ≈ 0.577
    ├── Some((6, 4)): 142/260 ≈ 0.546
      ├── Some((4, 0)): 11/24 ≈ 0.458
      ├── Some((4, 1)): 12/25 ≈ 0.480
      ├── Some((4, 2)): 27/41 ≈ 0.659
      ├── Some((4, 3)): 13/26 ≈ 0.500
      ├── Some((4, 4)): 15/28 ≈ 0.536
      ├── Some((4, 5)): 24/38 ≈ 0.632
      ├── Some((4, 6)): 10/22 ≈ 0.455
      ├── Some((4, 7)): 14/27 ≈ 0.519
      └── Some((4, 8)): 15/28 ≈ 0.536
    ├── Some((6, 5)): 130/242 ≈ 0.537
      ├── Some((5, 0)): 12/24 ≈ 0.500
      ├── Some((5, 1)): 14/26 ≈ 0.538
      ├── Some((5, 2)): 18/31 ≈ 0.581
      ├── Some((5, 3)): 17/30 ≈ 0.567
      ├── Some((5, 4)): 16/29 ≈ 0.552
      ├── Some((5, 5)): 15/27 ≈ 0.556
      ├── Some((5, 6)): 13/25 ≈ 0.520
      ├── Some((5, 7)): 14/26 ≈ 0.538
      └── Some((5, 8)): 11/23 ≈ 0.478
    ├── Some((6, 6)): 165/294 ≈ 0.561
      ├── Some((6, 0)): 30/47 ≈ 0.638
      ├── Some((6, 1)): 13/28 ≈ 0.464
      ├── Some((6, 2)): 15/30 ≈ 0.500
      ├── Some((6, 3)): 22/38 ≈ 0.579
      ├── Some((6, 4)): 25/42 ≈ 0.595
      ├── Some((6, 5)): 19/35 ≈ 0.543
      ├── Some((6, 7)): 23/39 ≈ 0.590
      └── Some((6, 8)): 18/34 ≈ 0.529
    ├── Some((6, 7)): 170/301 ≈ 0.565
      ├── Some((7, 0)): 19/35 ≈ 0.543
      ├── Some((7, 1)): 18/34 ≈ 0.529
      ├── Some((7, 2)): 27/44 ≈ 0.614
      ├── Some((7, 3)): 29/47 ≈ 0.617
      ├── Some((7, 4)): 25/42 ≈ 0.595
      ├── Some((7, 5)): 13/28 ≈ 0.464
      ├── Some((7, 7)): 25/42 ≈ 0.595
      └── Some((7, 8)): 13/28 ≈ 0.464
    └── Some((6, 8)): 152/275 ≈ 0.553
      ├── Some((8, 0)): 10/23 ≈ 0.435
      ├── Some((8, 1)): 18/32 ≈ 0.562
      ├── Some((8, 2)): 26/41 ≈ 0.634
      ├── Some((8, 3)): 20/34 ≈ 0.588
      ├── Some((8, 4)): 35/51 ≈ 0.686
      ├── Some((8, 5)): 4/15 ≈ 0.267
      ├── Some((8, 6)): 8/20 ≈ 0.400
      ├── Some((8, 7)): 13/26 ≈ 0.500
      └── Some((8, 8)): 18/32 ≈ 0.562
  ├── Some((7, 7)): 342/743 ≈ 0.460
    ├── Some((7, 0)): 43/94 ≈ 0.457
      ├── Some((0, 0)): 6/12 ≈ 0.500
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 9/16 ≈ 0.562
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 1/7 ≈ 0.143
      ├── Some((0, 6)): 7/13 ≈ 0.538
      └── Some((0, 8)): 9/16 ≈ 0.562
    ├── Some((7, 1)): 61/120 ≈ 0.508
      ├── Some((1, 0)): 2/8 ≈ 0.250
      ├── Some((1, 1)): 10/17 ≈ 0.588
      ├── Some((1, 2)): 10/17 ≈ 0.588
      ├── Some((1, 3)): 12/18 ≈ 0.667
      ├── Some((1, 4)): 11/17 ≈ 0.647
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 6/13 ≈ 0.462
      └── Some((1, 8)): 0/6 ≈ 0.000
    ├── Some((7, 2)): 50/104 ≈ 0.481
      ├── Some((2, 0)): 6/12 ≈ 0.500
      ├── Some((2, 1)): 1/7 ≈ 0.143
      ├── Some((2, 2)): 8/14 ≈ 0.571
      ├── Some((2, 3)): 10/16 ≈ 0.625
      ├── Some((2, 4)): 12/18 ≈ 0.667
      ├── Some((2, 5)): 0/5 ≈ 0.000
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 4/10 ≈ 0.400
    ├── Some((7, 3)): 41/91 ≈ 0.451
      ├── Some((3, 0)): 8/13 ≈ 0.615
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 5/11 ≈ 0.455
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 8/13 ≈ 0.615
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((7, 4)): 42/92 ≈ 0.457
      ├── Some((4, 0)): 1/6 ≈ 0.167
      ├── Some((4, 1)): 5/11 ≈ 0.455
      ├── Some((4, 2)): 8/13 ≈ 0.615
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 3/9 ≈ 0.333
      ├── Some((4, 6)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 8/13 ≈ 0.615
      └── Some((4, 8)): 7/13 ≈ 0.538
    ├── Some((7, 5)): 16/51 ≈ 0.314
      ├── Some((5, 0)): 4/7 ≈ 0.571
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 3/6 ≈ 0.500
      ├── Some((5, 4)): 3/7 ≈ 0.429
      ├── Some((5, 5)): 2/6 ≈ 0.333
      ├── Some((5, 6)): 1/5 ≈ 0.200
      ├── Some((5, 7)): 0/4 ≈ 0.000
      └── Some((5, 8)): 0/4 ≈ 0.000
    ├── Some((7, 6)): 53/109 ≈ 0.486
      ├── Some((6, 0)): 6/12 ≈ 0.500
      ├── Some((6, 1)): 11/17 ≈ 0.647
      ├── Some((6, 2)): 9/15 ≈ 0.600
      ├── Some((6, 3)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 4/10 ≈ 0.400
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 2/8 ≈ 0.250
      └── Some((6, 8)): 3/9 ≈ 0.333
    └── Some((7, 8)): 35/81 ≈ 0.432
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 2/7 ≈ 0.286
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 7/12 ≈ 0.583
      ├── Some((8, 4)): 9/14 ≈ 0.643
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 5/10 ≈ 0.500
      ├── Some((8, 7)): 0/5 ≈ 0.000
      └── Some((8, 8)): 5/10 ≈ 0.500
  └── Some((7, 8)): 1175/2207 ≈ 0.532
    ├── Some((8, 0)): 89/182 ≈ 0.489
      ├── Some((0, 0)): 8/19 ≈ 0.421
      ├── Some((0, 1)): 14/26 ≈ 0.538
      ├── Some((0, 2)): 10/21 ≈ 0.476
      ├── Some((0, 3)): 8/19 ≈ 0.421
      ├── Some((0, 4)): 7/18 ≈ 0.389
      ├── Some((0, 5)): 13/25 ≈ 0.520
      ├── Some((0, 6)): 14/26 ≈ 0.538
      └── Some((0, 8)): 15/27 ≈ 0.556
    ├── Some((8, 1)): 112/218 ≈ 0.514
      ├── Some((1, 0)): 18/30 ≈ 0.600
      ├── Some((1, 1)): 13/25 ≈ 0.520
      ├── Some((1, 2)): 12/24 ≈ 0.500
      ├── Some((1, 3)): 8/19 ≈ 0.421
      ├── Some((1, 4)): 17/29 ≈ 0.586
      ├── Some((1, 5)): 11/23 ≈ 0.478
      ├── Some((1, 6)): 22/35 ≈ 0.629
      ├── Some((1, 7)): 3/13 ≈ 0.231
      └── Some((1, 8)): 8/19 ≈ 0.421
    ├── Some((8, 2)): 122/233 ≈ 0.524
      ├── Some((2, 0)): 8/20 ≈ 0.400
      ├── Some((2, 1)): 31/45 ≈ 0.689
      ├── Some((2, 2)): 17/30 ≈ 0.567
      ├── Some((2, 3)): 10/22 ≈ 0.455
      ├── Some((2, 4)): 19/32 ≈ 0.594
      ├── Some((2, 5)): 15/28 ≈ 0.536
      ├── Some((2, 6)): 8/20 ≈ 0.400
      ├── Some((2, 7)): 6/17 ≈ 0.353
      └── Some((2, 8)): 7/18 ≈ 0.389
    ├── Some((8, 3)): 117/225 ≈ 0.520
      ├── Some((3, 0)): 26/39 ≈ 0.667
      ├── Some((3, 1)): 14/26 ≈ 0.538
      ├── Some((3, 2)): 12/24 ≈ 0.500
      ├── Some((3, 3)): 7/18 ≈ 0.389
      ├── Some((3, 4)): 15/27 ≈ 0.556
      ├── Some((3, 5)): 10/22 ≈ 0.455
      ├── Some((3, 6)): 17/30 ≈ 0.567
      ├── Some((3, 7)): 13/25 ≈ 0.520
      └── Some((3, 8)): 3/13 ≈ 0.231
    ├── Some((8, 4)): 159/288 ≈ 0.552
      ├── Some((4, 0)): 23/38 ≈ 0.605
      ├── Some((4, 1)): 9/22 ≈ 0.409
      ├── Some((4, 2)): 9/22 ≈ 0.409
      ├── Some((4, 3)): 23/38 ≈ 0.605
      ├── Some((4, 4)): 23/39 ≈ 0.590
      ├── Some((4, 5)): 13/27 ≈ 0.481
      ├── Some((4, 6)): 33/49 ≈ 0.673
      ├── Some((4, 7)): 19/34 ≈ 0.559
      └── Some((4, 8)): 6/18 ≈ 0.333
    ├── Some((8, 5)): 127/240 ≈ 0.529
      ├── Some((5, 0)): 14/27 ≈ 0.519
      ├── Some((5, 1)): 30/44 ≈ 0.682
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 3)): 9/21 ≈ 0.429
      ├── Some((5, 4)): 7/18 ≈ 0.389
      ├── Some((5, 5)): 11/23 ≈ 0.478
      ├── Some((5, 6)): 14/27 ≈ 0.519
      ├── Some((5, 7)): 12/25 ≈ 0.480
      └── Some((5, 8)): 17/30 ≈ 0.567
    ├── Some((8, 6)): 92/187 ≈ 0.492
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 22/34 ≈ 0.647
      ├── Some((6, 2)): 10/21 ≈ 0.476
      ├── Some((6, 3)): 1/10 ≈ 0.100
      ├── Some((6, 4)): 8/18 ≈ 0.444
      ├── Some((6, 5)): 6/16 ≈ 0.375
      ├── Some((6, 6)): 7/17 ≈ 0.412
      ├── Some((6, 7)): 15/26 ≈ 0.577
      └── Some((6, 8)): 16/27 ≈ 0.593
    ├── Some((8, 7)): 210/363 ≈ 0.579
      ├── Some((7, 0)): 32/52 ≈ 0.615
      ├── Some((7, 1)): 36/57 ≈ 0.632
      ├── Some((7, 2)): 18/36 ≈ 0.500
      ├── Some((7, 3)): 17/34 ≈ 0.500
      ├── Some((7, 4)): 21/39 ≈ 0.538
      ├── Some((7, 5)): 31/51 ≈ 0.608
      ├── Some((7, 6)): 15/32 ≈ 0.469
      └── Some((7, 7)): 40/61 ≈ 0.656
    └── Some((8, 8)): 147/270 ≈ 0.544
      ├── Some((8, 0)): 16/31 ≈ 0.516
      ├── Some((8, 1)): 26/43 ≈ 0.605
      ├── Some((8, 2)): 32/49 ≈ 0.653
      ├── Some((8, 3)): 12/26 ≈ 0.462
      ├── Some((8, 4)): 11/25 ≈ 0.440
      ├── Some((8, 5)): 24/41 ≈ 0.585
      ├── Some((8, 6)): 15/30 ≈ 0.500
      └── Some((8, 7)): 10/24 ≈ 0.417
├── Some((0, 8)): 9432/17850 ≈ 0.528
  ├── Some((8, 0)): 721/1419 ≈ 0.508
    ├── Some((0, 0)): 62/135 ≈ 0.459
      ├── Some((0, 1)): 2/11 ≈ 0.182
      ├── Some((0, 2)): 10/21 ≈ 0.476
      ├── Some((0, 3)): 8/18 ≈ 0.444
      ├── Some((0, 4)): 13/24 ≈ 0.542
      ├── Some((0, 5)): 13/24 ≈ 0.542
      ├── Some((0, 6)): 12/23 ≈ 0.522
      └── Some((0, 7)): 4/13 ≈ 0.308
    ├── Some((0, 1)): 63/136 ≈ 0.463
      ├── Some((1, 0)): 7/15 ≈ 0.467
      ├── Some((1, 1)): 2/9 ≈ 0.222
      ├── Some((1, 2)): 7/15 ≈ 0.467
      ├── Some((1, 3)): 5/13 ≈ 0.385
      ├── Some((1, 4)): 5/13 ≈ 0.385
      ├── Some((1, 5)): 6/14 ≈ 0.429
      ├── Some((1, 6)): 12/21 ≈ 0.571
      ├── Some((1, 7)): 12/21 ≈ 0.571
      └── Some((1, 8)): 6/14 ≈ 0.429
    ├── Some((0, 2)): 107/203 ≈ 0.527
      ├── Some((2, 0)): 16/27 ≈ 0.593
      ├── Some((2, 1)): 6/16 ≈ 0.375
      ├── Some((2, 2)): 6/16 ≈ 0.375
      ├── Some((2, 3)): 13/24 ≈ 0.542
      ├── Some((2, 4)): 15/26 ≈ 0.577
      ├── Some((2, 5)): 9/19 ≈ 0.474
      ├── Some((2, 6)): 14/25 ≈ 0.560
      ├── Some((2, 7)): 11/22 ≈ 0.500
      └── Some((2, 8)): 16/27 ≈ 0.593
    ├── Some((0, 3)): 67/142 ≈ 0.472
      ├── Some((3, 0)): 9/18 ≈ 0.500
      ├── Some((3, 1)): 9/18 ≈ 0.500
      ├── Some((3, 2)): 5/13 ≈ 0.385
      ├── Some((3, 3)): 10/19 ≈ 0.526
      ├── Some((3, 4)): 1/8 ≈ 0.125
      ├── Some((3, 5)): 4/12 ≈ 0.333
      ├── Some((3, 6)): 16/25 ≈ 0.640
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((0, 4)): 138/249 ≈ 0.554
      ├── Some((4, 0)): 14/26 ≈ 0.538
      ├── Some((4, 1)): 18/31 ≈ 0.581
      ├── Some((4, 2)): 18/31 ≈ 0.581
      ├── Some((4, 3)): 27/41 ≈ 0.659
      ├── Some((4, 4)): 5/16 ≈ 0.312
      ├── Some((4, 5)): 24/37 ≈ 0.649
      ├── Some((4, 6)): 12/24 ≈ 0.500
      ├── Some((4, 7)): 11/23 ≈ 0.478
      └── Some((4, 8)): 8/19 ≈ 0.421
    ├── Some((0, 5)): 84/168 ≈ 0.500
      ├── Some((5, 0)): 7/16 ≈ 0.438
      ├── Some((5, 1)): 10/19 ≈ 0.526
      ├── Some((5, 2)): 15/25 ≈ 0.600
      ├── Some((5, 3)): 12/21 ≈ 0.571
      ├── Some((5, 4)): 17/27 ≈ 0.630
      ├── Some((5, 5)): 5/14 ≈ 0.357
      ├── Some((5, 6)): 6/15 ≈ 0.400
      ├── Some((5, 7)): 7/16 ≈ 0.438
      └── Some((5, 8)): 5/14 ≈ 0.357
    ├── Some((0, 6)): 89/176 ≈ 0.506
      ├── Some((6, 0)): 4/13 ≈ 0.308
      ├── Some((6, 1)): 16/26 ≈ 0.615
      ├── Some((6, 2)): 4/13 ≈ 0.308
      ├── Some((6, 3)): 6/15 ≈ 0.400
      ├── Some((6, 4)): 11/21 ≈ 0.524
      ├── Some((6, 5)): 13/23 ≈ 0.565
      ├── Some((6, 6)): 9/19 ≈ 0.474
      ├── Some((6, 7)): 15/25 ≈ 0.600
      └── Some((6, 8)): 10/20 ≈ 0.500
    └── Some((0, 7)): 111/209 ≈ 0.531
      ├── Some((7, 0)): 13/24 ≈ 0.542
      ├── Some((7, 1)): 13/24 ≈ 0.542
      ├── Some((7, 2)): 13/24 ≈ 0.542
      ├── Some((7, 3)): 13/24 ≈ 0.542
      ├── Some((7, 4)): 20/31 ≈ 0.645
      ├── Some((7, 5)): 6/16 ≈ 0.375
      ├── Some((7, 6)): 10/21 ≈ 0.476
      ├── Some((7, 7)): 13/24 ≈ 0.542
      └── Some((7, 8)): 9/20 ≈ 0.450
  ├── Some((8, 1)): 1314/2443 ≈ 0.538
    ├── Some((1, 0)): 164/300 ≈ 0.547
      ├── Some((0, 0)): 23/40 ≈ 0.575
      ├── Some((0, 1)): 23/40 ≈ 0.575
      ├── Some((0, 2)): 18/35 ≈ 0.514
      ├── Some((0, 3)): 20/37 ≈ 0.541
      ├── Some((0, 4)): 23/40 ≈ 0.575
      ├── Some((0, 5)): 17/33 ≈ 0.515
      ├── Some((0, 6)): 18/35 ≈ 0.514
      └── Some((0, 7)): 22/39 ≈ 0.564
    ├── Some((1, 1)): 200/353 ≈ 0.567
      ├── Some((1, 0)): 32/52 ≈ 0.615
      ├── Some((1, 2)): 30/50 ≈ 0.600
      ├── Some((1, 3)): 18/36 ≈ 0.500
      ├── Some((1, 4)): 34/55 ≈ 0.618
      ├── Some((1, 5)): 27/47 ≈ 0.574
      ├── Some((1, 6)): 28/48 ≈ 0.583
      ├── Some((1, 7)): 3/16 ≈ 0.188
      └── Some((1, 8)): 28/48 ≈ 0.583
    ├── Some((1, 2)): 130/248 ≈ 0.524
      ├── Some((2, 0)): 12/25 ≈ 0.480
      ├── Some((2, 1)): 10/22 ≈ 0.455
      ├── Some((2, 2)): 20/34 ≈ 0.588
      ├── Some((2, 3)): 19/33 ≈ 0.576
      ├── Some((2, 4)): 8/20 ≈ 0.400
      ├── Some((2, 5)): 8/20 ≈ 0.400
      ├── Some((2, 6)): 13/26 ≈ 0.500
      ├── Some((2, 7)): 16/30 ≈ 0.533
      └── Some((2, 8)): 23/37 ≈ 0.622
    ├── Some((1, 3)): 224/388 ≈ 0.577
      ├── Some((3, 0)): 10/25 ≈ 0.400
      ├── Some((3, 1)): 38/58 ≈ 0.655
      ├── Some((3, 2)): 27/46 ≈ 0.587
      ├── Some((3, 3)): 35/55 ≈ 0.636
      ├── Some((3, 4)): 33/53 ≈ 0.623
      ├── Some((3, 5)): 29/48 ≈ 0.604
      ├── Some((3, 6)): 7/21 ≈ 0.333
      ├── Some((3, 7)): 30/49 ≈ 0.612
      └── Some((3, 8)): 15/32 ≈ 0.469
    ├── Some((1, 4)): 81/172 ≈ 0.471
      ├── Some((4, 0)): 15/26 ≈ 0.577
      ├── Some((4, 1)): 3/12 ≈ 0.250
      ├── Some((4, 2)): 7/17 ≈ 0.412
      ├── Some((4, 3)): 3/12 ≈ 0.250
      ├── Some((4, 4)): 11/22 ≈ 0.500
      ├── Some((4, 5)): 5/15 ≈ 0.333
      ├── Some((4, 6)): 7/17 ≈ 0.412
      ├── Some((4, 7)): 22/33 ≈ 0.667
      └── Some((4, 8)): 7/17 ≈ 0.412
    ├── Some((1, 5)): 175/316 ≈ 0.554
      ├── Some((5, 0)): 27/44 ≈ 0.614
      ├── Some((5, 1)): 14/29 ≈ 0.483
      ├── Some((5, 2)): 23/40 ≈ 0.575
      ├── Some((5, 3)): 20/36 ≈ 0.556
      ├── Some((5, 4)): 20/36 ≈ 0.556
      ├── Some((5, 5)): 11/25 ≈ 0.440
      ├── Some((5, 6)): 30/47 ≈ 0.638
      ├── Some((5, 7)): 25/42 ≈ 0.595
      └── Some((5, 8)): 4/16 ≈ 0.250
    ├── Some((1, 6)): 104/209 ≈ 0.498
      ├── Some((6, 0)): 18/31 ≈ 0.581
      ├── Some((6, 1)): 10/22 ≈ 0.455
      ├── Some((6, 2)): 8/19 ≈ 0.421
      ├── Some((6, 3)): 7/18 ≈ 0.389
      ├── Some((6, 4)): 17/29 ≈ 0.586
      ├── Some((6, 5)): 16/28 ≈ 0.571
      ├── Some((6, 6)): 12/24 ≈ 0.500
      ├── Some((6, 7)): 7/18 ≈ 0.389
      └── Some((6, 8)): 8/19 ≈ 0.421
    ├── Some((1, 7)): 167/304 ≈ 0.549
      ├── Some((7, 0)): 16/31 ≈ 0.516
      ├── Some((7, 1)): 16/31 ≈ 0.516
      ├── Some((7, 2)): 12/26 ≈ 0.462
      ├── Some((7, 3)): 21/37 ≈ 0.568
      ├── Some((7, 4)): 20/35 ≈ 0.571
      ├── Some((7, 5)): 29/45 ≈ 0.644
      ├── Some((7, 6)): 17/32 ≈ 0.531
      ├── Some((7, 7)): 20/35 ≈ 0.571
      └── Some((7, 8)): 16/31 ≈ 0.516
    └── Some((1, 8)): 68/152 ≈ 0.447
      ├── Some((8, 0)): 16/28 ≈ 0.571
      ├── Some((8, 2)): 3/12 ≈ 0.250
      ├── Some((8, 3)): 10/21 ≈ 0.476
      ├── Some((8, 4)): 2/11 ≈ 0.182
      ├── Some((8, 5)): 8/19 ≈ 0.421
      ├── Some((8, 6)): 7/17 ≈ 0.412
      ├── Some((8, 7)): 11/22 ≈ 0.500
      └── Some((8, 8)): 10/21 ≈ 0.476
  ├── Some((8, 2)): 1127/2123 ≈ 0.531
    ├── Some((2, 0)): 85/175 ≈ 0.486
      ├── Some((0, 0)): 15/27 ≈ 0.556
      ├── Some((0, 1)): 8/19 ≈ 0.421
      ├── Some((0, 2)): 13/24 ≈ 0.542
      ├── Some((0, 3)): 10/21 ≈ 0.476
      ├── Some((0, 4)): 4/14 ≈ 0.286
      ├── Some((0, 5)): 17/29 ≈ 0.586
      ├── Some((0, 6)): 11/22 ≈ 0.500
      └── Some((0, 7)): 7/18 ≈ 0.389
    ├── Some((2, 1)): 147/269 ≈ 0.546
      ├── Some((1, 0)): 5/16 ≈ 0.312
      ├── Some((1, 1)): 21/35 ≈ 0.600
      ├── Some((1, 2)): 25/40 ≈ 0.625
      ├── Some((1, 3)): 9/22 ≈ 0.409
      ├── Some((1, 4)): 26/41 ≈ 0.634
      ├── Some((1, 5)): 14/27 ≈ 0.519
      ├── Some((1, 6)): 12/25 ≈ 0.480
      ├── Some((1, 7)): 24/39 ≈ 0.615
      └── Some((1, 8)): 10/23 ≈ 0.435
    ├── Some((2, 2)): 146/268 ≈ 0.545
      ├── Some((2, 0)): 11/25 ≈ 0.440
      ├── Some((2, 1)): 19/35 ≈ 0.543
      ├── Some((2, 3)): 13/27 ≈ 0.481
      ├── Some((2, 4)): 5/17 ≈ 0.294
      ├── Some((2, 5)): 17/32 ≈ 0.531
      ├── Some((2, 6)): 28/45 ≈ 0.622
      ├── Some((2, 7)): 28/45 ≈ 0.622
      └── Some((2, 8)): 25/41 ≈ 0.610
    ├── Some((2, 3)): 63/140 ≈ 0.450
      ├── Some((3, 0)): 4/12 ≈ 0.333
      ├── Some((3, 1)): 11/20 ≈ 0.550
      ├── Some((3, 2)): 5/13 ≈ 0.385
      ├── Some((3, 3)): 9/18 ≈ 0.500
      ├── Some((3, 4)): 6/14 ≈ 0.429
      ├── Some((3, 5)): 6/14 ≈ 0.429
      ├── Some((3, 6)): 6/14 ≈ 0.429
      ├── Some((3, 7)): 6/15 ≈ 0.400
      └── Some((3, 8)): 10/19 ≈ 0.526
    ├── Some((2, 4)): 206/355 ≈ 0.580
      ├── Some((4, 0)): 37/55 ≈ 0.673
      ├── Some((4, 1)): 9/23 ≈ 0.391
      ├── Some((4, 2)): 20/36 ≈ 0.556
      ├── Some((4, 3)): 25/42 ≈ 0.595
      ├── Some((4, 4)): 15/31 ≈ 0.484
      ├── Some((4, 5)): 31/49 ≈ 0.633
      ├── Some((4, 6)): 21/38 ≈ 0.553
      ├── Some((4, 7)): 20/36 ≈ 0.556
      └── Some((4, 8)): 27/44 ≈ 0.614
    ├── Some((2, 5)): 127/239 ≈ 0.531
      ├── Some((5, 0)): 23/36 ≈ 0.639
      ├── Some((5, 1)): 16/29 ≈ 0.552
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 3)): 12/24 ≈ 0.500
      ├── Some((5, 4)): 20/33 ≈ 0.606
      ├── Some((5, 5)): 19/32 ≈ 0.594
      ├── Some((5, 6)): 8/20 ≈ 0.400
      ├── Some((5, 7)): 8/20 ≈ 0.400
      └── Some((5, 8)): 8/20 ≈ 0.400
    ├── Some((2, 6)): 124/235 ≈ 0.528
      ├── Some((6, 0)): 9/21 ≈ 0.429
      ├── Some((6, 1)): 16/29 ≈ 0.552
      ├── Some((6, 2)): 20/33 ≈ 0.606
      ├── Some((6, 3)): 12/24 ≈ 0.500
      ├── Some((6, 4)): 6/17 ≈ 0.353
      ├── Some((6, 5)): 20/33 ≈ 0.606
      ├── Some((6, 6)): 10/22 ≈ 0.455
      ├── Some((6, 7)): 6/17 ≈ 0.353
      └── Some((6, 8)): 25/38 ≈ 0.658
    ├── Some((2, 7)): 118/226 ≈ 0.522
      ├── Some((7, 0)): 15/27 ≈ 0.556
      ├── Some((7, 1)): 13/25 ≈ 0.520
      ├── Some((7, 2)): 10/22 ≈ 0.455
      ├── Some((7, 3)): 13/25 ≈ 0.520
      ├── Some((7, 4)): 15/27 ≈ 0.556
      ├── Some((7, 5)): 4/14 ≈ 0.286
      ├── Some((7, 6)): 27/40 ≈ 0.675
      ├── Some((7, 7)): 6/17 ≈ 0.353
      └── Some((7, 8)): 15/28 ≈ 0.536
    └── Some((2, 8)): 111/215 ≈ 0.516
      ├── Some((8, 0)): 10/22 ≈ 0.455
      ├── Some((8, 1)): 6/17 ≈ 0.353
      ├── Some((8, 3)): 17/30 ≈ 0.567
      ├── Some((8, 4)): 12/25 ≈ 0.480
      ├── Some((8, 5)): 19/33 ≈ 0.576
      ├── Some((8, 6)): 9/21 ≈ 0.429
      ├── Some((8, 7)): 20/34 ≈ 0.588
      └── Some((8, 8)): 18/32 ≈ 0.562
  ├── Some((8, 3)): 1140/2145 ≈ 0.531
    ├── Some((3, 0)): 98/196 ≈ 0.500
      ├── Some((0, 0)): 11/23 ≈ 0.478
      ├── Some((0, 1)): 3/13 ≈ 0.231
      ├── Some((0, 2)): 19/32 ≈ 0.594
      ├── Some((0, 3)): 9/21 ≈ 0.429
      ├── Some((0, 4)): 14/27 ≈ 0.519
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 13/25 ≈ 0.520
      └── Some((0, 7)): 17/30 ≈ 0.567
    ├── Some((3, 1)): 107/209 ≈ 0.512
      ├── Some((1, 0)): 18/30 ≈ 0.600
      ├── Some((1, 1)): 21/33 ≈ 0.636
      ├── Some((1, 2)): 18/30 ≈ 0.600
      ├── Some((1, 3)): 3/13 ≈ 0.231
      ├── Some((1, 4)): 9/20 ≈ 0.450
      ├── Some((1, 5)): 6/16 ≈ 0.375
      ├── Some((1, 6)): 7/18 ≈ 0.389
      ├── Some((1, 7)): 14/26 ≈ 0.538
      └── Some((1, 8)): 11/22 ≈ 0.500
    ├── Some((3, 2)): 85/175 ≈ 0.486
      ├── Some((2, 0)): 13/23 ≈ 0.565
      ├── Some((2, 1)): 10/20 ≈ 0.500
      ├── Some((2, 2)): 7/17 ≈ 0.412
      ├── Some((2, 3)): 12/22 ≈ 0.545
      ├── Some((2, 4)): 16/27 ≈ 0.593
      ├── Some((2, 5)): 6/16 ≈ 0.375
      ├── Some((2, 6)): 4/13 ≈ 0.308
      ├── Some((2, 7)): 8/18 ≈ 0.444
      └── Some((2, 8)): 8/18 ≈ 0.444
    ├── Some((3, 3)): 153/278 ≈ 0.550
      ├── Some((3, 0)): 26/43 ≈ 0.605
      ├── Some((3, 1)): 14/29 ≈ 0.483
      ├── Some((3, 2)): 12/26 ≈ 0.462
      ├── Some((3, 4)): 30/47 ≈ 0.638
      ├── Some((3, 5)): 14/29 ≈ 0.483
      ├── Some((3, 6)): 18/34 ≈ 0.529
      ├── Some((3, 7)): 29/46 ≈ 0.630
      └── Some((3, 8)): 9/23 ≈ 0.391
    ├── Some((3, 4)): 186/327 ≈ 0.569
      ├── Some((4, 0)): 7/20 ≈ 0.350
      ├── Some((4, 1)): 40/58 ≈ 0.690
      ├── Some((4, 2)): 24/40 ≈ 0.600
      ├── Some((4, 3)): 15/30 ≈ 0.500
      ├── Some((4, 4)): 24/40 ≈ 0.600
      ├── Some((4, 5)): 28/45 ≈ 0.622
      ├── Some((4, 6)): 26/43 ≈ 0.605
      ├── Some((4, 7)): 8/21 ≈ 0.381
      └── Some((4, 8)): 14/29 ≈ 0.483
    ├── Some((3, 5)): 190/333 ≈ 0.571
      ├── Some((5, 0)): 22/38 ≈ 0.579
      ├── Some((5, 1)): 19/35 ≈ 0.543
      ├── Some((5, 2)): 24/41 ≈ 0.585
      ├── Some((5, 3)): 22/38 ≈ 0.579
      ├── Some((5, 4)): 36/54 ≈ 0.667
      ├── Some((5, 5)): 11/25 ≈ 0.440
      ├── Some((5, 6)): 13/28 ≈ 0.464
      ├── Some((5, 7)): 30/47 ≈ 0.638
      └── Some((5, 8)): 12/26 ≈ 0.462
    ├── Some((3, 6)): 69/150 ≈ 0.460
      ├── Some((6, 0)): 14/24 ≈ 0.583
      ├── Some((6, 1)): 9/18 ≈ 0.500
      ├── Some((6, 2)): 6/15 ≈ 0.400
      ├── Some((6, 3)): 2/10 ≈ 0.200
      ├── Some((6, 4)): 9/18 ≈ 0.500
      ├── Some((6, 5)): 11/21 ≈ 0.524
      ├── Some((6, 6)): 8/17 ≈ 0.471
      ├── Some((6, 7)): 3/11 ≈ 0.273
      └── Some((6, 8)): 6/15 ≈ 0.400
    ├── Some((3, 7)): 121/230 ≈ 0.526
      ├── Some((7, 0)): 19/32 ≈ 0.594
      ├── Some((7, 1)): 5/16 ≈ 0.312
      ├── Some((7, 2)): 8/19 ≈ 0.421
      ├── Some((7, 3)): 7/18 ≈ 0.389
      ├── Some((7, 4)): 22/35 ≈ 0.629
      ├── Some((7, 5)): 14/26 ≈ 0.538
      ├── Some((7, 6)): 21/34 ≈ 0.618
      ├── Some((7, 7)): 9/20 ≈ 0.450
      └── Some((7, 8)): 16/29 ≈ 0.552
    └── Some((3, 8)): 131/246 ≈ 0.533
      ├── Some((8, 0)): 22/38 ≈ 0.579
      ├── Some((8, 1)): 7/20 ≈ 0.350
      ├── Some((8, 2)): 13/27 ≈ 0.481
      ├── Some((8, 4)): 8/21 ≈ 0.381
      ├── Some((8, 5)): 8/21 ≈ 0.381
      ├── Some((8, 6)): 28/44 ≈ 0.636
      ├── Some((8, 7)): 29/45 ≈ 0.644
      └── Some((8, 8)): 15/29 ≈ 0.517
  ├── Some((8, 4)): 663/1317 ≈ 0.503
    ├── Some((4, 0)): 68/138 ≈ 0.493
      ├── Some((0, 0)): 11/20 ≈ 0.550
      ├── Some((0, 1)): 4/12 ≈ 0.333
      ├── Some((0, 2)): 8/17 ≈ 0.471
      ├── Some((0, 3)): 9/18 ≈ 0.500
      ├── Some((0, 4)): 7/16 ≈ 0.438
      ├── Some((0, 5)): 5/13 ≈ 0.385
      ├── Some((0, 6)): 11/20 ≈ 0.550
      └── Some((0, 7)): 12/21 ≈ 0.571
    ├── Some((4, 1)): 92/174 ≈ 0.529
      ├── Some((1, 0)): 19/29 ≈ 0.655
      ├── Some((1, 1)): 8/17 ≈ 0.471
      ├── Some((1, 2)): 11/20 ≈ 0.550
      ├── Some((1, 3)): 11/20 ≈ 0.550
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 8/17 ≈ 0.471
      ├── Some((1, 7)): 0/7 ≈ 0.000
      └── Some((1, 8)): 13/23 ≈ 0.565
    ├── Some((4, 2)): 116/209 ≈ 0.555
      ├── Some((2, 0)): 11/21 ≈ 0.524
      ├── Some((2, 1)): 16/27 ≈ 0.593
      ├── Some((2, 2)): 9/19 ≈ 0.474
      ├── Some((2, 3)): 12/22 ≈ 0.545
      ├── Some((2, 4)): 9/19 ≈ 0.474
      ├── Some((2, 5)): 12/22 ≈ 0.545
      ├── Some((2, 6)): 15/25 ≈ 0.600
      ├── Some((2, 7)): 23/34 ≈ 0.676
      └── Some((2, 8)): 9/19 ≈ 0.474
    ├── Some((4, 3)): 76/150 ≈ 0.507
      ├── Some((3, 0)): 20/29 ≈ 0.690
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 2)): 9/17 ≈ 0.529
      ├── Some((3, 3)): 8/16 ≈ 0.500
      ├── Some((3, 4)): 14/23 ≈ 0.609
      ├── Some((3, 5)): 2/9 ≈ 0.222
      ├── Some((3, 6)): 7/15 ≈ 0.467
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 6/14 ≈ 0.429
    ├── Some((4, 4)): 64/132 ≈ 0.485
      ├── Some((4, 0)): 3/11 ≈ 0.273
      ├── Some((4, 1)): 11/20 ≈ 0.550
      ├── Some((4, 2)): 8/16 ≈ 0.500
      ├── Some((4, 3)): 11/20 ≈ 0.550
      ├── Some((4, 5)): 6/14 ≈ 0.429
      ├── Some((4, 6)): 8/16 ≈ 0.500
      ├── Some((4, 7)): 9/18 ≈ 0.500
      └── Some((4, 8)): 8/16 ≈ 0.500
    ├── Some((4, 5)): 58/123 ≈ 0.472
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 1)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 11/19 ≈ 0.579
      ├── Some((5, 5)): 9/16 ≈ 0.562
      ├── Some((5, 6)): 4/11 ≈ 0.364
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 8/15 ≈ 0.533
    ├── Some((4, 6)): 44/102 ≈ 0.431
      ├── Some((6, 0)): 8/15 ≈ 0.533
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 5/12 ≈ 0.417
      ├── Some((6, 4)): 2/8 ≈ 0.250
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 4/10 ≈ 0.400
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((4, 7)): 103/190 ≈ 0.542
      ├── Some((7, 0)): 10/20 ≈ 0.500
      ├── Some((7, 1)): 15/25 ≈ 0.600
      ├── Some((7, 2)): 11/21 ≈ 0.524
      ├── Some((7, 3)): 3/11 ≈ 0.273
      ├── Some((7, 4)): 12/22 ≈ 0.545
      ├── Some((7, 5)): 7/16 ≈ 0.438
      ├── Some((7, 6)): 14/24 ≈ 0.583
      ├── Some((7, 7)): 12/22 ≈ 0.545
      └── Some((7, 8)): 18/28 ≈ 0.643
    └── Some((4, 8)): 42/98 ≈ 0.429
      ├── Some((8, 0)): 8/15 ≈ 0.533
      ├── Some((8, 1)): 2/8 ≈ 0.250
      ├── Some((8, 2)): 5/12 ≈ 0.417
      ├── Some((8, 3)): 6/13 ≈ 0.462
      ├── Some((8, 5)): 4/11 ≈ 0.364
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 7/14 ≈ 0.500
      └── Some((8, 8)): 5/12 ≈ 0.417
  ├── Some((8, 5)): 1185/2223 ≈ 0.533
    ├── Some((5, 0)): 120/230 ≈ 0.522
      ├── Some((0, 0)): 17/31 ≈ 0.548
      ├── Some((0, 1)): 22/37 ≈ 0.595
      ├── Some((0, 2)): 4/15 ≈ 0.267
      ├── Some((0, 3)): 8/21 ≈ 0.381
      ├── Some((0, 4)): 20/35 ≈ 0.571
      ├── Some((0, 5)): 16/30 ≈ 0.533
      ├── Some((0, 6)): 14/28 ≈ 0.500
      └── Some((0, 7)): 18/32 ≈ 0.562
    ├── Some((5, 1)): 121/231 ≈ 0.524
      ├── Some((1, 0)): 20/33 ≈ 0.606
      ├── Some((1, 1)): 13/25 ≈ 0.520
      ├── Some((1, 2)): 7/18 ≈ 0.389
      ├── Some((1, 3)): 22/35 ≈ 0.629
      ├── Some((1, 4)): 15/27 ≈ 0.556
      ├── Some((1, 5)): 13/25 ≈ 0.520
      ├── Some((1, 6)): 10/22 ≈ 0.455
      ├── Some((1, 7)): 6/17 ≈ 0.353
      └── Some((1, 8)): 15/28 ≈ 0.536
    ├── Some((5, 2)): 138/257 ≈ 0.537
      ├── Some((2, 0)): 16/30 ≈ 0.533
      ├── Some((2, 1)): 10/23 ≈ 0.435
      ├── Some((2, 2)): 26/41 ≈ 0.634
      ├── Some((2, 3)): 28/43 ≈ 0.651
      ├── Some((2, 4)): 13/26 ≈ 0.500
      ├── Some((2, 5)): 15/28 ≈ 0.536
      ├── Some((2, 6)): 20/34 ≈ 0.588
      ├── Some((2, 7)): 2/12 ≈ 0.167
      └── Some((2, 8)): 7/19 ≈ 0.368
    ├── Some((5, 3)): 103/204 ≈ 0.505
      ├── Some((3, 0)): 17/29 ≈ 0.586
      ├── Some((3, 1)): 5/15 ≈ 0.333
      ├── Some((3, 2)): 13/25 ≈ 0.520
      ├── Some((3, 3)): 10/21 ≈ 0.476
      ├── Some((3, 4)): 16/28 ≈ 0.571
      ├── Some((3, 5)): 5/15 ≈ 0.333
      ├── Some((3, 6)): 11/22 ≈ 0.500
      ├── Some((3, 7)): 10/21 ≈ 0.476
      └── Some((3, 8)): 15/27 ≈ 0.556
    ├── Some((5, 4)): 164/296 ≈ 0.554
      ├── Some((4, 0)): 14/28 ≈ 0.500
      ├── Some((4, 1)): 10/23 ≈ 0.435
      ├── Some((4, 2)): 21/36 ≈ 0.583
      ├── Some((4, 3)): 23/39 ≈ 0.590
      ├── Some((4, 4)): 15/30 ≈ 0.500
      ├── Some((4, 5)): 27/43 ≈ 0.628
      ├── Some((4, 6)): 3/14 ≈ 0.214
      ├── Some((4, 7)): 26/42 ≈ 0.619
      └── Some((4, 8)): 24/40 ≈ 0.600
    ├── Some((5, 5)): 96/193 ≈ 0.497
      ├── Some((5, 0)): 13/25 ≈ 0.520
      ├── Some((5, 1)): 7/18 ≈ 0.389
      ├── Some((5, 2)): 9/21 ≈ 0.429
      ├── Some((5, 3)): 8/19 ≈ 0.421
      ├── Some((5, 4)): 12/24 ≈ 0.500
      ├── Some((5, 6)): 9/21 ≈ 0.429
      ├── Some((5, 7)): 17/30 ≈ 0.567
      └── Some((5, 8)): 21/34 ≈ 0.618
    ├── Some((5, 6)): 195/341 ≈ 0.572
      ├── Some((6, 0)): 14/29 ≈ 0.483
      ├── Some((6, 1)): 16/31 ≈ 0.516
      ├── Some((6, 2)): 41/59 ≈ 0.695
      ├── Some((6, 3)): 24/41 ≈ 0.585
      ├── Some((6, 4)): 18/34 ≈ 0.529
      ├── Some((6, 5)): 22/38 ≈ 0.579
      ├── Some((6, 6)): 25/42 ≈ 0.595
      ├── Some((6, 7)): 16/32 ≈ 0.500
      └── Some((6, 8)): 18/34 ≈ 0.529
    ├── Some((5, 7)): 137/255 ≈ 0.537
      ├── Some((7, 0)): 16/29 ≈ 0.552
      ├── Some((7, 1)): 20/34 ≈ 0.588
      ├── Some((7, 2)): 11/23 ≈ 0.478
      ├── Some((7, 3)): 11/23 ≈ 0.478
      ├── Some((7, 4)): 18/32 ≈ 0.562
      ├── Some((7, 5)): 12/25 ≈ 0.480
      ├── Some((7, 6)): 30/44 ≈ 0.682
      ├── Some((7, 7)): 11/24 ≈ 0.458
      └── Some((7, 8)): 8/20 ≈ 0.400
    └── Some((5, 8)): 110/215 ≈ 0.512
      ├── Some((8, 0)): 15/28 ≈ 0.536
      ├── Some((8, 1)): 19/33 ≈ 0.576
      ├── Some((8, 2)): 17/31 ≈ 0.548
      ├── Some((8, 3)): 5/16 ≈ 0.312
      ├── Some((8, 4)): 8/20 ≈ 0.400
      ├── Some((8, 6)): 25/40 ≈ 0.625
      ├── Some((8, 7)): 8/20 ≈ 0.400
      └── Some((8, 8)): 13/26 ≈ 0.500
  ├── Some((8, 6)): 1663/3037 ≈ 0.548
    ├── Some((6, 0)): 226/400 ≈ 0.565
      ├── Some((0, 0)): 38/62 ≈ 0.613
      ├── Some((0, 1)): 39/63 ≈ 0.619
      ├── Some((0, 2)): 29/51 ≈ 0.569
      ├── Some((0, 3)): 40/64 ≈ 0.625
      ├── Some((0, 4)): 26/48 ≈ 0.542
      ├── Some((0, 5)): 19/39 ≈ 0.487
      ├── Some((0, 6)): 11/28 ≈ 0.393
      └── Some((0, 7)): 23/44 ≈ 0.523
    ├── Some((6, 1)): 162/303 ≈ 0.535
      ├── Some((1, 0)): 21/37 ≈ 0.568
      ├── Some((1, 1)): 17/33 ≈ 0.515
      ├── Some((1, 2)): 7/20 ≈ 0.350
      ├── Some((1, 3)): 6/19 ≈ 0.316
      ├── Some((1, 4)): 19/35 ≈ 0.543
      ├── Some((1, 5)): 23/40 ≈ 0.575
      ├── Some((1, 6)): 21/38 ≈ 0.553
      ├── Some((1, 7)): 14/29 ≈ 0.483
      └── Some((1, 8)): 33/51 ≈ 0.647
    ├── Some((6, 2)): 112/226 ≈ 0.496
      ├── Some((2, 0)): 15/28 ≈ 0.536
      ├── Some((2, 1)): 16/30 ≈ 0.533
      ├── Some((2, 2)): 5/16 ≈ 0.312
      ├── Some((2, 3)): 9/21 ≈ 0.429
      ├── Some((2, 4)): 13/26 ≈ 0.500
      ├── Some((2, 5)): 3/14 ≈ 0.214
      ├── Some((2, 6)): 19/33 ≈ 0.576
      ├── Some((2, 7)): 4/15 ≈ 0.267
      └── Some((2, 8)): 27/42 ≈ 0.643
    ├── Some((6, 3)): 160/300 ≈ 0.533
      ├── Some((3, 0)): 7/20 ≈ 0.350
      ├── Some((3, 1)): 12/27 ≈ 0.444
      ├── Some((3, 2)): 18/34 ≈ 0.529
      ├── Some((3, 3)): 10/24 ≈ 0.417
      ├── Some((3, 4)): 28/45 ≈ 0.622
      ├── Some((3, 5)): 39/58 ≈ 0.672
      ├── Some((3, 6)): 11/25 ≈ 0.440
      ├── Some((3, 7)): 12/27 ≈ 0.444
      └── Some((3, 8)): 22/39 ≈ 0.564
    ├── Some((6, 4)): 210/376 ≈ 0.559
      ├── Some((4, 0)): 11/27 ≈ 0.407
      ├── Some((4, 1)): 36/57 ≈ 0.632
      ├── Some((4, 2)): 17/34 ≈ 0.500
      ├── Some((4, 3)): 30/50 ≈ 0.600
      ├── Some((4, 4)): 13/29 ≈ 0.448
      ├── Some((4, 5)): 14/31 ≈ 0.452
      ├── Some((4, 6)): 14/31 ≈ 0.452
      ├── Some((4, 7)): 44/66 ≈ 0.667
      └── Some((4, 8)): 30/50 ≈ 0.600
    ├── Some((6, 5)): 267/460 ≈ 0.580
      ├── Some((5, 0)): 6/21 ≈ 0.286
      ├── Some((5, 1)): 44/68 ≈ 0.647
      ├── Some((5, 2)): 28/50 ≈ 0.560
      ├── Some((5, 3)): 22/42 ≈ 0.524
      ├── Some((5, 4)): 55/81 ≈ 0.679
      ├── Some((5, 5)): 27/49 ≈ 0.551
      ├── Some((5, 6)): 37/60 ≈ 0.617
      ├── Some((5, 7)): 14/32 ≈ 0.438
      └── Some((5, 8)): 33/56 ≈ 0.589
    ├── Some((6, 6)): 147/281 ≈ 0.523
      ├── Some((6, 0)): 12/27 ≈ 0.444
      ├── Some((6, 1)): 26/44 ≈ 0.591
      ├── Some((6, 2)): 19/36 ≈ 0.528
      ├── Some((6, 3)): 12/28 ≈ 0.429
      ├── Some((6, 4)): 25/43 ≈ 0.581
      ├── Some((6, 5)): 18/35 ≈ 0.514
      ├── Some((6, 7)): 18/35 ≈ 0.514
      └── Some((6, 8)): 16/32 ≈ 0.500
    ├── Some((6, 7)): 200/361 ≈ 0.554
      ├── Some((7, 0)): 14/30 ≈ 0.467
      ├── Some((7, 1)): 25/43 ≈ 0.581
      ├── Some((7, 2)): 17/34 ≈ 0.500
      ├── Some((7, 3)): 29/48 ≈ 0.604
      ├── Some((7, 4)): 26/45 ≈ 0.578
      ├── Some((7, 5)): 21/39 ≈ 0.538
      ├── Some((7, 6)): 31/50 ≈ 0.620
      ├── Some((7, 7)): 20/37 ≈ 0.541
      └── Some((7, 8)): 17/34 ≈ 0.500
    └── Some((6, 8)): 179/329 ≈ 0.544
      ├── Some((8, 0)): 9/25 ≈ 0.360
      ├── Some((8, 1)): 22/41 ≈ 0.537
      ├── Some((8, 2)): 37/59 ≈ 0.627
      ├── Some((8, 3)): 14/31 ≈ 0.452
      ├── Some((8, 4)): 46/69 ≈ 0.667
      ├── Some((8, 5)): 21/40 ≈ 0.525
      ├── Some((8, 7)): 8/23 ≈ 0.348
      └── Some((8, 8)): 21/40 ≈ 0.525
  ├── Some((8, 7)): 1017/1934 ≈ 0.526
    ├── Some((7, 0)): 146/264 ≈ 0.553
      ├── Some((0, 0)): 16/31 ≈ 0.516
      ├── Some((0, 1)): 5/17 ≈ 0.294
      ├── Some((0, 2)): 20/35 ≈ 0.571
      ├── Some((0, 3)): 15/29 ≈ 0.517
      ├── Some((0, 4)): 17/32 ≈ 0.531
      ├── Some((0, 5)): 19/34 ≈ 0.559
      ├── Some((0, 6)): 36/53 ≈ 0.679
      └── Some((0, 7)): 17/32 ≈ 0.531
    ├── Some((7, 1)): 106/205 ≈ 0.517
      ├── Some((1, 0)): 13/24 ≈ 0.542
      ├── Some((1, 1)): 16/27 ≈ 0.593
      ├── Some((1, 2)): 5/15 ≈ 0.333
      ├── Some((1, 3)): 16/28 ≈ 0.571
      ├── Some((1, 4)): 7/17 ≈ 0.412
      ├── Some((1, 5)): 9/20 ≈ 0.450
      ├── Some((1, 6)): 10/21 ≈ 0.476
      ├── Some((1, 7)): 20/32 ≈ 0.625
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((7, 2)): 88/177 ≈ 0.497
      ├── Some((2, 0)): 16/26 ≈ 0.615
      ├── Some((2, 1)): 13/23 ≈ 0.565
      ├── Some((2, 2)): 9/19 ≈ 0.474
      ├── Some((2, 3)): 6/15 ≈ 0.400
      ├── Some((2, 4)): 11/21 ≈ 0.524
      ├── Some((2, 5)): 3/12 ≈ 0.250
      ├── Some((2, 6)): 9/19 ≈ 0.474
      ├── Some((2, 7)): 14/24 ≈ 0.583
      └── Some((2, 8)): 7/17 ≈ 0.412
    ├── Some((7, 3)): 64/140 ≈ 0.457
      ├── Some((3, 0)): 9/18 ≈ 0.500
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 2)): 13/22 ≈ 0.591
      ├── Some((3, 3)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 9/18 ≈ 0.500
      ├── Some((3, 5)): 2/9 ≈ 0.222
      ├── Some((3, 6)): 9/18 ≈ 0.500
      ├── Some((3, 7)): 2/9 ≈ 0.222
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((7, 4)): 108/208 ≈ 0.519
      ├── Some((4, 0)): 14/25 ≈ 0.560
      ├── Some((4, 1)): 13/24 ≈ 0.542
      ├── Some((4, 2)): 16/27 ≈ 0.593
      ├── Some((4, 3)): 5/15 ≈ 0.333
      ├── Some((4, 4)): 8/19 ≈ 0.421
      ├── Some((4, 5)): 8/19 ≈ 0.421
      ├── Some((4, 6)): 20/32 ≈ 0.625
      ├── Some((4, 7)): 13/24 ≈ 0.542
      └── Some((4, 8)): 11/22 ≈ 0.500
    ├── Some((7, 5)): 117/221 ≈ 0.529
      ├── Some((5, 0)): 8/19 ≈ 0.421
      ├── Some((5, 1)): 27/40 ≈ 0.675
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 19/31 ≈ 0.613
      ├── Some((5, 4)): 19/31 ≈ 0.613
      ├── Some((5, 5)): 7/18 ≈ 0.389
      ├── Some((5, 6)): 9/20 ≈ 0.450
      ├── Some((5, 7)): 11/22 ≈ 0.500
      └── Some((5, 8)): 6/17 ≈ 0.353
    ├── Some((7, 6)): 102/199 ≈ 0.513
      ├── Some((6, 0)): 9/20 ≈ 0.450
      ├── Some((6, 1)): 11/22 ≈ 0.500
      ├── Some((6, 2)): 14/25 ≈ 0.560
      ├── Some((6, 3)): 13/24 ≈ 0.542
      ├── Some((6, 4)): 17/28 ≈ 0.607
      ├── Some((6, 5)): 9/20 ≈ 0.450
      ├── Some((6, 6)): 8/18 ≈ 0.444
      ├── Some((6, 7)): 8/18 ≈ 0.444
      └── Some((6, 8)): 12/23 ≈ 0.522
    ├── Some((7, 7)): 145/263 ≈ 0.551
      ├── Some((7, 0)): 22/37 ≈ 0.595
      ├── Some((7, 1)): 9/22 ≈ 0.409
      ├── Some((7, 2)): 8/21 ≈ 0.381
      ├── Some((7, 3)): 19/34 ≈ 0.559
      ├── Some((7, 4)): 15/29 ≈ 0.517
      ├── Some((7, 5)): 21/36 ≈ 0.583
      ├── Some((7, 6)): 23/39 ≈ 0.590
      └── Some((7, 8)): 28/44 ≈ 0.636
    └── Some((7, 8)): 140/256 ≈ 0.547
      ├── Some((8, 0)): 25/41 ≈ 0.610
      ├── Some((8, 1)): 10/23 ≈ 0.435
      ├── Some((8, 2)): 23/38 ≈ 0.605
      ├── Some((8, 3)): 9/22 ≈ 0.409
      ├── Some((8, 4)): 18/33 ≈ 0.545
      ├── Some((8, 5)): 24/40 ≈ 0.600
      ├── Some((8, 6)): 14/28 ≈ 0.500
      └── Some((8, 8)): 16/30 ≈ 0.533
  └── Some((8, 8)): 601/1208 ≈ 0.498
    ├── Some((8, 0)): 82/162 ≈ 0.506
      ├── Some((0, 0)): 10/20 ≈ 0.500
      ├── Some((0, 1)): 10/20 ≈ 0.500
      ├── Some((0, 2)): 22/33 ≈ 0.667
      ├── Some((0, 3)): 15/26 ≈ 0.577
      ├── Some((0, 4)): 5/14 ≈ 0.357
      ├── Some((0, 5)): 2/11 ≈ 0.182
      ├── Some((0, 6)): 6/16 ≈ 0.375
      └── Some((0, 7)): 11/21 ≈ 0.524
    ├── Some((8, 1)): 152/265 ≈ 0.574
      ├── Some((1, 0)): 11/23 ≈ 0.478
      ├── Some((1, 1)): 16/28 ≈ 0.571
      ├── Some((1, 2)): 22/35 ≈ 0.629
      ├── Some((1, 3)): 19/32 ≈ 0.594
      ├── Some((1, 4)): 19/32 ≈ 0.594
      ├── Some((1, 5)): 17/30 ≈ 0.567
      ├── Some((1, 6)): 18/31 ≈ 0.581
      ├── Some((1, 7)): 22/35 ≈ 0.629
      └── Some((1, 8)): 7/18 ≈ 0.389
    ├── Some((8, 2)): 81/161 ≈ 0.503
      ├── Some((2, 0)): 11/20 ≈ 0.550
      ├── Some((2, 1)): 4/12 ≈ 0.333
      ├── Some((2, 2)): 13/22 ≈ 0.591
      ├── Some((2, 3)): 6/15 ≈ 0.400
      ├── Some((2, 4)): 9/18 ≈ 0.500
      ├── Some((2, 5)): 8/17 ≈ 0.471
      ├── Some((2, 6)): 14/24 ≈ 0.583
      ├── Some((2, 7)): 12/21 ≈ 0.571
      └── Some((2, 8)): 3/11 ≈ 0.273
    ├── Some((8, 3)): 58/125 ≈ 0.464
      ├── Some((3, 0)): 11/19 ≈ 0.579
      ├── Some((3, 1)): 6/14 ≈ 0.429
      ├── Some((3, 2)): 4/11 ≈ 0.364
      ├── Some((3, 3)): 4/11 ≈ 0.364
      ├── Some((3, 4)): 11/19 ≈ 0.579
      ├── Some((3, 5)): 5/12 ≈ 0.417
      ├── Some((3, 6)): 4/11 ≈ 0.364
      ├── Some((3, 7)): 2/9 ≈ 0.222
      └── Some((3, 8)): 10/18 ≈ 0.556
    ├── Some((8, 4)): 66/138 ≈ 0.478
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 4/12 ≈ 0.333
      ├── Some((4, 2)): 13/21 ≈ 0.619
      ├── Some((4, 3)): 14/22 ≈ 0.636
      ├── Some((4, 4)): 3/10 ≈ 0.300
      ├── Some((4, 5)): 7/15 ≈ 0.467
      ├── Some((4, 6)): 10/18 ≈ 0.556
      ├── Some((4, 7)): 4/12 ≈ 0.333
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((8, 5)): 73/149 ≈ 0.490
      ├── Some((5, 0)): 5/13 ≈ 0.385
      ├── Some((5, 1)): 11/20 ≈ 0.550
      ├── Some((5, 2)): 4/12 ≈ 0.333
      ├── Some((5, 3)): 6/14 ≈ 0.429
      ├── Some((5, 4)): 10/18 ≈ 0.556
      ├── Some((5, 5)): 17/26 ≈ 0.654
      ├── Some((5, 6)): 4/12 ≈ 0.333
      ├── Some((5, 7)): 11/20 ≈ 0.550
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((8, 6)): 38/94 ≈ 0.404
      ├── Some((6, 0)): 9/16 ≈ 0.562
      ├── Some((6, 1)): 2/8 ≈ 0.250
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 6)): 1/7 ≈ 0.143
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 5/11 ≈ 0.455
    └── Some((8, 7)): 50/113 ≈ 0.442
      ├── Some((7, 0)): 14/21 ≈ 0.667
      ├── Some((7, 1)): 12/19 ≈ 0.632
      ├── Some((7, 2)): 6/13 ≈ 0.462
      ├── Some((7, 3)): 5/12 ≈ 0.417
      ├── Some((7, 4)): 1/7 ≈ 0.143
      ├── Some((7, 5)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 4/11 ≈ 0.364
      ├── Some((7, 7)): 2/9 ≈ 0.222
      └── Some((7, 8)): 4/11 ≈ 0.364
├── Some((1, 0)): 3649/7241 ≈ 0.504
  ├── Some((0, 0)): 308/638 ≈ 0.483
    ├── Some((0, 1)): 37/78 ≈ 0.474
      ├── Some((1, 1)): 0/5 ≈ 0.000
      ├── Some((1, 2)): 10/15 ≈ 0.667
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 7/12 ≈ 0.583
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 8/13 ≈ 0.615
    ├── Some((0, 2)): 45/89 ≈ 0.506
      ├── Some((2, 0)): 8/13 ≈ 0.615
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 11/15 ≈ 0.733
      ├── Some((2, 4)): 6/11 ≈ 0.545
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 4/9 ≈ 0.444
      ├── Some((2, 7)): 4/9 ≈ 0.444
      └── Some((2, 8)): 1/6 ≈ 0.167
    ├── Some((0, 3)): 36/76 ≈ 0.474
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 6/10 ≈ 0.600
      ├── Some((3, 3)): 6/10 ≈ 0.600
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 1/5 ≈ 0.200
      ├── Some((3, 6)): 4/9 ≈ 0.444
      ├── Some((3, 7)): 5/9 ≈ 0.556
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((0, 4)): 33/72 ≈ 0.458
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 8/12 ≈ 0.667
      ├── Some((4, 2)): 2/7 ≈ 0.286
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 5/9 ≈ 0.556
      ├── Some((4, 5)): 1/5 ≈ 0.200
      ├── Some((4, 6)): 6/10 ≈ 0.600
      ├── Some((4, 7)): 4/8 ≈ 0.500
      └── Some((4, 8)): 4/8 ≈ 0.500
    ├── Some((0, 5)): 53/100 ≈ 0.530
      ├── Some((5, 0)): 14/19 ≈ 0.737
      ├── Some((5, 1)): 1/6 ≈ 0.167
      ├── Some((5, 2)): 7/12 ≈ 0.583
      ├── Some((5, 3)): 7/12 ≈ 0.583
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 5/11 ≈ 0.455
      ├── Some((5, 6)): 3/9 ≈ 0.333
      ├── Some((5, 7)): 7/12 ≈ 0.583
      └── Some((5, 8)): 7/12 ≈ 0.583
    ├── Some((0, 6)): 32/71 ≈ 0.451
      ├── Some((6, 0)): 7/11 ≈ 0.636
      ├── Some((6, 1)): 8/12 ≈ 0.667
      ├── Some((6, 2)): 2/6 ≈ 0.333
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 4/8 ≈ 0.500
      ├── Some((6, 6)): 3/8 ≈ 0.375
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 1/5 ≈ 0.200
    ├── Some((0, 7)): 45/89 ≈ 0.506
      ├── Some((7, 0)): 5/10 ≈ 0.500
      ├── Some((7, 1)): 7/12 ≈ 0.583
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 3/8 ≈ 0.375
      ├── Some((7, 6)): 8/12 ≈ 0.667
      ├── Some((7, 7)): 8/13 ≈ 0.615
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((0, 8)): 26/62 ≈ 0.419
      ├── Some((8, 0)): 4/8 ≈ 0.500
      ├── Some((8, 1)): 2/6 ≈ 0.333
      ├── Some((8, 2)): 4/8 ≈ 0.500
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 4/8 ≈ 0.500
      ├── Some((8, 7)): 5/9 ≈ 0.556
      └── Some((8, 8)): 2/6 ≈ 0.333
  ├── Some((0, 1)): 606/1148 ≈ 0.528
    ├── Some((1, 1)): 88/161 ≈ 0.547
      ├── Some((1, 2)): 12/23 ≈ 0.522
      ├── Some((1, 3)): 8/18 ≈ 0.444
      ├── Some((1, 4)): 17/28 ≈ 0.607
      ├── Some((1, 5)): 8/18 ≈ 0.444
      ├── Some((1, 6)): 24/35 ≈ 0.686
      ├── Some((1, 7)): 10/20 ≈ 0.500
      └── Some((1, 8)): 8/18 ≈ 0.444
    ├── Some((1, 2)): 93/168 ≈ 0.554
      ├── Some((2, 0)): 19/27 ≈ 0.704
      ├── Some((2, 1)): 5/13 ≈ 0.385
      ├── Some((2, 2)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 4/12 ≈ 0.333
      ├── Some((2, 4)): 15/24 ≈ 0.625
      ├── Some((2, 5)): 9/17 ≈ 0.529
      ├── Some((2, 6)): 12/21 ≈ 0.571
      ├── Some((2, 7)): 11/19 ≈ 0.579
      └── Some((2, 8)): 11/19 ≈ 0.579
    ├── Some((1, 3)): 82/152 ≈ 0.539
      ├── Some((3, 0)): 6/14 ≈ 0.429
      ├── Some((3, 1)): 2/9 ≈ 0.222
      ├── Some((3, 2)): 15/23 ≈ 0.652
      ├── Some((3, 3)): 4/11 ≈ 0.364
      ├── Some((3, 4)): 9/17 ≈ 0.529
      ├── Some((3, 5)): 7/15 ≈ 0.467
      ├── Some((3, 6)): 12/20 ≈ 0.600
      ├── Some((3, 7)): 9/17 ≈ 0.529
      └── Some((3, 8)): 18/25 ≈ 0.720
    ├── Some((1, 4)): 61/122 ≈ 0.500
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 9/16 ≈ 0.562
      ├── Some((4, 2)): 11/18 ≈ 0.611
      ├── Some((4, 3)): 9/16 ≈ 0.562
      ├── Some((4, 4)): 11/18 ≈ 0.611
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 6/13 ≈ 0.462
      └── Some((4, 8)): 2/8 ≈ 0.250
    ├── Some((1, 5)): 57/116 ≈ 0.491
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 11/17 ≈ 0.647
      ├── Some((5, 2)): 9/16 ≈ 0.562
      ├── Some((5, 3)): 11/17 ≈ 0.647
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 0/6 ≈ 0.000
      ├── Some((5, 7)): 9/16 ≈ 0.562
      └── Some((5, 8)): 1/7 ≈ 0.143
    ├── Some((1, 6)): 92/167 ≈ 0.551
      ├── Some((6, 0)): 8/16 ≈ 0.500
      ├── Some((6, 1)): 14/23 ≈ 0.609
      ├── Some((6, 2)): 6/14 ≈ 0.429
      ├── Some((6, 3)): 11/19 ≈ 0.579
      ├── Some((6, 4)): 14/23 ≈ 0.609
      ├── Some((6, 5)): 17/26 ≈ 0.654
      ├── Some((6, 6)): 5/13 ≈ 0.385
      ├── Some((6, 7)): 7/15 ≈ 0.467
      └── Some((6, 8)): 9/17 ≈ 0.529
    ├── Some((1, 7)): 73/140 ≈ 0.521
      ├── Some((7, 0)): 13/20 ≈ 0.650
      ├── Some((7, 1)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 9/17 ≈ 0.529
      ├── Some((7, 3)): 13/21 ≈ 0.619
      ├── Some((7, 4)): 6/13 ≈ 0.462
      ├── Some((7, 5)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 11/19 ≈ 0.579
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 7/14 ≈ 0.500
    └── Some((1, 8)): 60/121 ≈ 0.496
      ├── Some((8, 0)): 4/11 ≈ 0.364
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 6/13 ≈ 0.462
      ├── Some((8, 3)): 3/9 ≈ 0.333
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 2/8 ≈ 0.250
      ├── Some((8, 6)): 20/26 ≈ 0.769
      ├── Some((8, 7)): 3/10 ≈ 0.300
      └── Some((8, 8)): 9/16 ≈ 0.562
  ├── Some((0, 2)): 337/689 ≈ 0.489
    ├── Some((2, 0)): 37/76 ≈ 0.487
      ├── Some((0, 0)): 5/10 ≈ 0.500
      ├── Some((0, 1)): 1/6 ≈ 0.167
      ├── Some((0, 3)): 6/10 ≈ 0.600
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 6/11 ≈ 0.545
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 6/11 ≈ 0.545
      └── Some((0, 8)): 6/11 ≈ 0.545
    ├── Some((2, 1)): 36/75 ≈ 0.480
      ├── Some((1, 1)): 4/9 ≈ 0.444
      ├── Some((1, 2)): 0/5 ≈ 0.000
      ├── Some((1, 3)): 8/13 ≈ 0.615
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 7/12 ≈ 0.583
      ├── Some((1, 7)): 9/13 ≈ 0.692
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((2, 2)): 51/96 ≈ 0.531
      ├── Some((2, 0)): 4/10 ≈ 0.400
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 13/18 ≈ 0.722
      ├── Some((2, 5)): 10/15 ≈ 0.667
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 6/12 ≈ 0.500
      └── Some((2, 8)): 6/12 ≈ 0.500
    ├── Some((2, 3)): 32/69 ≈ 0.464
      ├── Some((3, 0)): 5/9 ≈ 0.556
      ├── Some((3, 1)): 7/11 ≈ 0.636
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 4/8 ≈ 0.500
      ├── Some((3, 4)): 6/10 ≈ 0.600
      ├── Some((3, 5)): 2/6 ≈ 0.333
      ├── Some((3, 6)): 2/6 ≈ 0.333
      ├── Some((3, 7)): 2/6 ≈ 0.333
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((2, 4)): 24/57 ≈ 0.421
      ├── Some((4, 0)): 1/5 ≈ 0.200
      ├── Some((4, 1)): 4/7 ≈ 0.571
      ├── Some((4, 2)): 3/6 ≈ 0.500
      ├── Some((4, 3)): 3/6 ≈ 0.500
      ├── Some((4, 4)): 3/7 ≈ 0.429
      ├── Some((4, 5)): 5/8 ≈ 0.625
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 3/7 ≈ 0.429
      └── Some((4, 8)): 1/5 ≈ 0.200
    ├── Some((2, 5)): 48/91 ≈ 0.527
      ├── Some((5, 0)): 6/11 ≈ 0.545
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 14/18 ≈ 0.778
      ├── Some((5, 3)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 6/11 ≈ 0.545
      ├── Some((5, 5)): 7/12 ≈ 0.583
      ├── Some((5, 6)): 1/6 ≈ 0.167
      ├── Some((5, 7)): 0/4 ≈ 0.000
      └── Some((5, 8)): 8/12 ≈ 0.667
    ├── Some((2, 6)): 32/69 ≈ 0.464
      ├── Some((6, 0)): 2/6 ≈ 0.333
      ├── Some((6, 1)): 1/5 ≈ 0.200
      ├── Some((6, 2)): 3/7 ≈ 0.429
      ├── Some((6, 3)): 5/9 ≈ 0.556
      ├── Some((6, 4)): 3/7 ≈ 0.429
      ├── Some((6, 5)): 4/8 ≈ 0.500
      ├── Some((6, 6)): 8/12 ≈ 0.667
      ├── Some((6, 7)): 2/6 ≈ 0.333
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((2, 7)): 58/105 ≈ 0.552
      ├── Some((7, 0)): 11/16 ≈ 0.688
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 7/12 ≈ 0.583
      ├── Some((7, 4)): 5/11 ≈ 0.455
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 10/15 ≈ 0.667
      ├── Some((7, 7)): 9/14 ≈ 0.643
      └── Some((7, 8)): 7/12 ≈ 0.583
    └── Some((2, 8)): 19/50 ≈ 0.380
      ├── Some((8, 0)): 2/5 ≈ 0.400
      ├── Some((8, 1)): 0/3 ≈ 0.000
      ├── Some((8, 2)): 2/5 ≈ 0.400
      ├── Some((8, 3)): 6/9 ≈ 0.667
      ├── Some((8, 4)): 3/6 ≈ 0.500
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 2/6 ≈ 0.333
      └── Some((8, 8)): 0/3 ≈ 0.000
  ├── Some((0, 3)): 340/694 ≈ 0.490
    ├── Some((3, 0)): 53/99 ≈ 0.535
      ├── Some((0, 0)): 5/11 ≈ 0.455
      ├── Some((0, 1)): 8/14 ≈ 0.571
      ├── Some((0, 2)): 8/14 ≈ 0.571
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 9/15 ≈ 0.600
      ├── Some((0, 6)): 6/12 ≈ 0.500
      ├── Some((0, 7)): 0/5 ≈ 0.000
      └── Some((0, 8)): 12/17 ≈ 0.706
    ├── Some((3, 1)): 55/101 ≈ 0.545
      ├── Some((1, 1)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 12/17 ≈ 0.706
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 6/12 ≈ 0.500
      ├── Some((1, 6)): 9/14 ≈ 0.643
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 9/15 ≈ 0.600
    ├── Some((3, 2)): 19/50 ≈ 0.380
      ├── Some((2, 0)): 0/3 ≈ 0.000
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 2/5 ≈ 0.400
      ├── Some((2, 3)): 2/5 ≈ 0.400
      ├── Some((2, 4)): 0/3 ≈ 0.000
      ├── Some((2, 5)): 2/6 ≈ 0.333
      ├── Some((2, 6)): 3/6 ≈ 0.500
      ├── Some((2, 7)): 2/6 ≈ 0.333
      └── Some((2, 8)): 7/10 ≈ 0.700
    ├── Some((3, 3)): 38/78 ≈ 0.487
      ├── Some((3, 0)): 7/12 ≈ 0.583
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 8/13 ≈ 0.615
      ├── Some((3, 5)): 8/13 ≈ 0.615
      ├── Some((3, 6)): 4/9 ≈ 0.444
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((3, 4)): 30/66 ≈ 0.455
      ├── Some((4, 0)): 5/9 ≈ 0.556
      ├── Some((4, 1)): 4/8 ≈ 0.500
      ├── Some((4, 2)): 7/11 ≈ 0.636
      ├── Some((4, 3)): 0/4 ≈ 0.000
      ├── Some((4, 4)): 1/5 ≈ 0.200
      ├── Some((4, 5)): 5/9 ≈ 0.556
      ├── Some((4, 6)): 2/6 ≈ 0.333
      ├── Some((4, 7)): 5/9 ≈ 0.556
      └── Some((4, 8)): 0/4 ≈ 0.000
    ├── Some((3, 5)): 33/71 ≈ 0.465
      ├── Some((5, 0)): 6/10 ≈ 0.600
      ├── Some((5, 1)): 3/7 ≈ 0.429
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 3/8 ≈ 0.375
      ├── Some((5, 4)): 2/6 ≈ 0.333
      ├── Some((5, 5)): 5/9 ≈ 0.556
      ├── Some((5, 6)): 1/5 ≈ 0.200
      ├── Some((5, 7)): 2/6 ≈ 0.333
      └── Some((5, 8)): 9/13 ≈ 0.692
    ├── Some((3, 6)): 23/56 ≈ 0.411
      ├── Some((6, 0)): 4/7 ≈ 0.571
      ├── Some((6, 1)): 2/6 ≈ 0.333
      ├── Some((6, 2)): 0/4 ≈ 0.000
      ├── Some((6, 3)): 3/6 ≈ 0.500
      ├── Some((6, 4)): 4/7 ≈ 0.571
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 2/6 ≈ 0.333
      ├── Some((6, 7)): 2/6 ≈ 0.333
      └── Some((6, 8)): 3/7 ≈ 0.429
    ├── Some((3, 7)): 42/83 ≈ 0.506
      ├── Some((7, 0)): 7/11 ≈ 0.636
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 7/11 ≈ 0.636
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 5/9 ≈ 0.556
      ├── Some((7, 7)): 10/14 ≈ 0.714
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((3, 8)): 46/89 ≈ 0.517
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 6/10 ≈ 0.600
      ├── Some((8, 2)): 6/11 ≈ 0.545
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 6/11 ≈ 0.545
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 7/11 ≈ 0.636
      ├── Some((8, 7)): 6/11 ≈ 0.545
      └── Some((8, 8)): 5/10 ≈ 0.500
  ├── Some((0, 4)): 271/573 ≈ 0.473
    ├── Some((4, 0)): 24/55 ≈ 0.436
      ├── Some((0, 0)): 0/4 ≈ 0.000
      ├── Some((0, 1)): 2/6 ≈ 0.333
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 0/4 ≈ 0.000
      ├── Some((0, 5)): 6/9 ≈ 0.667
      ├── Some((0, 6)): 3/7 ≈ 0.429
      ├── Some((0, 7)): 3/7 ≈ 0.429
      └── Some((0, 8)): 5/9 ≈ 0.556
    ├── Some((4, 1)): 26/58 ≈ 0.448
      ├── Some((1, 1)): 2/6 ≈ 0.333
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 8/12 ≈ 0.667
      ├── Some((1, 4)): 1/5 ≈ 0.200
      ├── Some((1, 5)): 2/6 ≈ 0.333
      ├── Some((1, 6)): 1/5 ≈ 0.200
      ├── Some((1, 7)): 5/9 ≈ 0.556
      └── Some((1, 8)): 4/8 ≈ 0.500
    ├── Some((4, 2)): 16/43 ≈ 0.372
      ├── Some((2, 0)): 0/3 ≈ 0.000
      ├── Some((2, 1)): 1/4 ≈ 0.250
      ├── Some((2, 2)): 1/4 ≈ 0.250
      ├── Some((2, 3)): 3/6 ≈ 0.500
      ├── Some((2, 4)): 2/5 ≈ 0.400
      ├── Some((2, 5)): 3/6 ≈ 0.500
      ├── Some((2, 6)): 2/5 ≈ 0.400
      ├── Some((2, 7)): 2/5 ≈ 0.400
      └── Some((2, 8)): 1/4 ≈ 0.250
    ├── Some((4, 3)): 24/55 ≈ 0.436
      ├── Some((3, 0)): 1/5 ≈ 0.200
      ├── Some((3, 1)): 4/7 ≈ 0.571
      ├── Some((3, 2)): 2/6 ≈ 0.333
      ├── Some((3, 3)): 4/7 ≈ 0.571
      ├── Some((3, 4)): 4/7 ≈ 0.571
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 5/8 ≈ 0.625
      ├── Some((3, 7)): 3/6 ≈ 0.500
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((4, 4)): 33/68 ≈ 0.485
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 13/16 ≈ 0.812
      ├── Some((4, 2)): 0/4 ≈ 0.000
      ├── Some((4, 3)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 5/9 ≈ 0.556
      ├── Some((4, 6)): 4/8 ≈ 0.500
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 4/8 ≈ 0.500
    ├── Some((4, 5)): 35/71 ≈ 0.493
      ├── Some((5, 0)): 0/4 ≈ 0.000
      ├── Some((5, 1)): 3/7 ≈ 0.429
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 8/12 ≈ 0.667
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 7/11 ≈ 0.636
      ├── Some((5, 6)): 4/8 ≈ 0.500
      ├── Some((5, 7)): 9/12 ≈ 0.750
      └── Some((5, 8)): 1/5 ≈ 0.200
    ├── Some((4, 6)): 43/81 ≈ 0.531
      ├── Some((6, 0)): 7/11 ≈ 0.636
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 5/9 ≈ 0.556
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 5/9 ≈ 0.556
      ├── Some((6, 6)): 5/9 ≈ 0.556
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 5/9 ≈ 0.556
    ├── Some((4, 7)): 43/82 ≈ 0.524
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 1/6 ≈ 0.167
      ├── Some((7, 2)): 10/14 ≈ 0.714
      ├── Some((7, 3)): 7/11 ≈ 0.636
      ├── Some((7, 4)): 0/4 ≈ 0.000
      ├── Some((7, 5)): 10/14 ≈ 0.714
      ├── Some((7, 6)): 0/4 ≈ 0.000
      ├── Some((7, 7)): 5/9 ≈ 0.556
      └── Some((7, 8)): 5/10 ≈ 0.500
    └── Some((4, 8)): 27/59 ≈ 0.458
      ├── Some((8, 0)): 3/6 ≈ 0.500
      ├── Some((8, 1)): 3/6 ≈ 0.500
      ├── Some((8, 2)): 6/9 ≈ 0.667
      ├── Some((8, 3)): 3/6 ≈ 0.500
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 5/8 ≈ 0.625
      ├── Some((8, 7)): 3/7 ≈ 0.429
      └── Some((8, 8)): 2/6 ≈ 0.333
  ├── Some((0, 5)): 758/1402 ≈ 0.541
    ├── Some((5, 0)): 95/171 ≈ 0.556
      ├── Some((0, 0)): 10/19 ≈ 0.526
      ├── Some((0, 1)): 18/28 ≈ 0.643
      ├── Some((0, 2)): 14/24 ≈ 0.583
      ├── Some((0, 3)): 11/20 ≈ 0.550
      ├── Some((0, 4)): 6/15 ≈ 0.400
      ├── Some((0, 6)): 16/26 ≈ 0.615
      ├── Some((0, 7)): 9/18 ≈ 0.500
      └── Some((0, 8)): 11/20 ≈ 0.550
    ├── Some((5, 1)): 78/147 ≈ 0.531
      ├── Some((1, 1)): 9/18 ≈ 0.500
      ├── Some((1, 2)): 3/11 ≈ 0.273
      ├── Some((1, 3)): 5/13 ≈ 0.385
      ├── Some((1, 4)): 16/25 ≈ 0.640
      ├── Some((1, 5)): 11/20 ≈ 0.550
      ├── Some((1, 6)): 15/24 ≈ 0.625
      ├── Some((1, 7)): 3/11 ≈ 0.273
      └── Some((1, 8)): 15/24 ≈ 0.625
    ├── Some((5, 2)): 65/129 ≈ 0.504
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 1)): 11/18 ≈ 0.611
      ├── Some((2, 2)): 8/15 ≈ 0.533
      ├── Some((2, 3)): 9/16 ≈ 0.562
      ├── Some((2, 4)): 2/9 ≈ 0.222
      ├── Some((2, 5)): 10/17 ≈ 0.588
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((5, 3)): 100/179 ≈ 0.559
      ├── Some((3, 0)): 13/22 ≈ 0.591
      ├── Some((3, 1)): 8/17 ≈ 0.471
      ├── Some((3, 2)): 11/20 ≈ 0.550
      ├── Some((3, 3)): 10/19 ≈ 0.526
      ├── Some((3, 4)): 15/24 ≈ 0.625
      ├── Some((3, 5)): 26/35 ≈ 0.743
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 11/20 ≈ 0.550
      └── Some((3, 8)): 1/8 ≈ 0.125
    ├── Some((5, 4)): 40/91 ≈ 0.440
      ├── Some((4, 0)): 7/13 ≈ 0.538
      ├── Some((4, 1)): 1/6 ≈ 0.167
      ├── Some((4, 2)): 7/13 ≈ 0.538
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 1/6 ≈ 0.167
      ├── Some((4, 6)): 4/10 ≈ 0.400
      ├── Some((4, 7)): 8/14 ≈ 0.571
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((5, 5)): 78/147 ≈ 0.531
      ├── Some((5, 0)): 9/18 ≈ 0.500
      ├── Some((5, 1)): 7/15 ≈ 0.467
      ├── Some((5, 2)): 3/11 ≈ 0.273
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 15/24 ≈ 0.625
      ├── Some((5, 6)): 16/25 ≈ 0.640
      ├── Some((5, 7)): 8/17 ≈ 0.471
      └── Some((5, 8)): 12/21 ≈ 0.571
    ├── Some((5, 6)): 88/162 ≈ 0.543
      ├── Some((6, 0)): 5/13 ≈ 0.385
      ├── Some((6, 1)): 9/17 ≈ 0.529
      ├── Some((6, 2)): 8/16 ≈ 0.500
      ├── Some((6, 3)): 9/17 ≈ 0.529
      ├── Some((6, 4)): 10/18 ≈ 0.556
      ├── Some((6, 5)): 18/27 ≈ 0.667
      ├── Some((6, 6)): 12/21 ≈ 0.571
      ├── Some((6, 7)): 6/14 ≈ 0.429
      └── Some((6, 8)): 10/18 ≈ 0.556
    ├── Some((5, 7)): 115/199 ≈ 0.578
      ├── Some((7, 0)): 11/20 ≈ 0.550
      ├── Some((7, 1)): 21/30 ≈ 0.700
      ├── Some((7, 2)): 11/20 ≈ 0.550
      ├── Some((7, 3)): 10/19 ≈ 0.526
      ├── Some((7, 4)): 7/16 ≈ 0.438
      ├── Some((7, 5)): 19/29 ≈ 0.655
      ├── Some((7, 6)): 9/18 ≈ 0.500
      ├── Some((7, 7)): 17/27 ≈ 0.630
      └── Some((7, 8)): 10/19 ≈ 0.526
    └── Some((5, 8)): 98/176 ≈ 0.557
      ├── Some((8, 0)): 8/16 ≈ 0.500
      ├── Some((8, 1)): 12/21 ≈ 0.571
      ├── Some((8, 2)): 2/10 ≈ 0.200
      ├── Some((8, 3)): 21/30 ≈ 0.700
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 11/20 ≈ 0.550
      ├── Some((8, 6)): 9/17 ≈ 0.529
      ├── Some((8, 7)): 19/28 ≈ 0.679
      └── Some((8, 8)): 11/20 ≈ 0.550
  ├── Some((0, 6)): 302/627 ≈ 0.482
    ├── Some((6, 0)): 22/54 ≈ 0.407
      ├── Some((0, 0)): 4/8 ≈ 0.500
      ├── Some((0, 1)): 0/4 ≈ 0.000
      ├── Some((0, 2)): 0/4 ≈ 0.000
      ├── Some((0, 3)): 2/6 ≈ 0.333
      ├── Some((0, 4)): 8/11 ≈ 0.727
      ├── Some((0, 5)): 1/5 ≈ 0.200
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 3/7 ≈ 0.429
    ├── Some((6, 1)): 45/86 ≈ 0.523
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 7/12 ≈ 0.583
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 14/19 ≈ 0.737
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 4/9 ≈ 0.444
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 6/11 ≈ 0.545
    ├── Some((6, 2)): 43/83 ≈ 0.518
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 7/11 ≈ 0.636
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 5/9 ≈ 0.556
      ├── Some((2, 4)): 7/11 ≈ 0.636
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 5/9 ≈ 0.556
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 5/9 ≈ 0.556
    ├── Some((6, 3)): 44/85 ≈ 0.518
      ├── Some((3, 0)): 5/9 ≈ 0.556
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 8/12 ≈ 0.667
      ├── Some((3, 3)): 6/10 ≈ 0.600
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 5/9 ≈ 0.556
      ├── Some((3, 7)): 5/10 ≈ 0.500
      └── Some((3, 8)): 5/10 ≈ 0.500
    ├── Some((6, 4)): 38/76 ≈ 0.500
      ├── Some((4, 0)): 2/6 ≈ 0.333
      ├── Some((4, 1)): 3/7 ≈ 0.429
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 4/8 ≈ 0.500
      ├── Some((4, 4)): 3/7 ≈ 0.429
      ├── Some((4, 5)): 9/13 ≈ 0.692
      ├── Some((4, 6)): 4/8 ≈ 0.500
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((6, 5)): 12/38 ≈ 0.316
      ├── Some((5, 0)): 2/4 ≈ 0.500
      ├── Some((5, 1)): 1/4 ≈ 0.250
      ├── Some((5, 2)): 3/5 ≈ 0.600
      ├── Some((5, 3)): 1/4 ≈ 0.250
      ├── Some((5, 4)): 1/4 ≈ 0.250
      ├── Some((5, 5)): 1/4 ≈ 0.250
      ├── Some((5, 6)): 1/4 ≈ 0.250
      ├── Some((5, 7)): 0/3 ≈ 0.000
      └── Some((5, 8)): 2/5 ≈ 0.400
    ├── Some((6, 6)): 26/59 ≈ 0.441
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 5/9 ≈ 0.556
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 4/8 ≈ 0.500
      ├── Some((6, 4)): 4/8 ≈ 0.500
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 7)): 7/11 ≈ 0.636
      └── Some((6, 8)): 2/6 ≈ 0.333
    ├── Some((6, 7)): 25/58 ≈ 0.431
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 5/8 ≈ 0.625
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 4/7 ≈ 0.571
      ├── Some((7, 5)): 3/7 ≈ 0.429
      ├── Some((7, 6)): 3/7 ≈ 0.429
      ├── Some((7, 7)): 1/5 ≈ 0.200
      └── Some((7, 8)): 4/7 ≈ 0.571
    └── Some((6, 8)): 46/87 ≈ 0.529
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 6/10 ≈ 0.600
      ├── Some((8, 2)): 5/10 ≈ 0.500
      ├── Some((8, 3)): 7/11 ≈ 0.636
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 6/10 ≈ 0.600
      ├── Some((8, 7)): 8/12 ≈ 0.667
      └── Some((8, 8)): 4/9 ≈ 0.444
  ├── Some((0, 7)): 382/767 ≈ 0.498
    ├── Some((7, 0)): 46/91 ≈ 0.505
      ├── Some((0, 0)): 4/10 ≈ 0.400
      ├── Some((0, 1)): 6/12 ≈ 0.500
      ├── Some((0, 2)): 10/15 ≈ 0.667
      ├── Some((0, 3)): 0/5 ≈ 0.000
      ├── Some((0, 4)): 6/12 ≈ 0.500
      ├── Some((0, 5)): 8/13 ≈ 0.615
      ├── Some((0, 6)): 7/12 ≈ 0.583
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((7, 1)): 61/111 ≈ 0.550
      ├── Some((1, 1)): 7/14 ≈ 0.500
      ├── Some((1, 2)): 11/17 ≈ 0.647
      ├── Some((1, 3)): 10/16 ≈ 0.625
      ├── Some((1, 4)): 12/18 ≈ 0.667
      ├── Some((1, 5)): 12/18 ≈ 0.667
      ├── Some((1, 6)): 1/7 ≈ 0.143
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((7, 2)): 25/60 ≈ 0.417
      ├── Some((2, 0)): 4/7 ≈ 0.571
      ├── Some((2, 1)): 0/4 ≈ 0.000
      ├── Some((2, 2)): 6/9 ≈ 0.667
      ├── Some((2, 3)): 2/6 ≈ 0.333
      ├── Some((2, 4)): 3/7 ≈ 0.429
      ├── Some((2, 5)): 3/7 ≈ 0.429
      ├── Some((2, 6)): 2/6 ≈ 0.333
      ├── Some((2, 7)): 3/7 ≈ 0.429
      └── Some((2, 8)): 2/6 ≈ 0.333
    ├── Some((7, 3)): 61/111 ≈ 0.550
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 11/16 ≈ 0.688
      ├── Some((3, 2)): 5/11 ≈ 0.455
      ├── Some((3, 3)): 8/13 ≈ 0.615
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 6/11 ≈ 0.545
      ├── Some((3, 6)): 5/11 ≈ 0.455
      ├── Some((3, 7)): 10/15 ≈ 0.667
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((7, 4)): 53/100 ≈ 0.530
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 11/16 ≈ 0.688
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 7/12 ≈ 0.583
      ├── Some((4, 5)): 3/9 ≈ 0.333
      ├── Some((4, 6)): 8/13 ≈ 0.615
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 7/12 ≈ 0.583
    ├── Some((7, 5)): 49/95 ≈ 0.516
      ├── Some((5, 0)): 2/7 ≈ 0.286
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 6/11 ≈ 0.545
      ├── Some((5, 3)): 14/19 ≈ 0.737
      ├── Some((5, 4)): 4/9 ≈ 0.444
      ├── Some((5, 5)): 8/13 ≈ 0.615
      ├── Some((5, 6)): 1/6 ≈ 0.167
      ├── Some((5, 7)): 1/6 ≈ 0.167
      └── Some((5, 8)): 7/12 ≈ 0.583
    ├── Some((7, 6)): 27/63 ≈ 0.429
      ├── Some((6, 0)): 2/6 ≈ 0.333
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 2/6 ≈ 0.333
      ├── Some((6, 3)): 4/8 ≈ 0.500
      ├── Some((6, 4)): 2/6 ≈ 0.333
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 2/6 ≈ 0.333
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 6/10 ≈ 0.600
    ├── Some((7, 7)): 24/59 ≈ 0.407
      ├── Some((7, 0)): 6/11 ≈ 0.545
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 9/13 ≈ 0.692
      ├── Some((7, 3)): 1/5 ≈ 0.200
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 0/4 ≈ 0.000
      ├── Some((7, 6)): 1/5 ≈ 0.200
      └── Some((7, 8)): 2/7 ≈ 0.286
    └── Some((7, 8)): 36/76 ≈ 0.474
      ├── Some((8, 0)): 1/5 ≈ 0.200
      ├── Some((8, 1)): 6/10 ≈ 0.600
      ├── Some((8, 2)): 1/6 ≈ 0.167
      ├── Some((8, 3)): 0/4 ≈ 0.000
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 5/10 ≈ 0.500
      ├── Some((8, 6)): 6/10 ≈ 0.600
      ├── Some((8, 7)): 5/10 ≈ 0.500
      └── Some((8, 8)): 9/13 ≈ 0.692
  └── Some((0, 8)): 345/702 ≈ 0.491
    ├── Some((8, 0)): 53/99 ≈ 0.535
      ├── Some((0, 0)): 0/5 ≈ 0.000
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 12/17 ≈ 0.706
      ├── Some((0, 3)): 8/14 ≈ 0.571
      ├── Some((0, 4)): 9/15 ≈ 0.600
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 5/11 ≈ 0.455
      └── Some((0, 7)): 7/13 ≈ 0.538
    ├── Some((8, 1)): 44/86 ≈ 0.512
      ├── Some((1, 1)): 5/11 ≈ 0.455
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 1/6 ≈ 0.167
      ├── Some((1, 5)): 0/5 ≈ 0.000
      ├── Some((1, 6)): 10/15 ≈ 0.667
      ├── Some((1, 7)): 11/16 ≈ 0.688
      └── Some((1, 8)): 8/13 ≈ 0.615
    ├── Some((8, 2)): 47/90 ≈ 0.522
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 4/9 ≈ 0.444
      ├── Some((2, 2)): 6/11 ≈ 0.545
      ├── Some((2, 3)): 9/13 ≈ 0.692
      ├── Some((2, 4)): 8/13 ≈ 0.615
      ├── Some((2, 5)): 1/6 ≈ 0.167
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 9/13 ≈ 0.692
      └── Some((2, 8)): 4/9 ≈ 0.444
    ├── Some((8, 3)): 17/47 ≈ 0.362
      ├── Some((3, 0)): 1/5 ≈ 0.200
      ├── Some((3, 1)): 2/5 ≈ 0.400
      ├── Some((3, 2)): 3/6 ≈ 0.500
      ├── Some((3, 3)): 3/6 ≈ 0.500
      ├── Some((3, 4)): 0/3 ≈ 0.000
      ├── Some((3, 5)): 0/3 ≈ 0.000
      ├── Some((3, 6)): 2/6 ≈ 0.333
      ├── Some((3, 7)): 3/6 ≈ 0.500
      └── Some((3, 8)): 3/6 ≈ 0.500
    ├── Some((8, 4)): 28/63 ≈ 0.444
      ├── Some((4, 0)): 5/8 ≈ 0.625
      ├── Some((4, 1)): 3/7 ≈ 0.429
      ├── Some((4, 2)): 4/8 ≈ 0.500
      ├── Some((4, 3)): 5/8 ≈ 0.625
      ├── Some((4, 4)): 3/7 ≈ 0.429
      ├── Some((4, 5)): 2/6 ≈ 0.333
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 5/9 ≈ 0.556
      └── Some((4, 8)): 0/4 ≈ 0.000
    ├── Some((8, 5)): 33/71 ≈ 0.465
      ├── Some((5, 0)): 2/6 ≈ 0.333
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 2/6 ≈ 0.333
      ├── Some((5, 4)): 3/7 ≈ 0.429
      ├── Some((5, 5)): 6/10 ≈ 0.600
      ├── Some((5, 6)): 7/11 ≈ 0.636
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 7/11 ≈ 0.636
    ├── Some((8, 6)): 52/97 ≈ 0.536
      ├── Some((6, 0)): 4/9 ≈ 0.444
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 5/10 ≈ 0.500
      ├── Some((6, 3)): 8/13 ≈ 0.615
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 5/10 ≈ 0.500
      ├── Some((6, 7)): 8/13 ≈ 0.615
      └── Some((6, 8)): 8/13 ≈ 0.615
    ├── Some((8, 7)): 28/63 ≈ 0.444
      ├── Some((7, 0)): 1/5 ≈ 0.200
      ├── Some((7, 1)): 4/8 ≈ 0.500
      ├── Some((7, 2)): 5/9 ≈ 0.556
      ├── Some((7, 3)): 1/5 ≈ 0.200
      ├── Some((7, 4)): 3/7 ≈ 0.429
      ├── Some((7, 5)): 6/9 ≈ 0.667
      ├── Some((7, 6)): 4/8 ≈ 0.500
      ├── Some((7, 7)): 3/7 ≈ 0.429
      └── Some((7, 8)): 0/4 ≈ 0.000
    └── Some((8, 8)): 43/85 ≈ 0.506
      ├── Some((8, 0)): 2/7 ≈ 0.286
      ├── Some((8, 1)): 6/12 ≈ 0.500
      ├── Some((8, 2)): 7/12 ≈ 0.583
      ├── Some((8, 3)): 9/14 ≈ 0.643
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 7/12 ≈ 0.583
      └── Some((8, 7)): 6/12 ≈ 0.500
├── Some((1, 1)): 7241/13855 ≈ 0.523
  ├── Some((1, 0)): 1007/1909 ≈ 0.528
    ├── Some((0, 0)): 120/224 ≈ 0.536
      ├── Some((0, 1)): 2/12 ≈ 0.167
      ├── Some((0, 2)): 15/28 ≈ 0.536
      ├── Some((0, 3)): 7/19 ≈ 0.368
      ├── Some((0, 4)): 22/36 ≈ 0.611
      ├── Some((0, 5)): 19/33 ≈ 0.576
      ├── Some((0, 6)): 21/35 ≈ 0.600
      ├── Some((0, 7)): 13/26 ≈ 0.500
      └── Some((0, 8)): 20/34 ≈ 0.588
    ├── Some((0, 1)): 102/197 ≈ 0.518
      ├── Some((1, 2)): 1/11 ≈ 0.091
      ├── Some((1, 3)): 28/44 ≈ 0.636
      ├── Some((1, 4)): 19/34 ≈ 0.559
      ├── Some((1, 5)): 11/24 ≈ 0.458
      ├── Some((1, 6)): 15/29 ≈ 0.517
      ├── Some((1, 7)): 16/30 ≈ 0.533
      └── Some((1, 8)): 11/24 ≈ 0.458
    ├── Some((0, 2)): 91/181 ≈ 0.503
      ├── Some((2, 0)): 22/33 ≈ 0.667
      ├── Some((2, 1)): 13/24 ≈ 0.542
      ├── Some((2, 2)): 11/21 ≈ 0.524
      ├── Some((2, 3)): 5/14 ≈ 0.357
      ├── Some((2, 4)): 1/9 ≈ 0.111
      ├── Some((2, 5)): 21/32 ≈ 0.656
      ├── Some((2, 6)): 7/17 ≈ 0.412
      ├── Some((2, 7)): 4/13 ≈ 0.308
      └── Some((2, 8)): 7/17 ≈ 0.412
    ├── Some((0, 3)): 135/247 ≈ 0.547
      ├── Some((3, 0)): 14/26 ≈ 0.538
      ├── Some((3, 1)): 10/22 ≈ 0.455
      ├── Some((3, 2)): 15/28 ≈ 0.536
      ├── Some((3, 3)): 22/35 ≈ 0.629
      ├── Some((3, 4)): 22/35 ≈ 0.629
      ├── Some((3, 5)): 10/22 ≈ 0.455
      ├── Some((3, 6)): 10/22 ≈ 0.455
      ├── Some((3, 7)): 12/24 ≈ 0.500
      └── Some((3, 8)): 19/32 ≈ 0.594
    ├── Some((0, 4)): 123/229 ≈ 0.537
      ├── Some((4, 0)): 14/26 ≈ 0.538
      ├── Some((4, 1)): 19/31 ≈ 0.613
      ├── Some((4, 2)): 7/18 ≈ 0.389
      ├── Some((4, 3)): 9/20 ≈ 0.450
      ├── Some((4, 4)): 11/23 ≈ 0.478
      ├── Some((4, 5)): 13/25 ≈ 0.520
      ├── Some((4, 6)): 18/30 ≈ 0.600
      ├── Some((4, 7)): 17/29 ≈ 0.586
      └── Some((4, 8)): 14/26 ≈ 0.538
    ├── Some((0, 5)): 119/223 ≈ 0.534
      ├── Some((5, 0)): 21/33 ≈ 0.636
      ├── Some((5, 1)): 6/17 ≈ 0.353
      ├── Some((5, 2)): 10/21 ≈ 0.476
      ├── Some((5, 3)): 21/33 ≈ 0.636
      ├── Some((5, 4)): 4/14 ≈ 0.286
      ├── Some((5, 5)): 11/22 ≈ 0.500
      ├── Some((5, 6)): 9/20 ≈ 0.450
      ├── Some((5, 7)): 22/35 ≈ 0.629
      └── Some((5, 8)): 15/27 ≈ 0.556
    ├── Some((0, 6)): 89/178 ≈ 0.500
      ├── Some((6, 0)): 12/22 ≈ 0.545
      ├── Some((6, 1)): 12/22 ≈ 0.545
      ├── Some((6, 2)): 7/16 ≈ 0.438
      ├── Some((6, 3)): 11/21 ≈ 0.524
      ├── Some((6, 4)): 12/22 ≈ 0.545
      ├── Some((6, 5)): 10/20 ≈ 0.500
      ├── Some((6, 6)): 9/19 ≈ 0.474
      ├── Some((6, 7)): 7/16 ≈ 0.438
      └── Some((6, 8)): 9/19 ≈ 0.474
    ├── Some((0, 7)): 131/241 ≈ 0.544
      ├── Some((7, 0)): 13/25 ≈ 0.520
      ├── Some((7, 1)): 13/25 ≈ 0.520
      ├── Some((7, 2)): 9/21 ≈ 0.429
      ├── Some((7, 3)): 10/22 ≈ 0.455
      ├── Some((7, 4)): 22/35 ≈ 0.629
      ├── Some((7, 5)): 14/26 ≈ 0.538
      ├── Some((7, 6)): 18/31 ≈ 0.581
      ├── Some((7, 7)): 15/27 ≈ 0.556
      └── Some((7, 8)): 16/28 ≈ 0.571
    └── Some((0, 8)): 96/188 ≈ 0.511
      ├── Some((8, 0)): 11/21 ≈ 0.524
      ├── Some((8, 1)): 10/20 ≈ 0.500
      ├── Some((8, 2)): 11/21 ≈ 0.524
      ├── Some((8, 3)): 12/22 ≈ 0.545
      ├── Some((8, 4)): 7/17 ≈ 0.412
      ├── Some((8, 5)): 6/16 ≈ 0.375
      ├── Some((8, 6)): 5/14 ≈ 0.357
      ├── Some((8, 7)): 19/30 ≈ 0.633
      └── Some((8, 8)): 15/26 ≈ 0.577
  ├── Some((1, 2)): 1090/2051 ≈ 0.531
    ├── Some((2, 0)): 132/244 ≈ 0.541
      ├── Some((0, 0)): 13/25 ≈ 0.520
      ├── Some((0, 1)): 20/33 ≈ 0.606
      ├── Some((0, 2)): 16/29 ≈ 0.552
      ├── Some((0, 3)): 10/22 ≈ 0.455
      ├── Some((0, 4)): 14/27 ≈ 0.519
      ├── Some((0, 5)): 8/19 ≈ 0.421
      ├── Some((0, 6)): 8/19 ≈ 0.421
      ├── Some((0, 7)): 20/33 ≈ 0.606
      └── Some((0, 8)): 23/36 ≈ 0.639
    ├── Some((2, 1)): 103/201 ≈ 0.512
      ├── Some((1, 0)): 15/29 ≈ 0.517
      ├── Some((1, 3)): 10/23 ≈ 0.435
      ├── Some((1, 4)): 28/44 ≈ 0.636
      ├── Some((1, 5)): 11/24 ≈ 0.458
      ├── Some((1, 6)): 14/28 ≈ 0.500
      ├── Some((1, 7)): 13/27 ≈ 0.481
      └── Some((1, 8)): 11/25 ≈ 0.440
    ├── Some((2, 2)): 128/238 ≈ 0.538
      ├── Some((2, 0)): 25/40 ≈ 0.625
      ├── Some((2, 1)): 11/24 ≈ 0.458
      ├── Some((2, 3)): 15/29 ≈ 0.517
      ├── Some((2, 4)): 23/38 ≈ 0.605
      ├── Some((2, 5)): 19/33 ≈ 0.576
      ├── Some((2, 6)): 9/21 ≈ 0.429
      ├── Some((2, 7)): 6/18 ≈ 0.333
      └── Some((2, 8)): 20/34 ≈ 0.588
    ├── Some((2, 3)): 116/220 ≈ 0.527
      ├── Some((3, 0)): 13/25 ≈ 0.520
      ├── Some((3, 1)): 19/31 ≈ 0.613
      ├── Some((3, 2)): 7/18 ≈ 0.389
      ├── Some((3, 3)): 15/27 ≈ 0.556
      ├── Some((3, 4)): 14/26 ≈ 0.538
      ├── Some((3, 5)): 12/24 ≈ 0.500
      ├── Some((3, 6)): 11/22 ≈ 0.500
      ├── Some((3, 7)): 4/14 ≈ 0.286
      └── Some((3, 8)): 20/32 ≈ 0.625
    ├── Some((2, 4)): 138/253 ≈ 0.545
      ├── Some((4, 0)): 16/29 ≈ 0.552
      ├── Some((4, 1)): 20/33 ≈ 0.606
      ├── Some((4, 2)): 18/31 ≈ 0.581
      ├── Some((4, 3)): 10/22 ≈ 0.455
      ├── Some((4, 4)): 8/20 ≈ 0.400
      ├── Some((4, 5)): 11/23 ≈ 0.478
      ├── Some((4, 6)): 21/35 ≈ 0.600
      ├── Some((4, 7)): 18/31 ≈ 0.581
      └── Some((4, 8)): 15/28 ≈ 0.536
    ├── Some((2, 5)): 143/260 ≈ 0.550
      ├── Some((5, 0)): 11/23 ≈ 0.478
      ├── Some((5, 1)): 9/21 ≈ 0.429
      ├── Some((5, 2)): 20/34 ≈ 0.588
      ├── Some((5, 3)): 14/27 ≈ 0.519
      ├── Some((5, 4)): 16/29 ≈ 0.552
      ├── Some((5, 5)): 5/16 ≈ 0.312
      ├── Some((5, 6)): 25/39 ≈ 0.641
      ├── Some((5, 7)): 33/48 ≈ 0.688
      └── Some((5, 8)): 10/22 ≈ 0.455
    ├── Some((2, 6)): 88/178 ≈ 0.494
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 17/28 ≈ 0.607
      ├── Some((6, 2)): 13/23 ≈ 0.565
      ├── Some((6, 3)): 9/19 ≈ 0.474
      ├── Some((6, 4)): 10/20 ≈ 0.500
      ├── Some((6, 5)): 6/15 ≈ 0.400
      ├── Some((6, 6)): 6/15 ≈ 0.400
      ├── Some((6, 7)): 5/14 ≈ 0.357
      └── Some((6, 8)): 15/26 ≈ 0.577
    ├── Some((2, 7)): 141/258 ≈ 0.547
      ├── Some((7, 0)): 13/26 ≈ 0.500
      ├── Some((7, 1)): 23/37 ≈ 0.622
      ├── Some((7, 2)): 28/42 ≈ 0.667
      ├── Some((7, 3)): 10/22 ≈ 0.455
      ├── Some((7, 4)): 11/23 ≈ 0.478
      ├── Some((7, 5)): 14/27 ≈ 0.519
      ├── Some((7, 6)): 14/27 ≈ 0.519
      ├── Some((7, 7)): 20/34 ≈ 0.588
      └── Some((7, 8)): 7/19 ≈ 0.368
    └── Some((2, 8)): 101/198 ≈ 0.510
      ├── Some((8, 0)): 11/22 ≈ 0.500
      ├── Some((8, 1)): 14/25 ≈ 0.560
      ├── Some((8, 2)): 4/14 ≈ 0.286
      ├── Some((8, 3)): 4/14 ≈ 0.286
      ├── Some((8, 4)): 12/23 ≈ 0.522
      ├── Some((8, 5)): 14/25 ≈ 0.560
      ├── Some((8, 6)): 8/18 ≈ 0.444
      ├── Some((8, 7)): 9/20 ≈ 0.450
      └── Some((8, 8)): 24/36 ≈ 0.667
  ├── Some((1, 3)): 887/1702 ≈ 0.521
    ├── Some((3, 0)): 120/222 ≈ 0.541
      ├── Some((0, 0)): 13/25 ≈ 0.520
      ├── Some((0, 1)): 21/33 ≈ 0.636
      ├── Some((0, 2)): 11/22 ≈ 0.500
      ├── Some((0, 3)): 14/26 ≈ 0.538
      ├── Some((0, 4)): 33/46 ≈ 0.717
      ├── Some((0, 5)): 9/20 ≈ 0.450
      ├── Some((0, 6)): 7/18 ≈ 0.389
      ├── Some((0, 7)): 9/20 ≈ 0.450
      └── Some((0, 8)): 2/11 ≈ 0.182
    ├── Some((3, 1)): 105/200 ≈ 0.525
      ├── Some((1, 0)): 14/28 ≈ 0.500
      ├── Some((1, 2)): 3/14 ≈ 0.214
      ├── Some((1, 4)): 14/28 ≈ 0.500
      ├── Some((1, 5)): 18/32 ≈ 0.562
      ├── Some((1, 6)): 15/29 ≈ 0.517
      ├── Some((1, 7)): 20/34 ≈ 0.588
      └── Some((1, 8)): 20/34 ≈ 0.588
    ├── Some((3, 2)): 69/145 ≈ 0.476
      ├── Some((2, 0)): 3/11 ≈ 0.273
      ├── Some((2, 1)): 10/19 ≈ 0.526
      ├── Some((2, 2)): 8/16 ≈ 0.500
      ├── Some((2, 3)): 12/21 ≈ 0.571
      ├── Some((2, 4)): 13/22 ≈ 0.591
      ├── Some((2, 5)): 5/13 ≈ 0.385
      ├── Some((2, 6)): 4/12 ≈ 0.333
      ├── Some((2, 7)): 2/9 ≈ 0.222
      └── Some((2, 8)): 12/21 ≈ 0.571
    ├── Some((3, 3)): 94/183 ≈ 0.514
      ├── Some((3, 0)): 10/21 ≈ 0.476
      ├── Some((3, 1)): 17/29 ≈ 0.586
      ├── Some((3, 2)): 4/14 ≈ 0.286
      ├── Some((3, 4)): 18/30 ≈ 0.600
      ├── Some((3, 5)): 13/24 ≈ 0.542
      ├── Some((3, 6)): 13/24 ≈ 0.542
      ├── Some((3, 7)): 9/20 ≈ 0.450
      └── Some((3, 8)): 9/20 ≈ 0.450
    ├── Some((3, 4)): 73/151 ≈ 0.483
      ├── Some((4, 0)): 16/25 ≈ 0.640
      ├── Some((4, 1)): 11/20 ≈ 0.550
      ├── Some((4, 2)): 7/16 ≈ 0.438
      ├── Some((4, 3)): 4/12 ≈ 0.333
      ├── Some((4, 4)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 6)): 1/8 ≈ 0.125
      ├── Some((4, 7)): 14/23 ≈ 0.609
      └── Some((4, 8)): 6/15 ≈ 0.400
    ├── Some((3, 5)): 126/230 ≈ 0.548
      ├── Some((5, 0)): 10/21 ≈ 0.476
      ├── Some((5, 1)): 16/28 ≈ 0.571
      ├── Some((5, 2)): 13/24 ≈ 0.542
      ├── Some((5, 3)): 15/27 ≈ 0.556
      ├── Some((5, 4)): 23/35 ≈ 0.657
      ├── Some((5, 5)): 14/26 ≈ 0.538
      ├── Some((5, 6)): 11/22 ≈ 0.500
      ├── Some((5, 7)): 12/23 ≈ 0.522
      └── Some((5, 8)): 12/23 ≈ 0.522
    ├── Some((3, 6)): 77/157 ≈ 0.490
      ├── Some((6, 0)): 14/23 ≈ 0.609
      ├── Some((6, 1)): 9/18 ≈ 0.500
      ├── Some((6, 2)): 9/18 ≈ 0.500
      ├── Some((6, 3)): 3/11 ≈ 0.273
      ├── Some((6, 4)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 6/15 ≈ 0.400
      ├── Some((6, 7)): 14/23 ≈ 0.609
      └── Some((6, 8)): 3/11 ≈ 0.273
    ├── Some((3, 7)): 163/284 ≈ 0.574
      ├── Some((7, 0)): 23/37 ≈ 0.622
      ├── Some((7, 1)): 17/30 ≈ 0.567
      ├── Some((7, 2)): 21/35 ≈ 0.600
      ├── Some((7, 3)): 12/25 ≈ 0.480
      ├── Some((7, 4)): 20/34 ≈ 0.588
      ├── Some((7, 5)): 14/27 ≈ 0.519
      ├── Some((7, 6)): 12/25 ≈ 0.480
      ├── Some((7, 7)): 15/28 ≈ 0.536
      └── Some((7, 8)): 28/42 ≈ 0.667
    └── Some((3, 8)): 59/129 ≈ 0.457
      ├── Some((8, 0)): 8/16 ≈ 0.500
      ├── Some((8, 1)): 4/11 ≈ 0.364
      ├── Some((8, 2)): 2/9 ≈ 0.222
      ├── Some((8, 3)): 4/11 ≈ 0.364
      ├── Some((8, 4)): 9/17 ≈ 0.529
      ├── Some((8, 5)): 6/14 ≈ 0.429
      ├── Some((8, 6)): 4/12 ≈ 0.333
      ├── Some((8, 7)): 10/18 ≈ 0.556
      └── Some((8, 8)): 12/20 ≈ 0.600
  ├── Some((1, 4)): 991/1881 ≈ 0.527
    ├── Some((4, 0)): 90/179 ≈ 0.503
      ├── Some((0, 0)): 11/21 ≈ 0.524
      ├── Some((0, 1)): 4/13 ≈ 0.308
      ├── Some((0, 2)): 12/22 ≈ 0.545
      ├── Some((0, 3)): 15/25 ≈ 0.600
      ├── Some((0, 4)): 5/14 ≈ 0.357
      ├── Some((0, 5)): 8/18 ≈ 0.444
      ├── Some((0, 6)): 17/28 ≈ 0.607
      ├── Some((0, 7)): 9/19 ≈ 0.474
      └── Some((0, 8)): 8/18 ≈ 0.444
    ├── Some((4, 1)): 64/139 ≈ 0.460
      ├── Some((1, 0)): 15/27 ≈ 0.556
      ├── Some((1, 2)): 10/21 ≈ 0.476
      ├── Some((1, 3)): 7/17 ≈ 0.412
      ├── Some((1, 5)): 6/16 ≈ 0.375
      ├── Some((1, 6)): 7/17 ≈ 0.412
      ├── Some((1, 7)): 7/17 ≈ 0.412
      └── Some((1, 8)): 12/23 ≈ 0.522
    ├── Some((4, 2)): 139/252 ≈ 0.552
      ├── Some((2, 0)): 19/32 ≈ 0.594
      ├── Some((2, 1)): 24/37 ≈ 0.649
      ├── Some((2, 2)): 9/21 ≈ 0.429
      ├── Some((2, 3)): 13/25 ≈ 0.520
      ├── Some((2, 4)): 9/21 ≈ 0.429
      ├── Some((2, 5)): 14/27 ≈ 0.519
      ├── Some((2, 6)): 17/30 ≈ 0.567
      ├── Some((2, 7)): 20/33 ≈ 0.606
      └── Some((2, 8)): 13/25 ≈ 0.520
    ├── Some((4, 3)): 85/172 ≈ 0.494
      ├── Some((3, 0)): 12/22 ≈ 0.545
      ├── Some((3, 1)): 11/21 ≈ 0.524
      ├── Some((3, 2)): 12/22 ≈ 0.545
      ├── Some((3, 3)): 7/16 ≈ 0.438
      ├── Some((3, 4)): 13/23 ≈ 0.565
      ├── Some((3, 5)): 10/20 ≈ 0.500
      ├── Some((3, 6)): 4/13 ≈ 0.308
      ├── Some((3, 7)): 6/15 ≈ 0.400
      └── Some((3, 8)): 9/19 ≈ 0.474
    ├── Some((4, 4)): 96/188 ≈ 0.511
      ├── Some((4, 0)): 6/17 ≈ 0.353
      ├── Some((4, 1)): 17/29 ≈ 0.586
      ├── Some((4, 2)): 13/25 ≈ 0.520
      ├── Some((4, 3)): 5/15 ≈ 0.333
      ├── Some((4, 5)): 15/27 ≈ 0.556
      ├── Some((4, 6)): 15/27 ≈ 0.556
      ├── Some((4, 7)): 18/30 ≈ 0.600
      └── Some((4, 8)): 6/17 ≈ 0.353
    ├── Some((4, 5)): 129/238 ≈ 0.542
      ├── Some((5, 0)): 19/32 ≈ 0.594
      ├── Some((5, 1)): 7/18 ≈ 0.389
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 3)): 11/23 ≈ 0.478
      ├── Some((5, 4)): 18/30 ≈ 0.600
      ├── Some((5, 5)): 15/27 ≈ 0.556
      ├── Some((5, 6)): 18/30 ≈ 0.600
      ├── Some((5, 7)): 18/30 ≈ 0.600
      └── Some((5, 8)): 11/23 ≈ 0.478
    ├── Some((4, 6)): 135/247 ≈ 0.547
      ├── Some((6, 0)): 15/28 ≈ 0.536
      ├── Some((6, 1)): 8/20 ≈ 0.400
      ├── Some((6, 2)): 5/16 ≈ 0.312
      ├── Some((6, 3)): 20/33 ≈ 0.606
      ├── Some((6, 4)): 12/24 ≈ 0.500
      ├── Some((6, 5)): 36/50 ≈ 0.720
      ├── Some((6, 6)): 8/20 ≈ 0.400
      ├── Some((6, 7)): 20/33 ≈ 0.606
      └── Some((6, 8)): 10/22 ≈ 0.455
    ├── Some((4, 7)): 96/188 ≈ 0.511
      ├── Some((7, 0)): 11/21 ≈ 0.524
      ├── Some((7, 1)): 10/20 ≈ 0.500
      ├── Some((7, 2)): 8/18 ≈ 0.444
      ├── Some((7, 3)): 18/29 ≈ 0.621
      ├── Some((7, 4)): 5/15 ≈ 0.333
      ├── Some((7, 5)): 15/26 ≈ 0.577
      ├── Some((7, 6)): 17/28 ≈ 0.607
      ├── Some((7, 7)): 9/19 ≈ 0.474
      └── Some((7, 8)): 2/11 ≈ 0.182
    └── Some((4, 8)): 156/277 ≈ 0.563
      ├── Some((8, 0)): 20/34 ≈ 0.588
      ├── Some((8, 1)): 17/30 ≈ 0.567
      ├── Some((8, 2)): 21/35 ≈ 0.600
      ├── Some((8, 3)): 19/33 ≈ 0.576
      ├── Some((8, 4)): 17/30 ≈ 0.567
      ├── Some((8, 5)): 20/34 ≈ 0.588
      ├── Some((8, 6)): 11/24 ≈ 0.458
      ├── Some((8, 7)): 12/25 ≈ 0.480
      └── Some((8, 8)): 18/31 ≈ 0.581
  ├── Some((1, 5)): 628/1250 ≈ 0.502
    ├── Some((5, 0)): 67/135 ≈ 0.496
      ├── Some((0, 0)): 8/15 ≈ 0.533
      ├── Some((0, 1)): 3/10 ≈ 0.300
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 8/16 ≈ 0.500
      ├── Some((0, 4)): 4/11 ≈ 0.364
      ├── Some((0, 5)): 11/19 ≈ 0.579
      ├── Some((0, 6)): 6/13 ≈ 0.462
      ├── Some((0, 7)): 14/22 ≈ 0.636
      └── Some((0, 8)): 9/17 ≈ 0.529
    ├── Some((5, 1)): 83/159 ≈ 0.522
      ├── Some((1, 0)): 13/24 ≈ 0.542
      ├── Some((1, 2)): 2/11 ≈ 0.182
      ├── Some((1, 3)): 13/24 ≈ 0.542
      ├── Some((1, 4)): 17/28 ≈ 0.607
      ├── Some((1, 6)): 10/21 ≈ 0.476
      ├── Some((1, 7)): 12/23 ≈ 0.522
      └── Some((1, 8)): 16/27 ≈ 0.593
    ├── Some((5, 2)): 101/185 ≈ 0.546
      ├── Some((2, 0)): 16/26 ≈ 0.615
      ├── Some((2, 1)): 5/14 ≈ 0.357
      ├── Some((2, 2)): 4/13 ≈ 0.308
      ├── Some((2, 3)): 7/16 ≈ 0.438
      ├── Some((2, 4)): 27/37 ≈ 0.730
      ├── Some((2, 5)): 16/26 ≈ 0.615
      ├── Some((2, 6)): 15/25 ≈ 0.600
      ├── Some((2, 7)): 7/16 ≈ 0.438
      └── Some((2, 8)): 3/11 ≈ 0.273
    ├── Some((5, 3)): 78/152 ≈ 0.513
      ├── Some((3, 0)): 6/14 ≈ 0.429
      ├── Some((3, 1)): 12/21 ≈ 0.571
      ├── Some((3, 2)): 12/21 ≈ 0.571
      ├── Some((3, 3)): 5/13 ≈ 0.385
      ├── Some((3, 4)): 19/27 ≈ 0.704
      ├── Some((3, 5)): 7/15 ≈ 0.467
      ├── Some((3, 6)): 9/17 ≈ 0.529
      ├── Some((3, 7)): 0/7 ≈ 0.000
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((5, 4)): 51/111 ≈ 0.459
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 15/22 ≈ 0.682
      ├── Some((4, 2)): 8/15 ≈ 0.533
      ├── Some((4, 3)): 11/18 ≈ 0.611
      ├── Some((4, 4)): 3/10 ≈ 0.300
      ├── Some((4, 5)): 1/7 ≈ 0.143
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 8/15 ≈ 0.533
      └── Some((4, 8)): 1/7 ≈ 0.143
    ├── Some((5, 5)): 98/181 ≈ 0.541
      ├── Some((5, 0)): 12/23 ≈ 0.522
      ├── Some((5, 1)): 13/24 ≈ 0.542
      ├── Some((5, 2)): 11/21 ≈ 0.524
      ├── Some((5, 3)): 16/27 ≈ 0.593
      ├── Some((5, 4)): 4/13 ≈ 0.308
      ├── Some((5, 6)): 22/33 ≈ 0.667
      ├── Some((5, 7)): 2/11 ≈ 0.182
      └── Some((5, 8)): 17/28 ≈ 0.607
    ├── Some((5, 6)): 39/92 ≈ 0.424
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 12/18 ≈ 0.667
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((5, 7)): 61/126 ≈ 0.484
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 8/15 ≈ 0.533
      ├── Some((7, 4)): 8/15 ≈ 0.533
      ├── Some((7, 5)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 4/11 ≈ 0.364
      ├── Some((7, 7)): 10/18 ≈ 0.556
      └── Some((7, 8)): 5/12 ≈ 0.417
    └── Some((5, 8)): 49/108 ≈ 0.454
      ├── Some((8, 0)): 3/9 ≈ 0.333
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 9/16 ≈ 0.562
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 6/13 ≈ 0.462
      ├── Some((8, 6)): 8/15 ≈ 0.533
      ├── Some((8, 7)): 2/8 ≈ 0.250
      └── Some((8, 8)): 3/9 ≈ 0.333
  ├── Some((1, 6)): 866/1665 ≈ 0.520
    ├── Some((6, 0)): 153/269 ≈ 0.569
      ├── Some((0, 0)): 14/27 ≈ 0.519
      ├── Some((0, 1)): 21/34 ≈ 0.618
      ├── Some((0, 2)): 17/30 ≈ 0.567
      ├── Some((0, 3)): 16/29 ≈ 0.552
      ├── Some((0, 4)): 4/15 ≈ 0.267
      ├── Some((0, 5)): 28/42 ≈ 0.667
      ├── Some((0, 6)): 26/40 ≈ 0.650
      ├── Some((0, 7)): 11/23 ≈ 0.478
      └── Some((0, 8)): 15/28 ≈ 0.536
    ├── Some((6, 1)): 65/139 ≈ 0.468
      ├── Some((1, 0)): 20/32 ≈ 0.625
      ├── Some((1, 2)): 8/19 ≈ 0.421
      ├── Some((1, 3)): 7/17 ≈ 0.412
      ├── Some((1, 4)): 7/17 ≈ 0.412
      ├── Some((1, 5)): 7/17 ≈ 0.412
      ├── Some((1, 7)): 10/21 ≈ 0.476
      └── Some((1, 8)): 5/15 ≈ 0.333
    ├── Some((6, 2)): 44/105 ≈ 0.419
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 4/11 ≈ 0.364
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 8/15 ≈ 0.533
      ├── Some((2, 6)): 9/16 ≈ 0.562
      ├── Some((2, 7)): 4/11 ≈ 0.364
      └── Some((2, 8)): 2/8 ≈ 0.250
    ├── Some((6, 3)): 149/264 ≈ 0.564
      ├── Some((3, 0)): 13/26 ≈ 0.500
      ├── Some((3, 1)): 19/32 ≈ 0.594
      ├── Some((3, 2)): 6/17 ≈ 0.353
      ├── Some((3, 3)): 10/22 ≈ 0.455
      ├── Some((3, 4)): 19/32 ≈ 0.594
      ├── Some((3, 5)): 17/30 ≈ 0.567
      ├── Some((3, 6)): 27/41 ≈ 0.659
      ├── Some((3, 7)): 17/30 ≈ 0.567
      └── Some((3, 8)): 20/33 ≈ 0.606
    ├── Some((6, 4)): 107/202 ≈ 0.530
      ├── Some((4, 0)): 4/13 ≈ 0.308
      ├── Some((4, 1)): 15/26 ≈ 0.577
      ├── Some((4, 2)): 19/30 ≈ 0.633
      ├── Some((4, 3)): 13/24 ≈ 0.542
      ├── Some((4, 4)): 13/24 ≈ 0.542
      ├── Some((4, 5)): 16/27 ≈ 0.593
      ├── Some((4, 6)): 2/11 ≈ 0.182
      ├── Some((4, 7)): 10/21 ≈ 0.476
      └── Some((4, 8)): 14/25 ≈ 0.560
    ├── Some((6, 5)): 83/166 ≈ 0.500
      ├── Some((5, 0)): 4/12 ≈ 0.333
      ├── Some((5, 1)): 5/14 ≈ 0.357
      ├── Some((5, 2)): 5/14 ≈ 0.357
      ├── Some((5, 3)): 11/20 ≈ 0.550
      ├── Some((5, 4)): 14/24 ≈ 0.583
      ├── Some((5, 5)): 9/18 ≈ 0.500
      ├── Some((5, 6)): 10/19 ≈ 0.526
      ├── Some((5, 7)): 11/20 ≈ 0.550
      └── Some((5, 8)): 14/24 ≈ 0.583
    ├── Some((6, 6)): 120/221 ≈ 0.543
      ├── Some((6, 0)): 26/40 ≈ 0.650
      ├── Some((6, 1)): 13/26 ≈ 0.500
      ├── Some((6, 2)): 6/17 ≈ 0.353
      ├── Some((6, 3)): 10/22 ≈ 0.455
      ├── Some((6, 4)): 23/37 ≈ 0.622
      ├── Some((6, 5)): 7/18 ≈ 0.389
      ├── Some((6, 7)): 13/26 ≈ 0.500
      └── Some((6, 8)): 21/34 ≈ 0.618
    ├── Some((6, 7)): 40/99 ≈ 0.404
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 1/7 ≈ 0.143
      ├── Some((7, 4)): 6/13 ≈ 0.462
      ├── Some((7, 5)): 7/14 ≈ 0.500
      ├── Some((7, 6)): 3/9 ≈ 0.333
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 8/15 ≈ 0.533
    └── Some((6, 8)): 105/199 ≈ 0.528
      ├── Some((8, 0)): 17/28 ≈ 0.607
      ├── Some((8, 1)): 11/21 ≈ 0.524
      ├── Some((8, 2)): 11/21 ≈ 0.524
      ├── Some((8, 3)): 19/30 ≈ 0.633
      ├── Some((8, 4)): 13/24 ≈ 0.542
      ├── Some((8, 5)): 4/13 ≈ 0.308
      ├── Some((8, 6)): 6/16 ≈ 0.375
      ├── Some((8, 7)): 14/25 ≈ 0.560
      └── Some((8, 8)): 10/20 ≈ 0.500
  ├── Some((1, 7)): 745/1455 ≈ 0.512
    ├── Some((7, 0)): 73/147 ≈ 0.497
      ├── Some((0, 0)): 9/17 ≈ 0.529
      ├── Some((0, 1)): 7/15 ≈ 0.467
      ├── Some((0, 2)): 11/20 ≈ 0.550
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 9/17 ≈ 0.529
      ├── Some((0, 6)): 15/24 ≈ 0.625
      ├── Some((0, 7)): 2/9 ≈ 0.222
      └── Some((0, 8)): 5/13 ≈ 0.385
    ├── Some((7, 1)): 82/161 ≈ 0.509
      ├── Some((1, 0)): 2/11 ≈ 0.182
      ├── Some((1, 2)): 15/27 ≈ 0.556
      ├── Some((1, 3)): 14/26 ≈ 0.538
      ├── Some((1, 4)): 23/36 ≈ 0.639
      ├── Some((1, 5)): 3/13 ≈ 0.231
      ├── Some((1, 6)): 14/26 ≈ 0.538
      └── Some((1, 8)): 10/21 ≈ 0.476
    ├── Some((7, 2)): 95/180 ≈ 0.528
      ├── Some((2, 0)): 12/22 ≈ 0.545
      ├── Some((2, 1)): 7/16 ≈ 0.438
      ├── Some((2, 2)): 14/24 ≈ 0.583
      ├── Some((2, 3)): 10/19 ≈ 0.526
      ├── Some((2, 4)): 9/18 ≈ 0.500
      ├── Some((2, 5)): 15/25 ≈ 0.600
      ├── Some((2, 6)): 7/16 ≈ 0.438
      ├── Some((2, 7)): 13/23 ≈ 0.565
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((7, 3)): 71/144 ≈ 0.493
      ├── Some((3, 0)): 3/11 ≈ 0.273
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 2)): 9/17 ≈ 0.529
      ├── Some((3, 3)): 5/13 ≈ 0.385
      ├── Some((3, 4)): 11/19 ≈ 0.579
      ├── Some((3, 5)): 7/15 ≈ 0.467
      ├── Some((3, 6)): 9/17 ≈ 0.529
      ├── Some((3, 7)): 14/23 ≈ 0.609
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((7, 4)): 84/163 ≈ 0.515
      ├── Some((4, 0)): 2/10 ≈ 0.200
      ├── Some((4, 1)): 10/19 ≈ 0.526
      ├── Some((4, 2)): 8/16 ≈ 0.500
      ├── Some((4, 3)): 4/12 ≈ 0.333
      ├── Some((4, 4)): 13/22 ≈ 0.591
      ├── Some((4, 5)): 13/22 ≈ 0.591
      ├── Some((4, 6)): 12/21 ≈ 0.571
      ├── Some((4, 7)): 12/21 ≈ 0.571
      └── Some((4, 8)): 10/19 ≈ 0.526
    ├── Some((7, 5)): 81/159 ≈ 0.509
      ├── Some((5, 0)): 7/15 ≈ 0.467
      ├── Some((5, 1)): 10/19 ≈ 0.526
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 8/17 ≈ 0.471
      ├── Some((5, 5)): 14/23 ≈ 0.609
      ├── Some((5, 6)): 16/25 ≈ 0.640
      ├── Some((5, 7)): 8/17 ≈ 0.471
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((7, 6)): 69/141 ≈ 0.489
      ├── Some((6, 0)): 9/17 ≈ 0.529
      ├── Some((6, 1)): 7/15 ≈ 0.467
      ├── Some((6, 2)): 12/20 ≈ 0.600
      ├── Some((6, 3)): 6/14 ≈ 0.429
      ├── Some((6, 4)): 4/12 ≈ 0.333
      ├── Some((6, 5)): 3/10 ≈ 0.300
      ├── Some((6, 6)): 12/20 ≈ 0.600
      ├── Some((6, 7)): 3/11 ≈ 0.273
      └── Some((6, 8)): 13/21 ≈ 0.619
    ├── Some((7, 7)): 83/162 ≈ 0.512
      ├── Some((7, 0)): 13/23 ≈ 0.565
      ├── Some((7, 1)): 14/25 ≈ 0.560
      ├── Some((7, 2)): 10/20 ≈ 0.500
      ├── Some((7, 3)): 12/22 ≈ 0.545
      ├── Some((7, 4)): 2/10 ≈ 0.200
      ├── Some((7, 5)): 8/18 ≈ 0.444
      ├── Some((7, 6)): 17/28 ≈ 0.607
      └── Some((7, 8)): 6/15 ≈ 0.400
    └── Some((7, 8)): 107/197 ≈ 0.543
      ├── Some((8, 0)): 11/21 ≈ 0.524
      ├── Some((8, 1)): 2/10 ≈ 0.200
      ├── Some((8, 2)): 13/23 ≈ 0.565
      ├── Some((8, 3)): 8/18 ≈ 0.444
      ├── Some((8, 4)): 14/24 ≈ 0.583
      ├── Some((8, 5)): 13/23 ≈ 0.565
      ├── Some((8, 6)): 10/20 ≈ 0.500
      ├── Some((8, 7)): 17/28 ≈ 0.607
      └── Some((8, 8)): 18/29 ≈ 0.621
  └── Some((1, 8)): 1026/1941 ≈ 0.529
    ├── Some((8, 0)): 135/247 ≈ 0.547
      ├── Some((0, 0)): 24/38 ≈ 0.632
      ├── Some((0, 1)): 11/23 ≈ 0.478
      ├── Some((0, 2)): 4/14 ≈ 0.286
      ├── Some((0, 3)): 13/25 ≈ 0.520
      ├── Some((0, 4)): 12/24 ≈ 0.500
      ├── Some((0, 5)): 21/34 ≈ 0.618
      ├── Some((0, 6)): 13/25 ≈ 0.520
      ├── Some((0, 7)): 14/27 ≈ 0.519
      └── Some((0, 8)): 23/36 ≈ 0.639
    ├── Some((8, 1)): 120/225 ≈ 0.533
      ├── Some((1, 0)): 15/30 ≈ 0.500
      ├── Some((1, 2)): 12/26 ≈ 0.462
      ├── Some((1, 3)): 13/27 ≈ 0.481
      ├── Some((1, 4)): 14/28 ≈ 0.500
      ├── Some((1, 5)): 10/24 ≈ 0.417
      ├── Some((1, 6)): 31/48 ≈ 0.646
      └── Some((1, 7)): 25/41 ≈ 0.610
    ├── Some((8, 2)): 120/225 ≈ 0.533
      ├── Some((2, 0)): 12/24 ≈ 0.500
      ├── Some((2, 1)): 8/19 ≈ 0.421
      ├── Some((2, 2)): 10/21 ≈ 0.476
      ├── Some((2, 3)): 10/21 ≈ 0.476
      ├── Some((2, 4)): 28/41 ≈ 0.683
      ├── Some((2, 5)): 22/35 ≈ 0.629
      ├── Some((2, 6)): 16/28 ≈ 0.571
      ├── Some((2, 7)): 7/18 ≈ 0.389
      └── Some((2, 8)): 6/17 ≈ 0.353
    ├── Some((8, 3)): 109/209 ≈ 0.522
      ├── Some((3, 0)): 20/32 ≈ 0.625
      ├── Some((3, 1)): 12/23 ≈ 0.522
      ├── Some((3, 2)): 13/24 ≈ 0.542
      ├── Some((3, 3)): 5/15 ≈ 0.333
      ├── Some((3, 4)): 15/27 ≈ 0.556
      ├── Some((3, 5)): 22/34 ≈ 0.647
      ├── Some((3, 6)): 6/16 ≈ 0.375
      ├── Some((3, 7)): 7/17 ≈ 0.412
      └── Some((3, 8)): 9/20 ≈ 0.450
    ├── Some((8, 4)): 95/187 ≈ 0.508
      ├── Some((4, 0)): 10/20 ≈ 0.500
      ├── Some((4, 1)): 11/21 ≈ 0.524
      ├── Some((4, 2)): 22/33 ≈ 0.667
      ├── Some((4, 3)): 9/19 ≈ 0.474
      ├── Some((4, 4)): 12/23 ≈ 0.522
      ├── Some((4, 5)): 5/14 ≈ 0.357
      ├── Some((4, 6)): 6/16 ≈ 0.375
      ├── Some((4, 7)): 9/19 ≈ 0.474
      └── Some((4, 8)): 11/21 ≈ 0.524
    ├── Some((8, 5)): 57/129 ≈ 0.442
      ├── Some((5, 0)): 4/12 ≈ 0.333
      ├── Some((5, 1)): 8/16 ≈ 0.500
      ├── Some((5, 2)): 5/13 ≈ 0.385
      ├── Some((5, 3)): 8/16 ≈ 0.500
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 4/12 ≈ 0.333
      ├── Some((5, 6)): 10/18 ≈ 0.556
      ├── Some((5, 7)): 6/14 ≈ 0.429
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((8, 6)): 105/203 ≈ 0.517
      ├── Some((6, 0)): 17/29 ≈ 0.586
      ├── Some((6, 1)): 21/33 ≈ 0.636
      ├── Some((6, 2)): 17/29 ≈ 0.586
      ├── Some((6, 3)): 13/24 ≈ 0.542
      ├── Some((6, 4)): 15/27 ≈ 0.556
      ├── Some((6, 5)): 3/12 ≈ 0.250
      ├── Some((6, 6)): 0/8 ≈ 0.000
      ├── Some((6, 7)): 9/20 ≈ 0.450
      └── Some((6, 8)): 9/20 ≈ 0.450
    ├── Some((8, 7)): 146/263 ≈ 0.555
      ├── Some((7, 0)): 19/32 ≈ 0.594
      ├── Some((7, 1)): 11/23 ≈ 0.478
      ├── Some((7, 2)): 15/28 ≈ 0.536
      ├── Some((7, 3)): 25/39 ≈ 0.641
      ├── Some((7, 4)): 13/26 ≈ 0.500
      ├── Some((7, 5)): 20/34 ≈ 0.588
      ├── Some((7, 6)): 16/29 ≈ 0.552
      ├── Some((7, 7)): 5/16 ≈ 0.312
      └── Some((7, 8)): 21/35 ≈ 0.600
    └── Some((8, 8)): 138/252 ≈ 0.548
      ├── Some((8, 0)): 21/36 ≈ 0.583
      ├── Some((8, 1)): 20/35 ≈ 0.571
      ├── Some((8, 2)): 28/44 ≈ 0.636
      ├── Some((8, 3)): 12/25 ≈ 0.480
      ├── Some((8, 4)): 11/24 ≈ 0.458
      ├── Some((8, 5)): 10/23 ≈ 0.435
      ├── Some((8, 6)): 10/23 ≈ 0.435
      └── Some((8, 7)): 26/41 ≈ 0.634
├── Some((1, 2)): 5614/10873 ≈ 0.516
  ├── Some((2, 0)): 423/861 ≈ 0.491
    ├── Some((0, 0)): 58/112 ≈ 0.518
      ├── Some((0, 1)): 15/21 ≈ 0.714
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 7/14 ≈ 0.500
      ├── Some((0, 5)): 4/10 ≈ 0.400
      ├── Some((0, 6)): 4/11 ≈ 0.364
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 8/15 ≈ 0.533
    ├── Some((0, 1)): 66/123 ≈ 0.537
      ├── Some((1, 0)): 1/7 ≈ 0.143
      ├── Some((1, 1)): 3/10 ≈ 0.300
      ├── Some((1, 3)): 11/19 ≈ 0.579
      ├── Some((1, 4)): 16/23 ≈ 0.696
      ├── Some((1, 5)): 10/17 ≈ 0.588
      ├── Some((1, 6)): 11/19 ≈ 0.579
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((0, 2)): 39/85 ≈ 0.459
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 7/13 ≈ 0.538
      ├── Some((2, 5)): 8/13 ≈ 0.615
      ├── Some((2, 6)): 5/11 ≈ 0.455
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 0/5 ≈ 0.000
    ├── Some((0, 3)): 48/98 ≈ 0.490
      ├── Some((3, 0)): 8/13 ≈ 0.615
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 7/12 ≈ 0.583
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 7/13 ≈ 0.538
      ├── Some((3, 6)): 6/12 ≈ 0.500
      ├── Some((3, 7)): 6/12 ≈ 0.500
      └── Some((3, 8)): 3/8 ≈ 0.375
    ├── Some((0, 4)): 44/92 ≈ 0.478
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 7/12 ≈ 0.583
      ├── Some((4, 2)): 1/6 ≈ 0.167
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 9/14 ≈ 0.643
      ├── Some((4, 6)): 7/13 ≈ 0.538
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((0, 5)): 22/59 ≈ 0.373
      ├── Some((5, 0)): 3/7 ≈ 0.429
      ├── Some((5, 1)): 4/8 ≈ 0.500
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 3/7 ≈ 0.429
      ├── Some((5, 4)): 0/4 ≈ 0.000
      ├── Some((5, 5)): 2/6 ≈ 0.333
      ├── Some((5, 6)): 3/7 ≈ 0.429
      ├── Some((5, 7)): 3/7 ≈ 0.429
      └── Some((5, 8)): 2/6 ≈ 0.333
    ├── Some((0, 6)): 50/101 ≈ 0.495
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 10/15 ≈ 0.667
      ├── Some((6, 5)): 7/13 ≈ 0.538
      ├── Some((6, 6)): 12/17 ≈ 0.706
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 2/8 ≈ 0.250
    ├── Some((0, 7)): 10/39 ≈ 0.256
      ├── Some((7, 0)): 2/5 ≈ 0.400
      ├── Some((7, 1)): 0/3 ≈ 0.000
      ├── Some((7, 2)): 0/3 ≈ 0.000
      ├── Some((7, 3)): 3/6 ≈ 0.500
      ├── Some((7, 4)): 1/4 ≈ 0.250
      ├── Some((7, 5)): 1/4 ≈ 0.250
      ├── Some((7, 6)): 0/3 ≈ 0.000
      ├── Some((7, 7)): 2/5 ≈ 0.400
      └── Some((7, 8)): 1/5 ≈ 0.200
    └── Some((0, 8)): 86/151 ≈ 0.570
      ├── Some((8, 0)): 12/19 ≈ 0.632
      ├── Some((8, 1)): 3/10 ≈ 0.300
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 12/19 ≈ 0.632
      ├── Some((8, 4)): 9/17 ≈ 0.529
      ├── Some((8, 5)): 2/9 ≈ 0.222
      ├── Some((8, 6)): 12/20 ≈ 0.600
      ├── Some((8, 7)): 13/20 ≈ 0.650
      └── Some((8, 8)): 15/22 ≈ 0.682
  ├── Some((2, 1)): 647/1249 ≈ 0.518
    ├── Some((1, 0)): 102/188 ≈ 0.543
      ├── Some((0, 0)): 12/22 ≈ 0.545
      ├── Some((0, 1)): 3/11 ≈ 0.273
      ├── Some((0, 2)): 17/27 ≈ 0.630
      ├── Some((0, 3)): 19/29 ≈ 0.655
      ├── Some((0, 4)): 18/28 ≈ 0.643
      ├── Some((0, 5)): 3/12 ≈ 0.250
      ├── Some((0, 6)): 13/23 ≈ 0.565
      ├── Some((0, 7)): 9/19 ≈ 0.474
      └── Some((0, 8)): 7/16 ≈ 0.438
    ├── Some((1, 1)): 71/142 ≈ 0.500
      ├── Some((1, 0)): 10/20 ≈ 0.500
      ├── Some((1, 3)): 4/13 ≈ 0.308
      ├── Some((1, 4)): 13/24 ≈ 0.542
      ├── Some((1, 5)): 4/13 ≈ 0.308
      ├── Some((1, 6)): 8/18 ≈ 0.444
      ├── Some((1, 7)): 20/31 ≈ 0.645
      └── Some((1, 8)): 11/22 ≈ 0.500
    ├── Some((1, 3)): 130/228 ≈ 0.570
      ├── Some((3, 0)): 7/17 ≈ 0.412
      ├── Some((3, 1)): 13/24 ≈ 0.542
      ├── Some((3, 2)): 20/31 ≈ 0.645
      ├── Some((3, 3)): 12/23 ≈ 0.522
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 16/27 ≈ 0.593
      ├── Some((3, 6)): 16/27 ≈ 0.593
      ├── Some((3, 7)): 13/24 ≈ 0.542
      └── Some((3, 8)): 24/36 ≈ 0.667
    ├── Some((1, 4)): 76/149 ≈ 0.510
      ├── Some((4, 0)): 9/17 ≈ 0.529
      ├── Some((4, 1)): 9/17 ≈ 0.529
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 8/16 ≈ 0.500
      ├── Some((4, 4)): 4/12 ≈ 0.333
      ├── Some((4, 5)): 16/24 ≈ 0.667
      ├── Some((4, 6)): 4/12 ≈ 0.333
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 10/18 ≈ 0.556
    ├── Some((1, 5)): 69/139 ≈ 0.496
      ├── Some((5, 0)): 5/12 ≈ 0.417
      ├── Some((5, 1)): 7/15 ≈ 0.467
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 5)): 13/21 ≈ 0.619
      ├── Some((5, 6)): 6/14 ≈ 0.429
      ├── Some((5, 7)): 10/18 ≈ 0.556
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((1, 6)): 76/149 ≈ 0.510
      ├── Some((6, 0)): 11/19 ≈ 0.579
      ├── Some((6, 1)): 8/16 ≈ 0.500
      ├── Some((6, 2)): 5/13 ≈ 0.385
      ├── Some((6, 3)): 12/20 ≈ 0.600
      ├── Some((6, 4)): 10/18 ≈ 0.556
      ├── Some((6, 5)): 5/13 ≈ 0.385
      ├── Some((6, 6)): 4/12 ≈ 0.333
      ├── Some((6, 7)): 8/16 ≈ 0.500
      └── Some((6, 8)): 13/21 ≈ 0.619
    ├── Some((1, 7)): 42/98 ≈ 0.429
      ├── Some((7, 0)): 10/17 ≈ 0.588
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 3/9 ≈ 0.333
      ├── Some((7, 4)): 6/12 ≈ 0.500
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 1/7 ≈ 0.143
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 2/8 ≈ 0.250
    └── Some((1, 8)): 80/155 ≈ 0.516
      ├── Some((8, 0)): 9/17 ≈ 0.529
      ├── Some((8, 1)): 9/17 ≈ 0.529
      ├── Some((8, 2)): 6/14 ≈ 0.429
      ├── Some((8, 3)): 11/20 ≈ 0.550
      ├── Some((8, 4)): 9/17 ≈ 0.529
      ├── Some((8, 5)): 10/18 ≈ 0.556
      ├── Some((8, 6)): 9/17 ≈ 0.529
      ├── Some((8, 7)): 13/22 ≈ 0.591
      └── Some((8, 8)): 4/12 ≈ 0.333
  ├── Some((2, 2)): 508/1009 ≈ 0.503
    ├── Some((2, 0)): 63/125 ≈ 0.504
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 4/11 ≈ 0.364
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 11/18 ≈ 0.611
      ├── Some((0, 4)): 1/7 ≈ 0.143
      ├── Some((0, 5)): 9/16 ≈ 0.562
      ├── Some((0, 6)): 14/21 ≈ 0.667
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 7/14 ≈ 0.500
    ├── Some((2, 1)): 41/93 ≈ 0.441
      ├── Some((1, 0)): 10/17 ≈ 0.588
      ├── Some((1, 1)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 2/8 ≈ 0.250
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 0/6 ≈ 0.000
    ├── Some((2, 3)): 81/152 ≈ 0.533
      ├── Some((3, 0)): 7/15 ≈ 0.467
      ├── Some((3, 1)): 8/16 ≈ 0.500
      ├── Some((3, 2)): 4/11 ≈ 0.364
      ├── Some((3, 3)): 3/10 ≈ 0.300
      ├── Some((3, 4)): 17/25 ≈ 0.680
      ├── Some((3, 5)): 6/14 ≈ 0.429
      ├── Some((3, 6)): 16/24 ≈ 0.667
      ├── Some((3, 7)): 10/18 ≈ 0.556
      └── Some((3, 8)): 10/18 ≈ 0.556
    ├── Some((2, 4)): 75/143 ≈ 0.524
      ├── Some((4, 0)): 10/18 ≈ 0.556
      ├── Some((4, 1)): 3/10 ≈ 0.300
      ├── Some((4, 2)): 13/21 ≈ 0.619
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 8/15 ≈ 0.533
      ├── Some((4, 5)): 9/17 ≈ 0.529
      ├── Some((4, 6)): 14/21 ≈ 0.667
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((2, 5)): 79/149 ≈ 0.530
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 13/21 ≈ 0.619
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 12/20 ≈ 0.600
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 8/16 ≈ 0.500
      ├── Some((5, 7)): 14/22 ≈ 0.636
      └── Some((5, 8)): 8/16 ≈ 0.500
    ├── Some((2, 6)): 69/134 ≈ 0.515
      ├── Some((6, 0)): 5/12 ≈ 0.417
      ├── Some((6, 1)): 4/11 ≈ 0.364
      ├── Some((6, 2)): 11/19 ≈ 0.579
      ├── Some((6, 3)): 5/12 ≈ 0.417
      ├── Some((6, 4)): 7/14 ≈ 0.500
      ├── Some((6, 5)): 14/22 ≈ 0.636
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((2, 7)): 40/91 ≈ 0.440
      ├── Some((7, 0)): 9/15 ≈ 0.600
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 1/6 ≈ 0.167
      ├── Some((7, 3)): 2/7 ≈ 0.286
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 6/12 ≈ 0.500
      ├── Some((7, 6)): 6/12 ≈ 0.500
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 1/6 ≈ 0.167
    └── Some((2, 8)): 60/121 ≈ 0.496
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 9/16 ≈ 0.562
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 3/9 ≈ 0.333
      ├── Some((8, 4)): 7/14 ≈ 0.500
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 15/22 ≈ 0.682
      ├── Some((8, 7)): 5/12 ≈ 0.417
      └── Some((8, 8)): 1/7 ≈ 0.143
  ├── Some((2, 3)): 818/1541 ≈ 0.531
    ├── Some((3, 0)): 129/226 ≈ 0.571
      ├── Some((0, 0)): 22/33 ≈ 0.667
      ├── Some((0, 1)): 24/36 ≈ 0.667
      ├── Some((0, 2)): 16/27 ≈ 0.593
      ├── Some((0, 3)): 11/22 ≈ 0.500
      ├── Some((0, 4)): 19/30 ≈ 0.633
      ├── Some((0, 5)): 8/18 ≈ 0.444
      ├── Some((0, 6)): 7/17 ≈ 0.412
      ├── Some((0, 7)): 13/24 ≈ 0.542
      └── Some((0, 8)): 8/18 ≈ 0.444
    ├── Some((3, 1)): 67/136 ≈ 0.493
      ├── Some((1, 0)): 3/11 ≈ 0.273
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 3)): 4/12 ≈ 0.333
      ├── Some((1, 4)): 15/24 ≈ 0.625
      ├── Some((1, 5)): 4/12 ≈ 0.333
      ├── Some((1, 6)): 2/10 ≈ 0.200
      ├── Some((1, 7)): 11/20 ≈ 0.550
      └── Some((1, 8)): 16/26 ≈ 0.615
    ├── Some((3, 2)): 80/155 ≈ 0.516
      ├── Some((2, 0)): 18/28 ≈ 0.643
      ├── Some((2, 1)): 15/25 ≈ 0.600
      ├── Some((2, 2)): 9/18 ≈ 0.500
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 9/18 ≈ 0.500
      ├── Some((2, 6)): 8/17 ≈ 0.471
      ├── Some((2, 7)): 8/17 ≈ 0.471
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((3, 3)): 92/173 ≈ 0.532
      ├── Some((3, 0)): 13/23 ≈ 0.565
      ├── Some((3, 1)): 11/21 ≈ 0.524
      ├── Some((3, 2)): 6/16 ≈ 0.375
      ├── Some((3, 4)): 21/32 ≈ 0.656
      ├── Some((3, 5)): 11/21 ≈ 0.524
      ├── Some((3, 6)): 11/21 ≈ 0.524
      ├── Some((3, 7)): 1/9 ≈ 0.111
      └── Some((3, 8)): 18/29 ≈ 0.621
    ├── Some((3, 4)): 80/155 ≈ 0.516
      ├── Some((4, 0)): 14/23 ≈ 0.609
      ├── Some((4, 1)): 4/12 ≈ 0.333
      ├── Some((4, 2)): 9/17 ≈ 0.529
      ├── Some((4, 3)): 10/19 ≈ 0.526
      ├── Some((4, 4)): 9/17 ≈ 0.529
      ├── Some((4, 5)): 12/21 ≈ 0.571
      ├── Some((4, 6)): 11/20 ≈ 0.550
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((3, 5)): 76/150 ≈ 0.507
      ├── Some((5, 0)): 16/25 ≈ 0.640
      ├── Some((5, 1)): 9/17 ≈ 0.529
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 4/12 ≈ 0.333
      ├── Some((5, 4)): 7/15 ≈ 0.467
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 9/17 ≈ 0.529
      ├── Some((5, 7)): 11/19 ≈ 0.579
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((3, 6)): 96/179 ≈ 0.536
      ├── Some((6, 0)): 13/23 ≈ 0.565
      ├── Some((6, 1)): 20/30 ≈ 0.667
      ├── Some((6, 2)): 17/27 ≈ 0.630
      ├── Some((6, 3)): 6/15 ≈ 0.400
      ├── Some((6, 4)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 8/17 ≈ 0.471
      ├── Some((6, 6)): 8/17 ≈ 0.471
      ├── Some((6, 7)): 13/23 ≈ 0.565
      └── Some((6, 8)): 0/7 ≈ 0.000
    ├── Some((3, 7)): 75/148 ≈ 0.507
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 12/21 ≈ 0.571
      ├── Some((7, 2)): 13/22 ≈ 0.591
      ├── Some((7, 3)): 6/14 ≈ 0.429
      ├── Some((7, 4)): 5/13 ≈ 0.385
      ├── Some((7, 5)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 9/17 ≈ 0.529
      ├── Some((7, 7)): 2/9 ≈ 0.222
      └── Some((7, 8)): 15/24 ≈ 0.625
    └── Some((3, 8)): 123/218 ≈ 0.564
      ├── Some((8, 0)): 16/27 ≈ 0.593
      ├── Some((8, 1)): 10/20 ≈ 0.500
      ├── Some((8, 2)): 7/17 ≈ 0.412
      ├── Some((8, 3)): 15/25 ≈ 0.600
      ├── Some((8, 4)): 20/31 ≈ 0.645
      ├── Some((8, 5)): 15/25 ≈ 0.600
      ├── Some((8, 6)): 15/26 ≈ 0.577
      ├── Some((8, 7)): 10/20 ≈ 0.500
      └── Some((8, 8)): 15/26 ≈ 0.577
  ├── Some((2, 4)): 590/1151 ≈ 0.513
    ├── Some((4, 0)): 73/139 ≈ 0.525
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 11/19 ≈ 0.579
      ├── Some((0, 3)): 8/15 ≈ 0.533
      ├── Some((0, 4)): 2/9 ≈ 0.222
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 11/19 ≈ 0.579
      ├── Some((0, 7)): 8/15 ≈ 0.533
      └── Some((0, 8)): 13/21 ≈ 0.619
    ├── Some((4, 1)): 31/76 ≈ 0.408
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 8/14 ≈ 0.571
    ├── Some((4, 2)): 94/169 ≈ 0.556
      ├── Some((2, 0)): 7/16 ≈ 0.438
      ├── Some((2, 1)): 10/19 ≈ 0.526
      ├── Some((2, 2)): 18/28 ≈ 0.643
      ├── Some((2, 3)): 13/23 ≈ 0.565
      ├── Some((2, 5)): 8/17 ≈ 0.471
      ├── Some((2, 6)): 14/24 ≈ 0.583
      ├── Some((2, 7)): 19/29 ≈ 0.655
      └── Some((2, 8)): 4/12 ≈ 0.333
    ├── Some((4, 3)): 87/159 ≈ 0.547
      ├── Some((3, 0)): 6/14 ≈ 0.429
      ├── Some((3, 1)): 2/9 ≈ 0.222
      ├── Some((3, 2)): 10/18 ≈ 0.556
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 16/25 ≈ 0.640
      ├── Some((3, 5)): 21/29 ≈ 0.724
      ├── Some((3, 6)): 4/12 ≈ 0.333
      ├── Some((3, 7)): 13/21 ≈ 0.619
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((4, 4)): 75/142 ≈ 0.528
      ├── Some((4, 0)): 25/34 ≈ 0.735
      ├── Some((4, 1)): 10/19 ≈ 0.526
      ├── Some((4, 2)): 3/11 ≈ 0.273
      ├── Some((4, 3)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 0/7 ≈ 0.000
      ├── Some((4, 7)): 9/18 ≈ 0.500
      └── Some((4, 8)): 13/22 ≈ 0.591
    ├── Some((4, 5)): 50/106 ≈ 0.472
      ├── Some((5, 0)): 11/17 ≈ 0.647
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 6/12 ≈ 0.500
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 3/9 ≈ 0.333
      ├── Some((5, 5)): 3/9 ≈ 0.333
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 2/8 ≈ 0.250
      └── Some((5, 8)): 8/15 ≈ 0.533
    ├── Some((4, 6)): 48/103 ≈ 0.466
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 6/12 ≈ 0.500
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 4/10 ≈ 0.400
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 1/7 ≈ 0.143
      ├── Some((6, 7)): 9/15 ≈ 0.600
      └── Some((6, 8)): 6/12 ≈ 0.500
    ├── Some((4, 7)): 69/133 ≈ 0.519
      ├── Some((7, 0)): 3/10 ≈ 0.300
      ├── Some((7, 1)): 7/14 ≈ 0.500
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 13/20 ≈ 0.650
      ├── Some((7, 4)): 11/19 ≈ 0.579
      ├── Some((7, 5)): 9/16 ≈ 0.562
      ├── Some((7, 6)): 5/12 ≈ 0.417
      ├── Some((7, 7)): 7/14 ≈ 0.500
      └── Some((7, 8)): 5/12 ≈ 0.417
    └── Some((4, 8)): 62/123 ≈ 0.504
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 7/14 ≈ 0.500
      ├── Some((8, 2)): 9/16 ≈ 0.562
      ├── Some((8, 3)): 8/15 ≈ 0.533
      ├── Some((8, 4)): 7/14 ≈ 0.500
      ├── Some((8, 5)): 12/19 ≈ 0.632
      ├── Some((8, 6)): 6/13 ≈ 0.462
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 4/11 ≈ 0.364
  ├── Some((2, 5)): 793/1499 ≈ 0.529
    ├── Some((5, 0)): 74/146 ≈ 0.507
      ├── Some((0, 0)): 9/17 ≈ 0.529
      ├── Some((0, 1)): 2/9 ≈ 0.222
      ├── Some((0, 2)): 16/24 ≈ 0.667
      ├── Some((0, 3)): 4/12 ≈ 0.333
      ├── Some((0, 4)): 6/14 ≈ 0.429
      ├── Some((0, 5)): 6/14 ≈ 0.429
      ├── Some((0, 6)): 2/9 ≈ 0.222
      ├── Some((0, 7)): 14/23 ≈ 0.609
      └── Some((0, 8)): 14/23 ≈ 0.609
    ├── Some((5, 1)): 96/179 ≈ 0.536
      ├── Some((1, 0)): 8/18 ≈ 0.444
      ├── Some((1, 1)): 5/15 ≈ 0.333
      ├── Some((1, 3)): 9/19 ≈ 0.474
      ├── Some((1, 4)): 5/15 ≈ 0.333
      ├── Some((1, 5)): 11/21 ≈ 0.524
      ├── Some((1, 6)): 30/41 ≈ 0.732
      ├── Some((1, 7)): 7/17 ≈ 0.412
      └── Some((1, 8)): 21/32 ≈ 0.656
    ├── Some((5, 2)): 72/143 ≈ 0.503
      ├── Some((2, 0)): 9/18 ≈ 0.500
      ├── Some((2, 1)): 6/15 ≈ 0.400
      ├── Some((2, 2)): 11/20 ≈ 0.550
      ├── Some((2, 3)): 5/13 ≈ 0.385
      ├── Some((2, 4)): 7/16 ≈ 0.438
      ├── Some((2, 6)): 11/20 ≈ 0.550
      ├── Some((2, 7)): 11/20 ≈ 0.550
      └── Some((2, 8)): 11/20 ≈ 0.550
    ├── Some((5, 3)): 94/176 ≈ 0.534
      ├── Some((3, 0)): 13/23 ≈ 0.565
      ├── Some((3, 1)): 10/19 ≈ 0.526
      ├── Some((3, 2)): 9/18 ≈ 0.500
      ├── Some((3, 3)): 9/18 ≈ 0.500
      ├── Some((3, 4)): 3/11 ≈ 0.273
      ├── Some((3, 5)): 12/21 ≈ 0.571
      ├── Some((3, 6)): 23/33 ≈ 0.697
      ├── Some((3, 7)): 10/19 ≈ 0.526
      └── Some((3, 8)): 4/13 ≈ 0.308
    ├── Some((5, 4)): 56/119 ≈ 0.471
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 13/20 ≈ 0.650
      ├── Some((4, 2)): 12/20 ≈ 0.600
      ├── Some((4, 3)): 4/11 ≈ 0.364
      ├── Some((4, 4)): 4/11 ≈ 0.364
      ├── Some((4, 5)): 3/10 ≈ 0.300
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 7/14 ≈ 0.500
      └── Some((4, 8)): 0/6 ≈ 0.000
    ├── Some((5, 5)): 127/223 ≈ 0.570
      ├── Some((5, 0)): 7/18 ≈ 0.389
      ├── Some((5, 1)): 18/30 ≈ 0.600
      ├── Some((5, 2)): 13/25 ≈ 0.520
      ├── Some((5, 3)): 10/21 ≈ 0.476
      ├── Some((5, 4)): 11/23 ≈ 0.478
      ├── Some((5, 6)): 17/29 ≈ 0.586
      ├── Some((5, 7)): 30/43 ≈ 0.698
      └── Some((5, 8)): 21/33 ≈ 0.636
    ├── Some((5, 6)): 89/168 ≈ 0.530
      ├── Some((6, 0)): 5/13 ≈ 0.385
      ├── Some((6, 1)): 8/17 ≈ 0.471
      ├── Some((6, 2)): 13/22 ≈ 0.591
      ├── Some((6, 3)): 5/13 ≈ 0.385
      ├── Some((6, 4)): 13/22 ≈ 0.591
      ├── Some((6, 5)): 7/15 ≈ 0.467
      ├── Some((6, 6)): 19/28 ≈ 0.679
      ├── Some((6, 7)): 12/21 ≈ 0.571
      └── Some((6, 8)): 7/16 ≈ 0.438
    ├── Some((5, 7)): 66/134 ≈ 0.493
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 5/12 ≈ 0.417
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 9/17 ≈ 0.529
      ├── Some((7, 5)): 3/10 ≈ 0.300
      ├── Some((7, 6)): 11/19 ≈ 0.579
      ├── Some((7, 7)): 5/12 ≈ 0.417
      └── Some((7, 8)): 10/18 ≈ 0.556
    └── Some((5, 8)): 118/210 ≈ 0.562
      ├── Some((8, 0)): 13/23 ≈ 0.565
      ├── Some((8, 1)): 16/27 ≈ 0.593
      ├── Some((8, 2)): 3/12 ≈ 0.250
      ├── Some((8, 3)): 14/24 ≈ 0.583
      ├── Some((8, 4)): 7/17 ≈ 0.412
      ├── Some((8, 5)): 23/34 ≈ 0.676
      ├── Some((8, 6)): 21/32 ≈ 0.656
      ├── Some((8, 7)): 7/17 ≈ 0.412
      └── Some((8, 8)): 13/23 ≈ 0.565
  ├── Some((2, 6)): 661/1273 ≈ 0.519
    ├── Some((6, 0)): 54/113 ≈ 0.478
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 7/14 ≈ 0.500
      ├── Some((0, 2)): 2/8 ≈ 0.250
      ├── Some((0, 3)): 2/8 ≈ 0.250
      ├── Some((0, 4)): 0/6 ≈ 0.000
      ├── Some((0, 5)): 11/18 ≈ 0.611
      ├── Some((0, 6)): 6/13 ≈ 0.462
      ├── Some((0, 7)): 11/18 ≈ 0.611
      └── Some((0, 8)): 12/19 ≈ 0.632
    ├── Some((6, 1)): 44/98 ≈ 0.449
      ├── Some((1, 0)): 3/9 ≈ 0.333
      ├── Some((1, 1)): 2/8 ≈ 0.250
      ├── Some((1, 3)): 6/13 ≈ 0.462
      ├── Some((1, 4)): 14/21 ≈ 0.667
      ├── Some((1, 5)): 5/12 ≈ 0.417
      ├── Some((1, 6)): 1/7 ≈ 0.143
      ├── Some((1, 7)): 3/10 ≈ 0.300
      └── Some((1, 8)): 10/17 ≈ 0.588
    ├── Some((6, 2)): 72/140 ≈ 0.514
      ├── Some((2, 0)): 8/17 ≈ 0.471
      ├── Some((2, 1)): 1/8 ≈ 0.125
      ├── Some((2, 2)): 5/13 ≈ 0.385
      ├── Some((2, 3)): 4/12 ≈ 0.333
      ├── Some((2, 4)): 5/14 ≈ 0.357
      ├── Some((2, 5)): 16/25 ≈ 0.640
      ├── Some((2, 7)): 15/24 ≈ 0.625
      └── Some((2, 8)): 17/26 ≈ 0.654
    ├── Some((6, 3)): 119/206 ≈ 0.578
      ├── Some((3, 0)): 5/14 ≈ 0.357
      ├── Some((3, 1)): 7/16 ≈ 0.438
      ├── Some((3, 2)): 14/24 ≈ 0.583
      ├── Some((3, 3)): 18/28 ≈ 0.643
      ├── Some((3, 4)): 10/19 ≈ 0.526
      ├── Some((3, 5)): 16/26 ≈ 0.615
      ├── Some((3, 6)): 12/22 ≈ 0.545
      ├── Some((3, 7)): 25/35 ≈ 0.714
      └── Some((3, 8)): 11/21 ≈ 0.524
    ├── Some((6, 4)): 88/163 ≈ 0.540
      ├── Some((4, 0)): 11/19 ≈ 0.579
      ├── Some((4, 1)): 12/21 ≈ 0.571
      ├── Some((4, 2)): 4/12 ≈ 0.333
      ├── Some((4, 3)): 14/23 ≈ 0.609
      ├── Some((4, 4)): 19/27 ≈ 0.704
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 7/15 ≈ 0.467
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 5/13 ≈ 0.385
    ├── Some((6, 5)): 91/167 ≈ 0.545
      ├── Some((5, 0)): 13/22 ≈ 0.591
      ├── Some((5, 1)): 6/14 ≈ 0.429
      ├── Some((5, 2)): 6/14 ≈ 0.429
      ├── Some((5, 3)): 4/12 ≈ 0.333
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 11/20 ≈ 0.550
      ├── Some((5, 6)): 13/22 ≈ 0.591
      ├── Some((5, 7)): 26/35 ≈ 0.743
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((6, 6)): 47/103 ≈ 0.456
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 11/18 ≈ 0.611
      ├── Some((6, 2)): 4/11 ≈ 0.364
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 5/12 ≈ 0.417
      └── Some((6, 8)): 4/11 ≈ 0.364
    ├── Some((6, 7)): 68/134 ≈ 0.507
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 10/18 ≈ 0.556
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 3/10 ≈ 0.300
      ├── Some((7, 4)): 4/11 ≈ 0.364
      ├── Some((7, 5)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 11/19 ≈ 0.579
      ├── Some((7, 7)): 7/14 ≈ 0.500
      └── Some((7, 8)): 11/19 ≈ 0.579
    └── Some((6, 8)): 78/148 ≈ 0.527
      ├── Some((8, 0)): 5/12 ≈ 0.417
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 17/25 ≈ 0.680
      ├── Some((8, 3)): 4/11 ≈ 0.364
      ├── Some((8, 4)): 7/15 ≈ 0.467
      ├── Some((8, 5)): 15/23 ≈ 0.652
      ├── Some((8, 6)): 6/14 ≈ 0.429
      ├── Some((8, 7)): 12/20 ≈ 0.600
      └── Some((8, 8)): 6/14 ≈ 0.429
  ├── Some((2, 7)): 672/1292 ≈ 0.520
    ├── Some((7, 0)): 57/118 ≈ 0.483
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 5/12 ≈ 0.417
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 9/16 ≈ 0.562
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 9/16 ≈ 0.562
      ├── Some((0, 6)): 8/15 ≈ 0.533
      ├── Some((0, 7)): 12/19 ≈ 0.632
      └── Some((0, 8)): 1/7 ≈ 0.143
    ├── Some((7, 1)): 66/132 ≈ 0.500
      ├── Some((1, 0)): 12/21 ≈ 0.571
      ├── Some((1, 1)): 10/18 ≈ 0.556
      ├── Some((1, 3)): 20/29 ≈ 0.690
      ├── Some((1, 4)): 3/11 ≈ 0.273
      ├── Some((1, 5)): 6/14 ≈ 0.429
      ├── Some((1, 6)): 2/9 ≈ 0.222
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 7/15 ≈ 0.467
    ├── Some((7, 2)): 142/239 ≈ 0.594
      ├── Some((2, 0)): 21/34 ≈ 0.618
      ├── Some((2, 1)): 34/47 ≈ 0.723
      ├── Some((2, 2)): 26/39 ≈ 0.667
      ├── Some((2, 3)): 11/23 ≈ 0.478
      ├── Some((2, 4)): 8/19 ≈ 0.421
      ├── Some((2, 5)): 5/15 ≈ 0.333
      ├── Some((2, 6)): 10/21 ≈ 0.476
      └── Some((2, 8)): 27/40 ≈ 0.675
    ├── Some((7, 3)): 39/91 ≈ 0.429
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 0/5 ≈ 0.000
      ├── Some((3, 3)): 5/11 ≈ 0.455
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 8/14 ≈ 0.571
      ├── Some((3, 6)): 2/8 ≈ 0.250
      ├── Some((3, 7)): 5/11 ≈ 0.455
      └── Some((3, 8)): 10/16 ≈ 0.625
    ├── Some((7, 4)): 90/166 ≈ 0.542
      ├── Some((4, 0)): 15/24 ≈ 0.625
      ├── Some((4, 1)): 16/25 ≈ 0.640
      ├── Some((4, 2)): 6/14 ≈ 0.429
      ├── Some((4, 3)): 2/9 ≈ 0.222
      ├── Some((4, 4)): 16/25 ≈ 0.640
      ├── Some((4, 5)): 11/20 ≈ 0.550
      ├── Some((4, 6)): 8/16 ≈ 0.500
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((7, 5)): 74/143 ≈ 0.517
      ├── Some((5, 0)): 12/20 ≈ 0.600
      ├── Some((5, 1)): 7/15 ≈ 0.467
      ├── Some((5, 2)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 5/12 ≈ 0.417
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 13/21 ≈ 0.619
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((7, 6)): 66/132 ≈ 0.500
      ├── Some((6, 0)): 6/13 ≈ 0.462
      ├── Some((6, 1)): 4/11 ≈ 0.364
      ├── Some((6, 2)): 6/13 ≈ 0.462
      ├── Some((6, 3)): 12/20 ≈ 0.600
      ├── Some((6, 4)): 2/9 ≈ 0.222
      ├── Some((6, 5)): 15/23 ≈ 0.652
      ├── Some((6, 6)): 12/20 ≈ 0.600
      ├── Some((6, 7)): 6/13 ≈ 0.462
      └── Some((6, 8)): 2/9 ≈ 0.222
    ├── Some((7, 7)): 76/146 ≈ 0.521
      ├── Some((7, 0)): 10/19 ≈ 0.526
      ├── Some((7, 1)): 13/22 ≈ 0.591
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 8/17 ≈ 0.471
      ├── Some((7, 4)): 18/27 ≈ 0.667
      ├── Some((7, 5)): 4/12 ≈ 0.333
      ├── Some((7, 6)): 7/15 ≈ 0.467
      └── Some((7, 8)): 8/17 ≈ 0.471
    └── Some((7, 8)): 61/124 ≈ 0.492
      ├── Some((8, 0)): 10/17 ≈ 0.588
      ├── Some((8, 1)): 3/10 ≈ 0.300
      ├── Some((8, 2)): 10/17 ≈ 0.588
      ├── Some((8, 3)): 10/17 ≈ 0.588
      ├── Some((8, 4)): 2/9 ≈ 0.222
      ├── Some((8, 5)): 1/7 ≈ 0.143
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 8/15 ≈ 0.533
      └── Some((8, 8)): 11/19 ≈ 0.579
  └── Some((2, 8)): 501/997 ≈ 0.503
    ├── Some((8, 0)): 47/98 ≈ 0.480
      ├── Some((0, 0)): 3/9 ≈ 0.333
      ├── Some((0, 1)): 3/9 ≈ 0.333
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 3/9 ≈ 0.333
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 8/14 ≈ 0.571
      ├── Some((0, 6)): 0/5 ≈ 0.000
      ├── Some((0, 7)): 17/22 ≈ 0.773
      └── Some((0, 8)): 8/14 ≈ 0.571
    ├── Some((8, 1)): 67/127 ≈ 0.528
      ├── Some((1, 0)): 11/19 ≈ 0.579
      ├── Some((1, 1)): 9/16 ≈ 0.562
      ├── Some((1, 3)): 9/17 ≈ 0.529
      ├── Some((1, 4)): 13/21 ≈ 0.619
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 3/10 ≈ 0.300
      ├── Some((1, 7)): 14/21 ≈ 0.667
      └── Some((1, 8)): 2/9 ≈ 0.222
    ├── Some((8, 2)): 66/126 ≈ 0.524
      ├── Some((2, 0)): 8/16 ≈ 0.500
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 14/22 ≈ 0.636
      ├── Some((2, 4)): 6/13 ≈ 0.462
      ├── Some((2, 5)): 10/18 ≈ 0.556
      ├── Some((2, 6)): 13/21 ≈ 0.619
      └── Some((2, 7)): 5/12 ≈ 0.417
    ├── Some((8, 3)): 49/101 ≈ 0.485
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 0/5 ≈ 0.000
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 2/8 ≈ 0.250
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 11/17 ≈ 0.647
      ├── Some((3, 6)): 14/19 ≈ 0.737
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 4/10 ≈ 0.400
    ├── Some((8, 4)): 84/151 ≈ 0.556
      ├── Some((4, 0)): 14/21 ≈ 0.667
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 14/22 ≈ 0.636
      ├── Some((4, 4)): 9/17 ≈ 0.529
      ├── Some((4, 5)): 10/18 ≈ 0.556
      ├── Some((4, 6)): 18/25 ≈ 0.720
      ├── Some((4, 7)): 1/8 ≈ 0.125
      └── Some((4, 8)): 1/8 ≈ 0.125
    ├── Some((8, 5)): 41/90 ≈ 0.456
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 11/16 ≈ 0.688
      ├── Some((5, 3)): 1/6 ≈ 0.167
      ├── Some((5, 4)): 3/9 ≈ 0.333
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 2/7 ≈ 0.286
      ├── Some((5, 7)): 9/14 ≈ 0.643
      └── Some((5, 8)): 2/7 ≈ 0.286
    ├── Some((8, 6)): 31/74 ≈ 0.419
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 4/8 ≈ 0.500
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((8, 7)): 65/125 ≈ 0.520
      ├── Some((7, 0)): 15/22 ≈ 0.682
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 9/16 ≈ 0.562
      ├── Some((7, 3)): 12/19 ≈ 0.632
      ├── Some((7, 4)): 8/15 ≈ 0.533
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 9/16 ≈ 0.562
      ├── Some((7, 7)): 1/7 ≈ 0.143
      └── Some((7, 8)): 1/7 ≈ 0.143
    └── Some((8, 8)): 51/104 ≈ 0.490
      ├── Some((8, 0)): 3/9 ≈ 0.333
      ├── Some((8, 1)): 12/18 ≈ 0.667
      ├── Some((8, 2)): 1/7 ≈ 0.143
      ├── Some((8, 3)): 6/13 ≈ 0.462
      ├── Some((8, 4)): 7/14 ≈ 0.500
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 6/13 ≈ 0.462
      └── Some((8, 7)): 12/19 ≈ 0.632
├── Some((1, 3)): 4535/8884 ≈ 0.510
  ├── Some((3, 0)): 517/1011 ≈ 0.511
    ├── Some((0, 0)): 50/102 ≈ 0.490
      ├── Some((0, 1)): 2/8 ≈ 0.250
      ├── Some((0, 2)): 9/16 ≈ 0.562
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 6/13 ≈ 0.462
      ├── Some((0, 5)): 10/17 ≈ 0.588
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 7/14 ≈ 0.500
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((0, 1)): 53/107 ≈ 0.495
      ├── Some((1, 0)): 4/11 ≈ 0.364
      ├── Some((1, 1)): 2/8 ≈ 0.250
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 4)): 2/8 ≈ 0.250
      ├── Some((1, 5)): 4/11 ≈ 0.364
      ├── Some((1, 6)): 14/21 ≈ 0.667
      ├── Some((1, 7)): 2/9 ≈ 0.222
      └── Some((1, 8)): 17/24 ≈ 0.708
    ├── Some((0, 2)): 66/125 ≈ 0.528
      ├── Some((2, 0)): 9/16 ≈ 0.562
      ├── Some((2, 1)): 9/16 ≈ 0.562
      ├── Some((2, 2)): 17/23 ≈ 0.739
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 2/8 ≈ 0.250
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 10/17 ≈ 0.588
    ├── Some((0, 3)): 34/79 ≈ 0.430
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 1/6 ≈ 0.167
      ├── Some((3, 6)): 5/11 ≈ 0.455
      ├── Some((3, 7)): 12/18 ≈ 0.667
      └── Some((3, 8)): 9/15 ≈ 0.600
    ├── Some((0, 4)): 74/136 ≈ 0.544
      ├── Some((4, 0)): 17/24 ≈ 0.708
      ├── Some((4, 1)): 6/13 ≈ 0.462
      ├── Some((4, 2)): 8/15 ≈ 0.533
      ├── Some((4, 3)): 2/8 ≈ 0.250
      ├── Some((4, 4)): 4/11 ≈ 0.364
      ├── Some((4, 5)): 8/15 ≈ 0.533
      ├── Some((4, 6)): 13/20 ≈ 0.650
      ├── Some((4, 7)): 13/20 ≈ 0.650
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((0, 5)): 59/115 ≈ 0.513
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 5/12 ≈ 0.417
      ├── Some((5, 3)): 2/8 ≈ 0.250
      ├── Some((5, 4)): 11/17 ≈ 0.647
      ├── Some((5, 5)): 14/20 ≈ 0.700
      ├── Some((5, 6)): 11/17 ≈ 0.647
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 1/7 ≈ 0.143
    ├── Some((0, 6)): 74/136 ≈ 0.544
      ├── Some((6, 0)): 6/13 ≈ 0.462
      ├── Some((6, 1)): 3/10 ≈ 0.300
      ├── Some((6, 2)): 10/17 ≈ 0.588
      ├── Some((6, 3)): 6/13 ≈ 0.462
      ├── Some((6, 4)): 14/21 ≈ 0.667
      ├── Some((6, 5)): 5/12 ≈ 0.417
      ├── Some((6, 6)): 16/22 ≈ 0.727
      ├── Some((6, 7)): 8/15 ≈ 0.533
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((0, 7)): 20/57 ≈ 0.351
      ├── Some((7, 0)): 3/7 ≈ 0.429
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 2/6 ≈ 0.333
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 2/6 ≈ 0.333
      ├── Some((7, 5)): 2/6 ≈ 0.333
      ├── Some((7, 6)): 0/4 ≈ 0.000
      ├── Some((7, 7)): 3/7 ≈ 0.429
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((0, 8)): 86/153 ≈ 0.562
      ├── Some((8, 0)): 11/19 ≈ 0.579
      ├── Some((8, 1)): 14/21 ≈ 0.667
      ├── Some((8, 2)): 11/19 ≈ 0.579
      ├── Some((8, 3)): 7/14 ≈ 0.500
      ├── Some((8, 4)): 16/23 ≈ 0.696
      ├── Some((8, 5)): 9/16 ≈ 0.562
      ├── Some((8, 6)): 1/8 ≈ 0.125
      ├── Some((8, 7)): 9/17 ≈ 0.529
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((3, 1)): 439/876 ≈ 0.501
    ├── Some((1, 0)): 73/136 ≈ 0.537
      ├── Some((0, 0)): 2/9 ≈ 0.222
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 10/17 ≈ 0.588
      ├── Some((0, 3)): 3/10 ≈ 0.300
      ├── Some((0, 4)): 7/14 ≈ 0.500
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 11/18 ≈ 0.611
      ├── Some((0, 7)): 11/18 ≈ 0.611
      └── Some((0, 8)): 14/21 ≈ 0.667
    ├── Some((1, 1)): 70/132 ≈ 0.530
      ├── Some((1, 0)): 6/15 ≈ 0.400
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 4)): 25/35 ≈ 0.714
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 2/10 ≈ 0.200
      ├── Some((1, 7)): 14/24 ≈ 0.583
      └── Some((1, 8)): 0/7 ≈ 0.000
    ├── Some((1, 2)): 60/117 ≈ 0.513
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 12/18 ≈ 0.667
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 6/13 ≈ 0.462
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 13/19 ≈ 0.684
    ├── Some((1, 4)): 56/111 ≈ 0.505
      ├── Some((4, 0)): 1/7 ≈ 0.143
      ├── Some((4, 1)): 15/21 ≈ 0.714
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 4/10 ≈ 0.400
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 9/15 ≈ 0.600
    ├── Some((1, 5)): 49/101 ≈ 0.485
      ├── Some((5, 0)): 6/12 ≈ 0.500
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 6/12 ≈ 0.500
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 7/12 ≈ 0.583
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 3/9 ≈ 0.333
      └── Some((5, 8)): 12/17 ≈ 0.706
    ├── Some((1, 6)): 39/86 ≈ 0.453
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 2/7 ≈ 0.286
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 8/13 ≈ 0.615
      ├── Some((6, 7)): 6/11 ≈ 0.545
      └── Some((6, 8)): 6/12 ≈ 0.500
    ├── Some((1, 7)): 51/104 ≈ 0.490
      ├── Some((7, 0)): 11/16 ≈ 0.688
      ├── Some((7, 1)): 8/14 ≈ 0.571
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 1/6 ≈ 0.167
      ├── Some((7, 4)): 3/9 ≈ 0.333
      ├── Some((7, 5)): 8/14 ≈ 0.571
      ├── Some((7, 6)): 9/15 ≈ 0.600
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((1, 8)): 40/88 ≈ 0.455
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 4/9 ≈ 0.444
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 4/9 ≈ 0.444
      ├── Some((8, 4)): 11/16 ≈ 0.688
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 0/5 ≈ 0.000
      ├── Some((8, 7)): 2/7 ≈ 0.286
      └── Some((8, 8)): 5/11 ≈ 0.455
  ├── Some((3, 2)): 643/1225 ≈ 0.525
    ├── Some((2, 0)): 45/98 ≈ 0.459
      ├── Some((0, 0)): 4/10 ≈ 0.400
      ├── Some((0, 1)): 7/13 ≈ 0.538
      ├── Some((0, 2)): 2/8 ≈ 0.250
      ├── Some((0, 3)): 1/6 ≈ 0.167
      ├── Some((0, 4)): 7/13 ≈ 0.538
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 10/15 ≈ 0.667
      ├── Some((0, 7)): 4/10 ≈ 0.400
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((2, 1)): 91/164 ≈ 0.555
      ├── Some((1, 0)): 15/24 ≈ 0.625
      ├── Some((1, 1)): 6/15 ≈ 0.400
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 12/21 ≈ 0.571
      ├── Some((1, 7)): 9/18 ≈ 0.500
      └── Some((1, 8)): 17/27 ≈ 0.630
    ├── Some((2, 2)): 104/182 ≈ 0.571
      ├── Some((2, 0)): 18/28 ≈ 0.643
      ├── Some((2, 1)): 1/9 ≈ 0.111
      ├── Some((2, 3)): 17/27 ≈ 0.630
      ├── Some((2, 4)): 23/33 ≈ 0.697
      ├── Some((2, 5)): 13/23 ≈ 0.565
      ├── Some((2, 6)): 9/19 ≈ 0.474
      ├── Some((2, 7)): 10/20 ≈ 0.500
      └── Some((2, 8)): 12/22 ≈ 0.545
    ├── Some((2, 3)): 66/128 ≈ 0.516
      ├── Some((3, 0)): 8/16 ≈ 0.500
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 4/11 ≈ 0.364
      ├── Some((3, 5)): 8/16 ≈ 0.500
      ├── Some((3, 6)): 11/19 ≈ 0.579
      ├── Some((3, 7)): 4/11 ≈ 0.364
      └── Some((3, 8)): 18/26 ≈ 0.692
    ├── Some((2, 4)): 95/170 ≈ 0.559
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 11/19 ≈ 0.579
      ├── Some((4, 2)): 13/22 ≈ 0.591
      ├── Some((4, 3)): 9/17 ≈ 0.529
      ├── Some((4, 4)): 9/17 ≈ 0.529
      ├── Some((4, 5)): 13/22 ≈ 0.591
      ├── Some((4, 6)): 11/19 ≈ 0.579
      ├── Some((4, 7)): 12/20 ≈ 0.600
      └── Some((4, 8)): 10/18 ≈ 0.556
    ├── Some((2, 5)): 65/127 ≈ 0.512
      ├── Some((5, 0)): 1/7 ≈ 0.143
      ├── Some((5, 1)): 8/15 ≈ 0.533
      ├── Some((5, 2)): 5/12 ≈ 0.417
      ├── Some((5, 3)): 2/8 ≈ 0.250
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 17/24 ≈ 0.708
      ├── Some((5, 6)): 7/14 ≈ 0.500
      ├── Some((5, 7)): 10/17 ≈ 0.588
      └── Some((5, 8)): 10/17 ≈ 0.588
    ├── Some((2, 6)): 54/111 ≈ 0.486
      ├── Some((6, 0)): 9/15 ≈ 0.600
      ├── Some((6, 1)): 8/15 ≈ 0.533
      ├── Some((6, 2)): 7/13 ≈ 0.538
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 7/14 ≈ 0.500
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 10/16 ≈ 0.625
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 0/6 ≈ 0.000
    ├── Some((2, 7)): 69/133 ≈ 0.519
      ├── Some((7, 0)): 7/14 ≈ 0.500
      ├── Some((7, 1)): 12/19 ≈ 0.632
      ├── Some((7, 2)): 15/22 ≈ 0.682
      ├── Some((7, 3)): 4/11 ≈ 0.364
      ├── Some((7, 4)): 3/10 ≈ 0.300
      ├── Some((7, 5)): 3/10 ≈ 0.300
      ├── Some((7, 6)): 11/18 ≈ 0.611
      ├── Some((7, 7)): 9/16 ≈ 0.562
      └── Some((7, 8)): 5/12 ≈ 0.417
    └── Some((2, 8)): 54/111 ≈ 0.486
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 6/12 ≈ 0.500
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 10/16 ≈ 0.625
      ├── Some((8, 4)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 3/9 ≈ 0.333
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((3, 3)): 353/726 ≈ 0.486
    ├── Some((3, 0)): 38/82 ≈ 0.463
      ├── Some((0, 0)): 7/11 ≈ 0.636
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 1/6 ≈ 0.167
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 6/11 ≈ 0.545
      ├── Some((0, 5)): 7/12 ≈ 0.583
      ├── Some((0, 6)): 6/11 ≈ 0.545
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 0/4 ≈ 0.000
    ├── Some((3, 1)): 28/67 ≈ 0.418
      ├── Some((1, 0)): 4/9 ≈ 0.444
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 5/9 ≈ 0.556
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 5/9 ≈ 0.556
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((3, 2)): 38/82 ≈ 0.463
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 2/7 ≈ 0.286
      ├── Some((2, 2)): 7/11 ≈ 0.636
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 5/10 ≈ 0.500
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 5/10 ≈ 0.500
    ├── Some((3, 4)): 45/93 ≈ 0.484
      ├── Some((4, 0)): 6/11 ≈ 0.545
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 3/8 ≈ 0.375
      ├── Some((4, 3)): 12/17 ≈ 0.706
      ├── Some((4, 4)): 1/6 ≈ 0.167
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 7/12 ≈ 0.583
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((3, 5)): 74/133 ≈ 0.556
      ├── Some((5, 0)): 10/16 ≈ 0.625
      ├── Some((5, 1)): 8/15 ≈ 0.533
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 7/14 ≈ 0.500
      ├── Some((5, 4)): 12/18 ≈ 0.667
      ├── Some((5, 5)): 10/17 ≈ 0.588
      ├── Some((5, 6)): 9/16 ≈ 0.562
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 11/17 ≈ 0.647
    ├── Some((3, 6)): 32/73 ≈ 0.438
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 5/9 ≈ 0.556
      ├── Some((6, 3)): 5/9 ≈ 0.556
      ├── Some((6, 4)): 5/9 ≈ 0.556
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 5/10 ≈ 0.500
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 1/5 ≈ 0.200
    ├── Some((3, 7)): 62/117 ≈ 0.530
      ├── Some((7, 0)): 14/20 ≈ 0.700
      ├── Some((7, 1)): 3/9 ≈ 0.333
      ├── Some((7, 2)): 12/18 ≈ 0.667
      ├── Some((7, 3)): 8/14 ≈ 0.571
      ├── Some((7, 4)): 6/12 ≈ 0.500
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 9/15 ≈ 0.600
    └── Some((3, 8)): 35/78 ≈ 0.449
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 5/10 ≈ 0.500
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 5/10 ≈ 0.500
      ├── Some((8, 7)): 6/11 ≈ 0.545
      └── Some((8, 8)): 4/9 ≈ 0.444
  ├── Some((3, 4)): 560/1084 ≈ 0.517
    ├── Some((4, 0)): 107/184 ≈ 0.582
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 8/16 ≈ 0.500
      ├── Some((0, 2)): 18/27 ≈ 0.667
      ├── Some((0, 3)): 8/16 ≈ 0.500
      ├── Some((0, 4)): 19/27 ≈ 0.704
      ├── Some((0, 5)): 12/21 ≈ 0.571
      ├── Some((0, 6)): 13/22 ≈ 0.591
      ├── Some((0, 7)): 12/21 ≈ 0.571
      └── Some((0, 8)): 10/18 ≈ 0.556
    ├── Some((4, 1)): 44/94 ≈ 0.468
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 2/8 ≈ 0.250
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 10/16 ≈ 0.625
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 9/16 ≈ 0.562
    ├── Some((4, 2)): 85/153 ≈ 0.556
      ├── Some((2, 0)): 12/20 ≈ 0.600
      ├── Some((2, 1)): 8/16 ≈ 0.500
      ├── Some((2, 2)): 11/19 ≈ 0.579
      ├── Some((2, 3)): 5/12 ≈ 0.417
      ├── Some((2, 4)): 11/19 ≈ 0.579
      ├── Some((2, 5)): 16/23 ≈ 0.696
      ├── Some((2, 6)): 7/14 ≈ 0.500
      ├── Some((2, 7)): 4/11 ≈ 0.364
      └── Some((2, 8)): 10/18 ≈ 0.556
    ├── Some((4, 3)): 63/122 ≈ 0.516
      ├── Some((3, 0)): 3/10 ≈ 0.300
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 9/17 ≈ 0.529
      ├── Some((3, 3)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 11/19 ≈ 0.579
      ├── Some((3, 6)): 1/8 ≈ 0.125
      ├── Some((3, 7)): 19/26 ≈ 0.731
      └── Some((3, 8)): 9/17 ≈ 0.529
    ├── Some((4, 4)): 38/85 ≈ 0.447
      ├── Some((4, 0)): 9/15 ≈ 0.600
      ├── Some((4, 1)): 1/6 ≈ 0.167
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 4/10 ≈ 0.400
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 8/14 ≈ 0.571
    ├── Some((4, 5)): 67/128 ≈ 0.523
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 3/9 ≈ 0.333
      ├── Some((5, 2)): 5/12 ≈ 0.417
      ├── Some((5, 3)): 9/16 ≈ 0.562
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 13/20 ≈ 0.650
      ├── Some((5, 6)): 9/16 ≈ 0.562
      ├── Some((5, 7)): 11/18 ≈ 0.611
      └── Some((5, 8)): 2/8 ≈ 0.250
    ├── Some((4, 6)): 44/94 ≈ 0.468
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 9/14 ≈ 0.643
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 5)): 9/15 ≈ 0.600
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 3/9 ≈ 0.333
    ├── Some((4, 7)): 47/99 ≈ 0.475
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 3/9 ≈ 0.333
      ├── Some((7, 2)): 6/12 ≈ 0.500
      ├── Some((7, 3)): 6/12 ≈ 0.500
      ├── Some((7, 4)): 8/13 ≈ 0.615
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 8/14 ≈ 0.571
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 7/13 ≈ 0.538
    └── Some((4, 8)): 64/124 ≈ 0.516
      ├── Some((8, 0)): 6/13 ≈ 0.462
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 11/18 ≈ 0.611
      ├── Some((8, 3)): 7/14 ≈ 0.500
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 6/13 ≈ 0.462
      ├── Some((8, 6)): 4/10 ≈ 0.400
      ├── Some((8, 7)): 13/19 ≈ 0.684
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((3, 5)): 541/1052 ≈ 0.514
    ├── Some((5, 0)): 51/104 ≈ 0.490
      ├── Some((0, 0)): 8/14 ≈ 0.571
      ├── Some((0, 1)): 3/9 ≈ 0.333
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 6/12 ≈ 0.500
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 10/16 ≈ 0.625
      ├── Some((0, 6)): 7/13 ≈ 0.538
      ├── Some((0, 7)): 7/13 ≈ 0.538
      └── Some((0, 8)): 1/6 ≈ 0.167
    ├── Some((5, 1)): 54/108 ≈ 0.500
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 9/16 ≈ 0.562
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 9/16 ≈ 0.562
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 9/16 ≈ 0.562
    ├── Some((5, 2)): 64/123 ≈ 0.520
      ├── Some((2, 0)): 4/10 ≈ 0.400
      ├── Some((2, 1)): 20/26 ≈ 0.769
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((5, 3)): 57/112 ≈ 0.509
      ├── Some((3, 0)): 0/6 ≈ 0.000
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 6/13 ≈ 0.462
      ├── Some((3, 3)): 4/11 ≈ 0.364
      ├── Some((3, 4)): 11/18 ≈ 0.611
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 14/21 ≈ 0.667
    ├── Some((5, 4)): 85/152 ≈ 0.559
      ├── Some((4, 0)): 6/13 ≈ 0.462
      ├── Some((4, 1)): 18/25 ≈ 0.720
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 11/19 ≈ 0.579
      ├── Some((4, 4)): 17/25 ≈ 0.680
      ├── Some((4, 5)): 5/12 ≈ 0.417
      ├── Some((4, 6)): 2/9 ≈ 0.222
      ├── Some((4, 7)): 10/18 ≈ 0.556
      └── Some((4, 8)): 11/19 ≈ 0.579
    ├── Some((5, 5)): 75/138 ≈ 0.543
      ├── Some((5, 0)): 16/24 ≈ 0.667
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 6/14 ≈ 0.429
      ├── Some((5, 3)): 11/19 ≈ 0.579
      ├── Some((5, 4)): 13/21 ≈ 0.619
      ├── Some((5, 6)): 2/9 ≈ 0.222
      ├── Some((5, 7)): 10/18 ≈ 0.556
      └── Some((5, 8)): 12/20 ≈ 0.600
    ├── Some((5, 6)): 43/92 ≈ 0.467
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 10/15 ≈ 0.667
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 7/13 ≈ 0.538
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 5/11 ≈ 0.455
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((5, 7)): 68/128 ≈ 0.531
      ├── Some((7, 0)): 7/14 ≈ 0.500
      ├── Some((7, 1)): 13/19 ≈ 0.684
      ├── Some((7, 2)): 9/16 ≈ 0.562
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 4)): 2/8 ≈ 0.250
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 7/14 ≈ 0.500
      ├── Some((7, 7)): 10/17 ≈ 0.588
      └── Some((7, 8)): 9/16 ≈ 0.562
    └── Some((5, 8)): 44/94 ≈ 0.468
      ├── Some((8, 0)): 2/7 ≈ 0.286
      ├── Some((8, 1)): 2/7 ≈ 0.286
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 8/13 ≈ 0.615
      ├── Some((8, 4)): 11/16 ≈ 0.688
      ├── Some((8, 5)): 3/9 ≈ 0.333
      ├── Some((8, 6)): 3/9 ≈ 0.333
      ├── Some((8, 7)): 8/14 ≈ 0.571
      └── Some((8, 8)): 3/9 ≈ 0.333
  ├── Some((3, 6)): 350/721 ≈ 0.485
    ├── Some((6, 0)): 30/68 ≈ 0.441
      ├── Some((0, 0)): 4/8 ≈ 0.500
      ├── Some((0, 1)): 2/6 ≈ 0.333
      ├── Some((0, 2)): 6/10 ≈ 0.600
      ├── Some((0, 3)): 5/9 ≈ 0.556
      ├── Some((0, 4)): 0/4 ≈ 0.000
      ├── Some((0, 5)): 9/13 ≈ 0.692
      ├── Some((0, 6)): 0/4 ≈ 0.000
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((6, 1)): 41/84 ≈ 0.488
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 7/12 ≈ 0.583
      ├── Some((1, 2)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 10/15 ≈ 0.667
      ├── Some((1, 5)): 7/12 ≈ 0.583
      ├── Some((1, 6)): 2/7 ≈ 0.286
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((6, 2)): 19/51 ≈ 0.373
      ├── Some((2, 0)): 3/6 ≈ 0.500
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 0/4 ≈ 0.000
      ├── Some((2, 3)): 2/6 ≈ 0.333
      ├── Some((2, 4)): 3/6 ≈ 0.500
      ├── Some((2, 5)): 3/6 ≈ 0.500
      ├── Some((2, 6)): 4/7 ≈ 0.571
      ├── Some((2, 7)): 0/4 ≈ 0.000
      └── Some((2, 8)): 3/6 ≈ 0.500
    ├── Some((6, 3)): 19/51 ≈ 0.373
      ├── Some((3, 0)): 3/7 ≈ 0.429
      ├── Some((3, 1)): 5/9 ≈ 0.556
      ├── Some((3, 2)): 1/5 ≈ 0.200
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 4)): 7/10 ≈ 0.700
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 7)): 2/6 ≈ 0.333
      └── Some((3, 8)): 1/5 ≈ 0.200
    ├── Some((6, 4)): 55/103 ≈ 0.534
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 12/17 ≈ 0.706
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 8/13 ≈ 0.615
      ├── Some((4, 4)): 7/12 ≈ 0.583
      ├── Some((4, 5)): 7/13 ≈ 0.538
      ├── Some((4, 6)): 8/13 ≈ 0.615
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((6, 5)): 50/97 ≈ 0.515
      ├── Some((5, 0)): 4/9 ≈ 0.444
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 11/16 ≈ 0.688
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 0/5 ≈ 0.000
      ├── Some((5, 5)): 9/14 ≈ 0.643
      ├── Some((5, 6)): 3/8 ≈ 0.375
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 7/12 ≈ 0.583
    ├── Some((6, 6)): 77/133 ≈ 0.579
      ├── Some((6, 0)): 10/17 ≈ 0.588
      ├── Some((6, 1)): 9/16 ≈ 0.562
      ├── Some((6, 2)): 6/13 ≈ 0.462
      ├── Some((6, 3)): 10/17 ≈ 0.588
      ├── Some((6, 4)): 14/21 ≈ 0.667
      ├── Some((6, 5)): 8/15 ≈ 0.533
      ├── Some((6, 7)): 11/18 ≈ 0.611
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((6, 7)): 25/61 ≈ 0.410
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 5/9 ≈ 0.556
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 2/6 ≈ 0.333
      ├── Some((7, 5)): 2/6 ≈ 0.333
      ├── Some((7, 6)): 5/9 ≈ 0.556
      ├── Some((7, 7)): 0/4 ≈ 0.000
      └── Some((7, 8)): 8/11 ≈ 0.727
    └── Some((6, 8)): 33/72 ≈ 0.458
      ├── Some((8, 0)): 8/12 ≈ 0.667
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 6/10 ≈ 0.600
      ├── Some((8, 4)): 7/11 ≈ 0.636
      ├── Some((8, 5)): 4/8 ≈ 0.500
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 2/6 ≈ 0.333
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((3, 7)): 623/1191 ≈ 0.523
    ├── Some((7, 0)): 73/138 ≈ 0.529
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 3/10 ≈ 0.300
      ├── Some((0, 2)): 12/19 ≈ 0.632
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 11/19 ≈ 0.579
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 3/10 ≈ 0.300
      ├── Some((0, 7)): 12/19 ≈ 0.632
      └── Some((0, 8)): 12/20 ≈ 0.600
    ├── Some((7, 1)): 77/144 ≈ 0.535
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 1)): 8/16 ≈ 0.500
      ├── Some((1, 2)): 8/16 ≈ 0.500
      ├── Some((1, 4)): 8/16 ≈ 0.500
      ├── Some((1, 5)): 11/20 ≈ 0.550
      ├── Some((1, 6)): 7/15 ≈ 0.467
      ├── Some((1, 7)): 8/16 ≈ 0.500
      └── Some((1, 8)): 16/25 ≈ 0.640
    ├── Some((7, 2)): 60/120 ≈ 0.500
      ├── Some((2, 0)): 9/16 ≈ 0.562
      ├── Some((2, 1)): 11/18 ≈ 0.611
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 3/9 ≈ 0.333
      ├── Some((2, 4)): 2/8 ≈ 0.250
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 12/19 ≈ 0.632
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 9/16 ≈ 0.562
    ├── Some((7, 3)): 85/155 ≈ 0.548
      ├── Some((3, 0)): 10/19 ≈ 0.526
      ├── Some((3, 1)): 2/10 ≈ 0.200
      ├── Some((3, 2)): 4/12 ≈ 0.333
      ├── Some((3, 3)): 11/20 ≈ 0.550
      ├── Some((3, 4)): 23/32 ≈ 0.719
      ├── Some((3, 5)): 16/25 ≈ 0.640
      ├── Some((3, 6)): 14/23 ≈ 0.609
      └── Some((3, 8)): 5/13 ≈ 0.385
    ├── Some((7, 4)): 48/102 ≈ 0.471
      ├── Some((4, 0)): 6/12 ≈ 0.500
      ├── Some((4, 1)): 2/8 ≈ 0.250
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 0/5 ≈ 0.000
      ├── Some((4, 5)): 9/15 ≈ 0.600
      ├── Some((4, 6)): 11/17 ≈ 0.647
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 2/8 ≈ 0.250
    ├── Some((7, 5)): 85/155 ≈ 0.548
      ├── Some((5, 0)): 10/18 ≈ 0.556
      ├── Some((5, 1)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 16/24 ≈ 0.667
      ├── Some((5, 3)): 9/17 ≈ 0.529
      ├── Some((5, 4)): 11/19 ≈ 0.579
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 9/17 ≈ 0.529
      ├── Some((5, 7)): 5/12 ≈ 0.417
      └── Some((5, 8)): 13/21 ≈ 0.619
    ├── Some((7, 6)): 49/103 ≈ 0.476
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 1/7 ≈ 0.143
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 8/14 ≈ 0.571
      ├── Some((6, 6)): 4/10 ≈ 0.400
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 12/18 ≈ 0.667
    ├── Some((7, 7)): 41/91 ≈ 0.451
      ├── Some((7, 0)): 9/16 ≈ 0.562
      ├── Some((7, 1)): 0/6 ≈ 0.000
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 6/12 ≈ 0.500
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 11/18 ≈ 0.611
      ├── Some((7, 6)): 4/10 ≈ 0.400
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((7, 8)): 104/182 ≈ 0.571
      ├── Some((8, 0)): 19/28 ≈ 0.679
      ├── Some((8, 1)): 13/22 ≈ 0.591
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 14/23 ≈ 0.609
      ├── Some((8, 4)): 7/15 ≈ 0.467
      ├── Some((8, 5)): 1/8 ≈ 0.125
      ├── Some((8, 6)): 7/16 ≈ 0.438
      ├── Some((8, 7)): 19/28 ≈ 0.679
      └── Some((8, 8)): 14/23 ≈ 0.609
  └── Some((3, 8)): 509/997 ≈ 0.511
    ├── Some((8, 0)): 51/103 ≈ 0.495
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 9/14 ≈ 0.643
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 8/14 ≈ 0.571
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 9/15 ≈ 0.600
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((8, 1)): 43/92 ≈ 0.467
      ├── Some((1, 0)): 1/7 ≈ 0.143
      ├── Some((1, 1)): 11/17 ≈ 0.647
      ├── Some((1, 2)): 2/8 ≈ 0.250
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 7/13 ≈ 0.538
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((8, 2)): 51/103 ≈ 0.495
      ├── Some((2, 0)): 8/14 ≈ 0.571
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 10/15 ≈ 0.667
      ├── Some((2, 4)): 2/7 ≈ 0.286
      ├── Some((2, 5)): 7/13 ≈ 0.538
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 8/14 ≈ 0.571
      └── Some((2, 8)): 2/8 ≈ 0.250
    ├── Some((8, 3)): 48/99 ≈ 0.485
      ├── Some((3, 0)): 7/13 ≈ 0.538
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 7/14 ≈ 0.500
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 9/16 ≈ 0.562
      ├── Some((3, 6)): 3/9 ≈ 0.333
      └── Some((3, 7)): 4/10 ≈ 0.400
    ├── Some((8, 4)): 67/126 ≈ 0.532
      ├── Some((4, 0)): 12/18 ≈ 0.667
      ├── Some((4, 1)): 9/16 ≈ 0.562
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 12/18 ≈ 0.667
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 0/6 ≈ 0.000
      ├── Some((4, 7)): 12/19 ≈ 0.632
      └── Some((4, 8)): 10/17 ≈ 0.588
    ├── Some((8, 5)): 64/122 ≈ 0.525
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 3/9 ≈ 0.333
      ├── Some((5, 2)): 7/14 ≈ 0.500
      ├── Some((5, 3)): 2/8 ≈ 0.250
      ├── Some((5, 4)): 8/14 ≈ 0.571
      ├── Some((5, 5)): 9/15 ≈ 0.600
      ├── Some((5, 6)): 15/21 ≈ 0.714
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 8/15 ≈ 0.533
    ├── Some((8, 6)): 78/141 ≈ 0.553
      ├── Some((6, 0)): 11/18 ≈ 0.611
      ├── Some((6, 1)): 2/8 ≈ 0.250
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 11/18 ≈ 0.611
      ├── Some((6, 4)): 12/19 ≈ 0.632
      ├── Some((6, 5)): 9/16 ≈ 0.562
      ├── Some((6, 6)): 11/18 ≈ 0.611
      ├── Some((6, 7)): 9/16 ≈ 0.562
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((8, 7)): 29/70 ≈ 0.414
      ├── Some((7, 0)): 8/12 ≈ 0.667
      ├── Some((7, 1)): 0/4 ≈ 0.000
      ├── Some((7, 2)): 7/11 ≈ 0.636
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 1/6 ≈ 0.167
      ├── Some((7, 6)): 2/7 ≈ 0.286
      ├── Some((7, 7)): 0/4 ≈ 0.000
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((8, 8)): 77/140 ≈ 0.550
      ├── Some((8, 0)): 13/21 ≈ 0.619
      ├── Some((8, 1)): 6/14 ≈ 0.429
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 4/11 ≈ 0.364
      ├── Some((8, 4)): 11/19 ≈ 0.579
      ├── Some((8, 5)): 15/23 ≈ 0.652
      ├── Some((8, 6)): 11/19 ≈ 0.579
      └── Some((8, 7)): 14/22 ≈ 0.636
├── Some((1, 4)): 2705/5478 ≈ 0.494
  ├── Some((4, 0)): 299/607 ≈ 0.493
    ├── Some((0, 0)): 42/79 ≈ 0.532
      ├── Some((0, 1)): 5/10 ≈ 0.500
      ├── Some((0, 2)): 2/7 ≈ 0.286
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 6/10 ≈ 0.600
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 9/13 ≈ 0.692
      ├── Some((0, 7)): 6/10 ≈ 0.600
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((0, 1)): 45/84 ≈ 0.536
      ├── Some((1, 0)): 5/10 ≈ 0.500
      ├── Some((1, 1)): 9/14 ≈ 0.643
      ├── Some((1, 2)): 0/5 ≈ 0.000
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 10/14 ≈ 0.714
      ├── Some((1, 7)): 6/11 ≈ 0.545
      └── Some((1, 8)): 6/11 ≈ 0.545
    ├── Some((0, 2)): 43/81 ≈ 0.531
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 5/9 ≈ 0.556
      ├── Some((2, 2)): 1/5 ≈ 0.200
      ├── Some((2, 3)): 12/16 ≈ 0.750
      ├── Some((2, 4)): 13/16 ≈ 0.812
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 5/9 ≈ 0.556
      ├── Some((2, 7)): 1/6 ≈ 0.167
      └── Some((2, 8)): 1/6 ≈ 0.167
    ├── Some((0, 3)): 22/52 ≈ 0.423
      ├── Some((3, 0)): 3/6 ≈ 0.500
      ├── Some((3, 1)): 8/11 ≈ 0.727
      ├── Some((3, 2)): 2/5 ≈ 0.400
      ├── Some((3, 3)): 3/6 ≈ 0.500
      ├── Some((3, 4)): 0/3 ≈ 0.000
      ├── Some((3, 5)): 3/6 ≈ 0.500
      ├── Some((3, 6)): 0/3 ≈ 0.000
      ├── Some((3, 7)): 2/6 ≈ 0.333
      └── Some((3, 8)): 1/5 ≈ 0.200
    ├── Some((0, 4)): 26/58 ≈ 0.448
      ├── Some((4, 1)): 5/9 ≈ 0.556
      ├── Some((4, 2)): 1/5 ≈ 0.200
      ├── Some((4, 3)): 3/7 ≈ 0.429
      ├── Some((4, 4)): 3/7 ≈ 0.429
      ├── Some((4, 5)): 2/6 ≈ 0.333
      ├── Some((4, 6)): 4/8 ≈ 0.500
      ├── Some((4, 7)): 1/5 ≈ 0.200
      └── Some((4, 8)): 6/10 ≈ 0.600
    ├── Some((0, 5)): 38/74 ≈ 0.514
      ├── Some((5, 0)): 4/8 ≈ 0.500
      ├── Some((5, 1)): 2/6 ≈ 0.333
      ├── Some((5, 2)): 7/11 ≈ 0.636
      ├── Some((5, 3)): 3/7 ≈ 0.429
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 5/9 ≈ 0.556
      ├── Some((5, 6)): 7/11 ≈ 0.636
      ├── Some((5, 7)): 3/7 ≈ 0.429
      └── Some((5, 8)): 5/9 ≈ 0.556
    ├── Some((0, 6)): 33/67 ≈ 0.493
      ├── Some((6, 0)): 4/7 ≈ 0.571
      ├── Some((6, 1)): 4/8 ≈ 0.500
      ├── Some((6, 2)): 5/8 ≈ 0.625
      ├── Some((6, 3)): 3/7 ≈ 0.429
      ├── Some((6, 4)): 4/8 ≈ 0.500
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 4/8 ≈ 0.500
      ├── Some((6, 7)): 3/7 ≈ 0.429
      └── Some((6, 8)): 4/8 ≈ 0.500
    ├── Some((0, 7)): 26/58 ≈ 0.448
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 3/6 ≈ 0.500
      ├── Some((7, 2)): 2/6 ≈ 0.333
      ├── Some((7, 3)): 3/7 ≈ 0.429
      ├── Some((7, 4)): 5/8 ≈ 0.625
      ├── Some((7, 5)): 3/7 ≈ 0.429
      ├── Some((7, 6)): 4/7 ≈ 0.571
      ├── Some((7, 7)): 4/7 ≈ 0.571
      └── Some((7, 8)): 1/5 ≈ 0.200
    └── Some((0, 8)): 23/53 ≈ 0.434
      ├── Some((8, 0)): 0/3 ≈ 0.000
      ├── Some((8, 1)): 3/6 ≈ 0.500
      ├── Some((8, 2)): 4/7 ≈ 0.571
      ├── Some((8, 3)): 3/6 ≈ 0.500
      ├── Some((8, 4)): 6/9 ≈ 0.667
      ├── Some((8, 5)): 0/3 ≈ 0.000
      ├── Some((8, 6)): 3/6 ≈ 0.500
      ├── Some((8, 7)): 2/6 ≈ 0.333
      └── Some((8, 8)): 2/6 ≈ 0.333
  ├── Some((4, 1)): 360/712 ≈ 0.506
    ├── Some((1, 0)): 58/108 ≈ 0.537
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 8/13 ≈ 0.615
      ├── Some((0, 4)): 14/19 ≈ 0.737
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 11/16 ≈ 0.688
      ├── Some((0, 7)): 0/5 ≈ 0.000
      └── Some((0, 8)): 8/14 ≈ 0.571
    ├── Some((1, 1)): 46/91 ≈ 0.505
      ├── Some((1, 0)): 11/17 ≈ 0.647
      ├── Some((1, 2)): 8/15 ≈ 0.533
      ├── Some((1, 3)): 10/16 ≈ 0.625
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 7/14 ≈ 0.500
    ├── Some((1, 2)): 34/74 ≈ 0.459
      ├── Some((2, 0)): 7/11 ≈ 0.636
      ├── Some((2, 1)): 7/11 ≈ 0.636
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 6/10 ≈ 0.600
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 0/4 ≈ 0.000
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 0/4 ≈ 0.000
    ├── Some((1, 3)): 43/87 ≈ 0.494
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 6/10 ≈ 0.600
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 9/13 ≈ 0.692
      ├── Some((3, 4)): 6/11 ≈ 0.545
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 6/11 ≈ 0.545
      ├── Some((3, 7)): 5/10 ≈ 0.500
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((1, 5)): 83/141 ≈ 0.589
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 23/28 ≈ 0.821
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 13/19 ≈ 0.684
      ├── Some((5, 5)): 8/15 ≈ 0.533
      ├── Some((5, 6)): 13/19 ≈ 0.684
      ├── Some((5, 7)): 1/7 ≈ 0.143
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((1, 6)): 37/78 ≈ 0.474
      ├── Some((6, 0)): 4/8 ≈ 0.500
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 4/9 ≈ 0.444
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 5/9 ≈ 0.556
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 5/9 ≈ 0.556
      ├── Some((6, 7)): 5/9 ≈ 0.556
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((1, 7)): 18/50 ≈ 0.360
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 5/8 ≈ 0.625
      ├── Some((7, 2)): 3/6 ≈ 0.500
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 0/3 ≈ 0.000
      ├── Some((7, 5)): 0/3 ≈ 0.000
      ├── Some((7, 6)): 2/6 ≈ 0.333
      ├── Some((7, 7)): 1/5 ≈ 0.200
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((1, 8)): 40/82 ≈ 0.488
      ├── Some((8, 0)): 0/4 ≈ 0.000
      ├── Some((8, 1)): 4/8 ≈ 0.500
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 12/16 ≈ 0.750
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 4/9 ≈ 0.444
      └── Some((8, 8)): 8/12 ≈ 0.667
  ├── Some((4, 2)): 331/662 ≈ 0.500
    ├── Some((2, 0)): 30/64 ≈ 0.469
      ├── Some((0, 0)): 3/7 ≈ 0.429
      ├── Some((0, 1)): 5/8 ≈ 0.625
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 3/7 ≈ 0.429
      ├── Some((0, 4)): 4/8 ≈ 0.500
      ├── Some((0, 5)): 5/8 ≈ 0.625
      ├── Some((0, 6)): 3/7 ≈ 0.429
      ├── Some((0, 7)): 1/5 ≈ 0.200
      └── Some((0, 8)): 5/8 ≈ 0.625
    ├── Some((2, 1)): 38/75 ≈ 0.507
      ├── Some((1, 0)): 7/11 ≈ 0.636
      ├── Some((1, 1)): 7/11 ≈ 0.636
      ├── Some((1, 2)): 5/10 ≈ 0.500
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 7/11 ≈ 0.636
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 7/12 ≈ 0.583
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((2, 2)): 22/53 ≈ 0.415
      ├── Some((2, 0)): 4/7 ≈ 0.571
      ├── Some((2, 1)): 2/6 ≈ 0.333
      ├── Some((2, 3)): 4/7 ≈ 0.571
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 2/6 ≈ 0.333
      ├── Some((2, 7)): 4/8 ≈ 0.500
      └── Some((2, 8)): 4/8 ≈ 0.500
    ├── Some((2, 3)): 44/84 ≈ 0.524
      ├── Some((3, 0)): 9/13 ≈ 0.692
      ├── Some((3, 1)): 5/9 ≈ 0.556
      ├── Some((3, 2)): 7/11 ≈ 0.636
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 5/9 ≈ 0.556
      ├── Some((3, 6)): 4/9 ≈ 0.444
      ├── Some((3, 7)): 5/9 ≈ 0.556
      └── Some((3, 8)): 5/10 ≈ 0.500
    ├── Some((2, 4)): 44/84 ≈ 0.524
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 5/10 ≈ 0.500
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 4)): 6/11 ≈ 0.545
      ├── Some((4, 5)): 6/11 ≈ 0.545
      ├── Some((4, 6)): 6/11 ≈ 0.545
      ├── Some((4, 7)): 7/12 ≈ 0.583
      └── Some((4, 8)): 7/12 ≈ 0.583
    ├── Some((2, 5)): 19/48 ≈ 0.396
      ├── Some((5, 0)): 0/3 ≈ 0.000
      ├── Some((5, 1)): 3/6 ≈ 0.500
      ├── Some((5, 2)): 1/4 ≈ 0.250
      ├── Some((5, 3)): 1/4 ≈ 0.250
      ├── Some((5, 4)): 6/9 ≈ 0.667
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 0/3 ≈ 0.000
      ├── Some((5, 7)): 5/8 ≈ 0.625
      └── Some((5, 8)): 1/5 ≈ 0.200
    ├── Some((2, 6)): 43/82 ≈ 0.524
      ├── Some((6, 0)): 4/8 ≈ 0.500
      ├── Some((6, 1)): 7/11 ≈ 0.636
      ├── Some((6, 2)): 4/8 ≈ 0.500
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 6/10 ≈ 0.600
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 6/10 ≈ 0.600
      └── Some((6, 8)): 5/9 ≈ 0.556
    ├── Some((2, 7)): 40/78 ≈ 0.513
      ├── Some((7, 0)): 2/7 ≈ 0.286
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 12/15 ≈ 0.800
      ├── Some((7, 5)): 6/10 ≈ 0.600
      ├── Some((7, 6)): 4/8 ≈ 0.500
      ├── Some((7, 7)): 9/13 ≈ 0.692
      └── Some((7, 8)): 0/4 ≈ 0.000
    └── Some((2, 8)): 51/93 ≈ 0.548
      ├── Some((8, 0)): 6/11 ≈ 0.545
      ├── Some((8, 1)): 4/9 ≈ 0.444
      ├── Some((8, 2)): 8/12 ≈ 0.667
      ├── Some((8, 3)): 5/10 ≈ 0.500
      ├── Some((8, 4)): 9/13 ≈ 0.692
      ├── Some((8, 5)): 8/12 ≈ 0.667
      ├── Some((8, 6)): 5/10 ≈ 0.500
      ├── Some((8, 7)): 6/11 ≈ 0.545
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((4, 3)): 370/729 ≈ 0.508
    ├── Some((3, 0)): 19/50 ≈ 0.380
      ├── Some((0, 0)): 0/3 ≈ 0.000
      ├── Some((0, 1)): 1/5 ≈ 0.200
      ├── Some((0, 2)): 2/5 ≈ 0.400
      ├── Some((0, 3)): 1/5 ≈ 0.200
      ├── Some((0, 4)): 2/6 ≈ 0.333
      ├── Some((0, 5)): 4/7 ≈ 0.571
      ├── Some((0, 6)): 4/7 ≈ 0.571
      ├── Some((0, 7)): 3/6 ≈ 0.500
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((3, 1)): 33/70 ≈ 0.471
      ├── Some((1, 0)): 4/9 ≈ 0.444
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 5/9 ≈ 0.556
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 6/10 ≈ 0.600
      ├── Some((1, 7)): 5/9 ≈ 0.556
      └── Some((1, 8)): 6/10 ≈ 0.600
    ├── Some((3, 2)): 50/94 ≈ 0.532
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 7/12 ≈ 0.583
      ├── Some((2, 2)): 8/12 ≈ 0.667
      ├── Some((2, 3)): 5/10 ≈ 0.500
      ├── Some((2, 4)): 5/10 ≈ 0.500
      ├── Some((2, 5)): 0/5 ≈ 0.000
      ├── Some((2, 6)): 8/13 ≈ 0.615
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 7/12 ≈ 0.583
    ├── Some((3, 3)): 45/87 ≈ 0.517
      ├── Some((3, 0)): 5/10 ≈ 0.500
      ├── Some((3, 1)): 8/13 ≈ 0.615
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 5/10 ≈ 0.500
      ├── Some((3, 6)): 13/18 ≈ 0.722
      ├── Some((3, 7)): 5/11 ≈ 0.455
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((3, 4)): 71/122 ≈ 0.582
      ├── Some((4, 0)): 11/17 ≈ 0.647
      ├── Some((4, 1)): 9/16 ≈ 0.562
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 15/21 ≈ 0.714
      ├── Some((4, 5)): 9/16 ≈ 0.562
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 10/16 ≈ 0.625
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((3, 5)): 33/70 ≈ 0.471
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 2/6 ≈ 0.333
      ├── Some((5, 2)): 4/8 ≈ 0.500
      ├── Some((5, 3)): 2/6 ≈ 0.333
      ├── Some((5, 4)): 2/7 ≈ 0.286
      ├── Some((5, 5)): 4/8 ≈ 0.500
      ├── Some((5, 6)): 4/8 ≈ 0.500
      ├── Some((5, 7)): 4/8 ≈ 0.500
      └── Some((5, 8)): 9/13 ≈ 0.692
    ├── Some((3, 6)): 54/99 ≈ 0.545
      ├── Some((6, 0)): 8/13 ≈ 0.615
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 5/10 ≈ 0.500
      ├── Some((6, 3)): 6/11 ≈ 0.545
      ├── Some((6, 4)): 8/13 ≈ 0.615
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 10/14 ≈ 0.714
      ├── Some((6, 7)): 2/7 ≈ 0.286
      └── Some((6, 8)): 7/12 ≈ 0.583
    ├── Some((3, 7)): 25/58 ≈ 0.431
      ├── Some((7, 0)): 4/7 ≈ 0.571
      ├── Some((7, 1)): 0/4 ≈ 0.000
      ├── Some((7, 2)): 3/6 ≈ 0.500
      ├── Some((7, 3)): 1/5 ≈ 0.200
      ├── Some((7, 4)): 2/6 ≈ 0.333
      ├── Some((7, 5)): 3/7 ≈ 0.429
      ├── Some((7, 6)): 2/6 ≈ 0.333
      ├── Some((7, 7)): 6/9 ≈ 0.667
      └── Some((7, 8)): 4/7 ≈ 0.571
    └── Some((3, 8)): 39/78 ≈ 0.500
      ├── Some((8, 0)): 5/9 ≈ 0.556
      ├── Some((8, 1)): 4/8 ≈ 0.500
      ├── Some((8, 2)): 4/9 ≈ 0.444
      ├── Some((8, 3)): 0/4 ≈ 0.000
      ├── Some((8, 4)): 5/9 ≈ 0.556
      ├── Some((8, 5)): 7/11 ≈ 0.636
      ├── Some((8, 6)): 12/16 ≈ 0.750
      ├── Some((8, 7)): 2/7 ≈ 0.286
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((4, 4)): 267/552 ≈ 0.484
    ├── Some((4, 0)): 39/77 ≈ 0.506
      ├── Some((0, 0)): 7/11 ≈ 0.636
      ├── Some((0, 1)): 2/6 ≈ 0.333
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 4/8 ≈ 0.500
      ├── Some((0, 4)): 1/5 ≈ 0.200
      ├── Some((0, 5)): 9/13 ≈ 0.692
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 5/9 ≈ 0.556
    ├── Some((4, 1)): 29/63 ≈ 0.460
      ├── Some((1, 0)): 6/10 ≈ 0.600
      ├── Some((1, 1)): 1/5 ≈ 0.200
      ├── Some((1, 2)): 6/10 ≈ 0.600
      ├── Some((1, 3)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 2/6 ≈ 0.333
      ├── Some((1, 6)): 7/11 ≈ 0.636
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((4, 2)): 33/68 ≈ 0.485
      ├── Some((2, 0)): 1/5 ≈ 0.200
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 3/7 ≈ 0.429
      ├── Some((2, 3)): 1/5 ≈ 0.200
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 7/11 ≈ 0.636
      ├── Some((2, 6)): 6/10 ≈ 0.600
      ├── Some((2, 7)): 4/8 ≈ 0.500
      └── Some((2, 8)): 8/11 ≈ 0.727
    ├── Some((4, 3)): 22/53 ≈ 0.415
      ├── Some((3, 0)): 3/6 ≈ 0.500
      ├── Some((3, 1)): 2/6 ≈ 0.333
      ├── Some((3, 2)): 3/6 ≈ 0.500
      ├── Some((3, 3)): 2/6 ≈ 0.333
      ├── Some((3, 4)): 4/7 ≈ 0.571
      ├── Some((3, 5)): 1/5 ≈ 0.200
      ├── Some((3, 6)): 3/6 ≈ 0.500
      ├── Some((3, 7)): 4/7 ≈ 0.571
      └── Some((3, 8)): 0/3 ≈ 0.000
    ├── Some((4, 5)): 33/68 ≈ 0.485
      ├── Some((5, 0)): 7/10 ≈ 0.700
      ├── Some((5, 1)): 5/9 ≈ 0.556
      ├── Some((5, 2)): 4/8 ≈ 0.500
      ├── Some((5, 3)): 5/9 ≈ 0.556
      ├── Some((5, 4)): 2/6 ≈ 0.333
      ├── Some((5, 5)): 3/7 ≈ 0.429
      ├── Some((5, 6)): 2/6 ≈ 0.333
      ├── Some((5, 7)): 1/5 ≈ 0.200
      └── Some((5, 8)): 3/7 ≈ 0.429
    ├── Some((4, 6)): 47/88 ≈ 0.534
      ├── Some((6, 0)): 4/9 ≈ 0.444
      ├── Some((6, 1)): 8/12 ≈ 0.667
      ├── Some((6, 2)): 10/14 ≈ 0.714
      ├── Some((6, 3)): 7/11 ≈ 0.636
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 5/9 ≈ 0.556
      ├── Some((6, 7)): 2/7 ≈ 0.286
      └── Some((6, 8)): 5/10 ≈ 0.500
    ├── Some((4, 7)): 39/77 ≈ 0.506
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 9/13 ≈ 0.692
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 4/8 ≈ 0.500
      ├── Some((7, 5)): 3/8 ≈ 0.375
      ├── Some((7, 6)): 5/9 ≈ 0.556
      ├── Some((7, 7)): 4/8 ≈ 0.500
      └── Some((7, 8)): 8/12 ≈ 0.667
    └── Some((4, 8)): 25/57 ≈ 0.439
      ├── Some((8, 0)): 3/6 ≈ 0.500
      ├── Some((8, 1)): 3/6 ≈ 0.500
      ├── Some((8, 2)): 3/6 ≈ 0.500
      ├── Some((8, 3)): 2/6 ≈ 0.333
      ├── Some((8, 4)): 7/10 ≈ 0.700
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 1/5 ≈ 0.200
      ├── Some((8, 7)): 2/6 ≈ 0.333
      └── Some((8, 8)): 2/6 ≈ 0.333
  ├── Some((4, 5)): 484/920 ≈ 0.526
    ├── Some((5, 0)): 66/120 ≈ 0.550
      ├── Some((0, 0)): 0/5 ≈ 0.000
      ├── Some((0, 1)): 7/13 ≈ 0.538
      ├── Some((0, 2)): 12/18 ≈ 0.667
      ├── Some((0, 3)): 3/9 ≈ 0.333
      ├── Some((0, 4)): 6/12 ≈ 0.500
      ├── Some((0, 5)): 10/16 ≈ 0.625
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 13/19 ≈ 0.684
      └── Some((0, 8)): 13/19 ≈ 0.684
    ├── Some((5, 1)): 98/162 ≈ 0.605
      ├── Some((1, 0)): 16/24 ≈ 0.667
      ├── Some((1, 1)): 4/12 ≈ 0.333
      ├── Some((1, 2)): 11/19 ≈ 0.579
      ├── Some((1, 3)): 8/16 ≈ 0.500
      ├── Some((1, 5)): 7/15 ≈ 0.467
      ├── Some((1, 6)): 13/21 ≈ 0.619
      ├── Some((1, 7)): 23/31 ≈ 0.742
      └── Some((1, 8)): 15/23 ≈ 0.652
    ├── Some((5, 2)): 19/52 ≈ 0.365
      ├── Some((2, 0)): 1/5 ≈ 0.200
      ├── Some((2, 1)): 3/6 ≈ 0.500
      ├── Some((2, 2)): 1/5 ≈ 0.200
      ├── Some((2, 3)): 4/7 ≈ 0.571
      ├── Some((2, 4)): 2/6 ≈ 0.333
      ├── Some((2, 5)): 4/7 ≈ 0.571
      ├── Some((2, 6)): 0/4 ≈ 0.000
      ├── Some((2, 7)): 2/6 ≈ 0.333
      └── Some((2, 8)): 1/5 ≈ 0.200
    ├── Some((5, 3)): 47/93 ≈ 0.505
      ├── Some((3, 0)): 6/11 ≈ 0.545
      ├── Some((3, 1)): 6/11 ≈ 0.545
      ├── Some((3, 2)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 1/6 ≈ 0.167
      ├── Some((3, 6)): 5/11 ≈ 0.455
      ├── Some((3, 7)): 9/14 ≈ 0.643
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((5, 4)): 44/89 ≈ 0.494
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 1)): 8/13 ≈ 0.615
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 8/14 ≈ 0.571
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 9/14 ≈ 0.643
    ├── Some((5, 5)): 40/83 ≈ 0.482
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 7/12 ≈ 0.583
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 6/11 ≈ 0.545
      ├── Some((5, 6)): 4/9 ≈ 0.444
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((5, 6)): 64/117 ≈ 0.547
      ├── Some((6, 0)): 9/15 ≈ 0.600
      ├── Some((6, 1)): 6/12 ≈ 0.500
      ├── Some((6, 2)): 3/9 ≈ 0.333
      ├── Some((6, 3)): 8/14 ≈ 0.571
      ├── Some((6, 4)): 8/14 ≈ 0.571
      ├── Some((6, 5)): 7/13 ≈ 0.538
      ├── Some((6, 6)): 10/16 ≈ 0.625
      ├── Some((6, 7)): 0/5 ≈ 0.000
      └── Some((6, 8)): 13/18 ≈ 0.722
    ├── Some((5, 7)): 69/124 ≈ 0.556
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 10/16 ≈ 0.625
      ├── Some((7, 2)): 13/19 ≈ 0.684
      ├── Some((7, 3)): 3/9 ≈ 0.333
      ├── Some((7, 4)): 5/11 ≈ 0.455
      ├── Some((7, 5)): 6/12 ≈ 0.500
      ├── Some((7, 6)): 12/18 ≈ 0.667
      ├── Some((7, 7)): 9/15 ≈ 0.600
      └── Some((7, 8)): 7/14 ≈ 0.500
    └── Some((5, 8)): 37/79 ≈ 0.468
      ├── Some((8, 0)): 6/11 ≈ 0.545
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 4/9 ≈ 0.444
      ├── Some((8, 3)): 5/10 ≈ 0.500
      ├── Some((8, 4)): 7/11 ≈ 0.636
      ├── Some((8, 5)): 8/12 ≈ 0.667
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 1/6 ≈ 0.167
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((4, 6)): 185/409 ≈ 0.452
    ├── Some((6, 0)): 19/44 ≈ 0.432
      ├── Some((0, 0)): 0/3 ≈ 0.000
      ├── Some((0, 1)): 1/4 ≈ 0.250
      ├── Some((0, 2)): 3/5 ≈ 0.600
      ├── Some((0, 3)): 2/5 ≈ 0.400
      ├── Some((0, 4)): 0/3 ≈ 0.000
      ├── Some((0, 5)): 5/7 ≈ 0.714
      ├── Some((0, 6)): 4/6 ≈ 0.667
      ├── Some((0, 7)): 2/5 ≈ 0.400
      └── Some((0, 8)): 2/5 ≈ 0.400
    ├── Some((6, 1)): 7/26 ≈ 0.269
      ├── Some((1, 0)): 0/2 ≈ 0.000
      ├── Some((1, 1)): 0/2 ≈ 0.000
      ├── Some((1, 2)): 1/3 ≈ 0.333
      ├── Some((1, 3)): 2/4 ≈ 0.500
      ├── Some((1, 5)): 0/3 ≈ 0.000
      ├── Some((1, 6)): 1/3 ≈ 0.333
      ├── Some((1, 7)): 0/3 ≈ 0.000
      └── Some((1, 8)): 3/5 ≈ 0.600
    ├── Some((6, 2)): 18/42 ≈ 0.429
      ├── Some((2, 0)): 4/6 ≈ 0.667
      ├── Some((2, 1)): 2/4 ≈ 0.500
      ├── Some((2, 2)): 4/6 ≈ 0.667
      ├── Some((2, 3)): 0/3 ≈ 0.000
      ├── Some((2, 4)): 2/5 ≈ 0.400
      ├── Some((2, 5)): 1/4 ≈ 0.250
      ├── Some((2, 6)): 0/3 ≈ 0.000
      ├── Some((2, 7)): 3/5 ≈ 0.600
      └── Some((2, 8)): 2/5 ≈ 0.400
    ├── Some((6, 3)): 17/41 ≈ 0.415
      ├── Some((3, 0)): 2/4 ≈ 0.500
      ├── Some((3, 1)): 3/5 ≈ 0.600
      ├── Some((3, 2)): 2/5 ≈ 0.400
      ├── Some((3, 3)): 1/4 ≈ 0.250
      ├── Some((3, 4)): 2/5 ≈ 0.400
      ├── Some((3, 5)): 3/5 ≈ 0.600
      ├── Some((3, 6)): 1/4 ≈ 0.250
      ├── Some((3, 7)): 0/3 ≈ 0.000
      └── Some((3, 8)): 2/5 ≈ 0.400
    ├── Some((6, 4)): 21/46 ≈ 0.457
      ├── Some((4, 0)): 2/5 ≈ 0.400
      ├── Some((4, 1)): 3/6 ≈ 0.500
      ├── Some((4, 2)): 2/5 ≈ 0.400
      ├── Some((4, 3)): 3/6 ≈ 0.500
      ├── Some((4, 4)): 2/5 ≈ 0.400
      ├── Some((4, 5)): 3/6 ≈ 0.500
      ├── Some((4, 7)): 4/7 ≈ 0.571
      └── Some((4, 8)): 2/5 ≈ 0.400
    ├── Some((6, 5)): 27/55 ≈ 0.491
      ├── Some((5, 0)): 3/6 ≈ 0.500
      ├── Some((5, 1)): 2/5 ≈ 0.400
      ├── Some((5, 2)): 3/6 ≈ 0.500
      ├── Some((5, 3)): 3/6 ≈ 0.500
      ├── Some((5, 4)): 0/3 ≈ 0.000
      ├── Some((5, 5)): 2/5 ≈ 0.400
      ├── Some((5, 6)): 6/9 ≈ 0.667
      ├── Some((5, 7)): 2/6 ≈ 0.333
      └── Some((5, 8)): 5/8 ≈ 0.625
    ├── Some((6, 6)): 24/50 ≈ 0.480
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 6/9 ≈ 0.667
      ├── Some((6, 2)): 4/7 ≈ 0.571
      ├── Some((6, 3)): 2/5 ≈ 0.400
      ├── Some((6, 4)): 5/8 ≈ 0.625
      ├── Some((6, 5)): 2/5 ≈ 0.400
      ├── Some((6, 7)): 4/7 ≈ 0.571
      └── Some((6, 8)): 0/3 ≈ 0.000
    ├── Some((6, 7)): 30/58 ≈ 0.517
      ├── Some((7, 0)): 2/5 ≈ 0.400
      ├── Some((7, 1)): 5/8 ≈ 0.625
      ├── Some((7, 2)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 5/8 ≈ 0.625
      ├── Some((7, 4)): 7/10 ≈ 0.700
      ├── Some((7, 5)): 4/7 ≈ 0.571
      ├── Some((7, 6)): 2/5 ≈ 0.400
      ├── Some((7, 7)): 0/3 ≈ 0.000
      └── Some((7, 8)): 3/6 ≈ 0.500
    └── Some((6, 8)): 21/46 ≈ 0.457
      ├── Some((8, 0)): 0/3 ≈ 0.000
      ├── Some((8, 1)): 1/4 ≈ 0.250
      ├── Some((8, 2)): 3/6 ≈ 0.500
      ├── Some((8, 3)): 2/5 ≈ 0.400
      ├── Some((8, 4)): 1/4 ≈ 0.250
      ├── Some((8, 5)): 4/6 ≈ 0.667
      ├── Some((8, 6)): 0/3 ≈ 0.000
      ├── Some((8, 7)): 5/7 ≈ 0.714
      └── Some((8, 8)): 4/7 ≈ 0.571
  ├── Some((4, 7)): 201/437 ≈ 0.460
    ├── Some((7, 0)): 13/36 ≈ 0.361
      ├── Some((0, 0)): 0/3 ≈ 0.000
      ├── Some((0, 1)): 2/4 ≈ 0.500
      ├── Some((0, 2)): 1/3 ≈ 0.333
      ├── Some((0, 3)): 2/4 ≈ 0.500
      ├── Some((0, 4)): 1/4 ≈ 0.250
      ├── Some((0, 5)): 1/4 ≈ 0.250
      ├── Some((0, 6)): 3/5 ≈ 0.600
      ├── Some((0, 7)): 1/4 ≈ 0.250
      └── Some((0, 8)): 2/4 ≈ 0.500
    ├── Some((7, 1)): 17/41 ≈ 0.415
      ├── Some((1, 0)): 0/3 ≈ 0.000
      ├── Some((1, 1)): 1/4 ≈ 0.250
      ├── Some((1, 2)): 0/3 ≈ 0.000
      ├── Some((1, 3)): 3/6 ≈ 0.500
      ├── Some((1, 5)): 3/6 ≈ 0.500
      ├── Some((1, 6)): 0/3 ≈ 0.000
      ├── Some((1, 7)): 7/10 ≈ 0.700
      └── Some((1, 8)): 2/5 ≈ 0.400
    ├── Some((7, 2)): 38/69 ≈ 0.551
      ├── Some((2, 0)): 6/9 ≈ 0.667
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 2/6 ≈ 0.333
      ├── Some((2, 3)): 7/10 ≈ 0.700
      ├── Some((2, 4)): 7/10 ≈ 0.700
      ├── Some((2, 5)): 7/10 ≈ 0.700
      ├── Some((2, 6)): 3/6 ≈ 0.500
      ├── Some((2, 7)): 2/6 ≈ 0.333
      └── Some((2, 8)): 2/6 ≈ 0.333
    ├── Some((7, 3)): 19/44 ≈ 0.432
      ├── Some((3, 0)): 3/6 ≈ 0.500
      ├── Some((3, 1)): 4/6 ≈ 0.667
      ├── Some((3, 2)): 1/4 ≈ 0.250
      ├── Some((3, 3)): 0/3 ≈ 0.000
      ├── Some((3, 4)): 2/5 ≈ 0.400
      ├── Some((3, 5)): 5/7 ≈ 0.714
      ├── Some((3, 6)): 1/4 ≈ 0.250
      ├── Some((3, 7)): 2/5 ≈ 0.400
      └── Some((3, 8)): 0/3 ≈ 0.000
    ├── Some((7, 4)): 30/59 ≈ 0.508
      ├── Some((4, 0)): 4/8 ≈ 0.500
      ├── Some((4, 1)): 7/10 ≈ 0.700
      ├── Some((4, 2)): 4/8 ≈ 0.500
      ├── Some((4, 3)): 5/8 ≈ 0.625
      ├── Some((4, 4)): 6/9 ≈ 0.667
      ├── Some((4, 5)): 0/4 ≈ 0.000
      ├── Some((4, 6)): 0/4 ≈ 0.000
      └── Some((4, 8)): 3/7 ≈ 0.429
    ├── Some((7, 5)): 14/37 ≈ 0.378
      ├── Some((5, 0)): 1/3 ≈ 0.333
      ├── Some((5, 1)): 1/4 ≈ 0.250
      ├── Some((5, 2)): 1/4 ≈ 0.250
      ├── Some((5, 3)): 2/4 ≈ 0.500
      ├── Some((5, 4)): 2/4 ≈ 0.500
      ├── Some((5, 5)): 0/3 ≈ 0.000
      ├── Some((5, 6)): 5/7 ≈ 0.714
      ├── Some((5, 7)): 2/4 ≈ 0.500
      └── Some((5, 8)): 0/3 ≈ 0.000
    ├── Some((7, 6)): 29/58 ≈ 0.500
      ├── Some((6, 0)): 5/8 ≈ 0.625
      ├── Some((6, 1)): 6/9 ≈ 0.667
      ├── Some((6, 2)): 0/3 ≈ 0.000
      ├── Some((6, 3)): 2/6 ≈ 0.333
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 0/3 ≈ 0.000
      ├── Some((6, 7)): 9/11 ≈ 0.818
      └── Some((6, 8)): 3/6 ≈ 0.500
    ├── Some((7, 7)): 24/51 ≈ 0.471
      ├── Some((7, 0)): 3/6 ≈ 0.500
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 7/10 ≈ 0.700
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 0/3 ≈ 0.000
      ├── Some((7, 5)): 4/7 ≈ 0.571
      ├── Some((7, 6)): 4/7 ≈ 0.571
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((7, 8)): 17/41 ≈ 0.415
      ├── Some((8, 0)): 1/4 ≈ 0.250
      ├── Some((8, 1)): 2/4 ≈ 0.500
      ├── Some((8, 2)): 2/4 ≈ 0.500
      ├── Some((8, 3)): 1/4 ≈ 0.250
      ├── Some((8, 4)): 3/5 ≈ 0.600
      ├── Some((8, 5)): 2/5 ≈ 0.400
      ├── Some((8, 6)): 1/4 ≈ 0.250
      ├── Some((8, 7)): 0/3 ≈ 0.000
      └── Some((8, 8)): 5/7 ≈ 0.714
  └── Some((4, 8)): 208/449 ≈ 0.463
    ├── Some((8, 0)): 35/66 ≈ 0.530
      ├── Some((0, 0)): 3/6 ≈ 0.500
      ├── Some((0, 1)): 3/6 ≈ 0.500
      ├── Some((0, 2)): 8/11 ≈ 0.727
      ├── Some((0, 3)): 2/6 ≈ 0.333
      ├── Some((0, 4)): 3/7 ≈ 0.429
      ├── Some((0, 5)): 5/8 ≈ 0.625
      ├── Some((0, 6)): 0/4 ≈ 0.000
      ├── Some((0, 7)): 2/6 ≈ 0.333
      └── Some((0, 8)): 8/11 ≈ 0.727
    ├── Some((8, 1)): 29/58 ≈ 0.500
      ├── Some((1, 0)): 4/7 ≈ 0.571
      ├── Some((1, 1)): 3/7 ≈ 0.429
      ├── Some((1, 2)): 4/8 ≈ 0.500
      ├── Some((1, 3)): 5/8 ≈ 0.625
      ├── Some((1, 5)): 2/6 ≈ 0.333
      ├── Some((1, 6)): 4/8 ≈ 0.500
      ├── Some((1, 7)): 1/5 ≈ 0.200
      └── Some((1, 8)): 5/8 ≈ 0.625
    ├── Some((8, 2)): 13/36 ≈ 0.361
      ├── Some((2, 0)): 1/4 ≈ 0.250
      ├── Some((2, 1)): 0/3 ≈ 0.000
      ├── Some((2, 2)): 0/3 ≈ 0.000
      ├── Some((2, 3)): 3/5 ≈ 0.600
      ├── Some((2, 4)): 2/4 ≈ 0.500
      ├── Some((2, 5)): 1/4 ≈ 0.250
      ├── Some((2, 6)): 2/4 ≈ 0.500
      ├── Some((2, 7)): 2/4 ≈ 0.500
      └── Some((2, 8)): 1/4 ≈ 0.250
    ├── Some((8, 3)): 33/64 ≈ 0.516
      ├── Some((3, 0)): 0/3 ≈ 0.000
      ├── Some((3, 1)): 6/9 ≈ 0.667
      ├── Some((3, 2)): 5/8 ≈ 0.625
      ├── Some((3, 3)): 2/6 ≈ 0.333
      ├── Some((3, 4)): 1/5 ≈ 0.200
      ├── Some((3, 5)): 6/9 ≈ 0.667
      ├── Some((3, 6)): 2/6 ≈ 0.333
      ├── Some((3, 7)): 4/7 ≈ 0.571
      └── Some((3, 8)): 7/10 ≈ 0.700
    ├── Some((8, 4)): 18/43 ≈ 0.419
      ├── Some((4, 0)): 2/5 ≈ 0.400
      ├── Some((4, 1)): 1/4 ≈ 0.250
      ├── Some((4, 2)): 2/5 ≈ 0.400
      ├── Some((4, 3)): 2/5 ≈ 0.400
      ├── Some((4, 4)): 3/6 ≈ 0.500
      ├── Some((4, 5)): 0/3 ≈ 0.000
      ├── Some((4, 6)): 5/8 ≈ 0.625
      └── Some((4, 7)): 3/6 ≈ 0.500
    ├── Some((8, 5)): 4/22 ≈ 0.182
      ├── Some((5, 0)): 0/2 ≈ 0.000
      ├── Some((5, 1)): 0/2 ≈ 0.000
      ├── Some((5, 2)): 0/2 ≈ 0.000
      ├── Some((5, 3)): 0/2 ≈ 0.000
      ├── Some((5, 4)): 1/2 ≈ 0.500
      ├── Some((5, 5)): 0/2 ≈ 0.000
      ├── Some((5, 6)): 1/3 ≈ 0.333
      ├── Some((5, 7)): 1/3 ≈ 0.333
      └── Some((5, 8)): 1/3 ≈ 0.333
    ├── Some((8, 6)): 28/57 ≈ 0.491
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 1/5 ≈ 0.200
      ├── Some((6, 2)): 2/5 ≈ 0.400
      ├── Some((6, 3)): 5/8 ≈ 0.625
      ├── Some((6, 4)): 3/6 ≈ 0.500
      ├── Some((6, 5)): 6/9 ≈ 0.667
      ├── Some((6, 6)): 5/8 ≈ 0.625
      ├── Some((6, 7)): 2/5 ≈ 0.400
      └── Some((6, 8)): 2/5 ≈ 0.400
    ├── Some((8, 7)): 21/47 ≈ 0.447
      ├── Some((7, 0)): 2/5 ≈ 0.400
      ├── Some((7, 1)): 2/5 ≈ 0.400
      ├── Some((7, 2)): 5/7 ≈ 0.714
      ├── Some((7, 3)): 2/5 ≈ 0.400
      ├── Some((7, 4)): 3/6 ≈ 0.500
      ├── Some((7, 5)): 2/5 ≈ 0.400
      ├── Some((7, 6)): 2/5 ≈ 0.400
      ├── Some((7, 7)): 1/4 ≈ 0.250
      └── Some((7, 8)): 1/4 ≈ 0.250
    └── Some((8, 8)): 27/55 ≈ 0.491
      ├── Some((8, 0)): 4/7 ≈ 0.571
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 3/6 ≈ 0.500
      ├── Some((8, 3)): 8/11 ≈ 0.727
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 3/6 ≈ 0.500
      ├── Some((8, 6)): 1/5 ≈ 0.200
      └── Some((8, 7)): 6/9 ≈ 0.667
├── Some((1, 5)): 5159/10035 ≈ 0.514
  ├── Some((5, 0)): 740/1401 ≈ 0.528
    ├── Some((0, 0)): 62/126 ≈ 0.492
      ├── Some((0, 1)): 12/20 ≈ 0.600
      ├── Some((0, 2)): 3/11 ≈ 0.273
      ├── Some((0, 3)): 0/7 ≈ 0.000
      ├── Some((0, 4)): 16/25 ≈ 0.640
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 6/14 ≈ 0.429
      └── Some((0, 8)): 12/20 ≈ 0.600
    ├── Some((0, 1)): 55/116 ≈ 0.474
      ├── Some((1, 0)): 9/17 ≈ 0.529
      ├── Some((1, 1)): 4/11 ≈ 0.364
      ├── Some((1, 2)): 7/15 ≈ 0.467
      ├── Some((1, 3)): 5/13 ≈ 0.385
      ├── Some((1, 4)): 20/28 ≈ 0.714
      ├── Some((1, 6)): 4/11 ≈ 0.364
      ├── Some((1, 7)): 1/8 ≈ 0.125
      └── Some((1, 8)): 4/12 ≈ 0.333
    ├── Some((0, 2)): 67/134 ≈ 0.500
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 1/8 ≈ 0.125
      ├── Some((2, 2)): 1/8 ≈ 0.125
      ├── Some((2, 3)): 15/23 ≈ 0.652
      ├── Some((2, 4)): 16/23 ≈ 0.696
      ├── Some((2, 5)): 4/11 ≈ 0.364
      ├── Some((2, 6)): 8/16 ≈ 0.500
      ├── Some((2, 7)): 11/19 ≈ 0.579
      └── Some((2, 8)): 4/11 ≈ 0.364
    ├── Some((0, 3)): 110/196 ≈ 0.561
      ├── Some((3, 0)): 17/27 ≈ 0.630
      ├── Some((3, 1)): 6/15 ≈ 0.400
      ├── Some((3, 2)): 17/27 ≈ 0.630
      ├── Some((3, 3)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 16/26 ≈ 0.615
      ├── Some((3, 5)): 27/37 ≈ 0.730
      ├── Some((3, 6)): 7/16 ≈ 0.438
      ├── Some((3, 7)): 10/20 ≈ 0.500
      └── Some((3, 8)): 2/10 ≈ 0.200
    ├── Some((0, 4)): 78/150 ≈ 0.520
      ├── Some((4, 0)): 15/24 ≈ 0.625
      ├── Some((4, 1)): 9/17 ≈ 0.529
      ├── Some((4, 2)): 5/13 ≈ 0.385
      ├── Some((4, 3)): 4/12 ≈ 0.333
      ├── Some((4, 4)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 16/24 ≈ 0.667
      ├── Some((4, 6)): 13/21 ≈ 0.619
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((0, 5)): 116/204 ≈ 0.569
      ├── Some((5, 1)): 18/29 ≈ 0.621
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 20/31 ≈ 0.645
      ├── Some((5, 4)): 15/26 ≈ 0.577
      ├── Some((5, 5)): 11/22 ≈ 0.500
      ├── Some((5, 6)): 19/30 ≈ 0.633
      ├── Some((5, 7)): 11/22 ≈ 0.500
      └── Some((5, 8)): 10/21 ≈ 0.476
    ├── Some((0, 6)): 80/153 ≈ 0.523
      ├── Some((6, 0)): 5/13 ≈ 0.385
      ├── Some((6, 1)): 10/18 ≈ 0.556
      ├── Some((6, 2)): 10/18 ≈ 0.556
      ├── Some((6, 3)): 10/18 ≈ 0.556
      ├── Some((6, 4)): 10/18 ≈ 0.556
      ├── Some((6, 5)): 5/13 ≈ 0.385
      ├── Some((6, 6)): 13/22 ≈ 0.591
      ├── Some((6, 7)): 9/17 ≈ 0.529
      └── Some((6, 8)): 7/15 ≈ 0.467
    ├── Some((0, 7)): 75/145 ≈ 0.517
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 11/19 ≈ 0.579
      ├── Some((7, 2)): 15/23 ≈ 0.652
      ├── Some((7, 3)): 7/15 ≈ 0.467
      ├── Some((7, 4)): 2/9 ≈ 0.222
      ├── Some((7, 5)): 8/16 ≈ 0.500
      ├── Some((7, 6)): 12/20 ≈ 0.600
      ├── Some((7, 7)): 9/17 ≈ 0.529
      └── Some((7, 8)): 5/12 ≈ 0.417
    └── Some((0, 8)): 96/176 ≈ 0.545
      ├── Some((8, 0)): 11/20 ≈ 0.550
      ├── Some((8, 1)): 7/15 ≈ 0.467
      ├── Some((8, 2)): 18/27 ≈ 0.667
      ├── Some((8, 3)): 9/18 ≈ 0.500
      ├── Some((8, 4)): 19/28 ≈ 0.679
      ├── Some((8, 5)): 11/20 ≈ 0.550
      ├── Some((8, 6)): 8/17 ≈ 0.471
      ├── Some((8, 7)): 9/18 ≈ 0.500
      └── Some((8, 8)): 4/12 ≈ 0.333
  ├── Some((5, 1)): 769/1450 ≈ 0.530
    ├── Some((1, 0)): 69/141 ≈ 0.489
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 3/11 ≈ 0.273
      ├── Some((0, 2)): 5/13 ≈ 0.385
      ├── Some((0, 3)): 5/13 ≈ 0.385
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 14/22 ≈ 0.636
      ├── Some((0, 6)): 7/15 ≈ 0.467
      ├── Some((0, 7)): 18/26 ≈ 0.692
      └── Some((0, 8)): 4/12 ≈ 0.333
    ├── Some((1, 1)): 66/137 ≈ 0.482
      ├── Some((1, 0)): 5/14 ≈ 0.357
      ├── Some((1, 2)): 10/20 ≈ 0.500
      ├── Some((1, 3)): 9/19 ≈ 0.474
      ├── Some((1, 4)): 12/22 ≈ 0.545
      ├── Some((1, 6)): 6/16 ≈ 0.375
      ├── Some((1, 7)): 18/29 ≈ 0.621
      └── Some((1, 8)): 6/16 ≈ 0.375
    ├── Some((1, 2)): 119/215 ≈ 0.553
      ├── Some((2, 0)): 5/15 ≈ 0.333
      ├── Some((2, 1)): 12/23 ≈ 0.522
      ├── Some((2, 2)): 16/27 ≈ 0.593
      ├── Some((2, 3)): 16/27 ≈ 0.593
      ├── Some((2, 4)): 11/22 ≈ 0.500
      ├── Some((2, 5)): 4/13 ≈ 0.308
      ├── Some((2, 6)): 18/29 ≈ 0.621
      ├── Some((2, 7)): 9/19 ≈ 0.474
      └── Some((2, 8)): 28/39 ≈ 0.718
    ├── Some((1, 3)): 66/137 ≈ 0.482
      ├── Some((3, 0)): 11/19 ≈ 0.579
      ├── Some((3, 1)): 9/17 ≈ 0.529
      ├── Some((3, 2)): 7/15 ≈ 0.467
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 11/19 ≈ 0.579
      ├── Some((3, 5)): 9/17 ≈ 0.529
      ├── Some((3, 6)): 0/7 ≈ 0.000
      ├── Some((3, 7)): 2/9 ≈ 0.222
      └── Some((3, 8)): 10/18 ≈ 0.556
    ├── Some((1, 4)): 136/239 ≈ 0.569
      ├── Some((4, 0)): 10/21 ≈ 0.476
      ├── Some((4, 1)): 8/19 ≈ 0.421
      ├── Some((4, 2)): 15/27 ≈ 0.556
      ├── Some((4, 3)): 24/36 ≈ 0.667
      ├── Some((4, 4)): 11/22 ≈ 0.500
      ├── Some((4, 5)): 11/22 ≈ 0.500
      ├── Some((4, 6)): 12/23 ≈ 0.522
      ├── Some((4, 7)): 20/32 ≈ 0.625
      └── Some((4, 8)): 24/36 ≈ 0.667
    ├── Some((1, 6)): 82/161 ≈ 0.509
      ├── Some((6, 0)): 17/26 ≈ 0.654
      ├── Some((6, 1)): 1/8 ≈ 0.125
      ├── Some((6, 2)): 9/18 ≈ 0.500
      ├── Some((6, 3)): 16/25 ≈ 0.640
      ├── Some((6, 4)): 5/13 ≈ 0.385
      ├── Some((6, 5)): 13/22 ≈ 0.591
      ├── Some((6, 6)): 5/14 ≈ 0.357
      ├── Some((6, 7)): 7/16 ≈ 0.438
      └── Some((6, 8)): 9/18 ≈ 0.500
    ├── Some((1, 7)): 101/189 ≈ 0.534
      ├── Some((7, 0)): 16/26 ≈ 0.615
      ├── Some((7, 1)): 5/14 ≈ 0.357
      ├── Some((7, 2)): 12/22 ≈ 0.545
      ├── Some((7, 3)): 10/20 ≈ 0.500
      ├── Some((7, 4)): 16/26 ≈ 0.615
      ├── Some((7, 5)): 9/18 ≈ 0.500
      ├── Some((7, 6)): 9/18 ≈ 0.500
      ├── Some((7, 7)): 11/21 ≈ 0.524
      └── Some((7, 8)): 13/23 ≈ 0.565
    └── Some((1, 8)): 130/230 ≈ 0.565
      ├── Some((8, 0)): 5/15 ≈ 0.333
      ├── Some((8, 1)): 15/26 ≈ 0.577
      ├── Some((8, 2)): 3/12 ≈ 0.250
      ├── Some((8, 3)): 14/25 ≈ 0.560
      ├── Some((8, 4)): 15/26 ≈ 0.577
      ├── Some((8, 5)): 24/36 ≈ 0.667
      ├── Some((8, 6)): 18/30 ≈ 0.600
      ├── Some((8, 7)): 14/25 ≈ 0.560
      └── Some((8, 8)): 22/34 ≈ 0.647
  ├── Some((5, 2)): 550/1076 ≈ 0.511
    ├── Some((2, 0)): 37/84 ≈ 0.440
      ├── Some((0, 0)): 4/9 ≈ 0.444
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 1/6 ≈ 0.167
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 8/13 ≈ 0.615
      ├── Some((0, 6)): 6/12 ≈ 0.500
      ├── Some((0, 7)): 7/12 ≈ 0.583
      └── Some((0, 8)): 1/6 ≈ 0.167
    ├── Some((2, 1)): 54/110 ≈ 0.491
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 3/10 ≈ 0.300
      ├── Some((1, 2)): 9/16 ≈ 0.562
      ├── Some((1, 3)): 8/15 ≈ 0.533
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 9/16 ≈ 0.562
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 9/16 ≈ 0.562
    ├── Some((2, 2)): 67/128 ≈ 0.523
      ├── Some((2, 0)): 13/21 ≈ 0.619
      ├── Some((2, 1)): 10/18 ≈ 0.556
      ├── Some((2, 3)): 11/19 ≈ 0.579
      ├── Some((2, 4)): 8/16 ≈ 0.500
      ├── Some((2, 5)): 7/14 ≈ 0.500
      ├── Some((2, 6)): 2/9 ≈ 0.222
      ├── Some((2, 7)): 8/16 ≈ 0.500
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((2, 3)): 53/108 ≈ 0.491
      ├── Some((3, 0)): 9/15 ≈ 0.600
      ├── Some((3, 1)): 9/15 ≈ 0.600
      ├── Some((3, 2)): 5/11 ≈ 0.455
      ├── Some((3, 3)): 7/13 ≈ 0.538
      ├── Some((3, 4)): 6/12 ≈ 0.500
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 7/14 ≈ 0.500
      ├── Some((3, 7)): 1/7 ≈ 0.143
      └── Some((3, 8)): 3/9 ≈ 0.333
    ├── Some((2, 4)): 79/145 ≈ 0.545
      ├── Some((4, 0)): 10/18 ≈ 0.556
      ├── Some((4, 1)): 4/11 ≈ 0.364
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 9/17 ≈ 0.529
      ├── Some((4, 4)): 11/19 ≈ 0.579
      ├── Some((4, 5)): 16/23 ≈ 0.696
      ├── Some((4, 6)): 18/25 ≈ 0.720
      ├── Some((4, 7)): 2/9 ≈ 0.222
      └── Some((4, 8)): 3/10 ≈ 0.300
    ├── Some((2, 5)): 87/157 ≈ 0.554
      ├── Some((5, 0)): 15/24 ≈ 0.625
      ├── Some((5, 1)): 9/18 ≈ 0.500
      ├── Some((5, 3)): 1/8 ≈ 0.125
      ├── Some((5, 4)): 19/28 ≈ 0.679
      ├── Some((5, 5)): 6/15 ≈ 0.400
      ├── Some((5, 6)): 11/20 ≈ 0.550
      ├── Some((5, 7)): 10/19 ≈ 0.526
      └── Some((5, 8)): 15/24 ≈ 0.625
    ├── Some((2, 6)): 67/128 ≈ 0.523
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 6/13 ≈ 0.462
      ├── Some((6, 2)): 2/9 ≈ 0.222
      ├── Some((6, 3)): 12/19 ≈ 0.632
      ├── Some((6, 4)): 1/7 ≈ 0.143
      ├── Some((6, 5)): 1/7 ≈ 0.143
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 11/18 ≈ 0.611
      └── Some((6, 8)): 19/26 ≈ 0.731
    ├── Some((2, 7)): 35/81 ≈ 0.432
      ├── Some((7, 0)): 7/12 ≈ 0.583
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 1/6 ≈ 0.167
      ├── Some((7, 3)): 2/7 ≈ 0.286
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 8/13 ≈ 0.615
      ├── Some((7, 6)): 2/7 ≈ 0.286
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 6/11 ≈ 0.545
    └── Some((2, 8)): 71/134 ≈ 0.530
      ├── Some((8, 0)): 12/19 ≈ 0.632
      ├── Some((8, 1)): 16/23 ≈ 0.696
      ├── Some((8, 2)): 15/22 ≈ 0.682
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 7/14 ≈ 0.500
      ├── Some((8, 5)): 3/10 ≈ 0.300
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 6/13 ≈ 0.462
      └── Some((8, 8)): 5/12 ≈ 0.417
  ├── Some((5, 3)): 604/1169 ≈ 0.517
    ├── Some((3, 0)): 97/173 ≈ 0.561
      ├── Some((0, 0)): 8/16 ≈ 0.500
      ├── Some((0, 1)): 10/18 ≈ 0.556
      ├── Some((0, 2)): 16/25 ≈ 0.640
      ├── Some((0, 3)): 6/14 ≈ 0.429
      ├── Some((0, 4)): 18/27 ≈ 0.667
      ├── Some((0, 5)): 9/17 ≈ 0.529
      ├── Some((0, 6)): 7/15 ≈ 0.467
      ├── Some((0, 7)): 17/26 ≈ 0.654
      └── Some((0, 8)): 6/14 ≈ 0.429
    ├── Some((3, 1)): 85/156 ≈ 0.545
      ├── Some((1, 0)): 7/16 ≈ 0.438
      ├── Some((1, 1)): 8/17 ≈ 0.471
      ├── Some((1, 2)): 13/22 ≈ 0.591
      ├── Some((1, 3)): 16/25 ≈ 0.640
      ├── Some((1, 4)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 5/13 ≈ 0.385
      ├── Some((1, 7)): 17/26 ≈ 0.654
      └── Some((1, 8)): 6/15 ≈ 0.400
    ├── Some((3, 2)): 68/132 ≈ 0.515
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 10/17 ≈ 0.588
      ├── Some((2, 2)): 11/18 ≈ 0.611
      ├── Some((2, 3)): 2/9 ≈ 0.222
      ├── Some((2, 4)): 9/16 ≈ 0.562
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 12/19 ≈ 0.632
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((3, 3)): 90/163 ≈ 0.552
      ├── Some((3, 0)): 7/16 ≈ 0.438
      ├── Some((3, 1)): 14/23 ≈ 0.609
      ├── Some((3, 2)): 13/22 ≈ 0.591
      ├── Some((3, 4)): 13/22 ≈ 0.591
      ├── Some((3, 5)): 2/10 ≈ 0.200
      ├── Some((3, 6)): 16/26 ≈ 0.615
      ├── Some((3, 7)): 9/18 ≈ 0.500
      └── Some((3, 8)): 15/25 ≈ 0.600
    ├── Some((3, 4)): 95/171 ≈ 0.556
      ├── Some((4, 0)): 2/9 ≈ 0.222
      ├── Some((4, 1)): 11/19 ≈ 0.579
      ├── Some((4, 2)): 10/18 ≈ 0.556
      ├── Some((4, 3)): 11/20 ≈ 0.550
      ├── Some((4, 4)): 13/22 ≈ 0.591
      ├── Some((4, 5)): 6/14 ≈ 0.429
      ├── Some((4, 6)): 14/23 ≈ 0.609
      ├── Some((4, 7)): 11/20 ≈ 0.550
      └── Some((4, 8)): 16/25 ≈ 0.640
    ├── Some((3, 5)): 44/97 ≈ 0.454
      ├── Some((5, 0)): 0/6 ≈ 0.000
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 3/9 ≈ 0.333
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 6)): 10/17 ≈ 0.588
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((3, 6)): 35/83 ≈ 0.422
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 0/5 ≈ 0.000
      ├── Some((6, 2)): 7/12 ≈ 0.583
      ├── Some((6, 3)): 7/12 ≈ 0.583
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 7/13 ≈ 0.538
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((3, 7)): 29/73 ≈ 0.397
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 1/6 ≈ 0.167
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 7/12 ≈ 0.583
      ├── Some((7, 7)): 5/10 ≈ 0.500
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((3, 8)): 60/120 ≈ 0.500
      ├── Some((8, 0)): 8/15 ≈ 0.533
      ├── Some((8, 1)): 7/14 ≈ 0.500
      ├── Some((8, 2)): 12/19 ≈ 0.632
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 2/8 ≈ 0.250
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 8/15 ≈ 0.533
      ├── Some((8, 7)): 10/17 ≈ 0.588
      └── Some((8, 8)): 3/9 ≈ 0.333
  ├── Some((5, 4)): 469/936 ≈ 0.501
    ├── Some((4, 0)): 32/75 ≈ 0.427
      ├── Some((0, 0)): 8/12 ≈ 0.667
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 5/10 ≈ 0.500
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 0/4 ≈ 0.000
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 6/11 ≈ 0.545
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 0/4 ≈ 0.000
    ├── Some((4, 1)): 30/72 ≈ 0.417
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 7/12 ≈ 0.583
      ├── Some((1, 2)): 2/7 ≈ 0.286
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 6/12 ≈ 0.500
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 2/7 ≈ 0.286
    ├── Some((4, 2)): 71/131 ≈ 0.542
      ├── Some((2, 0)): 12/19 ≈ 0.632
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 12/19 ≈ 0.632
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 13/19 ≈ 0.684
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 5/12 ≈ 0.417
    ├── Some((4, 3)): 49/100 ≈ 0.490
      ├── Some((3, 0)): 9/14 ≈ 0.643
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 7/12 ≈ 0.583
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 7/13 ≈ 0.538
      └── Some((3, 8)): 6/12 ≈ 0.500
    ├── Some((4, 4)): 44/93 ≈ 0.473
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 1)): 2/8 ≈ 0.250
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 15/21 ≈ 0.714
      ├── Some((4, 6)): 4/10 ≈ 0.400
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 3/9 ≈ 0.333
    ├── Some((4, 5)): 34/78 ≈ 0.436
      ├── Some((5, 0)): 0/5 ≈ 0.000
      ├── Some((5, 1)): 4/9 ≈ 0.444
      ├── Some((5, 2)): 3/8 ≈ 0.375
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 4/9 ≈ 0.444
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 7/13 ≈ 0.538
      └── Some((5, 8)): 6/12 ≈ 0.500
    ├── Some((4, 6)): 96/166 ≈ 0.578
      ├── Some((6, 0)): 16/23 ≈ 0.696
      ├── Some((6, 1)): 10/18 ≈ 0.556
      ├── Some((6, 2)): 15/23 ≈ 0.652
      ├── Some((6, 3)): 11/19 ≈ 0.579
      ├── Some((6, 4)): 13/21 ≈ 0.619
      ├── Some((6, 5)): 5/12 ≈ 0.417
      ├── Some((6, 6)): 7/15 ≈ 0.467
      ├── Some((6, 7)): 4/11 ≈ 0.364
      └── Some((6, 8)): 15/23 ≈ 0.652
    ├── Some((4, 7)): 43/91 ≈ 0.473
      ├── Some((7, 0)): 6/11 ≈ 0.545
      ├── Some((7, 1)): 1/6 ≈ 0.167
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 10/15 ≈ 0.667
      ├── Some((7, 4)): 6/12 ≈ 0.500
      ├── Some((7, 5)): 4/9 ≈ 0.444
      ├── Some((7, 6)): 7/12 ≈ 0.583
      ├── Some((7, 7)): 1/6 ≈ 0.167
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((4, 8)): 69/129 ≈ 0.535
      ├── Some((8, 0)): 8/15 ≈ 0.533
      ├── Some((8, 1)): 11/17 ≈ 0.647
      ├── Some((8, 2)): 5/11 ≈ 0.455
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 12/18 ≈ 0.667
      ├── Some((8, 7)): 9/16 ≈ 0.562
      └── Some((8, 8)): 9/16 ≈ 0.562
  ├── Some((5, 5)): 502/993 ≈ 0.506
    ├── Some((5, 0)): 82/152 ≈ 0.539
      ├── Some((0, 0)): 8/16 ≈ 0.500
      ├── Some((0, 1)): 13/21 ≈ 0.619
      ├── Some((0, 2)): 2/9 ≈ 0.222
      ├── Some((0, 3)): 9/17 ≈ 0.529
      ├── Some((0, 4)): 6/14 ≈ 0.429
      ├── Some((0, 5)): 19/27 ≈ 0.704
      ├── Some((0, 6)): 5/12 ≈ 0.417
      ├── Some((0, 7)): 9/17 ≈ 0.529
      └── Some((0, 8)): 10/18 ≈ 0.556
    ├── Some((5, 1)): 94/169 ≈ 0.556
      ├── Some((1, 0)): 5/14 ≈ 0.357
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 2)): 20/30 ≈ 0.667
      ├── Some((1, 3)): 18/28 ≈ 0.643
      ├── Some((1, 4)): 8/17 ≈ 0.471
      ├── Some((1, 6)): 4/13 ≈ 0.308
      ├── Some((1, 7)): 10/19 ≈ 0.526
      └── Some((1, 8)): 17/27 ≈ 0.630
    ├── Some((5, 2)): 46/100 ≈ 0.460
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 7/13 ≈ 0.538
      ├── Some((2, 4)): 6/12 ≈ 0.500
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 2/8 ≈ 0.250
      ├── Some((2, 7)): 9/15 ≈ 0.600
      └── Some((2, 8)): 4/10 ≈ 0.400
    ├── Some((5, 3)): 59/119 ≈ 0.496
      ├── Some((3, 0)): 1/7 ≈ 0.143
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 11/17 ≈ 0.647
      ├── Some((3, 4)): 7/14 ≈ 0.500
      ├── Some((3, 5)): 8/15 ≈ 0.533
      ├── Some((3, 6)): 7/14 ≈ 0.500
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 9/16 ≈ 0.562
    ├── Some((5, 4)): 44/97 ≈ 0.454
      ├── Some((4, 0)): 7/13 ≈ 0.538
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 1/6 ≈ 0.167
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 10/16 ≈ 0.625
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 7/13 ≈ 0.538
    ├── Some((5, 6)): 56/114 ≈ 0.491
      ├── Some((6, 0)): 10/17 ≈ 0.588
      ├── Some((6, 1)): 1/7 ≈ 0.143
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 2/8 ≈ 0.250
      ├── Some((6, 4)): 4/10 ≈ 0.400
      ├── Some((6, 5)): 9/16 ≈ 0.562
      ├── Some((6, 6)): 12/18 ≈ 0.667
      ├── Some((6, 7)): 12/19 ≈ 0.632
      └── Some((6, 8)): 2/8 ≈ 0.250
    ├── Some((5, 7)): 64/126 ≈ 0.508
      ├── Some((7, 0)): 13/20 ≈ 0.650
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 15/22 ≈ 0.682
      ├── Some((7, 4)): 11/18 ≈ 0.611
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 5/12 ≈ 0.417
      ├── Some((7, 7)): 2/8 ≈ 0.250
      └── Some((7, 8)): 1/7 ≈ 0.143
    └── Some((5, 8)): 56/115 ≈ 0.487
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 10/17 ≈ 0.588
      ├── Some((8, 3)): 9/16 ≈ 0.562
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((5, 6)): 645/1239 ≈ 0.521
    ├── Some((6, 0)): 59/120 ≈ 0.492
      ├── Some((0, 0)): 3/9 ≈ 0.333
      ├── Some((0, 1)): 4/11 ≈ 0.364
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 12/19 ≈ 0.632
      ├── Some((0, 4)): 4/11 ≈ 0.364
      ├── Some((0, 5)): 2/8 ≈ 0.250
      ├── Some((0, 6)): 3/10 ≈ 0.300
      ├── Some((0, 7)): 10/17 ≈ 0.588
      └── Some((0, 8)): 12/19 ≈ 0.632
    ├── Some((6, 1)): 51/108 ≈ 0.472
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 1)): 11/18 ≈ 0.611
      ├── Some((1, 2)): 11/18 ≈ 0.611
      ├── Some((1, 3)): 2/9 ≈ 0.222
      ├── Some((1, 4)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 5/12 ≈ 0.417
      └── Some((1, 8)): 3/10 ≈ 0.300
    ├── Some((6, 2)): 44/97 ≈ 0.454
      ├── Some((2, 0)): 8/14 ≈ 0.571
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 2)): 1/6 ≈ 0.167
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 0/5 ≈ 0.000
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 10/16 ≈ 0.625
      └── Some((2, 8)): 8/14 ≈ 0.571
    ├── Some((6, 3)): 113/196 ≈ 0.577
      ├── Some((3, 0)): 16/25 ≈ 0.640
      ├── Some((3, 1)): 13/22 ≈ 0.591
      ├── Some((3, 2)): 13/22 ≈ 0.591
      ├── Some((3, 3)): 17/27 ≈ 0.630
      ├── Some((3, 4)): 10/19 ≈ 0.526
      ├── Some((3, 5)): 12/21 ≈ 0.571
      ├── Some((3, 6)): 9/18 ≈ 0.500
      ├── Some((3, 7)): 12/21 ≈ 0.571
      └── Some((3, 8)): 11/20 ≈ 0.550
    ├── Some((6, 4)): 61/122 ≈ 0.500
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 7/14 ≈ 0.500
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 13/19 ≈ 0.684
      ├── Some((4, 4)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 11/18 ≈ 0.611
      ├── Some((4, 6)): 6/13 ≈ 0.462
      ├── Some((4, 7)): 3/9 ≈ 0.333
      └── Some((4, 8)): 3/9 ≈ 0.333
    ├── Some((6, 5)): 54/112 ≈ 0.482
      ├── Some((5, 0)): 9/16 ≈ 0.562
      ├── Some((5, 1)): 13/21 ≈ 0.619
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 5/12 ≈ 0.417
      ├── Some((5, 4)): 4/11 ≈ 0.364
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 7/14 ≈ 0.500
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((6, 6)): 89/163 ≈ 0.546
      ├── Some((6, 0)): 13/23 ≈ 0.565
      ├── Some((6, 1)): 8/17 ≈ 0.471
      ├── Some((6, 2)): 10/19 ≈ 0.526
      ├── Some((6, 3)): 7/16 ≈ 0.438
      ├── Some((6, 4)): 4/12 ≈ 0.333
      ├── Some((6, 5)): 10/19 ≈ 0.526
      ├── Some((6, 7)): 21/31 ≈ 0.677
      └── Some((6, 8)): 15/25 ≈ 0.600
    ├── Some((6, 7)): 88/161 ≈ 0.547
      ├── Some((7, 0)): 15/24 ≈ 0.625
      ├── Some((7, 1)): 11/19 ≈ 0.579
      ├── Some((7, 2)): 4/12 ≈ 0.333
      ├── Some((7, 3)): 10/18 ≈ 0.556
      ├── Some((7, 4)): 12/20 ≈ 0.600
      ├── Some((7, 5)): 4/12 ≈ 0.333
      ├── Some((7, 6)): 10/18 ≈ 0.556
      ├── Some((7, 7)): 9/17 ≈ 0.529
      └── Some((7, 8)): 12/20 ≈ 0.600
    └── Some((6, 8)): 86/159 ≈ 0.541
      ├── Some((8, 0)): 8/16 ≈ 0.500
      ├── Some((8, 1)): 10/18 ≈ 0.556
      ├── Some((8, 2)): 4/12 ≈ 0.333
      ├── Some((8, 3)): 3/11 ≈ 0.273
      ├── Some((8, 4)): 7/15 ≈ 0.467
      ├── Some((8, 5)): 19/27 ≈ 0.704
      ├── Some((8, 6)): 10/18 ≈ 0.556
      ├── Some((8, 7)): 7/15 ≈ 0.467
      └── Some((8, 8)): 17/26 ≈ 0.654
  ├── Some((5, 7)): 368/759 ≈ 0.485
    ├── Some((7, 0)): 29/67 ≈ 0.433
      ├── Some((0, 0)): 1/5 ≈ 0.200
      ├── Some((0, 1)): 4/8 ≈ 0.500
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 1/5 ≈ 0.200
      ├── Some((0, 4)): 8/12 ≈ 0.667
      ├── Some((0, 5)): 1/5 ≈ 0.200
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 5/9 ≈ 0.556
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((7, 1)): 31/70 ≈ 0.443
      ├── Some((1, 0)): 2/7 ≈ 0.286
      ├── Some((1, 1)): 0/4 ≈ 0.000
      ├── Some((1, 2)): 5/10 ≈ 0.500
      ├── Some((1, 3)): 1/6 ≈ 0.167
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 11/15 ≈ 0.733
      ├── Some((1, 7)): 5/10 ≈ 0.500
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((7, 2)): 34/75 ≈ 0.453
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 4/9 ≈ 0.444
      ├── Some((2, 2)): 0/4 ≈ 0.000
      ├── Some((2, 3)): 6/10 ≈ 0.600
      ├── Some((2, 4)): 8/12 ≈ 0.667
      ├── Some((2, 5)): 8/12 ≈ 0.667
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 1/6 ≈ 0.167
    ├── Some((7, 3)): 43/87 ≈ 0.494
      ├── Some((3, 0)): 3/8 ≈ 0.375
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 9/13 ≈ 0.692
      ├── Some((3, 3)): 9/14 ≈ 0.643
      ├── Some((3, 4)): 5/10 ≈ 0.500
      ├── Some((3, 5)): 0/5 ≈ 0.000
      ├── Some((3, 6)): 6/11 ≈ 0.545
      ├── Some((3, 7)): 6/11 ≈ 0.545
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((7, 4)): 59/110 ≈ 0.536
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 10/15 ≈ 0.667
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 4/10 ≈ 0.400
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 11/16 ≈ 0.688
      ├── Some((4, 6)): 11/16 ≈ 0.688
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((7, 5)): 55/104 ≈ 0.529
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 11/17 ≈ 0.647
      ├── Some((5, 3)): 8/14 ≈ 0.571
      ├── Some((5, 4)): 8/14 ≈ 0.571
      ├── Some((5, 5)): 5/11 ≈ 0.455
      ├── Some((5, 6)): 10/16 ≈ 0.625
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((7, 6)): 35/76 ≈ 0.461
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 5/9 ≈ 0.556
      ├── Some((6, 5)): 5/10 ≈ 0.500
      ├── Some((6, 6)): 5/10 ≈ 0.500
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((7, 7)): 45/90 ≈ 0.500
      ├── Some((7, 0)): 6/12 ≈ 0.500
      ├── Some((7, 1)): 8/14 ≈ 0.571
      ├── Some((7, 2)): 8/14 ≈ 0.571
      ├── Some((7, 3)): 2/7 ≈ 0.286
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 9/14 ≈ 0.643
      └── Some((7, 8)): 6/12 ≈ 0.500
    └── Some((7, 8)): 37/79 ≈ 0.468
      ├── Some((8, 0)): 2/7 ≈ 0.286
      ├── Some((8, 1)): 4/9 ≈ 0.444
      ├── Some((8, 2)): 3/8 ≈ 0.375
      ├── Some((8, 3)): 10/14 ≈ 0.714
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 1/5 ≈ 0.200
      ├── Some((8, 7)): 7/11 ≈ 0.636
      └── Some((8, 8)): 4/9 ≈ 0.444
  └── Some((5, 8)): 512/1011 ≈ 0.506
    ├── Some((8, 0)): 67/127 ≈ 0.528
      ├── Some((0, 0)): 5/12 ≈ 0.417
      ├── Some((0, 1)): 7/14 ≈ 0.500
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 12/19 ≈ 0.632
      ├── Some((0, 4)): 9/16 ≈ 0.562
      ├── Some((0, 5)): 13/19 ≈ 0.684
      ├── Some((0, 6)): 4/10 ≈ 0.400
      ├── Some((0, 7)): 4/10 ≈ 0.400
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((8, 1)): 62/120 ≈ 0.517
      ├── Some((1, 0)): 9/16 ≈ 0.562
      ├── Some((1, 1)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 3)): 4/11 ≈ 0.364
      ├── Some((1, 4)): 13/21 ≈ 0.619
      ├── Some((1, 6)): 14/21 ≈ 0.667
      ├── Some((1, 7)): 1/7 ≈ 0.143
      └── Some((1, 8)): 9/17 ≈ 0.529
    ├── Some((8, 2)): 84/151 ≈ 0.556
      ├── Some((2, 0)): 13/20 ≈ 0.650
      ├── Some((2, 1)): 7/14 ≈ 0.500
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 13/21 ≈ 0.619
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 13/21 ≈ 0.619
      ├── Some((2, 6)): 11/19 ≈ 0.579
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 4/11 ≈ 0.364
    ├── Some((8, 3)): 27/68 ≈ 0.397
      ├── Some((3, 0)): 3/8 ≈ 0.375
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 4/9 ≈ 0.444
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 6/10 ≈ 0.600
      ├── Some((3, 5)): 1/5 ≈ 0.200
      ├── Some((3, 6)): 1/5 ≈ 0.200
      ├── Some((3, 7)): 6/10 ≈ 0.600
      └── Some((3, 8)): 1/6 ≈ 0.167
    ├── Some((8, 4)): 35/81 ≈ 0.432
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 8/13 ≈ 0.615
      ├── Some((4, 2)): 2/7 ≈ 0.286
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 8/13 ≈ 0.615
      ├── Some((4, 5)): 0/5 ≈ 0.000
      ├── Some((4, 6)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 6/11 ≈ 0.545
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((8, 5)): 72/134 ≈ 0.537
      ├── Some((5, 0)): 8/16 ≈ 0.500
      ├── Some((5, 1)): 14/22 ≈ 0.636
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 3)): 12/20 ≈ 0.600
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 8/16 ≈ 0.500
      └── Some((5, 7)): 9/17 ≈ 0.529
    ├── Some((8, 6)): 71/133 ≈ 0.534
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 11/18 ≈ 0.611
      ├── Some((6, 2)): 2/8 ≈ 0.250
      ├── Some((6, 3)): 15/22 ≈ 0.682
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 6/13 ≈ 0.462
      ├── Some((6, 6)): 6/13 ≈ 0.462
      ├── Some((6, 7)): 5/12 ≈ 0.417
      └── Some((6, 8)): 13/20 ≈ 0.650
    ├── Some((8, 7)): 64/123 ≈ 0.520
      ├── Some((7, 0)): 0/6 ≈ 0.000
      ├── Some((7, 1)): 2/8 ≈ 0.250
      ├── Some((7, 2)): 11/18 ≈ 0.611
      ├── Some((7, 3)): 14/20 ≈ 0.700
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 12/18 ≈ 0.667
      ├── Some((7, 6)): 9/16 ≈ 0.562
      ├── Some((7, 7)): 5/12 ≈ 0.417
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((8, 8)): 30/73 ≈ 0.411
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 4/9 ≈ 0.444
      ├── Some((8, 3)): 4/9 ≈ 0.444
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 4/9 ≈ 0.444
      └── Some((8, 7)): 5/11 ≈ 0.455
├── Some((1, 6)): 4786/9347 ≈ 0.512
  ├── Some((6, 0)): 341/708 ≈ 0.482
    ├── Some((0, 0)): 51/97 ≈ 0.526
      ├── Some((0, 1)): 10/15 ≈ 0.667
      ├── Some((0, 2)): 8/14 ≈ 0.571
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 7/13 ≈ 0.538
      ├── Some((0, 6)): 9/14 ≈ 0.643
      ├── Some((0, 7)): 7/13 ≈ 0.538
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((0, 1)): 43/86 ≈ 0.500
      ├── Some((1, 0)): 3/8 ≈ 0.375
      ├── Some((1, 1)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 7/12 ≈ 0.583
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 8/13 ≈ 0.615
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 9/14 ≈ 0.643
    ├── Some((0, 2)): 26/62 ≈ 0.419
      ├── Some((2, 0)): 2/6 ≈ 0.333
      ├── Some((2, 1)): 3/7 ≈ 0.429
      ├── Some((2, 2)): 2/6 ≈ 0.333
      ├── Some((2, 3)): 3/7 ≈ 0.429
      ├── Some((2, 4)): 2/6 ≈ 0.333
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 2/6 ≈ 0.333
      ├── Some((2, 7)): 7/11 ≈ 0.636
      └── Some((2, 8)): 3/7 ≈ 0.429
    ├── Some((0, 3)): 39/81 ≈ 0.481
      ├── Some((3, 0)): 5/10 ≈ 0.500
      ├── Some((3, 1)): 6/10 ≈ 0.600
      ├── Some((3, 2)): 1/6 ≈ 0.167
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 6/10 ≈ 0.600
      ├── Some((3, 6)): 9/13 ≈ 0.692
      ├── Some((3, 7)): 1/6 ≈ 0.167
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((0, 4)): 18/49 ≈ 0.367
      ├── Some((4, 0)): 3/7 ≈ 0.429
      ├── Some((4, 1)): 2/6 ≈ 0.333
      ├── Some((4, 2)): 0/3 ≈ 0.000
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 4/7 ≈ 0.571
      ├── Some((4, 5)): 0/3 ≈ 0.000
      ├── Some((4, 6)): 0/3 ≈ 0.000
      ├── Some((4, 7)): 6/9 ≈ 0.667
      └── Some((4, 8)): 1/5 ≈ 0.200
    ├── Some((0, 5)): 37/78 ≈ 0.474
      ├── Some((5, 0)): 4/9 ≈ 0.444
      ├── Some((5, 1)): 6/10 ≈ 0.600
      ├── Some((5, 2)): 1/6 ≈ 0.167
      ├── Some((5, 3)): 2/7 ≈ 0.286
      ├── Some((5, 4)): 6/10 ≈ 0.600
      ├── Some((5, 5)): 0/4 ≈ 0.000
      ├── Some((5, 6)): 6/10 ≈ 0.600
      ├── Some((5, 7)): 6/10 ≈ 0.600
      └── Some((5, 8)): 6/11 ≈ 0.545
    ├── Some((0, 6)): 38/79 ≈ 0.481
      ├── Some((6, 1)): 5/10 ≈ 0.500
      ├── Some((6, 2)): 4/9 ≈ 0.444
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 11/16 ≈ 0.688
    ├── Some((0, 7)): 42/85 ≈ 0.494
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 7/11 ≈ 0.636
      ├── Some((7, 3)): 6/11 ≈ 0.545
      ├── Some((7, 4)): 6/11 ≈ 0.545
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 5/10 ≈ 0.500
      ├── Some((7, 7)): 0/4 ≈ 0.000
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((0, 8)): 46/90 ≈ 0.511
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 2/7 ≈ 0.286
      ├── Some((8, 2)): 9/13 ≈ 0.692
      ├── Some((8, 3)): 1/6 ≈ 0.167
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 5/10 ≈ 0.500
      ├── Some((8, 6)): 9/14 ≈ 0.643
      ├── Some((8, 7)): 7/12 ≈ 0.583
      └── Some((8, 8)): 5/10 ≈ 0.500
  ├── Some((6, 1)): 513/1007 ≈ 0.509
    ├── Some((1, 0)): 57/116 ≈ 0.491
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 13/19 ≈ 0.684
      ├── Some((0, 2)): 5/12 ≈ 0.417
      ├── Some((0, 3)): 3/9 ≈ 0.333
      ├── Some((0, 4)): 11/18 ≈ 0.611
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 6/13 ≈ 0.462
      ├── Some((0, 7)): 2/8 ≈ 0.250
      └── Some((0, 8)): 7/14 ≈ 0.500
    ├── Some((1, 1)): 83/153 ≈ 0.542
      ├── Some((1, 0)): 17/28 ≈ 0.607
      ├── Some((1, 2)): 11/21 ≈ 0.524
      ├── Some((1, 3)): 2/10 ≈ 0.200
      ├── Some((1, 4)): 19/30 ≈ 0.633
      ├── Some((1, 5)): 13/23 ≈ 0.565
      ├── Some((1, 7)): 10/20 ≈ 0.500
      └── Some((1, 8)): 10/20 ≈ 0.500
    ├── Some((1, 2)): 51/107 ≈ 0.477
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 10/16 ≈ 0.625
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 10/16 ≈ 0.625
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 1/7 ≈ 0.143
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 2/8 ≈ 0.250
    ├── Some((1, 3)): 56/114 ≈ 0.491
      ├── Some((3, 0)): 7/14 ≈ 0.500
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 11/17 ≈ 0.647
      ├── Some((3, 3)): 2/8 ≈ 0.250
      ├── Some((3, 4)): 7/14 ≈ 0.500
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 5/11 ≈ 0.455
      └── Some((3, 8)): 3/9 ≈ 0.333
    ├── Some((1, 4)): 67/130 ≈ 0.515
      ├── Some((4, 0)): 4/11 ≈ 0.364
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 12/19 ≈ 0.632
      ├── Some((4, 3)): 9/16 ≈ 0.562
      ├── Some((4, 4)): 3/10 ≈ 0.300
      ├── Some((4, 5)): 8/15 ≈ 0.533
      ├── Some((4, 6)): 3/10 ≈ 0.300
      ├── Some((4, 7)): 15/22 ≈ 0.682
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((1, 5)): 52/108 ≈ 0.481
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 9/15 ≈ 0.600
      ├── Some((5, 2)): 4/10 ≈ 0.400
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 9/16 ≈ 0.562
      ├── Some((5, 5)): 6/12 ≈ 0.500
      ├── Some((5, 6)): 2/8 ≈ 0.250
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((1, 7)): 59/118 ≈ 0.500
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 11/17 ≈ 0.647
      ├── Some((7, 4)): 13/19 ≈ 0.684
      ├── Some((7, 5)): 7/14 ≈ 0.500
      ├── Some((7, 6)): 7/14 ≈ 0.500
      ├── Some((7, 7)): 2/8 ≈ 0.250
      └── Some((7, 8)): 5/12 ≈ 0.417
    └── Some((1, 8)): 88/160 ≈ 0.550
      ├── Some((8, 0)): 5/13 ≈ 0.385
      ├── Some((8, 1)): 7/15 ≈ 0.467
      ├── Some((8, 2)): 25/33 ≈ 0.758
      ├── Some((8, 3)): 0/7 ≈ 0.000
      ├── Some((8, 4)): 21/30 ≈ 0.700
      ├── Some((8, 5)): 11/20 ≈ 0.550
      ├── Some((8, 6)): 2/9 ≈ 0.222
      ├── Some((8, 7)): 7/15 ≈ 0.467
      └── Some((8, 8)): 9/17 ≈ 0.529
  ├── Some((6, 2)): 636/1218 ≈ 0.522
    ├── Some((2, 0)): 83/153 ≈ 0.542
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 21/28 ≈ 0.750
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 1/8 ≈ 0.125
      ├── Some((0, 4)): 6/14 ≈ 0.429
      ├── Some((0, 5)): 10/18 ≈ 0.556
      ├── Some((0, 6)): 6/14 ≈ 0.429
      ├── Some((0, 7)): 10/18 ≈ 0.556
      └── Some((0, 8)): 11/19 ≈ 0.579
    ├── Some((2, 1)): 53/110 ≈ 0.482
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 3/10 ≈ 0.300
      ├── Some((1, 3)): 7/14 ≈ 0.500
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 3/10 ≈ 0.300
      ├── Some((1, 7)): 15/23 ≈ 0.652
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((2, 2)): 42/93 ≈ 0.452
      ├── Some((2, 0)): 1/7 ≈ 0.143
      ├── Some((2, 1)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 7/14 ≈ 0.500
      ├── Some((2, 5)): 0/6 ≈ 0.000
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 12/18 ≈ 0.667
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((2, 3)): 59/119 ≈ 0.496
      ├── Some((3, 0)): 14/20 ≈ 0.700
      ├── Some((3, 1)): 4/11 ≈ 0.364
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 2/8 ≈ 0.250
      ├── Some((3, 6)): 12/19 ≈ 0.632
      ├── Some((3, 7)): 4/11 ≈ 0.364
      └── Some((3, 8)): 8/15 ≈ 0.533
    ├── Some((2, 4)): 71/136 ≈ 0.522
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 7/14 ≈ 0.500
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 8/15 ≈ 0.533
      ├── Some((4, 6)): 9/16 ≈ 0.562
      ├── Some((4, 7)): 9/16 ≈ 0.562
      └── Some((4, 8)): 5/12 ≈ 0.417
    ├── Some((2, 5)): 52/108 ≈ 0.481
      ├── Some((5, 0)): 3/9 ≈ 0.333
      ├── Some((5, 1)): 11/17 ≈ 0.647
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 11/17 ≈ 0.647
      ├── Some((5, 5)): 5/11 ≈ 0.455
      ├── Some((5, 6)): 1/7 ≈ 0.143
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 3/9 ≈ 0.333
    ├── Some((2, 6)): 93/167 ≈ 0.557
      ├── Some((6, 0)): 9/18 ≈ 0.500
      ├── Some((6, 1)): 8/17 ≈ 0.471
      ├── Some((6, 3)): 12/21 ≈ 0.571
      ├── Some((6, 4)): 19/28 ≈ 0.679
      ├── Some((6, 5)): 8/17 ≈ 0.471
      ├── Some((6, 6)): 19/29 ≈ 0.655
      ├── Some((6, 7)): 12/21 ≈ 0.571
      └── Some((6, 8)): 6/15 ≈ 0.400
    ├── Some((2, 7)): 99/176 ≈ 0.562
      ├── Some((7, 0)): 11/20 ≈ 0.550
      ├── Some((7, 1)): 21/30 ≈ 0.700
      ├── Some((7, 2)): 7/15 ≈ 0.467
      ├── Some((7, 3)): 18/27 ≈ 0.667
      ├── Some((7, 4)): 12/21 ≈ 0.571
      ├── Some((7, 5)): 4/12 ≈ 0.333
      ├── Some((7, 6)): 6/14 ≈ 0.429
      ├── Some((7, 7)): 11/20 ≈ 0.550
      └── Some((7, 8)): 8/16 ≈ 0.500
    └── Some((2, 8)): 84/155 ≈ 0.542
      ├── Some((8, 0)): 5/12 ≈ 0.417
      ├── Some((8, 1)): 12/20 ≈ 0.600
      ├── Some((8, 2)): 13/21 ≈ 0.619
      ├── Some((8, 3)): 5/13 ≈ 0.385
      ├── Some((8, 4)): 6/14 ≈ 0.429
      ├── Some((8, 5)): 13/21 ≈ 0.619
      ├── Some((8, 6)): 10/18 ≈ 0.556
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 13/21 ≈ 0.619
  ├── Some((6, 3)): 532/1040 ≈ 0.512
    ├── Some((3, 0)): 86/153 ≈ 0.562
      ├── Some((0, 0)): 21/28 ≈ 0.750
      ├── Some((0, 1)): 7/14 ≈ 0.500
      ├── Some((0, 2)): 3/10 ≈ 0.300
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 7/15 ≈ 0.467
      ├── Some((0, 5)): 11/19 ≈ 0.579
      ├── Some((0, 6)): 5/12 ≈ 0.417
      ├── Some((0, 7)): 16/23 ≈ 0.696
      └── Some((0, 8)): 9/17 ≈ 0.529
    ├── Some((3, 1)): 44/94 ≈ 0.468
      ├── Some((1, 0)): 8/14 ≈ 0.571
      ├── Some((1, 1)): 8/15 ≈ 0.533
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 7/13 ≈ 0.538
      ├── Some((1, 4)): 2/8 ≈ 0.250
      ├── Some((1, 5)): 7/13 ≈ 0.538
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((3, 2)): 57/113 ≈ 0.504
      ├── Some((2, 0)): 13/19 ≈ 0.684
      ├── Some((2, 1)): 8/15 ≈ 0.533
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 2/8 ≈ 0.250
      ├── Some((2, 4)): 13/19 ≈ 0.684
      ├── Some((2, 5)): 12/18 ≈ 0.667
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 1/7 ≈ 0.143
      └── Some((2, 8)): 0/6 ≈ 0.000
    ├── Some((3, 3)): 55/110 ≈ 0.500
      ├── Some((3, 0)): 14/20 ≈ 0.700
      ├── Some((3, 1)): 4/11 ≈ 0.364
      ├── Some((3, 2)): 4/11 ≈ 0.364
      ├── Some((3, 4)): 12/19 ≈ 0.632
      ├── Some((3, 5)): 8/15 ≈ 0.533
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 4/11 ≈ 0.364
      └── Some((3, 8)): 3/9 ≈ 0.333
    ├── Some((3, 4)): 71/132 ≈ 0.538
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 4/11 ≈ 0.364
      ├── Some((4, 2)): 11/18 ≈ 0.611
      ├── Some((4, 3)): 17/24 ≈ 0.708
      ├── Some((4, 4)): 8/15 ≈ 0.533
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 1/7 ≈ 0.143
      ├── Some((4, 7)): 18/24 ≈ 0.750
      └── Some((4, 8)): 3/10 ≈ 0.300
    ├── Some((3, 5)): 70/131 ≈ 0.534
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 8/15 ≈ 0.533
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 3)): 2/8 ≈ 0.250
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 8/15 ≈ 0.533
      ├── Some((5, 6)): 8/15 ≈ 0.533
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 18/24 ≈ 0.750
    ├── Some((3, 6)): 52/105 ≈ 0.495
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 7/14 ≈ 0.500
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 14/21 ≈ 0.667
      └── Some((6, 8)): 2/8 ≈ 0.250
    ├── Some((3, 7)): 57/113 ≈ 0.504
      ├── Some((7, 0)): 7/13 ≈ 0.538
      ├── Some((7, 1)): 9/15 ≈ 0.600
      ├── Some((7, 2)): 7/13 ≈ 0.538
      ├── Some((7, 3)): 10/16 ≈ 0.625
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((3, 8)): 40/88 ≈ 0.455
      ├── Some((8, 0)): 4/9 ≈ 0.444
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 0/5 ≈ 0.000
      ├── Some((8, 3)): 7/12 ≈ 0.583
      ├── Some((8, 4)): 10/15 ≈ 0.667
      ├── Some((8, 5)): 7/12 ≈ 0.583
      ├── Some((8, 6)): 0/5 ≈ 0.000
      ├── Some((8, 7)): 2/7 ≈ 0.286
      └── Some((8, 8)): 6/12 ≈ 0.500
  ├── Some((6, 4)): 608/1170 ≈ 0.520
    ├── Some((4, 0)): 92/165 ≈ 0.558
      ├── Some((0, 0)): 21/29 ≈ 0.724
      ├── Some((0, 1)): 1/8 ≈ 0.125
      ├── Some((0, 2)): 3/11 ≈ 0.273
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 22/30 ≈ 0.733
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 6)): 8/16 ≈ 0.500
      ├── Some((0, 7)): 9/17 ≈ 0.529
      └── Some((0, 8)): 10/19 ≈ 0.526
    ├── Some((4, 1)): 58/117 ≈ 0.496
      ├── Some((1, 0)): 2/9 ≈ 0.222
      ├── Some((1, 1)): 13/21 ≈ 0.619
      ├── Some((1, 2)): 5/12 ≈ 0.417
      ├── Some((1, 3)): 10/18 ≈ 0.556
      ├── Some((1, 4)): 3/10 ≈ 0.300
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 4/11 ≈ 0.364
      └── Some((1, 8)): 15/22 ≈ 0.682
    ├── Some((4, 2)): 87/158 ≈ 0.551
      ├── Some((2, 0)): 21/28 ≈ 0.750
      ├── Some((2, 1)): 2/9 ≈ 0.222
      ├── Some((2, 2)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 12/20 ≈ 0.600
      ├── Some((2, 4)): 20/28 ≈ 0.714
      ├── Some((2, 5)): 8/16 ≈ 0.500
      ├── Some((2, 6)): 5/13 ≈ 0.385
      ├── Some((2, 7)): 5/13 ≈ 0.385
      └── Some((2, 8)): 7/15 ≈ 0.467
    ├── Some((4, 3)): 50/105 ≈ 0.476
      ├── Some((3, 0)): 0/6 ≈ 0.000
      ├── Some((3, 1)): 3/9 ≈ 0.333
      ├── Some((3, 2)): 10/16 ≈ 0.625
      ├── Some((3, 3)): 4/10 ≈ 0.400
      ├── Some((3, 4)): 12/18 ≈ 0.667
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 9/15 ≈ 0.600
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((4, 4)): 71/135 ≈ 0.526
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 14/22 ≈ 0.636
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 16/24 ≈ 0.667
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((4, 5)): 76/143 ≈ 0.531
      ├── Some((5, 0)): 5/12 ≈ 0.417
      ├── Some((5, 1)): 17/24 ≈ 0.708
      ├── Some((5, 2)): 12/20 ≈ 0.600
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 4/11 ≈ 0.364
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 7/14 ≈ 0.500
      └── Some((5, 8)): 13/21 ≈ 0.619
    ├── Some((4, 6)): 22/62 ≈ 0.355
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 6/11 ≈ 0.545
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((4, 7)): 76/143 ≈ 0.531
      ├── Some((7, 0)): 12/20 ≈ 0.600
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 16/23 ≈ 0.696
      ├── Some((7, 3)): 13/21 ≈ 0.619
      ├── Some((7, 4)): 13/21 ≈ 0.619
      ├── Some((7, 5)): 4/11 ≈ 0.364
      ├── Some((7, 6)): 3/10 ≈ 0.300
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 8/15 ≈ 0.533
    └── Some((4, 8)): 75/141 ≈ 0.532
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 9/16 ≈ 0.562
      ├── Some((8, 2)): 10/18 ≈ 0.556
      ├── Some((8, 3)): 6/13 ≈ 0.462
      ├── Some((8, 4)): 12/20 ≈ 0.600
      ├── Some((8, 5)): 3/10 ≈ 0.300
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 12/20 ≈ 0.600
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((6, 5)): 483/956 ≈ 0.505
    ├── Some((5, 0)): 55/108 ≈ 0.509
      ├── Some((0, 0)): 5/11 ≈ 0.455
      ├── Some((0, 1)): 9/15 ≈ 0.600
      ├── Some((0, 2)): 9/15 ≈ 0.600
      ├── Some((0, 3)): 9/15 ≈ 0.600
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 10/16 ≈ 0.625
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((5, 1)): 67/126 ≈ 0.532
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 1)): 3/10 ≈ 0.300
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 3)): 15/23 ≈ 0.652
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 14/22 ≈ 0.636
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 8/15 ≈ 0.533
    ├── Some((5, 2)): 25/64 ≈ 0.391
      ├── Some((2, 0)): 1/5 ≈ 0.200
      ├── Some((2, 1)): 0/4 ≈ 0.000
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 5/9 ≈ 0.556
      ├── Some((2, 4)): 0/4 ≈ 0.000
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 6/10 ≈ 0.600
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 7/11 ≈ 0.636
    ├── Some((5, 3)): 51/103 ≈ 0.495
      ├── Some((3, 0)): 7/13 ≈ 0.538
      ├── Some((3, 1)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 6/12 ≈ 0.500
      ├── Some((3, 3)): 9/15 ≈ 0.600
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 9/15 ≈ 0.600
      ├── Some((3, 6)): 6/12 ≈ 0.500
      ├── Some((3, 7)): 7/13 ≈ 0.538
      └── Some((3, 8)): 1/6 ≈ 0.167
    ├── Some((5, 4)): 50/101 ≈ 0.495
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 7/12 ≈ 0.583
      ├── Some((4, 2)): 7/12 ≈ 0.583
      ├── Some((4, 3)): 6/11 ≈ 0.545
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 7/12 ≈ 0.583
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((5, 5)): 78/141 ≈ 0.553
      ├── Some((5, 0)): 7/15 ≈ 0.467
      ├── Some((5, 1)): 16/23 ≈ 0.696
      ├── Some((5, 2)): 12/20 ≈ 0.600
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 10/18 ≈ 0.556
      ├── Some((5, 7)): 7/15 ≈ 0.467
      └── Some((5, 8)): 13/21 ≈ 0.619
    ├── Some((5, 6)): 59/114 ≈ 0.518
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 10/17 ≈ 0.588
      ├── Some((6, 2)): 8/15 ≈ 0.533
      ├── Some((6, 3)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 6/13 ≈ 0.462
      ├── Some((6, 6)): 9/16 ≈ 0.562
      ├── Some((6, 7)): 4/11 ≈ 0.364
      └── Some((6, 8)): 12/19 ≈ 0.632
    ├── Some((5, 7)): 49/100 ≈ 0.490
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 7/13 ≈ 0.538
      ├── Some((7, 2)): 8/13 ≈ 0.615
      ├── Some((7, 3)): 1/6 ≈ 0.167
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 6/12 ≈ 0.500
      ├── Some((7, 7)): 9/14 ≈ 0.643
      └── Some((7, 8)): 8/14 ≈ 0.571
    └── Some((5, 8)): 48/98 ≈ 0.490
      ├── Some((8, 0)): 8/13 ≈ 0.615
      ├── Some((8, 1)): 8/13 ≈ 0.615
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 3/9 ≈ 0.333
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 7/13 ≈ 0.538
      ├── Some((8, 6)): 10/15 ≈ 0.667
      ├── Some((8, 7)): 2/7 ≈ 0.286
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((6, 6)): 543/1059 ≈ 0.513
    ├── Some((6, 0)): 65/129 ≈ 0.504
      ├── Some((0, 0)): 8/15 ≈ 0.533
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 5/12 ≈ 0.417
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 10/17 ≈ 0.588
      ├── Some((0, 7)): 2/9 ≈ 0.222
      └── Some((0, 8)): 14/21 ≈ 0.667
    ├── Some((6, 1)): 50/106 ≈ 0.472
      ├── Some((1, 0)): 8/15 ≈ 0.533
      ├── Some((1, 1)): 10/17 ≈ 0.588
      ├── Some((1, 2)): 3/10 ≈ 0.300
      ├── Some((1, 3)): 5/12 ≈ 0.417
      ├── Some((1, 4)): 4/11 ≈ 0.364
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 7)): 2/9 ≈ 0.222
      └── Some((1, 8)): 9/16 ≈ 0.562
    ├── Some((6, 2)): 46/100 ≈ 0.460
      ├── Some((2, 0)): 6/12 ≈ 0.500
      ├── Some((2, 1)): 9/15 ≈ 0.600
      ├── Some((2, 2)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 1/7 ≈ 0.143
      ├── Some((2, 5)): 7/13 ≈ 0.538
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 2/8 ≈ 0.250
      └── Some((2, 8)): 7/13 ≈ 0.538
    ├── Some((6, 3)): 56/115 ≈ 0.487
      ├── Some((3, 0)): 12/18 ≈ 0.667
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 1/7 ≈ 0.143
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 1/7 ≈ 0.143
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 2/8 ≈ 0.250
      └── Some((3, 8)): 10/17 ≈ 0.588
    ├── Some((6, 4)): 70/136 ≈ 0.515
      ├── Some((4, 0)): 10/18 ≈ 0.556
      ├── Some((4, 1)): 19/26 ≈ 0.731
      ├── Some((4, 2)): 2/9 ≈ 0.222
      ├── Some((4, 3)): 12/19 ≈ 0.632
      ├── Some((4, 4)): 2/9 ≈ 0.222
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 5/12 ≈ 0.417
      ├── Some((4, 7)): 12/20 ≈ 0.600
      └── Some((4, 8)): 1/8 ≈ 0.125
    ├── Some((6, 5)): 83/155 ≈ 0.535
      ├── Some((5, 0)): 4/12 ≈ 0.333
      ├── Some((5, 1)): 3/11 ≈ 0.273
      ├── Some((5, 2)): 14/22 ≈ 0.636
      ├── Some((5, 3)): 9/17 ≈ 0.529
      ├── Some((5, 4)): 10/18 ≈ 0.556
      ├── Some((5, 5)): 10/18 ≈ 0.556
      ├── Some((5, 6)): 14/22 ≈ 0.636
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 10/18 ≈ 0.556
    ├── Some((6, 7)): 64/127 ≈ 0.504
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 4/11 ≈ 0.364
      ├── Some((7, 2)): 10/17 ≈ 0.588
      ├── Some((7, 3)): 3/10 ≈ 0.300
      ├── Some((7, 4)): 4/11 ≈ 0.364
      ├── Some((7, 5)): 10/17 ≈ 0.588
      ├── Some((7, 6)): 13/20 ≈ 0.650
      ├── Some((7, 7)): 12/19 ≈ 0.632
      └── Some((7, 8)): 0/6 ≈ 0.000
    └── Some((6, 8)): 108/190 ≈ 0.568
      ├── Some((8, 0)): 9/18 ≈ 0.500
      ├── Some((8, 1)): 12/21 ≈ 0.571
      ├── Some((8, 2)): 15/24 ≈ 0.625
      ├── Some((8, 3)): 11/20 ≈ 0.550
      ├── Some((8, 4)): 6/15 ≈ 0.400
      ├── Some((8, 5)): 6/15 ≈ 0.400
      ├── Some((8, 6)): 18/28 ≈ 0.643
      ├── Some((8, 7)): 23/32 ≈ 0.719
      └── Some((8, 8)): 7/16 ≈ 0.438
  ├── Some((6, 7)): 739/1392 ≈ 0.531
    ├── Some((7, 0)): 98/177 ≈ 0.554
      ├── Some((0, 0)): 11/20 ≈ 0.550
      ├── Some((0, 1)): 9/18 ≈ 0.500
      ├── Some((0, 2)): 7/15 ≈ 0.467
      ├── Some((0, 3)): 13/22 ≈ 0.591
      ├── Some((0, 4)): 6/14 ≈ 0.429
      ├── Some((0, 5)): 25/34 ≈ 0.735
      ├── Some((0, 6)): 16/25 ≈ 0.640
      ├── Some((0, 7)): 4/12 ≈ 0.333
      └── Some((0, 8)): 7/16 ≈ 0.438
    ├── Some((7, 1)): 80/152 ≈ 0.526
      ├── Some((1, 0)): 17/26 ≈ 0.654
      ├── Some((1, 1)): 7/16 ≈ 0.438
      ├── Some((1, 2)): 18/28 ≈ 0.643
      ├── Some((1, 3)): 1/9 ≈ 0.111
      ├── Some((1, 4)): 6/15 ≈ 0.400
      ├── Some((1, 5)): 7/16 ≈ 0.438
      ├── Some((1, 7)): 15/24 ≈ 0.625
      └── Some((1, 8)): 8/17 ≈ 0.471
    ├── Some((7, 2)): 102/183 ≈ 0.557
      ├── Some((2, 0)): 5/13 ≈ 0.385
      ├── Some((2, 1)): 16/25 ≈ 0.640
      ├── Some((2, 2)): 8/17 ≈ 0.471
      ├── Some((2, 3)): 7/16 ≈ 0.438
      ├── Some((2, 4)): 30/39 ≈ 0.769
      ├── Some((2, 5)): 12/21 ≈ 0.571
      ├── Some((2, 6)): 8/17 ≈ 0.471
      ├── Some((2, 7)): 5/14 ≈ 0.357
      └── Some((2, 8)): 11/20 ≈ 0.550
    ├── Some((7, 3)): 75/144 ≈ 0.521
      ├── Some((3, 0)): 10/18 ≈ 0.556
      ├── Some((3, 1)): 10/18 ≈ 0.556
      ├── Some((3, 2)): 5/12 ≈ 0.417
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 14/22 ≈ 0.636
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 7/14 ≈ 0.500
      ├── Some((3, 7)): 7/15 ≈ 0.467
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((7, 4)): 78/149 ≈ 0.523
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 4/11 ≈ 0.364
      ├── Some((4, 2)): 4/12 ≈ 0.333
      ├── Some((4, 3)): 7/15 ≈ 0.467
      ├── Some((4, 4)): 10/18 ≈ 0.556
      ├── Some((4, 5)): 7/15 ≈ 0.467
      ├── Some((4, 6)): 22/30 ≈ 0.733
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((7, 5)): 77/147 ≈ 0.524
      ├── Some((5, 0)): 13/21 ≈ 0.619
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 16/24 ≈ 0.667
      ├── Some((5, 3)): 8/16 ≈ 0.500
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 6/14 ≈ 0.429
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((7, 6)): 80/152 ≈ 0.526
      ├── Some((6, 0)): 1/8 ≈ 0.125
      ├── Some((6, 1)): 9/18 ≈ 0.500
      ├── Some((6, 2)): 14/23 ≈ 0.609
      ├── Some((6, 3)): 4/12 ≈ 0.333
      ├── Some((6, 4)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 18/28 ≈ 0.643
      ├── Some((6, 6)): 6/15 ≈ 0.400
      └── Some((6, 8)): 18/28 ≈ 0.643
    ├── Some((7, 7)): 70/137 ≈ 0.511
      ├── Some((7, 0)): 8/16 ≈ 0.500
      ├── Some((7, 1)): 4/12 ≈ 0.333
      ├── Some((7, 2)): 1/8 ≈ 0.125
      ├── Some((7, 3)): 8/17 ≈ 0.471
      ├── Some((7, 4)): 15/24 ≈ 0.625
      ├── Some((7, 5)): 7/15 ≈ 0.467
      ├── Some((7, 6)): 16/25 ≈ 0.640
      └── Some((7, 8)): 10/19 ≈ 0.526
    └── Some((7, 8)): 79/150 ≈ 0.527
      ├── Some((8, 0)): 5/12 ≈ 0.417
      ├── Some((8, 1)): 10/18 ≈ 0.556
      ├── Some((8, 2)): 10/18 ≈ 0.556
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 6/14 ≈ 0.429
      ├── Some((8, 5)): 11/19 ≈ 0.579
      ├── Some((8, 6)): 11/19 ≈ 0.579
      ├── Some((8, 7)): 7/15 ≈ 0.467
      └── Some((8, 8)): 11/19 ≈ 0.579
  └── Some((6, 8)): 391/796 ≈ 0.491
    ├── Some((8, 0)): 32/72 ≈ 0.444
      ├── Some((0, 0)): 4/8 ≈ 0.500
      ├── Some((0, 1)): 6/10 ≈ 0.600
      ├── Some((0, 2)): 0/4 ≈ 0.000
      ├── Some((0, 3)): 9/13 ≈ 0.692
      ├── Some((0, 4)): 4/8 ≈ 0.500
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((8, 1)): 37/80 ≈ 0.463
      ├── Some((1, 0)): 8/14 ≈ 0.571
      ├── Some((1, 1)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 2/7 ≈ 0.286
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 11/16 ≈ 0.688
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((8, 2)): 31/71 ≈ 0.437
      ├── Some((2, 0)): 4/8 ≈ 0.500
      ├── Some((2, 1)): 5/9 ≈ 0.556
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 6/10 ≈ 0.600
      ├── Some((2, 4)): 7/11 ≈ 0.636
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 1/5 ≈ 0.200
      ├── Some((2, 7)): 4/9 ≈ 0.444
      └── Some((2, 8)): 0/4 ≈ 0.000
    ├── Some((8, 3)): 68/124 ≈ 0.548
      ├── Some((3, 0)): 1/7 ≈ 0.143
      ├── Some((3, 1)): 12/18 ≈ 0.667
      ├── Some((3, 2)): 10/16 ≈ 0.625
      ├── Some((3, 3)): 15/21 ≈ 0.714
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 6/12 ≈ 0.500
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 9/15 ≈ 0.600
    ├── Some((8, 4)): 64/118 ≈ 0.542
      ├── Some((4, 0)): 8/14 ≈ 0.571
      ├── Some((4, 1)): 5/11 ≈ 0.455
      ├── Some((4, 2)): 13/19 ≈ 0.684
      ├── Some((4, 3)): 1/7 ≈ 0.143
      ├── Some((4, 4)): 10/16 ≈ 0.625
      ├── Some((4, 5)): 0/6 ≈ 0.000
      ├── Some((4, 6)): 15/21 ≈ 0.714
      ├── Some((4, 7)): 7/13 ≈ 0.538
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((8, 5)): 30/69 ≈ 0.435
      ├── Some((5, 0)): 4/9 ≈ 0.444
      ├── Some((5, 1)): 0/4 ≈ 0.000
      ├── Some((5, 2)): 0/4 ≈ 0.000
      ├── Some((5, 3)): 5/9 ≈ 0.556
      ├── Some((5, 4)): 5/9 ≈ 0.556
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 8/12 ≈ 0.667
      ├── Some((5, 7)): 2/7 ≈ 0.286
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((8, 6)): 76/134 ≈ 0.567
      ├── Some((6, 0)): 18/25 ≈ 0.720
      ├── Some((6, 1)): 9/16 ≈ 0.562
      ├── Some((6, 2)): 13/21 ≈ 0.619
      ├── Some((6, 3)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 1/8 ≈ 0.125
      ├── Some((6, 5)): 9/16 ≈ 0.562
      ├── Some((6, 6)): 10/18 ≈ 0.556
      └── Some((6, 7)): 8/15 ≈ 0.533
    ├── Some((8, 7)): 25/62 ≈ 0.403
      ├── Some((7, 0)): 1/5 ≈ 0.200
      ├── Some((7, 1)): 6/10 ≈ 0.600
      ├── Some((7, 2)): 0/4 ≈ 0.000
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 5/9 ≈ 0.556
      ├── Some((7, 5)): 1/5 ≈ 0.200
      ├── Some((7, 6)): 7/11 ≈ 0.636
      ├── Some((7, 7)): 2/6 ≈ 0.333
      └── Some((7, 8)): 2/7 ≈ 0.286
    └── Some((8, 8)): 27/65 ≈ 0.415
      ├── Some((8, 0)): 5/10 ≈ 0.500
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 3/8 ≈ 0.375
      ├── Some((8, 3)): 4/9 ≈ 0.444
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 1/5 ≈ 0.200
      └── Some((8, 7)): 7/11 ≈ 0.636
├── Some((1, 7)): 5740/11104 ≈ 0.517
  ├── Some((7, 0)): 674/1297 ≈ 0.520
    ├── Some((0, 0)): 104/186 ≈ 0.559
      ├── Some((0, 1)): 10/20 ≈ 0.500
      ├── Some((0, 2)): 12/22 ≈ 0.545
      ├── Some((0, 3)): 21/32 ≈ 0.656
      ├── Some((0, 4)): 22/33 ≈ 0.667
      ├── Some((0, 5)): 15/26 ≈ 0.577
      ├── Some((0, 6)): 8/18 ≈ 0.444
      ├── Some((0, 7)): 6/15 ≈ 0.400
      └── Some((0, 8)): 9/19 ≈ 0.474
    ├── Some((0, 1)): 45/100 ≈ 0.450
      ├── Some((1, 0)): 2/8 ≈ 0.250
      ├── Some((1, 1)): 8/15 ≈ 0.533
      ├── Some((1, 2)): 4/11 ≈ 0.364
      ├── Some((1, 3)): 8/15 ≈ 0.533
      ├── Some((1, 4)): 10/17 ≈ 0.588
      ├── Some((1, 5)): 4/11 ≈ 0.364
      ├── Some((1, 6)): 5/12 ≈ 0.417
      └── Some((1, 8)): 3/10 ≈ 0.300
    ├── Some((0, 2)): 53/112 ≈ 0.473
      ├── Some((2, 0)): 10/17 ≈ 0.588
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 2/8 ≈ 0.250
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 7/14 ≈ 0.500
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 10/17 ≈ 0.588
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 10/17 ≈ 0.588
    ├── Some((0, 3)): 97/177 ≈ 0.548
      ├── Some((3, 0)): 11/20 ≈ 0.550
      ├── Some((3, 1)): 11/20 ≈ 0.550
      ├── Some((3, 2)): 11/20 ≈ 0.550
      ├── Some((3, 3)): 12/21 ≈ 0.571
      ├── Some((3, 4)): 9/17 ≈ 0.529
      ├── Some((3, 5)): 13/22 ≈ 0.591
      ├── Some((3, 6)): 9/18 ≈ 0.500
      ├── Some((3, 7)): 16/25 ≈ 0.640
      └── Some((3, 8)): 5/13 ≈ 0.385
    ├── Some((0, 4)): 73/142 ≈ 0.514
      ├── Some((4, 0)): 9/17 ≈ 0.529
      ├── Some((4, 1)): 14/22 ≈ 0.636
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 9/17 ≈ 0.529
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 2/9 ≈ 0.222
      ├── Some((4, 6)): 11/19 ≈ 0.579
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 8/16 ≈ 0.500
    ├── Some((0, 5)): 74/143 ≈ 0.517
      ├── Some((5, 0)): 8/16 ≈ 0.500
      ├── Some((5, 1)): 9/17 ≈ 0.529
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 14/22 ≈ 0.636
      ├── Some((5, 7)): 13/21 ≈ 0.619
      └── Some((5, 8)): 5/12 ≈ 0.417
    ├── Some((0, 6)): 74/143 ≈ 0.517
      ├── Some((6, 0)): 5/12 ≈ 0.417
      ├── Some((6, 1)): 11/19 ≈ 0.579
      ├── Some((6, 2)): 7/15 ≈ 0.467
      ├── Some((6, 3)): 2/9 ≈ 0.222
      ├── Some((6, 4)): 12/20 ≈ 0.600
      ├── Some((6, 5)): 6/13 ≈ 0.462
      ├── Some((6, 6)): 9/17 ≈ 0.529
      ├── Some((6, 7)): 17/25 ≈ 0.680
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((0, 7)): 92/169 ≈ 0.544
      ├── Some((7, 1)): 4/13 ≈ 0.308
      ├── Some((7, 2)): 6/15 ≈ 0.400
      ├── Some((7, 3)): 8/17 ≈ 0.471
      ├── Some((7, 4)): 17/27 ≈ 0.630
      ├── Some((7, 5)): 14/24 ≈ 0.583
      ├── Some((7, 6)): 18/28 ≈ 0.643
      ├── Some((7, 7)): 10/19 ≈ 0.526
      └── Some((7, 8)): 15/25 ≈ 0.600
    └── Some((0, 8)): 61/124 ≈ 0.492
      ├── Some((8, 0)): 6/13 ≈ 0.462
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 17/24 ≈ 0.708
      ├── Some((8, 4)): 4/11 ≈ 0.364
      ├── Some((8, 5)): 10/17 ≈ 0.588
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 8/15 ≈ 0.533
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((7, 1)): 532/1052 ≈ 0.506
    ├── Some((1, 0)): 50/108 ≈ 0.463
      ├── Some((0, 0)): 15/21 ≈ 0.714
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 6/13 ≈ 0.462
      ├── Some((0, 5)): 2/8 ≈ 0.250
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 3/9 ≈ 0.333
      └── Some((0, 8)): 4/10 ≈ 0.400
    ├── Some((1, 1)): 62/126 ≈ 0.492
      ├── Some((1, 0)): 12/21 ≈ 0.571
      ├── Some((1, 2)): 5/14 ≈ 0.357
      ├── Some((1, 3)): 9/18 ≈ 0.500
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 6/15 ≈ 0.400
      ├── Some((1, 6)): 8/17 ≈ 0.471
      └── Some((1, 8)): 13/22 ≈ 0.591
    ├── Some((1, 2)): 79/151 ≈ 0.523
      ├── Some((2, 0)): 9/17 ≈ 0.529
      ├── Some((2, 1)): 4/12 ≈ 0.333
      ├── Some((2, 2)): 4/12 ≈ 0.333
      ├── Some((2, 3)): 5/13 ≈ 0.385
      ├── Some((2, 4)): 12/20 ≈ 0.600
      ├── Some((2, 5)): 20/28 ≈ 0.714
      ├── Some((2, 6)): 8/16 ≈ 0.500
      ├── Some((2, 7)): 6/14 ≈ 0.429
      └── Some((2, 8)): 10/18 ≈ 0.556
    ├── Some((1, 3)): 120/209 ≈ 0.574
      ├── Some((3, 0)): 27/38 ≈ 0.711
      ├── Some((3, 1)): 6/15 ≈ 0.400
      ├── Some((3, 2)): 9/19 ≈ 0.474
      ├── Some((3, 3)): 26/37 ≈ 0.703
      ├── Some((3, 4)): 6/15 ≈ 0.400
      ├── Some((3, 5)): 6/15 ≈ 0.400
      ├── Some((3, 6)): 16/26 ≈ 0.615
      ├── Some((3, 7)): 13/23 ≈ 0.565
      └── Some((3, 8)): 10/20 ≈ 0.500
    ├── Some((1, 4)): 100/181 ≈ 0.552
      ├── Some((4, 0)): 12/21 ≈ 0.571
      ├── Some((4, 1)): 9/18 ≈ 0.500
      ├── Some((4, 2)): 8/17 ≈ 0.471
      ├── Some((4, 3)): 9/18 ≈ 0.500
      ├── Some((4, 4)): 16/25 ≈ 0.640
      ├── Some((4, 5)): 18/27 ≈ 0.667
      ├── Some((4, 6)): 14/23 ≈ 0.609
      ├── Some((4, 7)): 7/16 ≈ 0.438
      └── Some((4, 8)): 6/15 ≈ 0.400
    ├── Some((1, 5)): 42/95 ≈ 0.442
      ├── Some((5, 0)): 3/9 ≈ 0.333
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 8/14 ≈ 0.571
      ├── Some((5, 5)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 1/6 ≈ 0.167
      ├── Some((5, 7)): 8/14 ≈ 0.571
      └── Some((5, 8)): 2/8 ≈ 0.250
    ├── Some((1, 6)): 41/94 ≈ 0.436
      ├── Some((6, 0)): 0/5 ≈ 0.000
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 2/8 ≈ 0.250
      ├── Some((6, 3)): 1/7 ≈ 0.143
      ├── Some((6, 4)): 8/14 ≈ 0.571
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 6)): 12/18 ≈ 0.667
      ├── Some((6, 7)): 1/7 ≈ 0.143
      └── Some((6, 8)): 7/13 ≈ 0.538
    └── Some((1, 8)): 37/87 ≈ 0.425
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 2/7 ≈ 0.286
      ├── Some((8, 2)): 3/8 ≈ 0.375
      ├── Some((8, 3)): 13/18 ≈ 0.722
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 3/9 ≈ 0.333
      ├── Some((8, 6)): 4/10 ≈ 0.400
      ├── Some((8, 7)): 3/9 ≈ 0.333
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((7, 2)): 549/1082 ≈ 0.507
    ├── Some((2, 0)): 47/100 ≈ 0.470
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 0/5 ≈ 0.000
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 10/15 ≈ 0.667
      ├── Some((0, 5)): 8/14 ≈ 0.571
      ├── Some((0, 6)): 7/13 ≈ 0.538
      ├── Some((0, 7)): 7/13 ≈ 0.538
      └── Some((0, 8)): 4/10 ≈ 0.400
    ├── Some((2, 1)): 88/159 ≈ 0.553
      ├── Some((1, 0)): 5/13 ≈ 0.385
      ├── Some((1, 1)): 14/23 ≈ 0.609
      ├── Some((1, 2)): 7/16 ≈ 0.438
      ├── Some((1, 3)): 5/14 ≈ 0.357
      ├── Some((1, 4)): 6/15 ≈ 0.400
      ├── Some((1, 5)): 20/29 ≈ 0.690
      ├── Some((1, 6)): 6/15 ≈ 0.400
      └── Some((1, 8)): 24/33 ≈ 0.727
    ├── Some((2, 2)): 32/77 ≈ 0.416
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 7/13 ≈ 0.538
      ├── Some((2, 7)): 1/6 ≈ 0.167
      └── Some((2, 8)): 3/9 ≈ 0.333
    ├── Some((2, 3)): 36/84 ≈ 0.429
      ├── Some((3, 0)): 6/11 ≈ 0.545
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 6/12 ≈ 0.500
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 8/13 ≈ 0.615
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((2, 4)): 64/125 ≈ 0.512
      ├── Some((4, 0)): 4/11 ≈ 0.364
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 7/14 ≈ 0.500
      ├── Some((4, 3)): 4/11 ≈ 0.364
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 14/20 ≈ 0.700
      ├── Some((4, 6)): 9/16 ≈ 0.562
      ├── Some((4, 7)): 8/15 ≈ 0.533
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((2, 5)): 40/90 ≈ 0.444
      ├── Some((5, 0)): 7/13 ≈ 0.538
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 3/8 ≈ 0.375
      ├── Some((5, 3)): 3/8 ≈ 0.375
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 5/11 ≈ 0.455
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 1/6 ≈ 0.167
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((2, 6)): 56/113 ≈ 0.496
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 8/15 ≈ 0.533
      ├── Some((6, 2)): 1/7 ≈ 0.143
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 9/16 ≈ 0.562
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 2/8 ≈ 0.250
      ├── Some((6, 7)): 10/16 ≈ 0.625
      └── Some((6, 8)): 11/17 ≈ 0.647
    ├── Some((2, 7)): 89/161 ≈ 0.553
      ├── Some((7, 0)): 21/30 ≈ 0.700
      ├── Some((7, 1)): 8/17 ≈ 0.471
      ├── Some((7, 3)): 12/21 ≈ 0.571
      ├── Some((7, 4)): 10/19 ≈ 0.526
      ├── Some((7, 5)): 5/13 ≈ 0.385
      ├── Some((7, 6)): 13/22 ≈ 0.591
      ├── Some((7, 7)): 12/21 ≈ 0.571
      └── Some((7, 8)): 8/17 ≈ 0.471
    └── Some((2, 8)): 97/172 ≈ 0.564
      ├── Some((8, 0)): 20/28 ≈ 0.714
      ├── Some((8, 1)): 10/19 ≈ 0.526
      ├── Some((8, 2)): 3/11 ≈ 0.273
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 13/22 ≈ 0.591
      ├── Some((8, 5)): 9/17 ≈ 0.529
      ├── Some((8, 6)): 17/26 ≈ 0.654
      ├── Some((8, 7)): 9/17 ≈ 0.529
      └── Some((8, 8)): 8/16 ≈ 0.500
  ├── Some((7, 3)): 720/1376 ≈ 0.523
    ├── Some((3, 0)): 66/133 ≈ 0.496
      ├── Some((0, 0)): 2/9 ≈ 0.222
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 5/12 ≈ 0.417
      ├── Some((0, 4)): 9/17 ≈ 0.529
      ├── Some((0, 5)): 11/19 ≈ 0.579
      ├── Some((0, 6)): 8/16 ≈ 0.500
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 11/19 ≈ 0.579
    ├── Some((3, 1)): 91/170 ≈ 0.535
      ├── Some((1, 0)): 8/18 ≈ 0.444
      ├── Some((1, 1)): 9/19 ≈ 0.474
      ├── Some((1, 2)): 13/23 ≈ 0.565
      ├── Some((1, 3)): 11/21 ≈ 0.524
      ├── Some((1, 4)): 24/34 ≈ 0.706
      ├── Some((1, 5)): 13/23 ≈ 0.565
      ├── Some((1, 6)): 7/16 ≈ 0.438
      └── Some((1, 8)): 6/15 ≈ 0.400
    ├── Some((3, 2)): 55/116 ≈ 0.474
      ├── Some((2, 0)): 2/8 ≈ 0.250
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 2)): 9/16 ≈ 0.562
      ├── Some((2, 3)): 12/19 ≈ 0.632
      ├── Some((2, 4)): 8/15 ≈ 0.533
      ├── Some((2, 5)): 6/13 ≈ 0.462
      ├── Some((2, 6)): 0/6 ≈ 0.000
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 8/15 ≈ 0.533
    ├── Some((3, 3)): 123/215 ≈ 0.572
      ├── Some((3, 0)): 16/28 ≈ 0.571
      ├── Some((3, 1)): 6/16 ≈ 0.375
      ├── Some((3, 2)): 15/26 ≈ 0.577
      ├── Some((3, 4)): 22/34 ≈ 0.647
      ├── Some((3, 5)): 22/34 ≈ 0.647
      ├── Some((3, 6)): 18/30 ≈ 0.600
      ├── Some((3, 7)): 5/15 ≈ 0.333
      └── Some((3, 8)): 19/31 ≈ 0.613
    ├── Some((3, 4)): 93/172 ≈ 0.541
      ├── Some((4, 0)): 8/16 ≈ 0.500
      ├── Some((4, 1)): 7/15 ≈ 0.467
      ├── Some((4, 2)): 15/24 ≈ 0.625
      ├── Some((4, 3)): 11/20 ≈ 0.550
      ├── Some((4, 4)): 9/18 ≈ 0.500
      ├── Some((4, 5)): 10/19 ≈ 0.526
      ├── Some((4, 6)): 19/28 ≈ 0.679
      ├── Some((4, 7)): 10/19 ≈ 0.526
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((3, 5)): 98/180 ≈ 0.544
      ├── Some((5, 0)): 16/25 ≈ 0.640
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 11/20 ≈ 0.550
      ├── Some((5, 3)): 6/15 ≈ 0.400
      ├── Some((5, 4)): 15/24 ≈ 0.625
      ├── Some((5, 5)): 10/19 ≈ 0.526
      ├── Some((5, 6)): 9/18 ≈ 0.500
      ├── Some((5, 7)): 19/29 ≈ 0.655
      └── Some((5, 8)): 8/17 ≈ 0.471
    ├── Some((3, 6)): 31/79 ≈ 0.392
      ├── Some((6, 0)): 6/12 ≈ 0.500
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 7/12 ≈ 0.583
    ├── Some((3, 7)): 109/195 ≈ 0.559
      ├── Some((7, 0)): 15/26 ≈ 0.577
      ├── Some((7, 1)): 14/25 ≈ 0.560
      ├── Some((7, 2)): 11/22 ≈ 0.500
      ├── Some((7, 4)): 9/19 ≈ 0.474
      ├── Some((7, 5)): 9/19 ≈ 0.474
      ├── Some((7, 6)): 19/30 ≈ 0.633
      ├── Some((7, 7)): 22/34 ≈ 0.647
      └── Some((7, 8)): 9/19 ≈ 0.474
    └── Some((3, 8)): 54/115 ≈ 0.470
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 5/12 ≈ 0.417
      ├── Some((8, 4)): 2/8 ≈ 0.250
      ├── Some((8, 5)): 2/8 ≈ 0.250
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 15/22 ≈ 0.682
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((7, 4)): 633/1226 ≈ 0.516
    ├── Some((4, 0)): 69/134 ≈ 0.515
      ├── Some((0, 0)): 7/14 ≈ 0.500
      ├── Some((0, 1)): 12/20 ≈ 0.600
      ├── Some((0, 2)): 9/16 ≈ 0.562
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 4/11 ≈ 0.364
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 9/16 ≈ 0.562
      ├── Some((0, 7)): 2/9 ≈ 0.222
      └── Some((0, 8)): 12/20 ≈ 0.600
    ├── Some((4, 1)): 67/132 ≈ 0.508
      ├── Some((1, 0)): 9/17 ≈ 0.529
      ├── Some((1, 1)): 5/13 ≈ 0.385
      ├── Some((1, 2)): 16/25 ≈ 0.640
      ├── Some((1, 3)): 7/15 ≈ 0.467
      ├── Some((1, 4)): 1/8 ≈ 0.125
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 13/22 ≈ 0.591
      └── Some((1, 8)): 2/9 ≈ 0.222
    ├── Some((4, 2)): 85/157 ≈ 0.541
      ├── Some((2, 0)): 0/7 ≈ 0.000
      ├── Some((2, 1)): 13/21 ≈ 0.619
      ├── Some((2, 2)): 6/14 ≈ 0.429
      ├── Some((2, 3)): 13/21 ≈ 0.619
      ├── Some((2, 4)): 9/17 ≈ 0.529
      ├── Some((2, 5)): 12/20 ≈ 0.600
      ├── Some((2, 6)): 8/16 ≈ 0.500
      ├── Some((2, 7)): 8/16 ≈ 0.500
      └── Some((2, 8)): 15/24 ≈ 0.625
    ├── Some((4, 3)): 55/114 ≈ 0.482
      ├── Some((3, 0)): 1/7 ≈ 0.143
      ├── Some((3, 1)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 10/17 ≈ 0.588
      ├── Some((3, 3)): 11/18 ≈ 0.611
      ├── Some((3, 4)): 0/6 ≈ 0.000
      ├── Some((3, 5)): 12/18 ≈ 0.667
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((4, 4)): 43/96 ≈ 0.448
      ├── Some((4, 0)): 6/13 ≈ 0.462
      ├── Some((4, 1)): 7/14 ≈ 0.500
      ├── Some((4, 2)): 8/15 ≈ 0.533
      ├── Some((4, 3)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 3/9 ≈ 0.333
      ├── Some((4, 6)): 6/13 ≈ 0.462
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 5/12 ≈ 0.417
    ├── Some((4, 5)): 83/155 ≈ 0.535
      ├── Some((5, 0)): 4/12 ≈ 0.333
      ├── Some((5, 1)): 5/13 ≈ 0.385
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 18/26 ≈ 0.692
      ├── Some((5, 4)): 8/16 ≈ 0.500
      ├── Some((5, 5)): 10/18 ≈ 0.556
      ├── Some((5, 6)): 5/13 ≈ 0.385
      ├── Some((5, 7)): 16/24 ≈ 0.667
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((4, 6)): 78/147 ≈ 0.531
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 13/21 ≈ 0.619
      ├── Some((6, 2)): 13/21 ≈ 0.619
      ├── Some((6, 3)): 13/21 ≈ 0.619
      ├── Some((6, 4)): 8/16 ≈ 0.500
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 3/10 ≈ 0.300
      ├── Some((6, 7)): 15/23 ≈ 0.652
      └── Some((6, 8)): 1/8 ≈ 0.125
    ├── Some((4, 7)): 68/133 ≈ 0.511
      ├── Some((7, 0)): 12/20 ≈ 0.600
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 10/18 ≈ 0.556
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 5)): 4/12 ≈ 0.333
      ├── Some((7, 6)): 12/21 ≈ 0.571
      ├── Some((7, 7)): 7/15 ≈ 0.467
      └── Some((7, 8)): 5/13 ≈ 0.385
    └── Some((4, 8)): 85/157 ≈ 0.541
      ├── Some((8, 0)): 9/17 ≈ 0.529
      ├── Some((8, 1)): 1/8 ≈ 0.125
      ├── Some((8, 2)): 13/22 ≈ 0.591
      ├── Some((8, 3)): 9/17 ≈ 0.529
      ├── Some((8, 4)): 12/20 ≈ 0.600
      ├── Some((8, 5)): 12/20 ≈ 0.600
      ├── Some((8, 6)): 11/19 ≈ 0.579
      ├── Some((8, 7)): 5/13 ≈ 0.385
      └── Some((8, 8)): 12/20 ≈ 0.600
  ├── Some((7, 5)): 486/972 ≈ 0.500
    ├── Some((5, 0)): 47/98 ≈ 0.480
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 10/16 ≈ 0.625
      ├── Some((0, 2)): 1/6 ≈ 0.167
      ├── Some((0, 3)): 8/14 ≈ 0.571
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 2/8 ≈ 0.250
      ├── Some((0, 6)): 4/10 ≈ 0.400
      ├── Some((0, 7)): 11/16 ≈ 0.688
      └── Some((0, 8)): 0/5 ≈ 0.000
    ├── Some((5, 1)): 78/143 ≈ 0.545
      ├── Some((1, 0)): 9/17 ≈ 0.529
      ├── Some((1, 1)): 7/15 ≈ 0.467
      ├── Some((1, 2)): 15/24 ≈ 0.625
      ├── Some((1, 3)): 6/14 ≈ 0.429
      ├── Some((1, 4)): 10/18 ≈ 0.556
      ├── Some((1, 5)): 9/17 ≈ 0.529
      ├── Some((1, 6)): 4/12 ≈ 0.333
      └── Some((1, 8)): 17/25 ≈ 0.680
    ├── Some((5, 2)): 61/118 ≈ 0.517
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 5/12 ≈ 0.417
      ├── Some((2, 2)): 9/16 ≈ 0.562
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 13/19 ≈ 0.684
      ├── Some((2, 5)): 11/17 ≈ 0.647
      ├── Some((2, 6)): 0/6 ≈ 0.000
      ├── Some((2, 7)): 1/7 ≈ 0.143
      └── Some((2, 8)): 11/17 ≈ 0.647
    ├── Some((5, 3)): 74/137 ≈ 0.540
      ├── Some((3, 0)): 4/11 ≈ 0.364
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 11/18 ≈ 0.611
      ├── Some((3, 3)): 3/10 ≈ 0.300
      ├── Some((3, 4)): 15/22 ≈ 0.682
      ├── Some((3, 5)): 9/16 ≈ 0.562
      ├── Some((3, 6)): 15/22 ≈ 0.682
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((5, 4)): 27/68 ≈ 0.397
      ├── Some((4, 0)): 8/12 ≈ 0.667
      ├── Some((4, 1)): 6/10 ≈ 0.600
      ├── Some((4, 2)): 0/4 ≈ 0.000
      ├── Some((4, 3)): 1/6 ≈ 0.167
      ├── Some((4, 4)): 6/10 ≈ 0.600
      ├── Some((4, 5)): 1/6 ≈ 0.167
      ├── Some((4, 6)): 0/4 ≈ 0.000
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((5, 5)): 61/118 ≈ 0.517
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 1)): 9/16 ≈ 0.562
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 8/15 ≈ 0.533
      ├── Some((5, 4)): 12/20 ≈ 0.600
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 0/6 ≈ 0.000
      └── Some((5, 8)): 14/22 ≈ 0.636
    ├── Some((5, 6)): 71/133 ≈ 0.534
      ├── Some((6, 0)): 6/13 ≈ 0.462
      ├── Some((6, 1)): 9/16 ≈ 0.562
      ├── Some((6, 2)): 11/18 ≈ 0.611
      ├── Some((6, 3)): 4/11 ≈ 0.364
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 12/19 ≈ 0.632
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 13/20 ≈ 0.650
    ├── Some((5, 7)): 28/70 ≈ 0.400
      ├── Some((7, 0)): 3/8 ≈ 0.375
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 6/12 ≈ 0.500
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 2/7 ≈ 0.286
      ├── Some((7, 7)): 2/7 ≈ 0.286
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((5, 8)): 39/86 ≈ 0.453
      ├── Some((8, 0)): 9/14 ≈ 0.643
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 7/12 ≈ 0.583
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((7, 6)): 620/1204 ≈ 0.515
    ├── Some((6, 0)): 68/133 ≈ 0.511
      ├── Some((0, 0)): 3/10 ≈ 0.300
      ├── Some((0, 1)): 1/8 ≈ 0.125
      ├── Some((0, 2)): 1/8 ≈ 0.125
      ├── Some((0, 3)): 1/8 ≈ 0.125
      ├── Some((0, 4)): 14/22 ≈ 0.636
      ├── Some((0, 5)): 15/22 ≈ 0.682
      ├── Some((0, 6)): 16/23 ≈ 0.696
      ├── Some((0, 7)): 9/17 ≈ 0.529
      └── Some((0, 8)): 7/14 ≈ 0.500
    ├── Some((6, 1)): 123/211 ≈ 0.583
      ├── Some((1, 0)): 8/18 ≈ 0.444
      ├── Some((1, 1)): 11/22 ≈ 0.500
      ├── Some((1, 2)): 7/17 ≈ 0.412
      ├── Some((1, 3)): 17/29 ≈ 0.586
      ├── Some((1, 4)): 7/17 ≈ 0.412
      ├── Some((1, 5)): 23/35 ≈ 0.657
      ├── Some((1, 6)): 33/45 ≈ 0.733
      └── Some((1, 8)): 16/27 ≈ 0.593
    ├── Some((6, 2)): 72/139 ≈ 0.518
      ├── Some((2, 0)): 13/21 ≈ 0.619
      ├── Some((2, 1)): 5/12 ≈ 0.417
      ├── Some((2, 2)): 3/10 ≈ 0.300
      ├── Some((2, 3)): 8/15 ≈ 0.533
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 8/15 ≈ 0.533
      ├── Some((2, 6)): 8/15 ≈ 0.533
      ├── Some((2, 7)): 3/10 ≈ 0.300
      └── Some((2, 8)): 14/22 ≈ 0.636
    ├── Some((6, 3)): 60/121 ≈ 0.496
      ├── Some((3, 0)): 7/14 ≈ 0.500
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 11/18 ≈ 0.611
      ├── Some((3, 3)): 2/8 ≈ 0.250
      ├── Some((3, 4)): 8/15 ≈ 0.533
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 4/10 ≈ 0.400
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 9/16 ≈ 0.562
    ├── Some((6, 4)): 76/145 ≈ 0.524
      ├── Some((4, 0)): 16/24 ≈ 0.667
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 10/18 ≈ 0.556
      ├── Some((4, 3)): 10/18 ≈ 0.556
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 5/12 ≈ 0.417
      ├── Some((4, 6)): 11/19 ≈ 0.579
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 3/10 ≈ 0.300
    ├── Some((6, 5)): 72/139 ≈ 0.518
      ├── Some((5, 0)): 3/10 ≈ 0.300
      ├── Some((5, 1)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 3)): 13/21 ≈ 0.619
      ├── Some((5, 4)): 2/9 ≈ 0.222
      ├── Some((5, 5)): 18/26 ≈ 0.692
      ├── Some((5, 6)): 15/23 ≈ 0.652
      ├── Some((5, 7)): 0/6 ≈ 0.000
      └── Some((5, 8)): 9/17 ≈ 0.529
    ├── Some((6, 6)): 16/53 ≈ 0.302
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 1/6 ≈ 0.167
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 0/4 ≈ 0.000
    ├── Some((6, 7)): 79/149 ≈ 0.530
      ├── Some((7, 0)): 11/20 ≈ 0.550
      ├── Some((7, 1)): 8/17 ≈ 0.471
      ├── Some((7, 2)): 0/7 ≈ 0.000
      ├── Some((7, 3)): 7/16 ≈ 0.438
      ├── Some((7, 4)): 17/26 ≈ 0.654
      ├── Some((7, 5)): 17/26 ≈ 0.654
      ├── Some((7, 7)): 11/20 ≈ 0.550
      └── Some((7, 8)): 7/16 ≈ 0.438
    └── Some((6, 8)): 54/113 ≈ 0.478
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 0/6 ≈ 0.000
      ├── Some((8, 3)): 9/16 ≈ 0.562
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 11/18 ≈ 0.611
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 1/7 ≈ 0.143
      └── Some((8, 8)): 12/18 ≈ 0.667
  ├── Some((7, 7)): 578/1132 ≈ 0.511
    ├── Some((7, 0)): 76/147 ≈ 0.517
      ├── Some((0, 0)): 1/8 ≈ 0.125
      ├── Some((0, 1)): 13/21 ≈ 0.619
      ├── Some((0, 2)): 12/20 ≈ 0.600
      ├── Some((0, 3)): 6/14 ≈ 0.429
      ├── Some((0, 4)): 15/23 ≈ 0.652
      ├── Some((0, 5)): 6/14 ≈ 0.429
      ├── Some((0, 6)): 4/11 ≈ 0.364
      ├── Some((0, 7)): 14/22 ≈ 0.636
      └── Some((0, 8)): 5/13 ≈ 0.385
    ├── Some((7, 1)): 81/155 ≈ 0.523
      ├── Some((1, 0)): 6/15 ≈ 0.400
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 2)): 8/17 ≈ 0.471
      ├── Some((1, 3)): 5/14 ≈ 0.357
      ├── Some((1, 4)): 6/15 ≈ 0.400
      ├── Some((1, 5)): 19/29 ≈ 0.655
      ├── Some((1, 6)): 10/19 ≈ 0.526
      └── Some((1, 8)): 15/25 ≈ 0.600
    ├── Some((7, 2)): 62/126 ≈ 0.492
      ├── Some((2, 0)): 1/8 ≈ 0.125
      ├── Some((2, 1)): 9/16 ≈ 0.562
      ├── Some((2, 2)): 8/15 ≈ 0.533
      ├── Some((2, 3)): 3/10 ≈ 0.300
      ├── Some((2, 4)): 15/22 ≈ 0.682
      ├── Some((2, 5)): 6/13 ≈ 0.462
      ├── Some((2, 6)): 10/17 ≈ 0.588
      ├── Some((2, 7)): 4/11 ≈ 0.364
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((7, 3)): 58/120 ≈ 0.483
      ├── Some((3, 0)): 6/13 ≈ 0.462
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 8/15 ≈ 0.533
      ├── Some((3, 5)): 4/11 ≈ 0.364
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 5/12 ≈ 0.417
    ├── Some((7, 4)): 51/110 ≈ 0.464
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 10/17 ≈ 0.588
      ├── Some((4, 2)): 6/13 ≈ 0.462
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 6/13 ≈ 0.462
      ├── Some((4, 7)): 5/12 ≈ 0.417
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((7, 5)): 80/153 ≈ 0.523
      ├── Some((5, 0)): 7/15 ≈ 0.467
      ├── Some((5, 1)): 20/29 ≈ 0.690
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 6/14 ≈ 0.429
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 15/24 ≈ 0.625
      └── Some((5, 8)): 1/8 ≈ 0.125
    ├── Some((7, 6)): 60/124 ≈ 0.484
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 9/17 ≈ 0.529
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 2/9 ≈ 0.222
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 5/12 ≈ 0.417
      ├── Some((6, 6)): 8/15 ≈ 0.533
      ├── Some((6, 7)): 14/21 ≈ 0.667
      └── Some((6, 8)): 4/11 ≈ 0.364
    └── Some((7, 8)): 110/196 ≈ 0.561
      ├── Some((8, 0)): 13/23 ≈ 0.565
      ├── Some((8, 1)): 14/24 ≈ 0.583
      ├── Some((8, 2)): 11/20 ≈ 0.550
      ├── Some((8, 3)): 5/14 ≈ 0.357
      ├── Some((8, 4)): 16/26 ≈ 0.615
      ├── Some((8, 5)): 12/21 ≈ 0.571
      ├── Some((8, 6)): 2/10 ≈ 0.200
      ├── Some((8, 7)): 21/31 ≈ 0.677
      └── Some((8, 8)): 16/26 ≈ 0.615
  └── Some((7, 8)): 948/1762 ≈ 0.538
    ├── Some((8, 0)): 54/119 ≈ 0.454
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 11/19 ≈ 0.579
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 4/11 ≈ 0.364
      ├── Some((0, 4)): 1/7 ≈ 0.143
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 13/21 ≈ 0.619
      ├── Some((0, 7)): 3/10 ≈ 0.300
      └── Some((0, 8)): 2/9 ≈ 0.222
    ├── Some((8, 1)): 142/249 ≈ 0.570
      ├── Some((1, 0)): 9/21 ≈ 0.429
      ├── Some((1, 1)): 9/21 ≈ 0.429
      ├── Some((1, 2)): 28/43 ≈ 0.651
      ├── Some((1, 3)): 10/22 ≈ 0.455
      ├── Some((1, 4)): 31/46 ≈ 0.674
      ├── Some((1, 5)): 12/25 ≈ 0.480
      ├── Some((1, 6)): 19/33 ≈ 0.576
      └── Some((1, 8)): 23/37 ≈ 0.622
    ├── Some((8, 2)): 108/200 ≈ 0.540
      ├── Some((2, 0)): 13/23 ≈ 0.565
      ├── Some((2, 1)): 14/24 ≈ 0.583
      ├── Some((2, 2)): 14/25 ≈ 0.560
      ├── Some((2, 3)): 8/18 ≈ 0.444
      ├── Some((2, 4)): 9/19 ≈ 0.474
      ├── Some((2, 5)): 18/29 ≈ 0.621
      ├── Some((2, 6)): 13/23 ≈ 0.565
      ├── Some((2, 7)): 7/17 ≈ 0.412
      └── Some((2, 8)): 11/21 ≈ 0.524
    ├── Some((8, 3)): 120/217 ≈ 0.553
      ├── Some((3, 0)): 6/16 ≈ 0.375
      ├── Some((3, 1)): 16/27 ≈ 0.593
      ├── Some((3, 2)): 9/19 ≈ 0.474
      ├── Some((3, 3)): 15/26 ≈ 0.577
      ├── Some((3, 4)): 18/29 ≈ 0.621
      ├── Some((3, 5)): 11/22 ≈ 0.500
      ├── Some((3, 6)): 6/16 ≈ 0.375
      ├── Some((3, 7)): 16/27 ≈ 0.593
      └── Some((3, 8)): 22/34 ≈ 0.647
    ├── Some((8, 4)): 139/245 ≈ 0.567
      ├── Some((4, 0)): 19/31 ≈ 0.613
      ├── Some((4, 1)): 21/33 ≈ 0.636
      ├── Some((4, 2)): 14/26 ≈ 0.538
      ├── Some((4, 3)): 19/31 ≈ 0.613
      ├── Some((4, 4)): 9/20 ≈ 0.450
      ├── Some((4, 5)): 23/36 ≈ 0.639
      ├── Some((4, 6)): 21/34 ≈ 0.618
      ├── Some((4, 7)): 5/15 ≈ 0.333
      └── Some((4, 8)): 7/18 ≈ 0.389
    ├── Some((8, 5)): 123/222 ≈ 0.554
      ├── Some((5, 0)): 13/24 ≈ 0.542
      ├── Some((5, 1)): 17/28 ≈ 0.607
      ├── Some((5, 2)): 8/19 ≈ 0.421
      ├── Some((5, 3)): 13/24 ≈ 0.542
      ├── Some((5, 4)): 14/25 ≈ 0.560
      ├── Some((5, 5)): 7/17 ≈ 0.412
      ├── Some((5, 6)): 23/35 ≈ 0.657
      ├── Some((5, 7)): 17/28 ≈ 0.607
      └── Some((5, 8)): 10/21 ≈ 0.476
    ├── Some((8, 6)): 86/168 ≈ 0.512
      ├── Some((6, 0)): 8/17 ≈ 0.471
      ├── Some((6, 1)): 12/21 ≈ 0.571
      ├── Some((6, 2)): 3/11 ≈ 0.273
      ├── Some((6, 3)): 12/22 ≈ 0.545
      ├── Some((6, 4)): 5/14 ≈ 0.357
      ├── Some((6, 5)): 18/28 ≈ 0.643
      ├── Some((6, 6)): 7/16 ≈ 0.438
      ├── Some((6, 7)): 9/18 ≈ 0.500
      └── Some((6, 8)): 11/20 ≈ 0.550
    ├── Some((8, 7)): 108/200 ≈ 0.540
      ├── Some((7, 0)): 9/20 ≈ 0.450
      ├── Some((7, 1)): 8/19 ≈ 0.421
      ├── Some((7, 2)): 16/28 ≈ 0.571
      ├── Some((7, 3)): 22/34 ≈ 0.647
      ├── Some((7, 4)): 8/19 ≈ 0.421
      ├── Some((7, 5)): 13/24 ≈ 0.542
      ├── Some((7, 6)): 10/21 ≈ 0.476
      └── Some((7, 7)): 22/34 ≈ 0.647
    └── Some((8, 8)): 68/141 ≈ 0.482
      ├── Some((8, 0)): 7/16 ≈ 0.438
      ├── Some((8, 1)): 8/17 ≈ 0.471
      ├── Some((8, 2)): 10/19 ≈ 0.526
      ├── Some((8, 3)): 10/19 ≈ 0.526
      ├── Some((8, 4)): 6/15 ≈ 0.400
      ├── Some((8, 5)): 12/22 ≈ 0.545
      ├── Some((8, 6)): 12/22 ≈ 0.545
      └── Some((8, 7)): 2/10 ≈ 0.200
├── Some((1, 8)): 3853/7620 ≈ 0.506
  ├── Some((8, 0)): 414/823 ≈ 0.503
    ├── Some((0, 0)): 36/77 ≈ 0.468
      ├── Some((0, 1)): 8/13 ≈ 0.615
      ├── Some((0, 2)): 1/6 ≈ 0.167
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 9/14 ≈ 0.643
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((0, 1)): 28/66 ≈ 0.424
      ├── Some((1, 0)): 1/5 ≈ 0.200
      ├── Some((1, 1)): 4/9 ≈ 0.444
      ├── Some((1, 2)): 10/14 ≈ 0.714
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 5/10 ≈ 0.500
      ├── Some((1, 5)): 0/4 ≈ 0.000
      ├── Some((1, 6)): 1/6 ≈ 0.167
      └── Some((1, 7)): 4/9 ≈ 0.444
    ├── Some((0, 2)): 53/102 ≈ 0.520
      ├── Some((2, 0)): 13/18 ≈ 0.722
      ├── Some((2, 1)): 7/12 ≈ 0.583
      ├── Some((2, 2)): 1/6 ≈ 0.167
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 7/12 ≈ 0.583
      ├── Some((2, 5)): 1/6 ≈ 0.167
      ├── Some((2, 6)): 7/13 ≈ 0.538
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 8/13 ≈ 0.615
    ├── Some((0, 3)): 75/132 ≈ 0.568
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 9/15 ≈ 0.600
      ├── Some((3, 4)): 13/19 ≈ 0.684
      ├── Some((3, 5)): 10/16 ≈ 0.625
      ├── Some((3, 6)): 10/16 ≈ 0.625
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 9/16 ≈ 0.562
    ├── Some((0, 4)): 61/113 ≈ 0.540
      ├── Some((4, 0)): 9/14 ≈ 0.643
      ├── Some((4, 1)): 7/12 ≈ 0.583
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 11/16 ≈ 0.688
      ├── Some((4, 7)): 7/13 ≈ 0.538
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((0, 5)): 38/80 ≈ 0.475
      ├── Some((5, 0)): 4/9 ≈ 0.444
      ├── Some((5, 1)): 4/9 ≈ 0.444
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 3)): 5/9 ≈ 0.556
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 6/10 ≈ 0.600
      ├── Some((5, 6)): 8/12 ≈ 0.667
      ├── Some((5, 7)): 4/9 ≈ 0.444
      └── Some((5, 8)): 2/7 ≈ 0.286
    ├── Some((0, 6)): 58/108 ≈ 0.537
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 7/13 ≈ 0.538
      ├── Some((6, 5)): 12/17 ≈ 0.706
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 13/18 ≈ 0.722
      └── Some((6, 8)): 11/16 ≈ 0.688
    ├── Some((0, 7)): 22/57 ≈ 0.386
      ├── Some((7, 0)): 4/8 ≈ 0.500
      ├── Some((7, 1)): 5/8 ≈ 0.625
      ├── Some((7, 2)): 0/4 ≈ 0.000
      ├── Some((7, 3)): 1/5 ≈ 0.200
      ├── Some((7, 4)): 5/9 ≈ 0.556
      ├── Some((7, 5)): 1/5 ≈ 0.200
      ├── Some((7, 6)): 0/4 ≈ 0.000
      ├── Some((7, 7)): 2/6 ≈ 0.333
      └── Some((7, 8)): 3/7 ≈ 0.429
    └── Some((0, 8)): 43/87 ≈ 0.494
      ├── Some((8, 1)): 6/12 ≈ 0.500
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 13/18 ≈ 0.722
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 7/13 ≈ 0.538
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((8, 1)): 629/1189 ≈ 0.529
    ├── Some((1, 0)): 78/148 ≈ 0.527
      ├── Some((0, 0)): 5/12 ≈ 0.417
      ├── Some((0, 1)): 1/8 ≈ 0.125
      ├── Some((0, 2)): 6/14 ≈ 0.429
      ├── Some((0, 3)): 16/24 ≈ 0.667
      ├── Some((0, 4)): 13/21 ≈ 0.619
      ├── Some((0, 5)): 4/11 ≈ 0.364
      ├── Some((0, 6)): 7/15 ≈ 0.467
      ├── Some((0, 7)): 6/14 ≈ 0.429
      └── Some((0, 8)): 20/28 ≈ 0.714
    ├── Some((1, 1)): 106/188 ≈ 0.564
      ├── Some((1, 0)): 16/28 ≈ 0.571
      ├── Some((1, 2)): 17/29 ≈ 0.586
      ├── Some((1, 3)): 12/23 ≈ 0.522
      ├── Some((1, 4)): 13/24 ≈ 0.542
      ├── Some((1, 5)): 8/19 ≈ 0.421
      ├── Some((1, 6)): 22/34 ≈ 0.647
      └── Some((1, 7)): 18/30 ≈ 0.600
    ├── Some((1, 2)): 105/187 ≈ 0.561
      ├── Some((2, 0)): 20/30 ≈ 0.667
      ├── Some((2, 1)): 7/16 ≈ 0.438
      ├── Some((2, 2)): 12/21 ≈ 0.571
      ├── Some((2, 3)): 14/23 ≈ 0.609
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 12/21 ≈ 0.571
      ├── Some((2, 6)): 11/20 ≈ 0.550
      ├── Some((2, 7)): 12/21 ≈ 0.571
      └── Some((2, 8)): 10/19 ≈ 0.526
    ├── Some((1, 3)): 29/74 ≈ 0.392
      ├── Some((3, 0)): 0/5 ≈ 0.000
      ├── Some((3, 1)): 0/5 ≈ 0.000
      ├── Some((3, 2)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 7/12 ≈ 0.583
      ├── Some((3, 5)): 1/6 ≈ 0.167
      ├── Some((3, 6)): 4/9 ≈ 0.444
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 6/11 ≈ 0.545
    ├── Some((1, 4)): 71/138 ≈ 0.514
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 13/20 ≈ 0.650
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 4/11 ≈ 0.364
      ├── Some((4, 4)): 4/11 ≈ 0.364
      ├── Some((4, 5)): 5/12 ≈ 0.417
      ├── Some((4, 6)): 11/19 ≈ 0.579
      ├── Some((4, 7)): 6/13 ≈ 0.462
      └── Some((4, 8)): 12/20 ≈ 0.600
    ├── Some((1, 5)): 95/173 ≈ 0.549
      ├── Some((5, 0)): 20/29 ≈ 0.690
      ├── Some((5, 1)): 11/20 ≈ 0.550
      ├── Some((5, 2)): 18/27 ≈ 0.667
      ├── Some((5, 3)): 8/17 ≈ 0.471
      ├── Some((5, 4)): 13/22 ≈ 0.591
      ├── Some((5, 5)): 6/14 ≈ 0.429
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 6/14 ≈ 0.429
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((1, 6)): 56/116 ≈ 0.483
      ├── Some((6, 0)): 13/20 ≈ 0.650
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 6/13 ≈ 0.462
      ├── Some((6, 3)): 11/18 ≈ 0.611
      ├── Some((6, 4)): 6/13 ≈ 0.462
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 2/8 ≈ 0.250
      ├── Some((6, 7)): 2/8 ≈ 0.250
      └── Some((6, 8)): 7/14 ≈ 0.500
    └── Some((1, 7)): 89/164 ≈ 0.543
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 10/18 ≈ 0.556
      ├── Some((7, 2)): 13/22 ≈ 0.591
      ├── Some((7, 3)): 10/18 ≈ 0.556
      ├── Some((7, 4)): 5/13 ≈ 0.385
      ├── Some((7, 5)): 7/15 ≈ 0.467
      ├── Some((7, 6)): 7/15 ≈ 0.467
      ├── Some((7, 7)): 9/17 ≈ 0.529
      └── Some((7, 8)): 18/27 ≈ 0.667
  ├── Some((8, 2)): 398/796 ≈ 0.500
    ├── Some((2, 0)): 46/91 ≈ 0.505
      ├── Some((0, 0)): 5/10 ≈ 0.500
      ├── Some((0, 1)): 5/10 ≈ 0.500
      ├── Some((0, 2)): 9/13 ≈ 0.692
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 5/10 ≈ 0.500
      ├── Some((0, 5)): 6/11 ≈ 0.545
      ├── Some((0, 6)): 6/11 ≈ 0.545
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((2, 1)): 31/70 ≈ 0.443
      ├── Some((1, 0)): 0/4 ≈ 0.000
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 6/11 ≈ 0.545
      ├── Some((1, 3)): 9/14 ≈ 0.643
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 7/12 ≈ 0.583
      └── Some((1, 7)): 0/4 ≈ 0.000
    ├── Some((2, 2)): 42/85 ≈ 0.494
      ├── Some((2, 0)): 0/5 ≈ 0.000
      ├── Some((2, 1)): 4/9 ≈ 0.444
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 7/12 ≈ 0.583
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 8/13 ≈ 0.615
      └── Some((2, 8)): 7/12 ≈ 0.583
    ├── Some((2, 3)): 49/95 ≈ 0.516
      ├── Some((3, 0)): 3/8 ≈ 0.375
      ├── Some((3, 1)): 0/5 ≈ 0.000
      ├── Some((3, 2)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 7/12 ≈ 0.583
      ├── Some((3, 4)): 7/12 ≈ 0.583
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 5/11 ≈ 0.455
      └── Some((3, 8)): 12/17 ≈ 0.706
    ├── Some((2, 4)): 51/98 ≈ 0.520
      ├── Some((4, 0)): 9/14 ≈ 0.643
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 1/6 ≈ 0.167
      ├── Some((4, 3)): 11/16 ≈ 0.688
      ├── Some((4, 4)): 1/6 ≈ 0.167
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 7/12 ≈ 0.583
      ├── Some((4, 7)): 8/13 ≈ 0.615
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((2, 5)): 45/90 ≈ 0.500
      ├── Some((5, 0)): 1/6 ≈ 0.167
      ├── Some((5, 1)): 5/10 ≈ 0.500
      ├── Some((5, 2)): 9/13 ≈ 0.692
      ├── Some((5, 3)): 5/10 ≈ 0.500
      ├── Some((5, 4)): 7/12 ≈ 0.583
      ├── Some((5, 5)): 4/9 ≈ 0.444
      ├── Some((5, 6)): 3/8 ≈ 0.375
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 5/10 ≈ 0.500
    ├── Some((2, 6)): 26/62 ≈ 0.419
      ├── Some((6, 0)): 6/10 ≈ 0.600
      ├── Some((6, 1)): 1/5 ≈ 0.200
      ├── Some((6, 2)): 5/9 ≈ 0.556
      ├── Some((6, 3)): 0/4 ≈ 0.000
      ├── Some((6, 4)): 2/6 ≈ 0.333
      ├── Some((6, 5)): 0/4 ≈ 0.000
      ├── Some((6, 6)): 2/6 ≈ 0.333
      ├── Some((6, 7)): 5/9 ≈ 0.556
      └── Some((6, 8)): 4/8 ≈ 0.500
    ├── Some((2, 7)): 36/77 ≈ 0.468
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 4/9 ≈ 0.444
      ├── Some((7, 2)): 5/9 ≈ 0.556
      ├── Some((7, 3)): 5/10 ≈ 0.500
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 5/10 ≈ 0.500
      ├── Some((7, 6)): 6/10 ≈ 0.600
      ├── Some((7, 7)): 6/10 ≈ 0.600
      └── Some((7, 8)): 2/7 ≈ 0.286
    └── Some((2, 8)): 72/127 ≈ 0.567
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 13/20 ≈ 0.650
      ├── Some((8, 3)): 1/7 ≈ 0.143
      ├── Some((8, 4)): 12/19 ≈ 0.632
      ├── Some((8, 5)): 11/18 ≈ 0.611
      ├── Some((8, 6)): 6/13 ≈ 0.462
      ├── Some((8, 7)): 19/25 ≈ 0.760
      └── Some((8, 8)): 3/10 ≈ 0.300
  ├── Some((8, 3)): 380/765 ≈ 0.497
    ├── Some((3, 0)): 39/81 ≈ 0.481
      ├── Some((0, 0)): 3/8 ≈ 0.375
      ├── Some((0, 1)): 0/4 ≈ 0.000
      ├── Some((0, 2)): 6/10 ≈ 0.600
      ├── Some((0, 3)): 5/9 ≈ 0.556
      ├── Some((0, 4)): 5/10 ≈ 0.500
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 8/12 ≈ 0.667
      ├── Some((0, 7)): 5/10 ≈ 0.500
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((3, 1)): 44/88 ≈ 0.500
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 13/18 ≈ 0.722
      ├── Some((1, 2)): 7/13 ≈ 0.538
      ├── Some((1, 3)): 9/14 ≈ 0.643
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 0/5 ≈ 0.000
      ├── Some((1, 6)): 1/6 ≈ 0.167
      └── Some((1, 7)): 8/14 ≈ 0.571
    ├── Some((3, 2)): 48/93 ≈ 0.516
      ├── Some((2, 0)): 6/11 ≈ 0.545
      ├── Some((2, 1)): 5/10 ≈ 0.500
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 8/13 ≈ 0.615
      ├── Some((2, 4)): 6/11 ≈ 0.545
      ├── Some((2, 5)): 5/10 ≈ 0.500
      ├── Some((2, 6)): 6/11 ≈ 0.545
      ├── Some((2, 7)): 5/10 ≈ 0.500
      └── Some((2, 8)): 4/9 ≈ 0.444
    ├── Some((3, 3)): 30/68 ≈ 0.441
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 0/4 ≈ 0.000
      ├── Some((3, 2)): 4/9 ≈ 0.444
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 9/14 ≈ 0.643
      ├── Some((3, 6)): 5/10 ≈ 0.500
      ├── Some((3, 7)): 5/10 ≈ 0.500
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((3, 4)): 40/82 ≈ 0.488
      ├── Some((4, 0)): 5/10 ≈ 0.500
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 1/6 ≈ 0.167
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 8/12 ≈ 0.667
      ├── Some((4, 6)): 6/10 ≈ 0.600
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 6/10 ≈ 0.600
    ├── Some((3, 5)): 59/108 ≈ 0.546
      ├── Some((5, 0)): 21/25 ≈ 0.840
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 6/12 ≈ 0.500
      ├── Some((5, 3)): 2/7 ≈ 0.286
      ├── Some((5, 4)): 3/9 ≈ 0.333
      ├── Some((5, 5)): 10/15 ≈ 0.667
      ├── Some((5, 6)): 2/8 ≈ 0.250
      ├── Some((5, 7)): 9/14 ≈ 0.643
      └── Some((5, 8)): 1/6 ≈ 0.167
    ├── Some((3, 6)): 34/73 ≈ 0.466
      ├── Some((6, 0)): 2/6 ≈ 0.333
      ├── Some((6, 1)): 8/12 ≈ 0.667
      ├── Some((6, 2)): 6/10 ≈ 0.600
      ├── Some((6, 3)): 2/6 ≈ 0.333
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 5/9 ≈ 0.556
      ├── Some((6, 6)): 2/6 ≈ 0.333
      ├── Some((6, 7)): 4/8 ≈ 0.500
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((3, 7)): 36/76 ≈ 0.474
      ├── Some((7, 0)): 7/11 ≈ 0.636
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 3)): 6/10 ≈ 0.600
      ├── Some((7, 4)): 7/11 ≈ 0.636
      ├── Some((7, 5)): 0/4 ≈ 0.000
      ├── Some((7, 6)): 6/10 ≈ 0.600
      ├── Some((7, 7)): 0/4 ≈ 0.000
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((3, 8)): 49/95 ≈ 0.516
      ├── Some((8, 0)): 1/6 ≈ 0.167
      ├── Some((8, 1)): 6/12 ≈ 0.500
      ├── Some((8, 2)): 8/14 ≈ 0.571
      ├── Some((8, 4)): 9/15 ≈ 0.600
      ├── Some((8, 5)): 8/14 ≈ 0.571
      ├── Some((8, 6)): 10/15 ≈ 0.667
      ├── Some((8, 7)): 2/7 ≈ 0.286
      └── Some((8, 8)): 5/11 ≈ 0.455
  ├── Some((8, 4)): 263/560 ≈ 0.470
    ├── Some((4, 0)): 34/69 ≈ 0.493
      ├── Some((0, 0)): 2/6 ≈ 0.333
      ├── Some((0, 1)): 3/7 ≈ 0.429
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 0/4 ≈ 0.000
      ├── Some((0, 4)): 1/5 ≈ 0.200
      ├── Some((0, 5)): 7/11 ≈ 0.636
      ├── Some((0, 6)): 4/8 ≈ 0.500
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 8/11 ≈ 0.727
    ├── Some((4, 1)): 54/97 ≈ 0.557
      ├── Some((1, 0)): 12/17 ≈ 0.706
      ├── Some((1, 1)): 6/11 ≈ 0.545
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 7/12 ≈ 0.583
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 6/11 ≈ 0.545
      └── Some((1, 7)): 11/16 ≈ 0.688
    ├── Some((4, 2)): 24/55 ≈ 0.436
      ├── Some((2, 0)): 1/5 ≈ 0.200
      ├── Some((2, 1)): 3/6 ≈ 0.500
      ├── Some((2, 2)): 2/6 ≈ 0.333
      ├── Some((2, 3)): 0/4 ≈ 0.000
      ├── Some((2, 4)): 4/7 ≈ 0.571
      ├── Some((2, 5)): 5/8 ≈ 0.625
      ├── Some((2, 6)): 1/5 ≈ 0.200
      ├── Some((2, 7)): 3/6 ≈ 0.500
      └── Some((2, 8)): 4/7 ≈ 0.571
    ├── Some((4, 3)): 22/52 ≈ 0.423
      ├── Some((3, 0)): 3/6 ≈ 0.500
      ├── Some((3, 1)): 3/6 ≈ 0.500
      ├── Some((3, 2)): 0/3 ≈ 0.000
      ├── Some((3, 3)): 3/6 ≈ 0.500
      ├── Some((3, 4)): 6/9 ≈ 0.667
      ├── Some((3, 5)): 4/7 ≈ 0.571
      ├── Some((3, 6)): 2/6 ≈ 0.333
      ├── Some((3, 7)): 0/4 ≈ 0.000
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((4, 4)): 19/48 ≈ 0.396
      ├── Some((4, 0)): 0/3 ≈ 0.000
      ├── Some((4, 1)): 3/7 ≈ 0.429
      ├── Some((4, 2)): 0/3 ≈ 0.000
      ├── Some((4, 3)): 3/7 ≈ 0.429
      ├── Some((4, 5)): 5/8 ≈ 0.625
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 4/7 ≈ 0.571
      └── Some((4, 8)): 3/7 ≈ 0.429
    ├── Some((4, 5)): 53/95 ≈ 0.558
      ├── Some((5, 0)): 2/7 ≈ 0.286
      ├── Some((5, 1)): 1/6 ≈ 0.167
      ├── Some((5, 2)): 6/11 ≈ 0.545
      ├── Some((5, 3)): 6/11 ≈ 0.545
      ├── Some((5, 4)): 7/11 ≈ 0.636
      ├── Some((5, 5)): 5/10 ≈ 0.500
      ├── Some((5, 6)): 5/10 ≈ 0.500
      ├── Some((5, 7)): 12/16 ≈ 0.750
      └── Some((5, 8)): 8/12 ≈ 0.667
    ├── Some((4, 6)): 14/40 ≈ 0.350
      ├── Some((6, 0)): 1/4 ≈ 0.250
      ├── Some((6, 1)): 2/4 ≈ 0.500
      ├── Some((6, 2)): 2/5 ≈ 0.400
      ├── Some((6, 3)): 0/3 ≈ 0.000
      ├── Some((6, 4)): 2/5 ≈ 0.400
      ├── Some((6, 5)): 1/4 ≈ 0.250
      ├── Some((6, 6)): 2/5 ≈ 0.400
      ├── Some((6, 7)): 2/5 ≈ 0.400
      └── Some((6, 8)): 1/4 ≈ 0.250
    ├── Some((4, 7)): 23/54 ≈ 0.426
      ├── Some((7, 0)): 3/6 ≈ 0.500
      ├── Some((7, 1)): 7/10 ≈ 0.700
      ├── Some((7, 2)): 2/5 ≈ 0.400
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 4/7 ≈ 0.571
      ├── Some((7, 5)): 1/5 ≈ 0.200
      ├── Some((7, 6)): 0/3 ≈ 0.000
      ├── Some((7, 7)): 1/5 ≈ 0.200
      └── Some((7, 8)): 3/6 ≈ 0.500
    └── Some((4, 8)): 20/49 ≈ 0.408
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 0/3 ≈ 0.000
      ├── Some((8, 2)): 5/8 ≈ 0.625
      ├── Some((8, 3)): 3/7 ≈ 0.429
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 7/10 ≈ 0.700
      └── Some((8, 8)): 0/3 ≈ 0.000
  ├── Some((8, 5)): 423/839 ≈ 0.504
    ├── Some((5, 0)): 59/110 ≈ 0.536
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 9/14 ≈ 0.643
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 7/13 ≈ 0.538
      ├── Some((0, 4)): 6/12 ≈ 0.500
      ├── Some((0, 5)): 7/13 ≈ 0.538
      ├── Some((0, 6)): 10/15 ≈ 0.667
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((5, 1)): 35/76 ≈ 0.461
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 8/13 ≈ 0.615
      ├── Some((1, 2)): 1/6 ≈ 0.167
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 8/13 ≈ 0.615
      ├── Some((1, 5)): 8/13 ≈ 0.615
      ├── Some((1, 6)): 3/8 ≈ 0.375
      └── Some((1, 7)): 1/6 ≈ 0.167
    ├── Some((5, 2)): 52/100 ≈ 0.520
      ├── Some((2, 0)): 11/16 ≈ 0.688
      ├── Some((2, 1)): 2/7 ≈ 0.286
      ├── Some((2, 2)): 0/5 ≈ 0.000
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 9/14 ≈ 0.643
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 7/12 ≈ 0.583
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 15/20 ≈ 0.750
    ├── Some((5, 3)): 39/82 ≈ 0.476
      ├── Some((3, 0)): 8/12 ≈ 0.667
      ├── Some((3, 1)): 4/9 ≈ 0.444
      ├── Some((3, 2)): 4/9 ≈ 0.444
      ├── Some((3, 3)): 4/9 ≈ 0.444
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 5/9 ≈ 0.556
      ├── Some((3, 6)): 5/9 ≈ 0.556
      ├── Some((3, 7)): 1/6 ≈ 0.167
      └── Some((3, 8)): 5/10 ≈ 0.500
    ├── Some((5, 4)): 38/81 ≈ 0.469
      ├── Some((4, 0)): 7/11 ≈ 0.636
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 10/14 ≈ 0.714
      ├── Some((4, 3)): 0/4 ≈ 0.000
      ├── Some((4, 4)): 6/11 ≈ 0.545
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((5, 5)): 58/109 ≈ 0.532
      ├── Some((5, 0)): 2/8 ≈ 0.250
      ├── Some((5, 1)): 8/15 ≈ 0.533
      ├── Some((5, 2)): 5/11 ≈ 0.455
      ├── Some((5, 3)): 7/14 ≈ 0.500
      ├── Some((5, 4)): 10/16 ≈ 0.625
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 14/20 ≈ 0.700
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((5, 6)): 37/79 ≈ 0.468
      ├── Some((6, 0)): 8/12 ≈ 0.667
      ├── Some((6, 1)): 5/9 ≈ 0.556
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 10/14 ≈ 0.714
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((5, 7)): 49/96 ≈ 0.510
      ├── Some((7, 0)): 8/13 ≈ 0.615
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 7/12 ≈ 0.583
      ├── Some((7, 3)): 3/8 ≈ 0.375
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 2/7 ≈ 0.286
      └── Some((7, 8)): 13/18 ≈ 0.722
    └── Some((5, 8)): 55/105 ≈ 0.524
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 13/19 ≈ 0.684
      ├── Some((8, 2)): 5/11 ≈ 0.455
      ├── Some((8, 3)): 11/17 ≈ 0.647
      ├── Some((8, 4)): 2/8 ≈ 0.250
      ├── Some((8, 6)): 2/8 ≈ 0.250
      ├── Some((8, 7)): 7/14 ≈ 0.500
      └── Some((8, 8)): 11/17 ≈ 0.647
  ├── Some((8, 6)): 428/847 ≈ 0.505
    ├── Some((6, 0)): 63/117 ≈ 0.538
      ├── Some((0, 0)): 6/12 ≈ 0.500
      ├── Some((0, 1)): 3/9 ≈ 0.333
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 10/16 ≈ 0.625
      ├── Some((0, 4)): 6/12 ≈ 0.500
      ├── Some((0, 5)): 7/13 ≈ 0.538
      ├── Some((0, 6)): 8/14 ≈ 0.571
      ├── Some((0, 7)): 9/15 ≈ 0.600
      └── Some((0, 8)): 6/12 ≈ 0.500
    ├── Some((6, 1)): 28/66 ≈ 0.424
      ├── Some((1, 0)): 2/7 ≈ 0.286
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 5/9 ≈ 0.556
      ├── Some((1, 4)): 5/9 ≈ 0.556
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 4/9 ≈ 0.444
      └── Some((1, 7)): 4/9 ≈ 0.444
    ├── Some((6, 2)): 73/130 ≈ 0.562
      ├── Some((2, 0)): 8/15 ≈ 0.533
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 18/24 ≈ 0.750
      ├── Some((2, 5)): 6/13 ≈ 0.462
      ├── Some((2, 6)): 11/17 ≈ 0.647
      ├── Some((2, 7)): 9/15 ≈ 0.600
      └── Some((2, 8)): 9/15 ≈ 0.600
    ├── Some((6, 3)): 18/51 ≈ 0.353
      ├── Some((3, 0)): 2/6 ≈ 0.333
      ├── Some((3, 1)): 5/8 ≈ 0.625
      ├── Some((3, 2)): 2/6 ≈ 0.333
      ├── Some((3, 3)): 0/3 ≈ 0.000
      ├── Some((3, 4)): 1/5 ≈ 0.200
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 0/4 ≈ 0.000
      ├── Some((3, 7)): 5/8 ≈ 0.625
      └── Some((3, 8)): 3/6 ≈ 0.500
    ├── Some((6, 4)): 47/94 ≈ 0.500
      ├── Some((4, 0)): 0/5 ≈ 0.000
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 4/10 ≈ 0.400
      ├── Some((4, 3)): 10/15 ≈ 0.667
      ├── Some((4, 4)): 10/15 ≈ 0.667
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 9/14 ≈ 0.643
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((6, 5)): 13/43 ≈ 0.302
      ├── Some((5, 0)): 1/4 ≈ 0.250
      ├── Some((5, 1)): 0/3 ≈ 0.000
      ├── Some((5, 2)): 1/5 ≈ 0.200
      ├── Some((5, 3)): 2/5 ≈ 0.400
      ├── Some((5, 4)): 2/5 ≈ 0.400
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 1/5 ≈ 0.200
      ├── Some((5, 7)): 2/5 ≈ 0.400
      └── Some((5, 8)): 2/5 ≈ 0.400
    ├── Some((6, 6)): 57/108 ≈ 0.528
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 9/15 ≈ 0.600
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 10/16 ≈ 0.625
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 12/18 ≈ 0.667
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((6, 7)): 43/89 ≈ 0.483
      ├── Some((7, 0)): 3/8 ≈ 0.375
      ├── Some((7, 1)): 6/11 ≈ 0.545
      ├── Some((7, 2)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 3/8 ≈ 0.375
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 4/9 ≈ 0.444
      ├── Some((7, 7)): 6/11 ≈ 0.545
      └── Some((7, 8)): 7/12 ≈ 0.583
    └── Some((6, 8)): 86/148 ≈ 0.581
      ├── Some((8, 0)): 15/23 ≈ 0.652
      ├── Some((8, 1)): 8/16 ≈ 0.500
      ├── Some((8, 2)): 9/17 ≈ 0.529
      ├── Some((8, 3)): 16/24 ≈ 0.667
      ├── Some((8, 4)): 17/25 ≈ 0.680
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 6/13 ≈ 0.462
      └── Some((8, 8)): 9/17 ≈ 0.529
  ├── Some((8, 7)): 534/1028 ≈ 0.519
    ├── Some((7, 0)): 73/134 ≈ 0.545
      ├── Some((0, 0)): 3/9 ≈ 0.333
      ├── Some((0, 1)): 14/20 ≈ 0.700
      ├── Some((0, 2)): 12/19 ≈ 0.632
      ├── Some((0, 3)): 2/8 ≈ 0.250
      ├── Some((0, 4)): 7/14 ≈ 0.500
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 8/15 ≈ 0.533
      ├── Some((0, 7)): 6/13 ≈ 0.462
      └── Some((0, 8)): 14/21 ≈ 0.667
    ├── Some((7, 1)): 83/147 ≈ 0.565
      ├── Some((1, 0)): 11/19 ≈ 0.579
      ├── Some((1, 1)): 11/19 ≈ 0.579
      ├── Some((1, 2)): 13/21 ≈ 0.619
      ├── Some((1, 3)): 12/20 ≈ 0.600
      ├── Some((1, 4)): 16/24 ≈ 0.667
      ├── Some((1, 5)): 7/15 ≈ 0.467
      ├── Some((1, 6)): 9/17 ≈ 0.529
      └── Some((1, 7)): 4/11 ≈ 0.364
    ├── Some((7, 2)): 73/134 ≈ 0.545
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 1)): 11/17 ≈ 0.647
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 11/18 ≈ 0.611
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 10/17 ≈ 0.588
      ├── Some((2, 7)): 11/18 ≈ 0.611
      └── Some((2, 8)): 11/18 ≈ 0.611
    ├── Some((7, 3)): 44/92 ≈ 0.478
      ├── Some((3, 0)): 6/12 ≈ 0.500
      ├── Some((3, 1)): 3/8 ≈ 0.375
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 4/9 ≈ 0.444
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 10/15 ≈ 0.667
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 6/11 ≈ 0.545
    ├── Some((7, 4)): 86/152 ≈ 0.566
      ├── Some((4, 0)): 11/19 ≈ 0.579
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 7/14 ≈ 0.500
      ├── Some((4, 3)): 14/21 ≈ 0.667
      ├── Some((4, 4)): 9/16 ≈ 0.562
      ├── Some((4, 5)): 16/23 ≈ 0.696
      ├── Some((4, 6)): 11/19 ≈ 0.579
      ├── Some((4, 7)): 8/15 ≈ 0.533
      └── Some((4, 8)): 5/12 ≈ 0.417
    ├── Some((7, 5)): 46/95 ≈ 0.484
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 8/13 ≈ 0.615
      ├── Some((5, 2)): 7/12 ≈ 0.583
      ├── Some((5, 3)): 6/11 ≈ 0.545
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 6/11 ≈ 0.545
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 4/10 ≈ 0.400
    ├── Some((7, 6)): 43/91 ≈ 0.473
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 9/14 ≈ 0.643
      ├── Some((6, 4)): 4/10 ≈ 0.400
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 11/16 ≈ 0.688
    ├── Some((7, 7)): 35/79 ≈ 0.443
      ├── Some((7, 0)): 3/8 ≈ 0.375
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 2/7 ≈ 0.286
      ├── Some((7, 4)): 8/13 ≈ 0.615
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 3/8 ≈ 0.375
      └── Some((7, 8)): 8/14 ≈ 0.571
    └── Some((7, 8)): 51/103 ≈ 0.495
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 2/8 ≈ 0.250
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 8/15 ≈ 0.533
      ├── Some((8, 4)): 12/19 ≈ 0.632
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 4/10 ≈ 0.400
      └── Some((8, 8)): 11/18 ≈ 0.611
  └── Some((8, 8)): 384/772 ≈ 0.497
    ├── Some((8, 0)): 67/123 ≈ 0.545
      ├── Some((0, 0)): 5/11 ≈ 0.455
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 10/16 ≈ 0.625
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 12/18 ≈ 0.667
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 10/16 ≈ 0.625
      ├── Some((0, 7)): 10/17 ≈ 0.588
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((8, 1)): 48/97 ≈ 0.495
      ├── Some((1, 0)): 9/15 ≈ 0.600
      ├── Some((1, 1)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 1/7 ≈ 0.143
      ├── Some((1, 3)): 8/14 ≈ 0.571
      ├── Some((1, 4)): 2/8 ≈ 0.250
      ├── Some((1, 5)): 9/15 ≈ 0.600
      ├── Some((1, 6)): 9/15 ≈ 0.600
      └── Some((1, 7)): 3/9 ≈ 0.333
    ├── Some((8, 2)): 33/75 ≈ 0.440
      ├── Some((2, 0)): 1/5 ≈ 0.200
      ├── Some((2, 1)): 4/9 ≈ 0.444
      ├── Some((2, 2)): 5/10 ≈ 0.500
      ├── Some((2, 3)): 1/5 ≈ 0.200
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 8/12 ≈ 0.667
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((8, 3)): 64/119 ≈ 0.538
      ├── Some((3, 0)): 4/10 ≈ 0.400
      ├── Some((3, 1)): 7/13 ≈ 0.538
      ├── Some((3, 2)): 9/15 ≈ 0.600
      ├── Some((3, 3)): 7/13 ≈ 0.538
      ├── Some((3, 4)): 3/9 ≈ 0.333
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 9/15 ≈ 0.600
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 17/23 ≈ 0.739
    ├── Some((8, 4)): 52/102 ≈ 0.510
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 7/12 ≈ 0.583
      ├── Some((4, 2)): 9/14 ≈ 0.643
      ├── Some((4, 3)): 8/13 ≈ 0.615
      ├── Some((4, 4)): 7/13 ≈ 0.538
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 8/13 ≈ 0.615
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 3/9 ≈ 0.333
    ├── Some((8, 5)): 39/83 ≈ 0.470
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 5/10 ≈ 0.500
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 3)): 5/10 ≈ 0.500
      ├── Some((5, 4)): 6/11 ≈ 0.545
      ├── Some((5, 5)): 8/12 ≈ 0.667
      ├── Some((5, 6)): 0/4 ≈ 0.000
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 5/10 ≈ 0.500
    ├── Some((8, 6)): 33/75 ≈ 0.440
      ├── Some((6, 0)): 6/10 ≈ 0.600
      ├── Some((6, 1)): 8/12 ≈ 0.667
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 5/10 ≈ 0.500
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 3/8 ≈ 0.375
    └── Some((8, 7)): 48/97 ≈ 0.495
      ├── Some((7, 0)): 8/13 ≈ 0.615
      ├── Some((7, 1)): 8/13 ≈ 0.615
      ├── Some((7, 2)): 6/12 ≈ 0.500
      ├── Some((7, 3)): 3/8 ≈ 0.375
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 7/13 ≈ 0.538
      ├── Some((7, 7)): 2/7 ≈ 0.286
      └── Some((7, 8)): 7/13 ≈ 0.538
├── Some((2, 0)): 9161/17357 ≈ 0.528
  ├── Some((0, 0)): 895/1718 ≈ 0.521
    ├── Some((0, 1)): 122/230 ≈ 0.530
      ├── Some((1, 0)): 18/31 ≈ 0.581
      ├── Some((1, 1)): 14/26 ≈ 0.538
      ├── Some((1, 2)): 22/35 ≈ 0.629
      ├── Some((1, 3)): 15/27 ≈ 0.556
      ├── Some((1, 4)): 7/18 ≈ 0.389
      ├── Some((1, 5)): 8/19 ≈ 0.421
      ├── Some((1, 6)): 17/29 ≈ 0.586
      ├── Some((1, 7)): 12/24 ≈ 0.500
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((0, 2)): 103/202 ≈ 0.510
      ├── Some((2, 1)): 6/17 ≈ 0.353
      ├── Some((2, 2)): 20/33 ≈ 0.606
      ├── Some((2, 3)): 9/21 ≈ 0.429
      ├── Some((2, 4)): 13/26 ≈ 0.500
      ├── Some((2, 5)): 14/27 ≈ 0.519
      ├── Some((2, 6)): 12/24 ≈ 0.500
      ├── Some((2, 7)): 17/30 ≈ 0.567
      └── Some((2, 8)): 11/23 ≈ 0.478
    ├── Some((0, 3)): 120/227 ≈ 0.529
      ├── Some((3, 0)): 14/26 ≈ 0.538
      ├── Some((3, 1)): 7/18 ≈ 0.389
      ├── Some((3, 2)): 27/40 ≈ 0.675
      ├── Some((3, 3)): 16/29 ≈ 0.552
      ├── Some((3, 4)): 9/20 ≈ 0.450
      ├── Some((3, 5)): 8/19 ≈ 0.421
      ├── Some((3, 6)): 8/19 ≈ 0.421
      ├── Some((3, 7)): 13/25 ≈ 0.520
      └── Some((3, 8)): 17/30 ≈ 0.567
    ├── Some((0, 4)): 132/245 ≈ 0.539
      ├── Some((4, 0)): 18/31 ≈ 0.581
      ├── Some((4, 1)): 15/27 ≈ 0.556
      ├── Some((4, 2)): 17/30 ≈ 0.567
      ├── Some((4, 3)): 6/17 ≈ 0.353
      ├── Some((4, 4)): 20/33 ≈ 0.606
      ├── Some((4, 5)): 16/29 ≈ 0.552
      ├── Some((4, 6)): 6/17 ≈ 0.353
      ├── Some((4, 7)): 17/30 ≈ 0.567
      └── Some((4, 8)): 17/30 ≈ 0.567
    ├── Some((0, 5)): 144/263 ≈ 0.548
      ├── Some((5, 0)): 13/26 ≈ 0.500
      ├── Some((5, 1)): 23/37 ≈ 0.622
      ├── Some((5, 2)): 23/37 ≈ 0.622
      ├── Some((5, 3)): 8/20 ≈ 0.400
      ├── Some((5, 4)): 4/15 ≈ 0.267
      ├── Some((5, 5)): 18/32 ≈ 0.562
      ├── Some((5, 6)): 14/27 ≈ 0.519
      ├── Some((5, 7)): 28/43 ≈ 0.651
      └── Some((5, 8)): 12/25 ≈ 0.480
    ├── Some((0, 6)): 112/215 ≈ 0.521
      ├── Some((6, 0)): 17/29 ≈ 0.586
      ├── Some((6, 1)): 11/22 ≈ 0.500
      ├── Some((6, 2)): 8/19 ≈ 0.421
      ├── Some((6, 3)): 16/28 ≈ 0.571
      ├── Some((6, 4)): 15/26 ≈ 0.577
      ├── Some((6, 5)): 11/22 ≈ 0.500
      ├── Some((6, 6)): 17/29 ≈ 0.586
      ├── Some((6, 7)): 9/20 ≈ 0.450
      └── Some((6, 8)): 8/19 ≈ 0.421
    ├── Some((0, 7)): 86/175 ≈ 0.491
      ├── Some((7, 0)): 7/16 ≈ 0.438
      ├── Some((7, 1)): 11/21 ≈ 0.524
      ├── Some((7, 2)): 3/12 ≈ 0.250
      ├── Some((7, 3)): 6/15 ≈ 0.400
      ├── Some((7, 4)): 8/18 ≈ 0.444
      ├── Some((7, 5)): 22/33 ≈ 0.667
      ├── Some((7, 6)): 8/18 ≈ 0.444
      ├── Some((7, 7)): 13/23 ≈ 0.565
      └── Some((7, 8)): 8/18 ≈ 0.444
    └── Some((0, 8)): 76/160 ≈ 0.475
      ├── Some((8, 0)): 4/13 ≈ 0.308
      ├── Some((8, 1)): 11/20 ≈ 0.550
      ├── Some((8, 2)): 4/13 ≈ 0.308
      ├── Some((8, 3)): 13/23 ≈ 0.565
      ├── Some((8, 4)): 7/16 ≈ 0.438
      ├── Some((8, 5)): 12/22 ≈ 0.545
      ├── Some((8, 6)): 5/14 ≈ 0.357
      ├── Some((8, 7)): 9/18 ≈ 0.500
      └── Some((8, 8)): 11/20 ≈ 0.550
  ├── Some((0, 1)): 627/1250 ≈ 0.502
    ├── Some((1, 0)): 63/129 ≈ 0.488
      ├── Some((0, 0)): 6/14 ≈ 0.429
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 10/19 ≈ 0.526
      ├── Some((0, 4)): 2/9 ≈ 0.222
      ├── Some((0, 5)): 5/13 ≈ 0.385
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 13/22 ≈ 0.591
      └── Some((0, 8)): 12/21 ≈ 0.571
    ├── Some((1, 1)): 53/114 ≈ 0.465
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 7/15 ≈ 0.467
      ├── Some((1, 3)): 9/17 ≈ 0.529
      ├── Some((1, 4)): 4/11 ≈ 0.364
      ├── Some((1, 5)): 5/13 ≈ 0.385
      ├── Some((1, 6)): 8/16 ≈ 0.500
      ├── Some((1, 7)): 13/21 ≈ 0.619
      └── Some((1, 8)): 1/8 ≈ 0.125
    ├── Some((1, 2)): 67/135 ≈ 0.496
      ├── Some((2, 1)): 2/9 ≈ 0.222
      ├── Some((2, 2)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 15/24 ≈ 0.625
      ├── Some((2, 4)): 8/17 ≈ 0.471
      ├── Some((2, 5)): 9/18 ≈ 0.500
      ├── Some((2, 6)): 13/22 ≈ 0.591
      ├── Some((2, 7)): 4/12 ≈ 0.333
      └── Some((2, 8)): 8/17 ≈ 0.471
    ├── Some((1, 3)): 93/174 ≈ 0.534
      ├── Some((3, 0)): 4/12 ≈ 0.333
      ├── Some((3, 1)): 14/23 ≈ 0.609
      ├── Some((3, 2)): 12/21 ≈ 0.571
      ├── Some((3, 3)): 10/19 ≈ 0.526
      ├── Some((3, 4)): 16/26 ≈ 0.615
      ├── Some((3, 5)): 18/28 ≈ 0.643
      ├── Some((3, 6)): 7/16 ≈ 0.438
      ├── Some((3, 7)): 2/10 ≈ 0.200
      └── Some((3, 8)): 9/18 ≈ 0.500
    ├── Some((1, 4)): 95/176 ≈ 0.540
      ├── Some((4, 0)): 8/17 ≈ 0.471
      ├── Some((4, 1)): 9/18 ≈ 0.500
      ├── Some((4, 2)): 11/20 ≈ 0.550
      ├── Some((4, 3)): 20/29 ≈ 0.690
      ├── Some((4, 4)): 6/15 ≈ 0.400
      ├── Some((4, 5)): 5/13 ≈ 0.385
      ├── Some((4, 6)): 10/19 ≈ 0.526
      ├── Some((4, 7)): 12/21 ≈ 0.571
      └── Some((4, 8)): 14/23 ≈ 0.609
    ├── Some((1, 5)): 79/153 ≈ 0.516
      ├── Some((5, 0)): 2/9 ≈ 0.222
      ├── Some((5, 1)): 19/28 ≈ 0.679
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 10/19 ≈ 0.526
      ├── Some((5, 4)): 8/16 ≈ 0.500
      ├── Some((5, 5)): 14/23 ≈ 0.609
      ├── Some((5, 6)): 0/7 ≈ 0.000
      ├── Some((5, 7)): 9/18 ≈ 0.500
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((1, 6)): 55/117 ≈ 0.470
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 12/19 ≈ 0.632
      ├── Some((6, 2)): 1/7 ≈ 0.143
      ├── Some((6, 3)): 5/12 ≈ 0.417
      ├── Some((6, 4)): 2/9 ≈ 0.222
      ├── Some((6, 5)): 13/20 ≈ 0.650
      ├── Some((6, 6)): 10/17 ≈ 0.588
      ├── Some((6, 7)): 6/13 ≈ 0.462
      └── Some((6, 8)): 4/11 ≈ 0.364
    ├── Some((1, 7)): 61/126 ≈ 0.484
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 18/25 ≈ 0.720
      ├── Some((7, 3)): 3/10 ≈ 0.300
      ├── Some((7, 4)): 2/9 ≈ 0.222
      ├── Some((7, 5)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 4/11 ≈ 0.364
      ├── Some((7, 7)): 6/13 ≈ 0.462
      └── Some((7, 8)): 8/16 ≈ 0.500
    └── Some((1, 8)): 60/125 ≈ 0.480
      ├── Some((8, 0)): 4/11 ≈ 0.364
      ├── Some((8, 1)): 10/17 ≈ 0.588
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 3/10 ≈ 0.300
      ├── Some((8, 4)): 7/14 ≈ 0.500
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 8/15 ≈ 0.533
      └── Some((8, 8)): 12/20 ≈ 0.600
  ├── Some((0, 2)): 991/1884 ≈ 0.526
    ├── Some((2, 1)): 143/265 ≈ 0.540
      ├── Some((1, 0)): 13/26 ≈ 0.500
      ├── Some((1, 1)): 9/21 ≈ 0.429
      ├── Some((1, 2)): 17/31 ≈ 0.548
      ├── Some((1, 3)): 20/34 ≈ 0.588
      ├── Some((1, 4)): 14/27 ≈ 0.519
      ├── Some((1, 5)): 23/38 ≈ 0.605
      ├── Some((1, 6)): 13/26 ≈ 0.500
      ├── Some((1, 7)): 23/38 ≈ 0.605
      └── Some((1, 8)): 10/23 ≈ 0.435
    ├── Some((2, 2)): 152/279 ≈ 0.545
      ├── Some((2, 1)): 14/31 ≈ 0.452
      ├── Some((2, 3)): 22/40 ≈ 0.550
      ├── Some((2, 4)): 27/46 ≈ 0.587
      ├── Some((2, 5)): 34/55 ≈ 0.618
      ├── Some((2, 6)): 13/29 ≈ 0.448
      ├── Some((2, 7)): 21/39 ≈ 0.538
      └── Some((2, 8)): 20/38 ≈ 0.526
    ├── Some((2, 3)): 80/169 ≈ 0.473
      ├── Some((3, 0)): 8/18 ≈ 0.444
      ├── Some((3, 1)): 10/20 ≈ 0.500
      ├── Some((3, 2)): 7/17 ≈ 0.412
      ├── Some((3, 3)): 3/12 ≈ 0.250
      ├── Some((3, 4)): 15/26 ≈ 0.577
      ├── Some((3, 5)): 8/18 ≈ 0.444
      ├── Some((3, 6)): 14/25 ≈ 0.560
      ├── Some((3, 7)): 13/23 ≈ 0.565
      └── Some((3, 8)): 1/9 ≈ 0.111
    ├── Some((2, 4)): 181/322 ≈ 0.562
      ├── Some((4, 0)): 23/39 ≈ 0.590
      ├── Some((4, 1)): 11/25 ≈ 0.440
      ├── Some((4, 2)): 15/30 ≈ 0.500
      ├── Some((4, 3)): 17/32 ≈ 0.531
      ├── Some((4, 4)): 17/33 ≈ 0.515
      ├── Some((4, 5)): 12/26 ≈ 0.462
      ├── Some((4, 6)): 26/43 ≈ 0.605
      ├── Some((4, 7)): 37/55 ≈ 0.673
      └── Some((4, 8)): 22/38 ≈ 0.579
    ├── Some((2, 5)): 83/173 ≈ 0.480
      ├── Some((5, 0)): 8/18 ≈ 0.444
      ├── Some((5, 1)): 24/35 ≈ 0.686
      ├── Some((5, 2)): 12/22 ≈ 0.545
      ├── Some((5, 3)): 7/17 ≈ 0.412
      ├── Some((5, 4)): 7/17 ≈ 0.412
      ├── Some((5, 5)): 5/14 ≈ 0.357
      ├── Some((5, 6)): 4/13 ≈ 0.308
      ├── Some((5, 7)): 7/17 ≈ 0.412
      └── Some((5, 8)): 9/19 ≈ 0.474
    ├── Some((2, 6)): 67/148 ≈ 0.453
      ├── Some((6, 0)): 13/23 ≈ 0.565
      ├── Some((6, 1)): 10/19 ≈ 0.526
      ├── Some((6, 2)): 4/13 ≈ 0.308
      ├── Some((6, 3)): 7/16 ≈ 0.438
      ├── Some((6, 4)): 8/17 ≈ 0.471
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 4/13 ≈ 0.308
      ├── Some((6, 7)): 8/17 ≈ 0.471
      └── Some((6, 8)): 3/11 ≈ 0.273
    ├── Some((2, 7)): 194/341 ≈ 0.569
      ├── Some((7, 0)): 21/37 ≈ 0.568
      ├── Some((7, 1)): 18/34 ≈ 0.529
      ├── Some((7, 2)): 9/23 ≈ 0.391
      ├── Some((7, 3)): 26/43 ≈ 0.605
      ├── Some((7, 4)): 34/52 ≈ 0.654
      ├── Some((7, 5)): 14/29 ≈ 0.483
      ├── Some((7, 6)): 22/38 ≈ 0.579
      ├── Some((7, 7)): 32/50 ≈ 0.640
      └── Some((7, 8)): 18/34 ≈ 0.529
    └── Some((2, 8)): 91/186 ≈ 0.489
      ├── Some((8, 0)): 8/18 ≈ 0.444
      ├── Some((8, 1)): 15/26 ≈ 0.577
      ├── Some((8, 2)): 14/25 ≈ 0.560
      ├── Some((8, 3)): 9/20 ≈ 0.450
      ├── Some((8, 4)): 15/26 ≈ 0.577
      ├── Some((8, 5)): 4/14 ≈ 0.286
      ├── Some((8, 6)): 14/25 ≈ 0.560
      ├── Some((8, 7)): 4/14 ≈ 0.286
      └── Some((8, 8)): 7/17 ≈ 0.412
  ├── Some((0, 3)): 970/1847 ≈ 0.525
    ├── Some((3, 0)): 142/256 ≈ 0.555
      ├── Some((0, 0)): 19/33 ≈ 0.576
      ├── Some((0, 1)): 23/38 ≈ 0.605
      ├── Some((0, 2)): 14/28 ≈ 0.500
      ├── Some((0, 4)): 10/23 ≈ 0.435
      ├── Some((0, 5)): 15/29 ≈ 0.517
      ├── Some((0, 6)): 18/32 ≈ 0.562
      ├── Some((0, 7)): 17/31 ≈ 0.548
      └── Some((0, 8)): 26/41 ≈ 0.634
    ├── Some((3, 1)): 86/173 ≈ 0.497
      ├── Some((1, 0)): 7/16 ≈ 0.438
      ├── Some((1, 1)): 8/18 ≈ 0.444
      ├── Some((1, 2)): 5/14 ≈ 0.357
      ├── Some((1, 3)): 12/22 ≈ 0.545
      ├── Some((1, 4)): 18/28 ≈ 0.643
      ├── Some((1, 5)): 5/14 ≈ 0.357
      ├── Some((1, 6)): 9/19 ≈ 0.474
      ├── Some((1, 7)): 6/15 ≈ 0.400
      └── Some((1, 8)): 16/26 ≈ 0.615
    ├── Some((3, 2)): 77/159 ≈ 0.484
      ├── Some((2, 1)): 8/18 ≈ 0.444
      ├── Some((2, 2)): 14/25 ≈ 0.560
      ├── Some((2, 3)): 14/25 ≈ 0.560
      ├── Some((2, 4)): 0/8 ≈ 0.000
      ├── Some((2, 5)): 15/26 ≈ 0.577
      ├── Some((2, 6)): 2/11 ≈ 0.182
      ├── Some((2, 7)): 22/34 ≈ 0.647
      └── Some((2, 8)): 2/11 ≈ 0.182
    ├── Some((3, 3)): 131/240 ≈ 0.546
      ├── Some((3, 0)): 10/23 ≈ 0.435
      ├── Some((3, 1)): 27/42 ≈ 0.643
      ├── Some((3, 2)): 6/18 ≈ 0.333
      ├── Some((3, 4)): 16/30 ≈ 0.533
      ├── Some((3, 5)): 24/39 ≈ 0.615
      ├── Some((3, 6)): 13/26 ≈ 0.500
      ├── Some((3, 7)): 5/16 ≈ 0.312
      └── Some((3, 8)): 30/45 ≈ 0.667
    ├── Some((3, 4)): 85/171 ≈ 0.497
      ├── Some((4, 0)): 10/19 ≈ 0.526
      ├── Some((4, 1)): 12/22 ≈ 0.545
      ├── Some((4, 2)): 10/20 ≈ 0.500
      ├── Some((4, 3)): 6/15 ≈ 0.400
      ├── Some((4, 4)): 5/14 ≈ 0.357
      ├── Some((4, 5)): 11/21 ≈ 0.524
      ├── Some((4, 6)): 11/21 ≈ 0.524
      ├── Some((4, 7)): 12/22 ≈ 0.545
      └── Some((4, 8)): 7/16 ≈ 0.438
    ├── Some((3, 5)): 116/218 ≈ 0.532
      ├── Some((5, 0)): 9/20 ≈ 0.450
      ├── Some((5, 1)): 9/20 ≈ 0.450
      ├── Some((5, 2)): 10/21 ≈ 0.476
      ├── Some((5, 3)): 10/21 ≈ 0.476
      ├── Some((5, 4)): 19/31 ≈ 0.613
      ├── Some((5, 5)): 20/32 ≈ 0.625
      ├── Some((5, 6)): 18/30 ≈ 0.600
      ├── Some((5, 7)): 13/24 ≈ 0.542
      └── Some((5, 8)): 7/18 ≈ 0.389
    ├── Some((3, 6)): 79/162 ≈ 0.488
      ├── Some((6, 0)): 9/18 ≈ 0.500
      ├── Some((6, 1)): 7/16 ≈ 0.438
      ├── Some((6, 2)): 9/18 ≈ 0.500
      ├── Some((6, 3)): 16/26 ≈ 0.615
      ├── Some((6, 4)): 10/20 ≈ 0.500
      ├── Some((6, 5)): 4/13 ≈ 0.308
      ├── Some((6, 6)): 11/21 ≈ 0.524
      ├── Some((6, 7)): 9/18 ≈ 0.500
      └── Some((6, 8)): 3/11 ≈ 0.273
    ├── Some((3, 7)): 133/243 ≈ 0.547
      ├── Some((7, 0)): 19/32 ≈ 0.594
      ├── Some((7, 1)): 20/33 ≈ 0.606
      ├── Some((7, 2)): 9/20 ≈ 0.450
      ├── Some((7, 3)): 18/31 ≈ 0.581
      ├── Some((7, 4)): 16/28 ≈ 0.571
      ├── Some((7, 5)): 13/25 ≈ 0.520
      ├── Some((7, 6)): 23/36 ≈ 0.639
      ├── Some((7, 7)): 12/24 ≈ 0.500
      └── Some((7, 8)): 3/13 ≈ 0.231
    └── Some((3, 8)): 120/224 ≈ 0.536
      ├── Some((8, 0)): 11/22 ≈ 0.500
      ├── Some((8, 1)): 9/20 ≈ 0.450
      ├── Some((8, 2)): 11/22 ≈ 0.500
      ├── Some((8, 3)): 19/31 ≈ 0.613
      ├── Some((8, 4)): 15/27 ≈ 0.556
      ├── Some((8, 5)): 17/29 ≈ 0.586
      ├── Some((8, 6)): 11/22 ≈ 0.500
      ├── Some((8, 7)): 16/28 ≈ 0.571
      └── Some((8, 8)): 11/22 ≈ 0.500
  ├── Some((0, 4)): 1295/2404 ≈ 0.539
    ├── Some((4, 0)): 139/260 ≈ 0.535
      ├── Some((0, 0)): 17/32 ≈ 0.531
      ├── Some((0, 1)): 9/22 ≈ 0.409
      ├── Some((0, 2)): 19/35 ≈ 0.543
      ├── Some((0, 3)): 15/30 ≈ 0.500
      ├── Some((0, 5)): 14/29 ≈ 0.483
      ├── Some((0, 6)): 15/30 ≈ 0.500
      ├── Some((0, 7)): 18/33 ≈ 0.545
      └── Some((0, 8)): 31/48 ≈ 0.646
    ├── Some((4, 1)): 132/250 ≈ 0.528
      ├── Some((1, 0)): 12/25 ≈ 0.480
      ├── Some((1, 1)): 15/28 ≈ 0.536
      ├── Some((1, 2)): 18/32 ≈ 0.562
      ├── Some((1, 3)): 9/21 ≈ 0.429
      ├── Some((1, 4)): 9/21 ≈ 0.429
      ├── Some((1, 5)): 20/34 ≈ 0.588
      ├── Some((1, 6)): 17/31 ≈ 0.548
      ├── Some((1, 7)): 15/28 ≈ 0.536
      └── Some((1, 8)): 16/29 ≈ 0.552
    ├── Some((4, 2)): 157/287 ≈ 0.547
      ├── Some((2, 1)): 14/29 ≈ 0.483
      ├── Some((2, 2)): 24/41 ≈ 0.585
      ├── Some((2, 3)): 16/32 ≈ 0.500
      ├── Some((2, 4)): 10/24 ≈ 0.417
      ├── Some((2, 5)): 24/41 ≈ 0.585
      ├── Some((2, 6)): 12/27 ≈ 0.444
      ├── Some((2, 7)): 28/45 ≈ 0.622
      └── Some((2, 8)): 29/47 ≈ 0.617
    ├── Some((4, 3)): 212/368 ≈ 0.576
      ├── Some((3, 0)): 33/52 ≈ 0.635
      ├── Some((3, 1)): 20/37 ≈ 0.541
      ├── Some((3, 2)): 17/33 ≈ 0.515
      ├── Some((3, 3)): 18/34 ≈ 0.529
      ├── Some((3, 4)): 25/43 ≈ 0.581
      ├── Some((3, 5)): 22/39 ≈ 0.564
      ├── Some((3, 6)): 18/34 ≈ 0.529
      ├── Some((3, 7)): 24/42 ≈ 0.571
      └── Some((3, 8)): 34/53 ≈ 0.642
    ├── Some((4, 4)): 157/287 ≈ 0.547
      ├── Some((4, 0)): 9/23 ≈ 0.391
      ├── Some((4, 1)): 20/36 ≈ 0.556
      ├── Some((4, 2)): 22/39 ≈ 0.564
      ├── Some((4, 3)): 24/41 ≈ 0.585
      ├── Some((4, 5)): 20/37 ≈ 0.541
      ├── Some((4, 6)): 30/48 ≈ 0.625
      ├── Some((4, 7)): 19/35 ≈ 0.543
      └── Some((4, 8)): 12/27 ≈ 0.444
    ├── Some((4, 5)): 104/207 ≈ 0.502
      ├── Some((5, 0)): 11/22 ≈ 0.500
      ├── Some((5, 1)): 11/22 ≈ 0.500
      ├── Some((5, 2)): 7/18 ≈ 0.389
      ├── Some((5, 3)): 8/19 ≈ 0.421
      ├── Some((5, 4)): 12/24 ≈ 0.500
      ├── Some((5, 5)): 25/38 ≈ 0.658
      ├── Some((5, 6)): 11/22 ≈ 0.500
      ├── Some((5, 7)): 11/22 ≈ 0.500
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((4, 6)): 113/221 ≈ 0.511
      ├── Some((6, 0)): 7/18 ≈ 0.389
      ├── Some((6, 1)): 10/22 ≈ 0.455
      ├── Some((6, 2)): 7/18 ≈ 0.389
      ├── Some((6, 3)): 12/24 ≈ 0.500
      ├── Some((6, 4)): 11/23 ≈ 0.478
      ├── Some((6, 5)): 22/35 ≈ 0.629
      ├── Some((6, 6)): 18/31 ≈ 0.581
      ├── Some((6, 7)): 12/24 ≈ 0.500
      └── Some((6, 8)): 13/25 ≈ 0.520
    ├── Some((4, 7)): 147/272 ≈ 0.540
      ├── Some((7, 0)): 13/26 ≈ 0.500
      ├── Some((7, 1)): 13/26 ≈ 0.500
      ├── Some((7, 2)): 6/18 ≈ 0.333
      ├── Some((7, 3)): 13/26 ≈ 0.500
      ├── Some((7, 4)): 14/28 ≈ 0.500
      ├── Some((7, 5)): 27/42 ≈ 0.643
      ├── Some((7, 6)): 15/29 ≈ 0.517
      ├── Some((7, 7)): 21/36 ≈ 0.583
      └── Some((7, 8)): 25/40 ≈ 0.625
    └── Some((4, 8)): 133/251 ≈ 0.530
      ├── Some((8, 0)): 9/21 ≈ 0.429
      ├── Some((8, 1)): 21/35 ≈ 0.600
      ├── Some((8, 2)): 12/25 ≈ 0.480
      ├── Some((8, 3)): 7/19 ≈ 0.368
      ├── Some((8, 4)): 5/16 ≈ 0.312
      ├── Some((8, 5)): 28/42 ≈ 0.667
      ├── Some((8, 6)): 18/32 ≈ 0.562
      ├── Some((8, 7)): 12/25 ≈ 0.480
      └── Some((8, 8)): 21/35 ≈ 0.600
  ├── Some((0, 5)): 936/1789 ≈ 0.523
    ├── Some((5, 0)): 89/177 ≈ 0.503
      ├── Some((0, 0)): 8/19 ≈ 0.421
      ├── Some((0, 1)): 17/29 ≈ 0.586
      ├── Some((0, 2)): 7/17 ≈ 0.412
      ├── Some((0, 3)): 17/29 ≈ 0.586
      ├── Some((0, 4)): 11/22 ≈ 0.500
      ├── Some((0, 6)): 5/15 ≈ 0.333
      ├── Some((0, 7)): 12/23 ≈ 0.522
      └── Some((0, 8)): 11/22 ≈ 0.500
    ├── Some((5, 1)): 78/160 ≈ 0.488
      ├── Some((1, 0)): 9/18 ≈ 0.500
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 3)): 5/14 ≈ 0.357
      ├── Some((1, 4)): 8/17 ≈ 0.471
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 9/18 ≈ 0.500
      ├── Some((1, 7)): 8/17 ≈ 0.471
      └── Some((1, 8)): 7/16 ≈ 0.438
    ├── Some((5, 2)): 149/265 ≈ 0.562
      ├── Some((2, 1)): 11/24 ≈ 0.458
      ├── Some((2, 2)): 23/38 ≈ 0.605
      ├── Some((2, 3)): 20/35 ≈ 0.571
      ├── Some((2, 4)): 18/33 ≈ 0.545
      ├── Some((2, 5)): 11/24 ≈ 0.458
      ├── Some((2, 6)): 37/54 ≈ 0.685
      ├── Some((2, 7)): 16/30 ≈ 0.533
      └── Some((2, 8)): 12/26 ≈ 0.462
    ├── Some((5, 3)): 89/177 ≈ 0.503
      ├── Some((3, 0)): 3/12 ≈ 0.250
      ├── Some((3, 1)): 10/20 ≈ 0.500
      ├── Some((3, 2)): 13/23 ≈ 0.565
      ├── Some((3, 3)): 14/24 ≈ 0.583
      ├── Some((3, 4)): 13/23 ≈ 0.565
      ├── Some((3, 5)): 3/12 ≈ 0.250
      ├── Some((3, 6)): 7/17 ≈ 0.412
      ├── Some((3, 7)): 20/31 ≈ 0.645
      └── Some((3, 8)): 5/14 ≈ 0.357
    ├── Some((5, 4)): 104/199 ≈ 0.523
      ├── Some((4, 0)): 18/29 ≈ 0.621
      ├── Some((4, 1)): 9/19 ≈ 0.474
      ├── Some((4, 2)): 9/20 ≈ 0.450
      ├── Some((4, 3)): 11/22 ≈ 0.500
      ├── Some((4, 4)): 17/28 ≈ 0.607
      ├── Some((4, 5)): 5/15 ≈ 0.333
      ├── Some((4, 6)): 4/13 ≈ 0.308
      ├── Some((4, 7)): 15/26 ≈ 0.577
      └── Some((4, 8)): 15/26 ≈ 0.577
    ├── Some((5, 5)): 71/149 ≈ 0.477
      ├── Some((5, 0)): 10/20 ≈ 0.500
      ├── Some((5, 1)): 6/16 ≈ 0.375
      ├── Some((5, 2)): 8/18 ≈ 0.444
      ├── Some((5, 3)): 12/22 ≈ 0.545
      ├── Some((5, 4)): 10/20 ≈ 0.500
      ├── Some((5, 6)): 5/14 ≈ 0.357
      ├── Some((5, 7)): 2/10 ≈ 0.200
      └── Some((5, 8)): 17/28 ≈ 0.607
    ├── Some((5, 6)): 118/220 ≈ 0.536
      ├── Some((6, 0)): 14/25 ≈ 0.560
      ├── Some((6, 1)): 6/16 ≈ 0.375
      ├── Some((6, 2)): 12/23 ≈ 0.522
      ├── Some((6, 3)): 15/27 ≈ 0.556
      ├── Some((6, 4)): 9/20 ≈ 0.450
      ├── Some((6, 5)): 18/30 ≈ 0.600
      ├── Some((6, 6)): 14/25 ≈ 0.560
      ├── Some((6, 7)): 10/21 ≈ 0.476
      └── Some((6, 8)): 20/32 ≈ 0.625
    ├── Some((5, 7)): 143/257 ≈ 0.556
      ├── Some((7, 0)): 20/33 ≈ 0.606
      ├── Some((7, 1)): 5/16 ≈ 0.312
      ├── Some((7, 2)): 10/22 ≈ 0.455
      ├── Some((7, 3)): 14/26 ≈ 0.538
      ├── Some((7, 4)): 16/29 ≈ 0.552
      ├── Some((7, 5)): 24/37 ≈ 0.649
      ├── Some((7, 6)): 15/28 ≈ 0.536
      ├── Some((7, 7)): 20/33 ≈ 0.606
      └── Some((7, 8)): 19/32 ≈ 0.594
    └── Some((5, 8)): 94/184 ≈ 0.511
      ├── Some((8, 0)): 10/20 ≈ 0.500
      ├── Some((8, 1)): 13/23 ≈ 0.565
      ├── Some((8, 2)): 14/24 ≈ 0.583
      ├── Some((8, 3)): 18/28 ≈ 0.643
      ├── Some((8, 4)): 8/18 ≈ 0.444
      ├── Some((8, 5)): 9/19 ≈ 0.474
      ├── Some((8, 6)): 8/18 ≈ 0.444
      ├── Some((8, 7)): 8/18 ≈ 0.444
      └── Some((8, 8)): 6/15 ≈ 0.400
  ├── Some((0, 6)): 1162/2177 ≈ 0.534
    ├── Some((6, 0)): 127/239 ≈ 0.531
      ├── Some((0, 0)): 15/29 ≈ 0.517
      ├── Some((0, 1)): 10/23 ≈ 0.435
      ├── Some((0, 2)): 22/37 ≈ 0.595
      ├── Some((0, 3)): 15/29 ≈ 0.517
      ├── Some((0, 4)): 10/23 ≈ 0.435
      ├── Some((0, 5)): 17/31 ≈ 0.548
      ├── Some((0, 7)): 19/33 ≈ 0.576
      └── Some((0, 8)): 19/33 ≈ 0.576
    ├── Some((6, 1)): 140/259 ≈ 0.541
      ├── Some((1, 0)): 13/26 ≈ 0.500
      ├── Some((1, 1)): 9/21 ≈ 0.429
      ├── Some((1, 2)): 23/37 ≈ 0.622
      ├── Some((1, 3)): 12/25 ≈ 0.480
      ├── Some((1, 4)): 17/31 ≈ 0.548
      ├── Some((1, 5)): 7/19 ≈ 0.368
      ├── Some((1, 6)): 30/45 ≈ 0.667
      ├── Some((1, 7)): 21/35 ≈ 0.600
      └── Some((1, 8)): 7/19 ≈ 0.368
    ├── Some((6, 2)): 80/168 ≈ 0.476
      ├── Some((2, 1)): 12/23 ≈ 0.522
      ├── Some((2, 2)): 9/20 ≈ 0.450
      ├── Some((2, 3)): 13/25 ≈ 0.520
      ├── Some((2, 4)): 10/21 ≈ 0.476
      ├── Some((2, 5)): 5/15 ≈ 0.333
      ├── Some((2, 6)): 6/16 ≈ 0.375
      ├── Some((2, 7)): 10/21 ≈ 0.476
      └── Some((2, 8)): 14/26 ≈ 0.538
    ├── Some((6, 3)): 123/233 ≈ 0.528
      ├── Some((3, 0)): 29/43 ≈ 0.674
      ├── Some((3, 1)): 13/25 ≈ 0.520
      ├── Some((3, 2)): 8/19 ≈ 0.421
      ├── Some((3, 3)): 11/23 ≈ 0.478
      ├── Some((3, 4)): 9/21 ≈ 0.429
      ├── Some((3, 5)): 15/28 ≈ 0.536
      ├── Some((3, 6)): 8/19 ≈ 0.421
      ├── Some((3, 7)): 16/29 ≈ 0.552
      └── Some((3, 8)): 13/25 ≈ 0.520
    ├── Some((6, 4)): 109/212 ≈ 0.514
      ├── Some((4, 0)): 6/17 ≈ 0.353
      ├── Some((4, 1)): 18/30 ≈ 0.600
      ├── Some((4, 2)): 26/39 ≈ 0.667
      ├── Some((4, 3)): 10/21 ≈ 0.476
      ├── Some((4, 4)): 10/21 ≈ 0.476
      ├── Some((4, 5)): 12/24 ≈ 0.500
      ├── Some((4, 6)): 5/15 ≈ 0.333
      ├── Some((4, 7)): 8/19 ≈ 0.421
      └── Some((4, 8)): 13/25 ≈ 0.520
    ├── Some((6, 5)): 119/227 ≈ 0.524
      ├── Some((5, 0)): 20/33 ≈ 0.606
      ├── Some((5, 1)): 12/24 ≈ 0.500
      ├── Some((5, 2)): 20/33 ≈ 0.606
      ├── Some((5, 3)): 13/25 ≈ 0.520
      ├── Some((5, 4)): 16/28 ≈ 0.571
      ├── Some((5, 5)): 11/23 ≈ 0.478
      ├── Some((5, 6)): 10/22 ≈ 0.455
      ├── Some((5, 7)): 3/13 ≈ 0.231
      └── Some((5, 8)): 13/25 ≈ 0.520
    ├── Some((6, 6)): 137/254 ≈ 0.539
      ├── Some((6, 0)): 15/30 ≈ 0.500
      ├── Some((6, 1)): 10/23 ≈ 0.435
      ├── Some((6, 2)): 8/21 ≈ 0.381
      ├── Some((6, 3)): 44/62 ≈ 0.710
      ├── Some((6, 4)): 10/23 ≈ 0.435
      ├── Some((6, 5)): 22/38 ≈ 0.579
      ├── Some((6, 7)): 4/16 ≈ 0.250
      └── Some((6, 8)): 24/40 ≈ 0.600
    ├── Some((6, 7)): 221/378 ≈ 0.585
      ├── Some((7, 0)): 18/35 ≈ 0.514
      ├── Some((7, 1)): 26/44 ≈ 0.591
      ├── Some((7, 2)): 26/44 ≈ 0.591
      ├── Some((7, 3)): 24/42 ≈ 0.571
      ├── Some((7, 4)): 29/47 ≈ 0.617
      ├── Some((7, 5)): 15/31 ≈ 0.484
      ├── Some((7, 6)): 13/28 ≈ 0.464
      ├── Some((7, 7)): 19/36 ≈ 0.528
      └── Some((7, 8)): 50/70 ≈ 0.714
    └── Some((6, 8)): 105/206 ≈ 0.510
      ├── Some((8, 0)): 8/19 ≈ 0.421
      ├── Some((8, 1)): 6/16 ≈ 0.375
      ├── Some((8, 2)): 17/29 ≈ 0.586
      ├── Some((8, 3)): 7/18 ≈ 0.389
      ├── Some((8, 4)): 9/20 ≈ 0.450
      ├── Some((8, 5)): 11/22 ≈ 0.500
      ├── Some((8, 6)): 13/24 ≈ 0.542
      ├── Some((8, 7)): 14/26 ≈ 0.538
      └── Some((8, 8)): 19/31 ≈ 0.613
  ├── Some((0, 7)): 1224/2283 ≈ 0.536
    ├── Some((7, 0)): 153/280 ≈ 0.546
      ├── Some((0, 0)): 26/43 ≈ 0.605
      ├── Some((0, 1)): 19/35 ≈ 0.543
      ├── Some((0, 2)): 8/22 ≈ 0.364
      ├── Some((0, 3)): 4/16 ≈ 0.250
      ├── Some((0, 4)): 24/41 ≈ 0.585
      ├── Some((0, 5)): 33/51 ≈ 0.647
      ├── Some((0, 6)): 27/44 ≈ 0.614
      └── Some((0, 8)): 12/27 ≈ 0.444
    ├── Some((7, 1)): 162/293 ≈ 0.553
      ├── Some((1, 0)): 12/26 ≈ 0.462
      ├── Some((1, 1)): 17/31 ≈ 0.548
      ├── Some((1, 2)): 21/36 ≈ 0.583
      ├── Some((1, 3)): 25/40 ≈ 0.625
      ├── Some((1, 4)): 15/29 ≈ 0.517
      ├── Some((1, 5)): 19/34 ≈ 0.559
      ├── Some((1, 6)): 26/41 ≈ 0.634
      ├── Some((1, 7)): 13/27 ≈ 0.481
      └── Some((1, 8)): 14/28 ≈ 0.500
    ├── Some((7, 2)): 81/170 ≈ 0.476
      ├── Some((2, 1)): 7/18 ≈ 0.389
      ├── Some((2, 2)): 10/21 ≈ 0.476
      ├── Some((2, 3)): 10/21 ≈ 0.476
      ├── Some((2, 4)): 11/22 ≈ 0.500
      ├── Some((2, 5)): 13/25 ≈ 0.520
      ├── Some((2, 6)): 21/33 ≈ 0.636
      ├── Some((2, 7)): 6/16 ≈ 0.375
      └── Some((2, 8)): 3/13 ≈ 0.231
    ├── Some((7, 3)): 185/327 ≈ 0.566
      ├── Some((3, 0)): 15/30 ≈ 0.500
      ├── Some((3, 1)): 16/31 ≈ 0.516
      ├── Some((3, 2)): 17/32 ≈ 0.531
      ├── Some((3, 3)): 6/19 ≈ 0.316
      ├── Some((3, 4)): 37/55 ≈ 0.673
      ├── Some((3, 5)): 38/56 ≈ 0.679
      ├── Some((3, 6)): 12/27 ≈ 0.444
      ├── Some((3, 7)): 18/34 ≈ 0.529
      └── Some((3, 8)): 25/42 ≈ 0.595
    ├── Some((7, 4)): 61/139 ≈ 0.439
      ├── Some((4, 0)): 12/21 ≈ 0.571
      ├── Some((4, 1)): 6/14 ≈ 0.429
      ├── Some((4, 2)): 6/15 ≈ 0.400
      ├── Some((4, 3)): 10/19 ≈ 0.526
      ├── Some((4, 4)): 4/12 ≈ 0.333
      ├── Some((4, 5)): 7/16 ≈ 0.438
      ├── Some((4, 6)): 7/16 ≈ 0.438
      ├── Some((4, 7)): 5/13 ≈ 0.385
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((7, 5)): 116/224 ≈ 0.518
      ├── Some((5, 0)): 2/12 ≈ 0.167
      ├── Some((5, 1)): 12/24 ≈ 0.500
      ├── Some((5, 2)): 10/22 ≈ 0.455
      ├── Some((5, 3)): 6/17 ≈ 0.353
      ├── Some((5, 4)): 10/22 ≈ 0.455
      ├── Some((5, 5)): 21/34 ≈ 0.618
      ├── Some((5, 6)): 15/27 ≈ 0.556
      ├── Some((5, 7)): 16/29 ≈ 0.552
      └── Some((5, 8)): 23/36 ≈ 0.639
    ├── Some((7, 6)): 120/230 ≈ 0.522
      ├── Some((6, 0)): 14/26 ≈ 0.538
      ├── Some((6, 1)): 5/16 ≈ 0.312
      ├── Some((6, 2)): 14/26 ≈ 0.538
      ├── Some((6, 3)): 15/27 ≈ 0.556
      ├── Some((6, 4)): 15/28 ≈ 0.536
      ├── Some((6, 5)): 20/33 ≈ 0.606
      ├── Some((6, 6)): 13/25 ≈ 0.520
      ├── Some((6, 7)): 13/25 ≈ 0.520
      └── Some((6, 8)): 11/23 ≈ 0.478
    ├── Some((7, 7)): 161/292 ≈ 0.551
      ├── Some((7, 0)): 26/43 ≈ 0.605
      ├── Some((7, 1)): 28/46 ≈ 0.609
      ├── Some((7, 2)): 22/39 ≈ 0.564
      ├── Some((7, 3)): 18/34 ≈ 0.529
      ├── Some((7, 4)): 12/27 ≈ 0.444
      ├── Some((7, 5)): 18/34 ≈ 0.529
      ├── Some((7, 6)): 27/45 ≈ 0.600
      └── Some((7, 8)): 9/23 ≈ 0.391
    └── Some((7, 8)): 185/327 ≈ 0.566
      ├── Some((8, 0)): 20/36 ≈ 0.556
      ├── Some((8, 1)): 26/43 ≈ 0.605
      ├── Some((8, 2)): 25/42 ≈ 0.595
      ├── Some((8, 3)): 22/38 ≈ 0.579
      ├── Some((8, 4)): 28/45 ≈ 0.622
      ├── Some((8, 5)): 10/24 ≈ 0.417
      ├── Some((8, 6)): 4/16 ≈ 0.250
      ├── Some((8, 7)): 21/37 ≈ 0.568
      └── Some((8, 8)): 28/45 ≈ 0.622
  └── Some((0, 8)): 1061/2004 ≈ 0.529
    ├── Some((8, 0)): 155/278 ≈ 0.558
      ├── Some((0, 0)): 20/35 ≈ 0.571
      ├── Some((0, 1)): 16/31 ≈ 0.516
      ├── Some((0, 2)): 15/30 ≈ 0.500
      ├── Some((0, 3)): 10/24 ≈ 0.417
      ├── Some((0, 4)): 17/32 ≈ 0.531
      ├── Some((0, 5)): 23/39 ≈ 0.590
      ├── Some((0, 6)): 25/41 ≈ 0.610
      └── Some((0, 7)): 29/45 ≈ 0.644
    ├── Some((8, 1)): 109/210 ≈ 0.519
      ├── Some((1, 0)): 1/10 ≈ 0.100
      ├── Some((1, 1)): 5/15 ≈ 0.333
      ├── Some((1, 2)): 6/17 ≈ 0.353
      ├── Some((1, 3)): 7/18 ≈ 0.389
      ├── Some((1, 4)): 26/39 ≈ 0.667
      ├── Some((1, 5)): 19/31 ≈ 0.613
      ├── Some((1, 6)): 13/25 ≈ 0.520
      ├── Some((1, 7)): 10/21 ≈ 0.476
      └── Some((1, 8)): 21/33 ≈ 0.636
    ├── Some((8, 2)): 70/150 ≈ 0.467
      ├── Some((2, 1)): 12/22 ≈ 0.545
      ├── Some((2, 2)): 8/18 ≈ 0.444
      ├── Some((2, 3)): 7/17 ≈ 0.412
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 8/18 ≈ 0.444
      ├── Some((2, 6)): 7/17 ≈ 0.412
      ├── Some((2, 7)): 7/17 ≈ 0.412
      └── Some((2, 8)): 14/25 ≈ 0.560
    ├── Some((8, 3)): 119/225 ≈ 0.529
      ├── Some((3, 0)): 6/17 ≈ 0.353
      ├── Some((3, 1)): 16/28 ≈ 0.571
      ├── Some((3, 2)): 17/29 ≈ 0.586
      ├── Some((3, 3)): 15/27 ≈ 0.556
      ├── Some((3, 4)): 6/17 ≈ 0.353
      ├── Some((3, 5)): 13/25 ≈ 0.520
      ├── Some((3, 6)): 14/26 ≈ 0.538
      ├── Some((3, 7)): 15/27 ≈ 0.556
      └── Some((3, 8)): 16/28 ≈ 0.571
    ├── Some((8, 4)): 147/266 ≈ 0.553
      ├── Some((4, 0)): 18/31 ≈ 0.581
      ├── Some((4, 1)): 18/32 ≈ 0.562
      ├── Some((4, 2)): 11/24 ≈ 0.458
      ├── Some((4, 3)): 18/32 ≈ 0.562
      ├── Some((4, 4)): 10/22 ≈ 0.455
      ├── Some((4, 5)): 13/26 ≈ 0.500
      ├── Some((4, 6)): 14/27 ≈ 0.519
      ├── Some((4, 7)): 9/21 ≈ 0.429
      └── Some((4, 8)): 35/50 ≈ 0.700
    ├── Some((8, 5)): 98/193 ≈ 0.508
      ├── Some((5, 0)): 19/30 ≈ 0.633
      ├── Some((5, 1)): 15/26 ≈ 0.577
      ├── Some((5, 2)): 14/25 ≈ 0.560
      ├── Some((5, 3)): 4/14 ≈ 0.286
      ├── Some((5, 4)): 12/23 ≈ 0.522
      ├── Some((5, 5)): 13/24 ≈ 0.542
      ├── Some((5, 6)): 7/17 ≈ 0.412
      ├── Some((5, 7)): 5/15 ≈ 0.333
      └── Some((5, 8)): 8/18 ≈ 0.444
    ├── Some((8, 6)): 84/172 ≈ 0.488
      ├── Some((6, 0)): 4/13 ≈ 0.308
      ├── Some((6, 1)): 15/25 ≈ 0.600
      ├── Some((6, 2)): 3/12 ≈ 0.250
      ├── Some((6, 3)): 9/19 ≈ 0.474
      ├── Some((6, 4)): 10/20 ≈ 0.500
      ├── Some((6, 5)): 12/22 ≈ 0.545
      ├── Some((6, 6)): 10/20 ≈ 0.500
      ├── Some((6, 7)): 11/21 ≈ 0.524
      └── Some((6, 8)): 9/19 ≈ 0.474
    ├── Some((8, 7)): 169/298 ≈ 0.567
      ├── Some((7, 0)): 18/32 ≈ 0.562
      ├── Some((7, 1)): 13/27 ≈ 0.481
      ├── Some((7, 2)): 22/37 ≈ 0.595
      ├── Some((7, 3)): 7/19 ≈ 0.368
      ├── Some((7, 4)): 20/35 ≈ 0.571
      ├── Some((7, 5)): 29/45 ≈ 0.644
      ├── Some((7, 6)): 18/32 ≈ 0.562
      ├── Some((7, 7)): 27/42 ≈ 0.643
      └── Some((7, 8)): 14/28 ≈ 0.500
    └── Some((8, 8)): 110/211 ≈ 0.521
      ├── Some((8, 0)): 7/18 ≈ 0.389
      ├── Some((8, 1)): 17/30 ≈ 0.567
      ├── Some((8, 2)): 23/37 ≈ 0.622
      ├── Some((8, 3)): 11/23 ≈ 0.478
      ├── Some((8, 4)): 8/20 ≈ 0.400
      ├── Some((8, 5)): 24/38 ≈ 0.632
      ├── Some((8, 6)): 10/22 ≈ 0.455
      └── Some((8, 7)): 10/22 ≈ 0.455
├── Some((2, 1)): 5911/11419 ≈ 0.518
  ├── Some((1, 0)): 676/1303 ≈ 0.519
    ├── Some((0, 0)): 99/179 ≈ 0.553
      ├── Some((0, 1)): 15/25 ≈ 0.600
      ├── Some((0, 2)): 18/28 ≈ 0.643
      ├── Some((0, 3)): 15/25 ≈ 0.600
      ├── Some((0, 4)): 17/27 ≈ 0.630
      ├── Some((0, 5)): 10/20 ≈ 0.500
      ├── Some((0, 6)): 9/19 ≈ 0.474
      ├── Some((0, 7)): 10/20 ≈ 0.500
      └── Some((0, 8)): 5/14 ≈ 0.357
    ├── Some((0, 1)): 78/149 ≈ 0.523
      ├── Some((1, 1)): 15/24 ≈ 0.625
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 3)): 1/8 ≈ 0.125
      ├── Some((1, 4)): 8/17 ≈ 0.471
      ├── Some((1, 5)): 10/19 ≈ 0.526
      ├── Some((1, 6)): 10/19 ≈ 0.526
      ├── Some((1, 7)): 12/21 ≈ 0.571
      └── Some((1, 8)): 13/22 ≈ 0.591
    ├── Some((0, 2)): 95/174 ≈ 0.546
      ├── Some((2, 0)): 24/35 ≈ 0.686
      ├── Some((2, 2)): 9/19 ≈ 0.474
      ├── Some((2, 3)): 0/8 ≈ 0.000
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 5/14 ≈ 0.357
      ├── Some((2, 6)): 15/25 ≈ 0.600
      ├── Some((2, 7)): 14/24 ≈ 0.583
      └── Some((2, 8)): 22/33 ≈ 0.667
    ├── Some((0, 3)): 66/132 ≈ 0.500
      ├── Some((3, 0)): 5/12 ≈ 0.417
      ├── Some((3, 1)): 1/8 ≈ 0.125
      ├── Some((3, 2)): 8/15 ≈ 0.533
      ├── Some((3, 3)): 10/18 ≈ 0.556
      ├── Some((3, 4)): 4/11 ≈ 0.364
      ├── Some((3, 5)): 9/16 ≈ 0.562
      ├── Some((3, 6)): 12/20 ≈ 0.600
      ├── Some((3, 7)): 10/18 ≈ 0.556
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((0, 4)): 59/121 ≈ 0.488
      ├── Some((4, 0)): 9/16 ≈ 0.562
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 15/22 ≈ 0.682
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 7/14 ≈ 0.500
      └── Some((4, 8)): 0/6 ≈ 0.000
    ├── Some((0, 5)): 70/138 ≈ 0.507
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 8/16 ≈ 0.500
      ├── Some((5, 4)): 12/20 ≈ 0.600
      ├── Some((5, 5)): 12/20 ≈ 0.600
      ├── Some((5, 6)): 9/17 ≈ 0.529
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((0, 6)): 85/159 ≈ 0.535
      ├── Some((6, 0)): 12/20 ≈ 0.600
      ├── Some((6, 1)): 16/25 ≈ 0.640
      ├── Some((6, 2)): 2/9 ≈ 0.222
      ├── Some((6, 3)): 7/15 ≈ 0.467
      ├── Some((6, 4)): 4/12 ≈ 0.333
      ├── Some((6, 5)): 16/25 ≈ 0.640
      ├── Some((6, 6)): 7/15 ≈ 0.467
      ├── Some((6, 7)): 17/26 ≈ 0.654
      └── Some((6, 8)): 3/11 ≈ 0.273
    ├── Some((0, 7)): 51/109 ≈ 0.468
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 8/15 ≈ 0.533
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 1/7 ≈ 0.143
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 7/14 ≈ 0.500
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 11/17 ≈ 0.647
    └── Some((0, 8)): 72/141 ≈ 0.511
      ├── Some((8, 0)): 1/8 ≈ 0.125
      ├── Some((8, 1)): 18/26 ≈ 0.692
      ├── Some((8, 2)): 9/17 ≈ 0.529
      ├── Some((8, 3)): 3/10 ≈ 0.300
      ├── Some((8, 4)): 11/19 ≈ 0.579
      ├── Some((8, 5)): 15/23 ≈ 0.652
      ├── Some((8, 6)): 0/7 ≈ 0.000
      ├── Some((8, 7)): 11/19 ≈ 0.579
      └── Some((8, 8)): 3/11 ≈ 0.273
  ├── Some((1, 1)): 582/1141 ≈ 0.510
    ├── Some((1, 0)): 68/136 ≈ 0.500
      ├── Some((0, 0)): 3/10 ≈ 0.300
      ├── Some((0, 1)): 15/23 ≈ 0.652
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 4/11 ≈ 0.364
      ├── Some((0, 4)): 10/18 ≈ 0.556
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 6)): 4/11 ≈ 0.364
      ├── Some((0, 7)): 8/16 ≈ 0.500
      └── Some((0, 8)): 11/19 ≈ 0.579
    ├── Some((1, 2)): 74/145 ≈ 0.510
      ├── Some((2, 0)): 16/25 ≈ 0.640
      ├── Some((2, 2)): 15/24 ≈ 0.625
      ├── Some((2, 3)): 7/16 ≈ 0.438
      ├── Some((2, 4)): 5/13 ≈ 0.385
      ├── Some((2, 5)): 6/14 ≈ 0.429
      ├── Some((2, 6)): 7/16 ≈ 0.438
      ├── Some((2, 7)): 10/19 ≈ 0.526
      └── Some((2, 8)): 8/17 ≈ 0.471
    ├── Some((1, 3)): 84/160 ≈ 0.525
      ├── Some((3, 0)): 9/18 ≈ 0.500
      ├── Some((3, 1)): 8/16 ≈ 0.500
      ├── Some((3, 2)): 3/11 ≈ 0.273
      ├── Some((3, 3)): 15/24 ≈ 0.625
      ├── Some((3, 4)): 7/15 ≈ 0.467
      ├── Some((3, 5)): 9/18 ≈ 0.500
      ├── Some((3, 6)): 17/26 ≈ 0.654
      ├── Some((3, 7)): 8/16 ≈ 0.500
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((1, 4)): 66/133 ≈ 0.496
      ├── Some((4, 0)): 6/13 ≈ 0.462
      ├── Some((4, 1)): 7/14 ≈ 0.500
      ├── Some((4, 2)): 6/13 ≈ 0.462
      ├── Some((4, 3)): 7/15 ≈ 0.467
      ├── Some((4, 4)): 15/23 ≈ 0.652
      ├── Some((4, 5)): 3/10 ≈ 0.300
      ├── Some((4, 6)): 7/15 ≈ 0.467
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((1, 5)): 86/162 ≈ 0.531
      ├── Some((5, 0)): 11/20 ≈ 0.550
      ├── Some((5, 1)): 21/30 ≈ 0.700
      ├── Some((5, 2)): 4/12 ≈ 0.333
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 10/19 ≈ 0.526
      ├── Some((5, 5)): 15/24 ≈ 0.625
      ├── Some((5, 6)): 8/16 ≈ 0.500
      ├── Some((5, 7)): 4/12 ≈ 0.333
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((1, 6)): 37/89 ≈ 0.416
      ├── Some((6, 0)): 5/11 ≈ 0.455
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 7/13 ≈ 0.538
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 0/5 ≈ 0.000
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 3/9 ≈ 0.333
    ├── Some((1, 7)): 111/198 ≈ 0.561
      ├── Some((7, 0)): 19/29 ≈ 0.655
      ├── Some((7, 1)): 11/21 ≈ 0.524
      ├── Some((7, 2)): 7/16 ≈ 0.438
      ├── Some((7, 3)): 13/23 ≈ 0.565
      ├── Some((7, 4)): 16/26 ≈ 0.615
      ├── Some((7, 5)): 4/13 ≈ 0.308
      ├── Some((7, 6)): 9/18 ≈ 0.500
      ├── Some((7, 7)): 16/26 ≈ 0.615
      └── Some((7, 8)): 15/25 ≈ 0.600
    └── Some((1, 8)): 55/117 ≈ 0.470
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 4/11 ≈ 0.364
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 9/16 ≈ 0.562
      ├── Some((8, 4)): 14/21 ≈ 0.667
      ├── Some((8, 5)): 6/13 ≈ 0.462
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 5/12 ≈ 0.417
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((1, 2)): 535/1060 ≈ 0.505
    ├── Some((2, 0)): 130/224 ≈ 0.580
      ├── Some((0, 0)): 6/16 ≈ 0.375
      ├── Some((0, 1)): 10/20 ≈ 0.500
      ├── Some((0, 2)): 13/23 ≈ 0.565
      ├── Some((0, 3)): 14/24 ≈ 0.583
      ├── Some((0, 4)): 22/33 ≈ 0.667
      ├── Some((0, 5)): 19/30 ≈ 0.633
      ├── Some((0, 6)): 6/16 ≈ 0.375
      ├── Some((0, 7)): 12/22 ≈ 0.545
      └── Some((0, 8)): 28/39 ≈ 0.718
    ├── Some((2, 2)): 38/90 ≈ 0.422
      ├── Some((2, 0)): 3/10 ≈ 0.300
      ├── Some((2, 3)): 1/8 ≈ 0.125
      ├── Some((2, 4)): 4/11 ≈ 0.364
      ├── Some((2, 5)): 7/15 ≈ 0.467
      ├── Some((2, 6)): 1/8 ≈ 0.125
      ├── Some((2, 7)): 5/12 ≈ 0.417
      └── Some((2, 8)): 17/25 ≈ 0.680
    ├── Some((2, 3)): 45/100 ≈ 0.450
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 13/19 ≈ 0.684
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 9/16 ≈ 0.562
      ├── Some((3, 4)): 1/7 ≈ 0.143
      ├── Some((3, 5)): 1/7 ≈ 0.143
      ├── Some((3, 6)): 4/10 ≈ 0.400
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 4/10 ≈ 0.400
    ├── Some((2, 4)): 46/102 ≈ 0.451
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 2/8 ≈ 0.250
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 9/16 ≈ 0.562
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 2/8 ≈ 0.250
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((2, 5)): 42/96 ≈ 0.438
      ├── Some((5, 0)): 1/6 ≈ 0.167
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 4/10 ≈ 0.400
      ├── Some((5, 3)): 10/16 ≈ 0.625
      ├── Some((5, 4)): 2/8 ≈ 0.250
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 8/14 ≈ 0.571
      └── Some((5, 8)): 3/9 ≈ 0.333
    ├── Some((2, 6)): 58/120 ≈ 0.483
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 4/11 ≈ 0.364
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 5/12 ≈ 0.417
      ├── Some((6, 4)): 13/20 ≈ 0.650
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 6)): 11/18 ≈ 0.611
      ├── Some((6, 7)): 5/12 ≈ 0.417
      └── Some((6, 8)): 9/16 ≈ 0.562
    ├── Some((2, 7)): 100/182 ≈ 0.549
      ├── Some((7, 0)): 15/24 ≈ 0.625
      ├── Some((7, 1)): 3/11 ≈ 0.273
      ├── Some((7, 2)): 3/11 ≈ 0.273
      ├── Some((7, 3)): 11/20 ≈ 0.550
      ├── Some((7, 4)): 9/18 ≈ 0.500
      ├── Some((7, 5)): 10/19 ≈ 0.526
      ├── Some((7, 6)): 18/28 ≈ 0.643
      ├── Some((7, 7)): 13/22 ≈ 0.591
      └── Some((7, 8)): 18/28 ≈ 0.643
    └── Some((2, 8)): 75/145 ≈ 0.517
      ├── Some((8, 0)): 6/13 ≈ 0.462
      ├── Some((8, 1)): 10/18 ≈ 0.556
      ├── Some((8, 2)): 10/18 ≈ 0.556
      ├── Some((8, 3)): 11/19 ≈ 0.579
      ├── Some((8, 4)): 4/11 ≈ 0.364
      ├── Some((8, 5)): 8/16 ≈ 0.500
      ├── Some((8, 6)): 11/19 ≈ 0.579
      ├── Some((8, 7)): 11/19 ≈ 0.579
      └── Some((8, 8)): 4/11 ≈ 0.364
  ├── Some((1, 3)): 974/1810 ≈ 0.538
    ├── Some((3, 0)): 61/131 ≈ 0.466
      ├── Some((0, 0)): 10/18 ≈ 0.556
      ├── Some((0, 1)): 3/10 ≈ 0.300
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 5/13 ≈ 0.385
      ├── Some((0, 4)): 11/19 ≈ 0.579
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 6)): 9/17 ≈ 0.529
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 7/15 ≈ 0.467
    ├── Some((3, 1)): 122/222 ≈ 0.550
      ├── Some((1, 0)): 19/32 ≈ 0.594
      ├── Some((1, 1)): 9/21 ≈ 0.429
      ├── Some((1, 2)): 21/34 ≈ 0.618
      ├── Some((1, 4)): 23/36 ≈ 0.639
      ├── Some((1, 5)): 9/21 ≈ 0.429
      ├── Some((1, 6)): 18/31 ≈ 0.581
      ├── Some((1, 7)): 5/16 ≈ 0.312
      └── Some((1, 8)): 17/30 ≈ 0.567
    ├── Some((3, 2)): 168/287 ≈ 0.585
      ├── Some((2, 0)): 24/39 ≈ 0.615
      ├── Some((2, 2)): 21/36 ≈ 0.583
      ├── Some((2, 3)): 32/48 ≈ 0.667
      ├── Some((2, 4)): 13/27 ≈ 0.481
      ├── Some((2, 5)): 27/43 ≈ 0.628
      ├── Some((2, 6)): 8/21 ≈ 0.381
      ├── Some((2, 7)): 16/30 ≈ 0.533
      └── Some((2, 8)): 26/42 ≈ 0.619
    ├── Some((3, 3)): 116/213 ≈ 0.545
      ├── Some((3, 0)): 13/25 ≈ 0.520
      ├── Some((3, 1)): 16/28 ≈ 0.571
      ├── Some((3, 2)): 17/29 ≈ 0.586
      ├── Some((3, 4)): 13/25 ≈ 0.520
      ├── Some((3, 5)): 20/33 ≈ 0.606
      ├── Some((3, 6)): 7/18 ≈ 0.389
      ├── Some((3, 7)): 18/30 ≈ 0.600
      └── Some((3, 8)): 12/24 ≈ 0.500
    ├── Some((3, 4)): 121/220 ≈ 0.550
      ├── Some((4, 0)): 9/20 ≈ 0.450
      ├── Some((4, 1)): 14/25 ≈ 0.560
      ├── Some((4, 2)): 19/31 ≈ 0.613
      ├── Some((4, 3)): 10/21 ≈ 0.476
      ├── Some((4, 4)): 12/23 ≈ 0.522
      ├── Some((4, 5)): 4/14 ≈ 0.286
      ├── Some((4, 6)): 10/21 ≈ 0.476
      ├── Some((4, 7)): 7/17 ≈ 0.412
      └── Some((4, 8)): 35/47 ≈ 0.745
    ├── Some((3, 5)): 60/129 ≈ 0.465
      ├── Some((5, 0)): 9/17 ≈ 0.529
      ├── Some((5, 1)): 3/10 ≈ 0.300
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 13/21 ≈ 0.619
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 6/14 ≈ 0.429
      ├── Some((5, 7)): 7/15 ≈ 0.467
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((3, 6)): 102/192 ≈ 0.531
      ├── Some((6, 0)): 16/27 ≈ 0.593
      ├── Some((6, 1)): 3/12 ≈ 0.250
      ├── Some((6, 2)): 21/32 ≈ 0.656
      ├── Some((6, 3)): 13/23 ≈ 0.565
      ├── Some((6, 4)): 3/12 ≈ 0.250
      ├── Some((6, 5)): 17/28 ≈ 0.607
      ├── Some((6, 6)): 11/21 ≈ 0.524
      ├── Some((6, 7)): 4/13 ≈ 0.308
      └── Some((6, 8)): 13/23 ≈ 0.565
    ├── Some((3, 7)): 111/206 ≈ 0.539
      ├── Some((7, 0)): 16/27 ≈ 0.593
      ├── Some((7, 1)): 19/30 ≈ 0.633
      ├── Some((7, 2)): 7/17 ≈ 0.412
      ├── Some((7, 3)): 15/26 ≈ 0.577
      ├── Some((7, 4)): 20/31 ≈ 0.645
      ├── Some((7, 5)): 4/13 ≈ 0.308
      ├── Some((7, 6)): 10/20 ≈ 0.500
      ├── Some((7, 7)): 5/15 ≈ 0.333
      └── Some((7, 8)): 15/26 ≈ 0.577
    └── Some((3, 8)): 113/209 ≈ 0.541
      ├── Some((8, 0)): 15/26 ≈ 0.577
      ├── Some((8, 1)): 8/18 ≈ 0.444
      ├── Some((8, 2)): 18/29 ≈ 0.621
      ├── Some((8, 3)): 16/27 ≈ 0.593
      ├── Some((8, 4)): 7/17 ≈ 0.412
      ├── Some((8, 5)): 5/15 ≈ 0.333
      ├── Some((8, 6)): 17/28 ≈ 0.607
      ├── Some((8, 7)): 8/18 ≈ 0.444
      └── Some((8, 8)): 18/30 ≈ 0.600
  ├── Some((1, 4)): 812/1536 ≈ 0.529
    ├── Some((4, 0)): 116/208 ≈ 0.558
      ├── Some((0, 0)): 17/28 ≈ 0.607
      ├── Some((0, 1)): 11/21 ≈ 0.524
      ├── Some((0, 2)): 11/21 ≈ 0.524
      ├── Some((0, 3)): 19/30 ≈ 0.633
      ├── Some((0, 4)): 15/25 ≈ 0.600
      ├── Some((0, 5)): 11/21 ≈ 0.524
      ├── Some((0, 6)): 12/22 ≈ 0.545
      ├── Some((0, 7)): 11/21 ≈ 0.524
      └── Some((0, 8)): 8/18 ≈ 0.444
    ├── Some((4, 1)): 97/181 ≈ 0.536
      ├── Some((1, 0)): 14/25 ≈ 0.560
      ├── Some((1, 1)): 11/22 ≈ 0.500
      ├── Some((1, 2)): 4/13 ≈ 0.308
      ├── Some((1, 3)): 9/19 ≈ 0.474
      ├── Some((1, 5)): 20/31 ≈ 0.645
      ├── Some((1, 6)): 9/19 ≈ 0.474
      ├── Some((1, 7)): 21/33 ≈ 0.636
      └── Some((1, 8)): 8/18 ≈ 0.444
    ├── Some((4, 2)): 85/163 ≈ 0.521
      ├── Some((2, 0)): 6/15 ≈ 0.400
      ├── Some((2, 2)): 17/27 ≈ 0.630
      ├── Some((2, 3)): 8/18 ≈ 0.444
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 6/15 ≈ 0.400
      ├── Some((2, 6)): 11/21 ≈ 0.524
      ├── Some((2, 7)): 10/20 ≈ 0.500
      └── Some((2, 8)): 20/31 ≈ 0.645
    ├── Some((4, 3)): 70/141 ≈ 0.496
      ├── Some((3, 0)): 4/11 ≈ 0.364
      ├── Some((3, 1)): 7/15 ≈ 0.467
      ├── Some((3, 2)): 5/13 ≈ 0.385
      ├── Some((3, 3)): 5/13 ≈ 0.385
      ├── Some((3, 4)): 10/18 ≈ 0.556
      ├── Some((3, 5)): 9/17 ≈ 0.529
      ├── Some((3, 6)): 12/20 ≈ 0.600
      ├── Some((3, 7)): 7/15 ≈ 0.467
      └── Some((3, 8)): 10/18 ≈ 0.556
    ├── Some((4, 4)): 118/211 ≈ 0.559
      ├── Some((4, 0)): 29/42 ≈ 0.690
      ├── Some((4, 1)): 19/31 ≈ 0.613
      ├── Some((4, 2)): 16/28 ≈ 0.571
      ├── Some((4, 3)): 7/18 ≈ 0.389
      ├── Some((4, 5)): 9/20 ≈ 0.450
      ├── Some((4, 6)): 17/29 ≈ 0.586
      ├── Some((4, 7)): 8/19 ≈ 0.421
      └── Some((4, 8)): 12/23 ≈ 0.522
    ├── Some((4, 5)): 59/125 ≈ 0.472
      ├── Some((5, 0)): 5/12 ≈ 0.417
      ├── Some((5, 1)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 3)): 9/17 ≈ 0.529
      ├── Some((5, 4)): 6/13 ≈ 0.462
      ├── Some((5, 5)): 3/10 ≈ 0.300
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 14/22 ≈ 0.636
      └── Some((5, 8)): 4/11 ≈ 0.364
    ├── Some((4, 6)): 110/200 ≈ 0.550
      ├── Some((6, 0)): 4/13 ≈ 0.308
      ├── Some((6, 1)): 14/24 ≈ 0.583
      ├── Some((6, 2)): 7/17 ≈ 0.412
      ├── Some((6, 3)): 20/30 ≈ 0.667
      ├── Some((6, 4)): 11/21 ≈ 0.524
      ├── Some((6, 5)): 18/28 ≈ 0.643
      ├── Some((6, 6)): 8/18 ≈ 0.444
      ├── Some((6, 7)): 14/24 ≈ 0.583
      └── Some((6, 8)): 14/24 ≈ 0.583
    ├── Some((4, 7)): 59/125 ≈ 0.472
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 10/18 ≈ 0.556
      ├── Some((7, 3)): 8/15 ≈ 0.533
      ├── Some((7, 4)): 10/18 ≈ 0.556
      ├── Some((7, 5)): 12/20 ≈ 0.600
      ├── Some((7, 6)): 3/10 ≈ 0.300
      ├── Some((7, 7)): 2/9 ≈ 0.222
      └── Some((7, 8)): 2/9 ≈ 0.222
    └── Some((4, 8)): 97/181 ≈ 0.536
      ├── Some((8, 0)): 16/26 ≈ 0.615
      ├── Some((8, 1)): 13/22 ≈ 0.591
      ├── Some((8, 2)): 20/30 ≈ 0.667
      ├── Some((8, 3)): 17/27 ≈ 0.630
      ├── Some((8, 4)): 11/20 ≈ 0.550
      ├── Some((8, 5)): 4/13 ≈ 0.308
      ├── Some((8, 6)): 1/9 ≈ 0.111
      ├── Some((8, 7)): 7/16 ≈ 0.438
      └── Some((8, 8)): 8/17 ≈ 0.471
  ├── Some((1, 5)): 572/1124 ≈ 0.509
    ├── Some((5, 0)): 106/186 ≈ 0.570
      ├── Some((0, 0)): 13/22 ≈ 0.591
      ├── Some((0, 1)): 10/19 ≈ 0.526
      ├── Some((0, 2)): 9/17 ≈ 0.529
      ├── Some((0, 3)): 15/24 ≈ 0.625
      ├── Some((0, 4)): 6/14 ≈ 0.429
      ├── Some((0, 5)): 16/25 ≈ 0.640
      ├── Some((0, 6)): 11/20 ≈ 0.550
      ├── Some((0, 7)): 13/22 ≈ 0.591
      └── Some((0, 8)): 13/22 ≈ 0.591
    ├── Some((5, 1)): 40/90 ≈ 0.444
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 13/19 ≈ 0.684
      ├── Some((1, 3)): 3/9 ≈ 0.333
      ├── Some((1, 4)): 1/7 ≈ 0.143
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((5, 2)): 55/113 ≈ 0.487
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 2)): 14/22 ≈ 0.636
      ├── Some((2, 3)): 8/15 ≈ 0.533
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 7/14 ≈ 0.500
      ├── Some((2, 6)): 1/7 ≈ 0.143
      ├── Some((2, 7)): 3/10 ≈ 0.300
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((5, 3)): 53/110 ≈ 0.482
      ├── Some((3, 0)): 4/10 ≈ 0.400
      ├── Some((3, 1)): 2/8 ≈ 0.250
      ├── Some((3, 2)): 9/16 ≈ 0.562
      ├── Some((3, 3)): 12/18 ≈ 0.667
      ├── Some((3, 4)): 3/9 ≈ 0.333
      ├── Some((3, 5)): 10/17 ≈ 0.588
      ├── Some((3, 6)): 4/10 ≈ 0.400
      ├── Some((3, 7)): 2/8 ≈ 0.250
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((5, 4)): 56/115 ≈ 0.487
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 16/22 ≈ 0.727
      ├── Some((4, 7)): 7/14 ≈ 0.500
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((5, 5)): 94/169 ≈ 0.556
      ├── Some((5, 0)): 22/32 ≈ 0.688
      ├── Some((5, 1)): 13/23 ≈ 0.565
      ├── Some((5, 2)): 15/25 ≈ 0.600
      ├── Some((5, 3)): 6/15 ≈ 0.400
      ├── Some((5, 4)): 18/28 ≈ 0.643
      ├── Some((5, 6)): 9/18 ≈ 0.500
      ├── Some((5, 7)): 4/12 ≈ 0.333
      └── Some((5, 8)): 6/15 ≈ 0.400
    ├── Some((5, 6)): 56/115 ≈ 0.487
      ├── Some((6, 0)): 11/18 ≈ 0.611
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 6/13 ≈ 0.462
      ├── Some((6, 4)): 12/18 ≈ 0.667
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 6)): 5/12 ≈ 0.417
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 3/9 ≈ 0.333
    ├── Some((5, 7)): 82/152 ≈ 0.539
      ├── Some((7, 0)): 8/16 ≈ 0.500
      ├── Some((7, 1)): 9/17 ≈ 0.529
      ├── Some((7, 2)): 13/21 ≈ 0.619
      ├── Some((7, 3)): 7/14 ≈ 0.500
      ├── Some((7, 4)): 6/13 ≈ 0.462
      ├── Some((7, 5)): 11/19 ≈ 0.579
      ├── Some((7, 6)): 11/19 ≈ 0.579
      ├── Some((7, 7)): 5/12 ≈ 0.417
      └── Some((7, 8)): 12/20 ≈ 0.600
    └── Some((5, 8)): 29/73 ≈ 0.397
      ├── Some((8, 0)): 7/11 ≈ 0.636
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 1/6 ≈ 0.167
      ├── Some((8, 3)): 6/11 ≈ 0.545
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 7/12 ≈ 0.583
      ├── Some((8, 7)): 0/4 ≈ 0.000
      └── Some((8, 8)): 1/6 ≈ 0.167
  ├── Some((1, 6)): 492/985 ≈ 0.499
    ├── Some((6, 0)): 71/133 ≈ 0.534
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 21/27 ≈ 0.778
      ├── Some((0, 2)): 3/10 ≈ 0.300
      ├── Some((0, 3)): 9/16 ≈ 0.562
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 2/9 ≈ 0.222
      ├── Some((0, 6)): 5/12 ≈ 0.417
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 11/18 ≈ 0.611
    ├── Some((6, 1)): 67/128 ≈ 0.523
      ├── Some((1, 0)): 14/22 ≈ 0.636
      ├── Some((1, 1)): 4/11 ≈ 0.364
      ├── Some((1, 2)): 15/23 ≈ 0.652
      ├── Some((1, 3)): 5/12 ≈ 0.417
      ├── Some((1, 4)): 13/21 ≈ 0.619
      ├── Some((1, 5)): 7/15 ≈ 0.467
      ├── Some((1, 7)): 4/11 ≈ 0.364
      └── Some((1, 8)): 5/12 ≈ 0.417
    ├── Some((6, 2)): 73/136 ≈ 0.537
      ├── Some((2, 0)): 4/11 ≈ 0.364
      ├── Some((2, 2)): 10/18 ≈ 0.556
      ├── Some((2, 3)): 18/26 ≈ 0.692
      ├── Some((2, 4)): 4/12 ≈ 0.333
      ├── Some((2, 5)): 12/20 ≈ 0.600
      ├── Some((2, 6)): 11/19 ≈ 0.579
      ├── Some((2, 7)): 7/15 ≈ 0.467
      └── Some((2, 8)): 6/14 ≈ 0.429
    ├── Some((6, 3)): 58/115 ≈ 0.504
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 6/13 ≈ 0.462
      ├── Some((3, 2)): 11/17 ≈ 0.647
      ├── Some((3, 3)): 10/16 ≈ 0.625
      ├── Some((3, 4)): 2/8 ≈ 0.250
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 5/11 ≈ 0.455
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 10/16 ≈ 0.625
    ├── Some((6, 4)): 48/100 ≈ 0.480
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 9/15 ≈ 0.600
      ├── Some((4, 2)): 8/14 ≈ 0.571
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 7/13 ≈ 0.538
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 3/9 ≈ 0.333
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((6, 5)): 16/50 ≈ 0.320
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 4/7 ≈ 0.571
      ├── Some((5, 2)): 0/3 ≈ 0.000
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 0/4 ≈ 0.000
      ├── Some((5, 6)): 1/5 ≈ 0.200
      ├── Some((5, 7)): 5/8 ≈ 0.625
      └── Some((5, 8)): 3/7 ≈ 0.429
    ├── Some((6, 6)): 58/115 ≈ 0.504
      ├── Some((6, 0)): 3/10 ≈ 0.300
      ├── Some((6, 1)): 13/20 ≈ 0.650
      ├── Some((6, 2)): 2/9 ≈ 0.222
      ├── Some((6, 3)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 12/19 ≈ 0.632
      ├── Some((6, 5)): 9/16 ≈ 0.562
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((6, 7)): 60/117 ≈ 0.513
      ├── Some((7, 0)): 5/11 ≈ 0.455
      ├── Some((7, 1)): 10/17 ≈ 0.588
      ├── Some((7, 2)): 7/14 ≈ 0.500
      ├── Some((7, 3)): 5/12 ≈ 0.417
      ├── Some((7, 4)): 12/18 ≈ 0.667
      ├── Some((7, 5)): 2/8 ≈ 0.250
      ├── Some((7, 6)): 2/8 ≈ 0.250
      ├── Some((7, 7)): 15/21 ≈ 0.714
      └── Some((7, 8)): 1/7 ≈ 0.143
    └── Some((6, 8)): 41/90 ≈ 0.456
      ├── Some((8, 0)): 8/13 ≈ 0.615
      ├── Some((8, 1)): 8/13 ≈ 0.615
      ├── Some((8, 2)): 8/13 ≈ 0.615
      ├── Some((8, 3)): 1/6 ≈ 0.167
      ├── Some((8, 4)): 0/5 ≈ 0.000
      ├── Some((8, 5)): 3/9 ≈ 0.333
      ├── Some((8, 6)): 8/14 ≈ 0.571
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 1/6 ≈ 0.167
  ├── Some((1, 7)): 506/1009 ≈ 0.501
    ├── Some((7, 0)): 62/121 ≈ 0.512
      ├── Some((0, 0)): 4/10 ≈ 0.400
      ├── Some((0, 1)): 10/17 ≈ 0.588
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 3/9 ≈ 0.333
      ├── Some((0, 4)): 13/19 ≈ 0.684
      ├── Some((0, 5)): 11/18 ≈ 0.611
      ├── Some((0, 6)): 8/15 ≈ 0.533
      ├── Some((0, 7)): 8/15 ≈ 0.533
      └── Some((0, 8)): 1/7 ≈ 0.143
    ├── Some((7, 1)): 55/111 ≈ 0.495
      ├── Some((1, 0)): 8/15 ≈ 0.533
      ├── Some((1, 1)): 10/17 ≈ 0.588
      ├── Some((1, 2)): 6/13 ≈ 0.462
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 9/16 ≈ 0.562
      ├── Some((1, 6)): 8/15 ≈ 0.533
      └── Some((1, 8)): 4/11 ≈ 0.364
    ├── Some((7, 2)): 37/84 ≈ 0.440
      ├── Some((2, 0)): 0/5 ≈ 0.000
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 8/14 ≈ 0.571
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 1/6 ≈ 0.167
      ├── Some((2, 6)): 9/15 ≈ 0.600
      ├── Some((2, 7)): 10/16 ≈ 0.625
      └── Some((2, 8)): 1/7 ≈ 0.143
    ├── Some((7, 3)): 66/126 ≈ 0.524
      ├── Some((3, 0)): 7/14 ≈ 0.500
      ├── Some((3, 1)): 6/13 ≈ 0.462
      ├── Some((3, 2)): 11/17 ≈ 0.647
      ├── Some((3, 3)): 9/16 ≈ 0.562
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 12/18 ≈ 0.667
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 1/7 ≈ 0.143
      └── Some((3, 8)): 8/15 ≈ 0.533
    ├── Some((7, 4)): 58/115 ≈ 0.504
      ├── Some((4, 0)): 13/19 ≈ 0.684
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 12/18 ≈ 0.667
      ├── Some((4, 4)): 9/16 ≈ 0.562
      ├── Some((4, 5)): 0/6 ≈ 0.000
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 5/12 ≈ 0.417
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((7, 5)): 70/132 ≈ 0.530
      ├── Some((5, 0)): 9/16 ≈ 0.562
      ├── Some((5, 1)): 2/8 ≈ 0.250
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 7/14 ≈ 0.500
      ├── Some((5, 4)): 12/19 ≈ 0.632
      ├── Some((5, 5)): 4/11 ≈ 0.364
      ├── Some((5, 6)): 14/21 ≈ 0.667
      ├── Some((5, 7)): 9/16 ≈ 0.562
      └── Some((5, 8)): 10/17 ≈ 0.588
    ├── Some((7, 6)): 76/141 ≈ 0.539
      ├── Some((6, 0)): 13/21 ≈ 0.619
      ├── Some((6, 1)): 5/12 ≈ 0.417
      ├── Some((6, 2)): 8/15 ≈ 0.533
      ├── Some((6, 3)): 13/21 ≈ 0.619
      ├── Some((6, 4)): 7/14 ≈ 0.500
      ├── Some((6, 5)): 6/13 ≈ 0.462
      ├── Some((6, 6)): 8/15 ≈ 0.533
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((7, 7)): 27/69 ≈ 0.391
      ├── Some((7, 0)): 5/10 ≈ 0.500
      ├── Some((7, 1)): 1/6 ≈ 0.167
      ├── Some((7, 2)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 1/6 ≈ 0.167
      ├── Some((7, 5)): 6/12 ≈ 0.500
      ├── Some((7, 6)): 4/9 ≈ 0.444
      └── Some((7, 8)): 1/6 ≈ 0.167
    └── Some((7, 8)): 54/109 ≈ 0.495
      ├── Some((8, 0)): 9/15 ≈ 0.600
      ├── Some((8, 1)): 7/13 ≈ 0.538
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 8/14 ≈ 0.571
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 9/15 ≈ 0.600
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 1/7 ≈ 0.143
      └── Some((8, 8)): 5/11 ≈ 0.455
  └── Some((1, 8)): 762/1450 ≈ 0.526
    ├── Some((8, 0)): 122/216 ≈ 0.565
      ├── Some((0, 0)): 12/22 ≈ 0.545
      ├── Some((0, 1)): 17/28 ≈ 0.607
      ├── Some((0, 2)): 12/22 ≈ 0.545
      ├── Some((0, 3)): 7/17 ≈ 0.412
      ├── Some((0, 4)): 10/20 ≈ 0.500
      ├── Some((0, 5)): 13/24 ≈ 0.542
      ├── Some((0, 6)): 10/20 ≈ 0.500
      ├── Some((0, 7)): 15/26 ≈ 0.577
      └── Some((0, 8)): 25/36 ≈ 0.694
    ├── Some((8, 1)): 46/104 ≈ 0.442
      ├── Some((1, 0)): 13/21 ≈ 0.619
      ├── Some((1, 1)): 3/10 ≈ 0.300
      ├── Some((1, 2)): 4/11 ≈ 0.364
      ├── Some((1, 3)): 1/8 ≈ 0.125
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 0/6 ≈ 0.000
      ├── Some((1, 6)): 8/16 ≈ 0.500
      └── Some((1, 7)): 9/17 ≈ 0.529
    ├── Some((8, 2)): 134/233 ≈ 0.575
      ├── Some((2, 0)): 15/27 ≈ 0.556
      ├── Some((2, 2)): 15/27 ≈ 0.556
      ├── Some((2, 3)): 23/36 ≈ 0.639
      ├── Some((2, 4)): 10/22 ≈ 0.455
      ├── Some((2, 5)): 19/32 ≈ 0.594
      ├── Some((2, 6)): 11/23 ≈ 0.478
      ├── Some((2, 7)): 23/36 ≈ 0.639
      └── Some((2, 8)): 17/29 ≈ 0.586
    ├── Some((8, 3)): 90/170 ≈ 0.529
      ├── Some((3, 0)): 10/19 ≈ 0.526
      ├── Some((3, 1)): 14/23 ≈ 0.609
      ├── Some((3, 2)): 10/19 ≈ 0.526
      ├── Some((3, 3)): 9/18 ≈ 0.500
      ├── Some((3, 4)): 16/25 ≈ 0.640
      ├── Some((3, 5)): 12/21 ≈ 0.571
      ├── Some((3, 6)): 7/16 ≈ 0.438
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 6/15 ≈ 0.400
    ├── Some((8, 4)): 69/139 ≈ 0.496
      ├── Some((4, 0)): 10/18 ≈ 0.556
      ├── Some((4, 1)): 8/16 ≈ 0.500
      ├── Some((4, 2)): 9/17 ≈ 0.529
      ├── Some((4, 3)): 5/12 ≈ 0.417
      ├── Some((4, 4)): 11/19 ≈ 0.579
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 5/12 ≈ 0.417
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 6/14 ≈ 0.429
    ├── Some((8, 5)): 71/142 ≈ 0.500
      ├── Some((5, 0)): 6/14 ≈ 0.429
      ├── Some((5, 1)): 12/20 ≈ 0.600
      ├── Some((5, 2)): 11/19 ≈ 0.579
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 0/7 ≈ 0.000
      ├── Some((5, 6)): 1/8 ≈ 0.125
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 20/28 ≈ 0.714
    ├── Some((8, 6)): 32/82 ≈ 0.390
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 7/12 ≈ 0.583
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 0/5 ≈ 0.000
    ├── Some((8, 7)): 103/188 ≈ 0.548
      ├── Some((7, 0)): 23/33 ≈ 0.697
      ├── Some((7, 1)): 12/22 ≈ 0.545
      ├── Some((7, 2)): 10/20 ≈ 0.500
      ├── Some((7, 3)): 4/13 ≈ 0.308
      ├── Some((7, 4)): 15/25 ≈ 0.600
      ├── Some((7, 5)): 0/7 ≈ 0.000
      ├── Some((7, 6)): 8/17 ≈ 0.471
      ├── Some((7, 7)): 13/23 ≈ 0.565
      └── Some((7, 8)): 17/27 ≈ 0.630
    └── Some((8, 8)): 94/175 ≈ 0.537
      ├── Some((8, 0)): 12/22 ≈ 0.545
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 17/28 ≈ 0.607
      ├── Some((8, 3)): 6/15 ≈ 0.400
      ├── Some((8, 4)): 10/20 ≈ 0.500
      ├── Some((8, 5)): 11/21 ≈ 0.524
      ├── Some((8, 6)): 11/21 ≈ 0.524
      └── Some((8, 7)): 21/32 ≈ 0.656
├── Some((2, 2)): 9981/18847 ≈ 0.530
  ├── Some((2, 0)): 1356/2545 ≈ 0.533
    ├── Some((0, 0)): 148/279 ≈ 0.530
      ├── Some((0, 1)): 31/49 ≈ 0.633
      ├── Some((0, 2)): 17/33 ≈ 0.515
      ├── Some((0, 3)): 13/28 ≈ 0.464
      ├── Some((0, 4)): 10/25 ≈ 0.400
      ├── Some((0, 5)): 26/44 ≈ 0.591
      ├── Some((0, 6)): 24/41 ≈ 0.585
      ├── Some((0, 7)): 13/28 ≈ 0.464
      └── Some((0, 8)): 14/30 ≈ 0.467
    ├── Some((0, 1)): 157/293 ≈ 0.536
      ├── Some((1, 0)): 18/33 ≈ 0.545
      ├── Some((1, 1)): 23/39 ≈ 0.590
      ├── Some((1, 2)): 20/36 ≈ 0.556
      ├── Some((1, 3)): 13/27 ≈ 0.481
      ├── Some((1, 4)): 16/31 ≈ 0.516
      ├── Some((1, 5)): 21/37 ≈ 0.568
      ├── Some((1, 6)): 20/36 ≈ 0.556
      ├── Some((1, 7)): 17/32 ≈ 0.531
      └── Some((1, 8)): 8/21 ≈ 0.381
    ├── Some((0, 2)): 133/257 ≈ 0.518
      ├── Some((2, 1)): 24/43 ≈ 0.558
      ├── Some((2, 3)): 21/39 ≈ 0.538
      ├── Some((2, 4)): 17/34 ≈ 0.500
      ├── Some((2, 5)): 20/38 ≈ 0.526
      ├── Some((2, 6)): 17/34 ≈ 0.500
      ├── Some((2, 7)): 16/33 ≈ 0.485
      └── Some((2, 8)): 18/35 ≈ 0.514
    ├── Some((0, 3)): 156/292 ≈ 0.534
      ├── Some((3, 0)): 14/29 ≈ 0.483
      ├── Some((3, 1)): 26/43 ≈ 0.605
      ├── Some((3, 2)): 6/19 ≈ 0.316
      ├── Some((3, 3)): 7/20 ≈ 0.350
      ├── Some((3, 4)): 20/36 ≈ 0.556
      ├── Some((3, 5)): 8/21 ≈ 0.381
      ├── Some((3, 6)): 33/50 ≈ 0.660
      ├── Some((3, 7)): 25/41 ≈ 0.610
      └── Some((3, 8)): 17/32 ≈ 0.531
    ├── Some((0, 4)): 167/308 ≈ 0.542
      ├── Some((4, 0)): 24/41 ≈ 0.585
      ├── Some((4, 1)): 20/36 ≈ 0.556
      ├── Some((4, 2)): 12/26 ≈ 0.462
      ├── Some((4, 3)): 19/35 ≈ 0.543
      ├── Some((4, 4)): 7/20 ≈ 0.350
      ├── Some((4, 5)): 17/32 ≈ 0.531
      ├── Some((4, 6)): 21/37 ≈ 0.568
      ├── Some((4, 7)): 26/43 ≈ 0.605
      └── Some((4, 8)): 21/37 ≈ 0.568
    ├── Some((0, 5)): 87/185 ≈ 0.470
      ├── Some((5, 0)): 8/19 ≈ 0.421
      ├── Some((5, 1)): 17/29 ≈ 0.586
      ├── Some((5, 2)): 20/32 ≈ 0.625
      ├── Some((5, 3)): 10/21 ≈ 0.476
      ├── Some((5, 4)): 5/15 ≈ 0.333
      ├── Some((5, 5)): 13/25 ≈ 0.520
      ├── Some((5, 6)): 1/10 ≈ 0.100
      ├── Some((5, 7)): 4/14 ≈ 0.286
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((0, 6)): 129/250 ≈ 0.516
      ├── Some((6, 0)): 24/39 ≈ 0.615
      ├── Some((6, 1)): 12/25 ≈ 0.480
      ├── Some((6, 2)): 8/20 ≈ 0.400
      ├── Some((6, 3)): 25/40 ≈ 0.625
      ├── Some((6, 4)): 15/29 ≈ 0.517
      ├── Some((6, 5)): 14/28 ≈ 0.500
      ├── Some((6, 6)): 12/25 ≈ 0.480
      ├── Some((6, 7)): 8/20 ≈ 0.400
      └── Some((6, 8)): 10/23 ≈ 0.435
    ├── Some((0, 7)): 127/247 ≈ 0.514
      ├── Some((7, 0)): 20/34 ≈ 0.588
      ├── Some((7, 1)): 20/34 ≈ 0.588
      ├── Some((7, 2)): 18/32 ≈ 0.562
      ├── Some((7, 3)): 12/25 ≈ 0.480
      ├── Some((7, 4)): 18/32 ≈ 0.562
      ├── Some((7, 5)): 8/20 ≈ 0.400
      ├── Some((7, 6)): 10/23 ≈ 0.435
      ├── Some((7, 7)): 8/20 ≈ 0.400
      └── Some((7, 8)): 13/26 ≈ 0.500
    └── Some((0, 8)): 251/433 ≈ 0.580
      ├── Some((8, 0)): 41/63 ≈ 0.651
      ├── Some((8, 1)): 17/35 ≈ 0.486
      ├── Some((8, 2)): 35/56 ≈ 0.625
      ├── Some((8, 3)): 31/52 ≈ 0.596
      ├── Some((8, 4)): 21/40 ≈ 0.525
      ├── Some((8, 5)): 22/41 ≈ 0.537
      ├── Some((8, 6)): 21/40 ≈ 0.525
      ├── Some((8, 7)): 31/52 ≈ 0.596
      └── Some((8, 8)): 32/53 ≈ 0.604
  ├── Some((2, 1)): 1717/3166 ≈ 0.542
    ├── Some((1, 0)): 205/374 ≈ 0.548
      ├── Some((0, 0)): 16/33 ≈ 0.485
      ├── Some((0, 1)): 20/38 ≈ 0.526
      ├── Some((0, 2)): 26/46 ≈ 0.565
      ├── Some((0, 3)): 23/42 ≈ 0.548
      ├── Some((0, 4)): 18/36 ≈ 0.500
      ├── Some((0, 5)): 22/41 ≈ 0.537
      ├── Some((0, 6)): 38/59 ≈ 0.644
      ├── Some((0, 7)): 11/27 ≈ 0.407
      └── Some((0, 8)): 31/51 ≈ 0.608
    ├── Some((1, 1)): 189/349 ≈ 0.542
      ├── Some((1, 0)): 35/57 ≈ 0.614
      ├── Some((1, 2)): 16/34 ≈ 0.471
      ├── Some((1, 3)): 13/30 ≈ 0.433
      ├── Some((1, 4)): 36/58 ≈ 0.621
      ├── Some((1, 5)): 21/41 ≈ 0.512
      ├── Some((1, 6)): 18/37 ≈ 0.486
      ├── Some((1, 7)): 19/38 ≈ 0.500
      └── Some((1, 8)): 31/53 ≈ 0.585
    ├── Some((1, 2)): 221/398 ≈ 0.555
      ├── Some((2, 0)): 53/83 ≈ 0.639
      ├── Some((2, 3)): 18/40 ≈ 0.450
      ├── Some((2, 4)): 30/55 ≈ 0.545
      ├── Some((2, 5)): 21/43 ≈ 0.488
      ├── Some((2, 6)): 26/50 ≈ 0.520
      ├── Some((2, 7)): 40/67 ≈ 0.597
      └── Some((2, 8)): 33/59 ≈ 0.559
    ├── Some((1, 3)): 162/308 ≈ 0.526
      ├── Some((3, 0)): 25/42 ≈ 0.595
      ├── Some((3, 1)): 28/46 ≈ 0.609
      ├── Some((3, 2)): 10/25 ≈ 0.400
      ├── Some((3, 3)): 19/36 ≈ 0.528
      ├── Some((3, 4)): 25/42 ≈ 0.595
      ├── Some((3, 5)): 8/22 ≈ 0.364
      ├── Some((3, 6)): 8/22 ≈ 0.364
      ├── Some((3, 7)): 21/38 ≈ 0.553
      └── Some((3, 8)): 18/34 ≈ 0.529
    ├── Some((1, 4)): 172/323 ≈ 0.533
      ├── Some((4, 0)): 15/31 ≈ 0.484
      ├── Some((4, 1)): 11/26 ≈ 0.423
      ├── Some((4, 2)): 18/35 ≈ 0.514
      ├── Some((4, 3)): 17/33 ≈ 0.515
      ├── Some((4, 4)): 14/30 ≈ 0.467
      ├── Some((4, 5)): 30/49 ≈ 0.612
      ├── Some((4, 6)): 18/35 ≈ 0.514
      ├── Some((4, 7)): 25/43 ≈ 0.581
      └── Some((4, 8)): 23/40 ≈ 0.575
    ├── Some((1, 5)): 243/431 ≈ 0.564
      ├── Some((5, 0)): 16/35 ≈ 0.457
      ├── Some((5, 1)): 22/42 ≈ 0.524
      ├── Some((5, 2)): 16/35 ≈ 0.457
      ├── Some((5, 3)): 27/48 ≈ 0.562
      ├── Some((5, 4)): 59/85 ≈ 0.694
      ├── Some((5, 5)): 19/38 ≈ 0.500
      ├── Some((5, 6)): 28/49 ≈ 0.571
      ├── Some((5, 7)): 29/50 ≈ 0.580
      └── Some((5, 8)): 27/48 ≈ 0.562
    ├── Some((1, 6)): 168/317 ≈ 0.530
      ├── Some((6, 0)): 20/37 ≈ 0.541
      ├── Some((6, 1)): 17/33 ≈ 0.515
      ├── Some((6, 2)): 18/35 ≈ 0.514
      ├── Some((6, 3)): 19/36 ≈ 0.528
      ├── Some((6, 4)): 18/35 ≈ 0.514
      ├── Some((6, 5)): 2/14 ≈ 0.143
      ├── Some((6, 6)): 17/34 ≈ 0.500
      ├── Some((6, 7)): 28/46 ≈ 0.609
      └── Some((6, 8)): 28/46 ≈ 0.609
    ├── Some((1, 7)): 198/363 ≈ 0.545
      ├── Some((7, 0)): 20/38 ≈ 0.526
      ├── Some((7, 1)): 27/46 ≈ 0.587
      ├── Some((7, 2)): 18/36 ≈ 0.500
      ├── Some((7, 3)): 9/24 ≈ 0.375
      ├── Some((7, 4)): 19/37 ≈ 0.514
      ├── Some((7, 5)): 37/58 ≈ 0.638
      ├── Some((7, 6)): 24/43 ≈ 0.558
      ├── Some((7, 7)): 17/35 ≈ 0.486
      └── Some((7, 8)): 26/45 ≈ 0.578
    └── Some((1, 8)): 158/302 ≈ 0.523
      ├── Some((8, 0)): 13/28 ≈ 0.464
      ├── Some((8, 1)): 8/22 ≈ 0.364
      ├── Some((8, 2)): 16/32 ≈ 0.500
      ├── Some((8, 3)): 15/31 ≈ 0.484
      ├── Some((8, 4)): 23/40 ≈ 0.575
      ├── Some((8, 5)): 19/36 ≈ 0.528
      ├── Some((8, 6)): 6/19 ≈ 0.316
      ├── Some((8, 7)): 26/44 ≈ 0.591
      └── Some((8, 8)): 31/49 ≈ 0.633
  ├── Some((2, 3)): 940/1823 ≈ 0.516
    ├── Some((3, 0)): 89/179 ≈ 0.497
      ├── Some((0, 0)): 14/24 ≈ 0.583
      ├── Some((0, 1)): 11/21 ≈ 0.524
      ├── Some((0, 2)): 8/18 ≈ 0.444
      ├── Some((0, 3)): 5/14 ≈ 0.357
      ├── Some((0, 4)): 9/19 ≈ 0.474
      ├── Some((0, 5)): 12/22 ≈ 0.545
      ├── Some((0, 6)): 8/18 ≈ 0.444
      ├── Some((0, 7)): 10/20 ≈ 0.500
      └── Some((0, 8)): 12/22 ≈ 0.545
    ├── Some((3, 1)): 91/183 ≈ 0.497
      ├── Some((1, 0)): 10/20 ≈ 0.500
      ├── Some((1, 1)): 8/18 ≈ 0.444
      ├── Some((1, 2)): 10/20 ≈ 0.500
      ├── Some((1, 3)): 6/16 ≈ 0.375
      ├── Some((1, 4)): 9/19 ≈ 0.474
      ├── Some((1, 5)): 5/15 ≈ 0.333
      ├── Some((1, 6)): 18/29 ≈ 0.621
      ├── Some((1, 7)): 18/29 ≈ 0.621
      └── Some((1, 8)): 6/16 ≈ 0.375
    ├── Some((3, 2)): 102/199 ≈ 0.513
      ├── Some((2, 0)): 6/18 ≈ 0.333
      ├── Some((2, 1)): 18/32 ≈ 0.562
      ├── Some((2, 4)): 12/25 ≈ 0.480
      ├── Some((2, 5)): 15/29 ≈ 0.517
      ├── Some((2, 6)): 15/29 ≈ 0.517
      ├── Some((2, 7)): 23/38 ≈ 0.605
      └── Some((2, 8)): 13/27 ≈ 0.481
    ├── Some((3, 3)): 141/258 ≈ 0.547
      ├── Some((3, 0)): 14/28 ≈ 0.500
      ├── Some((3, 1)): 29/45 ≈ 0.644
      ├── Some((3, 2)): 18/33 ≈ 0.545
      ├── Some((3, 4)): 18/33 ≈ 0.545
      ├── Some((3, 5)): 8/21 ≈ 0.381
      ├── Some((3, 6)): 11/25 ≈ 0.440
      ├── Some((3, 7)): 32/49 ≈ 0.653
      └── Some((3, 8)): 10/23 ≈ 0.435
    ├── Some((3, 4)): 96/190 ≈ 0.505
      ├── Some((4, 0)): 6/16 ≈ 0.375
      ├── Some((4, 1)): 9/20 ≈ 0.450
      ├── Some((4, 2)): 8/18 ≈ 0.444
      ├── Some((4, 3)): 6/16 ≈ 0.375
      ├── Some((4, 4)): 28/40 ≈ 0.700
      ├── Some((4, 5)): 16/27 ≈ 0.593
      ├── Some((4, 6)): 3/12 ≈ 0.250
      ├── Some((4, 7)): 2/11 ≈ 0.182
      └── Some((4, 8)): 17/29 ≈ 0.586
    ├── Some((3, 5)): 170/300 ≈ 0.567
      ├── Some((5, 0)): 23/38 ≈ 0.605
      ├── Some((5, 1)): 24/39 ≈ 0.615
      ├── Some((5, 2)): 4/15 ≈ 0.267
      ├── Some((5, 3)): 21/36 ≈ 0.583
      ├── Some((5, 4)): 17/31 ≈ 0.548
      ├── Some((5, 5)): 26/42 ≈ 0.619
      ├── Some((5, 6)): 20/35 ≈ 0.571
      ├── Some((5, 7)): 24/39 ≈ 0.615
      └── Some((5, 8)): 11/24 ≈ 0.458
    ├── Some((3, 6)): 71/152 ≈ 0.467
      ├── Some((6, 0)): 6/15 ≈ 0.400
      ├── Some((6, 1)): 4/12 ≈ 0.333
      ├── Some((6, 2)): 11/20 ≈ 0.550
      ├── Some((6, 3)): 13/23 ≈ 0.565
      ├── Some((6, 4)): 7/16 ≈ 0.438
      ├── Some((6, 5)): 10/19 ≈ 0.526
      ├── Some((6, 6)): 8/17 ≈ 0.471
      ├── Some((6, 7)): 11/20 ≈ 0.550
      └── Some((6, 8)): 1/9 ≈ 0.111
    ├── Some((3, 7)): 99/195 ≈ 0.508
      ├── Some((7, 0)): 12/23 ≈ 0.522
      ├── Some((7, 1)): 15/26 ≈ 0.577
      ├── Some((7, 2)): 7/17 ≈ 0.412
      ├── Some((7, 3)): 18/29 ≈ 0.621
      ├── Some((7, 4)): 8/18 ≈ 0.444
      ├── Some((7, 5)): 9/19 ≈ 0.474
      ├── Some((7, 6)): 8/18 ≈ 0.444
      ├── Some((7, 7)): 9/20 ≈ 0.450
      └── Some((7, 8)): 13/24 ≈ 0.542
    └── Some((3, 8)): 80/166 ≈ 0.482
      ├── Some((8, 0)): 12/22 ≈ 0.545
      ├── Some((8, 1)): 12/22 ≈ 0.545
      ├── Some((8, 2)): 14/24 ≈ 0.583
      ├── Some((8, 3)): 15/25 ≈ 0.600
      ├── Some((8, 4)): 6/15 ≈ 0.400
      ├── Some((8, 5)): 7/17 ≈ 0.412
      ├── Some((8, 6)): 9/19 ≈ 0.474
      ├── Some((8, 7)): 1/9 ≈ 0.111
      └── Some((8, 8)): 3/12 ≈ 0.250
  ├── Some((2, 4)): 833/1635 ≈ 0.509
    ├── Some((4, 0)): 87/174 ≈ 0.500
      ├── Some((0, 0)): 6/15 ≈ 0.400
      ├── Some((0, 1)): 12/22 ≈ 0.545
      ├── Some((0, 2)): 11/21 ≈ 0.524
      ├── Some((0, 3)): 7/16 ≈ 0.438
      ├── Some((0, 4)): 9/19 ≈ 0.474
      ├── Some((0, 5)): 16/26 ≈ 0.615
      ├── Some((0, 6)): 9/19 ≈ 0.474
      ├── Some((0, 7)): 10/20 ≈ 0.500
      └── Some((0, 8)): 6/15 ≈ 0.400
    ├── Some((4, 1)): 95/186 ≈ 0.511
      ├── Some((1, 0)): 2/11 ≈ 0.182
      ├── Some((1, 1)): 19/30 ≈ 0.633
      ├── Some((1, 2)): 3/12 ≈ 0.250
      ├── Some((1, 3)): 23/34 ≈ 0.676
      ├── Some((1, 4)): 10/20 ≈ 0.500
      ├── Some((1, 5)): 12/22 ≈ 0.545
      ├── Some((1, 6)): 4/13 ≈ 0.308
      ├── Some((1, 7)): 15/26 ≈ 0.577
      └── Some((1, 8)): 7/17 ≈ 0.412
    ├── Some((4, 2)): 132/241 ≈ 0.548
      ├── Some((2, 0)): 13/27 ≈ 0.481
      ├── Some((2, 1)): 35/53 ≈ 0.660
      ├── Some((2, 3)): 20/36 ≈ 0.556
      ├── Some((2, 5)): 19/35 ≈ 0.543
      ├── Some((2, 6)): 13/28 ≈ 0.464
      ├── Some((2, 7)): 11/25 ≈ 0.440
      └── Some((2, 8)): 20/36 ≈ 0.556
    ├── Some((4, 3)): 105/201 ≈ 0.522
      ├── Some((3, 0)): 18/29 ≈ 0.621
      ├── Some((3, 1)): 4/14 ≈ 0.286
      ├── Some((3, 2)): 5/15 ≈ 0.333
      ├── Some((3, 3)): 16/27 ≈ 0.593
      ├── Some((3, 4)): 18/30 ≈ 0.600
      ├── Some((3, 5)): 8/18 ≈ 0.444
      ├── Some((3, 6)): 12/23 ≈ 0.522
      ├── Some((3, 7)): 16/27 ≈ 0.593
      └── Some((3, 8)): 7/17 ≈ 0.412
    ├── Some((4, 4)): 76/157 ≈ 0.484
      ├── Some((4, 0)): 12/22 ≈ 0.545
      ├── Some((4, 1)): 6/16 ≈ 0.375
      ├── Some((4, 2)): 11/21 ≈ 0.524
      ├── Some((4, 3)): 6/16 ≈ 0.375
      ├── Some((4, 5)): 3/12 ≈ 0.250
      ├── Some((4, 6)): 12/23 ≈ 0.522
      ├── Some((4, 7)): 10/20 ≈ 0.500
      └── Some((4, 8)): 15/26 ≈ 0.577
    ├── Some((4, 5)): 52/119 ≈ 0.437
      ├── Some((5, 0)): 3/10 ≈ 0.300
      ├── Some((5, 1)): 1/8 ≈ 0.125
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 11/19 ≈ 0.579
      ├── Some((5, 5)): 11/19 ≈ 0.579
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 1/8 ≈ 0.125
      └── Some((5, 8)): 8/16 ≈ 0.500
    ├── Some((4, 6)): 59/131 ≈ 0.450
      ├── Some((6, 0)): 20/28 ≈ 0.714
      ├── Some((6, 1)): 6/14 ≈ 0.429
      ├── Some((6, 2)): 5/13 ≈ 0.385
      ├── Some((6, 3)): 2/9 ≈ 0.222
      ├── Some((6, 4)): 3/11 ≈ 0.273
      ├── Some((6, 5)): 3/11 ≈ 0.273
      ├── Some((6, 6)): 8/16 ≈ 0.500
      ├── Some((6, 7)): 3/11 ≈ 0.273
      └── Some((6, 8)): 9/17 ≈ 0.529
    ├── Some((4, 7)): 151/269 ≈ 0.561
      ├── Some((7, 0)): 21/35 ≈ 0.600
      ├── Some((7, 1)): 14/27 ≈ 0.519
      ├── Some((7, 2)): 9/21 ≈ 0.429
      ├── Some((7, 3)): 20/33 ≈ 0.606
      ├── Some((7, 4)): 12/25 ≈ 0.480
      ├── Some((7, 5)): 19/32 ≈ 0.594
      ├── Some((7, 6)): 21/35 ≈ 0.600
      ├── Some((7, 7)): 20/33 ≈ 0.606
      └── Some((7, 8)): 14/27 ≈ 0.519
    └── Some((4, 8)): 75/156 ≈ 0.481
      ├── Some((8, 0)): 12/21 ≈ 0.571
      ├── Some((8, 1)): 3/11 ≈ 0.273
      ├── Some((8, 2)): 14/23 ≈ 0.609
      ├── Some((8, 3)): 5/14 ≈ 0.357
      ├── Some((8, 4)): 9/18 ≈ 0.500
      ├── Some((8, 5)): 7/16 ≈ 0.438
      ├── Some((8, 6)): 10/19 ≈ 0.526
      ├── Some((8, 7)): 10/19 ≈ 0.526
      └── Some((8, 8)): 5/14 ≈ 0.357
  ├── Some((2, 5)): 1401/2623 ≈ 0.534
    ├── Some((5, 0)): 174/320 ≈ 0.544
      ├── Some((0, 0)): 15/31 ≈ 0.484
      ├── Some((0, 1)): 34/52 ≈ 0.654
      ├── Some((0, 2)): 21/38 ≈ 0.553
      ├── Some((0, 3)): 17/33 ≈ 0.515
      ├── Some((0, 4)): 9/23 ≈ 0.391
      ├── Some((0, 5)): 17/33 ≈ 0.515
      ├── Some((0, 6)): 22/39 ≈ 0.564
      ├── Some((0, 7)): 26/43 ≈ 0.605
      └── Some((0, 8)): 12/27 ≈ 0.444
    ├── Some((5, 1)): 123/242 ≈ 0.508
      ├── Some((1, 0)): 15/29 ≈ 0.517
      ├── Some((1, 1)): 20/34 ≈ 0.588
      ├── Some((1, 2)): 13/26 ≈ 0.500
      ├── Some((1, 3)): 28/43 ≈ 0.651
      ├── Some((1, 4)): 4/15 ≈ 0.267
      ├── Some((1, 5)): 21/36 ≈ 0.583
      ├── Some((1, 6)): 6/18 ≈ 0.333
      ├── Some((1, 7)): 12/25 ≈ 0.480
      └── Some((1, 8)): 4/15 ≈ 0.267
    ├── Some((5, 2)): 224/395 ≈ 0.567
      ├── Some((2, 0)): 56/86 ≈ 0.651
      ├── Some((2, 1)): 13/32 ≈ 0.406
      ├── Some((2, 3)): 39/65 ≈ 0.600
      ├── Some((2, 4)): 31/56 ≈ 0.554
      ├── Some((2, 6)): 28/52 ≈ 0.538
      ├── Some((2, 7)): 30/54 ≈ 0.556
      └── Some((2, 8)): 26/49 ≈ 0.531
    ├── Some((5, 3)): 116/231 ≈ 0.502
      ├── Some((3, 0)): 13/26 ≈ 0.500
      ├── Some((3, 1)): 18/32 ≈ 0.562
      ├── Some((3, 2)): 16/29 ≈ 0.552
      ├── Some((3, 3)): 11/23 ≈ 0.478
      ├── Some((3, 4)): 20/34 ≈ 0.588
      ├── Some((3, 5)): 11/24 ≈ 0.458
      ├── Some((3, 6)): 6/17 ≈ 0.353
      ├── Some((3, 7)): 9/21 ≈ 0.429
      └── Some((3, 8)): 11/24 ≈ 0.458
    ├── Some((5, 4)): 95/198 ≈ 0.480
      ├── Some((4, 0)): 7/18 ≈ 0.389
      ├── Some((4, 1)): 15/27 ≈ 0.556
      ├── Some((4, 2)): 7/18 ≈ 0.389
      ├── Some((4, 3)): 14/26 ≈ 0.538
      ├── Some((4, 4)): 7/18 ≈ 0.389
      ├── Some((4, 5)): 5/15 ≈ 0.333
      ├── Some((4, 6)): 12/24 ≈ 0.500
      ├── Some((4, 7)): 17/29 ≈ 0.586
      └── Some((4, 8)): 11/22 ≈ 0.500
    ├── Some((5, 5)): 162/302 ≈ 0.536
      ├── Some((5, 0)): 25/44 ≈ 0.568
      ├── Some((5, 1)): 4/17 ≈ 0.235
      ├── Some((5, 2)): 31/51 ≈ 0.608
      ├── Some((5, 3)): 17/34 ≈ 0.500
      ├── Some((5, 4)): 14/30 ≈ 0.467
      ├── Some((5, 6)): 20/38 ≈ 0.526
      ├── Some((5, 7)): 28/47 ≈ 0.596
      └── Some((5, 8)): 22/40 ≈ 0.550
    ├── Some((5, 6)): 120/238 ≈ 0.504
      ├── Some((6, 0)): 8/20 ≈ 0.400
      ├── Some((6, 1)): 16/29 ≈ 0.552
      ├── Some((6, 2)): 15/28 ≈ 0.536
      ├── Some((6, 3)): 14/27 ≈ 0.519
      ├── Some((6, 4)): 12/25 ≈ 0.480
      ├── Some((6, 5)): 16/29 ≈ 0.552
      ├── Some((6, 6)): 12/25 ≈ 0.480
      ├── Some((6, 7)): 16/30 ≈ 0.533
      └── Some((6, 8)): 11/24 ≈ 0.458
    ├── Some((5, 7)): 227/399 ≈ 0.569
      ├── Some((7, 0)): 21/39 ≈ 0.538
      ├── Some((7, 1)): 35/56 ≈ 0.625
      ├── Some((7, 2)): 35/56 ≈ 0.625
      ├── Some((7, 3)): 14/31 ≈ 0.452
      ├── Some((7, 4)): 34/55 ≈ 0.618
      ├── Some((7, 5)): 12/28 ≈ 0.429
      ├── Some((7, 6)): 27/46 ≈ 0.587
      ├── Some((7, 7)): 25/44 ≈ 0.568
      └── Some((7, 8)): 24/43 ≈ 0.558
    └── Some((5, 8)): 159/297 ≈ 0.535
      ├── Some((8, 0)): 13/27 ≈ 0.481
      ├── Some((8, 1)): 21/37 ≈ 0.568
      ├── Some((8, 2)): 21/37 ≈ 0.568
      ├── Some((8, 3)): 16/31 ≈ 0.516
      ├── Some((8, 4)): 13/28 ≈ 0.464
      ├── Some((8, 5)): 14/29 ≈ 0.483
      ├── Some((8, 6)): 17/32 ≈ 0.531
      ├── Some((8, 7)): 22/38 ≈ 0.579
      └── Some((8, 8)): 21/37 ≈ 0.568
  ├── Some((2, 6)): 1089/2083 ≈ 0.523
    ├── Some((6, 0)): 87/180 ≈ 0.483
      ├── Some((0, 0)): 8/18 ≈ 0.444
      ├── Some((0, 1)): 18/29 ≈ 0.621
      ├── Some((0, 2)): 5/14 ≈ 0.357
      ├── Some((0, 3)): 12/23 ≈ 0.522
      ├── Some((0, 4)): 7/17 ≈ 0.412
      ├── Some((0, 5)): 7/17 ≈ 0.412
      ├── Some((0, 6)): 16/27 ≈ 0.593
      ├── Some((0, 7)): 5/15 ≈ 0.333
      └── Some((0, 8)): 9/19 ≈ 0.474
    ├── Some((6, 1)): 186/329 ≈ 0.565
      ├── Some((1, 0)): 16/31 ≈ 0.516
      ├── Some((1, 1)): 17/32 ≈ 0.531
      ├── Some((1, 2)): 40/58 ≈ 0.690
      ├── Some((1, 3)): 24/41 ≈ 0.585
      ├── Some((1, 4)): 13/28 ≈ 0.464
      ├── Some((1, 5)): 34/52 ≈ 0.654
      ├── Some((1, 6)): 10/24 ≈ 0.417
      ├── Some((1, 7)): 16/31 ≈ 0.516
      └── Some((1, 8)): 16/31 ≈ 0.516
    ├── Some((6, 2)): 87/180 ≈ 0.483
      ├── Some((2, 0)): 9/21 ≈ 0.429
      ├── Some((2, 1)): 12/25 ≈ 0.480
      ├── Some((2, 3)): 15/29 ≈ 0.517
      ├── Some((2, 4)): 15/29 ≈ 0.517
      ├── Some((2, 5)): 12/25 ≈ 0.480
      ├── Some((2, 7)): 20/35 ≈ 0.571
      └── Some((2, 8)): 4/15 ≈ 0.267
    ├── Some((6, 3)): 136/255 ≈ 0.533
      ├── Some((3, 0)): 22/36 ≈ 0.611
      ├── Some((3, 1)): 5/16 ≈ 0.312
      ├── Some((3, 2)): 28/43 ≈ 0.651
      ├── Some((3, 3)): 17/31 ≈ 0.548
      ├── Some((3, 4)): 9/21 ≈ 0.429
      ├── Some((3, 5)): 7/19 ≈ 0.368
      ├── Some((3, 6)): 14/27 ≈ 0.519
      ├── Some((3, 7)): 18/32 ≈ 0.562
      └── Some((3, 8)): 15/29 ≈ 0.517
    ├── Some((6, 4)): 187/331 ≈ 0.565
      ├── Some((4, 0)): 26/43 ≈ 0.605
      ├── Some((4, 1)): 35/53 ≈ 0.660
      ├── Some((4, 2)): 20/36 ≈ 0.556
      ├── Some((4, 3)): 6/19 ≈ 0.316
      ├── Some((4, 4)): 16/31 ≈ 0.516
      ├── Some((4, 5)): 23/39 ≈ 0.590
      ├── Some((4, 6)): 24/41 ≈ 0.585
      ├── Some((4, 7)): 17/33 ≈ 0.515
      └── Some((4, 8)): 19/35 ≈ 0.543
    ├── Some((6, 5)): 124/237 ≈ 0.523
      ├── Some((5, 0)): 22/35 ≈ 0.629
      ├── Some((5, 1)): 12/24 ≈ 0.500
      ├── Some((5, 2)): 23/37 ≈ 0.622
      ├── Some((5, 3)): 13/25 ≈ 0.520
      ├── Some((5, 4)): 7/18 ≈ 0.389
      ├── Some((5, 5)): 8/20 ≈ 0.400
      ├── Some((5, 6)): 13/26 ≈ 0.500
      ├── Some((5, 7)): 11/23 ≈ 0.478
      └── Some((5, 8)): 15/28 ≈ 0.536
    ├── Some((6, 6)): 87/180 ≈ 0.483
      ├── Some((6, 0)): 2/11 ≈ 0.182
      ├── Some((6, 1)): 4/14 ≈ 0.286
      ├── Some((6, 2)): 15/27 ≈ 0.556
      ├── Some((6, 3)): 16/29 ≈ 0.552
      ├── Some((6, 4)): 17/30 ≈ 0.567
      ├── Some((6, 5)): 19/32 ≈ 0.594
      ├── Some((6, 7)): 3/13 ≈ 0.231
      └── Some((6, 8)): 11/23 ≈ 0.478
    ├── Some((6, 7)): 90/184 ≈ 0.489
      ├── Some((7, 0)): 15/26 ≈ 0.577
      ├── Some((7, 1)): 13/24 ≈ 0.542
      ├── Some((7, 2)): 9/19 ≈ 0.474
      ├── Some((7, 3)): 7/17 ≈ 0.412
      ├── Some((7, 4)): 9/19 ≈ 0.474
      ├── Some((7, 5)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 13/24 ≈ 0.542
      ├── Some((7, 7)): 3/12 ≈ 0.250
      └── Some((7, 8)): 10/21 ≈ 0.476
    └── Some((6, 8)): 104/206 ≈ 0.505
      ├── Some((8, 0)): 8/19 ≈ 0.421
      ├── Some((8, 1)): 10/22 ≈ 0.455
      ├── Some((8, 2)): 27/40 ≈ 0.675
      ├── Some((8, 3)): 26/39 ≈ 0.667
      ├── Some((8, 4)): 9/20 ≈ 0.450
      ├── Some((8, 5)): 7/18 ≈ 0.389
      ├── Some((8, 6)): 10/22 ≈ 0.455
      ├── Some((8, 7)): 2/11 ≈ 0.182
      └── Some((8, 8)): 4/14 ≈ 0.286
  ├── Some((2, 7)): 1542/2866 ≈ 0.538
    ├── Some((7, 0)): 170/317 ≈ 0.536
      ├── Some((0, 0)): 14/30 ≈ 0.467
      ├── Some((0, 1)): 12/27 ≈ 0.444
      ├── Some((0, 2)): 21/38 ≈ 0.553
      ├── Some((0, 3)): 26/44 ≈ 0.591
      ├── Some((0, 4)): 3/15 ≈ 0.200
      ├── Some((0, 5)): 29/47 ≈ 0.617
      ├── Some((0, 6)): 25/42 ≈ 0.595
      ├── Some((0, 7)): 22/39 ≈ 0.564
      └── Some((0, 8)): 18/34 ≈ 0.529
    ├── Some((7, 1)): 219/391 ≈ 0.560
      ├── Some((1, 0)): 18/36 ≈ 0.500
      ├── Some((1, 1)): 37/58 ≈ 0.638
      ├── Some((1, 2)): 32/53 ≈ 0.604
      ├── Some((1, 3)): 15/32 ≈ 0.469
      ├── Some((1, 4)): 21/40 ≈ 0.525
      ├── Some((1, 5)): 27/47 ≈ 0.574
      ├── Some((1, 6)): 16/33 ≈ 0.485
      ├── Some((1, 7)): 27/47 ≈ 0.574
      └── Some((1, 8)): 25/44 ≈ 0.568
    ├── Some((7, 2)): 110/224 ≈ 0.491
      ├── Some((2, 0)): 16/33 ≈ 0.485
      ├── Some((2, 1)): 8/23 ≈ 0.348
      ├── Some((2, 3)): 23/41 ≈ 0.561
      ├── Some((2, 4)): 11/26 ≈ 0.423
      ├── Some((2, 5)): 2/14 ≈ 0.143
      ├── Some((2, 6)): 18/35 ≈ 0.514
      └── Some((2, 8)): 31/51 ≈ 0.608
    ├── Some((7, 3)): 215/385 ≈ 0.558
      ├── Some((3, 0)): 18/36 ≈ 0.500
      ├── Some((3, 1)): 9/24 ≈ 0.375
      ├── Some((3, 2)): 25/44 ≈ 0.568
      ├── Some((3, 3)): 32/53 ≈ 0.604
      ├── Some((3, 4)): 19/37 ≈ 0.514
      ├── Some((3, 5)): 34/55 ≈ 0.618
      ├── Some((3, 6)): 21/40 ≈ 0.525
      ├── Some((3, 7)): 19/37 ≈ 0.514
      └── Some((3, 8)): 37/58 ≈ 0.638
    ├── Some((7, 4)): 127/250 ≈ 0.508
      ├── Some((4, 0)): 22/37 ≈ 0.595
      ├── Some((4, 1)): 4/15 ≈ 0.267
      ├── Some((4, 2)): 10/23 ≈ 0.435
      ├── Some((4, 3)): 1/11 ≈ 0.091
      ├── Some((4, 4)): 19/34 ≈ 0.559
      ├── Some((4, 5)): 19/34 ≈ 0.559
      ├── Some((4, 6)): 17/32 ≈ 0.531
      ├── Some((4, 7)): 10/23 ≈ 0.435
      └── Some((4, 8)): 24/40 ≈ 0.600
    ├── Some((7, 5)): 191/348 ≈ 0.549
      ├── Some((5, 0)): 34/54 ≈ 0.630
      ├── Some((5, 1)): 22/40 ≈ 0.550
      ├── Some((5, 2)): 32/52 ≈ 0.615
      ├── Some((5, 3)): 25/43 ≈ 0.581
      ├── Some((5, 4)): 24/42 ≈ 0.571
      ├── Some((5, 5)): 7/21 ≈ 0.333
      ├── Some((5, 6)): 19/36 ≈ 0.528
      ├── Some((5, 7)): 16/33 ≈ 0.485
      └── Some((5, 8)): 11/26 ≈ 0.423
    ├── Some((7, 6)): 158/298 ≈ 0.530
      ├── Some((6, 0)): 13/28 ≈ 0.464
      ├── Some((6, 1)): 13/28 ≈ 0.464
      ├── Some((6, 2)): 14/29 ≈ 0.483
      ├── Some((6, 3)): 20/36 ≈ 0.556
      ├── Some((6, 4)): 23/39 ≈ 0.590
      ├── Some((6, 5)): 27/44 ≈ 0.614
      ├── Some((6, 6)): 6/19 ≈ 0.316
      ├── Some((6, 7)): 28/45 ≈ 0.622
      └── Some((6, 8)): 14/29 ≈ 0.483
    ├── Some((7, 7)): 159/300 ≈ 0.530
      ├── Some((7, 0)): 24/43 ≈ 0.558
      ├── Some((7, 1)): 40/61 ≈ 0.656
      ├── Some((7, 2)): 25/44 ≈ 0.568
      ├── Some((7, 3)): 10/26 ≈ 0.385
      ├── Some((7, 4)): 24/43 ≈ 0.558
      ├── Some((7, 5)): 13/29 ≈ 0.448
      ├── Some((7, 6)): 15/32 ≈ 0.469
      └── Some((7, 8)): 7/21 ≈ 0.333
    └── Some((7, 8)): 193/352 ≈ 0.548
      ├── Some((8, 0)): 34/54 ≈ 0.630
      ├── Some((8, 1)): 19/37 ≈ 0.514
      ├── Some((8, 2)): 35/55 ≈ 0.636
      ├── Some((8, 3)): 36/56 ≈ 0.643
      ├── Some((8, 4)): 13/29 ≈ 0.448
      ├── Some((8, 5)): 6/20 ≈ 0.300
      ├── Some((8, 6)): 14/31 ≈ 0.452
      ├── Some((8, 7)): 17/34 ≈ 0.500
      └── Some((8, 8)): 18/35 ≈ 0.514
  └── Some((2, 8)): 1102/2105 ≈ 0.524
    ├── Some((8, 0)): 168/303 ≈ 0.554
      ├── Some((0, 0)): 18/33 ≈ 0.545
      ├── Some((0, 1)): 9/22 ≈ 0.409
      ├── Some((0, 2)): 34/51 ≈ 0.667
      ├── Some((0, 3)): 13/27 ≈ 0.481
      ├── Some((0, 4)): 28/44 ≈ 0.636
      ├── Some((0, 5)): 21/37 ≈ 0.568
      ├── Some((0, 6)): 24/40 ≈ 0.600
      ├── Some((0, 7)): 9/22 ≈ 0.409
      └── Some((0, 8)): 12/26 ≈ 0.462
    ├── Some((8, 1)): 145/268 ≈ 0.541
      ├── Some((1, 0)): 29/44 ≈ 0.659
      ├── Some((1, 1)): 18/32 ≈ 0.562
      ├── Some((1, 2)): 9/22 ≈ 0.409
      ├── Some((1, 3)): 12/25 ≈ 0.480
      ├── Some((1, 4)): 5/17 ≈ 0.294
      ├── Some((1, 5)): 8/20 ≈ 0.400
      ├── Some((1, 6)): 15/29 ≈ 0.517
      ├── Some((1, 7)): 11/24 ≈ 0.458
      └── Some((1, 8)): 38/54 ≈ 0.704
    ├── Some((8, 2)): 152/279 ≈ 0.545
      ├── Some((2, 0)): 11/27 ≈ 0.407
      ├── Some((2, 1)): 37/58 ≈ 0.638
      ├── Some((2, 3)): 29/49 ≈ 0.592
      ├── Some((2, 4)): 6/20 ≈ 0.300
      ├── Some((2, 5)): 19/37 ≈ 0.514
      ├── Some((2, 6)): 16/33 ≈ 0.485
      └── Some((2, 7)): 33/54 ≈ 0.611
    ├── Some((8, 3)): 133/250 ≈ 0.532
      ├── Some((3, 0)): 7/19 ≈ 0.368
      ├── Some((3, 1)): 23/37 ≈ 0.622
      ├── Some((3, 2)): 37/52 ≈ 0.712
      ├── Some((3, 3)): 7/19 ≈ 0.368
      ├── Some((3, 4)): 7/19 ≈ 0.368
      ├── Some((3, 5)): 14/27 ≈ 0.519
      ├── Some((3, 6)): 19/33 ≈ 0.576
      ├── Some((3, 7)): 7/19 ≈ 0.368
      └── Some((3, 8)): 11/24 ≈ 0.458
    ├── Some((8, 4)): 90/184 ≈ 0.489
      ├── Some((4, 0)): 23/35 ≈ 0.657
      ├── Some((4, 1)): 10/21 ≈ 0.476
      ├── Some((4, 2)): 6/16 ≈ 0.375
      ├── Some((4, 3)): 13/24 ≈ 0.542
      ├── Some((4, 4)): 6/16 ≈ 0.375
      ├── Some((4, 5)): 0/8 ≈ 0.000
      ├── Some((4, 6)): 10/21 ≈ 0.476
      ├── Some((4, 7)): 9/19 ≈ 0.474
      └── Some((4, 8)): 12/23 ≈ 0.522
    ├── Some((8, 5)): 139/259 ≈ 0.537
      ├── Some((5, 0)): 14/27 ≈ 0.519
      ├── Some((5, 1)): 12/25 ≈ 0.480
      ├── Some((5, 2)): 24/38 ≈ 0.632
      ├── Some((5, 3)): 21/35 ≈ 0.600
      ├── Some((5, 4)): 6/18 ≈ 0.333
      ├── Some((5, 5)): 12/25 ≈ 0.480
      ├── Some((5, 6)): 13/26 ≈ 0.500
      ├── Some((5, 7)): 12/25 ≈ 0.480
      └── Some((5, 8)): 25/39 ≈ 0.641
    ├── Some((8, 6)): 86/178 ≈ 0.483
      ├── Some((6, 0)): 4/13 ≈ 0.308
      ├── Some((6, 1)): 9/19 ≈ 0.474
      ├── Some((6, 2)): 16/27 ≈ 0.593
      ├── Some((6, 3)): 14/25 ≈ 0.560
      ├── Some((6, 4)): 9/20 ≈ 0.450
      ├── Some((6, 5)): 17/28 ≈ 0.607
      ├── Some((6, 6)): 3/12 ≈ 0.250
      ├── Some((6, 7)): 4/13 ≈ 0.308
      └── Some((6, 8)): 9/20 ≈ 0.450
    ├── Some((8, 7)): 87/180 ≈ 0.483
      ├── Some((7, 0)): 8/18 ≈ 0.444
      ├── Some((7, 1)): 6/16 ≈ 0.375
      ├── Some((7, 2)): 11/22 ≈ 0.500
      ├── Some((7, 3)): 9/19 ≈ 0.474
      ├── Some((7, 4)): 10/20 ≈ 0.500
      ├── Some((7, 5)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 7/17 ≈ 0.412
      ├── Some((7, 7)): 16/27 ≈ 0.593
      └── Some((7, 8)): 9/19 ≈ 0.474
    └── Some((8, 8)): 102/203 ≈ 0.502
      ├── Some((8, 0)): 8/20 ≈ 0.400
      ├── Some((8, 1)): 14/27 ≈ 0.519
      ├── Some((8, 2)): 13/26 ≈ 0.500
      ├── Some((8, 3)): 22/36 ≈ 0.611
      ├── Some((8, 4)): 7/19 ≈ 0.368
      ├── Some((8, 5)): 15/28 ≈ 0.536
      ├── Some((8, 6)): 6/17 ≈ 0.353
      └── Some((8, 7)): 16/29 ≈ 0.552
├── Some((2, 3)): 10245/19327 ≈ 0.530
  ├── Some((3, 0)): 952/1829 ≈ 0.521
    ├── Some((0, 0)): 78/161 ≈ 0.484
      ├── Some((0, 1)): 7/17 ≈ 0.412
      ├── Some((0, 2)): 9/19 ≈ 0.474
      ├── Some((0, 3)): 7/17 ≈ 0.412
      ├── Some((0, 4)): 20/32 ≈ 0.625
      ├── Some((0, 5)): 4/13 ≈ 0.308
      ├── Some((0, 6)): 8/18 ≈ 0.444
      ├── Some((0, 7)): 11/22 ≈ 0.500
      └── Some((0, 8)): 11/22 ≈ 0.500
    ├── Some((0, 1)): 93/184 ≈ 0.505
      ├── Some((1, 0)): 12/22 ≈ 0.545
      ├── Some((1, 1)): 26/37 ≈ 0.703
      ├── Some((1, 2)): 15/26 ≈ 0.577
      ├── Some((1, 3)): 8/18 ≈ 0.444
      ├── Some((1, 4)): 4/13 ≈ 0.308
      ├── Some((1, 5)): 5/14 ≈ 0.357
      ├── Some((1, 6)): 7/17 ≈ 0.412
      ├── Some((1, 7)): 7/17 ≈ 0.412
      └── Some((1, 8)): 9/19 ≈ 0.474
    ├── Some((0, 2)): 115/218 ≈ 0.528
      ├── Some((2, 0)): 15/28 ≈ 0.536
      ├── Some((2, 1)): 8/20 ≈ 0.400
      ├── Some((2, 2)): 12/25 ≈ 0.480
      ├── Some((2, 4)): 28/43 ≈ 0.651
      ├── Some((2, 5)): 18/32 ≈ 0.562
      ├── Some((2, 6)): 8/20 ≈ 0.400
      ├── Some((2, 7)): 1/10 ≈ 0.100
      └── Some((2, 8)): 25/39 ≈ 0.641
    ├── Some((0, 3)): 141/256 ≈ 0.551
      ├── Some((3, 1)): 12/26 ≈ 0.462
      ├── Some((3, 2)): 17/31 ≈ 0.548
      ├── Some((3, 3)): 28/44 ≈ 0.636
      ├── Some((3, 4)): 15/29 ≈ 0.517
      ├── Some((3, 5)): 2/13 ≈ 0.154
      ├── Some((3, 6)): 28/44 ≈ 0.636
      ├── Some((3, 7)): 17/32 ≈ 0.531
      └── Some((3, 8)): 21/36 ≈ 0.583
    ├── Some((0, 4)): 81/166 ≈ 0.488
      ├── Some((4, 0)): 10/20 ≈ 0.500
      ├── Some((4, 1)): 11/21 ≈ 0.524
      ├── Some((4, 2)): 21/31 ≈ 0.677
      ├── Some((4, 3)): 5/14 ≈ 0.357
      ├── Some((4, 4)): 5/14 ≈ 0.357
      ├── Some((4, 5)): 6/15 ≈ 0.400
      ├── Some((4, 6)): 8/17 ≈ 0.471
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 6/15 ≈ 0.400
    ├── Some((0, 5)): 87/175 ≈ 0.497
      ├── Some((5, 0)): 15/25 ≈ 0.600
      ├── Some((5, 1)): 3/12 ≈ 0.250
      ├── Some((5, 2)): 11/21 ≈ 0.524
      ├── Some((5, 3)): 10/20 ≈ 0.500
      ├── Some((5, 4)): 14/24 ≈ 0.583
      ├── Some((5, 5)): 1/9 ≈ 0.111
      ├── Some((5, 6)): 10/20 ≈ 0.500
      ├── Some((5, 7)): 10/20 ≈ 0.500
      └── Some((5, 8)): 13/23 ≈ 0.565
    ├── Some((0, 6)): 99/193 ≈ 0.513
      ├── Some((6, 0)): 16/27 ≈ 0.593
      ├── Some((6, 1)): 13/24 ≈ 0.542
      ├── Some((6, 2)): 6/16 ≈ 0.375
      ├── Some((6, 3)): 15/26 ≈ 0.577
      ├── Some((6, 4)): 8/18 ≈ 0.444
      ├── Some((6, 5)): 9/19 ≈ 0.474
      ├── Some((6, 6)): 5/15 ≈ 0.333
      ├── Some((6, 7)): 8/18 ≈ 0.444
      └── Some((6, 8)): 18/29 ≈ 0.621
    ├── Some((0, 7)): 135/247 ≈ 0.547
      ├── Some((7, 0)): 14/26 ≈ 0.538
      ├── Some((7, 1)): 18/31 ≈ 0.581
      ├── Some((7, 2)): 22/35 ≈ 0.629
      ├── Some((7, 3)): 15/27 ≈ 0.556
      ├── Some((7, 4)): 11/23 ≈ 0.478
      ├── Some((7, 5)): 23/36 ≈ 0.639
      ├── Some((7, 6)): 16/29 ≈ 0.552
      ├── Some((7, 7)): 6/17 ≈ 0.353
      └── Some((7, 8)): 10/22 ≈ 0.455
    └── Some((0, 8)): 122/228 ≈ 0.535
      ├── Some((8, 0)): 10/22 ≈ 0.455
      ├── Some((8, 1)): 17/29 ≈ 0.586
      ├── Some((8, 2)): 13/25 ≈ 0.520
      ├── Some((8, 3)): 1/10 ≈ 0.100
      ├── Some((8, 4)): 18/30 ≈ 0.600
      ├── Some((8, 5)): 13/25 ≈ 0.520
      ├── Some((8, 6)): 17/29 ≈ 0.586
      ├── Some((8, 7)): 17/29 ≈ 0.586
      └── Some((8, 8)): 16/28 ≈ 0.571
  ├── Some((3, 1)): 1339/2497 ≈ 0.536
    ├── Some((1, 0)): 100/203 ≈ 0.493
      ├── Some((0, 0)): 10/21 ≈ 0.476
      ├── Some((0, 1)): 4/14 ≈ 0.286
      ├── Some((0, 2)): 11/23 ≈ 0.478
      ├── Some((0, 3)): 9/20 ≈ 0.450
      ├── Some((0, 4)): 2/11 ≈ 0.182
      ├── Some((0, 5)): 7/18 ≈ 0.389
      ├── Some((0, 6)): 21/34 ≈ 0.618
      ├── Some((0, 7)): 13/25 ≈ 0.520
      └── Some((0, 8)): 23/36 ≈ 0.639
    ├── Some((1, 1)): 157/291 ≈ 0.540
      ├── Some((1, 0)): 19/36 ≈ 0.528
      ├── Some((1, 2)): 18/35 ≈ 0.514
      ├── Some((1, 3)): 30/48 ≈ 0.625
      ├── Some((1, 4)): 22/39 ≈ 0.564
      ├── Some((1, 5)): 27/45 ≈ 0.600
      ├── Some((1, 6)): 14/30 ≈ 0.467
      ├── Some((1, 7)): 11/26 ≈ 0.423
      └── Some((1, 8)): 15/31 ≈ 0.484
    ├── Some((1, 2)): 134/256 ≈ 0.523
      ├── Some((2, 0)): 28/45 ≈ 0.622
      ├── Some((2, 1)): 11/25 ≈ 0.440
      ├── Some((2, 2)): 20/36 ≈ 0.556
      ├── Some((2, 4)): 23/40 ≈ 0.575
      ├── Some((2, 5)): 7/20 ≈ 0.350
      ├── Some((2, 6)): 12/27 ≈ 0.444
      ├── Some((2, 7)): 21/37 ≈ 0.568
      └── Some((2, 8)): 11/25 ≈ 0.440
    ├── Some((1, 3)): 143/270 ≈ 0.530
      ├── Some((3, 0)): 21/38 ≈ 0.553
      ├── Some((3, 2)): 10/24 ≈ 0.417
      ├── Some((3, 3)): 9/23 ≈ 0.391
      ├── Some((3, 4)): 27/45 ≈ 0.600
      ├── Some((3, 5)): 11/26 ≈ 0.423
      ├── Some((3, 6)): 12/27 ≈ 0.444
      ├── Some((3, 7)): 13/28 ≈ 0.464
      └── Some((3, 8)): 39/58 ≈ 0.672
    ├── Some((1, 4)): 77/167 ≈ 0.461
      ├── Some((4, 0)): 2/11 ≈ 0.182
      ├── Some((4, 1)): 9/19 ≈ 0.474
      ├── Some((4, 2)): 6/16 ≈ 0.375
      ├── Some((4, 3)): 13/23 ≈ 0.565
      ├── Some((4, 4)): 13/23 ≈ 0.565
      ├── Some((4, 5)): 8/18 ≈ 0.444
      ├── Some((4, 6)): 7/17 ≈ 0.412
      ├── Some((4, 7)): 6/16 ≈ 0.375
      └── Some((4, 8)): 13/23 ≈ 0.565
    ├── Some((1, 5)): 152/283 ≈ 0.537
      ├── Some((5, 0)): 16/30 ≈ 0.533
      ├── Some((5, 1)): 24/40 ≈ 0.600
      ├── Some((5, 2)): 7/19 ≈ 0.368
      ├── Some((5, 3)): 17/32 ≈ 0.531
      ├── Some((5, 4)): 20/35 ≈ 0.571
      ├── Some((5, 5)): 17/32 ≈ 0.531
      ├── Some((5, 6)): 10/23 ≈ 0.435
      ├── Some((5, 7)): 19/34 ≈ 0.559
      └── Some((5, 8)): 22/37 ≈ 0.595
    ├── Some((1, 6)): 231/400 ≈ 0.577
      ├── Some((6, 0)): 27/46 ≈ 0.587
      ├── Some((6, 1)): 33/53 ≈ 0.623
      ├── Some((6, 2)): 37/58 ≈ 0.638
      ├── Some((6, 3)): 13/29 ≈ 0.448
      ├── Some((6, 4)): 38/59 ≈ 0.644
      ├── Some((6, 5)): 7/22 ≈ 0.318
      ├── Some((6, 6)): 32/52 ≈ 0.615
      ├── Some((6, 7)): 22/40 ≈ 0.550
      └── Some((6, 8)): 22/40 ≈ 0.550
    ├── Some((1, 7)): 184/331 ≈ 0.556
      ├── Some((7, 0)): 15/30 ≈ 0.500
      ├── Some((7, 1)): 20/36 ≈ 0.556
      ├── Some((7, 2)): 17/33 ≈ 0.515
      ├── Some((7, 3)): 15/31 ≈ 0.484
      ├── Some((7, 4)): 29/47 ≈ 0.617
      ├── Some((7, 5)): 11/26 ≈ 0.423
      ├── Some((7, 6)): 32/50 ≈ 0.640
      ├── Some((7, 7)): 36/54 ≈ 0.667
      └── Some((7, 8)): 9/23 ≈ 0.391
    └── Some((1, 8)): 160/295 ≈ 0.542
      ├── Some((8, 0)): 2/13 ≈ 0.154
      ├── Some((8, 1)): 8/21 ≈ 0.381
      ├── Some((8, 2)): 34/51 ≈ 0.667
      ├── Some((8, 3)): 9/23 ≈ 0.391
      ├── Some((8, 4)): 10/24 ≈ 0.417
      ├── Some((8, 5)): 19/35 ≈ 0.543
      ├── Some((8, 6)): 25/41 ≈ 0.610
      ├── Some((8, 7)): 36/54 ≈ 0.667
      └── Some((8, 8)): 17/32 ≈ 0.531
  ├── Some((3, 2)): 2004/3628 ≈ 0.552
    ├── Some((2, 0)): 258/465 ≈ 0.555
      ├── Some((0, 0)): 47/74 ≈ 0.635
      ├── Some((0, 1)): 29/52 ≈ 0.558
      ├── Some((0, 2)): 26/49 ≈ 0.531
      ├── Some((0, 3)): 26/49 ≈ 0.531
      ├── Some((0, 4)): 44/70 ≈ 0.629
      ├── Some((0, 5)): 12/31 ≈ 0.387
      ├── Some((0, 6)): 20/41 ≈ 0.488
      ├── Some((0, 7)): 32/56 ≈ 0.571
      └── Some((0, 8)): 21/42 ≈ 0.500
    ├── Some((2, 1)): 280/499 ≈ 0.561
      ├── Some((1, 0)): 45/72 ≈ 0.625
      ├── Some((1, 1)): 35/60 ≈ 0.583
      ├── Some((1, 2)): 31/56 ≈ 0.554
      ├── Some((1, 3)): 43/70 ≈ 0.614
      ├── Some((1, 4)): 25/48 ≈ 0.521
      ├── Some((1, 5)): 40/66 ≈ 0.606
      ├── Some((1, 6)): 20/42 ≈ 0.476
      ├── Some((1, 7)): 19/40 ≈ 0.475
      └── Some((1, 8)): 22/44 ≈ 0.500
    ├── Some((2, 2)): 262/472 ≈ 0.555
      ├── Some((2, 0)): 45/77 ≈ 0.584
      ├── Some((2, 1)): 18/42 ≈ 0.429
      ├── Some((2, 4)): 26/53 ≈ 0.491
      ├── Some((2, 5)): 29/57 ≈ 0.509
      ├── Some((2, 6)): 65/102 ≈ 0.637
      ├── Some((2, 7)): 32/61 ≈ 0.525
      └── Some((2, 8)): 46/79 ≈ 0.582
    ├── Some((2, 4)): 283/504 ≈ 0.562
      ├── Some((4, 0)): 12/31 ≈ 0.387
      ├── Some((4, 1)): 35/61 ≈ 0.574
      ├── Some((4, 2)): 40/67 ≈ 0.597
      ├── Some((4, 3)): 55/85 ≈ 0.647
      ├── Some((4, 4)): 12/31 ≈ 0.387
      ├── Some((4, 5)): 38/64 ≈ 0.594
      ├── Some((4, 6)): 40/67 ≈ 0.597
      ├── Some((4, 7)): 24/47 ≈ 0.511
      └── Some((4, 8)): 26/50 ≈ 0.520
    ├── Some((2, 5)): 173/334 ≈ 0.518
      ├── Some((5, 0)): 29/49 ≈ 0.592
      ├── Some((5, 1)): 11/27 ≈ 0.407
      ├── Some((5, 2)): 10/26 ≈ 0.385
      ├── Some((5, 3)): 11/27 ≈ 0.407
      ├── Some((5, 4)): 25/44 ≈ 0.568
      ├── Some((5, 5)): 17/34 ≈ 0.500
      ├── Some((5, 6)): 26/45 ≈ 0.578
      ├── Some((5, 7)): 21/39 ≈ 0.538
      └── Some((5, 8)): 23/42 ≈ 0.548
    ├── Some((2, 6)): 323/564 ≈ 0.573
      ├── Some((6, 0)): 59/91 ≈ 0.648
      ├── Some((6, 1)): 44/73 ≈ 0.603
      ├── Some((6, 2)): 16/37 ≈ 0.432
      ├── Some((6, 3)): 39/67 ≈ 0.582
      ├── Some((6, 4)): 35/62 ≈ 0.565
      ├── Some((6, 5)): 22/45 ≈ 0.489
      ├── Some((6, 6)): 41/69 ≈ 0.594
      ├── Some((6, 7)): 29/54 ≈ 0.537
      └── Some((6, 8)): 38/65 ≈ 0.585
    ├── Some((2, 7)): 166/323 ≈ 0.514
      ├── Some((7, 0)): 11/27 ≈ 0.407
      ├── Some((7, 1)): 17/34 ≈ 0.500
      ├── Some((7, 2)): 26/45 ≈ 0.578
      ├── Some((7, 3)): 7/21 ≈ 0.333
      ├── Some((7, 4)): 20/38 ≈ 0.526
      ├── Some((7, 5)): 16/33 ≈ 0.485
      ├── Some((7, 6)): 23/42 ≈ 0.548
      ├── Some((7, 7)): 17/34 ≈ 0.500
      └── Some((7, 8)): 28/48 ≈ 0.583
    └── Some((2, 8)): 258/466 ≈ 0.554
      ├── Some((8, 0)): 32/56 ≈ 0.571
      ├── Some((8, 1)): 37/62 ≈ 0.597
      ├── Some((8, 2)): 17/38 ≈ 0.447
      ├── Some((8, 3)): 18/39 ≈ 0.462
      ├── Some((8, 4)): 16/36 ≈ 0.444
      ├── Some((8, 5)): 69/100 ≈ 0.690
      ├── Some((8, 6)): 44/71 ≈ 0.620
      ├── Some((8, 7)): 10/28 ≈ 0.357
      └── Some((8, 8)): 15/35 ≈ 0.429
  ├── Some((3, 3)): 1159/2187 ≈ 0.530
    ├── Some((3, 0)): 159/295 ≈ 0.539
      ├── Some((0, 0)): 21/37 ≈ 0.568
      ├── Some((0, 1)): 18/33 ≈ 0.545
      ├── Some((0, 2)): 25/41 ≈ 0.610
      ├── Some((0, 3)): 22/38 ≈ 0.579
      ├── Some((0, 4)): 16/31 ≈ 0.516
      ├── Some((0, 5)): 5/17 ≈ 0.294
      ├── Some((0, 6)): 17/32 ≈ 0.531
      ├── Some((0, 7)): 22/38 ≈ 0.579
      └── Some((0, 8)): 13/27 ≈ 0.481
    ├── Some((3, 1)): 167/308 ≈ 0.542
      ├── Some((1, 0)): 30/47 ≈ 0.638
      ├── Some((1, 1)): 19/35 ≈ 0.543
      ├── Some((1, 2)): 7/20 ≈ 0.350
      ├── Some((1, 3)): 19/35 ≈ 0.543
      ├── Some((1, 4)): 23/40 ≈ 0.575
      ├── Some((1, 5)): 16/31 ≈ 0.516
      ├── Some((1, 6)): 22/38 ≈ 0.579
      ├── Some((1, 7)): 6/19 ≈ 0.316
      └── Some((1, 8)): 25/42 ≈ 0.595
    ├── Some((3, 2)): 152/285 ≈ 0.533
      ├── Some((2, 0)): 13/28 ≈ 0.464
      ├── Some((2, 1)): 33/52 ≈ 0.635
      ├── Some((2, 2)): 10/25 ≈ 0.400
      ├── Some((2, 4)): 23/40 ≈ 0.575
      ├── Some((2, 5)): 18/35 ≈ 0.514
      ├── Some((2, 6)): 17/33 ≈ 0.515
      ├── Some((2, 7)): 22/39 ≈ 0.564
      └── Some((2, 8)): 16/32 ≈ 0.500
    ├── Some((3, 4)): 68/153 ≈ 0.444
      ├── Some((4, 0)): 10/20 ≈ 0.500
      ├── Some((4, 1)): 5/14 ≈ 0.357
      ├── Some((4, 2)): 10/20 ≈ 0.500
      ├── Some((4, 3)): 8/18 ≈ 0.444
      ├── Some((4, 4)): 11/21 ≈ 0.524
      ├── Some((4, 5)): 4/13 ≈ 0.308
      ├── Some((4, 6)): 7/16 ≈ 0.438
      ├── Some((4, 7)): 6/15 ≈ 0.400
      └── Some((4, 8)): 6/15 ≈ 0.400
    ├── Some((3, 5)): 127/247 ≈ 0.514
      ├── Some((5, 0)): 9/21 ≈ 0.429
      ├── Some((5, 1)): 18/32 ≈ 0.562
      ├── Some((5, 2)): 16/30 ≈ 0.533
      ├── Some((5, 3)): 10/23 ≈ 0.435
      ├── Some((5, 4)): 18/32 ≈ 0.562
      ├── Some((5, 5)): 4/15 ≈ 0.267
      ├── Some((5, 6)): 29/44 ≈ 0.659
      ├── Some((5, 7)): 9/22 ≈ 0.409
      └── Some((5, 8)): 14/27 ≈ 0.519
    ├── Some((3, 6)): 195/350 ≈ 0.557
      ├── Some((6, 0)): 32/51 ≈ 0.627
      ├── Some((6, 1)): 16/32 ≈ 0.500
      ├── Some((6, 2)): 32/51 ≈ 0.627
      ├── Some((6, 3)): 33/52 ≈ 0.635
      ├── Some((6, 4)): 19/36 ≈ 0.528
      ├── Some((6, 5)): 12/27 ≈ 0.444
      ├── Some((6, 6)): 16/32 ≈ 0.500
      ├── Some((6, 7)): 17/34 ≈ 0.500
      └── Some((6, 8)): 17/34 ≈ 0.500
    ├── Some((3, 7)): 138/263 ≈ 0.525
      ├── Some((7, 0)): 13/26 ≈ 0.500
      ├── Some((7, 1)): 15/29 ≈ 0.517
      ├── Some((7, 2)): 22/37 ≈ 0.595
      ├── Some((7, 3)): 14/28 ≈ 0.500
      ├── Some((7, 4)): 25/40 ≈ 0.625
      ├── Some((7, 5)): 8/20 ≈ 0.400
      ├── Some((7, 6)): 17/31 ≈ 0.548
      ├── Some((7, 7)): 11/24 ≈ 0.458
      └── Some((7, 8)): 13/27 ≈ 0.481
    └── Some((3, 8)): 152/285 ≈ 0.533
      ├── Some((8, 0)): 11/25 ≈ 0.440
      ├── Some((8, 1)): 8/21 ≈ 0.381
      ├── Some((8, 2)): 19/34 ≈ 0.559
      ├── Some((8, 3)): 23/39 ≈ 0.590
      ├── Some((8, 4)): 11/25 ≈ 0.440
      ├── Some((8, 5)): 26/42 ≈ 0.619
      ├── Some((8, 6)): 11/25 ≈ 0.440
      ├── Some((8, 7)): 29/45 ≈ 0.644
      └── Some((8, 8)): 14/28 ≈ 0.500
  ├── Some((3, 4)): 1433/2658 ≈ 0.539
    ├── Some((4, 0)): 149/280 ≈ 0.532
      ├── Some((0, 0)): 24/40 ≈ 0.600
      ├── Some((0, 1)): 27/43 ≈ 0.628
      ├── Some((0, 2)): 19/34 ≈ 0.559
      ├── Some((0, 3)): 16/31 ≈ 0.516
      ├── Some((0, 4)): 13/27 ≈ 0.481
      ├── Some((0, 5)): 7/20 ≈ 0.350
      ├── Some((0, 6)): 17/32 ≈ 0.531
      ├── Some((0, 7)): 4/16 ≈ 0.250
      └── Some((0, 8)): 21/36 ≈ 0.583
    ├── Some((4, 1)): 118/233 ≈ 0.506
      ├── Some((1, 0)): 8/20 ≈ 0.400
      ├── Some((1, 1)): 12/25 ≈ 0.480
      ├── Some((1, 2)): 1/11 ≈ 0.091
      ├── Some((1, 3)): 13/26 ≈ 0.500
      ├── Some((1, 4)): 10/22 ≈ 0.455
      ├── Some((1, 5)): 21/35 ≈ 0.600
      ├── Some((1, 6)): 17/30 ≈ 0.567
      ├── Some((1, 7)): 19/33 ≈ 0.576
      └── Some((1, 8)): 17/30 ≈ 0.567
    ├── Some((4, 2)): 192/345 ≈ 0.557
      ├── Some((2, 0)): 22/41 ≈ 0.537
      ├── Some((2, 1)): 32/53 ≈ 0.604
      ├── Some((2, 2)): 6/20 ≈ 0.300
      ├── Some((2, 4)): 12/29 ≈ 0.414
      ├── Some((2, 5)): 17/35 ≈ 0.486
      ├── Some((2, 6)): 35/56 ≈ 0.625
      ├── Some((2, 7)): 40/62 ≈ 0.645
      └── Some((2, 8)): 28/48 ≈ 0.583
    ├── Some((4, 3)): 104/211 ≈ 0.493
      ├── Some((3, 0)): 5/17 ≈ 0.294
      ├── Some((3, 1)): 3/14 ≈ 0.214
      ├── Some((3, 2)): 29/45 ≈ 0.644
      ├── Some((3, 3)): 7/19 ≈ 0.368
      ├── Some((3, 5)): 17/31 ≈ 0.548
      ├── Some((3, 6)): 17/31 ≈ 0.548
      ├── Some((3, 7)): 10/23 ≈ 0.435
      └── Some((3, 8)): 16/30 ≈ 0.533
    ├── Some((4, 4)): 218/384 ≈ 0.568
      ├── Some((4, 0)): 8/24 ≈ 0.333
      ├── Some((4, 1)): 26/47 ≈ 0.553
      ├── Some((4, 2)): 37/60 ≈ 0.617
      ├── Some((4, 3)): 42/65 ≈ 0.646
      ├── Some((4, 5)): 26/47 ≈ 0.553
      ├── Some((4, 6)): 34/56 ≈ 0.607
      ├── Some((4, 7)): 18/37 ≈ 0.486
      └── Some((4, 8)): 26/47 ≈ 0.553
    ├── Some((4, 5)): 119/235 ≈ 0.506
      ├── Some((5, 0)): 15/28 ≈ 0.536
      ├── Some((5, 1)): 17/31 ≈ 0.548
      ├── Some((5, 2)): 18/32 ≈ 0.562
      ├── Some((5, 3)): 10/22 ≈ 0.455
      ├── Some((5, 4)): 24/38 ≈ 0.632
      ├── Some((5, 5)): 17/31 ≈ 0.548
      ├── Some((5, 6)): 3/14 ≈ 0.214
      ├── Some((5, 7)): 6/18 ≈ 0.333
      └── Some((5, 8)): 8/20 ≈ 0.400
    ├── Some((4, 6)): 135/259 ≈ 0.521
      ├── Some((6, 0)): 9/22 ≈ 0.409
      ├── Some((6, 1)): 17/31 ≈ 0.548
      ├── Some((6, 2)): 33/49 ≈ 0.673
      ├── Some((6, 3)): 16/30 ≈ 0.533
      ├── Some((6, 4)): 25/40 ≈ 0.625
      ├── Some((6, 5)): 2/13 ≈ 0.154
      ├── Some((6, 6)): 14/28 ≈ 0.500
      ├── Some((6, 7)): 6/18 ≈ 0.333
      └── Some((6, 8)): 13/27 ≈ 0.481
    ├── Some((4, 7)): 202/360 ≈ 0.561
      ├── Some((7, 0)): 20/37 ≈ 0.541
      ├── Some((7, 1)): 31/50 ≈ 0.620
      ├── Some((7, 2)): 11/26 ≈ 0.423
      ├── Some((7, 3)): 40/60 ≈ 0.667
      ├── Some((7, 4)): 18/35 ≈ 0.514
      ├── Some((7, 5)): 20/37 ≈ 0.541
      ├── Some((7, 6)): 18/35 ≈ 0.514
      ├── Some((7, 7)): 23/41 ≈ 0.561
      └── Some((7, 8)): 21/38 ≈ 0.553
    └── Some((4, 8)): 195/350 ≈ 0.557
      ├── Some((8, 0)): 33/52 ≈ 0.635
      ├── Some((8, 1)): 27/45 ≈ 0.600
      ├── Some((8, 2)): 9/24 ≈ 0.375
      ├── Some((8, 3)): 14/30 ≈ 0.467
      ├── Some((8, 4)): 25/43 ≈ 0.581
      ├── Some((8, 5)): 21/38 ≈ 0.553
      ├── Some((8, 6)): 27/45 ≈ 0.600
      ├── Some((8, 7)): 13/29 ≈ 0.448
      └── Some((8, 8)): 25/43 ≈ 0.581
  ├── Some((3, 5)): 671/1338 ≈ 0.501
    ├── Some((5, 0)): 64/133 ≈ 0.481
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 3/10 ≈ 0.300
      ├── Some((0, 2)): 8/16 ≈ 0.500
      ├── Some((0, 3)): 2/9 ≈ 0.222
      ├── Some((0, 4)): 8/16 ≈ 0.500
      ├── Some((0, 5)): 12/20 ≈ 0.600
      ├── Some((0, 6)): 10/18 ≈ 0.556
      ├── Some((0, 7)): 4/12 ≈ 0.333
      └── Some((0, 8)): 12/20 ≈ 0.600
    ├── Some((5, 1)): 37/91 ≈ 0.407
      ├── Some((1, 0)): 2/8 ≈ 0.250
      ├── Some((1, 1)): 2/8 ≈ 0.250
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 5/11 ≈ 0.455
      ├── Some((1, 6)): 3/9 ≈ 0.333
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 10/16 ≈ 0.625
    ├── Some((5, 2)): 81/159 ≈ 0.509
      ├── Some((2, 0)): 8/18 ≈ 0.444
      ├── Some((2, 1)): 18/28 ≈ 0.643
      ├── Some((2, 2)): 9/19 ≈ 0.474
      ├── Some((2, 4)): 13/23 ≈ 0.565
      ├── Some((2, 5)): 8/18 ≈ 0.444
      ├── Some((2, 6)): 2/10 ≈ 0.200
      ├── Some((2, 7)): 13/23 ≈ 0.565
      └── Some((2, 8)): 9/19 ≈ 0.474
    ├── Some((5, 3)): 73/147 ≈ 0.497
      ├── Some((3, 0)): 20/30 ≈ 0.667
      ├── Some((3, 1)): 2/10 ≈ 0.200
      ├── Some((3, 2)): 5/14 ≈ 0.357
      ├── Some((3, 3)): 10/20 ≈ 0.500
      ├── Some((3, 4)): 12/22 ≈ 0.545
      ├── Some((3, 6)): 15/25 ≈ 0.600
      ├── Some((3, 7)): 2/10 ≈ 0.200
      └── Some((3, 8)): 6/15 ≈ 0.400
    ├── Some((5, 4)): 89/171 ≈ 0.520
      ├── Some((4, 0)): 11/20 ≈ 0.550
      ├── Some((4, 1)): 8/17 ≈ 0.471
      ├── Some((4, 2)): 4/13 ≈ 0.308
      ├── Some((4, 3)): 0/7 ≈ 0.000
      ├── Some((4, 4)): 10/19 ≈ 0.526
      ├── Some((4, 5)): 12/22 ≈ 0.545
      ├── Some((4, 6)): 10/19 ≈ 0.526
      ├── Some((4, 7)): 18/28 ≈ 0.643
      └── Some((4, 8)): 15/25 ≈ 0.600
    ├── Some((5, 5)): 82/161 ≈ 0.509
      ├── Some((5, 0)): 10/20 ≈ 0.500
      ├── Some((5, 1)): 12/22 ≈ 0.545
      ├── Some((5, 2)): 10/20 ≈ 0.500
      ├── Some((5, 3)): 7/17 ≈ 0.412
      ├── Some((5, 4)): 6/15 ≈ 0.400
      ├── Some((5, 6)): 8/18 ≈ 0.444
      ├── Some((5, 7)): 4/13 ≈ 0.308
      └── Some((5, 8)): 24/35 ≈ 0.686
    ├── Some((5, 6)): 129/229 ≈ 0.563
      ├── Some((6, 0)): 9/20 ≈ 0.450
      ├── Some((6, 1)): 21/33 ≈ 0.636
      ├── Some((6, 2)): 17/28 ≈ 0.607
      ├── Some((6, 3)): 21/33 ≈ 0.636
      ├── Some((6, 4)): 2/11 ≈ 0.182
      ├── Some((6, 5)): 16/27 ≈ 0.593
      ├── Some((6, 6)): 14/25 ≈ 0.560
      ├── Some((6, 7)): 12/23 ≈ 0.522
      └── Some((6, 8)): 17/28 ≈ 0.607
    ├── Some((5, 7)): 68/139 ≈ 0.489
      ├── Some((7, 0)): 4/12 ≈ 0.333
      ├── Some((7, 1)): 10/18 ≈ 0.556
      ├── Some((7, 2)): 9/17 ≈ 0.529
      ├── Some((7, 3)): 18/27 ≈ 0.667
      ├── Some((7, 4)): 12/20 ≈ 0.600
      ├── Some((7, 5)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 8/16 ≈ 0.500
      ├── Some((7, 7)): 1/8 ≈ 0.125
      └── Some((7, 8)): 3/11 ≈ 0.273
    └── Some((5, 8)): 47/107 ≈ 0.439
      ├── Some((8, 0)): 11/18 ≈ 0.611
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 1/7 ≈ 0.143
      ├── Some((8, 3)): 8/15 ≈ 0.533
      ├── Some((8, 4)): 8/15 ≈ 0.533
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 4/10 ≈ 0.400
      ├── Some((8, 7)): 1/7 ≈ 0.143
      └── Some((8, 8)): 5/12 ≈ 0.417
  ├── Some((3, 6)): 1135/2146 ≈ 0.529
    ├── Some((6, 0)): 132/248 ≈ 0.532
      ├── Some((0, 0)): 12/24 ≈ 0.500
      ├── Some((0, 1)): 13/26 ≈ 0.500
      ├── Some((0, 2)): 14/27 ≈ 0.519
      ├── Some((0, 3)): 9/21 ≈ 0.429
      ├── Some((0, 4)): 11/23 ≈ 0.478
      ├── Some((0, 5)): 10/22 ≈ 0.455
      ├── Some((0, 6)): 26/40 ≈ 0.650
      ├── Some((0, 7)): 13/26 ≈ 0.500
      └── Some((0, 8)): 24/38 ≈ 0.632
    ├── Some((6, 1)): 149/273 ≈ 0.546
      ├── Some((1, 0)): 15/29 ≈ 0.517
      ├── Some((1, 1)): 8/20 ≈ 0.400
      ├── Some((1, 2)): 18/32 ≈ 0.562
      ├── Some((1, 3)): 29/44 ≈ 0.659
      ├── Some((1, 4)): 14/28 ≈ 0.500
      ├── Some((1, 5)): 32/48 ≈ 0.667
      ├── Some((1, 6)): 18/32 ≈ 0.562
      ├── Some((1, 7)): 8/20 ≈ 0.400
      └── Some((1, 8)): 7/19 ≈ 0.368
    ├── Some((6, 2)): 125/237 ≈ 0.527
      ├── Some((2, 0)): 11/24 ≈ 0.458
      ├── Some((2, 1)): 12/26 ≈ 0.462
      ├── Some((2, 2)): 24/39 ≈ 0.615
      ├── Some((2, 4)): 25/41 ≈ 0.610
      ├── Some((2, 5)): 16/30 ≈ 0.533
      ├── Some((2, 6)): 6/18 ≈ 0.333
      ├── Some((2, 7)): 11/24 ≈ 0.458
      └── Some((2, 8)): 19/34 ≈ 0.559
    ├── Some((6, 3)): 133/249 ≈ 0.534
      ├── Some((3, 0)): 12/26 ≈ 0.462
      ├── Some((3, 1)): 21/36 ≈ 0.583
      ├── Some((3, 2)): 15/29 ≈ 0.517
      ├── Some((3, 3)): 15/29 ≈ 0.517
      ├── Some((3, 4)): 21/36 ≈ 0.583
      ├── Some((3, 5)): 17/31 ≈ 0.548
      ├── Some((3, 7)): 17/32 ≈ 0.531
      └── Some((3, 8)): 15/29 ≈ 0.517
    ├── Some((6, 4)): 93/188 ≈ 0.495
      ├── Some((4, 0)): 16/27 ≈ 0.593
      ├── Some((4, 1)): 6/16 ≈ 0.375
      ├── Some((4, 2)): 17/28 ≈ 0.607
      ├── Some((4, 3)): 4/13 ≈ 0.308
      ├── Some((4, 4)): 9/20 ≈ 0.450
      ├── Some((4, 5)): 13/24 ≈ 0.542
      ├── Some((4, 6)): 9/20 ≈ 0.450
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 10/21 ≈ 0.476
    ├── Some((6, 5)): 160/290 ≈ 0.552
      ├── Some((5, 0)): 16/31 ≈ 0.516
      ├── Some((5, 1)): 8/21 ≈ 0.381
      ├── Some((5, 2)): 10/23 ≈ 0.435
      ├── Some((5, 3)): 18/33 ≈ 0.545
      ├── Some((5, 4)): 20/35 ≈ 0.571
      ├── Some((5, 5)): 23/38 ≈ 0.605
      ├── Some((5, 6)): 21/36 ≈ 0.583
      ├── Some((5, 7)): 9/22 ≈ 0.409
      └── Some((5, 8)): 34/50 ≈ 0.680
    ├── Some((6, 6)): 153/279 ≈ 0.548
      ├── Some((6, 0)): 34/52 ≈ 0.654
      ├── Some((6, 1)): 25/42 ≈ 0.595
      ├── Some((6, 2)): 13/28 ≈ 0.464
      ├── Some((6, 3)): 29/46 ≈ 0.630
      ├── Some((6, 4)): 13/28 ≈ 0.464
      ├── Some((6, 5)): 16/32 ≈ 0.500
      ├── Some((6, 7)): 15/30 ≈ 0.500
      └── Some((6, 8)): 7/20 ≈ 0.350
    ├── Some((6, 7)): 100/199 ≈ 0.503
      ├── Some((7, 0)): 8/19 ≈ 0.421
      ├── Some((7, 1)): 5/15 ≈ 0.333
      ├── Some((7, 2)): 12/23 ≈ 0.522
      ├── Some((7, 3)): 13/24 ≈ 0.542
      ├── Some((7, 4)): 12/23 ≈ 0.522
      ├── Some((7, 5)): 13/24 ≈ 0.542
      ├── Some((7, 6)): 10/21 ≈ 0.476
      ├── Some((7, 7)): 9/20 ≈ 0.450
      └── Some((7, 8)): 17/29 ≈ 0.586
    └── Some((6, 8)): 89/182 ≈ 0.489
      ├── Some((8, 0)): 12/23 ≈ 0.522
      ├── Some((8, 1)): 17/28 ≈ 0.607
      ├── Some((8, 2)): 1/9 ≈ 0.111
      ├── Some((8, 3)): 2/11 ≈ 0.182
      ├── Some((8, 4)): 15/26 ≈ 0.577
      ├── Some((8, 5)): 13/24 ≈ 0.542
      ├── Some((8, 6)): 6/16 ≈ 0.375
      ├── Some((8, 7)): 11/22 ≈ 0.500
      └── Some((8, 8)): 11/22 ≈ 0.500
  ├── Some((3, 7)): 660/1318 ≈ 0.501
    ├── Some((7, 0)): 68/139 ≈ 0.489
      ├── Some((0, 0)): 5/13 ≈ 0.385
      ├── Some((0, 1)): 7/15 ≈ 0.467
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 5/13 ≈ 0.385
      ├── Some((0, 4)): 11/19 ≈ 0.579
      ├── Some((0, 5)): 6/14 ≈ 0.429
      ├── Some((0, 6)): 8/16 ≈ 0.500
      ├── Some((0, 7)): 11/19 ≈ 0.579
      └── Some((0, 8)): 10/18 ≈ 0.556
    ├── Some((7, 1)): 55/119 ≈ 0.462
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 1)): 7/14 ≈ 0.500
      ├── Some((1, 2)): 11/19 ≈ 0.579
      ├── Some((1, 3)): 1/8 ≈ 0.125
      ├── Some((1, 4)): 3/10 ≈ 0.300
      ├── Some((1, 5)): 3/10 ≈ 0.300
      ├── Some((1, 6)): 2/9 ≈ 0.222
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 15/22 ≈ 0.682
    ├── Some((7, 2)): 81/158 ≈ 0.513
      ├── Some((2, 0)): 8/17 ≈ 0.471
      ├── Some((2, 1)): 7/16 ≈ 0.438
      ├── Some((2, 2)): 11/21 ≈ 0.524
      ├── Some((2, 4)): 13/23 ≈ 0.565
      ├── Some((2, 5)): 12/22 ≈ 0.545
      ├── Some((2, 6)): 7/16 ≈ 0.438
      ├── Some((2, 7)): 14/24 ≈ 0.583
      └── Some((2, 8)): 8/18 ≈ 0.444
    ├── Some((7, 3)): 69/140 ≈ 0.493
      ├── Some((3, 0)): 2/10 ≈ 0.200
      ├── Some((3, 1)): 17/26 ≈ 0.654
      ├── Some((3, 2)): 7/16 ≈ 0.438
      ├── Some((3, 3)): 6/15 ≈ 0.400
      ├── Some((3, 4)): 5/13 ≈ 0.385
      ├── Some((3, 5)): 6/15 ≈ 0.400
      ├── Some((3, 6)): 12/21 ≈ 0.571
      └── Some((3, 8)): 14/23 ≈ 0.609
    ├── Some((7, 4)): 69/140 ≈ 0.493
      ├── Some((4, 0)): 1/8 ≈ 0.125
      ├── Some((4, 1)): 7/15 ≈ 0.467
      ├── Some((4, 2)): 3/11 ≈ 0.273
      ├── Some((4, 3)): 20/28 ≈ 0.714
      ├── Some((4, 4)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 5/13 ≈ 0.385
      ├── Some((4, 6)): 7/15 ≈ 0.467
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 12/20 ≈ 0.600
    ├── Some((7, 5)): 69/140 ≈ 0.493
      ├── Some((5, 0)): 11/19 ≈ 0.579
      ├── Some((5, 1)): 8/16 ≈ 0.500
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 14/23 ≈ 0.609
      ├── Some((5, 4)): 15/24 ≈ 0.625
      ├── Some((5, 5)): 1/8 ≈ 0.125
      ├── Some((5, 6)): 10/18 ≈ 0.556
      ├── Some((5, 7)): 1/8 ≈ 0.125
      └── Some((5, 8)): 1/8 ≈ 0.125
    ├── Some((7, 6)): 89/170 ≈ 0.524
      ├── Some((6, 0)): 15/24 ≈ 0.625
      ├── Some((6, 1)): 7/16 ≈ 0.438
      ├── Some((6, 2)): 9/18 ≈ 0.500
      ├── Some((6, 3)): 23/33 ≈ 0.697
      ├── Some((6, 4)): 3/11 ≈ 0.273
      ├── Some((6, 5)): 15/24 ≈ 0.625
      ├── Some((6, 6)): 4/12 ≈ 0.333
      ├── Some((6, 7)): 7/16 ≈ 0.438
      └── Some((6, 8)): 6/15 ≈ 0.400
    ├── Some((7, 7)): 83/161 ≈ 0.516
      ├── Some((7, 0)): 8/18 ≈ 0.444
      ├── Some((7, 1)): 4/13 ≈ 0.308
      ├── Some((7, 2)): 7/16 ≈ 0.438
      ├── Some((7, 3)): 11/21 ≈ 0.524
      ├── Some((7, 4)): 9/19 ≈ 0.474
      ├── Some((7, 5)): 13/23 ≈ 0.565
      ├── Some((7, 6)): 16/26 ≈ 0.615
      └── Some((7, 8)): 14/24 ≈ 0.583
    └── Some((7, 8)): 76/150 ≈ 0.507
      ├── Some((8, 0)): 6/14 ≈ 0.429
      ├── Some((8, 1)): 7/15 ≈ 0.467
      ├── Some((8, 2)): 7/15 ≈ 0.467
      ├── Some((8, 3)): 6/14 ≈ 0.429
      ├── Some((8, 4)): 10/18 ≈ 0.556
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 7/15 ≈ 0.467
      ├── Some((8, 7)): 10/19 ≈ 0.526
      └── Some((8, 8)): 15/24 ≈ 0.625
  └── Some((3, 8)): 892/1725 ≈ 0.517
    ├── Some((8, 0)): 97/189 ≈ 0.513
      ├── Some((0, 0)): 8/18 ≈ 0.444
      ├── Some((0, 1)): 14/25 ≈ 0.560
      ├── Some((0, 2)): 13/23 ≈ 0.565
      ├── Some((0, 3)): 11/21 ≈ 0.524
      ├── Some((0, 4)): 12/22 ≈ 0.545
      ├── Some((0, 5)): 12/22 ≈ 0.545
      ├── Some((0, 6)): 10/20 ≈ 0.500
      ├── Some((0, 7)): 13/24 ≈ 0.542
      └── Some((0, 8)): 4/13 ≈ 0.308
    ├── Some((8, 1)): 88/175 ≈ 0.503
      ├── Some((1, 0)): 9/19 ≈ 0.474
      ├── Some((1, 1)): 10/20 ≈ 0.500
      ├── Some((1, 2)): 16/26 ≈ 0.615
      ├── Some((1, 3)): 6/15 ≈ 0.400
      ├── Some((1, 4)): 17/28 ≈ 0.607
      ├── Some((1, 5)): 4/13 ≈ 0.308
      ├── Some((1, 6)): 5/14 ≈ 0.357
      ├── Some((1, 7)): 18/29 ≈ 0.621
      └── Some((1, 8)): 2/10 ≈ 0.200
    ├── Some((8, 2)): 79/161 ≈ 0.491
      ├── Some((2, 0)): 10/20 ≈ 0.500
      ├── Some((2, 1)): 7/17 ≈ 0.412
      ├── Some((2, 2)): 7/17 ≈ 0.412
      ├── Some((2, 4)): 8/18 ≈ 0.444
      ├── Some((2, 5)): 14/25 ≈ 0.560
      ├── Some((2, 6)): 5/14 ≈ 0.357
      ├── Some((2, 7)): 11/22 ≈ 0.500
      └── Some((2, 8)): 16/27 ≈ 0.593
    ├── Some((8, 3)): 102/196 ≈ 0.520
      ├── Some((3, 0)): 14/26 ≈ 0.538
      ├── Some((3, 1)): 14/26 ≈ 0.538
      ├── Some((3, 2)): 15/28 ≈ 0.536
      ├── Some((3, 3)): 9/21 ≈ 0.429
      ├── Some((3, 4)): 5/16 ≈ 0.312
      ├── Some((3, 5)): 24/37 ≈ 0.649
      ├── Some((3, 6)): 20/33 ≈ 0.606
      └── Some((3, 7)): 0/8 ≈ 0.000
    ├── Some((8, 4)): 102/196 ≈ 0.520
      ├── Some((4, 0)): 3/12 ≈ 0.250
      ├── Some((4, 1)): 3/12 ≈ 0.250
      ├── Some((4, 2)): 11/21 ≈ 0.524
      ├── Some((4, 3)): 14/25 ≈ 0.560
      ├── Some((4, 4)): 12/23 ≈ 0.522
      ├── Some((4, 5)): 10/20 ≈ 0.500
      ├── Some((4, 6)): 17/28 ≈ 0.607
      ├── Some((4, 7)): 14/25 ≈ 0.560
      └── Some((4, 8)): 18/29 ≈ 0.621
    ├── Some((8, 5)): 125/230 ≈ 0.543
      ├── Some((5, 0)): 25/38 ≈ 0.658
      ├── Some((5, 1)): 7/18 ≈ 0.389
      ├── Some((5, 2)): 9/20 ≈ 0.450
      ├── Some((5, 3)): 19/31 ≈ 0.613
      ├── Some((5, 4)): 17/29 ≈ 0.586
      ├── Some((5, 5)): 14/26 ≈ 0.538
      ├── Some((5, 6)): 13/25 ≈ 0.520
      ├── Some((5, 7)): 1/10 ≈ 0.100
      └── Some((5, 8)): 20/32 ≈ 0.625
    ├── Some((8, 6)): 83/167 ≈ 0.497
      ├── Some((6, 0)): 8/17 ≈ 0.471
      ├── Some((6, 1)): 14/24 ≈ 0.583
      ├── Some((6, 2)): 2/10 ≈ 0.200
      ├── Some((6, 3)): 11/21 ≈ 0.524
      ├── Some((6, 4)): 10/20 ≈ 0.500
      ├── Some((6, 5)): 1/9 ≈ 0.111
      ├── Some((6, 6)): 17/27 ≈ 0.630
      ├── Some((6, 7)): 13/23 ≈ 0.565
      └── Some((6, 8)): 6/15 ≈ 0.400
    ├── Some((8, 7)): 96/187 ≈ 0.513
      ├── Some((7, 0)): 13/24 ≈ 0.542
      ├── Some((7, 1)): 13/24 ≈ 0.542
      ├── Some((7, 2)): 11/21 ≈ 0.524
      ├── Some((7, 3)): 13/24 ≈ 0.542
      ├── Some((7, 4)): 23/34 ≈ 0.676
      ├── Some((7, 5)): 8/18 ≈ 0.444
      ├── Some((7, 6)): 9/19 ≈ 0.474
      ├── Some((7, 7)): 4/13 ≈ 0.308
      └── Some((7, 8)): 1/9 ≈ 0.111
    └── Some((8, 8)): 120/223 ≈ 0.538
      ├── Some((8, 0)): 13/26 ≈ 0.500
      ├── Some((8, 1)): 17/31 ≈ 0.548
      ├── Some((8, 2)): 16/29 ≈ 0.552
      ├── Some((8, 3)): 6/17 ≈ 0.353
      ├── Some((8, 4)): 16/29 ≈ 0.552
      ├── Some((8, 5)): 10/22 ≈ 0.455
      ├── Some((8, 6)): 32/47 ≈ 0.681
      └── Some((8, 7)): 9/21 ≈ 0.429
├── Some((2, 4)): 12093/22677 ≈ 0.533
  ├── Some((4, 0)): 1313/2469 ≈ 0.532
    ├── Some((0, 0)): 134/257 ≈ 0.521
      ├── Some((0, 1)): 24/41 ≈ 0.585
      ├── Some((0, 2)): 12/26 ≈ 0.462
      ├── Some((0, 3)): 16/31 ≈ 0.516
      ├── Some((0, 4)): 25/42 ≈ 0.595
      ├── Some((0, 5)): 13/28 ≈ 0.464
      ├── Some((0, 6)): 16/31 ≈ 0.516
      ├── Some((0, 7)): 12/26 ≈ 0.462
      └── Some((0, 8)): 16/31 ≈ 0.516
    ├── Some((0, 1)): 133/256 ≈ 0.520
      ├── Some((1, 0)): 16/30 ≈ 0.533
      ├── Some((1, 1)): 15/29 ≈ 0.517
      ├── Some((1, 2)): 10/23 ≈ 0.435
      ├── Some((1, 3)): 28/44 ≈ 0.636
      ├── Some((1, 4)): 6/18 ≈ 0.333
      ├── Some((1, 5)): 7/19 ≈ 0.368
      ├── Some((1, 6)): 21/36 ≈ 0.583
      ├── Some((1, 7)): 12/25 ≈ 0.480
      └── Some((1, 8)): 17/31 ≈ 0.548
    ├── Some((0, 2)): 119/234 ≈ 0.509
      ├── Some((2, 0)): 17/32 ≈ 0.531
      ├── Some((2, 1)): 19/34 ≈ 0.559
      ├── Some((2, 2)): 8/21 ≈ 0.381
      ├── Some((2, 3)): 9/22 ≈ 0.409
      ├── Some((2, 5)): 22/38 ≈ 0.579
      ├── Some((2, 6)): 24/40 ≈ 0.600
      ├── Some((2, 7)): 10/24 ≈ 0.417
      └── Some((2, 8)): 9/22 ≈ 0.409
    ├── Some((0, 3)): 199/355 ≈ 0.561
      ├── Some((3, 0)): 17/33 ≈ 0.515
      ├── Some((3, 1)): 16/32 ≈ 0.500
      ├── Some((3, 2)): 18/35 ≈ 0.514
      ├── Some((3, 3)): 18/35 ≈ 0.514
      ├── Some((3, 4)): 27/45 ≈ 0.600
      ├── Some((3, 5)): 34/53 ≈ 0.642
      ├── Some((3, 6)): 19/36 ≈ 0.528
      ├── Some((3, 7)): 29/47 ≈ 0.617
      └── Some((3, 8)): 21/38 ≈ 0.553
    ├── Some((0, 4)): 261/446 ≈ 0.585
      ├── Some((4, 1)): 58/85 ≈ 0.682
      ├── Some((4, 2)): 20/41 ≈ 0.488
      ├── Some((4, 3)): 21/42 ≈ 0.500
      ├── Some((4, 4)): 24/46 ≈ 0.522
      ├── Some((4, 5)): 37/61 ≈ 0.607
      ├── Some((4, 6)): 20/41 ≈ 0.488
      ├── Some((4, 7)): 54/81 ≈ 0.667
      └── Some((4, 8)): 26/48 ≈ 0.542
    ├── Some((0, 5)): 86/182 ≈ 0.473
      ├── Some((5, 0)): 12/23 ≈ 0.522
      ├── Some((5, 1)): 8/18 ≈ 0.444
      ├── Some((5, 2)): 10/21 ≈ 0.476
      ├── Some((5, 3)): 7/17 ≈ 0.412
      ├── Some((5, 4)): 8/18 ≈ 0.444
      ├── Some((5, 5)): 10/21 ≈ 0.476
      ├── Some((5, 6)): 8/19 ≈ 0.421
      ├── Some((5, 7)): 9/20 ≈ 0.450
      └── Some((5, 8)): 13/24 ≈ 0.542
    ├── Some((0, 6)): 111/222 ≈ 0.500
      ├── Some((6, 0)): 22/36 ≈ 0.611
      ├── Some((6, 1)): 23/37 ≈ 0.622
      ├── Some((6, 2)): 20/34 ≈ 0.588
      ├── Some((6, 3)): 6/17 ≈ 0.353
      ├── Some((6, 4)): 10/22 ≈ 0.455
      ├── Some((6, 5)): 1/11 ≈ 0.091
      ├── Some((6, 6)): 13/26 ≈ 0.500
      ├── Some((6, 7)): 12/25 ≈ 0.480
      └── Some((6, 8)): 3/13 ≈ 0.231
    ├── Some((0, 7)): 133/256 ≈ 0.520
      ├── Some((7, 0)): 6/18 ≈ 0.333
      ├── Some((7, 1)): 20/35 ≈ 0.571
      ├── Some((7, 2)): 7/19 ≈ 0.368
      ├── Some((7, 3)): 17/31 ≈ 0.548
      ├── Some((7, 4)): 34/50 ≈ 0.680
      ├── Some((7, 5)): 11/24 ≈ 0.458
      ├── Some((7, 6)): 15/29 ≈ 0.517
      ├── Some((7, 7)): 12/26 ≈ 0.462
      └── Some((7, 8)): 10/23 ≈ 0.435
    └── Some((0, 8)): 136/260 ≈ 0.523
      ├── Some((8, 0)): 9/22 ≈ 0.409
      ├── Some((8, 1)): 15/29 ≈ 0.517
      ├── Some((8, 2)): 28/43 ≈ 0.651
      ├── Some((8, 3)): 10/23 ≈ 0.435
      ├── Some((8, 4)): 11/24 ≈ 0.458
      ├── Some((8, 5)): 18/32 ≈ 0.562
      ├── Some((8, 6)): 14/28 ≈ 0.500
      ├── Some((8, 7)): 9/22 ≈ 0.409
      └── Some((8, 8)): 21/36 ≈ 0.583
  ├── Some((4, 1)): 1546/2869 ≈ 0.539
    ├── Some((1, 0)): 117/235 ≈ 0.498
      ├── Some((0, 0)): 21/35 ≈ 0.600
      ├── Some((0, 1)): 13/26 ≈ 0.500
      ├── Some((0, 2)): 6/18 ≈ 0.333
      ├── Some((0, 3)): 18/32 ≈ 0.562
      ├── Some((0, 4)): 8/20 ≈ 0.400
      ├── Some((0, 5)): 13/26 ≈ 0.500
      ├── Some((0, 6)): 15/28 ≈ 0.536
      ├── Some((0, 7)): 13/26 ≈ 0.500
      └── Some((0, 8)): 10/23 ≈ 0.435
    ├── Some((1, 1)): 234/413 ≈ 0.567
      ├── Some((1, 0)): 13/32 ≈ 0.406
      ├── Some((1, 2)): 37/61 ≈ 0.607
      ├── Some((1, 3)): 28/51 ≈ 0.549
      ├── Some((1, 4)): 31/54 ≈ 0.574
      ├── Some((1, 5)): 30/53 ≈ 0.566
      ├── Some((1, 6)): 12/30 ≈ 0.400
      ├── Some((1, 7)): 55/82 ≈ 0.671
      └── Some((1, 8)): 27/49 ≈ 0.551
    ├── Some((1, 2)): 197/358 ≈ 0.550
      ├── Some((2, 0)): 17/35 ≈ 0.486
      ├── Some((2, 1)): 31/53 ≈ 0.585
      ├── Some((2, 2)): 25/45 ≈ 0.556
      ├── Some((2, 3)): 19/38 ≈ 0.500
      ├── Some((2, 5)): 25/45 ≈ 0.556
      ├── Some((2, 6)): 25/45 ≈ 0.556
      ├── Some((2, 7)): 27/48 ≈ 0.562
      └── Some((2, 8)): 27/48 ≈ 0.562
    ├── Some((1, 3)): 167/312 ≈ 0.535
      ├── Some((3, 0)): 12/27 ≈ 0.444
      ├── Some((3, 1)): 13/28 ≈ 0.464
      ├── Some((3, 2)): 12/27 ≈ 0.444
      ├── Some((3, 3)): 24/41 ≈ 0.585
      ├── Some((3, 4)): 16/32 ≈ 0.500
      ├── Some((3, 5)): 21/38 ≈ 0.553
      ├── Some((3, 6)): 33/51 ≈ 0.647
      ├── Some((3, 7)): 28/46 ≈ 0.609
      └── Some((3, 8)): 7/21 ≈ 0.333
    ├── Some((1, 4)): 119/238 ≈ 0.500
      ├── Some((4, 0)): 11/25 ≈ 0.440
      ├── Some((4, 2)): 7/20 ≈ 0.350
      ├── Some((4, 3)): 18/34 ≈ 0.529
      ├── Some((4, 4)): 22/39 ≈ 0.564
      ├── Some((4, 5)): 14/29 ≈ 0.483
      ├── Some((4, 6)): 27/44 ≈ 0.614
      ├── Some((4, 7)): 5/17 ≈ 0.294
      └── Some((4, 8)): 14/29 ≈ 0.483
    ├── Some((1, 5)): 139/269 ≈ 0.517
      ├── Some((5, 0)): 24/40 ≈ 0.600
      ├── Some((5, 1)): 11/25 ≈ 0.440
      ├── Some((5, 2)): 14/28 ≈ 0.500
      ├── Some((5, 3)): 14/28 ≈ 0.500
      ├── Some((5, 4)): 8/21 ≈ 0.381
      ├── Some((5, 5)): 21/36 ≈ 0.583
      ├── Some((5, 6)): 24/40 ≈ 0.600
      ├── Some((5, 7)): 14/28 ≈ 0.500
      └── Some((5, 8)): 9/22 ≈ 0.409
    ├── Some((1, 6)): 174/323 ≈ 0.539
      ├── Some((6, 0)): 9/23 ≈ 0.391
      ├── Some((6, 1)): 9/23 ≈ 0.391
      ├── Some((6, 2)): 30/49 ≈ 0.612
      ├── Some((6, 3)): 16/32 ≈ 0.500
      ├── Some((6, 4)): 21/38 ≈ 0.553
      ├── Some((6, 5)): 21/38 ≈ 0.553
      ├── Some((6, 6)): 31/50 ≈ 0.620
      ├── Some((6, 7)): 17/33 ≈ 0.515
      └── Some((6, 8)): 19/36 ≈ 0.528
    ├── Some((1, 7)): 152/289 ≈ 0.526
      ├── Some((7, 0)): 16/31 ≈ 0.516
      ├── Some((7, 1)): 17/33 ≈ 0.515
      ├── Some((7, 2)): 20/36 ≈ 0.556
      ├── Some((7, 3)): 18/34 ≈ 0.529
      ├── Some((7, 4)): 36/54 ≈ 0.667
      ├── Some((7, 5)): 15/30 ≈ 0.500
      ├── Some((7, 6)): 3/15 ≈ 0.200
      ├── Some((7, 7)): 5/17 ≈ 0.294
      └── Some((7, 8)): 22/38 ≈ 0.579
    └── Some((1, 8)): 246/431 ≈ 0.571
      ├── Some((8, 0)): 18/36 ≈ 0.500
      ├── Some((8, 1)): 21/40 ≈ 0.525
      ├── Some((8, 2)): 34/56 ≈ 0.607
      ├── Some((8, 3)): 43/66 ≈ 0.652
      ├── Some((8, 4)): 28/49 ≈ 0.571
      ├── Some((8, 5)): 18/37 ≈ 0.486
      ├── Some((8, 6)): 18/37 ≈ 0.486
      ├── Some((8, 7)): 38/60 ≈ 0.633
      └── Some((8, 8)): 28/49 ≈ 0.571
  ├── Some((4, 2)): 1285/2421 ≈ 0.531
    ├── Some((2, 0)): 117/235 ≈ 0.498
      ├── Some((0, 0)): 3/14 ≈ 0.214
      ├── Some((0, 1)): 12/25 ≈ 0.480
      ├── Some((0, 2)): 11/24 ≈ 0.458
      ├── Some((0, 3)): 21/36 ≈ 0.583
      ├── Some((0, 4)): 10/23 ≈ 0.435
      ├── Some((0, 5)): 15/29 ≈ 0.517
      ├── Some((0, 6)): 6/18 ≈ 0.333
      ├── Some((0, 7)): 31/46 ≈ 0.674
      └── Some((0, 8)): 7/19 ≈ 0.368
    ├── Some((2, 1)): 159/301 ≈ 0.528
      ├── Some((1, 0)): 13/28 ≈ 0.464
      ├── Some((1, 1)): 28/46 ≈ 0.609
      ├── Some((1, 2)): 13/28 ≈ 0.464
      ├── Some((1, 3)): 18/34 ≈ 0.529
      ├── Some((1, 4)): 32/50 ≈ 0.640
      ├── Some((1, 5)): 10/24 ≈ 0.417
      ├── Some((1, 6)): 13/28 ≈ 0.464
      ├── Some((1, 7)): 12/27 ≈ 0.444
      └── Some((1, 8)): 19/35 ≈ 0.543
    ├── Some((2, 2)): 197/358 ≈ 0.550
      ├── Some((2, 0)): 21/42 ≈ 0.500
      ├── Some((2, 1)): 25/47 ≈ 0.532
      ├── Some((2, 3)): 30/54 ≈ 0.556
      ├── Some((2, 5)): 28/51 ≈ 0.549
      ├── Some((2, 6)): 28/51 ≈ 0.549
      ├── Some((2, 7)): 30/54 ≈ 0.556
      └── Some((2, 8)): 34/58 ≈ 0.586
    ├── Some((2, 3)): 160/302 ≈ 0.530
      ├── Some((3, 0)): 21/38 ≈ 0.553
      ├── Some((3, 1)): 22/39 ≈ 0.564
      ├── Some((3, 2)): 27/44 ≈ 0.614
      ├── Some((3, 3)): 18/34 ≈ 0.529
      ├── Some((3, 4)): 15/30 ≈ 0.500
      ├── Some((3, 5)): 16/32 ≈ 0.500
      ├── Some((3, 6)): 25/42 ≈ 0.595
      ├── Some((3, 7)): 4/16 ≈ 0.250
      └── Some((3, 8)): 11/26 ≈ 0.423
    ├── Some((2, 5)): 173/322 ≈ 0.537
      ├── Some((5, 0)): 14/30 ≈ 0.467
      ├── Some((5, 1)): 13/28 ≈ 0.464
      ├── Some((5, 2)): 20/37 ≈ 0.541
      ├── Some((5, 3)): 19/36 ≈ 0.528
      ├── Some((5, 4)): 18/34 ≈ 0.529
      ├── Some((5, 5)): 36/55 ≈ 0.655
      ├── Some((5, 6)): 18/34 ≈ 0.529
      ├── Some((5, 7)): 23/40 ≈ 0.575
      └── Some((5, 8)): 12/27 ≈ 0.444
    ├── Some((2, 6)): 226/402 ≈ 0.562
      ├── Some((6, 0)): 29/49 ≈ 0.592
      ├── Some((6, 1)): 34/55 ≈ 0.618
      ├── Some((6, 2)): 33/54 ≈ 0.611
      ├── Some((6, 3)): 16/34 ≈ 0.471
      ├── Some((6, 4)): 12/29 ≈ 0.414
      ├── Some((6, 5)): 12/29 ≈ 0.414
      ├── Some((6, 6)): 30/51 ≈ 0.588
      ├── Some((6, 7)): 25/45 ≈ 0.556
      └── Some((6, 8)): 34/55 ≈ 0.618
    ├── Some((2, 7)): 114/230 ≈ 0.496
      ├── Some((7, 0)): 10/22 ≈ 0.455
      ├── Some((7, 1)): 17/31 ≈ 0.548
      ├── Some((7, 2)): 15/28 ≈ 0.536
      ├── Some((7, 3)): 9/21 ≈ 0.429
      ├── Some((7, 4)): 17/31 ≈ 0.548
      ├── Some((7, 5)): 5/16 ≈ 0.312
      ├── Some((7, 6)): 15/28 ≈ 0.536
      ├── Some((7, 7)): 7/19 ≈ 0.368
      └── Some((7, 8)): 19/33 ≈ 0.576
    └── Some((2, 8)): 139/270 ≈ 0.515
      ├── Some((8, 0)): 10/23 ≈ 0.435
      ├── Some((8, 1)): 15/30 ≈ 0.500
      ├── Some((8, 2)): 17/32 ≈ 0.531
      ├── Some((8, 3)): 20/35 ≈ 0.571
      ├── Some((8, 4)): 25/41 ≈ 0.610
      ├── Some((8, 5)): 23/39 ≈ 0.590
      ├── Some((8, 6)): 15/30 ≈ 0.500
      ├── Some((8, 7)): 10/23 ≈ 0.435
      └── Some((8, 8)): 4/16 ≈ 0.250
  ├── Some((4, 3)): 1320/2481 ≈ 0.532
    ├── Some((3, 0)): 165/304 ≈ 0.543
      ├── Some((0, 0)): 19/35 ≈ 0.543
      ├── Some((0, 1)): 10/24 ≈ 0.417
      ├── Some((0, 2)): 16/31 ≈ 0.516
      ├── Some((0, 3)): 19/35 ≈ 0.543
      ├── Some((0, 4)): 23/39 ≈ 0.590
      ├── Some((0, 5)): 13/27 ≈ 0.481
      ├── Some((0, 6)): 6/19 ≈ 0.316
      ├── Some((0, 7)): 31/48 ≈ 0.646
      └── Some((0, 8)): 28/45 ≈ 0.622
    ├── Some((3, 1)): 135/258 ≈ 0.523
      ├── Some((1, 0)): 15/29 ≈ 0.517
      ├── Some((1, 1)): 20/35 ≈ 0.571
      ├── Some((1, 2)): 7/19 ≈ 0.368
      ├── Some((1, 3)): 23/38 ≈ 0.605
      ├── Some((1, 4)): 5/17 ≈ 0.294
      ├── Some((1, 5)): 11/24 ≈ 0.458
      ├── Some((1, 6)): 12/25 ≈ 0.480
      ├── Some((1, 7)): 30/45 ≈ 0.667
      └── Some((1, 8)): 12/25 ≈ 0.480
    ├── Some((3, 2)): 178/323 ≈ 0.551
      ├── Some((2, 0)): 16/33 ≈ 0.485
      ├── Some((2, 1)): 20/38 ≈ 0.526
      ├── Some((2, 2)): 15/32 ≈ 0.469
      ├── Some((2, 3)): 46/68 ≈ 0.676
      ├── Some((2, 5)): 27/46 ≈ 0.587
      ├── Some((2, 6)): 9/24 ≈ 0.375
      ├── Some((2, 7)): 23/42 ≈ 0.548
      └── Some((2, 8)): 21/39 ≈ 0.538
    ├── Some((3, 3)): 93/193 ≈ 0.482
      ├── Some((3, 0)): 11/23 ≈ 0.478
      ├── Some((3, 1)): 4/15 ≈ 0.267
      ├── Some((3, 2)): 16/29 ≈ 0.552
      ├── Some((3, 4)): 13/26 ≈ 0.500
      ├── Some((3, 5)): 8/20 ≈ 0.400
      ├── Some((3, 6)): 18/32 ≈ 0.562
      ├── Some((3, 7)): 12/25 ≈ 0.480
      └── Some((3, 8)): 10/22 ≈ 0.455
    ├── Some((3, 4)): 140/266 ≈ 0.526
      ├── Some((4, 0)): 16/31 ≈ 0.516
      ├── Some((4, 1)): 19/35 ≈ 0.543
      ├── Some((4, 2)): 23/40 ≈ 0.575
      ├── Some((4, 4)): 13/28 ≈ 0.464
      ├── Some((4, 5)): 25/42 ≈ 0.595
      ├── Some((4, 6)): 7/20 ≈ 0.350
      ├── Some((4, 7)): 18/34 ≈ 0.529
      └── Some((4, 8)): 19/35 ≈ 0.543
    ├── Some((3, 5)): 150/281 ≈ 0.534
      ├── Some((5, 0)): 6/18 ≈ 0.333
      ├── Some((5, 1)): 12/26 ≈ 0.462
      ├── Some((5, 2)): 20/35 ≈ 0.571
      ├── Some((5, 3)): 13/27 ≈ 0.481
      ├── Some((5, 4)): 8/21 ≈ 0.381
      ├── Some((5, 5)): 27/43 ≈ 0.628
      ├── Some((5, 6)): 17/32 ≈ 0.531
      ├── Some((5, 7)): 19/34 ≈ 0.559
      └── Some((5, 8)): 28/44 ≈ 0.636
    ├── Some((3, 6)): 158/293 ≈ 0.539
      ├── Some((6, 0)): 21/37 ≈ 0.568
      ├── Some((6, 1)): 20/36 ≈ 0.556
      ├── Some((6, 2)): 12/26 ≈ 0.462
      ├── Some((6, 3)): 21/37 ≈ 0.568
      ├── Some((6, 4)): 14/28 ≈ 0.500
      ├── Some((6, 5)): 26/42 ≈ 0.619
      ├── Some((6, 6)): 9/22 ≈ 0.409
      ├── Some((6, 7)): 9/22 ≈ 0.409
      └── Some((6, 8)): 26/42 ≈ 0.619
    ├── Some((3, 7)): 115/228 ≈ 0.504
      ├── Some((7, 0)): 10/22 ≈ 0.455
      ├── Some((7, 1)): 6/17 ≈ 0.353
      ├── Some((7, 2)): 22/36 ≈ 0.611
      ├── Some((7, 3)): 26/41 ≈ 0.634
      ├── Some((7, 4)): 13/26 ≈ 0.500
      ├── Some((7, 5)): 6/17 ≈ 0.353
      ├── Some((7, 6)): 6/17 ≈ 0.353
      ├── Some((7, 7)): 16/30 ≈ 0.533
      └── Some((7, 8)): 9/21 ≈ 0.429
    └── Some((3, 8)): 185/334 ≈ 0.554
      ├── Some((8, 0)): 15/31 ≈ 0.484
      ├── Some((8, 1)): 30/48 ≈ 0.625
      ├── Some((8, 2)): 19/35 ≈ 0.543
      ├── Some((8, 3)): 32/50 ≈ 0.640
      ├── Some((8, 4)): 10/25 ≈ 0.400
      ├── Some((8, 5)): 24/41 ≈ 0.585
      ├── Some((8, 6)): 19/36 ≈ 0.528
      ├── Some((8, 7)): 12/27 ≈ 0.444
      └── Some((8, 8)): 23/40 ≈ 0.575
  ├── Some((4, 4)): 1055/2022 ≈ 0.522
    ├── Some((4, 0)): 100/204 ≈ 0.490
      ├── Some((0, 0)): 9/20 ≈ 0.450
      ├── Some((0, 1)): 14/26 ≈ 0.538
      ├── Some((0, 2)): 10/21 ≈ 0.476
      ├── Some((0, 3)): 14/26 ≈ 0.538
      ├── Some((0, 4)): 11/23 ≈ 0.478
      ├── Some((0, 5)): 14/26 ≈ 0.538
      ├── Some((0, 6)): 6/17 ≈ 0.353
      ├── Some((0, 7)): 8/19 ≈ 0.421
      └── Some((0, 8)): 13/25 ≈ 0.520
    ├── Some((4, 1)): 133/256 ≈ 0.520
      ├── Some((1, 0)): 14/28 ≈ 0.500
      ├── Some((1, 1)): 22/37 ≈ 0.595
      ├── Some((1, 2)): 13/27 ≈ 0.481
      ├── Some((1, 3)): 1/11 ≈ 0.091
      ├── Some((1, 4)): 11/24 ≈ 0.458
      ├── Some((1, 5)): 16/30 ≈ 0.533
      ├── Some((1, 6)): 7/19 ≈ 0.368
      ├── Some((1, 7)): 21/36 ≈ 0.583
      └── Some((1, 8)): 28/43 ≈ 0.651
    ├── Some((4, 2)): 215/379 ≈ 0.567
      ├── Some((2, 0)): 39/62 ≈ 0.629
      ├── Some((2, 1)): 26/46 ≈ 0.565
      ├── Some((2, 2)): 24/44 ≈ 0.545
      ├── Some((2, 3)): 23/43 ≈ 0.535
      ├── Some((2, 5)): 19/38 ≈ 0.500
      ├── Some((2, 6)): 34/56 ≈ 0.607
      ├── Some((2, 7)): 21/40 ≈ 0.525
      └── Some((2, 8)): 28/49 ≈ 0.571
    ├── Some((4, 3)): 149/280 ≈ 0.532
      ├── Some((3, 0)): 13/27 ≈ 0.481
      ├── Some((3, 1)): 23/39 ≈ 0.590
      ├── Some((3, 2)): 8/21 ≈ 0.381
      ├── Some((3, 3)): 8/21 ≈ 0.381
      ├── Some((3, 4)): 15/29 ≈ 0.517
      ├── Some((3, 5)): 16/31 ≈ 0.516
      ├── Some((3, 6)): 15/29 ≈ 0.517
      ├── Some((3, 7)): 17/32 ≈ 0.531
      └── Some((3, 8)): 33/50 ≈ 0.660
    ├── Some((4, 5)): 127/246 ≈ 0.516
      ├── Some((5, 0)): 27/42 ≈ 0.643
      ├── Some((5, 1)): 14/27 ≈ 0.519
      ├── Some((5, 2)): 18/32 ≈ 0.562
      ├── Some((5, 3)): 18/32 ≈ 0.562
      ├── Some((5, 4)): 13/26 ≈ 0.500
      ├── Some((5, 5)): 11/24 ≈ 0.458
      ├── Some((5, 6)): 16/30 ≈ 0.533
      ├── Some((5, 7)): 3/14 ≈ 0.214
      └── Some((5, 8)): 6/18 ≈ 0.333
    ├── Some((4, 6)): 61/142 ≈ 0.430
      ├── Some((6, 0)): 13/23 ≈ 0.565
      ├── Some((6, 1)): 4/13 ≈ 0.308
      ├── Some((6, 2)): 8/17 ≈ 0.471
      ├── Some((6, 3)): 4/13 ≈ 0.308
      ├── Some((6, 4)): 14/24 ≈ 0.583
      ├── Some((6, 5)): 3/11 ≈ 0.273
      ├── Some((6, 6)): 7/16 ≈ 0.438
      ├── Some((6, 7)): 2/10 ≈ 0.200
      └── Some((6, 8)): 5/14 ≈ 0.357
    ├── Some((4, 7)): 83/177 ≈ 0.469
      ├── Some((7, 0)): 4/13 ≈ 0.308
      ├── Some((7, 1)): 6/16 ≈ 0.375
      ├── Some((7, 2)): 3/12 ≈ 0.250
      ├── Some((7, 3)): 4/14 ≈ 0.286
      ├── Some((7, 4)): 9/20 ≈ 0.450
      ├── Some((7, 5)): 8/18 ≈ 0.444
      ├── Some((7, 6)): 19/31 ≈ 0.613
      ├── Some((7, 7)): 19/31 ≈ 0.613
      └── Some((7, 8)): 10/21 ≈ 0.476
    └── Some((4, 8)): 187/337 ≈ 0.555
      ├── Some((8, 0)): 22/39 ≈ 0.564
      ├── Some((8, 1)): 12/27 ≈ 0.444
      ├── Some((8, 2)): 8/22 ≈ 0.364
      ├── Some((8, 3)): 18/35 ≈ 0.514
      ├── Some((8, 4)): 23/40 ≈ 0.575
      ├── Some((8, 5)): 13/28 ≈ 0.464
      ├── Some((8, 6)): 24/42 ≈ 0.571
      ├── Some((8, 7)): 31/49 ≈ 0.633
      └── Some((8, 8)): 35/54 ≈ 0.648
  ├── Some((4, 5)): 2113/3836 ≈ 0.551
    ├── Some((5, 0)): 209/387 ≈ 0.540
      ├── Some((0, 0)): 20/39 ≈ 0.513
      ├── Some((0, 1)): 20/39 ≈ 0.513
      ├── Some((0, 2)): 24/44 ≈ 0.545
      ├── Some((0, 3)): 17/35 ≈ 0.486
      ├── Some((0, 4)): 18/37 ≈ 0.486
      ├── Some((0, 5)): 35/57 ≈ 0.614
      ├── Some((0, 6)): 15/33 ≈ 0.455
      ├── Some((0, 7)): 29/50 ≈ 0.580
      └── Some((0, 8)): 31/52 ≈ 0.596
    ├── Some((5, 1)): 278/492 ≈ 0.565
      ├── Some((1, 0)): 21/43 ≈ 0.488
      ├── Some((1, 1)): 30/54 ≈ 0.556
      ├── Some((1, 2)): 53/81 ≈ 0.654
      ├── Some((1, 3)): 47/74 ≈ 0.635
      ├── Some((1, 4)): 22/44 ≈ 0.500
      ├── Some((1, 5)): 32/56 ≈ 0.571
      ├── Some((1, 6)): 27/50 ≈ 0.540
      ├── Some((1, 7)): 19/40 ≈ 0.475
      └── Some((1, 8)): 26/49 ≈ 0.531
    ├── Some((5, 2)): 303/530 ≈ 0.572
      ├── Some((2, 0)): 55/87 ≈ 0.632
      ├── Some((2, 1)): 30/57 ≈ 0.526
      ├── Some((2, 2)): 50/81 ≈ 0.617
      ├── Some((2, 3)): 12/33 ≈ 0.364
      ├── Some((2, 5)): 39/68 ≈ 0.574
      ├── Some((2, 6)): 25/50 ≈ 0.500
      ├── Some((2, 7)): 33/61 ≈ 0.541
      └── Some((2, 8)): 59/92 ≈ 0.641
    ├── Some((5, 3)): 205/381 ≈ 0.538
      ├── Some((3, 0)): 4/18 ≈ 0.222
      ├── Some((3, 1)): 25/45 ≈ 0.556
      ├── Some((3, 2)): 37/60 ≈ 0.617
      ├── Some((3, 3)): 19/38 ≈ 0.500
      ├── Some((3, 4)): 24/44 ≈ 0.545
      ├── Some((3, 5)): 29/50 ≈ 0.580
      ├── Some((3, 6)): 17/36 ≈ 0.472
      ├── Some((3, 7)): 15/33 ≈ 0.455
      └── Some((3, 8)): 34/56 ≈ 0.607
    ├── Some((5, 4)): 253/454 ≈ 0.557
      ├── Some((4, 0)): 17/39 ≈ 0.436
      ├── Some((4, 1)): 38/65 ≈ 0.585
      ├── Some((4, 2)): 41/69 ≈ 0.594
      ├── Some((4, 3)): 30/55 ≈ 0.545
      ├── Some((4, 4)): 0/13 ≈ 0.000
      ├── Some((4, 6)): 32/58 ≈ 0.552
      ├── Some((4, 7)): 56/87 ≈ 0.644
      └── Some((4, 8)): 39/67 ≈ 0.582
    ├── Some((5, 5)): 222/407 ≈ 0.545
      ├── Some((5, 0)): 26/49 ≈ 0.531
      ├── Some((5, 1)): 32/56 ≈ 0.571
      ├── Some((5, 2)): 9/26 ≈ 0.346
      ├── Some((5, 3)): 27/50 ≈ 0.540
      ├── Some((5, 4)): 30/54 ≈ 0.556
      ├── Some((5, 6)): 46/73 ≈ 0.630
      ├── Some((5, 7)): 18/39 ≈ 0.462
      └── Some((5, 8)): 34/59 ≈ 0.576
    ├── Some((5, 6)): 180/342 ≈ 0.526
      ├── Some((6, 0)): 28/48 ≈ 0.583
      ├── Some((6, 1)): 26/45 ≈ 0.578
      ├── Some((6, 2)): 13/30 ≈ 0.433
      ├── Some((6, 3)): 11/27 ≈ 0.407
      ├── Some((6, 4)): 16/33 ≈ 0.485
      ├── Some((6, 5)): 29/49 ≈ 0.592
      ├── Some((6, 6)): 12/28 ≈ 0.429
      ├── Some((6, 7)): 16/33 ≈ 0.485
      └── Some((6, 8)): 28/48 ≈ 0.583
    ├── Some((5, 7)): 178/339 ≈ 0.525
      ├── Some((7, 0)): 14/31 ≈ 0.452
      ├── Some((7, 1)): 15/32 ≈ 0.469
      ├── Some((7, 2)): 23/42 ≈ 0.548
      ├── Some((7, 3)): 33/53 ≈ 0.623
      ├── Some((7, 4)): 30/50 ≈ 0.600
      ├── Some((7, 5)): 6/20 ≈ 0.300
      ├── Some((7, 6)): 17/35 ≈ 0.486
      ├── Some((7, 7)): 27/47 ≈ 0.574
      └── Some((7, 8)): 12/28 ≈ 0.429
    └── Some((5, 8)): 285/503 ≈ 0.567
      ├── Some((8, 0)): 35/60 ≈ 0.583
      ├── Some((8, 1)): 16/36 ≈ 0.444
      ├── Some((8, 2)): 22/44 ≈ 0.500
      ├── Some((8, 3)): 36/61 ≈ 0.590
      ├── Some((8, 4)): 36/61 ≈ 0.590
      ├── Some((8, 5)): 28/52 ≈ 0.538
      ├── Some((8, 6)): 40/66 ≈ 0.606
      ├── Some((8, 7)): 31/55 ≈ 0.564
      └── Some((8, 8)): 41/67 ≈ 0.612
  ├── Some((4, 6)): 1285/2421 ≈ 0.531
    ├── Some((6, 0)): 119/233 ≈ 0.511
      ├── Some((0, 0)): 10/22 ≈ 0.455
      ├── Some((0, 1)): 15/28 ≈ 0.536
      ├── Some((0, 2)): 10/22 ≈ 0.455
      ├── Some((0, 3)): 9/21 ≈ 0.429
      ├── Some((0, 4)): 23/37 ≈ 0.622
      ├── Some((0, 5)): 9/21 ≈ 0.429
      ├── Some((0, 6)): 17/30 ≈ 0.567
      ├── Some((0, 7)): 17/30 ≈ 0.567
      └── Some((0, 8)): 9/21 ≈ 0.429
    ├── Some((6, 1)): 82/175 ≈ 0.469
      ├── Some((1, 0)): 11/22 ≈ 0.500
      ├── Some((1, 1)): 9/19 ≈ 0.474
      ├── Some((1, 2)): 2/11 ≈ 0.182
      ├── Some((1, 3)): 3/12 ≈ 0.250
      ├── Some((1, 4)): 12/23 ≈ 0.522
      ├── Some((1, 5)): 7/17 ≈ 0.412
      ├── Some((1, 6)): 18/29 ≈ 0.621
      ├── Some((1, 7)): 12/23 ≈ 0.522
      └── Some((1, 8)): 8/18 ≈ 0.444
    ├── Some((6, 2)): 175/319 ≈ 0.549
      ├── Some((2, 0)): 31/51 ≈ 0.608
      ├── Some((2, 1)): 18/35 ≈ 0.514
      ├── Some((2, 2)): 15/32 ≈ 0.469
      ├── Some((2, 3)): 28/47 ≈ 0.596
      ├── Some((2, 5)): 17/34 ≈ 0.500
      ├── Some((2, 6)): 20/38 ≈ 0.526
      ├── Some((2, 7)): 23/41 ≈ 0.561
      └── Some((2, 8)): 22/40 ≈ 0.550
    ├── Some((6, 3)): 208/368 ≈ 0.565
      ├── Some((3, 0)): 20/37 ≈ 0.541
      ├── Some((3, 1)): 38/58 ≈ 0.655
      ├── Some((3, 2)): 22/40 ≈ 0.550
      ├── Some((3, 3)): 27/45 ≈ 0.600
      ├── Some((3, 4)): 19/36 ≈ 0.528
      ├── Some((3, 5)): 15/31 ≈ 0.484
      ├── Some((3, 6)): 17/34 ≈ 0.500
      ├── Some((3, 7)): 22/40 ≈ 0.550
      └── Some((3, 8)): 27/46 ≈ 0.587
    ├── Some((6, 4)): 210/371 ≈ 0.566
      ├── Some((4, 0)): 20/39 ≈ 0.513
      ├── Some((4, 1)): 31/52 ≈ 0.596
      ├── Some((4, 2)): 22/41 ≈ 0.537
      ├── Some((4, 3)): 20/39 ≈ 0.513
      ├── Some((4, 4)): 33/54 ≈ 0.611
      ├── Some((4, 5)): 24/44 ≈ 0.545
      ├── Some((4, 7)): 28/49 ≈ 0.571
      └── Some((4, 8)): 31/52 ≈ 0.596
    ├── Some((6, 5)): 146/275 ≈ 0.531
      ├── Some((5, 0)): 16/30 ≈ 0.533
      ├── Some((5, 1)): 20/35 ≈ 0.571
      ├── Some((5, 2)): 16/31 ≈ 0.516
      ├── Some((5, 3)): 10/23 ≈ 0.435
      ├── Some((5, 4)): 22/37 ≈ 0.595
      ├── Some((5, 5)): 27/43 ≈ 0.628
      ├── Some((5, 6)): 5/17 ≈ 0.294
      ├── Some((5, 7)): 4/16 ≈ 0.250
      └── Some((5, 8)): 26/42 ≈ 0.619
    ├── Some((6, 6)): 143/270 ≈ 0.530
      ├── Some((6, 0)): 12/27 ≈ 0.444
      ├── Some((6, 1)): 28/46 ≈ 0.609
      ├── Some((6, 2)): 22/39 ≈ 0.564
      ├── Some((6, 3)): 26/44 ≈ 0.591
      ├── Some((6, 4)): 7/20 ≈ 0.350
      ├── Some((6, 5)): 24/41 ≈ 0.585
      ├── Some((6, 7)): 10/24 ≈ 0.417
      └── Some((6, 8)): 13/28 ≈ 0.464
    ├── Some((6, 7)): 86/182 ≈ 0.473
      ├── Some((7, 0)): 13/24 ≈ 0.542
      ├── Some((7, 1)): 15/26 ≈ 0.577
      ├── Some((7, 2)): 9/20 ≈ 0.450
      ├── Some((7, 3)): 5/15 ≈ 0.333
      ├── Some((7, 4)): 1/10 ≈ 0.100
      ├── Some((7, 5)): 7/17 ≈ 0.412
      ├── Some((7, 6)): 13/24 ≈ 0.542
      ├── Some((7, 7)): 12/23 ≈ 0.522
      └── Some((7, 8)): 11/22 ≈ 0.500
    └── Some((6, 8)): 115/227 ≈ 0.507
      ├── Some((8, 0)): 12/24 ≈ 0.500
      ├── Some((8, 1)): 16/29 ≈ 0.552
      ├── Some((8, 2)): 8/20 ≈ 0.400
      ├── Some((8, 3)): 23/37 ≈ 0.622
      ├── Some((8, 4)): 11/23 ≈ 0.478
      ├── Some((8, 5)): 11/23 ≈ 0.478
      ├── Some((8, 6)): 7/18 ≈ 0.389
      ├── Some((8, 7)): 9/21 ≈ 0.429
      └── Some((8, 8)): 18/31 ≈ 0.581
  ├── Some((4, 7)): 1127/2147 ≈ 0.525
    ├── Some((7, 0)): 134/253 ≈ 0.530
      ├── Some((0, 0)): 17/31 ≈ 0.548
      ├── Some((0, 1)): 5/16 ≈ 0.312
      ├── Some((0, 2)): 27/42 ≈ 0.643
      ├── Some((0, 3)): 20/34 ≈ 0.588
      ├── Some((0, 4)): 5/16 ≈ 0.312
      ├── Some((0, 5)): 16/30 ≈ 0.533
      ├── Some((0, 6)): 17/31 ≈ 0.548
      ├── Some((0, 7)): 8/20 ≈ 0.400
      └── Some((0, 8)): 18/32 ≈ 0.562
    ├── Some((7, 1)): 176/315 ≈ 0.559
      ├── Some((1, 0)): 30/47 ≈ 0.638
      ├── Some((1, 1)): 21/37 ≈ 0.568
      ├── Some((1, 2)): 27/43 ≈ 0.628
      ├── Some((1, 3)): 15/30 ≈ 0.500
      ├── Some((1, 4)): 14/29 ≈ 0.483
      ├── Some((1, 5)): 12/26 ≈ 0.462
      ├── Some((1, 6)): 8/21 ≈ 0.381
      ├── Some((1, 7)): 21/37 ≈ 0.568
      └── Some((1, 8)): 28/44 ≈ 0.636
    ├── Some((7, 2)): 137/257 ≈ 0.533
      ├── Some((2, 0)): 14/29 ≈ 0.483
      ├── Some((2, 1)): 12/26 ≈ 0.462
      ├── Some((2, 2)): 6/18 ≈ 0.333
      ├── Some((2, 3)): 20/36 ≈ 0.556
      ├── Some((2, 5)): 21/37 ≈ 0.568
      ├── Some((2, 6)): 14/29 ≈ 0.483
      ├── Some((2, 7)): 17/32 ≈ 0.531
      └── Some((2, 8)): 32/49 ≈ 0.653
    ├── Some((7, 3)): 189/335 ≈ 0.564
      ├── Some((3, 0)): 26/43 ≈ 0.605
      ├── Some((3, 1)): 28/45 ≈ 0.622
      ├── Some((3, 2)): 27/44 ≈ 0.614
      ├── Some((3, 3)): 21/38 ≈ 0.553
      ├── Some((3, 4)): 18/34 ≈ 0.529
      ├── Some((3, 5)): 14/29 ≈ 0.483
      ├── Some((3, 6)): 18/34 ≈ 0.529
      ├── Some((3, 7)): 9/23 ≈ 0.391
      └── Some((3, 8)): 27/44 ≈ 0.614
    ├── Some((7, 4)): 105/208 ≈ 0.505
      ├── Some((4, 0)): 9/21 ≈ 0.429
      ├── Some((4, 1)): 9/21 ≈ 0.429
      ├── Some((4, 2)): 14/27 ≈ 0.519
      ├── Some((4, 3)): 20/34 ≈ 0.588
      ├── Some((4, 4)): 9/21 ≈ 0.429
      ├── Some((4, 5)): 13/26 ≈ 0.500
      ├── Some((4, 6)): 23/38 ≈ 0.605
      └── Some((4, 8)): 7/19 ≈ 0.368
    ├── Some((7, 5)): 87/181 ≈ 0.481
      ├── Some((5, 0)): 19/30 ≈ 0.633
      ├── Some((5, 1)): 6/16 ≈ 0.375
      ├── Some((5, 2)): 2/11 ≈ 0.182
      ├── Some((5, 3)): 11/22 ≈ 0.500
      ├── Some((5, 4)): 13/24 ≈ 0.542
      ├── Some((5, 5)): 4/13 ≈ 0.308
      ├── Some((5, 6)): 12/23 ≈ 0.522
      ├── Some((5, 7)): 10/21 ≈ 0.476
      └── Some((5, 8)): 9/20 ≈ 0.450
    ├── Some((7, 6)): 93/190 ≈ 0.489
      ├── Some((6, 0)): 17/28 ≈ 0.607
      ├── Some((6, 1)): 18/29 ≈ 0.621
      ├── Some((6, 2)): 10/21 ≈ 0.476
      ├── Some((6, 3)): 12/23 ≈ 0.522
      ├── Some((6, 4)): 13/24 ≈ 0.542
      ├── Some((6, 5)): 9/20 ≈ 0.450
      ├── Some((6, 6)): 6/16 ≈ 0.375
      ├── Some((6, 7)): 4/14 ≈ 0.286
      └── Some((6, 8)): 4/14 ≈ 0.286
    ├── Some((7, 7)): 57/133 ≈ 0.429
      ├── Some((7, 0)): 9/19 ≈ 0.474
      ├── Some((7, 1)): 5/14 ≈ 0.357
      ├── Some((7, 2)): 15/25 ≈ 0.600
      ├── Some((7, 3)): 9/19 ≈ 0.474
      ├── Some((7, 4)): 7/17 ≈ 0.412
      ├── Some((7, 5)): 6/15 ≈ 0.400
      ├── Some((7, 6)): 2/10 ≈ 0.200
      └── Some((7, 8)): 4/13 ≈ 0.308
    └── Some((7, 8)): 148/274 ≈ 0.540
      ├── Some((8, 0)): 10/23 ≈ 0.435
      ├── Some((8, 1)): 5/17 ≈ 0.294
      ├── Some((8, 2)): 19/33 ≈ 0.576
      ├── Some((8, 3)): 29/45 ≈ 0.644
      ├── Some((8, 4)): 19/34 ≈ 0.559
      ├── Some((8, 5)): 26/41 ≈ 0.634
      ├── Some((8, 6)): 11/24 ≈ 0.458
      ├── Some((8, 7)): 8/21 ≈ 0.381
      └── Some((8, 8)): 20/35 ≈ 0.571
  └── Some((4, 8)): 1048/2010 ≈ 0.521
    ├── Some((8, 0)): 70/152 ≈ 0.461
      ├── Some((0, 0)): 3/11 ≈ 0.273
      ├── Some((0, 1)): 11/20 ≈ 0.550
      ├── Some((0, 2)): 14/24 ≈ 0.583
      ├── Some((0, 3)): 8/17 ≈ 0.471
      ├── Some((0, 4)): 15/25 ≈ 0.600
      ├── Some((0, 5)): 5/14 ≈ 0.357
      ├── Some((0, 6)): 5/14 ≈ 0.357
      ├── Some((0, 7)): 7/16 ≈ 0.438
      └── Some((0, 8)): 2/10 ≈ 0.200
    ├── Some((8, 1)): 113/219 ≈ 0.516
      ├── Some((1, 0)): 13/25 ≈ 0.520
      ├── Some((1, 1)): 13/25 ≈ 0.520
      ├── Some((1, 2)): 11/22 ≈ 0.500
      ├── Some((1, 3)): 12/24 ≈ 0.500
      ├── Some((1, 4)): 12/24 ≈ 0.500
      ├── Some((1, 5)): 15/27 ≈ 0.556
      ├── Some((1, 6)): 7/18 ≈ 0.389
      ├── Some((1, 7)): 9/20 ≈ 0.450
      └── Some((1, 8)): 21/33 ≈ 0.636
    ├── Some((8, 2)): 90/183 ≈ 0.492
      ├── Some((2, 0)): 12/24 ≈ 0.500
      ├── Some((2, 1)): 12/24 ≈ 0.500
      ├── Some((2, 2)): 7/18 ≈ 0.389
      ├── Some((2, 3)): 16/28 ≈ 0.571
      ├── Some((2, 5)): 16/28 ≈ 0.571
      ├── Some((2, 6)): 16/28 ≈ 0.571
      ├── Some((2, 7)): 5/15 ≈ 0.333
      └── Some((2, 8)): 6/17 ≈ 0.353
    ├── Some((8, 3)): 155/282 ≈ 0.550
      ├── Some((3, 0)): 6/18 ≈ 0.333
      ├── Some((3, 1)): 19/34 ≈ 0.559
      ├── Some((3, 2)): 18/32 ≈ 0.562
      ├── Some((3, 3)): 18/32 ≈ 0.562
      ├── Some((3, 4)): 26/41 ≈ 0.634
      ├── Some((3, 5)): 20/35 ≈ 0.571
      ├── Some((3, 6)): 14/28 ≈ 0.500
      ├── Some((3, 7)): 11/24 ≈ 0.458
      └── Some((3, 8)): 22/37 ≈ 0.595
    ├── Some((8, 4)): 162/292 ≈ 0.555
      ├── Some((4, 0)): 18/34 ≈ 0.529
      ├── Some((4, 1)): 14/29 ≈ 0.483
      ├── Some((4, 2)): 15/31 ≈ 0.484
      ├── Some((4, 3)): 12/27 ≈ 0.444
      ├── Some((4, 4)): 20/36 ≈ 0.556
      ├── Some((4, 5)): 27/44 ≈ 0.614
      ├── Some((4, 6)): 26/43 ≈ 0.605
      └── Some((4, 7)): 29/47 ≈ 0.617
    ├── Some((8, 5)): 109/213 ≈ 0.512
      ├── Some((5, 0)): 13/25 ≈ 0.520
      ├── Some((5, 1)): 21/33 ≈ 0.636
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 11/22 ≈ 0.500
      ├── Some((5, 4)): 10/21 ≈ 0.476
      ├── Some((5, 5)): 18/30 ≈ 0.600
      ├── Some((5, 6)): 13/25 ≈ 0.520
      ├── Some((5, 7)): 6/17 ≈ 0.353
      └── Some((5, 8)): 6/17 ≈ 0.353
    ├── Some((8, 6)): 72/155 ≈ 0.465
      ├── Some((6, 0)): 6/15 ≈ 0.400
      ├── Some((6, 1)): 9/18 ≈ 0.500
      ├── Some((6, 2)): 2/10 ≈ 0.200
      ├── Some((6, 3)): 12/22 ≈ 0.545
      ├── Some((6, 4)): 9/18 ≈ 0.500
      ├── Some((6, 5)): 4/13 ≈ 0.308
      ├── Some((6, 6)): 7/16 ≈ 0.438
      ├── Some((6, 7)): 13/23 ≈ 0.565
      └── Some((6, 8)): 9/19 ≈ 0.474
    ├── Some((8, 7)): 142/262 ≈ 0.542
      ├── Some((7, 0)): 34/50 ≈ 0.680
      ├── Some((7, 1)): 5/17 ≈ 0.294
      ├── Some((7, 2)): 15/29 ≈ 0.517
      ├── Some((7, 3)): 12/25 ≈ 0.480
      ├── Some((7, 4)): 18/32 ≈ 0.562
      ├── Some((7, 5)): 32/47 ≈ 0.681
      ├── Some((7, 6)): 11/24 ≈ 0.458
      ├── Some((7, 7)): 2/12 ≈ 0.167
      └── Some((7, 8)): 12/25 ≈ 0.480
    └── Some((8, 8)): 134/251 ≈ 0.534
      ├── Some((8, 0)): 14/28 ≈ 0.500
      ├── Some((8, 1)): 22/38 ≈ 0.579
      ├── Some((8, 2)): 10/23 ≈ 0.435
      ├── Some((8, 3)): 10/23 ≈ 0.435
      ├── Some((8, 4)): 37/54 ≈ 0.685
      ├── Some((8, 5)): 14/28 ≈ 0.500
      ├── Some((8, 6)): 10/24 ≈ 0.417
      └── Some((8, 7)): 17/32 ≈ 0.531
├── Some((2, 5)): 12817/23988 ≈ 0.534
  ├── Some((5, 0)): 1805/3322 ≈ 0.543
    ├── Some((0, 0)): 165/316 ≈ 0.522
      ├── Some((0, 1)): 16/34 ≈ 0.471
      ├── Some((0, 2)): 13/30 ≈ 0.433
      ├── Some((0, 3)): 19/38 ≈ 0.500
      ├── Some((0, 4)): 17/35 ≈ 0.486
      ├── Some((0, 5)): 37/59 ≈ 0.627
      ├── Some((0, 6)): 28/48 ≈ 0.583
      ├── Some((0, 7)): 14/31 ≈ 0.452
      └── Some((0, 8)): 21/40 ≈ 0.525
    ├── Some((0, 1)): 196/363 ≈ 0.540
      ├── Some((1, 0)): 12/28 ≈ 0.429
      ├── Some((1, 1)): 16/34 ≈ 0.471
      ├── Some((1, 2)): 22/41 ≈ 0.537
      ├── Some((1, 3)): 8/23 ≈ 0.348
      ├── Some((1, 4)): 13/30 ≈ 0.433
      ├── Some((1, 5)): 24/43 ≈ 0.558
      ├── Some((1, 6)): 39/61 ≈ 0.639
      ├── Some((1, 7)): 20/38 ≈ 0.526
      └── Some((1, 8)): 42/64 ≈ 0.656
    ├── Some((0, 2)): 180/339 ≈ 0.531
      ├── Some((2, 0)): 32/54 ≈ 0.593
      ├── Some((2, 1)): 13/31 ≈ 0.419
      ├── Some((2, 2)): 19/38 ≈ 0.500
      ├── Some((2, 3)): 19/38 ≈ 0.500
      ├── Some((2, 4)): 27/48 ≈ 0.562
      ├── Some((2, 6)): 30/52 ≈ 0.577
      ├── Some((2, 7)): 16/34 ≈ 0.471
      └── Some((2, 8)): 23/43 ≈ 0.535
    ├── Some((0, 3)): 90/196 ≈ 0.459
      ├── Some((3, 0)): 13/25 ≈ 0.520
      ├── Some((3, 1)): 15/28 ≈ 0.536
      ├── Some((3, 2)): 8/19 ≈ 0.421
      ├── Some((3, 3)): 6/17 ≈ 0.353
      ├── Some((3, 4)): 8/19 ≈ 0.421
      ├── Some((3, 5)): 6/17 ≈ 0.353
      ├── Some((3, 6)): 8/20 ≈ 0.400
      ├── Some((3, 7)): 9/21 ≈ 0.429
      └── Some((3, 8)): 16/29 ≈ 0.552
    ├── Some((0, 4)): 203/374 ≈ 0.543
      ├── Some((4, 0)): 39/61 ≈ 0.639
      ├── Some((4, 1)): 30/51 ≈ 0.588
      ├── Some((4, 2)): 8/23 ≈ 0.348
      ├── Some((4, 3)): 21/40 ≈ 0.525
      ├── Some((4, 4)): 28/48 ≈ 0.583
      ├── Some((4, 5)): 24/44 ≈ 0.545
      ├── Some((4, 6)): 10/26 ≈ 0.385
      ├── Some((4, 7)): 23/42 ≈ 0.548
      └── Some((4, 8)): 19/38 ≈ 0.500
    ├── Some((0, 5)): 149/291 ≈ 0.512
      ├── Some((5, 1)): 9/25 ≈ 0.360
      ├── Some((5, 2)): 24/44 ≈ 0.545
      ├── Some((5, 3)): 17/35 ≈ 0.486
      ├── Some((5, 4)): 15/32 ≈ 0.469
      ├── Some((5, 5)): 39/61 ≈ 0.639
      ├── Some((5, 6)): 2/14 ≈ 0.143
      ├── Some((5, 7)): 23/42 ≈ 0.548
      └── Some((5, 8)): 19/37 ≈ 0.514
    ├── Some((0, 6)): 289/504 ≈ 0.573
      ├── Some((6, 0)): 24/46 ≈ 0.522
      ├── Some((6, 1)): 37/62 ≈ 0.597
      ├── Some((6, 2)): 31/55 ≈ 0.564
      ├── Some((6, 3)): 36/61 ≈ 0.590
      ├── Some((6, 4)): 17/38 ≈ 0.447
      ├── Some((6, 5)): 49/76 ≈ 0.645
      ├── Some((6, 6)): 54/82 ≈ 0.659
      ├── Some((6, 7)): 25/48 ≈ 0.521
      └── Some((6, 8)): 15/35 ≈ 0.429
    ├── Some((0, 7)): 238/427 ≈ 0.557
      ├── Some((7, 0)): 21/41 ≈ 0.512
      ├── Some((7, 1)): 42/66 ≈ 0.636
      ├── Some((7, 2)): 18/37 ≈ 0.486
      ├── Some((7, 3)): 36/59 ≈ 0.610
      ├── Some((7, 4)): 23/44 ≈ 0.523
      ├── Some((7, 5)): 15/33 ≈ 0.455
      ├── Some((7, 6)): 16/35 ≈ 0.457
      ├── Some((7, 7)): 33/55 ≈ 0.600
      └── Some((7, 8)): 33/56 ≈ 0.589
    └── Some((0, 8)): 294/511 ≈ 0.575
      ├── Some((8, 0)): 43/69 ≈ 0.623
      ├── Some((8, 1)): 22/44 ≈ 0.500
      ├── Some((8, 2)): 20/41 ≈ 0.488
      ├── Some((8, 3)): 26/49 ≈ 0.531
      ├── Some((8, 4)): 32/56 ≈ 0.571
      ├── Some((8, 5)): 36/61 ≈ 0.590
      ├── Some((8, 6)): 49/76 ≈ 0.645
      ├── Some((8, 7)): 35/60 ≈ 0.583
      └── Some((8, 8)): 30/54 ≈ 0.556
  ├── Some((5, 1)): 1459/2728 ≈ 0.535
    ├── Some((1, 0)): 199/360 ≈ 0.553
      ├── Some((0, 0)): 24/42 ≈ 0.571
      ├── Some((0, 1)): 28/47 ≈ 0.596
      ├── Some((0, 2)): 36/56 ≈ 0.643
      ├── Some((0, 3)): 18/35 ≈ 0.514
      ├── Some((0, 4)): 29/48 ≈ 0.604
      ├── Some((0, 5)): 8/23 ≈ 0.348
      ├── Some((0, 6)): 13/29 ≈ 0.448
      ├── Some((0, 7)): 27/46 ≈ 0.587
      └── Some((0, 8)): 16/33 ≈ 0.485
    ├── Some((1, 1)): 229/405 ≈ 0.565
      ├── Some((1, 0)): 25/46 ≈ 0.543
      ├── Some((1, 2)): 20/40 ≈ 0.500
      ├── Some((1, 3)): 22/42 ≈ 0.524
      ├── Some((1, 4)): 34/57 ≈ 0.596
      ├── Some((1, 5)): 37/61 ≈ 0.607
      ├── Some((1, 6)): 29/51 ≈ 0.569
      ├── Some((1, 7)): 34/57 ≈ 0.596
      └── Some((1, 8)): 28/50 ≈ 0.560
    ├── Some((1, 2)): 145/278 ≈ 0.522
      ├── Some((2, 0)): 11/26 ≈ 0.423
      ├── Some((2, 1)): 28/47 ≈ 0.596
      ├── Some((2, 2)): 11/26 ≈ 0.423
      ├── Some((2, 3)): 17/34 ≈ 0.500
      ├── Some((2, 4)): 25/43 ≈ 0.581
      ├── Some((2, 6)): 20/37 ≈ 0.541
      ├── Some((2, 7)): 20/37 ≈ 0.541
      └── Some((2, 8)): 12/27 ≈ 0.444
    ├── Some((1, 3)): 150/285 ≈ 0.526
      ├── Some((3, 0)): 18/33 ≈ 0.545
      ├── Some((3, 1)): 14/29 ≈ 0.483
      ├── Some((3, 2)): 13/27 ≈ 0.481
      ├── Some((3, 3)): 12/26 ≈ 0.462
      ├── Some((3, 4)): 35/52 ≈ 0.673
      ├── Some((3, 5)): 21/37 ≈ 0.568
      ├── Some((3, 6)): 17/32 ≈ 0.531
      ├── Some((3, 7)): 11/25 ≈ 0.440
      └── Some((3, 8)): 9/23 ≈ 0.391
    ├── Some((1, 4)): 130/255 ≈ 0.510
      ├── Some((4, 0)): 27/43 ≈ 0.628
      ├── Some((4, 1)): 9/22 ≈ 0.409
      ├── Some((4, 2)): 13/27 ≈ 0.481
      ├── Some((4, 3)): 16/30 ≈ 0.533
      ├── Some((4, 4)): 16/30 ≈ 0.533
      ├── Some((4, 5)): 9/22 ≈ 0.409
      ├── Some((4, 6)): 8/21 ≈ 0.381
      ├── Some((4, 7)): 13/27 ≈ 0.481
      └── Some((4, 8)): 18/32 ≈ 0.562
    ├── Some((1, 5)): 128/251 ≈ 0.510
      ├── Some((5, 0)): 20/37 ≈ 0.541
      ├── Some((5, 2)): 13/28 ≈ 0.464
      ├── Some((5, 3)): 31/49 ≈ 0.633
      ├── Some((5, 4)): 23/40 ≈ 0.575
      ├── Some((5, 5)): 18/34 ≈ 0.529
      ├── Some((5, 6)): 4/16 ≈ 0.250
      ├── Some((5, 7)): 11/26 ≈ 0.423
      └── Some((5, 8)): 7/20 ≈ 0.350
    ├── Some((1, 6)): 144/276 ≈ 0.522
      ├── Some((6, 0)): 16/31 ≈ 0.516
      ├── Some((6, 1)): 9/22 ≈ 0.409
      ├── Some((6, 2)): 17/32 ≈ 0.531
      ├── Some((6, 3)): 37/55 ≈ 0.673
      ├── Some((6, 4)): 12/26 ≈ 0.462
      ├── Some((6, 5)): 17/32 ≈ 0.531
      ├── Some((6, 6)): 16/31 ≈ 0.516
      ├── Some((6, 7)): 3/14 ≈ 0.214
      └── Some((6, 8)): 17/32 ≈ 0.531
    ├── Some((1, 7)): 243/425 ≈ 0.572
      ├── Some((7, 0)): 42/65 ≈ 0.646
      ├── Some((7, 1)): 41/64 ≈ 0.641
      ├── Some((7, 2)): 27/48 ≈ 0.562
      ├── Some((7, 3)): 16/34 ≈ 0.471
      ├── Some((7, 4)): 5/20 ≈ 0.250
      ├── Some((7, 5)): 36/58 ≈ 0.621
      ├── Some((7, 6)): 40/63 ≈ 0.635
      ├── Some((7, 7)): 15/33 ≈ 0.455
      └── Some((7, 8)): 20/39 ≈ 0.513
    └── Some((1, 8)): 90/192 ≈ 0.469
      ├── Some((8, 0)): 10/21 ≈ 0.476
      ├── Some((8, 1)): 17/29 ≈ 0.586
      ├── Some((8, 2)): 10/22 ≈ 0.455
      ├── Some((8, 3)): 9/20 ≈ 0.450
      ├── Some((8, 4)): 9/20 ≈ 0.450
      ├── Some((8, 5)): 3/13 ≈ 0.231
      ├── Some((8, 6)): 16/28 ≈ 0.571
      ├── Some((8, 7)): 4/14 ≈ 0.286
      └── Some((8, 8)): 12/24 ≈ 0.500
  ├── Some((5, 2)): 1676/3101 ≈ 0.540
    ├── Some((2, 0)): 224/411 ≈ 0.545
      ├── Some((0, 0)): 36/59 ≈ 0.610
      ├── Some((0, 1)): 19/39 ≈ 0.487
      ├── Some((0, 2)): 27/48 ≈ 0.562
      ├── Some((0, 3)): 27/48 ≈ 0.562
      ├── Some((0, 4)): 11/28 ≈ 0.393
      ├── Some((0, 5)): 24/45 ≈ 0.533
      ├── Some((0, 6)): 28/50 ≈ 0.560
      ├── Some((0, 7)): 33/56 ≈ 0.589
      └── Some((0, 8)): 18/37 ≈ 0.486
    ├── Some((2, 1)): 263/470 ≈ 0.560
      ├── Some((1, 0)): 26/48 ≈ 0.542
      ├── Some((1, 1)): 14/33 ≈ 0.424
      ├── Some((1, 2)): 24/46 ≈ 0.522
      ├── Some((1, 3)): 32/56 ≈ 0.571
      ├── Some((1, 4)): 35/59 ≈ 0.593
      ├── Some((1, 5)): 29/52 ≈ 0.558
      ├── Some((1, 6)): 29/52 ≈ 0.558
      ├── Some((1, 7)): 49/76 ≈ 0.645
      └── Some((1, 8)): 25/47 ≈ 0.532
    ├── Some((2, 2)): 256/459 ≈ 0.558
      ├── Some((2, 0)): 25/51 ≈ 0.490
      ├── Some((2, 1)): 18/42 ≈ 0.429
      ├── Some((2, 3)): 57/91 ≈ 0.626
      ├── Some((2, 4)): 37/66 ≈ 0.561
      ├── Some((2, 6)): 31/59 ≈ 0.525
      ├── Some((2, 7)): 65/101 ≈ 0.644
      └── Some((2, 8)): 23/48 ≈ 0.479
    ├── Some((2, 3)): 135/272 ≈ 0.496
      ├── Some((3, 0)): 16/31 ≈ 0.516
      ├── Some((3, 1)): 12/26 ≈ 0.462
      ├── Some((3, 2)): 12/27 ≈ 0.444
      ├── Some((3, 3)): 19/35 ≈ 0.543
      ├── Some((3, 4)): 10/24 ≈ 0.417
      ├── Some((3, 5)): 21/37 ≈ 0.568
      ├── Some((3, 6)): 13/28 ≈ 0.464
      ├── Some((3, 7)): 18/34 ≈ 0.529
      └── Some((3, 8)): 14/29 ≈ 0.483
    ├── Some((2, 4)): 180/342 ≈ 0.526
      ├── Some((4, 0)): 15/32 ≈ 0.469
      ├── Some((4, 1)): 27/47 ≈ 0.574
      ├── Some((4, 2)): 16/33 ≈ 0.485
      ├── Some((4, 3)): 36/57 ≈ 0.632
      ├── Some((4, 4)): 9/24 ≈ 0.375
      ├── Some((4, 5)): 17/35 ≈ 0.486
      ├── Some((4, 6)): 15/32 ≈ 0.469
      ├── Some((4, 7)): 30/50 ≈ 0.600
      └── Some((4, 8)): 14/31 ≈ 0.452
    ├── Some((2, 6)): 229/418 ≈ 0.548
      ├── Some((6, 0)): 36/59 ≈ 0.610
      ├── Some((6, 1)): 23/43 ≈ 0.535
      ├── Some((6, 2)): 33/56 ≈ 0.589
      ├── Some((6, 3)): 15/33 ≈ 0.455
      ├── Some((6, 4)): 22/42 ≈ 0.524
      ├── Some((6, 5)): 19/39 ≈ 0.487
      ├── Some((6, 6)): 24/45 ≈ 0.533
      ├── Some((6, 7)): 27/48 ≈ 0.562
      └── Some((6, 8)): 30/52 ≈ 0.577
    ├── Some((2, 7)): 190/358 ≈ 0.531
      ├── Some((7, 0)): 10/26 ≈ 0.385
      ├── Some((7, 1)): 33/54 ≈ 0.611
      ├── Some((7, 2)): 31/52 ≈ 0.596
      ├── Some((7, 3)): 21/40 ≈ 0.525
      ├── Some((7, 4)): 24/44 ≈ 0.545
      ├── Some((7, 5)): 17/35 ≈ 0.486
      ├── Some((7, 6)): 18/36 ≈ 0.500
      ├── Some((7, 7)): 6/21 ≈ 0.286
      └── Some((7, 8)): 29/49 ≈ 0.592
    └── Some((2, 8)): 198/370 ≈ 0.535
      ├── Some((8, 0)): 15/33 ≈ 0.455
      ├── Some((8, 1)): 23/43 ≈ 0.535
      ├── Some((8, 2)): 16/34 ≈ 0.471
      ├── Some((8, 3)): 5/19 ≈ 0.263
      ├── Some((8, 4)): 43/66 ≈ 0.652
      ├── Some((8, 5)): 22/42 ≈ 0.524
      ├── Some((8, 6)): 31/52 ≈ 0.596
      ├── Some((8, 7)): 21/40 ≈ 0.525
      └── Some((8, 8)): 21/40 ≈ 0.525
  ├── Some((5, 3)): 1074/2062 ≈ 0.521
    ├── Some((3, 0)): 88/182 ≈ 0.484
      ├── Some((0, 0)): 15/26 ≈ 0.577
      ├── Some((0, 1)): 8/18 ≈ 0.444
      ├── Some((0, 2)): 6/16 ≈ 0.375
      ├── Some((0, 3)): 12/23 ≈ 0.522
      ├── Some((0, 4)): 10/21 ≈ 0.476
      ├── Some((0, 5)): 1/10 ≈ 0.100
      ├── Some((0, 6)): 6/16 ≈ 0.375
      ├── Some((0, 7)): 15/26 ≈ 0.577
      └── Some((0, 8)): 14/25 ≈ 0.560
    ├── Some((3, 1)): 194/341 ≈ 0.569
      ├── Some((1, 0)): 18/34 ≈ 0.529
      ├── Some((1, 1)): 29/46 ≈ 0.630
      ├── Some((1, 2)): 18/34 ≈ 0.529
      ├── Some((1, 3)): 24/41 ≈ 0.585
      ├── Some((1, 4)): 22/38 ≈ 0.579
      ├── Some((1, 5)): 19/35 ≈ 0.543
      ├── Some((1, 6)): 20/36 ≈ 0.556
      ├── Some((1, 7)): 19/35 ≈ 0.543
      └── Some((1, 8)): 24/41 ≈ 0.585
    ├── Some((3, 2)): 113/220 ≈ 0.514
      ├── Some((2, 0)): 18/32 ≈ 0.562
      ├── Some((2, 1)): 19/33 ≈ 0.576
      ├── Some((2, 2)): 15/29 ≈ 0.517
      ├── Some((2, 3)): 20/34 ≈ 0.588
      ├── Some((2, 4)): 8/20 ≈ 0.400
      ├── Some((2, 6)): 10/23 ≈ 0.435
      ├── Some((2, 7)): 7/19 ≈ 0.368
      └── Some((2, 8)): 15/29 ≈ 0.517
    ├── Some((3, 3)): 125/238 ≈ 0.525
      ├── Some((3, 0)): 10/23 ≈ 0.435
      ├── Some((3, 1)): 22/37 ≈ 0.595
      ├── Some((3, 2)): 5/17 ≈ 0.294
      ├── Some((3, 4)): 18/32 ≈ 0.562
      ├── Some((3, 5)): 19/34 ≈ 0.559
      ├── Some((3, 6)): 10/23 ≈ 0.435
      ├── Some((3, 7)): 23/38 ≈ 0.605
      └── Some((3, 8)): 18/33 ≈ 0.545
    ├── Some((3, 4)): 67/148 ≈ 0.453
      ├── Some((4, 0)): 3/11 ≈ 0.273
      ├── Some((4, 1)): 8/17 ≈ 0.471
      ├── Some((4, 2)): 12/22 ≈ 0.545
      ├── Some((4, 3)): 7/16 ≈ 0.438
      ├── Some((4, 4)): 10/19 ≈ 0.526
      ├── Some((4, 5)): 12/22 ≈ 0.545
      ├── Some((4, 6)): 4/12 ≈ 0.333
      ├── Some((4, 7)): 3/11 ≈ 0.273
      └── Some((4, 8)): 8/17 ≈ 0.471
    ├── Some((3, 5)): 80/169 ≈ 0.473
      ├── Some((5, 0)): 9/20 ≈ 0.450
      ├── Some((5, 1)): 8/19 ≈ 0.421
      ├── Some((5, 2)): 5/15 ≈ 0.333
      ├── Some((5, 4)): 8/19 ≈ 0.421
      ├── Some((5, 5)): 12/23 ≈ 0.522
      ├── Some((5, 6)): 21/33 ≈ 0.636
      ├── Some((5, 7)): 13/25 ≈ 0.520
      └── Some((5, 8)): 4/14 ≈ 0.286
    ├── Some((3, 6)): 109/214 ≈ 0.509
      ├── Some((6, 0)): 10/21 ≈ 0.476
      ├── Some((6, 1)): 3/13 ≈ 0.231
      ├── Some((6, 2)): 11/23 ≈ 0.478
      ├── Some((6, 3)): 16/28 ≈ 0.571
      ├── Some((6, 4)): 16/28 ≈ 0.571
      ├── Some((6, 5)): 5/15 ≈ 0.333
      ├── Some((6, 6)): 15/27 ≈ 0.556
      ├── Some((6, 7)): 18/31 ≈ 0.581
      └── Some((6, 8)): 15/27 ≈ 0.556
    ├── Some((3, 7)): 150/276 ≈ 0.543
      ├── Some((7, 0)): 16/30 ≈ 0.533
      ├── Some((7, 1)): 23/38 ≈ 0.605
      ├── Some((7, 2)): 17/31 ≈ 0.548
      ├── Some((7, 3)): 28/44 ≈ 0.636
      ├── Some((7, 4)): 27/42 ≈ 0.643
      ├── Some((7, 5)): 14/28 ≈ 0.500
      ├── Some((7, 6)): 10/23 ≈ 0.435
      ├── Some((7, 7)): 5/17 ≈ 0.294
      └── Some((7, 8)): 9/22 ≈ 0.409
    └── Some((3, 8)): 148/273 ≈ 0.542
      ├── Some((8, 0)): 4/15 ≈ 0.267
      ├── Some((8, 1)): 17/31 ≈ 0.548
      ├── Some((8, 2)): 2/13 ≈ 0.154
      ├── Some((8, 3)): 23/38 ≈ 0.605
      ├── Some((8, 4)): 27/43 ≈ 0.628
      ├── Some((8, 5)): 23/38 ≈ 0.605
      ├── Some((8, 6)): 19/34 ≈ 0.559
      ├── Some((8, 7)): 8/21 ≈ 0.381
      └── Some((8, 8)): 24/39 ≈ 0.615
  ├── Some((5, 4)): 2047/3735 ≈ 0.548
    ├── Some((4, 0)): 220/404 ≈ 0.545
      ├── Some((0, 0)): 31/53 ≈ 0.585
      ├── Some((0, 1)): 22/42 ≈ 0.524
      ├── Some((0, 2)): 24/44 ≈ 0.545
      ├── Some((0, 3)): 24/44 ≈ 0.545
      ├── Some((0, 4)): 23/43 ≈ 0.535
      ├── Some((0, 5)): 28/49 ≈ 0.571
      ├── Some((0, 6)): 22/42 ≈ 0.524
      ├── Some((0, 7)): 29/51 ≈ 0.569
      └── Some((0, 8)): 16/35 ≈ 0.457
    ├── Some((4, 1)): 243/439 ≈ 0.554
      ├── Some((1, 0)): 30/53 ≈ 0.566
      ├── Some((1, 1)): 15/34 ≈ 0.441
      ├── Some((1, 2)): 25/47 ≈ 0.532
      ├── Some((1, 3)): 13/31 ≈ 0.419
      ├── Some((1, 4)): 16/35 ≈ 0.457
      ├── Some((1, 5)): 49/75 ≈ 0.653
      ├── Some((1, 6)): 28/50 ≈ 0.560
      ├── Some((1, 7)): 29/51 ≈ 0.569
      └── Some((1, 8)): 38/62 ≈ 0.613
    ├── Some((4, 2)): 239/433 ≈ 0.552
      ├── Some((2, 0)): 23/46 ≈ 0.500
      ├── Some((2, 1)): 25/48 ≈ 0.521
      ├── Some((2, 2)): 25/48 ≈ 0.521
      ├── Some((2, 3)): 57/87 ≈ 0.655
      ├── Some((2, 4)): 51/80 ≈ 0.637
      ├── Some((2, 6)): 15/35 ≈ 0.429
      ├── Some((2, 7)): 24/47 ≈ 0.511
      └── Some((2, 8)): 19/41 ≈ 0.463
    ├── Some((4, 3)): 206/383 ≈ 0.538
      ├── Some((3, 0)): 30/51 ≈ 0.588
      ├── Some((3, 1)): 6/21 ≈ 0.286
      ├── Some((3, 2)): 41/64 ≈ 0.641
      ├── Some((3, 3)): 17/36 ≈ 0.472
      ├── Some((3, 4)): 18/37 ≈ 0.486
      ├── Some((3, 5)): 20/39 ≈ 0.513
      ├── Some((3, 6)): 25/46 ≈ 0.543
      ├── Some((3, 7)): 20/39 ≈ 0.513
      └── Some((3, 8)): 28/49 ≈ 0.571
    ├── Some((4, 4)): 385/653 ≈ 0.590
      ├── Some((4, 0)): 57/93 ≈ 0.613
      ├── Some((4, 1)): 36/67 ≈ 0.537
      ├── Some((4, 2)): 35/65 ≈ 0.538
      ├── Some((4, 3)): 32/61 ≈ 0.525
      ├── Some((4, 5)): 55/90 ≈ 0.611
      ├── Some((4, 6)): 49/83 ≈ 0.590
      ├── Some((4, 7)): 69/107 ≈ 0.645
      └── Some((4, 8)): 51/86 ≈ 0.593
    ├── Some((4, 5)): 195/366 ≈ 0.533
      ├── Some((5, 0)): 16/35 ≈ 0.457
      ├── Some((5, 1)): 8/25 ≈ 0.320
      ├── Some((5, 2)): 26/48 ≈ 0.542
      ├── Some((5, 3)): 41/66 ≈ 0.621
      ├── Some((5, 5)): 33/57 ≈ 0.579
      ├── Some((5, 6)): 32/56 ≈ 0.571
      ├── Some((5, 7)): 12/30 ≈ 0.400
      └── Some((5, 8)): 26/48 ≈ 0.542
    ├── Some((4, 6)): 249/449 ≈ 0.555
      ├── Some((6, 0)): 50/76 ≈ 0.658
      ├── Some((6, 1)): 27/49 ≈ 0.551
      ├── Some((6, 2)): 14/33 ≈ 0.424
      ├── Some((6, 3)): 27/49 ≈ 0.551
      ├── Some((6, 4)): 15/34 ≈ 0.441
      ├── Some((6, 5)): 14/33 ≈ 0.424
      ├── Some((6, 6)): 44/70 ≈ 0.629
      ├── Some((6, 7)): 30/53 ≈ 0.566
      └── Some((6, 8)): 28/51 ≈ 0.549
    ├── Some((4, 7)): 168/324 ≈ 0.519
      ├── Some((7, 0)): 23/41 ≈ 0.561
      ├── Some((7, 1)): 18/35 ≈ 0.514
      ├── Some((7, 2)): 14/30 ≈ 0.467
      ├── Some((7, 3)): 28/47 ≈ 0.596
      ├── Some((7, 4)): 19/36 ≈ 0.528
      ├── Some((7, 5)): 15/32 ≈ 0.469
      ├── Some((7, 6)): 17/34 ≈ 0.500
      ├── Some((7, 7)): 17/34 ≈ 0.500
      └── Some((7, 8)): 17/34 ≈ 0.500
    └── Some((4, 8)): 142/283 ≈ 0.502
      ├── Some((8, 0)): 12/27 ≈ 0.444
      ├── Some((8, 1)): 26/44 ≈ 0.591
      ├── Some((8, 2)): 29/47 ≈ 0.617
      ├── Some((8, 3)): 7/20 ≈ 0.350
      ├── Some((8, 4)): 15/31 ≈ 0.484
      ├── Some((8, 5)): 7/20 ≈ 0.350
      ├── Some((8, 6)): 22/39 ≈ 0.564
      ├── Some((8, 7)): 11/26 ≈ 0.423
      └── Some((8, 8)): 13/28 ≈ 0.464
  ├── Some((5, 5)): 1060/2037 ≈ 0.520
    ├── Some((5, 0)): 90/189 ≈ 0.476
      ├── Some((0, 0)): 11/22 ≈ 0.500
      ├── Some((0, 1)): 10/21 ≈ 0.476
      ├── Some((0, 2)): 11/22 ≈ 0.500
      ├── Some((0, 3)): 20/32 ≈ 0.625
      ├── Some((0, 4)): 3/13 ≈ 0.231
      ├── Some((0, 5)): 13/25 ≈ 0.520
      ├── Some((0, 6)): 10/21 ≈ 0.476
      ├── Some((0, 7)): 10/21 ≈ 0.476
      └── Some((0, 8)): 2/11 ≈ 0.182
    ├── Some((5, 1)): 131/253 ≈ 0.518
      ├── Some((1, 0)): 20/35 ≈ 0.571
      ├── Some((1, 1)): 3/14 ≈ 0.214
      ├── Some((1, 2)): 4/15 ≈ 0.267
      ├── Some((1, 3)): 21/36 ≈ 0.583
      ├── Some((1, 4)): 12/25 ≈ 0.480
      ├── Some((1, 5)): 11/24 ≈ 0.458
      ├── Some((1, 6)): 42/59 ≈ 0.712
      ├── Some((1, 7)): 9/22 ≈ 0.409
      └── Some((1, 8)): 9/22 ≈ 0.409
    ├── Some((5, 2)): 97/200 ≈ 0.485
      ├── Some((2, 0)): 15/29 ≈ 0.517
      ├── Some((2, 1)): 24/39 ≈ 0.615
      ├── Some((2, 2)): 7/19 ≈ 0.368
      ├── Some((2, 3)): 13/26 ≈ 0.500
      ├── Some((2, 4)): 5/16 ≈ 0.312
      ├── Some((2, 6)): 8/20 ≈ 0.400
      ├── Some((2, 7)): 21/35 ≈ 0.600
      └── Some((2, 8)): 4/15 ≈ 0.267
    ├── Some((5, 3)): 180/328 ≈ 0.549
      ├── Some((3, 0)): 9/23 ≈ 0.391
      ├── Some((3, 1)): 5/18 ≈ 0.278
      ├── Some((3, 2)): 30/48 ≈ 0.625
      ├── Some((3, 3)): 32/51 ≈ 0.627
      ├── Some((3, 4)): 23/40 ≈ 0.575
      ├── Some((3, 5)): 30/48 ≈ 0.625
      ├── Some((3, 6)): 24/41 ≈ 0.585
      ├── Some((3, 7)): 17/33 ≈ 0.515
      └── Some((3, 8)): 10/25 ≈ 0.400
    ├── Some((5, 4)): 117/231 ≈ 0.506
      ├── Some((4, 0)): 8/20 ≈ 0.400
      ├── Some((4, 1)): 16/29 ≈ 0.552
      ├── Some((4, 2)): 21/35 ≈ 0.600
      ├── Some((4, 3)): 18/31 ≈ 0.581
      ├── Some((4, 4)): 11/23 ≈ 0.478
      ├── Some((4, 5)): 18/31 ≈ 0.581
      ├── Some((4, 6)): 7/19 ≈ 0.368
      ├── Some((4, 7)): 12/25 ≈ 0.480
      └── Some((4, 8)): 6/17 ≈ 0.353
    ├── Some((5, 6)): 123/241 ≈ 0.510
      ├── Some((6, 0)): 7/19 ≈ 0.368
      ├── Some((6, 1)): 12/25 ≈ 0.480
      ├── Some((6, 2)): 23/37 ≈ 0.622
      ├── Some((6, 3)): 10/23 ≈ 0.435
      ├── Some((6, 4)): 12/25 ≈ 0.480
      ├── Some((6, 5)): 8/20 ≈ 0.400
      ├── Some((6, 6)): 11/24 ≈ 0.458
      ├── Some((6, 7)): 20/34 ≈ 0.588
      └── Some((6, 8)): 19/33 ≈ 0.576
    ├── Some((5, 7)): 214/378 ≈ 0.566
      ├── Some((7, 0)): 22/40 ≈ 0.550
      ├── Some((7, 1)): 13/29 ≈ 0.448
      ├── Some((7, 2)): 22/40 ≈ 0.550
      ├── Some((7, 3)): 37/57 ≈ 0.649
      ├── Some((7, 4)): 26/45 ≈ 0.578
      ├── Some((7, 5)): 35/55 ≈ 0.636
      ├── Some((7, 6)): 29/48 ≈ 0.604
      ├── Some((7, 7)): 12/28 ≈ 0.429
      └── Some((7, 8)): 18/35 ≈ 0.514
    └── Some((5, 8)): 107/216 ≈ 0.495
      ├── Some((8, 0)): 4/14 ≈ 0.286
      ├── Some((8, 1)): 9/21 ≈ 0.429
      ├── Some((8, 2)): 15/28 ≈ 0.536
      ├── Some((8, 3)): 13/25 ≈ 0.520
      ├── Some((8, 4)): 13/26 ≈ 0.500
      ├── Some((8, 5)): 11/23 ≈ 0.478
      ├── Some((8, 6)): 9/21 ≈ 0.429
      ├── Some((8, 7)): 5/16 ≈ 0.312
      └── Some((8, 8)): 27/41 ≈ 0.659
  ├── Some((5, 6)): 1649/3055 ≈ 0.540
    ├── Some((6, 0)): 149/288 ≈ 0.517
      ├── Some((0, 0)): 12/27 ≈ 0.444
      ├── Some((0, 1)): 9/23 ≈ 0.391
      ├── Some((0, 2)): 18/34 ≈ 0.529
      ├── Some((0, 3)): 34/52 ≈ 0.654
      ├── Some((0, 4)): 15/30 ≈ 0.500
      ├── Some((0, 5)): 14/29 ≈ 0.483
      ├── Some((0, 6)): 16/31 ≈ 0.516
      ├── Some((0, 7)): 16/32 ≈ 0.500
      └── Some((0, 8)): 14/29 ≈ 0.483
    ├── Some((6, 1)): 183/340 ≈ 0.538
      ├── Some((1, 0)): 19/37 ≈ 0.514
      ├── Some((1, 1)): 33/53 ≈ 0.623
      ├── Some((1, 2)): 22/40 ≈ 0.550
      ├── Some((1, 3)): 18/35 ≈ 0.514
      ├── Some((1, 4)): 5/18 ≈ 0.278
      ├── Some((1, 5)): 22/40 ≈ 0.550
      ├── Some((1, 6)): 9/24 ≈ 0.375
      ├── Some((1, 7)): 19/37 ≈ 0.514
      └── Some((1, 8)): 35/55 ≈ 0.636
    ├── Some((6, 2)): 206/375 ≈ 0.549
      ├── Some((2, 0)): 27/49 ≈ 0.551
      ├── Some((2, 1)): 21/41 ≈ 0.512
      ├── Some((2, 2)): 34/57 ≈ 0.596
      ├── Some((2, 3)): 17/36 ≈ 0.472
      ├── Some((2, 4)): 18/37 ≈ 0.486
      ├── Some((2, 6)): 12/30 ≈ 0.400
      ├── Some((2, 7)): 39/63 ≈ 0.619
      └── Some((2, 8)): 37/61 ≈ 0.607
    ├── Some((6, 3)): 145/281 ≈ 0.516
      ├── Some((3, 0)): 22/38 ≈ 0.579
      ├── Some((3, 1)): 8/21 ≈ 0.381
      ├── Some((3, 2)): 10/24 ≈ 0.417
      ├── Some((3, 3)): 20/36 ≈ 0.556
      ├── Some((3, 4)): 15/30 ≈ 0.500
      ├── Some((3, 5)): 8/21 ≈ 0.381
      ├── Some((3, 6)): 18/34 ≈ 0.529
      ├── Some((3, 7)): 22/38 ≈ 0.579
      └── Some((3, 8)): 22/38 ≈ 0.579
    ├── Some((6, 4)): 246/435 ≈ 0.566
      ├── Some((4, 0)): 23/43 ≈ 0.535
      ├── Some((4, 1)): 35/58 ≈ 0.603
      ├── Some((4, 2)): 30/52 ≈ 0.577
      ├── Some((4, 3)): 29/51 ≈ 0.569
      ├── Some((4, 4)): 26/47 ≈ 0.553
      ├── Some((4, 5)): 40/63 ≈ 0.635
      ├── Some((4, 6)): 27/48 ≈ 0.562
      ├── Some((4, 7)): 12/29 ≈ 0.414
      └── Some((4, 8)): 23/43 ≈ 0.535
    ├── Some((6, 5)): 271/473 ≈ 0.573
      ├── Some((5, 0)): 33/58 ≈ 0.569
      ├── Some((5, 1)): 28/52 ≈ 0.538
      ├── Some((5, 2)): 44/72 ≈ 0.611
      ├── Some((5, 3)): 47/75 ≈ 0.627
      ├── Some((5, 4)): 32/57 ≈ 0.561
      ├── Some((5, 5)): 33/59 ≈ 0.559
      ├── Some((5, 7)): 8/26 ≈ 0.308
      └── Some((5, 8)): 45/73 ≈ 0.616
    ├── Some((6, 6)): 210/381 ≈ 0.551
      ├── Some((6, 0)): 32/55 ≈ 0.582
      ├── Some((6, 1)): 11/29 ≈ 0.379
      ├── Some((6, 2)): 32/55 ≈ 0.582
      ├── Some((6, 3)): 33/56 ≈ 0.589
      ├── Some((6, 4)): 19/39 ≈ 0.487
      ├── Some((6, 5)): 13/31 ≈ 0.419
      ├── Some((6, 7)): 25/46 ≈ 0.543
      └── Some((6, 8)): 44/69 ≈ 0.638
    ├── Some((6, 7)): 110/226 ≈ 0.487
      ├── Some((7, 0)): 13/26 ≈ 0.500
      ├── Some((7, 1)): 10/22 ≈ 0.455
      ├── Some((7, 2)): 12/25 ≈ 0.480
      ├── Some((7, 3)): 17/31 ≈ 0.548
      ├── Some((7, 4)): 11/24 ≈ 0.458
      ├── Some((7, 5)): 9/21 ≈ 0.429
      ├── Some((7, 6)): 7/19 ≈ 0.368
      ├── Some((7, 7)): 15/28 ≈ 0.536
      └── Some((7, 8)): 16/29 ≈ 0.552
    └── Some((6, 8)): 128/255 ≈ 0.502
      ├── Some((8, 0)): 9/22 ≈ 0.409
      ├── Some((8, 1)): 19/34 ≈ 0.559
      ├── Some((8, 2)): 24/40 ≈ 0.600
      ├── Some((8, 3)): 10/23 ≈ 0.435
      ├── Some((8, 4)): 15/30 ≈ 0.500
      ├── Some((8, 5)): 3/14 ≈ 0.214
      ├── Some((8, 6)): 19/34 ≈ 0.559
      ├── Some((8, 7)): 16/31 ≈ 0.516
      └── Some((8, 8)): 12/26 ≈ 0.462
  ├── Some((5, 7)): 1072/2058 ≈ 0.521
    ├── Some((7, 0)): 126/239 ≈ 0.527
      ├── Some((0, 0)): 18/31 ≈ 0.581
      ├── Some((0, 1)): 12/24 ≈ 0.500
      ├── Some((0, 2)): 12/24 ≈ 0.500
      ├── Some((0, 3)): 13/25 ≈ 0.520
      ├── Some((0, 4)): 19/32 ≈ 0.594
      ├── Some((0, 5)): 19/32 ≈ 0.594
      ├── Some((0, 6)): 13/26 ≈ 0.500
      ├── Some((0, 7)): 13/26 ≈ 0.500
      └── Some((0, 8)): 7/18 ≈ 0.389
    ├── Some((7, 1)): 110/215 ≈ 0.512
      ├── Some((1, 0)): 11/23 ≈ 0.478
      ├── Some((1, 1)): 13/25 ≈ 0.520
      ├── Some((1, 2)): 17/29 ≈ 0.586
      ├── Some((1, 3)): 5/15 ≈ 0.333
      ├── Some((1, 4)): 24/37 ≈ 0.649
      ├── Some((1, 5)): 8/19 ≈ 0.421
      ├── Some((1, 6)): 11/23 ≈ 0.478
      ├── Some((1, 7)): 12/24 ≈ 0.500
      └── Some((1, 8)): 8/19 ≈ 0.421
    ├── Some((7, 2)): 122/233 ≈ 0.524
      ├── Some((2, 0)): 22/37 ≈ 0.595
      ├── Some((2, 1)): 8/20 ≈ 0.400
      ├── Some((2, 2)): 11/24 ≈ 0.458
      ├── Some((2, 3)): 13/27 ≈ 0.481
      ├── Some((2, 4)): 18/32 ≈ 0.562
      ├── Some((2, 6)): 16/30 ≈ 0.533
      ├── Some((2, 7)): 24/39 ≈ 0.615
      └── Some((2, 8)): 10/23 ≈ 0.435
    ├── Some((7, 3)): 194/341 ≈ 0.569
      ├── Some((3, 0)): 15/31 ≈ 0.484
      ├── Some((3, 1)): 6/19 ≈ 0.316
      ├── Some((3, 2)): 22/39 ≈ 0.564
      ├── Some((3, 3)): 22/39 ≈ 0.564
      ├── Some((3, 4)): 37/55 ≈ 0.673
      ├── Some((3, 5)): 5/18 ≈ 0.278
      ├── Some((3, 6)): 31/49 ≈ 0.633
      ├── Some((3, 7)): 25/42 ≈ 0.595
      └── Some((3, 8)): 30/48 ≈ 0.625
    ├── Some((7, 4)): 136/255 ≈ 0.533
      ├── Some((4, 0)): 25/40 ≈ 0.625
      ├── Some((4, 1)): 12/25 ≈ 0.480
      ├── Some((4, 2)): 13/26 ≈ 0.500
      ├── Some((4, 3)): 27/42 ≈ 0.643
      ├── Some((4, 4)): 8/20 ≈ 0.400
      ├── Some((4, 5)): 12/25 ≈ 0.480
      ├── Some((4, 6)): 8/20 ≈ 0.400
      ├── Some((4, 7)): 7/19 ≈ 0.368
      └── Some((4, 8)): 23/37 ≈ 0.622
    ├── Some((7, 5)): 122/233 ≈ 0.524
      ├── Some((5, 0)): 16/30 ≈ 0.533
      ├── Some((5, 1)): 12/25 ≈ 0.480
      ├── Some((5, 2)): 14/28 ≈ 0.500
      ├── Some((5, 3)): 9/22 ≈ 0.409
      ├── Some((5, 4)): 12/25 ≈ 0.480
      ├── Some((5, 5)): 14/28 ≈ 0.500
      ├── Some((5, 6)): 29/45 ≈ 0.644
      └── Some((5, 8)): 15/29 ≈ 0.517
    ├── Some((7, 6)): 82/172 ≈ 0.477
      ├── Some((6, 0)): 5/14 ≈ 0.357
      ├── Some((6, 1)): 12/22 ≈ 0.545
      ├── Some((6, 2)): 10/20 ≈ 0.500
      ├── Some((6, 3)): 14/25 ≈ 0.560
      ├── Some((6, 4)): 3/12 ≈ 0.250
      ├── Some((6, 5)): 9/19 ≈ 0.474
      ├── Some((6, 6)): 12/22 ≈ 0.545
      ├── Some((6, 7)): 8/18 ≈ 0.444
      └── Some((6, 8)): 9/19 ≈ 0.474
    ├── Some((7, 7)): 73/158 ≈ 0.462
      ├── Some((7, 0)): 12/23 ≈ 0.522
      ├── Some((7, 1)): 11/22 ≈ 0.500
      ├── Some((7, 2)): 1/10 ≈ 0.100
      ├── Some((7, 3)): 13/25 ≈ 0.520
      ├── Some((7, 4)): 6/16 ≈ 0.375
      ├── Some((7, 5)): 4/14 ≈ 0.286
      ├── Some((7, 6)): 5/15 ≈ 0.333
      └── Some((7, 8)): 20/32 ≈ 0.625
    └── Some((7, 8)): 107/211 ≈ 0.507
      ├── Some((8, 0)): 8/19 ≈ 0.421
      ├── Some((8, 1)): 17/29 ≈ 0.586
      ├── Some((8, 2)): 12/24 ≈ 0.500
      ├── Some((8, 3)): 16/28 ≈ 0.571
      ├── Some((8, 4)): 6/17 ≈ 0.353
      ├── Some((8, 5)): 7/18 ≈ 0.389
      ├── Some((8, 6)): 5/15 ≈ 0.333
      ├── Some((8, 7)): 19/31 ≈ 0.613
      └── Some((8, 8)): 17/29 ≈ 0.586
  └── Some((5, 8)): 975/1889 ≈ 0.516
    ├── Some((8, 0)): 105/206 ≈ 0.510
      ├── Some((0, 0)): 10/21 ≈ 0.476
      ├── Some((0, 1)): 18/30 ≈ 0.600
      ├── Some((0, 2)): 14/25 ≈ 0.560
      ├── Some((0, 3)): 11/22 ≈ 0.500
      ├── Some((0, 4)): 11/22 ≈ 0.500
      ├── Some((0, 5)): 9/20 ≈ 0.450
      ├── Some((0, 6)): 11/22 ≈ 0.500
      ├── Some((0, 7)): 16/28 ≈ 0.571
      └── Some((0, 8)): 5/15 ≈ 0.333
    ├── Some((8, 1)): 154/280 ≈ 0.550
      ├── Some((1, 0)): 18/32 ≈ 0.562
      ├── Some((1, 1)): 7/19 ≈ 0.368
      ├── Some((1, 2)): 26/41 ≈ 0.634
      ├── Some((1, 3)): 14/28 ≈ 0.500
      ├── Some((1, 4)): 8/20 ≈ 0.400
      ├── Some((1, 5)): 15/29 ≈ 0.517
      ├── Some((1, 6)): 23/38 ≈ 0.605
      ├── Some((1, 7)): 20/35 ≈ 0.571
      └── Some((1, 8)): 22/37 ≈ 0.595
    ├── Some((8, 2)): 115/221 ≈ 0.520
      ├── Some((2, 0)): 10/22 ≈ 0.455
      ├── Some((2, 1)): 22/36 ≈ 0.611
      ├── Some((2, 2)): 16/30 ≈ 0.533
      ├── Some((2, 3)): 11/24 ≈ 0.458
      ├── Some((2, 4)): 21/35 ≈ 0.600
      ├── Some((2, 6)): 8/20 ≈ 0.400
      ├── Some((2, 7)): 8/20 ≈ 0.400
      └── Some((2, 8)): 19/33 ≈ 0.576
    ├── Some((8, 3)): 100/199 ≈ 0.503
      ├── Some((3, 0)): 11/22 ≈ 0.500
      ├── Some((3, 1)): 16/28 ≈ 0.571
      ├── Some((3, 2)): 4/14 ≈ 0.286
      ├── Some((3, 3)): 10/21 ≈ 0.476
      ├── Some((3, 4)): 16/28 ≈ 0.571
      ├── Some((3, 5)): 6/16 ≈ 0.375
      ├── Some((3, 6)): 8/19 ≈ 0.421
      ├── Some((3, 7)): 15/26 ≈ 0.577
      └── Some((3, 8)): 13/24 ≈ 0.542
    ├── Some((8, 4)): 199/346 ≈ 0.575
      ├── Some((4, 0)): 11/26 ≈ 0.423
      ├── Some((4, 1)): 38/56 ≈ 0.679
      ├── Some((4, 2)): 13/28 ≈ 0.464
      ├── Some((4, 3)): 24/41 ≈ 0.585
      ├── Some((4, 4)): 14/29 ≈ 0.483
      ├── Some((4, 5)): 17/33 ≈ 0.515
      ├── Some((4, 6)): 36/54 ≈ 0.667
      ├── Some((4, 7)): 28/45 ≈ 0.622
      └── Some((4, 8)): 17/33 ≈ 0.515
    ├── Some((8, 5)): 57/131 ≈ 0.435
      ├── Some((5, 0)): 5/14 ≈ 0.357
      ├── Some((5, 1)): 6/15 ≈ 0.400
      ├── Some((5, 2)): 10/20 ≈ 0.500
      ├── Some((5, 3)): 5/14 ≈ 0.357
      ├── Some((5, 4)): 4/13 ≈ 0.308
      ├── Some((5, 5)): 5/14 ≈ 0.357
      ├── Some((5, 6)): 2/10 ≈ 0.200
      └── Some((5, 7)): 19/30 ≈ 0.633
    ├── Some((8, 6)): 132/247 ≈ 0.534
      ├── Some((6, 0)): 13/26 ≈ 0.500
      ├── Some((6, 1)): 3/13 ≈ 0.231
      ├── Some((6, 2)): 10/22 ≈ 0.455
      ├── Some((6, 3)): 10/22 ≈ 0.455
      ├── Some((6, 4)): 35/50 ≈ 0.700
      ├── Some((6, 5)): 16/29 ≈ 0.552
      ├── Some((6, 6)): 10/22 ≈ 0.455
      ├── Some((6, 7)): 23/37 ≈ 0.622
      └── Some((6, 8)): 12/25 ≈ 0.480
    ├── Some((8, 7)): 32/89 ≈ 0.360
      ├── Some((7, 0)): 0/6 ≈ 0.000
      ├── Some((7, 1)): 3/9 ≈ 0.333
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 1/7 ≈ 0.143
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 1/7 ≈ 0.143
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 7/14 ≈ 0.500
    └── Some((8, 8)): 81/169 ≈ 0.479
      ├── Some((8, 0)): 17/29 ≈ 0.586
      ├── Some((8, 1)): 9/20 ≈ 0.450
      ├── Some((8, 2)): 3/13 ≈ 0.231
      ├── Some((8, 3)): 9/20 ≈ 0.450
      ├── Some((8, 4)): 19/31 ≈ 0.613
      ├── Some((8, 5)): 10/21 ≈ 0.476
      ├── Some((8, 6)): 12/24 ≈ 0.500
      └── Some((8, 7)): 1/10 ≈ 0.100
├── Some((2, 6)): 9099/17244 ≈ 0.528
  ├── Some((6, 0)): 822/1590 ≈ 0.517
    ├── Some((0, 0)): 104/196 ≈ 0.531
      ├── Some((0, 1)): 11/22 ≈ 0.500
      ├── Some((0, 2)): 12/23 ≈ 0.522
      ├── Some((0, 3)): 14/25 ≈ 0.560
      ├── Some((0, 4)): 16/28 ≈ 0.571
      ├── Some((0, 5)): 8/19 ≈ 0.421
      ├── Some((0, 6)): 14/26 ≈ 0.538
      ├── Some((0, 7)): 18/30 ≈ 0.600
      └── Some((0, 8)): 11/22 ≈ 0.500
    ├── Some((0, 1)): 71/147 ≈ 0.483
      ├── Some((1, 0)): 8/16 ≈ 0.500
      ├── Some((1, 1)): 2/10 ≈ 0.200
      ├── Some((1, 2)): 8/16 ≈ 0.500
      ├── Some((1, 3)): 15/24 ≈ 0.625
      ├── Some((1, 4)): 10/19 ≈ 0.526
      ├── Some((1, 5)): 3/11 ≈ 0.273
      ├── Some((1, 6)): 6/14 ≈ 0.429
      ├── Some((1, 7)): 7/15 ≈ 0.467
      └── Some((1, 8)): 12/21 ≈ 0.571
    ├── Some((0, 2)): 70/145 ≈ 0.483
      ├── Some((2, 0)): 7/16 ≈ 0.438
      ├── Some((2, 1)): 12/22 ≈ 0.545
      ├── Some((2, 2)): 15/25 ≈ 0.600
      ├── Some((2, 3)): 8/18 ≈ 0.444
      ├── Some((2, 4)): 3/11 ≈ 0.273
      ├── Some((2, 5)): 6/15 ≈ 0.400
      ├── Some((2, 7)): 11/21 ≈ 0.524
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((0, 3)): 104/196 ≈ 0.531
      ├── Some((3, 0)): 7/17 ≈ 0.412
      ├── Some((3, 1)): 8/18 ≈ 0.444
      ├── Some((3, 2)): 9/19 ≈ 0.474
      ├── Some((3, 3)): 6/16 ≈ 0.375
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 12/22 ≈ 0.545
      ├── Some((3, 6)): 8/18 ≈ 0.444
      ├── Some((3, 7)): 15/26 ≈ 0.577
      └── Some((3, 8)): 30/41 ≈ 0.732
    ├── Some((0, 4)): 104/196 ≈ 0.531
      ├── Some((4, 0)): 9/19 ≈ 0.474
      ├── Some((4, 1)): 16/27 ≈ 0.593
      ├── Some((4, 2)): 12/22 ≈ 0.545
      ├── Some((4, 3)): 22/33 ≈ 0.667
      ├── Some((4, 4)): 2/11 ≈ 0.182
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 11/21 ≈ 0.524
      ├── Some((4, 7)): 14/24 ≈ 0.583
      └── Some((4, 8)): 9/19 ≈ 0.474
    ├── Some((0, 5)): 111/206 ≈ 0.539
      ├── Some((5, 0)): 4/13 ≈ 0.308
      ├── Some((5, 1)): 6/16 ≈ 0.375
      ├── Some((5, 2)): 7/17 ≈ 0.412
      ├── Some((5, 3)): 8/18 ≈ 0.444
      ├── Some((5, 4)): 16/27 ≈ 0.593
      ├── Some((5, 5)): 20/31 ≈ 0.645
      ├── Some((5, 6)): 15/26 ≈ 0.577
      ├── Some((5, 7)): 25/37 ≈ 0.676
      └── Some((5, 8)): 9/20 ≈ 0.450
    ├── Some((0, 6)): 105/197 ≈ 0.533
      ├── Some((6, 1)): 13/25 ≈ 0.520
      ├── Some((6, 2)): 10/21 ≈ 0.476
      ├── Some((6, 3)): 16/28 ≈ 0.571
      ├── Some((6, 4)): 10/21 ≈ 0.476
      ├── Some((6, 5)): 18/30 ≈ 0.600
      ├── Some((6, 6)): 12/23 ≈ 0.522
      ├── Some((6, 7)): 13/25 ≈ 0.520
      └── Some((6, 8)): 12/23 ≈ 0.522
    ├── Some((0, 7)): 45/106 ≈ 0.425
      ├── Some((7, 0)): 7/14 ≈ 0.500
      ├── Some((7, 1)): 3/9 ≈ 0.333
      ├── Some((7, 2)): 4/11 ≈ 0.364
      ├── Some((7, 3)): 9/16 ≈ 0.562
      ├── Some((7, 4)): 4/11 ≈ 0.364
      ├── Some((7, 5)): 8/15 ≈ 0.533
      ├── Some((7, 6)): 3/9 ≈ 0.333
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 3/9 ≈ 0.333
    └── Some((0, 8)): 107/200 ≈ 0.535
      ├── Some((8, 0)): 8/18 ≈ 0.444
      ├── Some((8, 1)): 20/31 ≈ 0.645
      ├── Some((8, 2)): 13/24 ≈ 0.542
      ├── Some((8, 3)): 7/17 ≈ 0.412
      ├── Some((8, 4)): 15/26 ≈ 0.577
      ├── Some((8, 5)): 11/21 ≈ 0.524
      ├── Some((8, 6)): 4/13 ≈ 0.308
      ├── Some((8, 7)): 22/33 ≈ 0.667
      └── Some((8, 8)): 6/16 ≈ 0.375
  ├── Some((6, 1)): 1226/2285 ≈ 0.537
    ├── Some((1, 0)): 172/307 ≈ 0.560
      ├── Some((0, 0)): 12/26 ≈ 0.462
      ├── Some((0, 1)): 15/29 ≈ 0.517
      ├── Some((0, 2)): 26/42 ≈ 0.619
      ├── Some((0, 3)): 25/41 ≈ 0.610
      ├── Some((0, 4)): 33/50 ≈ 0.660
      ├── Some((0, 5)): 16/31 ≈ 0.516
      ├── Some((0, 6)): 16/31 ≈ 0.516
      ├── Some((0, 7)): 14/28 ≈ 0.500
      └── Some((0, 8)): 14/28 ≈ 0.500
    ├── Some((1, 1)): 167/300 ≈ 0.557
      ├── Some((1, 0)): 22/39 ≈ 0.564
      ├── Some((1, 2)): 39/58 ≈ 0.672
      ├── Some((1, 3)): 24/41 ≈ 0.585
      ├── Some((1, 4)): 18/34 ≈ 0.529
      ├── Some((1, 5)): 17/33 ≈ 0.515
      ├── Some((1, 6)): 11/26 ≈ 0.423
      ├── Some((1, 7)): 14/30 ≈ 0.467
      └── Some((1, 8)): 21/38 ≈ 0.553
    ├── Some((1, 2)): 185/327 ≈ 0.566
      ├── Some((2, 0)): 28/47 ≈ 0.596
      ├── Some((2, 1)): 24/42 ≈ 0.571
      ├── Some((2, 2)): 39/59 ≈ 0.661
      ├── Some((2, 3)): 10/25 ≈ 0.400
      ├── Some((2, 4)): 24/42 ≈ 0.571
      ├── Some((2, 5)): 30/49 ≈ 0.612
      ├── Some((2, 7)): 17/34 ≈ 0.500
      └── Some((2, 8)): 12/28 ≈ 0.429
    ├── Some((1, 3)): 136/254 ≈ 0.535
      ├── Some((3, 0)): 12/25 ≈ 0.480
      ├── Some((3, 1)): 10/22 ≈ 0.455
      ├── Some((3, 2)): 22/36 ≈ 0.611
      ├── Some((3, 3)): 13/26 ≈ 0.500
      ├── Some((3, 4)): 18/32 ≈ 0.562
      ├── Some((3, 5)): 17/30 ≈ 0.567
      ├── Some((3, 6)): 20/34 ≈ 0.588
      ├── Some((3, 7)): 3/13 ≈ 0.231
      └── Some((3, 8)): 21/35 ≈ 0.600
    ├── Some((1, 4)): 120/230 ≈ 0.522
      ├── Some((4, 0)): 7/18 ≈ 0.389
      ├── Some((4, 1)): 20/33 ≈ 0.606
      ├── Some((4, 2)): 15/28 ≈ 0.536
      ├── Some((4, 3)): 4/14 ≈ 0.286
      ├── Some((4, 4)): 17/30 ≈ 0.567
      ├── Some((4, 5)): 27/41 ≈ 0.659
      ├── Some((4, 6)): 13/25 ≈ 0.520
      ├── Some((4, 7)): 8/20 ≈ 0.400
      └── Some((4, 8)): 8/20 ≈ 0.400
    ├── Some((1, 5)): 134/251 ≈ 0.534
      ├── Some((5, 0)): 9/21 ≈ 0.429
      ├── Some((5, 1)): 17/31 ≈ 0.548
      ├── Some((5, 2)): 16/29 ≈ 0.552
      ├── Some((5, 3)): 9/21 ≈ 0.429
      ├── Some((5, 4)): 3/13 ≈ 0.231
      ├── Some((5, 5)): 34/49 ≈ 0.694
      ├── Some((5, 6)): 18/32 ≈ 0.562
      ├── Some((5, 7)): 21/35 ≈ 0.600
      └── Some((5, 8)): 7/19 ≈ 0.368
    ├── Some((1, 6)): 101/201 ≈ 0.502
      ├── Some((6, 0)): 6/17 ≈ 0.353
      ├── Some((6, 2)): 17/30 ≈ 0.567
      ├── Some((6, 3)): 7/18 ≈ 0.389
      ├── Some((6, 4)): 7/19 ≈ 0.368
      ├── Some((6, 5)): 16/29 ≈ 0.552
      ├── Some((6, 6)): 14/27 ≈ 0.519
      ├── Some((6, 7)): 11/23 ≈ 0.478
      └── Some((6, 8)): 23/37 ≈ 0.622
    ├── Some((1, 7)): 91/186 ≈ 0.489
      ├── Some((7, 0)): 9/20 ≈ 0.450
      ├── Some((7, 1)): 5/15 ≈ 0.333
      ├── Some((7, 2)): 16/27 ≈ 0.593
      ├── Some((7, 3)): 15/26 ≈ 0.577
      ├── Some((7, 4)): 14/25 ≈ 0.560
      ├── Some((7, 5)): 12/23 ≈ 0.522
      ├── Some((7, 6)): 13/24 ≈ 0.542
      ├── Some((7, 7)): 6/16 ≈ 0.375
      └── Some((7, 8)): 1/9 ≈ 0.111
    └── Some((1, 8)): 119/228 ≈ 0.522
      ├── Some((8, 0)): 0/9 ≈ 0.000
      ├── Some((8, 1)): 7/18 ≈ 0.389
      ├── Some((8, 2)): 22/35 ≈ 0.629
      ├── Some((8, 3)): 9/21 ≈ 0.429
      ├── Some((8, 4)): 7/18 ≈ 0.389
      ├── Some((8, 5)): 20/33 ≈ 0.606
      ├── Some((8, 6)): 16/29 ≈ 0.552
      ├── Some((8, 7)): 15/28 ≈ 0.536
      └── Some((8, 8)): 23/36 ≈ 0.639
  ├── Some((6, 2)): 757/1477 ≈ 0.513
    ├── Some((2, 0)): 138/250 ≈ 0.552
      ├── Some((0, 0)): 13/25 ≈ 0.520
      ├── Some((0, 1)): 28/42 ≈ 0.667
      ├── Some((0, 2)): 14/26 ≈ 0.538
      ├── Some((0, 3)): 10/22 ≈ 0.455
      ├── Some((0, 4)): 19/32 ≈ 0.594
      ├── Some((0, 5)): 13/25 ≈ 0.520
      ├── Some((0, 6)): 16/29 ≈ 0.552
      ├── Some((0, 7)): 11/23 ≈ 0.478
      └── Some((0, 8)): 13/25 ≈ 0.520
    ├── Some((2, 1)): 101/195 ≈ 0.518
      ├── Some((1, 0)): 15/26 ≈ 0.577
      ├── Some((1, 1)): 4/14 ≈ 0.286
      ├── Some((1, 2)): 11/22 ≈ 0.500
      ├── Some((1, 3)): 7/17 ≈ 0.412
      ├── Some((1, 4)): 15/26 ≈ 0.577
      ├── Some((1, 5)): 1/9 ≈ 0.111
      ├── Some((1, 6)): 18/29 ≈ 0.621
      ├── Some((1, 7)): 13/24 ≈ 0.542
      └── Some((1, 8)): 16/27 ≈ 0.593
    ├── Some((2, 2)): 73/152 ≈ 0.480
      ├── Some((2, 0)): 18/30 ≈ 0.600
      ├── Some((2, 1)): 6/16 ≈ 0.375
      ├── Some((2, 3)): 10/21 ≈ 0.476
      ├── Some((2, 4)): 14/26 ≈ 0.538
      ├── Some((2, 5)): 6/17 ≈ 0.353
      ├── Some((2, 7)): 12/24 ≈ 0.500
      └── Some((2, 8)): 6/17 ≈ 0.353
    ├── Some((2, 3)): 91/180 ≈ 0.506
      ├── Some((3, 0)): 12/22 ≈ 0.545
      ├── Some((3, 1)): 6/15 ≈ 0.400
      ├── Some((3, 2)): 8/18 ≈ 0.444
      ├── Some((3, 3)): 6/15 ≈ 0.400
      ├── Some((3, 4)): 9/19 ≈ 0.474
      ├── Some((3, 5)): 8/18 ≈ 0.444
      ├── Some((3, 6)): 12/22 ≈ 0.545
      ├── Some((3, 7)): 13/23 ≈ 0.565
      └── Some((3, 8)): 16/27 ≈ 0.593
    ├── Some((2, 4)): 61/134 ≈ 0.455
      ├── Some((4, 0)): 1/8 ≈ 0.125
      ├── Some((4, 1)): 4/12 ≈ 0.333
      ├── Some((4, 2)): 8/16 ≈ 0.500
      ├── Some((4, 3)): 12/21 ≈ 0.571
      ├── Some((4, 4)): 9/17 ≈ 0.529
      ├── Some((4, 5)): 6/14 ≈ 0.429
      ├── Some((4, 6)): 4/12 ≈ 0.333
      ├── Some((4, 7)): 11/19 ≈ 0.579
      └── Some((4, 8)): 6/14 ≈ 0.429
    ├── Some((2, 5)): 112/212 ≈ 0.528
      ├── Some((5, 0)): 5/15 ≈ 0.333
      ├── Some((5, 1)): 16/28 ≈ 0.571
      ├── Some((5, 2)): 13/24 ≈ 0.542
      ├── Some((5, 3)): 23/35 ≈ 0.657
      ├── Some((5, 4)): 3/13 ≈ 0.231
      ├── Some((5, 5)): 4/14 ≈ 0.286
      ├── Some((5, 6)): 13/25 ≈ 0.520
      ├── Some((5, 7)): 26/38 ≈ 0.684
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((2, 7)): 139/252 ≈ 0.552
      ├── Some((7, 0)): 8/20 ≈ 0.400
      ├── Some((7, 1)): 15/28 ≈ 0.536
      ├── Some((7, 2)): 7/18 ≈ 0.389
      ├── Some((7, 3)): 14/27 ≈ 0.519
      ├── Some((7, 4)): 16/29 ≈ 0.552
      ├── Some((7, 5)): 4/15 ≈ 0.267
      ├── Some((7, 6)): 18/31 ≈ 0.581
      ├── Some((7, 7)): 33/47 ≈ 0.702
      └── Some((7, 8)): 23/36 ≈ 0.639
    └── Some((2, 8)): 41/101 ≈ 0.406
      ├── Some((8, 0)): 4/11 ≈ 0.364
      ├── Some((8, 1)): 3/9 ≈ 0.333
      ├── Some((8, 2)): 4/11 ≈ 0.364
      ├── Some((8, 3)): 10/17 ≈ 0.588
      ├── Some((8, 4)): 6/13 ≈ 0.462
      ├── Some((8, 5)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 2/8 ≈ 0.250
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((6, 3)): 1180/2207 ≈ 0.535
    ├── Some((3, 0)): 135/251 ≈ 0.538
      ├── Some((0, 0)): 3/13 ≈ 0.231
      ├── Some((0, 1)): 14/27 ≈ 0.519
      ├── Some((0, 2)): 17/30 ≈ 0.567
      ├── Some((0, 3)): 7/19 ≈ 0.368
      ├── Some((0, 4)): 10/22 ≈ 0.455
      ├── Some((0, 5)): 13/26 ≈ 0.500
      ├── Some((0, 6)): 15/28 ≈ 0.536
      ├── Some((0, 7)): 37/52 ≈ 0.712
      └── Some((0, 8)): 19/33 ≈ 0.576
    ├── Some((3, 1)): 188/330 ≈ 0.570
      ├── Some((1, 0)): 24/40 ≈ 0.600
      ├── Some((1, 1)): 31/48 ≈ 0.646
      ├── Some((1, 2)): 11/25 ≈ 0.440
      ├── Some((1, 3)): 17/32 ≈ 0.531
      ├── Some((1, 4)): 20/36 ≈ 0.556
      ├── Some((1, 5)): 22/38 ≈ 0.579
      ├── Some((1, 6)): 14/29 ≈ 0.483
      ├── Some((1, 7)): 30/47 ≈ 0.638
      └── Some((1, 8)): 18/34 ≈ 0.529
    ├── Some((3, 2)): 131/245 ≈ 0.535
      ├── Some((2, 0)): 19/34 ≈ 0.559
      ├── Some((2, 1)): 28/44 ≈ 0.636
      ├── Some((2, 2)): 16/30 ≈ 0.533
      ├── Some((2, 3)): 15/29 ≈ 0.517
      ├── Some((2, 4)): 6/18 ≈ 0.333
      ├── Some((2, 5)): 24/40 ≈ 0.600
      ├── Some((2, 7)): 10/23 ≈ 0.435
      └── Some((2, 8)): 12/26 ≈ 0.462
    ├── Some((3, 3)): 102/202 ≈ 0.505
      ├── Some((3, 0)): 18/32 ≈ 0.562
      ├── Some((3, 1)): 16/29 ≈ 0.552
      ├── Some((3, 2)): 6/17 ≈ 0.353
      ├── Some((3, 4)): 8/20 ≈ 0.400
      ├── Some((3, 5)): 11/23 ≈ 0.478
      ├── Some((3, 6)): 11/23 ≈ 0.478
      ├── Some((3, 7)): 20/34 ≈ 0.588
      └── Some((3, 8)): 11/23 ≈ 0.478
    ├── Some((3, 4)): 120/229 ≈ 0.524
      ├── Some((4, 0)): 18/31 ≈ 0.581
      ├── Some((4, 1)): 8/19 ≈ 0.421
      ├── Some((4, 2)): 16/29 ≈ 0.552
      ├── Some((4, 3)): 11/23 ≈ 0.478
      ├── Some((4, 4)): 15/28 ≈ 0.536
      ├── Some((4, 5)): 5/16 ≈ 0.312
      ├── Some((4, 6)): 14/26 ≈ 0.538
      ├── Some((4, 7)): 24/37 ≈ 0.649
      └── Some((4, 8)): 8/19 ≈ 0.421
    ├── Some((3, 5)): 141/260 ≈ 0.542
      ├── Some((5, 0)): 18/32 ≈ 0.562
      ├── Some((5, 1)): 17/31 ≈ 0.548
      ├── Some((5, 2)): 13/26 ≈ 0.500
      ├── Some((5, 3)): 20/34 ≈ 0.588
      ├── Some((5, 4)): 16/29 ≈ 0.552
      ├── Some((5, 5)): 16/29 ≈ 0.552
      ├── Some((5, 6)): 12/25 ≈ 0.480
      ├── Some((5, 7)): 3/13 ≈ 0.231
      └── Some((5, 8)): 26/40 ≈ 0.650
    ├── Some((3, 6)): 115/221 ≈ 0.520
      ├── Some((6, 0)): 8/20 ≈ 0.400
      ├── Some((6, 1)): 10/23 ≈ 0.435
      ├── Some((6, 2)): 25/40 ≈ 0.625
      ├── Some((6, 4)): 9/21 ≈ 0.429
      ├── Some((6, 5)): 14/27 ≈ 0.519
      ├── Some((6, 6)): 22/36 ≈ 0.611
      ├── Some((6, 7)): 15/28 ≈ 0.536
      └── Some((6, 8)): 12/25 ≈ 0.480
    ├── Some((3, 7)): 119/227 ≈ 0.524
      ├── Some((7, 0)): 18/31 ≈ 0.581
      ├── Some((7, 1)): 22/35 ≈ 0.629
      ├── Some((7, 2)): 14/26 ≈ 0.538
      ├── Some((7, 3)): 10/22 ≈ 0.455
      ├── Some((7, 4)): 7/18 ≈ 0.389
      ├── Some((7, 5)): 5/16 ≈ 0.312
      ├── Some((7, 6)): 8/19 ≈ 0.421
      ├── Some((7, 7)): 25/38 ≈ 0.658
      └── Some((7, 8)): 9/21 ≈ 0.429
    └── Some((3, 8)): 128/241 ≈ 0.531
      ├── Some((8, 0)): 16/29 ≈ 0.552
      ├── Some((8, 1)): 10/22 ≈ 0.455
      ├── Some((8, 2)): 3/13 ≈ 0.231
      ├── Some((8, 3)): 13/26 ≈ 0.500
      ├── Some((8, 4)): 19/32 ≈ 0.594
      ├── Some((8, 5)): 30/44 ≈ 0.682
      ├── Some((8, 6)): 8/20 ≈ 0.400
      ├── Some((8, 7)): 16/29 ≈ 0.552
      └── Some((8, 8)): 12/25 ≈ 0.480
  ├── Some((6, 4)): 1043/1972 ≈ 0.529
    ├── Some((4, 0)): 123/230 ≈ 0.535
      ├── Some((0, 0)): 18/30 ≈ 0.600
      ├── Some((0, 1)): 6/17 ≈ 0.353
      ├── Some((0, 2)): 16/28 ≈ 0.571
      ├── Some((0, 3)): 14/26 ≈ 0.538
      ├── Some((0, 4)): 12/24 ≈ 0.500
      ├── Some((0, 5)): 11/23 ≈ 0.478
      ├── Some((0, 6)): 15/27 ≈ 0.556
      ├── Some((0, 7)): 20/33 ≈ 0.606
      └── Some((0, 8)): 10/21 ≈ 0.476
    ├── Some((4, 1)): 123/230 ≈ 0.535
      ├── Some((1, 0)): 10/22 ≈ 0.455
      ├── Some((1, 1)): 6/17 ≈ 0.353
      ├── Some((1, 2)): 9/20 ≈ 0.450
      ├── Some((1, 3)): 16/28 ≈ 0.571
      ├── Some((1, 4)): 12/24 ≈ 0.500
      ├── Some((1, 5)): 13/25 ≈ 0.520
      ├── Some((1, 6)): 25/38 ≈ 0.658
      ├── Some((1, 7)): 14/26 ≈ 0.538
      └── Some((1, 8)): 17/29 ≈ 0.586
    ├── Some((4, 2)): 129/239 ≈ 0.540
      ├── Some((2, 0)): 19/33 ≈ 0.576
      ├── Some((2, 1)): 16/30 ≈ 0.533
      ├── Some((2, 2)): 19/33 ≈ 0.576
      ├── Some((2, 3)): 7/19 ≈ 0.368
      ├── Some((2, 4)): 7/19 ≈ 0.368
      ├── Some((2, 5)): 17/31 ≈ 0.548
      ├── Some((2, 7)): 22/37 ≈ 0.595
      └── Some((2, 8)): 21/36 ≈ 0.583
    ├── Some((4, 3)): 136/250 ≈ 0.544
      ├── Some((3, 0)): 20/33 ≈ 0.606
      ├── Some((3, 1)): 17/30 ≈ 0.567
      ├── Some((3, 2)): 16/29 ≈ 0.552
      ├── Some((3, 3)): 17/30 ≈ 0.567
      ├── Some((3, 4)): 23/36 ≈ 0.639
      ├── Some((3, 5)): 11/23 ≈ 0.478
      ├── Some((3, 6)): 11/23 ≈ 0.478
      ├── Some((3, 7)): 8/20 ≈ 0.400
      └── Some((3, 8)): 13/25 ≈ 0.520
    ├── Some((4, 4)): 147/266 ≈ 0.553
      ├── Some((4, 0)): 12/26 ≈ 0.462
      ├── Some((4, 1)): 20/35 ≈ 0.571
      ├── Some((4, 2)): 14/28 ≈ 0.500
      ├── Some((4, 3)): 19/34 ≈ 0.559
      ├── Some((4, 5)): 26/42 ≈ 0.619
      ├── Some((4, 6)): 18/33 ≈ 0.545
      ├── Some((4, 7)): 25/40 ≈ 0.625
      └── Some((4, 8)): 13/27 ≈ 0.481
    ├── Some((4, 5)): 91/182 ≈ 0.500
      ├── Some((5, 0)): 7/17 ≈ 0.412
      ├── Some((5, 1)): 10/20 ≈ 0.500
      ├── Some((5, 2)): 16/27 ≈ 0.593
      ├── Some((5, 3)): 11/21 ≈ 0.524
      ├── Some((5, 4)): 9/19 ≈ 0.474
      ├── Some((5, 5)): 15/26 ≈ 0.577
      ├── Some((5, 6)): 1/9 ≈ 0.111
      ├── Some((5, 7)): 10/20 ≈ 0.500
      └── Some((5, 8)): 11/22 ≈ 0.500
    ├── Some((4, 6)): 53/123 ≈ 0.431
      ├── Some((6, 0)): 6/15 ≈ 0.400
      ├── Some((6, 1)): 10/19 ≈ 0.526
      ├── Some((6, 2)): 1/8 ≈ 0.125
      ├── Some((6, 3)): 4/12 ≈ 0.333
      ├── Some((6, 5)): 12/21 ≈ 0.571
      ├── Some((6, 6)): 5/14 ≈ 0.357
      ├── Some((6, 7)): 5/14 ≈ 0.357
      └── Some((6, 8)): 10/19 ≈ 0.526
    ├── Some((4, 7)): 107/206 ≈ 0.519
      ├── Some((7, 0)): 13/24 ≈ 0.542
      ├── Some((7, 1)): 14/26 ≈ 0.538
      ├── Some((7, 2)): 24/36 ≈ 0.667
      ├── Some((7, 3)): 3/12 ≈ 0.250
      ├── Some((7, 4)): 10/21 ≈ 0.476
      ├── Some((7, 5)): 8/19 ≈ 0.421
      ├── Some((7, 6)): 22/34 ≈ 0.647
      ├── Some((7, 7)): 7/18 ≈ 0.389
      └── Some((7, 8)): 5/15 ≈ 0.333
    └── Some((4, 8)): 133/245 ≈ 0.543
      ├── Some((8, 0)): 18/31 ≈ 0.581
      ├── Some((8, 1)): 19/32 ≈ 0.594
      ├── Some((8, 2)): 17/30 ≈ 0.567
      ├── Some((8, 3)): 16/29 ≈ 0.552
      ├── Some((8, 4)): 11/23 ≈ 0.478
      ├── Some((8, 5)): 16/29 ≈ 0.552
      ├── Some((8, 6)): 15/27 ≈ 0.556
      ├── Some((8, 7)): 7/18 ≈ 0.389
      └── Some((8, 8)): 13/25 ≈ 0.520
  ├── Some((6, 5)): 924/1767 ≈ 0.523
    ├── Some((5, 0)): 98/190 ≈ 0.516
      ├── Some((0, 0)): 6/16 ≈ 0.375
      ├── Some((0, 1)): 9/19 ≈ 0.474
      ├── Some((0, 2)): 7/17 ≈ 0.412
      ├── Some((0, 3)): 20/31 ≈ 0.645
      ├── Some((0, 4)): 20/31 ≈ 0.645
      ├── Some((0, 5)): 17/28 ≈ 0.607
      ├── Some((0, 6)): 4/13 ≈ 0.308
      ├── Some((0, 7)): 10/20 ≈ 0.500
      └── Some((0, 8)): 5/14 ≈ 0.357
    ├── Some((5, 1)): 119/221 ≈ 0.538
      ├── Some((1, 0)): 12/23 ≈ 0.522
      ├── Some((1, 1)): 27/40 ≈ 0.675
      ├── Some((1, 2)): 10/21 ≈ 0.476
      ├── Some((1, 3)): 16/28 ≈ 0.571
      ├── Some((1, 4)): 25/38 ≈ 0.658
      ├── Some((1, 5)): 6/16 ≈ 0.375
      ├── Some((1, 6)): 10/21 ≈ 0.476
      ├── Some((1, 7)): 5/15 ≈ 0.333
      └── Some((1, 8)): 7/18 ≈ 0.389
    ├── Some((5, 2)): 87/173 ≈ 0.503
      ├── Some((2, 0)): 2/11 ≈ 0.182
      ├── Some((2, 1)): 23/35 ≈ 0.657
      ├── Some((2, 2)): 12/23 ≈ 0.522
      ├── Some((2, 3)): 15/26 ≈ 0.577
      ├── Some((2, 4)): 14/25 ≈ 0.560
      ├── Some((2, 5)): 4/14 ≈ 0.286
      ├── Some((2, 7)): 12/23 ≈ 0.522
      └── Some((2, 8)): 5/15 ≈ 0.333
    ├── Some((5, 3)): 99/191 ≈ 0.518
      ├── Some((3, 0)): 5/14 ≈ 0.357
      ├── Some((3, 1)): 9/19 ≈ 0.474
      ├── Some((3, 2)): 6/16 ≈ 0.375
      ├── Some((3, 3)): 12/22 ≈ 0.545
      ├── Some((3, 4)): 17/28 ≈ 0.607
      ├── Some((3, 5)): 16/27 ≈ 0.593
      ├── Some((3, 6)): 5/14 ≈ 0.357
      ├── Some((3, 7)): 13/24 ≈ 0.542
      └── Some((3, 8)): 15/26 ≈ 0.577
    ├── Some((5, 4)): 84/168 ≈ 0.500
      ├── Some((4, 0)): 10/20 ≈ 0.500
      ├── Some((4, 1)): 8/17 ≈ 0.471
      ├── Some((4, 2)): 2/10 ≈ 0.200
      ├── Some((4, 3)): 7/16 ≈ 0.438
      ├── Some((4, 4)): 5/14 ≈ 0.357
      ├── Some((4, 5)): 12/22 ≈ 0.545
      ├── Some((4, 6)): 8/17 ≈ 0.471
      ├── Some((4, 7)): 25/35 ≈ 0.714
      └── Some((4, 8)): 7/16 ≈ 0.438
    ├── Some((5, 5)): 88/175 ≈ 0.503
      ├── Some((5, 0)): 5/15 ≈ 0.333
      ├── Some((5, 1)): 19/31 ≈ 0.613
      ├── Some((5, 2)): 20/32 ≈ 0.625
      ├── Some((5, 3)): 14/25 ≈ 0.560
      ├── Some((5, 4)): 5/15 ≈ 0.333
      ├── Some((5, 6)): 9/19 ≈ 0.474
      ├── Some((5, 7)): 9/20 ≈ 0.450
      └── Some((5, 8)): 7/17 ≈ 0.412
    ├── Some((5, 6)): 145/259 ≈ 0.560
      ├── Some((6, 0)): 20/35 ≈ 0.571
      ├── Some((6, 1)): 21/36 ≈ 0.583
      ├── Some((6, 2)): 15/29 ≈ 0.517
      ├── Some((6, 3)): 12/25 ≈ 0.480
      ├── Some((6, 4)): 28/43 ≈ 0.651
      ├── Some((6, 6)): 18/32 ≈ 0.562
      ├── Some((6, 7)): 15/29 ≈ 0.517
      └── Some((6, 8)): 15/29 ≈ 0.517
    ├── Some((5, 7)): 74/153 ≈ 0.484
      ├── Some((7, 0)): 15/24 ≈ 0.625
      ├── Some((7, 1)): 9/18 ≈ 0.500
      ├── Some((7, 2)): 9/18 ≈ 0.500
      ├── Some((7, 3)): 4/12 ≈ 0.333
      ├── Some((7, 4)): 4/12 ≈ 0.333
      ├── Some((7, 5)): 17/26 ≈ 0.654
      ├── Some((7, 6)): 9/18 ≈ 0.500
      ├── Some((7, 7)): 2/10 ≈ 0.200
      └── Some((7, 8)): 5/14 ≈ 0.357
    └── Some((5, 8)): 129/236 ≈ 0.547
      ├── Some((8, 0)): 9/20 ≈ 0.450
      ├── Some((8, 1)): 16/28 ≈ 0.571
      ├── Some((8, 2)): 23/36 ≈ 0.639
      ├── Some((8, 3)): 8/19 ≈ 0.421
      ├── Some((8, 4)): 11/23 ≈ 0.478
      ├── Some((8, 5)): 15/27 ≈ 0.556
      ├── Some((8, 6)): 10/21 ≈ 0.476
      ├── Some((8, 7)): 17/29 ≈ 0.586
      └── Some((8, 8)): 19/32 ≈ 0.594
  ├── Some((6, 6)): 1061/2003 ≈ 0.530
    ├── Some((6, 0)): 125/239 ≈ 0.523
      ├── Some((0, 0)): 17/30 ≈ 0.567
      ├── Some((0, 1)): 9/21 ≈ 0.429
      ├── Some((0, 2)): 10/22 ≈ 0.455
      ├── Some((0, 3)): 16/29 ≈ 0.552
      ├── Some((0, 4)): 4/15 ≈ 0.267
      ├── Some((0, 5)): 16/29 ≈ 0.552
      ├── Some((0, 6)): 25/39 ≈ 0.641
      ├── Some((0, 7)): 19/32 ≈ 0.594
      └── Some((0, 8)): 9/21 ≈ 0.429
    ├── Some((6, 1)): 154/283 ≈ 0.544
      ├── Some((1, 0)): 15/29 ≈ 0.517
      ├── Some((1, 1)): 16/30 ≈ 0.533
      ├── Some((1, 2)): 21/36 ≈ 0.583
      ├── Some((1, 3)): 12/26 ≈ 0.462
      ├── Some((1, 4)): 31/47 ≈ 0.660
      ├── Some((1, 5)): 8/21 ≈ 0.381
      ├── Some((1, 6)): 20/35 ≈ 0.571
      ├── Some((1, 7)): 15/29 ≈ 0.517
      └── Some((1, 8)): 15/29 ≈ 0.517
    ├── Some((6, 2)): 133/251 ≈ 0.530
      ├── Some((2, 0)): 14/28 ≈ 0.500
      ├── Some((2, 1)): 21/37 ≈ 0.568
      ├── Some((2, 2)): 17/32 ≈ 0.531
      ├── Some((2, 3)): 6/18 ≈ 0.333
      ├── Some((2, 4)): 16/31 ≈ 0.516
      ├── Some((2, 5)): 22/38 ≈ 0.579
      ├── Some((2, 7)): 17/32 ≈ 0.531
      └── Some((2, 8)): 19/34 ≈ 0.559
    ├── Some((6, 3)): 156/286 ≈ 0.545
      ├── Some((3, 0)): 29/45 ≈ 0.644
      ├── Some((3, 1)): 10/23 ≈ 0.435
      ├── Some((3, 2)): 14/28 ≈ 0.500
      ├── Some((3, 3)): 25/41 ≈ 0.610
      ├── Some((3, 4)): 12/26 ≈ 0.462
      ├── Some((3, 5)): 22/37 ≈ 0.595
      ├── Some((3, 6)): 4/16 ≈ 0.250
      ├── Some((3, 7)): 21/36 ≈ 0.583
      └── Some((3, 8)): 18/33 ≈ 0.545
    ├── Some((6, 4)): 65/146 ≈ 0.445
      ├── Some((4, 0)): 4/12 ≈ 0.333
      ├── Some((4, 1)): 11/20 ≈ 0.550
      ├── Some((4, 2)): 3/11 ≈ 0.273
      ├── Some((4, 3)): 13/23 ≈ 0.565
      ├── Some((4, 4)): 7/16 ≈ 0.438
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 6)): 4/13 ≈ 0.308
      ├── Some((4, 7)): 5/14 ≈ 0.357
      └── Some((4, 8)): 10/19 ≈ 0.526
    ├── Some((6, 5)): 103/206 ≈ 0.500
      ├── Some((5, 0)): 13/25 ≈ 0.520
      ├── Some((5, 1)): 7/18 ≈ 0.389
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 12/24 ≈ 0.500
      ├── Some((5, 4)): 5/15 ≈ 0.333
      ├── Some((5, 5)): 16/28 ≈ 0.571
      ├── Some((5, 6)): 11/23 ≈ 0.478
      ├── Some((5, 7)): 8/19 ≈ 0.421
      └── Some((5, 8)): 19/31 ≈ 0.613
    ├── Some((6, 7)): 159/290 ≈ 0.548
      ├── Some((7, 0)): 25/41 ≈ 0.610
      ├── Some((7, 1)): 16/30 ≈ 0.533
      ├── Some((7, 2)): 3/14 ≈ 0.214
      ├── Some((7, 3)): 14/28 ≈ 0.500
      ├── Some((7, 4)): 19/34 ≈ 0.559
      ├── Some((7, 5)): 21/36 ≈ 0.583
      ├── Some((7, 6)): 25/41 ≈ 0.610
      ├── Some((7, 7)): 17/32 ≈ 0.531
      └── Some((7, 8)): 18/33 ≈ 0.545
    └── Some((6, 8)): 166/301 ≈ 0.551
      ├── Some((8, 0)): 9/22 ≈ 0.409
      ├── Some((8, 1)): 9/22 ≈ 0.409
      ├── Some((8, 2)): 33/50 ≈ 0.660
      ├── Some((8, 3)): 8/21 ≈ 0.381
      ├── Some((8, 4)): 23/39 ≈ 0.590
      ├── Some((8, 5)): 15/30 ≈ 0.500
      ├── Some((8, 6)): 14/28 ≈ 0.500
      ├── Some((8, 7)): 32/49 ≈ 0.653
      └── Some((8, 8)): 23/39 ≈ 0.590
  ├── Some((6, 7)): 1182/2210 ≈ 0.535
    ├── Some((7, 0)): 155/282 ≈ 0.550
      ├── Some((0, 0)): 5/17 ≈ 0.294
      ├── Some((0, 1)): 23/38 ≈ 0.605
      ├── Some((0, 2)): 18/33 ≈ 0.545
      ├── Some((0, 3)): 32/48 ≈ 0.667
      ├── Some((0, 4)): 14/28 ≈ 0.500
      ├── Some((0, 5)): 14/28 ≈ 0.500
      ├── Some((0, 6)): 33/49 ≈ 0.673
      ├── Some((0, 7)): 11/24 ≈ 0.458
      └── Some((0, 8)): 4/16 ≈ 0.250
    ├── Some((7, 1)): 153/279 ≈ 0.548
      ├── Some((1, 0)): 37/53 ≈ 0.698
      ├── Some((1, 1)): 15/29 ≈ 0.517
      ├── Some((1, 2)): 13/27 ≈ 0.481
      ├── Some((1, 3)): 20/35 ≈ 0.571
      ├── Some((1, 4)): 30/46 ≈ 0.652
      ├── Some((1, 5)): 6/18 ≈ 0.333
      ├── Some((1, 6)): 4/15 ≈ 0.267
      ├── Some((1, 7)): 13/27 ≈ 0.481
      └── Some((1, 8)): 14/28 ≈ 0.500
    ├── Some((7, 2)): 75/160 ≈ 0.469
      ├── Some((2, 0)): 12/23 ≈ 0.522
      ├── Some((2, 1)): 8/19 ≈ 0.421
      ├── Some((2, 2)): 12/23 ≈ 0.522
      ├── Some((2, 3)): 3/12 ≈ 0.250
      ├── Some((2, 4)): 10/21 ≈ 0.476
      ├── Some((2, 5)): 1/9 ≈ 0.111
      ├── Some((2, 7)): 12/23 ≈ 0.522
      └── Some((2, 8)): 17/29 ≈ 0.586
    ├── Some((7, 3)): 115/222 ≈ 0.518
      ├── Some((3, 0)): 4/14 ≈ 0.286
      ├── Some((3, 1)): 17/29 ≈ 0.586
      ├── Some((3, 2)): 11/23 ≈ 0.478
      ├── Some((3, 3)): 22/35 ≈ 0.629
      ├── Some((3, 4)): 12/24 ≈ 0.500
      ├── Some((3, 5)): 10/21 ≈ 0.476
      ├── Some((3, 6)): 14/26 ≈ 0.538
      ├── Some((3, 7)): 10/22 ≈ 0.455
      └── Some((3, 8)): 15/27 ≈ 0.556
    ├── Some((7, 4)): 107/210 ≈ 0.510
      ├── Some((4, 0)): 15/27 ≈ 0.556
      ├── Some((4, 1)): 27/40 ≈ 0.675
      ├── Some((4, 2)): 14/26 ≈ 0.538
      ├── Some((4, 3)): 8/19 ≈ 0.421
      ├── Some((4, 4)): 2/11 ≈ 0.182
      ├── Some((4, 5)): 13/25 ≈ 0.520
      ├── Some((4, 6)): 7/18 ≈ 0.389
      ├── Some((4, 7)): 10/21 ≈ 0.476
      └── Some((4, 8)): 10/22 ≈ 0.455
    ├── Some((7, 5)): 241/408 ≈ 0.591
      ├── Some((5, 0)): 50/71 ≈ 0.704
      ├── Some((5, 1)): 26/45 ≈ 0.578
      ├── Some((5, 2)): 17/34 ≈ 0.500
      ├── Some((5, 3)): 16/33 ≈ 0.485
      ├── Some((5, 4)): 47/68 ≈ 0.691
      ├── Some((5, 5)): 19/36 ≈ 0.528
      ├── Some((5, 6)): 24/42 ≈ 0.571
      ├── Some((5, 7)): 19/37 ≈ 0.514
      └── Some((5, 8)): 23/41 ≈ 0.561
    ├── Some((7, 6)): 115/222 ≈ 0.518
      ├── Some((6, 0)): 14/27 ≈ 0.519
      ├── Some((6, 1)): 11/24 ≈ 0.458
      ├── Some((6, 2)): 11/24 ≈ 0.458
      ├── Some((6, 3)): 11/24 ≈ 0.458
      ├── Some((6, 4)): 14/27 ≈ 0.519
      ├── Some((6, 5)): 16/30 ≈ 0.533
      ├── Some((6, 6)): 23/37 ≈ 0.622
      └── Some((6, 8)): 15/28 ≈ 0.536
    ├── Some((7, 7)): 164/296 ≈ 0.554
      ├── Some((7, 0)): 21/38 ≈ 0.553
      ├── Some((7, 1)): 35/55 ≈ 0.636
      ├── Some((7, 2)): 34/53 ≈ 0.642
      ├── Some((7, 3)): 32/51 ≈ 0.627
      ├── Some((7, 4)): 1/12 ≈ 0.083
      ├── Some((7, 5)): 6/20 ≈ 0.300
      ├── Some((7, 6)): 8/22 ≈ 0.364
      └── Some((7, 8)): 26/44 ≈ 0.591
    └── Some((7, 8)): 56/130 ≈ 0.431
      ├── Some((8, 0)): 2/9 ≈ 0.222
      ├── Some((8, 1)): 2/9 ≈ 0.222
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 8/17 ≈ 0.471
      ├── Some((8, 4)): 7/15 ≈ 0.467
      ├── Some((8, 5)): 5/13 ≈ 0.385
      ├── Some((8, 6)): 5/13 ≈ 0.385
      ├── Some((8, 7)): 7/15 ≈ 0.467
      └── Some((8, 8)): 11/20 ≈ 0.550
  └── Some((6, 8)): 904/1732 ≈ 0.522
    ├── Some((8, 0)): 96/187 ≈ 0.513
      ├── Some((0, 0)): 20/31 ≈ 0.645
      ├── Some((0, 1)): 5/14 ≈ 0.357
      ├── Some((0, 2)): 9/19 ≈ 0.474
      ├── Some((0, 3)): 11/21 ≈ 0.524
      ├── Some((0, 4)): 9/19 ≈ 0.474
      ├── Some((0, 5)): 14/25 ≈ 0.560
      ├── Some((0, 6)): 5/14 ≈ 0.357
      ├── Some((0, 7)): 7/17 ≈ 0.412
      └── Some((0, 8)): 15/26 ≈ 0.577
    ├── Some((8, 1)): 185/316 ≈ 0.585
      ├── Some((1, 0)): 33/49 ≈ 0.673
      ├── Some((1, 1)): 24/39 ≈ 0.615
      ├── Some((1, 2)): 29/45 ≈ 0.644
      ├── Some((1, 3)): 16/30 ≈ 0.533
      ├── Some((1, 4)): 15/29 ≈ 0.517
      ├── Some((1, 5)): 12/25 ≈ 0.480
      ├── Some((1, 6)): 16/30 ≈ 0.533
      ├── Some((1, 7)): 14/28 ≈ 0.500
      └── Some((1, 8)): 25/40 ≈ 0.625
    ├── Some((8, 2)): 121/224 ≈ 0.540
      ├── Some((2, 0)): 24/38 ≈ 0.632
      ├── Some((2, 1)): 16/29 ≈ 0.552
      ├── Some((2, 2)): 7/19 ≈ 0.368
      ├── Some((2, 3)): 11/23 ≈ 0.478
      ├── Some((2, 4)): 21/35 ≈ 0.600
      ├── Some((2, 5)): 13/26 ≈ 0.500
      ├── Some((2, 7)): 19/32 ≈ 0.594
      └── Some((2, 8)): 9/21 ≈ 0.429
    ├── Some((8, 3)): 120/222 ≈ 0.541
      ├── Some((3, 0)): 8/19 ≈ 0.421
      ├── Some((3, 1)): 13/24 ≈ 0.542
      ├── Some((3, 2)): 13/24 ≈ 0.542
      ├── Some((3, 3)): 4/14 ≈ 0.286
      ├── Some((3, 4)): 17/29 ≈ 0.586
      ├── Some((3, 5)): 18/30 ≈ 0.600
      ├── Some((3, 6)): 21/33 ≈ 0.636
      ├── Some((3, 7)): 15/27 ≈ 0.556
      └── Some((3, 8)): 10/21 ≈ 0.476
    ├── Some((8, 4)): 75/155 ≈ 0.484
      ├── Some((4, 0)): 10/19 ≈ 0.526
      ├── Some((4, 1)): 9/18 ≈ 0.500
      ├── Some((4, 2)): 5/14 ≈ 0.357
      ├── Some((4, 3)): 11/20 ≈ 0.550
      ├── Some((4, 4)): 1/9 ≈ 0.111
      ├── Some((4, 5)): 15/24 ≈ 0.625
      ├── Some((4, 6)): 3/11 ≈ 0.273
      ├── Some((4, 7)): 13/22 ≈ 0.591
      └── Some((4, 8)): 8/17 ≈ 0.471
    ├── Some((8, 5)): 88/175 ≈ 0.503
      ├── Some((5, 0)): 10/20 ≈ 0.500
      ├── Some((5, 1)): 10/20 ≈ 0.500
      ├── Some((5, 2)): 17/27 ≈ 0.630
      ├── Some((5, 3)): 7/16 ≈ 0.438
      ├── Some((5, 4)): 4/13 ≈ 0.308
      ├── Some((5, 5)): 14/24 ≈ 0.583
      ├── Some((5, 6)): 5/14 ≈ 0.357
      ├── Some((5, 7)): 8/17 ≈ 0.471
      └── Some((5, 8)): 13/23 ≈ 0.565
    ├── Some((8, 6)): 37/95 ≈ 0.389
      ├── Some((6, 0)): 2/9 ≈ 0.222
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 2/9 ≈ 0.222
      ├── Some((6, 3)): 12/20 ≈ 0.600
      ├── Some((6, 4)): 2/9 ≈ 0.222
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 5/12 ≈ 0.417
      └── Some((6, 7)): 3/10 ≈ 0.300
    ├── Some((8, 7)): 94/184 ≈ 0.511
      ├── Some((7, 0)): 21/32 ≈ 0.656
      ├── Some((7, 1)): 16/26 ≈ 0.615
      ├── Some((7, 2)): 9/19 ≈ 0.474
      ├── Some((7, 3)): 3/12 ≈ 0.250
      ├── Some((7, 4)): 8/18 ≈ 0.444
      ├── Some((7, 5)): 3/12 ≈ 0.250
      ├── Some((7, 6)): 6/15 ≈ 0.400
      ├── Some((7, 7)): 12/22 ≈ 0.545
      └── Some((7, 8)): 16/27 ≈ 0.593
    └── Some((8, 8)): 87/173 ≈ 0.503
      ├── Some((8, 0)): 14/25 ≈ 0.560
      ├── Some((8, 1)): 11/22 ≈ 0.500
      ├── Some((8, 2)): 22/34 ≈ 0.647
      ├── Some((8, 3)): 3/12 ≈ 0.250
      ├── Some((8, 4)): 12/23 ≈ 0.522
      ├── Some((8, 5)): 6/16 ≈ 0.375
      ├── Some((8, 6)): 12/23 ≈ 0.522
      └── Some((8, 7)): 7/17 ≈ 0.412
├── Some((2, 7)): 10369/19552 ≈ 0.530
  ├── Some((7, 0)): 904/1747 ≈ 0.517
    ├── Some((0, 0)): 58/129 ≈ 0.450
      ├── Some((0, 1)): 11/20 ≈ 0.550
      ├── Some((0, 2)): 5/14 ≈ 0.357
      ├── Some((0, 3)): 6/15 ≈ 0.400
      ├── Some((0, 4)): 10/19 ≈ 0.526
      ├── Some((0, 5)): 0/7 ≈ 0.000
      ├── Some((0, 6)): 7/16 ≈ 0.438
      ├── Some((0, 7)): 10/19 ≈ 0.526
      └── Some((0, 8)): 9/18 ≈ 0.500
    ├── Some((0, 1)): 128/236 ≈ 0.542
      ├── Some((1, 0)): 21/33 ≈ 0.636
      ├── Some((1, 1)): 13/25 ≈ 0.520
      ├── Some((1, 2)): 13/25 ≈ 0.520
      ├── Some((1, 3)): 13/25 ≈ 0.520
      ├── Some((1, 4)): 15/27 ≈ 0.556
      ├── Some((1, 5)): 11/23 ≈ 0.478
      ├── Some((1, 6)): 21/34 ≈ 0.618
      ├── Some((1, 7)): 11/23 ≈ 0.478
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((0, 2)): 78/161 ≈ 0.484
      ├── Some((2, 0)): 6/16 ≈ 0.375
      ├── Some((2, 1)): 8/18 ≈ 0.444
      ├── Some((2, 2)): 7/17 ≈ 0.412
      ├── Some((2, 3)): 4/13 ≈ 0.308
      ├── Some((2, 4)): 9/20 ≈ 0.450
      ├── Some((2, 5)): 21/33 ≈ 0.636
      ├── Some((2, 6)): 16/27 ≈ 0.593
      └── Some((2, 8)): 6/16 ≈ 0.375
    ├── Some((0, 3)): 81/165 ≈ 0.491
      ├── Some((3, 0)): 15/25 ≈ 0.600
      ├── Some((3, 1)): 10/19 ≈ 0.526
      ├── Some((3, 2)): 7/16 ≈ 0.438
      ├── Some((3, 3)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 9/18 ≈ 0.500
      ├── Some((3, 5)): 15/25 ≈ 0.600
      ├── Some((3, 6)): 4/13 ≈ 0.308
      ├── Some((3, 7)): 9/18 ≈ 0.500
      └── Some((3, 8)): 4/13 ≈ 0.308
    ├── Some((0, 4)): 176/306 ≈ 0.575
      ├── Some((4, 0)): 15/29 ≈ 0.517
      ├── Some((4, 1)): 18/33 ≈ 0.545
      ├── Some((4, 2)): 9/22 ≈ 0.409
      ├── Some((4, 3)): 4/15 ≈ 0.267
      ├── Some((4, 4)): 20/35 ≈ 0.571
      ├── Some((4, 5)): 16/30 ≈ 0.533
      ├── Some((4, 6)): 18/33 ≈ 0.545
      ├── Some((4, 7)): 35/51 ≈ 0.686
      └── Some((4, 8)): 41/57 ≈ 0.719
    ├── Some((0, 5)): 88/176 ≈ 0.500
      ├── Some((5, 0)): 17/27 ≈ 0.630
      ├── Some((5, 1)): 0/8 ≈ 0.000
      ├── Some((5, 2)): 6/15 ≈ 0.400
      ├── Some((5, 3)): 4/13 ≈ 0.308
      ├── Some((5, 4)): 11/21 ≈ 0.524
      ├── Some((5, 5)): 16/26 ≈ 0.615
      ├── Some((5, 6)): 9/19 ≈ 0.474
      ├── Some((5, 7)): 18/29 ≈ 0.621
      └── Some((5, 8)): 7/17 ≈ 0.412
    ├── Some((0, 6)): 129/237 ≈ 0.544
      ├── Some((6, 0)): 6/17 ≈ 0.353
      ├── Some((6, 1)): 26/39 ≈ 0.667
      ├── Some((6, 2)): 11/23 ≈ 0.478
      ├── Some((6, 3)): 17/29 ≈ 0.586
      ├── Some((6, 4)): 13/25 ≈ 0.520
      ├── Some((6, 5)): 11/23 ≈ 0.478
      ├── Some((6, 6)): 11/23 ≈ 0.478
      ├── Some((6, 7)): 8/19 ≈ 0.421
      └── Some((6, 8)): 25/38 ≈ 0.658
    ├── Some((0, 7)): 87/175 ≈ 0.497
      ├── Some((7, 1)): 18/29 ≈ 0.621
      ├── Some((7, 2)): 8/18 ≈ 0.444
      ├── Some((7, 3)): 9/20 ≈ 0.450
      ├── Some((7, 4)): 9/20 ≈ 0.450
      ├── Some((7, 5)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 11/22 ≈ 0.500
      ├── Some((7, 7)): 11/22 ≈ 0.500
      └── Some((7, 8)): 11/22 ≈ 0.500
    └── Some((0, 8)): 78/161 ≈ 0.484
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 5/14 ≈ 0.357
      ├── Some((8, 3)): 7/16 ≈ 0.438
      ├── Some((8, 4)): 6/15 ≈ 0.400
      ├── Some((8, 5)): 4/12 ≈ 0.333
      ├── Some((8, 6)): 11/20 ≈ 0.550
      ├── Some((8, 7)): 12/22 ≈ 0.545
      └── Some((8, 8)): 17/27 ≈ 0.630
  ├── Some((7, 1)): 697/1385 ≈ 0.503
    ├── Some((1, 0)): 85/165 ≈ 0.515
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 7/15 ≈ 0.467
      ├── Some((0, 2)): 12/21 ≈ 0.571
      ├── Some((0, 3)): 10/19 ≈ 0.526
      ├── Some((0, 4)): 10/19 ≈ 0.526
      ├── Some((0, 5)): 11/20 ≈ 0.550
      ├── Some((0, 6)): 13/22 ≈ 0.591
      ├── Some((0, 7)): 7/16 ≈ 0.438
      └── Some((0, 8)): 8/17 ≈ 0.471
    ├── Some((1, 1)): 57/123 ≈ 0.463
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 2)): 2/9 ≈ 0.222
      ├── Some((1, 3)): 2/9 ≈ 0.222
      ├── Some((1, 4)): 12/21 ≈ 0.571
      ├── Some((1, 5)): 8/17 ≈ 0.471
      ├── Some((1, 6)): 10/19 ≈ 0.526
      ├── Some((1, 7)): 2/9 ≈ 0.222
      └── Some((1, 8)): 10/19 ≈ 0.526
    ├── Some((1, 2)): 86/167 ≈ 0.515
      ├── Some((2, 0)): 14/25 ≈ 0.560
      ├── Some((2, 1)): 10/20 ≈ 0.500
      ├── Some((2, 2)): 10/20 ≈ 0.500
      ├── Some((2, 3)): 11/21 ≈ 0.524
      ├── Some((2, 4)): 4/13 ≈ 0.308
      ├── Some((2, 5)): 12/22 ≈ 0.545
      ├── Some((2, 6)): 15/26 ≈ 0.577
      └── Some((2, 8)): 9/19 ≈ 0.474
    ├── Some((1, 3)): 108/199 ≈ 0.543
      ├── Some((3, 0)): 27/38 ≈ 0.711
      ├── Some((3, 1)): 9/19 ≈ 0.474
      ├── Some((3, 2)): 10/20 ≈ 0.500
      ├── Some((3, 3)): 19/30 ≈ 0.633
      ├── Some((3, 4)): 6/16 ≈ 0.375
      ├── Some((3, 5)): 11/21 ≈ 0.524
      ├── Some((3, 6)): 3/12 ≈ 0.250
      ├── Some((3, 7)): 3/12 ≈ 0.250
      └── Some((3, 8)): 19/30 ≈ 0.633
    ├── Some((1, 4)): 52/115 ≈ 0.452
      ├── Some((4, 0)): 4/11 ≈ 0.364
      ├── Some((4, 1)): 2/9 ≈ 0.222
      ├── Some((4, 2)): 0/6 ≈ 0.000
      ├── Some((4, 3)): 17/24 ≈ 0.708
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 4/11 ≈ 0.364
      ├── Some((4, 7)): 10/18 ≈ 0.556
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((1, 5)): 73/148 ≈ 0.493
      ├── Some((5, 0)): 10/19 ≈ 0.526
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 13/22 ≈ 0.591
      ├── Some((5, 4)): 10/19 ≈ 0.526
      ├── Some((5, 5)): 4/12 ≈ 0.333
      ├── Some((5, 6)): 9/17 ≈ 0.529
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((1, 6)): 85/165 ≈ 0.515
      ├── Some((6, 0)): 7/16 ≈ 0.438
      ├── Some((6, 1)): 13/22 ≈ 0.591
      ├── Some((6, 2)): 8/17 ≈ 0.471
      ├── Some((6, 3)): 5/13 ≈ 0.385
      ├── Some((6, 4)): 7/16 ≈ 0.438
      ├── Some((6, 5)): 6/14 ≈ 0.429
      ├── Some((6, 6)): 19/28 ≈ 0.679
      ├── Some((6, 7)): 8/17 ≈ 0.471
      └── Some((6, 8)): 12/21 ≈ 0.571
    ├── Some((1, 7)): 67/138 ≈ 0.486
      ├── Some((7, 0)): 3/11 ≈ 0.273
      ├── Some((7, 2)): 6/15 ≈ 0.400
      ├── Some((7, 3)): 11/20 ≈ 0.550
      ├── Some((7, 4)): 14/24 ≈ 0.583
      ├── Some((7, 5)): 14/24 ≈ 0.583
      ├── Some((7, 6)): 0/7 ≈ 0.000
      ├── Some((7, 7)): 7/16 ≈ 0.438
      └── Some((7, 8)): 11/20 ≈ 0.550
    └── Some((1, 8)): 84/164 ≈ 0.512
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 1)): 11/20 ≈ 0.550
      ├── Some((8, 2)): 15/24 ≈ 0.625
      ├── Some((8, 3)): 10/19 ≈ 0.526
      ├── Some((8, 4)): 4/12 ≈ 0.333
      ├── Some((8, 5)): 7/16 ≈ 0.438
      ├── Some((8, 6)): 3/11 ≈ 0.273
      ├── Some((8, 7)): 17/27 ≈ 0.630
      └── Some((8, 8)): 6/15 ≈ 0.400
  ├── Some((7, 2)): 1358/2531 ≈ 0.537
    ├── Some((2, 0)): 128/253 ≈ 0.506
      ├── Some((0, 0)): 14/28 ≈ 0.500
      ├── Some((0, 1)): 18/33 ≈ 0.545
      ├── Some((0, 2)): 16/30 ≈ 0.533
      ├── Some((0, 3)): 1/11 ≈ 0.091
      ├── Some((0, 4)): 6/18 ≈ 0.333
      ├── Some((0, 5)): 15/29 ≈ 0.517
      ├── Some((0, 6)): 22/37 ≈ 0.595
      ├── Some((0, 7)): 12/26 ≈ 0.462
      └── Some((0, 8)): 24/40 ≈ 0.600
    ├── Some((2, 1)): 196/358 ≈ 0.547
      ├── Some((1, 0)): 18/35 ≈ 0.514
      ├── Some((1, 1)): 25/44 ≈ 0.568
      ├── Some((1, 2)): 23/41 ≈ 0.561
      ├── Some((1, 3)): 20/38 ≈ 0.526
      ├── Some((1, 4)): 37/58 ≈ 0.638
      ├── Some((1, 5)): 14/30 ≈ 0.467
      ├── Some((1, 6)): 32/52 ≈ 0.615
      ├── Some((1, 7)): 11/27 ≈ 0.407
      └── Some((1, 8)): 15/32 ≈ 0.469
    ├── Some((2, 2)): 145/280 ≈ 0.518
      ├── Some((2, 0)): 21/41 ≈ 0.512
      ├── Some((2, 1)): 38/61 ≈ 0.623
      ├── Some((2, 3)): 18/37 ≈ 0.486
      ├── Some((2, 4)): 8/24 ≈ 0.333
      ├── Some((2, 5)): 27/48 ≈ 0.562
      ├── Some((2, 6)): 12/29 ≈ 0.414
      └── Some((2, 8)): 20/39 ≈ 0.513
    ├── Some((2, 3)): 339/570 ≈ 0.595
      ├── Some((3, 0)): 25/48 ≈ 0.521
      ├── Some((3, 1)): 52/80 ≈ 0.650
      ├── Some((3, 2)): 42/69 ≈ 0.609
      ├── Some((3, 3)): 60/90 ≈ 0.667
      ├── Some((3, 4)): 31/56 ≈ 0.554
      ├── Some((3, 5)): 37/63 ≈ 0.587
      ├── Some((3, 6)): 48/76 ≈ 0.632
      ├── Some((3, 7)): 29/53 ≈ 0.547
      └── Some((3, 8)): 14/34 ≈ 0.412
    ├── Some((2, 4)): 145/280 ≈ 0.518
      ├── Some((4, 0)): 9/23 ≈ 0.391
      ├── Some((4, 1)): 10/24 ≈ 0.417
      ├── Some((4, 2)): 10/24 ≈ 0.417
      ├── Some((4, 3)): 20/36 ≈ 0.556
      ├── Some((4, 4)): 10/24 ≈ 0.417
      ├── Some((4, 5)): 16/31 ≈ 0.516
      ├── Some((4, 6)): 22/38 ≈ 0.579
      ├── Some((4, 7)): 25/41 ≈ 0.610
      └── Some((4, 8)): 22/38 ≈ 0.579
    ├── Some((2, 5)): 94/199 ≈ 0.472
      ├── Some((5, 0)): 13/25 ≈ 0.520
      ├── Some((5, 1)): 10/22 ≈ 0.455
      ├── Some((5, 2)): 10/22 ≈ 0.455
      ├── Some((5, 3)): 12/24 ≈ 0.500
      ├── Some((5, 4)): 12/24 ≈ 0.500
      ├── Some((5, 5)): 18/31 ≈ 0.581
      ├── Some((5, 6)): 2/11 ≈ 0.182
      ├── Some((5, 7)): 5/15 ≈ 0.333
      └── Some((5, 8)): 12/24 ≈ 0.500
    ├── Some((2, 6)): 215/387 ≈ 0.556
      ├── Some((6, 0)): 20/39 ≈ 0.513
      ├── Some((6, 1)): 22/41 ≈ 0.537
      ├── Some((6, 2)): 25/44 ≈ 0.568
      ├── Some((6, 3)): 17/35 ≈ 0.486
      ├── Some((6, 4)): 31/52 ≈ 0.596
      ├── Some((6, 5)): 25/44 ≈ 0.568
      ├── Some((6, 6)): 37/58 ≈ 0.638
      ├── Some((6, 7)): 14/31 ≈ 0.452
      └── Some((6, 8)): 23/42 ≈ 0.548
    └── Some((2, 8)): 96/203 ≈ 0.473
      ├── Some((8, 0)): 7/18 ≈ 0.389
      ├── Some((8, 1)): 10/22 ≈ 0.455
      ├── Some((8, 2)): 7/18 ≈ 0.389
      ├── Some((8, 3)): 6/17 ≈ 0.353
      ├── Some((8, 4)): 4/14 ≈ 0.286
      ├── Some((8, 5)): 13/26 ≈ 0.500
      ├── Some((8, 6)): 23/37 ≈ 0.622
      ├── Some((8, 7)): 7/18 ≈ 0.389
      └── Some((8, 8)): 19/32 ≈ 0.594
  ├── Some((7, 3)): 1348/2514 ≈ 0.536
    ├── Some((3, 0)): 144/271 ≈ 0.531
      ├── Some((0, 0)): 10/23 ≈ 0.435
      ├── Some((0, 1)): 17/31 ≈ 0.548
      ├── Some((0, 2)): 10/23 ≈ 0.435
      ├── Some((0, 3)): 21/36 ≈ 0.583
      ├── Some((0, 4)): 20/35 ≈ 0.571
      ├── Some((0, 5)): 10/23 ≈ 0.435
      ├── Some((0, 6)): 16/30 ≈ 0.533
      ├── Some((0, 7)): 28/44 ≈ 0.636
      └── Some((0, 8)): 12/25 ≈ 0.480
    ├── Some((3, 1)): 115/227 ≈ 0.507
      ├── Some((1, 0)): 13/26 ≈ 0.500
      ├── Some((1, 1)): 11/23 ≈ 0.478
      ├── Some((1, 2)): 6/17 ≈ 0.353
      ├── Some((1, 3)): 8/20 ≈ 0.400
      ├── Some((1, 4)): 20/34 ≈ 0.588
      ├── Some((1, 5)): 18/31 ≈ 0.581
      ├── Some((1, 6)): 7/18 ≈ 0.389
      ├── Some((1, 7)): 10/22 ≈ 0.455
      └── Some((1, 8)): 21/35 ≈ 0.600
    ├── Some((3, 2)): 105/211 ≈ 0.498
      ├── Some((2, 0)): 11/24 ≈ 0.458
      ├── Some((2, 1)): 13/26 ≈ 0.500
      ├── Some((2, 2)): 19/33 ≈ 0.576
      ├── Some((2, 3)): 8/20 ≈ 0.400
      ├── Some((2, 4)): 11/24 ≈ 0.458
      ├── Some((2, 5)): 11/24 ≈ 0.458
      ├── Some((2, 6)): 11/24 ≈ 0.458
      └── Some((2, 8)): 21/35 ≈ 0.600
    ├── Some((3, 3)): 141/266 ≈ 0.530
      ├── Some((3, 0)): 8/22 ≈ 0.364
      ├── Some((3, 1)): 14/29 ≈ 0.483
      ├── Some((3, 2)): 9/23 ≈ 0.391
      ├── Some((3, 4)): 21/37 ≈ 0.568
      ├── Some((3, 5)): 21/37 ≈ 0.568
      ├── Some((3, 6)): 19/35 ≈ 0.543
      ├── Some((3, 7)): 22/39 ≈ 0.564
      └── Some((3, 8)): 26/43 ≈ 0.605
    ├── Some((3, 4)): 145/272 ≈ 0.533
      ├── Some((4, 0)): 13/27 ≈ 0.481
      ├── Some((4, 1)): 21/36 ≈ 0.583
      ├── Some((4, 2)): 9/22 ≈ 0.409
      ├── Some((4, 3)): 31/47 ≈ 0.660
      ├── Some((4, 4)): 15/29 ≈ 0.517
      ├── Some((4, 5)): 21/36 ≈ 0.583
      ├── Some((4, 6)): 11/25 ≈ 0.440
      ├── Some((4, 7)): 16/30 ≈ 0.533
      └── Some((4, 8)): 7/19 ≈ 0.368
    ├── Some((3, 5)): 165/303 ≈ 0.545
      ├── Some((5, 0)): 20/36 ≈ 0.556
      ├── Some((5, 1)): 11/25 ≈ 0.440
      ├── Some((5, 2)): 9/23 ≈ 0.391
      ├── Some((5, 3)): 22/38 ≈ 0.579
      ├── Some((5, 4)): 3/15 ≈ 0.200
      ├── Some((5, 5)): 25/41 ≈ 0.610
      ├── Some((5, 6)): 17/32 ≈ 0.531
      ├── Some((5, 7)): 23/39 ≈ 0.590
      └── Some((5, 8)): 35/53 ≈ 0.660
    ├── Some((3, 6)): 186/334 ≈ 0.557
      ├── Some((6, 0)): 20/36 ≈ 0.556
      ├── Some((6, 1)): 12/27 ≈ 0.444
      ├── Some((6, 2)): 25/42 ≈ 0.595
      ├── Some((6, 3)): 21/38 ≈ 0.553
      ├── Some((6, 4)): 29/47 ≈ 0.617
      ├── Some((6, 5)): 12/27 ≈ 0.444
      ├── Some((6, 6)): 26/43 ≈ 0.605
      ├── Some((6, 7)): 27/44 ≈ 0.614
      └── Some((6, 8)): 14/29 ≈ 0.483
    ├── Some((3, 7)): 166/304 ≈ 0.546
      ├── Some((7, 0)): 18/35 ≈ 0.514
      ├── Some((7, 1)): 12/27 ≈ 0.444
      ├── Some((7, 2)): 19/36 ≈ 0.528
      ├── Some((7, 4)): 30/49 ≈ 0.612
      ├── Some((7, 5)): 23/41 ≈ 0.561
      ├── Some((7, 6)): 17/33 ≈ 0.515
      ├── Some((7, 7)): 30/49 ≈ 0.612
      └── Some((7, 8)): 17/33 ≈ 0.515
    └── Some((3, 8)): 180/325 ≈ 0.554
      ├── Some((8, 0)): 21/37 ≈ 0.568
      ├── Some((8, 1)): 19/35 ≈ 0.543
      ├── Some((8, 2)): 12/27 ≈ 0.444
      ├── Some((8, 3)): 18/34 ≈ 0.529
      ├── Some((8, 4)): 26/43 ≈ 0.605
      ├── Some((8, 5)): 21/37 ≈ 0.568
      ├── Some((8, 6)): 28/45 ≈ 0.622
      ├── Some((8, 7)): 15/30 ≈ 0.500
      └── Some((8, 8)): 20/36 ≈ 0.556
  ├── Some((7, 4)): 2196/3955 ≈ 0.555
    ├── Some((4, 0)): 230/419 ≈ 0.549
      ├── Some((0, 0)): 30/52 ≈ 0.577
      ├── Some((0, 1)): 25/46 ≈ 0.543
      ├── Some((0, 2)): 24/45 ≈ 0.533
      ├── Some((0, 3)): 27/48 ≈ 0.562
      ├── Some((0, 4)): 15/33 ≈ 0.455
      ├── Some((0, 5)): 19/39 ≈ 0.487
      ├── Some((0, 6)): 16/35 ≈ 0.457
      ├── Some((0, 7)): 43/67 ≈ 0.642
      └── Some((0, 8)): 31/53 ≈ 0.585
    ├── Some((4, 1)): 154/302 ≈ 0.510
      ├── Some((1, 0)): 10/25 ≈ 0.400
      ├── Some((1, 1)): 11/26 ≈ 0.423
      ├── Some((1, 2)): 30/49 ≈ 0.612
      ├── Some((1, 3)): 19/36 ≈ 0.528
      ├── Some((1, 4)): 20/37 ≈ 0.541
      ├── Some((1, 5)): 26/44 ≈ 0.591
      ├── Some((1, 6)): 18/35 ≈ 0.514
      ├── Some((1, 7)): 13/29 ≈ 0.448
      └── Some((1, 8)): 6/20 ≈ 0.300
    ├── Some((4, 2)): 126/257 ≈ 0.490
      ├── Some((2, 0)): 20/38 ≈ 0.526
      ├── Some((2, 1)): 18/35 ≈ 0.514
      ├── Some((2, 2)): 24/42 ≈ 0.571
      ├── Some((2, 3)): 11/26 ≈ 0.423
      ├── Some((2, 4)): 15/31 ≈ 0.484
      ├── Some((2, 5)): 8/22 ≈ 0.364
      ├── Some((2, 6)): 5/18 ≈ 0.278
      └── Some((2, 8)): 25/44 ≈ 0.568
    ├── Some((4, 3)): 318/552 ≈ 0.576
      ├── Some((3, 0)): 50/79 ≈ 0.633
      ├── Some((3, 1)): 9/27 ≈ 0.333
      ├── Some((3, 2)): 56/86 ≈ 0.651
      ├── Some((3, 3)): 25/49 ≈ 0.510
      ├── Some((3, 4)): 44/72 ≈ 0.611
      ├── Some((3, 5)): 30/55 ≈ 0.545
      ├── Some((3, 6)): 32/58 ≈ 0.552
      ├── Some((3, 7)): 37/64 ≈ 0.578
      └── Some((3, 8)): 35/61 ≈ 0.574
    ├── Some((4, 4)): 387/655 ≈ 0.591
      ├── Some((4, 0)): 59/95 ≈ 0.621
      ├── Some((4, 1)): 51/86 ≈ 0.593
      ├── Some((4, 2)): 71/110 ≈ 0.645
      ├── Some((4, 3)): 36/67 ≈ 0.537
      ├── Some((4, 5)): 35/65 ≈ 0.538
      ├── Some((4, 6)): 35/65 ≈ 0.538
      ├── Some((4, 7)): 31/60 ≈ 0.517
      └── Some((4, 8)): 68/106 ≈ 0.642
    ├── Some((4, 5)): 293/515 ≈ 0.569
      ├── Some((5, 0)): 28/52 ≈ 0.538
      ├── Some((5, 1)): 34/59 ≈ 0.576
      ├── Some((5, 2)): 18/39 ≈ 0.462
      ├── Some((5, 3)): 34/59 ≈ 0.576
      ├── Some((5, 4)): 41/67 ≈ 0.612
      ├── Some((5, 5)): 22/44 ≈ 0.500
      ├── Some((5, 6)): 40/66 ≈ 0.606
      ├── Some((5, 7)): 34/59 ≈ 0.576
      └── Some((5, 8)): 42/69 ≈ 0.609
    ├── Some((4, 6)): 273/485 ≈ 0.563
      ├── Some((6, 0)): 28/51 ≈ 0.549
      ├── Some((6, 1)): 29/53 ≈ 0.547
      ├── Some((6, 2)): 22/44 ≈ 0.500
      ├── Some((6, 3)): 32/56 ≈ 0.571
      ├── Some((6, 4)): 6/22 ≈ 0.273
      ├── Some((6, 5)): 15/35 ≈ 0.429
      ├── Some((6, 6)): 55/84 ≈ 0.655
      ├── Some((6, 7)): 35/60 ≈ 0.583
      └── Some((6, 8)): 51/79 ≈ 0.646
    ├── Some((4, 7)): 158/308 ≈ 0.513
      ├── Some((7, 0)): 49/74 ≈ 0.662
      ├── Some((7, 1)): 9/25 ≈ 0.360
      ├── Some((7, 2)): 11/28 ≈ 0.393
      ├── Some((7, 3)): 6/21 ≈ 0.286
      ├── Some((7, 5)): 35/58 ≈ 0.603
      ├── Some((7, 6)): 19/38 ≈ 0.500
      ├── Some((7, 7)): 22/42 ≈ 0.524
      └── Some((7, 8)): 6/21 ≈ 0.286
    └── Some((4, 8)): 257/461 ≈ 0.557
      ├── Some((8, 0)): 36/60 ≈ 0.600
      ├── Some((8, 1)): 29/52 ≈ 0.558
      ├── Some((8, 2)): 30/53 ≈ 0.566
      ├── Some((8, 3)): 38/63 ≈ 0.603
      ├── Some((8, 4)): 29/52 ≈ 0.558
      ├── Some((8, 5)): 37/61 ≈ 0.607
      ├── Some((8, 6)): 13/32 ≈ 0.406
      ├── Some((8, 7)): 18/38 ≈ 0.474
      └── Some((8, 8)): 27/49 ≈ 0.551
  ├── Some((7, 5)): 999/1913 ≈ 0.522
    ├── Some((5, 0)): 174/306 ≈ 0.569
      ├── Some((0, 0)): 20/35 ≈ 0.571
      ├── Some((0, 1)): 27/42 ≈ 0.643
      ├── Some((0, 2)): 19/34 ≈ 0.559
      ├── Some((0, 3)): 10/23 ≈ 0.435
      ├── Some((0, 4)): 27/43 ≈ 0.628
      ├── Some((0, 5)): 18/33 ≈ 0.545
      ├── Some((0, 6)): 14/28 ≈ 0.500
      ├── Some((0, 7)): 17/31 ≈ 0.548
      └── Some((0, 8)): 21/36 ≈ 0.583
    ├── Some((5, 1)): 109/210 ≈ 0.519
      ├── Some((1, 0)): 12/23 ≈ 0.522
      ├── Some((1, 1)): 8/19 ≈ 0.421
      ├── Some((1, 2)): 22/34 ≈ 0.647
      ├── Some((1, 3)): 8/19 ≈ 0.421
      ├── Some((1, 4)): 16/28 ≈ 0.571
      ├── Some((1, 5)): 9/20 ≈ 0.450
      ├── Some((1, 6)): 11/22 ≈ 0.500
      ├── Some((1, 7)): 12/23 ≈ 0.522
      └── Some((1, 8)): 10/21 ≈ 0.476
    ├── Some((5, 2)): 131/243 ≈ 0.539
      ├── Some((2, 0)): 26/41 ≈ 0.634
      ├── Some((2, 1)): 16/30 ≈ 0.533
      ├── Some((2, 2)): 20/35 ≈ 0.571
      ├── Some((2, 3)): 21/36 ≈ 0.583
      ├── Some((2, 4)): 1/11 ≈ 0.091
      ├── Some((2, 5)): 16/30 ≈ 0.533
      ├── Some((2, 6)): 10/23 ≈ 0.435
      └── Some((2, 8)): 21/36 ≈ 0.583
    ├── Some((5, 3)): 69/149 ≈ 0.463
      ├── Some((3, 0)): 12/21 ≈ 0.571
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 2)): 4/12 ≈ 0.333
      ├── Some((3, 3)): 10/19 ≈ 0.526
      ├── Some((3, 4)): 8/17 ≈ 0.471
      ├── Some((3, 5)): 10/19 ≈ 0.526
      ├── Some((3, 6)): 8/17 ≈ 0.471
      ├── Some((3, 7)): 7/16 ≈ 0.438
      └── Some((3, 8)): 5/14 ≈ 0.357
    ├── Some((5, 4)): 151/273 ≈ 0.553
      ├── Some((4, 0)): 21/35 ≈ 0.600
      ├── Some((4, 1)): 20/34 ≈ 0.588
      ├── Some((4, 2)): 13/26 ≈ 0.500
      ├── Some((4, 3)): 27/42 ≈ 0.643
      ├── Some((4, 4)): 14/27 ≈ 0.519
      ├── Some((4, 5)): 14/27 ≈ 0.519
      ├── Some((4, 6)): 12/25 ≈ 0.480
      ├── Some((4, 7)): 20/34 ≈ 0.588
      └── Some((4, 8)): 9/22 ≈ 0.409
    ├── Some((5, 5)): 67/146 ≈ 0.459
      ├── Some((5, 0)): 11/21 ≈ 0.524
      ├── Some((5, 1)): 6/16 ≈ 0.375
      ├── Some((5, 2)): 7/17 ≈ 0.412
      ├── Some((5, 3)): 7/17 ≈ 0.412
      ├── Some((5, 4)): 8/18 ≈ 0.444
      ├── Some((5, 6)): 9/19 ≈ 0.474
      ├── Some((5, 7)): 13/23 ≈ 0.565
      └── Some((5, 8)): 5/14 ≈ 0.357
    ├── Some((5, 6)): 116/221 ≈ 0.525
      ├── Some((6, 0)): 6/17 ≈ 0.353
      ├── Some((6, 1)): 16/28 ≈ 0.571
      ├── Some((6, 2)): 13/25 ≈ 0.520
      ├── Some((6, 3)): 21/34 ≈ 0.618
      ├── Some((6, 4)): 14/26 ≈ 0.538
      ├── Some((6, 5)): 20/32 ≈ 0.625
      ├── Some((6, 6)): 10/21 ≈ 0.476
      ├── Some((6, 7)): 7/18 ≈ 0.389
      └── Some((6, 8)): 8/19 ≈ 0.421
    ├── Some((5, 7)): 90/181 ≈ 0.497
      ├── Some((7, 0)): 15/27 ≈ 0.556
      ├── Some((7, 1)): 11/22 ≈ 0.500
      ├── Some((7, 2)): 10/21 ≈ 0.476
      ├── Some((7, 3)): 11/22 ≈ 0.500
      ├── Some((7, 4)): 7/18 ≈ 0.389
      ├── Some((7, 6)): 15/27 ≈ 0.556
      ├── Some((7, 7)): 5/15 ≈ 0.333
      └── Some((7, 8)): 16/28 ≈ 0.571
    └── Some((5, 8)): 91/183 ≈ 0.497
      ├── Some((8, 0)): 4/13 ≈ 0.308
      ├── Some((8, 1)): 14/25 ≈ 0.560
      ├── Some((8, 2)): 7/17 ≈ 0.412
      ├── Some((8, 3)): 10/20 ≈ 0.500
      ├── Some((8, 4)): 12/22 ≈ 0.545
      ├── Some((8, 5)): 18/29 ≈ 0.621
      ├── Some((8, 6)): 4/13 ≈ 0.308
      ├── Some((8, 7)): 14/25 ≈ 0.560
      └── Some((8, 8)): 8/18 ≈ 0.444
  ├── Some((7, 6)): 1178/2222 ≈ 0.530
    ├── Some((6, 0)): 156/285 ≈ 0.547
      ├── Some((0, 0)): 16/30 ≈ 0.533
      ├── Some((0, 1)): 11/24 ≈ 0.458
      ├── Some((0, 2)): 21/36 ≈ 0.583
      ├── Some((0, 3)): 19/34 ≈ 0.559
      ├── Some((0, 4)): 14/28 ≈ 0.500
      ├── Some((0, 5)): 11/24 ≈ 0.458
      ├── Some((0, 6)): 15/29 ≈ 0.517
      ├── Some((0, 7)): 23/38 ≈ 0.605
      └── Some((0, 8)): 25/41 ≈ 0.610
    ├── Some((6, 1)): 118/228 ≈ 0.518
      ├── Some((1, 0)): 1/10 ≈ 0.100
      ├── Some((1, 1)): 19/32 ≈ 0.594
      ├── Some((1, 2)): 26/40 ≈ 0.650
      ├── Some((1, 3)): 7/18 ≈ 0.389
      ├── Some((1, 4)): 9/21 ≈ 0.429
      ├── Some((1, 5)): 17/30 ≈ 0.567
      ├── Some((1, 6)): 12/24 ≈ 0.500
      ├── Some((1, 7)): 12/25 ≈ 0.480
      └── Some((1, 8)): 14/27 ≈ 0.519
    ├── Some((6, 2)): 153/281 ≈ 0.544
      ├── Some((2, 0)): 23/40 ≈ 0.575
      ├── Some((2, 1)): 18/34 ≈ 0.529
      ├── Some((2, 2)): 16/32 ≈ 0.500
      ├── Some((2, 3)): 20/36 ≈ 0.556
      ├── Some((2, 4)): 15/30 ≈ 0.500
      ├── Some((2, 5)): 14/29 ≈ 0.483
      ├── Some((2, 6)): 17/33 ≈ 0.515
      └── Some((2, 8)): 29/46 ≈ 0.630
    ├── Some((6, 3)): 140/261 ≈ 0.536
      ├── Some((3, 0)): 14/27 ≈ 0.519
      ├── Some((3, 1)): 16/29 ≈ 0.552
      ├── Some((3, 2)): 15/28 ≈ 0.536
      ├── Some((3, 3)): 16/30 ≈ 0.533
      ├── Some((3, 4)): 19/33 ≈ 0.576
      ├── Some((3, 5)): 21/35 ≈ 0.600
      ├── Some((3, 6)): 17/31 ≈ 0.548
      ├── Some((3, 7)): 8/20 ≈ 0.400
      └── Some((3, 8)): 14/27 ≈ 0.519
    ├── Some((6, 4)): 188/333 ≈ 0.565
      ├── Some((4, 0)): 25/42 ≈ 0.595
      ├── Some((4, 1)): 14/29 ≈ 0.483
      ├── Some((4, 2)): 10/24 ≈ 0.417
      ├── Some((4, 3)): 21/37 ≈ 0.568
      ├── Some((4, 4)): 23/39 ≈ 0.590
      ├── Some((4, 5)): 29/46 ≈ 0.630
      ├── Some((4, 6)): 24/41 ≈ 0.585
      ├── Some((4, 7)): 16/31 ≈ 0.516
      └── Some((4, 8)): 26/43 ≈ 0.605
    ├── Some((6, 5)): 111/217 ≈ 0.512
      ├── Some((5, 0)): 10/22 ≈ 0.455
      ├── Some((5, 1)): 22/35 ≈ 0.629
      ├── Some((5, 2)): 10/22 ≈ 0.455
      ├── Some((5, 3)): 13/25 ≈ 0.520
      ├── Some((5, 4)): 21/34 ≈ 0.618
      ├── Some((5, 5)): 2/11 ≈ 0.182
      ├── Some((5, 6)): 18/31 ≈ 0.581
      ├── Some((5, 7)): 6/17 ≈ 0.353
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((6, 6)): 89/183 ≈ 0.486
      ├── Some((6, 0)): 7/18 ≈ 0.389
      ├── Some((6, 1)): 12/24 ≈ 0.500
      ├── Some((6, 2)): 27/41 ≈ 0.659
      ├── Some((6, 3)): 2/11 ≈ 0.182
      ├── Some((6, 4)): 9/20 ≈ 0.450
      ├── Some((6, 5)): 5/16 ≈ 0.312
      ├── Some((6, 7)): 18/31 ≈ 0.581
      └── Some((6, 8)): 9/21 ≈ 0.429
    ├── Some((6, 7)): 158/288 ≈ 0.549
      ├── Some((7, 0)): 38/57 ≈ 0.667
      ├── Some((7, 1)): 9/23 ≈ 0.391
      ├── Some((7, 2)): 11/26 ≈ 0.423
      ├── Some((7, 3)): 25/42 ≈ 0.595
      ├── Some((7, 4)): 23/40 ≈ 0.575
      ├── Some((7, 5)): 19/35 ≈ 0.543
      ├── Some((7, 7)): 10/24 ≈ 0.417
      └── Some((7, 8)): 23/40 ≈ 0.575
    └── Some((6, 8)): 65/145 ≈ 0.448
      ├── Some((8, 0)): 13/23 ≈ 0.565
      ├── Some((8, 1)): 3/11 ≈ 0.273
      ├── Some((8, 2)): 4/13 ≈ 0.308
      ├── Some((8, 3)): 11/20 ≈ 0.550
      ├── Some((8, 4)): 8/17 ≈ 0.471
      ├── Some((8, 5)): 16/26 ≈ 0.615
      ├── Some((8, 6)): 1/9 ≈ 0.111
      ├── Some((8, 7)): 5/14 ≈ 0.357
      └── Some((8, 8)): 3/11 ≈ 0.273
  ├── Some((7, 7)): 753/1483 ≈ 0.508
    ├── Some((7, 0)): 139/253 ≈ 0.549
      ├── Some((0, 0)): 13/25 ≈ 0.520
      ├── Some((0, 1)): 11/23 ≈ 0.478
      ├── Some((0, 2)): 23/36 ≈ 0.639
      ├── Some((0, 3)): 12/24 ≈ 0.500
      ├── Some((0, 4)): 21/34 ≈ 0.618
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 17/30 ≈ 0.567
      ├── Some((0, 7)): 14/27 ≈ 0.519
      └── Some((0, 8)): 16/29 ≈ 0.552
    ├── Some((7, 1)): 63/138 ≈ 0.457
      ├── Some((1, 0)): 2/10 ≈ 0.200
      ├── Some((1, 1)): 3/11 ≈ 0.273
      ├── Some((1, 2)): 4/12 ≈ 0.333
      ├── Some((1, 3)): 4/12 ≈ 0.333
      ├── Some((1, 4)): 7/15 ≈ 0.467
      ├── Some((1, 5)): 14/23 ≈ 0.609
      ├── Some((1, 6)): 7/15 ≈ 0.467
      ├── Some((1, 7)): 9/18 ≈ 0.500
      └── Some((1, 8)): 12/21 ≈ 0.571
    ├── Some((7, 2)): 90/180 ≈ 0.500
      ├── Some((2, 0)): 8/19 ≈ 0.421
      ├── Some((2, 1)): 7/18 ≈ 0.389
      ├── Some((2, 2)): 16/28 ≈ 0.571
      ├── Some((2, 3)): 13/25 ≈ 0.520
      ├── Some((2, 4)): 18/30 ≈ 0.600
      ├── Some((2, 5)): 9/20 ≈ 0.450
      ├── Some((2, 6)): 2/11 ≈ 0.182
      └── Some((2, 8)): 16/28 ≈ 0.571
    ├── Some((7, 3)): 66/142 ≈ 0.465
      ├── Some((3, 0)): 9/18 ≈ 0.500
      ├── Some((3, 1)): 7/15 ≈ 0.467
      ├── Some((3, 2)): 8/17 ≈ 0.471
      ├── Some((3, 3)): 17/26 ≈ 0.654
      ├── Some((3, 4)): 6/14 ≈ 0.429
      ├── Some((3, 5)): 5/13 ≈ 0.385
      ├── Some((3, 6)): 2/10 ≈ 0.200
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((7, 4)): 143/259 ≈ 0.552
      ├── Some((4, 0)): 18/31 ≈ 0.581
      ├── Some((4, 1)): 16/29 ≈ 0.552
      ├── Some((4, 2)): 10/22 ≈ 0.455
      ├── Some((4, 3)): 16/29 ≈ 0.552
      ├── Some((4, 4)): 20/33 ≈ 0.606
      ├── Some((4, 5)): 15/28 ≈ 0.536
      ├── Some((4, 6)): 13/25 ≈ 0.520
      ├── Some((4, 7)): 24/38 ≈ 0.632
      └── Some((4, 8)): 11/23 ≈ 0.478
    ├── Some((7, 5)): 90/180 ≈ 0.500
      ├── Some((5, 0)): 9/19 ≈ 0.474
      ├── Some((5, 1)): 22/33 ≈ 0.667
      ├── Some((5, 2)): 9/19 ≈ 0.474
      ├── Some((5, 3)): 13/23 ≈ 0.565
      ├── Some((5, 4)): 11/21 ≈ 0.524
      ├── Some((5, 5)): 4/13 ≈ 0.308
      ├── Some((5, 6)): 4/13 ≈ 0.308
      ├── Some((5, 7)): 5/14 ≈ 0.357
      └── Some((5, 8)): 13/24 ≈ 0.542
    ├── Some((7, 6)): 80/164 ≈ 0.488
      ├── Some((6, 0)): 16/26 ≈ 0.615
      ├── Some((6, 1)): 2/10 ≈ 0.200
      ├── Some((6, 2)): 9/18 ≈ 0.500
      ├── Some((6, 3)): 11/21 ≈ 0.524
      ├── Some((6, 4)): 3/11 ≈ 0.273
      ├── Some((6, 5)): 9/19 ≈ 0.474
      ├── Some((6, 6)): 12/22 ≈ 0.545
      ├── Some((6, 7)): 10/20 ≈ 0.500
      └── Some((6, 8)): 7/16 ≈ 0.438
    └── Some((7, 8)): 81/166 ≈ 0.488
      ├── Some((8, 0)): 10/20 ≈ 0.500
      ├── Some((8, 1)): 5/14 ≈ 0.357
      ├── Some((8, 2)): 19/29 ≈ 0.655
      ├── Some((8, 3)): 12/22 ≈ 0.545
      ├── Some((8, 4)): 11/21 ≈ 0.524
      ├── Some((8, 5)): 9/18 ≈ 0.500
      ├── Some((8, 6)): 6/15 ≈ 0.400
      ├── Some((8, 7)): 6/15 ≈ 0.400
      └── Some((8, 8)): 3/11 ≈ 0.273
  └── Some((7, 8)): 935/1801 ≈ 0.519
    ├── Some((8, 0)): 159/282 ≈ 0.564
      ├── Some((0, 0)): 8/20 ≈ 0.400
      ├── Some((0, 1)): 8/20 ≈ 0.400
      ├── Some((0, 2)): 12/25 ≈ 0.480
      ├── Some((0, 3)): 21/35 ≈ 0.600
      ├── Some((0, 4)): 22/36 ≈ 0.611
      ├── Some((0, 5)): 16/30 ≈ 0.533
      ├── Some((0, 6)): 26/41 ≈ 0.634
      ├── Some((0, 7)): 21/35 ≈ 0.600
      └── Some((0, 8)): 24/39 ≈ 0.615
    ├── Some((8, 1)): 115/217 ≈ 0.530
      ├── Some((1, 0)): 15/27 ≈ 0.556
      ├── Some((1, 1)): 19/31 ≈ 0.613
      ├── Some((1, 2)): 8/19 ≈ 0.421
      ├── Some((1, 3)): 16/28 ≈ 0.571
      ├── Some((1, 4)): 22/34 ≈ 0.647
      ├── Some((1, 5)): 10/21 ≈ 0.476
      ├── Some((1, 6)): 8/19 ≈ 0.421
      ├── Some((1, 7)): 11/22 ≈ 0.500
      └── Some((1, 8)): 5/15 ≈ 0.333
    ├── Some((8, 2)): 64/140 ≈ 0.457
      ├── Some((2, 0)): 17/28 ≈ 0.607
      ├── Some((2, 1)): 10/20 ≈ 0.500
      ├── Some((2, 2)): 4/13 ≈ 0.308
      ├── Some((2, 3)): 3/12 ≈ 0.250
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 13/23 ≈ 0.565
      ├── Some((2, 6)): 3/12 ≈ 0.250
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((8, 3)): 91/181 ≈ 0.503
      ├── Some((3, 0)): 11/21 ≈ 0.524
      ├── Some((3, 1)): 6/16 ≈ 0.375
      ├── Some((3, 2)): 13/24 ≈ 0.542
      ├── Some((3, 3)): 11/21 ≈ 0.524
      ├── Some((3, 4)): 5/14 ≈ 0.357
      ├── Some((3, 5)): 23/34 ≈ 0.676
      ├── Some((3, 6)): 10/20 ≈ 0.500
      ├── Some((3, 7)): 3/12 ≈ 0.250
      └── Some((3, 8)): 8/18 ≈ 0.444
    ├── Some((8, 4)): 106/204 ≈ 0.520
      ├── Some((4, 0)): 20/32 ≈ 0.625
      ├── Some((4, 1)): 3/12 ≈ 0.250
      ├── Some((4, 2)): 6/16 ≈ 0.375
      ├── Some((4, 3)): 8/18 ≈ 0.444
      ├── Some((4, 4)): 8/19 ≈ 0.421
      ├── Some((4, 5)): 12/23 ≈ 0.522
      ├── Some((4, 6)): 13/24 ≈ 0.542
      ├── Some((4, 7)): 18/30 ≈ 0.600
      └── Some((4, 8)): 17/29 ≈ 0.586
    ├── Some((8, 5)): 92/183 ≈ 0.503
      ├── Some((5, 0)): 14/25 ≈ 0.560
      ├── Some((5, 1)): 13/23 ≈ 0.565
      ├── Some((5, 2)): 11/21 ≈ 0.524
      ├── Some((5, 3)): 9/19 ≈ 0.474
      ├── Some((5, 4)): 11/21 ≈ 0.524
      ├── Some((5, 5)): 12/22 ≈ 0.545
      ├── Some((5, 6)): 0/8 ≈ 0.000
      ├── Some((5, 7)): 16/27 ≈ 0.593
      └── Some((5, 8)): 6/16 ≈ 0.375
    ├── Some((8, 6)): 76/158 ≈ 0.481
      ├── Some((6, 0)): 3/11 ≈ 0.273
      ├── Some((6, 1)): 5/14 ≈ 0.357
      ├── Some((6, 2)): 16/26 ≈ 0.615
      ├── Some((6, 3)): 2/10 ≈ 0.200
      ├── Some((6, 4)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 10/19 ≈ 0.526
      ├── Some((6, 6)): 9/18 ≈ 0.500
      ├── Some((6, 7)): 10/19 ≈ 0.526
      └── Some((6, 8)): 11/21 ≈ 0.524
    ├── Some((8, 7)): 144/260 ≈ 0.554
      ├── Some((7, 0)): 14/28 ≈ 0.500
      ├── Some((7, 1)): 38/55 ≈ 0.691
      ├── Some((7, 2)): 23/38 ≈ 0.605
      ├── Some((7, 3)): 16/31 ≈ 0.516
      ├── Some((7, 4)): 15/29 ≈ 0.517
      ├── Some((7, 5)): 14/28 ≈ 0.500
      ├── Some((7, 6)): 8/21 ≈ 0.381
      └── Some((7, 7)): 15/29 ≈ 0.517
    └── Some((8, 8)): 87/175 ≈ 0.497
      ├── Some((8, 0)): 14/25 ≈ 0.560
      ├── Some((8, 1)): 5/15 ≈ 0.333
      ├── Some((8, 2)): 3/12 ≈ 0.250
      ├── Some((8, 3)): 11/22 ≈ 0.500
      ├── Some((8, 4)): 17/29 ≈ 0.586
      ├── Some((8, 5)): 14/25 ≈ 0.560
      ├── Some((8, 6)): 9/20 ≈ 0.450
      └── Some((8, 7)): 14/26 ≈ 0.538
├── Some((2, 8)): 8263/15721 ≈ 0.526
  ├── Some((8, 0)): 815/1571 ≈ 0.519
    ├── Some((0, 0)): 99/187 ≈ 0.529
      ├── Some((0, 1)): 9/20 ≈ 0.450
      ├── Some((0, 2)): 10/21 ≈ 0.476
      ├── Some((0, 3)): 7/17 ≈ 0.412
      ├── Some((0, 4)): 15/26 ≈ 0.577
      ├── Some((0, 5)): 13/24 ≈ 0.542
      ├── Some((0, 6)): 17/28 ≈ 0.607
      ├── Some((0, 7)): 6/16 ≈ 0.375
      └── Some((0, 8)): 22/34 ≈ 0.647
    ├── Some((0, 1)): 98/186 ≈ 0.527
      ├── Some((1, 0)): 7/16 ≈ 0.438
      ├── Some((1, 1)): 13/23 ≈ 0.565
      ├── Some((1, 2)): 9/19 ≈ 0.474
      ├── Some((1, 3)): 15/25 ≈ 0.600
      ├── Some((1, 4)): 13/23 ≈ 0.565
      ├── Some((1, 5)): 8/18 ≈ 0.444
      ├── Some((1, 6)): 1/9 ≈ 0.111
      ├── Some((1, 7)): 16/26 ≈ 0.615
      └── Some((1, 8)): 16/26 ≈ 0.615
    ├── Some((0, 2)): 70/144 ≈ 0.486
      ├── Some((2, 0)): 6/15 ≈ 0.400
      ├── Some((2, 1)): 10/19 ≈ 0.526
      ├── Some((2, 2)): 11/20 ≈ 0.550
      ├── Some((2, 3)): 13/23 ≈ 0.565
      ├── Some((2, 4)): 11/21 ≈ 0.524
      ├── Some((2, 5)): 9/18 ≈ 0.500
      ├── Some((2, 6)): 8/17 ≈ 0.471
      └── Some((2, 7)): 2/10 ≈ 0.200
    ├── Some((0, 3)): 121/219 ≈ 0.553
      ├── Some((3, 0)): 16/27 ≈ 0.593
      ├── Some((3, 1)): 13/24 ≈ 0.542
      ├── Some((3, 2)): 11/22 ≈ 0.500
      ├── Some((3, 3)): 7/17 ≈ 0.412
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 26/37 ≈ 0.703
      ├── Some((3, 6)): 13/24 ≈ 0.542
      ├── Some((3, 7)): 14/25 ≈ 0.560
      └── Some((3, 8)): 13/24 ≈ 0.542
    ├── Some((0, 4)): 114/209 ≈ 0.545
      ├── Some((4, 0)): 24/35 ≈ 0.686
      ├── Some((4, 1)): 11/22 ≈ 0.500
      ├── Some((4, 2)): 4/13 ≈ 0.308
      ├── Some((4, 3)): 19/30 ≈ 0.633
      ├── Some((4, 4)): 13/24 ≈ 0.542
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 15/26 ≈ 0.577
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 10/21 ≈ 0.476
    ├── Some((0, 5)): 72/147 ≈ 0.490
      ├── Some((5, 0)): 11/20 ≈ 0.550
      ├── Some((5, 1)): 1/8 ≈ 0.125
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 7/15 ≈ 0.467
      ├── Some((5, 5)): 10/19 ≈ 0.526
      ├── Some((5, 6)): 8/16 ≈ 0.500
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 14/23 ≈ 0.609
    ├── Some((0, 6)): 98/186 ≈ 0.527
      ├── Some((6, 0)): 23/33 ≈ 0.697
      ├── Some((6, 1)): 9/19 ≈ 0.474
      ├── Some((6, 2)): 4/13 ≈ 0.308
      ├── Some((6, 3)): 5/14 ≈ 0.357
      ├── Some((6, 4)): 13/23 ≈ 0.565
      ├── Some((6, 5)): 8/18 ≈ 0.444
      ├── Some((6, 6)): 20/30 ≈ 0.667
      ├── Some((6, 7)): 9/19 ≈ 0.474
      └── Some((6, 8)): 7/16 ≈ 0.438
    ├── Some((0, 7)): 70/144 ≈ 0.486
      ├── Some((7, 0)): 13/22 ≈ 0.591
      ├── Some((7, 1)): 10/18 ≈ 0.556
      ├── Some((7, 2)): 7/15 ≈ 0.467
      ├── Some((7, 3)): 7/15 ≈ 0.467
      ├── Some((7, 4)): 7/15 ≈ 0.467
      ├── Some((7, 5)): 7/15 ≈ 0.467
      ├── Some((7, 6)): 9/17 ≈ 0.529
      ├── Some((7, 7)): 4/12 ≈ 0.333
      └── Some((7, 8)): 6/14 ≈ 0.429
    └── Some((0, 8)): 73/148 ≈ 0.493
      ├── Some((8, 1)): 15/25 ≈ 0.600
      ├── Some((8, 2)): 13/23 ≈ 0.565
      ├── Some((8, 3)): 7/16 ≈ 0.438
      ├── Some((8, 4)): 11/21 ≈ 0.524
      ├── Some((8, 5)): 7/16 ≈ 0.438
      ├── Some((8, 6)): 9/18 ≈ 0.500
      ├── Some((8, 7)): 8/17 ≈ 0.471
      └── Some((8, 8)): 3/11 ≈ 0.273
  ├── Some((8, 1)): 892/1704 ≈ 0.523
    ├── Some((1, 0)): 65/138 ≈ 0.471
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 6/14 ≈ 0.429
      ├── Some((0, 2)): 1/8 ≈ 0.125
      ├── Some((0, 3)): 12/21 ≈ 0.571
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 16/25 ≈ 0.640
      ├── Some((0, 6)): 9/18 ≈ 0.500
      ├── Some((0, 7)): 7/15 ≈ 0.467
      └── Some((0, 8)): 1/8 ≈ 0.125
    ├── Some((1, 1)): 106/200 ≈ 0.530
      ├── Some((1, 0)): 19/31 ≈ 0.613
      ├── Some((1, 2)): 13/25 ≈ 0.520
      ├── Some((1, 3)): 6/16 ≈ 0.375
      ├── Some((1, 4)): 16/28 ≈ 0.571
      ├── Some((1, 5)): 22/35 ≈ 0.629
      ├── Some((1, 6)): 16/28 ≈ 0.571
      ├── Some((1, 7)): 8/19 ≈ 0.421
      └── Some((1, 8)): 6/17 ≈ 0.353
    ├── Some((1, 2)): 150/264 ≈ 0.568
      ├── Some((2, 0)): 12/25 ≈ 0.480
      ├── Some((2, 1)): 17/31 ≈ 0.548
      ├── Some((2, 2)): 19/33 ≈ 0.576
      ├── Some((2, 3)): 17/31 ≈ 0.548
      ├── Some((2, 4)): 18/32 ≈ 0.562
      ├── Some((2, 5)): 20/34 ≈ 0.588
      ├── Some((2, 6)): 21/36 ≈ 0.583
      └── Some((2, 7)): 26/41 ≈ 0.634
    ├── Some((1, 3)): 84/167 ≈ 0.503
      ├── Some((3, 0)): 3/11 ≈ 0.273
      ├── Some((3, 1)): 13/23 ≈ 0.565
      ├── Some((3, 2)): 10/19 ≈ 0.526
      ├── Some((3, 3)): 11/21 ≈ 0.524
      ├── Some((3, 4)): 6/15 ≈ 0.400
      ├── Some((3, 5)): 7/16 ≈ 0.438
      ├── Some((3, 6)): 8/17 ≈ 0.471
      ├── Some((3, 7)): 10/19 ≈ 0.526
      └── Some((3, 8)): 15/25 ≈ 0.600
    ├── Some((1, 4)): 79/160 ≈ 0.494
      ├── Some((4, 0)): 7/16 ≈ 0.438
      ├── Some((4, 1)): 3/11 ≈ 0.273
      ├── Some((4, 2)): 13/22 ≈ 0.591
      ├── Some((4, 3)): 8/17 ≈ 0.471
      ├── Some((4, 4)): 13/23 ≈ 0.565
      ├── Some((4, 5)): 10/19 ≈ 0.526
      ├── Some((4, 6)): 12/21 ≈ 0.571
      ├── Some((4, 7)): 9/18 ≈ 0.500
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((1, 5)): 94/182 ≈ 0.516
      ├── Some((5, 0)): 16/26 ≈ 0.615
      ├── Some((5, 1)): 7/16 ≈ 0.438
      ├── Some((5, 2)): 11/21 ≈ 0.524
      ├── Some((5, 3)): 9/19 ≈ 0.474
      ├── Some((5, 4)): 18/28 ≈ 0.643
      ├── Some((5, 5)): 9/19 ≈ 0.474
      ├── Some((5, 6)): 6/15 ≈ 0.400
      ├── Some((5, 7)): 5/14 ≈ 0.357
      └── Some((5, 8)): 13/23 ≈ 0.565
    ├── Some((1, 6)): 90/176 ≈ 0.511
      ├── Some((6, 0)): 10/20 ≈ 0.500
      ├── Some((6, 1)): 18/28 ≈ 0.643
      ├── Some((6, 2)): 2/10 ≈ 0.200
      ├── Some((6, 3)): 2/10 ≈ 0.200
      ├── Some((6, 4)): 9/19 ≈ 0.474
      ├── Some((6, 5)): 13/23 ≈ 0.565
      ├── Some((6, 6)): 4/13 ≈ 0.308
      ├── Some((6, 7)): 14/24 ≈ 0.583
      └── Some((6, 8)): 18/28 ≈ 0.643
    ├── Some((1, 7)): 107/201 ≈ 0.532
      ├── Some((7, 0)): 13/23 ≈ 0.565
      ├── Some((7, 1)): 9/19 ≈ 0.474
      ├── Some((7, 2)): 13/23 ≈ 0.565
      ├── Some((7, 3)): 9/19 ≈ 0.474
      ├── Some((7, 4)): 12/22 ≈ 0.545
      ├── Some((7, 5)): 6/16 ≈ 0.375
      ├── Some((7, 6)): 14/25 ≈ 0.560
      ├── Some((7, 7)): 16/27 ≈ 0.593
      └── Some((7, 8)): 15/26 ≈ 0.577
    └── Some((1, 8)): 116/215 ≈ 0.540
      ├── Some((8, 0)): 9/21 ≈ 0.429
      ├── Some((8, 2)): 18/31 ≈ 0.581
      ├── Some((8, 3)): 15/28 ≈ 0.536
      ├── Some((8, 4)): 6/17 ≈ 0.353
      ├── Some((8, 5)): 8/19 ≈ 0.421
      ├── Some((8, 6)): 18/31 ≈ 0.581
      ├── Some((8, 7)): 18/31 ≈ 0.581
      └── Some((8, 8)): 23/36 ≈ 0.639
  ├── Some((8, 2)): 1087/2039 ≈ 0.533
    ├── Some((2, 0)): 130/246 ≈ 0.528
      ├── Some((0, 0)): 6/17 ≈ 0.353
      ├── Some((0, 1)): 17/30 ≈ 0.567
      ├── Some((0, 2)): 16/29 ≈ 0.552
      ├── Some((0, 3)): 15/28 ≈ 0.536
      ├── Some((0, 4)): 28/43 ≈ 0.651
      ├── Some((0, 5)): 6/17 ≈ 0.353
      ├── Some((0, 6)): 8/20 ≈ 0.400
      ├── Some((0, 7)): 23/37 ≈ 0.622
      └── Some((0, 8)): 11/24 ≈ 0.458
    ├── Some((2, 1)): 98/197 ≈ 0.497
      ├── Some((1, 0)): 8/19 ≈ 0.421
      ├── Some((1, 1)): 8/19 ≈ 0.421
      ├── Some((1, 2)): 23/35 ≈ 0.657
      ├── Some((1, 3)): 8/19 ≈ 0.421
      ├── Some((1, 4)): 15/26 ≈ 0.577
      ├── Some((1, 5)): 3/12 ≈ 0.250
      ├── Some((1, 6)): 4/14 ≈ 0.286
      ├── Some((1, 7)): 11/22 ≈ 0.500
      └── Some((1, 8)): 18/30 ≈ 0.600
    ├── Some((2, 2)): 100/201 ≈ 0.498
      ├── Some((2, 0)): 26/43 ≈ 0.605
      ├── Some((2, 1)): 6/18 ≈ 0.333
      ├── Some((2, 3)): 9/22 ≈ 0.409
      ├── Some((2, 4)): 18/33 ≈ 0.545
      ├── Some((2, 5)): 17/32 ≈ 0.531
      ├── Some((2, 6)): 18/33 ≈ 0.545
      └── Some((2, 7)): 6/19 ≈ 0.316
    ├── Some((2, 3)): 138/259 ≈ 0.533
      ├── Some((3, 0)): 22/36 ≈ 0.611
      ├── Some((3, 1)): 11/24 ≈ 0.458
      ├── Some((3, 2)): 15/28 ≈ 0.536
      ├── Some((3, 3)): 8/20 ≈ 0.400
      ├── Some((3, 4)): 15/28 ≈ 0.536
      ├── Some((3, 5)): 17/31 ≈ 0.548
      ├── Some((3, 6)): 13/26 ≈ 0.500
      ├── Some((3, 7)): 16/30 ≈ 0.533
      └── Some((3, 8)): 21/35 ≈ 0.600
    ├── Some((2, 4)): 206/359 ≈ 0.574
      ├── Some((4, 0)): 11/26 ≈ 0.423
      ├── Some((4, 1)): 15/31 ≈ 0.484
      ├── Some((4, 2)): 35/54 ≈ 0.648
      ├── Some((4, 3)): 12/27 ≈ 0.444
      ├── Some((4, 4)): 37/56 ≈ 0.661
      ├── Some((4, 5)): 32/51 ≈ 0.627
      ├── Some((4, 6)): 8/22 ≈ 0.364
      ├── Some((4, 7)): 31/49 ≈ 0.633
      └── Some((4, 8)): 24/42 ≈ 0.571
    ├── Some((2, 5)): 103/205 ≈ 0.502
      ├── Some((5, 0)): 15/27 ≈ 0.556
      ├── Some((5, 1)): 2/11 ≈ 0.182
      ├── Some((5, 2)): 11/23 ≈ 0.478
      ├── Some((5, 3)): 10/21 ≈ 0.476
      ├── Some((5, 4)): 13/25 ≈ 0.520
      ├── Some((5, 5)): 21/34 ≈ 0.618
      ├── Some((5, 6)): 9/20 ≈ 0.450
      ├── Some((5, 7)): 17/29 ≈ 0.586
      └── Some((5, 8)): 4/14 ≈ 0.286
    ├── Some((2, 6)): 178/318 ≈ 0.560
      ├── Some((6, 0)): 11/25 ≈ 0.440
      ├── Some((6, 1)): 33/50 ≈ 0.660
      ├── Some((6, 2)): 12/26 ≈ 0.462
      ├── Some((6, 3)): 9/23 ≈ 0.391
      ├── Some((6, 4)): 29/46 ≈ 0.630
      ├── Some((6, 5)): 25/42 ≈ 0.595
      ├── Some((6, 6)): 16/31 ≈ 0.516
      ├── Some((6, 7)): 27/44 ≈ 0.614
      └── Some((6, 8)): 15/30 ≈ 0.500
    └── Some((2, 7)): 134/253 ≈ 0.530
      ├── Some((7, 0)): 22/36 ≈ 0.611
      ├── Some((7, 1)): 12/25 ≈ 0.480
      ├── Some((7, 2)): 6/18 ≈ 0.333
      ├── Some((7, 3)): 16/30 ≈ 0.533
      ├── Some((7, 4)): 15/28 ≈ 0.536
      ├── Some((7, 5)): 9/21 ≈ 0.429
      ├── Some((7, 6)): 17/31 ≈ 0.548
      ├── Some((7, 7)): 11/24 ≈ 0.458
      └── Some((7, 8)): 25/39 ≈ 0.641
  ├── Some((8, 3)): 1645/2985 ≈ 0.551
    ├── Some((3, 0)): 136/261 ≈ 0.521
      ├── Some((0, 0)): 10/23 ≈ 0.435
      ├── Some((0, 1)): 12/25 ≈ 0.480
      ├── Some((0, 2)): 19/34 ≈ 0.559
      ├── Some((0, 3)): 9/22 ≈ 0.409
      ├── Some((0, 4)): 12/25 ≈ 0.480
      ├── Some((0, 5)): 19/34 ≈ 0.559
      ├── Some((0, 6)): 14/28 ≈ 0.500
      ├── Some((0, 7)): 17/31 ≈ 0.548
      └── Some((0, 8)): 23/38 ≈ 0.605
    ├── Some((3, 1)): 147/278 ≈ 0.529
      ├── Some((1, 0)): 21/37 ≈ 0.568
      ├── Some((1, 1)): 5/17 ≈ 0.294
      ├── Some((1, 2)): 41/59 ≈ 0.695
      ├── Some((1, 3)): 12/26 ≈ 0.462
      ├── Some((1, 4)): 5/17 ≈ 0.294
      ├── Some((1, 5)): 9/22 ≈ 0.409
      ├── Some((1, 6)): 15/30 ≈ 0.500
      ├── Some((1, 7)): 27/44 ≈ 0.614
      └── Some((1, 8)): 11/25 ≈ 0.440
    ├── Some((3, 2)): 183/332 ≈ 0.551
      ├── Some((2, 0)): 34/55 ≈ 0.618
      ├── Some((2, 1)): 20/38 ≈ 0.526
      ├── Some((2, 2)): 17/34 ≈ 0.500
      ├── Some((2, 3)): 11/27 ≈ 0.407
      ├── Some((2, 4)): 21/39 ≈ 0.538
      ├── Some((2, 5)): 27/47 ≈ 0.574
      ├── Some((2, 6)): 15/32 ≈ 0.469
      └── Some((2, 7)): 38/59 ≈ 0.644
    ├── Some((3, 3)): 151/284 ≈ 0.532
      ├── Some((3, 0)): 13/28 ≈ 0.464
      ├── Some((3, 1)): 21/38 ≈ 0.553
      ├── Some((3, 2)): 34/53 ≈ 0.642
      ├── Some((3, 4)): 23/41 ≈ 0.561
      ├── Some((3, 5)): 20/37 ≈ 0.541
      ├── Some((3, 6)): 13/28 ≈ 0.464
      ├── Some((3, 7)): 9/23 ≈ 0.391
      └── Some((3, 8)): 18/35 ≈ 0.514
    ├── Some((3, 4)): 171/314 ≈ 0.545
      ├── Some((4, 0)): 21/37 ≈ 0.568
      ├── Some((4, 1)): 12/27 ≈ 0.444
      ├── Some((4, 2)): 13/28 ≈ 0.464
      ├── Some((4, 3)): 20/36 ≈ 0.556
      ├── Some((4, 4)): 12/27 ≈ 0.444
      ├── Some((4, 5)): 20/36 ≈ 0.556
      ├── Some((4, 6)): 41/59 ≈ 0.695
      ├── Some((4, 7)): 19/35 ≈ 0.543
      └── Some((4, 8)): 13/28 ≈ 0.464
    ├── Some((3, 5)): 168/310 ≈ 0.542
      ├── Some((5, 0)): 35/53 ≈ 0.660
      ├── Some((5, 1)): 15/30 ≈ 0.500
      ├── Some((5, 2)): 16/31 ≈ 0.516
      ├── Some((5, 3)): 19/35 ≈ 0.543
      ├── Some((5, 4)): 15/30 ≈ 0.500
      ├── Some((5, 5)): 15/30 ≈ 0.500
      ├── Some((5, 6)): 17/32 ≈ 0.531
      ├── Some((5, 7)): 19/35 ≈ 0.543
      └── Some((5, 8)): 17/33 ≈ 0.515
    ├── Some((3, 6)): 226/396 ≈ 0.571
      ├── Some((6, 0)): 14/31 ≈ 0.452
      ├── Some((6, 1)): 24/43 ≈ 0.558
      ├── Some((6, 2)): 40/61 ≈ 0.656
      ├── Some((6, 3)): 29/49 ≈ 0.592
      ├── Some((6, 4)): 29/49 ≈ 0.592
      ├── Some((6, 5)): 24/43 ≈ 0.558
      ├── Some((6, 6)): 28/47 ≈ 0.596
      ├── Some((6, 7)): 21/39 ≈ 0.538
      └── Some((6, 8)): 16/33 ≈ 0.485
    ├── Some((3, 7)): 209/371 ≈ 0.563
      ├── Some((7, 0)): 24/42 ≈ 0.571
      ├── Some((7, 1)): 34/54 ≈ 0.630
      ├── Some((7, 2)): 18/35 ≈ 0.514
      ├── Some((7, 3)): 12/28 ≈ 0.429
      ├── Some((7, 4)): 29/48 ≈ 0.604
      ├── Some((7, 5)): 22/40 ≈ 0.550
      ├── Some((7, 6)): 29/48 ≈ 0.604
      ├── Some((7, 7)): 15/32 ≈ 0.469
      └── Some((7, 8)): 25/43 ≈ 0.581
    └── Some((3, 8)): 254/438 ≈ 0.580
      ├── Some((8, 0)): 47/73 ≈ 0.644
      ├── Some((8, 1)): 32/56 ≈ 0.571
      ├── Some((8, 2)): 18/38 ≈ 0.474
      ├── Some((8, 4)): 14/33 ≈ 0.424
      ├── Some((8, 5)): 52/79 ≈ 0.658
      ├── Some((8, 6)): 17/37 ≈ 0.459
      ├── Some((8, 7)): 59/87 ≈ 0.678
      └── Some((8, 8)): 15/34 ≈ 0.441
  ├── Some((8, 4)): 694/1361 ≈ 0.510
    ├── Some((4, 0)): 109/198 ≈ 0.551
      ├── Some((0, 0)): 7/17 ≈ 0.412
      ├── Some((0, 1)): 8/18 ≈ 0.444
      ├── Some((0, 2)): 5/14 ≈ 0.357
      ├── Some((0, 3)): 13/23 ≈ 0.565
      ├── Some((0, 4)): 13/23 ≈ 0.565
      ├── Some((0, 5)): 14/24 ≈ 0.583
      ├── Some((0, 6)): 16/26 ≈ 0.615
      ├── Some((0, 7)): 10/20 ≈ 0.500
      └── Some((0, 8)): 22/32 ≈ 0.688
    ├── Some((4, 1)): 35/87 ≈ 0.402
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 2/8 ≈ 0.250
      ├── Some((1, 4)): 1/6 ≈ 0.167
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 1/6 ≈ 0.167
      └── Some((1, 8)): 6/12 ≈ 0.500
    ├── Some((4, 2)): 105/193 ≈ 0.544
      ├── Some((2, 0)): 13/24 ≈ 0.542
      ├── Some((2, 1)): 22/34 ≈ 0.647
      ├── Some((2, 2)): 25/37 ≈ 0.676
      ├── Some((2, 3)): 7/18 ≈ 0.389
      ├── Some((2, 4)): 8/19 ≈ 0.421
      ├── Some((2, 5)): 20/32 ≈ 0.625
      ├── Some((2, 6)): 6/16 ≈ 0.375
      └── Some((2, 7)): 3/12 ≈ 0.250
    ├── Some((4, 3)): 75/149 ≈ 0.503
      ├── Some((3, 0)): 12/20 ≈ 0.600
      ├── Some((3, 1)): 15/24 ≈ 0.625
      ├── Some((3, 2)): 3/11 ≈ 0.273
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 5/13 ≈ 0.385
      ├── Some((3, 5)): 4/12 ≈ 0.333
      ├── Some((3, 6)): 10/18 ≈ 0.556
      ├── Some((3, 7)): 8/16 ≈ 0.500
      └── Some((3, 8)): 11/19 ≈ 0.579
    ├── Some((4, 4)): 101/187 ≈ 0.540
      ├── Some((4, 0)): 19/30 ≈ 0.633
      ├── Some((4, 1)): 11/22 ≈ 0.500
      ├── Some((4, 2)): 14/25 ≈ 0.560
      ├── Some((4, 3)): 14/25 ≈ 0.560
      ├── Some((4, 5)): 6/16 ≈ 0.375
      ├── Some((4, 6)): 8/18 ≈ 0.444
      ├── Some((4, 7)): 22/34 ≈ 0.647
      └── Some((4, 8)): 6/16 ≈ 0.375
    ├── Some((4, 5)): 33/84 ≈ 0.393
      ├── Some((5, 0)): 2/7 ≈ 0.286
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 5/11 ≈ 0.455
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 5/11 ≈ 0.455
      ├── Some((5, 7)): 1/6 ≈ 0.167
      └── Some((5, 8)): 7/13 ≈ 0.538
    ├── Some((4, 6)): 55/118 ≈ 0.466
      ├── Some((6, 0)): 11/19 ≈ 0.579
      ├── Some((6, 1)): 9/16 ≈ 0.562
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 3)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 0/6 ≈ 0.000
      ├── Some((6, 5)): 6/13 ≈ 0.462
      ├── Some((6, 6)): 4/11 ≈ 0.364
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 3/10 ≈ 0.300
    ├── Some((4, 7)): 83/161 ≈ 0.516
      ├── Some((7, 0)): 10/19 ≈ 0.526
      ├── Some((7, 1)): 4/12 ≈ 0.333
      ├── Some((7, 2)): 10/19 ≈ 0.526
      ├── Some((7, 3)): 0/7 ≈ 0.000
      ├── Some((7, 4)): 10/19 ≈ 0.526
      ├── Some((7, 5)): 11/20 ≈ 0.550
      ├── Some((7, 6)): 13/22 ≈ 0.591
      ├── Some((7, 7)): 14/23 ≈ 0.609
      └── Some((7, 8)): 10/19 ≈ 0.526
    └── Some((4, 8)): 98/183 ≈ 0.536
      ├── Some((8, 0)): 10/21 ≈ 0.476
      ├── Some((8, 1)): 13/24 ≈ 0.542
      ├── Some((8, 2)): 9/19 ≈ 0.474
      ├── Some((8, 3)): 20/32 ≈ 0.625
      ├── Some((8, 5)): 18/29 ≈ 0.621
      ├── Some((8, 6)): 9/19 ≈ 0.474
      ├── Some((8, 7)): 4/13 ≈ 0.308
      └── Some((8, 8)): 14/25 ≈ 0.560
  ├── Some((8, 5)): 836/1608 ≈ 0.520
    ├── Some((5, 0)): 92/178 ≈ 0.517
      ├── Some((0, 0)): 9/19 ≈ 0.474
      ├── Some((0, 1)): 11/21 ≈ 0.524
      ├── Some((0, 2)): 7/16 ≈ 0.438
      ├── Some((0, 3)): 11/21 ≈ 0.524
      ├── Some((0, 4)): 14/24 ≈ 0.583
      ├── Some((0, 5)): 16/26 ≈ 0.615
      ├── Some((0, 6)): 8/17 ≈ 0.471
      ├── Some((0, 7)): 14/24 ≈ 0.583
      └── Some((0, 8)): 1/9 ≈ 0.111
    ├── Some((5, 1)): 87/170 ≈ 0.512
      ├── Some((1, 0)): 7/16 ≈ 0.438
      ├── Some((1, 1)): 2/10 ≈ 0.200
      ├── Some((1, 2)): 12/21 ≈ 0.571
      ├── Some((1, 3)): 22/32 ≈ 0.688
      ├── Some((1, 4)): 6/15 ≈ 0.400
      ├── Some((1, 5)): 6/15 ≈ 0.400
      ├── Some((1, 6)): 4/13 ≈ 0.308
      ├── Some((1, 7)): 9/18 ≈ 0.500
      └── Some((1, 8)): 19/29 ≈ 0.655
    ├── Some((5, 2)): 127/229 ≈ 0.555
      ├── Some((2, 0)): 10/22 ≈ 0.455
      ├── Some((2, 1)): 20/33 ≈ 0.606
      ├── Some((2, 2)): 13/25 ≈ 0.520
      ├── Some((2, 3)): 22/35 ≈ 0.629
      ├── Some((2, 4)): 9/21 ≈ 0.429
      ├── Some((2, 5)): 16/29 ≈ 0.552
      ├── Some((2, 6)): 20/33 ≈ 0.606
      └── Some((2, 7)): 17/30 ≈ 0.567
    ├── Some((5, 3)): 85/167 ≈ 0.509
      ├── Some((3, 0)): 8/17 ≈ 0.471
      ├── Some((3, 1)): 10/19 ≈ 0.526
      ├── Some((3, 2)): 14/24 ≈ 0.583
      ├── Some((3, 3)): 6/15 ≈ 0.400
      ├── Some((3, 4)): 11/20 ≈ 0.550
      ├── Some((3, 5)): 10/19 ≈ 0.526
      ├── Some((3, 6)): 2/10 ≈ 0.200
      ├── Some((3, 7)): 11/20 ≈ 0.550
      └── Some((3, 8)): 13/22 ≈ 0.591
    ├── Some((5, 4)): 70/145 ≈ 0.483
      ├── Some((4, 0)): 13/22 ≈ 0.591
      ├── Some((4, 1)): 8/16 ≈ 0.500
      ├── Some((4, 2)): 6/14 ≈ 0.429
      ├── Some((4, 3)): 9/18 ≈ 0.500
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 2/9 ≈ 0.222
      ├── Some((4, 6)): 2/10 ≈ 0.200
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 16/25 ≈ 0.640
    ├── Some((5, 5)): 97/185 ≈ 0.524
      ├── Some((5, 0)): 28/40 ≈ 0.700
      ├── Some((5, 1)): 17/29 ≈ 0.586
      ├── Some((5, 2)): 10/21 ≈ 0.476
      ├── Some((5, 3)): 6/16 ≈ 0.375
      ├── Some((5, 4)): 4/14 ≈ 0.286
      ├── Some((5, 6)): 18/30 ≈ 0.600
      ├── Some((5, 7)): 6/16 ≈ 0.375
      └── Some((5, 8)): 8/18 ≈ 0.444
    ├── Some((5, 6)): 141/250 ≈ 0.564
      ├── Some((6, 0)): 15/27 ≈ 0.556
      ├── Some((6, 1)): 12/24 ≈ 0.500
      ├── Some((6, 2)): 18/30 ≈ 0.600
      ├── Some((6, 3)): 21/34 ≈ 0.618
      ├── Some((6, 4)): 20/32 ≈ 0.625
      ├── Some((6, 5)): 17/29 ≈ 0.586
      ├── Some((6, 6)): 13/25 ≈ 0.520
      ├── Some((6, 7)): 9/20 ≈ 0.450
      └── Some((6, 8)): 16/28 ≈ 0.571
    ├── Some((5, 7)): 39/96 ≈ 0.406
      ├── Some((7, 0)): 5/11 ≈ 0.455
      ├── Some((7, 1)): 3/9 ≈ 0.333
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 4)): 10/17 ≈ 0.588
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 2/8 ≈ 0.250
      ├── Some((7, 7)): 7/14 ≈ 0.500
      └── Some((7, 8)): 3/9 ≈ 0.333
    └── Some((5, 8)): 98/187 ≈ 0.524
      ├── Some((8, 0)): 11/22 ≈ 0.500
      ├── Some((8, 1)): 20/32 ≈ 0.625
      ├── Some((8, 2)): 16/28 ≈ 0.571
      ├── Some((8, 3)): 6/16 ≈ 0.375
      ├── Some((8, 4)): 18/30 ≈ 0.600
      ├── Some((8, 6)): 1/10 ≈ 0.100
      ├── Some((8, 7)): 6/17 ≈ 0.353
      └── Some((8, 8)): 19/31 ≈ 0.613
  ├── Some((8, 6)): 742/1445 ≈ 0.513
    ├── Some((6, 0)): 87/167 ≈ 0.521
      ├── Some((0, 0)): 7/16 ≈ 0.438
      ├── Some((0, 1)): 11/20 ≈ 0.550
      ├── Some((0, 2)): 9/18 ≈ 0.500
      ├── Some((0, 3)): 4/12 ≈ 0.333
      ├── Some((0, 4)): 8/17 ≈ 0.471
      ├── Some((0, 5)): 13/22 ≈ 0.591
      ├── Some((0, 6)): 6/14 ≈ 0.429
      ├── Some((0, 7)): 8/17 ≈ 0.471
      └── Some((0, 8)): 21/30 ≈ 0.700
    ├── Some((6, 1)): 90/172 ≈ 0.523
      ├── Some((1, 0)): 4/12 ≈ 0.333
      ├── Some((1, 1)): 17/27 ≈ 0.630
      ├── Some((1, 2)): 4/12 ≈ 0.333
      ├── Some((1, 3)): 16/26 ≈ 0.615
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 9/18 ≈ 0.500
      ├── Some((1, 6)): 6/15 ≈ 0.400
      ├── Some((1, 7)): 16/26 ≈ 0.615
      └── Some((1, 8)): 8/17 ≈ 0.471
    ├── Some((6, 2)): 101/188 ≈ 0.537
      ├── Some((2, 0)): 9/20 ≈ 0.450
      ├── Some((2, 1)): 3/12 ≈ 0.250
      ├── Some((2, 2)): 29/41 ≈ 0.707
      ├── Some((2, 3)): 11/22 ≈ 0.500
      ├── Some((2, 4)): 14/25 ≈ 0.560
      ├── Some((2, 5)): 10/21 ≈ 0.476
      ├── Some((2, 6)): 4/13 ≈ 0.308
      └── Some((2, 7)): 21/33 ≈ 0.636
    ├── Some((6, 3)): 87/167 ≈ 0.521
      ├── Some((3, 0)): 10/19 ≈ 0.526
      ├── Some((3, 1)): 11/20 ≈ 0.550
      ├── Some((3, 2)): 6/15 ≈ 0.400
      ├── Some((3, 3)): 10/19 ≈ 0.526
      ├── Some((3, 4)): 19/28 ≈ 0.679
      ├── Some((3, 5)): 3/11 ≈ 0.273
      ├── Some((3, 6)): 15/24 ≈ 0.625
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 8/17 ≈ 0.471
    ├── Some((6, 4)): 77/152 ≈ 0.507
      ├── Some((4, 0)): 6/14 ≈ 0.429
      ├── Some((4, 1)): 5/13 ≈ 0.385
      ├── Some((4, 2)): 4/12 ≈ 0.333
      ├── Some((4, 3)): 7/15 ≈ 0.467
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 7/15 ≈ 0.467
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 19/28 ≈ 0.679
      └── Some((4, 8)): 17/26 ≈ 0.654
    ├── Some((6, 5)): 70/142 ≈ 0.493
      ├── Some((5, 0)): 19/28 ≈ 0.679
      ├── Some((5, 1)): 11/19 ≈ 0.579
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 1/8 ≈ 0.125
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 8/16 ≈ 0.500
      ├── Some((5, 6)): 10/18 ≈ 0.556
      ├── Some((5, 7)): 3/11 ≈ 0.273
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((6, 6)): 72/145 ≈ 0.497
      ├── Some((6, 0)): 15/25 ≈ 0.600
      ├── Some((6, 1)): 5/14 ≈ 0.357
      ├── Some((6, 2)): 13/23 ≈ 0.565
      ├── Some((6, 3)): 17/27 ≈ 0.630
      ├── Some((6, 4)): 0/7 ≈ 0.000
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 7)): 8/17 ≈ 0.471
      └── Some((6, 8)): 4/13 ≈ 0.308
    ├── Some((6, 7)): 83/161 ≈ 0.516
      ├── Some((7, 0)): 1/9 ≈ 0.111
      ├── Some((7, 1)): 7/16 ≈ 0.438
      ├── Some((7, 2)): 13/22 ≈ 0.591
      ├── Some((7, 3)): 21/30 ≈ 0.700
      ├── Some((7, 4)): 10/19 ≈ 0.526
      ├── Some((7, 5)): 4/12 ≈ 0.333
      ├── Some((7, 6)): 9/18 ≈ 0.500
      ├── Some((7, 7)): 13/22 ≈ 0.591
      └── Some((7, 8)): 4/12 ≈ 0.333
    └── Some((6, 8)): 75/150 ≈ 0.500
      ├── Some((8, 0)): 14/24 ≈ 0.583
      ├── Some((8, 1)): 12/22 ≈ 0.545
      ├── Some((8, 2)): 13/23 ≈ 0.565
      ├── Some((8, 3)): 6/15 ≈ 0.400
      ├── Some((8, 4)): 13/23 ≈ 0.565
      ├── Some((8, 5)): 5/14 ≈ 0.357
      ├── Some((8, 7)): 8/17 ≈ 0.471
      └── Some((8, 8)): 3/11 ≈ 0.273
  ├── Some((8, 7)): 684/1344 ≈ 0.509
    ├── Some((7, 0)): 57/121 ≈ 0.471
      ├── Some((0, 0)): 9/17 ≈ 0.529
      ├── Some((0, 1)): 14/21 ≈ 0.667
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 4/11 ≈ 0.364
      ├── Some((0, 4)): 3/10 ≈ 0.300
      ├── Some((0, 5)): 0/6 ≈ 0.000
      ├── Some((0, 6)): 14/21 ≈ 0.667
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((7, 1)): 32/82 ≈ 0.390
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 7/13 ≈ 0.538
      ├── Some((1, 3)): 10/16 ≈ 0.625
      ├── Some((1, 4)): 0/5 ≈ 0.000
      ├── Some((1, 5)): 7/13 ≈ 0.538
      ├── Some((1, 6)): 1/6 ≈ 0.167
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((7, 2)): 75/149 ≈ 0.503
      ├── Some((2, 0)): 5/14 ≈ 0.357
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 11/20 ≈ 0.550
      ├── Some((2, 3)): 13/23 ≈ 0.565
      ├── Some((2, 4)): 0/7 ≈ 0.000
      ├── Some((2, 5)): 13/23 ≈ 0.565
      ├── Some((2, 6)): 16/26 ≈ 0.615
      └── Some((2, 7)): 9/18 ≈ 0.500
    ├── Some((7, 3)): 98/182 ≈ 0.538
      ├── Some((3, 0)): 3/11 ≈ 0.273
      ├── Some((3, 1)): 9/18 ≈ 0.500
      ├── Some((3, 2)): 11/20 ≈ 0.550
      ├── Some((3, 3)): 19/29 ≈ 0.655
      ├── Some((3, 4)): 9/18 ≈ 0.500
      ├── Some((3, 5)): 9/18 ≈ 0.500
      ├── Some((3, 6)): 19/29 ≈ 0.655
      ├── Some((3, 7)): 5/14 ≈ 0.357
      └── Some((3, 8)): 14/24 ≈ 0.583
    ├── Some((7, 4)): 132/231 ≈ 0.571
      ├── Some((4, 0)): 18/29 ≈ 0.621
      ├── Some((4, 1)): 11/22 ≈ 0.500
      ├── Some((4, 2)): 25/37 ≈ 0.676
      ├── Some((4, 3)): 8/18 ≈ 0.444
      ├── Some((4, 4)): 10/21 ≈ 0.476
      ├── Some((4, 5)): 18/29 ≈ 0.621
      ├── Some((4, 6)): 6/16 ≈ 0.375
      ├── Some((4, 7)): 22/34 ≈ 0.647
      └── Some((4, 8)): 13/24 ≈ 0.542
    ├── Some((7, 5)): 105/193 ≈ 0.544
      ├── Some((5, 0)): 13/23 ≈ 0.565
      ├── Some((5, 1)): 5/14 ≈ 0.357
      ├── Some((5, 2)): 9/19 ≈ 0.474
      ├── Some((5, 3)): 11/21 ≈ 0.524
      ├── Some((5, 4)): 8/17 ≈ 0.471
      ├── Some((5, 5)): 12/22 ≈ 0.545
      ├── Some((5, 6)): 11/21 ≈ 0.524
      ├── Some((5, 7)): 13/23 ≈ 0.565
      └── Some((5, 8)): 22/32 ≈ 0.688
    ├── Some((7, 6)): 57/122 ≈ 0.467
      ├── Some((6, 0)): 3/10 ≈ 0.300
      ├── Some((6, 1)): 15/23 ≈ 0.652
      ├── Some((6, 2)): 3/10 ≈ 0.300
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 2/9 ≈ 0.222
      ├── Some((6, 5)): 7/14 ≈ 0.500
      ├── Some((6, 6)): 3/10 ≈ 0.300
      ├── Some((6, 7)): 10/18 ≈ 0.556
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((7, 7)): 64/132 ≈ 0.485
      ├── Some((7, 0)): 5/13 ≈ 0.385
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 9/17 ≈ 0.529
      ├── Some((7, 3)): 5/13 ≈ 0.385
      ├── Some((7, 4)): 10/19 ≈ 0.526
      ├── Some((7, 5)): 11/20 ≈ 0.550
      ├── Some((7, 6)): 6/14 ≈ 0.429
      └── Some((7, 8)): 11/20 ≈ 0.550
    └── Some((7, 8)): 63/131 ≈ 0.481
      ├── Some((8, 0)): 6/14 ≈ 0.429
      ├── Some((8, 1)): 16/25 ≈ 0.640
      ├── Some((8, 2)): 5/13 ≈ 0.385
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 11/20 ≈ 0.550
      ├── Some((8, 6)): 5/13 ≈ 0.385
      └── Some((8, 8)): 8/17 ≈ 0.471
  └── Some((8, 8)): 868/1663 ≈ 0.522
    ├── Some((8, 0)): 117/221 ≈ 0.529
      ├── Some((0, 0)): 19/31 ≈ 0.613
      ├── Some((0, 1)): 14/26 ≈ 0.538
      ├── Some((0, 2)): 6/16 ≈ 0.375
      ├── Some((0, 3)): 23/36 ≈ 0.639
      ├── Some((0, 4)): 5/15 ≈ 0.333
      ├── Some((0, 5)): 8/19 ≈ 0.421
      ├── Some((0, 6)): 14/26 ≈ 0.538
      ├── Some((0, 7)): 19/31 ≈ 0.613
      └── Some((0, 8)): 9/20 ≈ 0.450
    ├── Some((8, 1)): 123/230 ≈ 0.535
      ├── Some((1, 0)): 16/28 ≈ 0.571
      ├── Some((1, 1)): 28/41 ≈ 0.683
      ├── Some((1, 2)): 13/25 ≈ 0.520
      ├── Some((1, 3)): 8/19 ≈ 0.421
      ├── Some((1, 4)): 12/24 ≈ 0.500
      ├── Some((1, 5)): 4/14 ≈ 0.286
      ├── Some((1, 6)): 17/29 ≈ 0.586
      ├── Some((1, 7)): 17/30 ≈ 0.567
      └── Some((1, 8)): 8/19 ≈ 0.421
    ├── Some((8, 2)): 123/230 ≈ 0.535
      ├── Some((2, 0)): 27/42 ≈ 0.643
      ├── Some((2, 1)): 14/27 ≈ 0.519
      ├── Some((2, 2)): 19/33 ≈ 0.576
      ├── Some((2, 3)): 9/21 ≈ 0.429
      ├── Some((2, 4)): 17/31 ≈ 0.548
      ├── Some((2, 5)): 12/25 ≈ 0.480
      ├── Some((2, 6)): 10/23 ≈ 0.435
      └── Some((2, 7)): 14/27 ≈ 0.519
    ├── Some((8, 3)): 94/186 ≈ 0.505
      ├── Some((3, 0)): 14/25 ≈ 0.560
      ├── Some((3, 1)): 8/18 ≈ 0.444
      ├── Some((3, 2)): 7/17 ≈ 0.412
      ├── Some((3, 3)): 12/22 ≈ 0.545
      ├── Some((3, 4)): 9/19 ≈ 0.474
      ├── Some((3, 5)): 2/11 ≈ 0.182
      ├── Some((3, 6)): 18/29 ≈ 0.621
      ├── Some((3, 7)): 11/21 ≈ 0.524
      └── Some((3, 8)): 13/23 ≈ 0.565
    ├── Some((8, 4)): 79/163 ≈ 0.485
      ├── Some((4, 0)): 9/18 ≈ 0.500
      ├── Some((4, 1)): 11/21 ≈ 0.524
      ├── Some((4, 2)): 7/16 ≈ 0.438
      ├── Some((4, 3)): 3/11 ≈ 0.273
      ├── Some((4, 4)): 14/24 ≈ 0.583
      ├── Some((4, 5)): 3/11 ≈ 0.273
      ├── Some((4, 6)): 9/18 ≈ 0.500
      ├── Some((4, 7)): 12/22 ≈ 0.545
      └── Some((4, 8)): 11/21 ≈ 0.524
    ├── Some((8, 5)): 114/217 ≈ 0.525
      ├── Some((5, 0)): 21/33 ≈ 0.636
      ├── Some((5, 1)): 12/24 ≈ 0.500
      ├── Some((5, 2)): 6/16 ≈ 0.375
      ├── Some((5, 3)): 6/16 ≈ 0.375
      ├── Some((5, 4)): 10/21 ≈ 0.476
      ├── Some((5, 5)): 19/31 ≈ 0.613
      ├── Some((5, 6)): 13/25 ≈ 0.520
      ├── Some((5, 7)): 11/22 ≈ 0.500
      └── Some((5, 8)): 16/28 ≈ 0.571
    ├── Some((8, 6)): 81/166 ≈ 0.488
      ├── Some((6, 0)): 8/17 ≈ 0.471
      ├── Some((6, 1)): 3/12 ≈ 0.250
      ├── Some((6, 2)): 5/14 ≈ 0.357
      ├── Some((6, 3)): 5/14 ≈ 0.357
      ├── Some((6, 4)): 12/22 ≈ 0.545
      ├── Some((6, 5)): 6/15 ≈ 0.400
      ├── Some((6, 6)): 16/26 ≈ 0.615
      ├── Some((6, 7)): 11/21 ≈ 0.524
      └── Some((6, 8)): 14/24 ≈ 0.583
    └── Some((8, 7)): 136/249 ≈ 0.546
      ├── Some((7, 0)): 4/15 ≈ 0.267
      ├── Some((7, 1)): 16/29 ≈ 0.552
      ├── Some((7, 2)): 15/28 ≈ 0.536
      ├── Some((7, 3)): 18/31 ≈ 0.581
      ├── Some((7, 4)): 12/24 ≈ 0.500
      ├── Some((7, 5)): 18/31 ≈ 0.581
      ├── Some((7, 6)): 19/32 ≈ 0.594
      ├── Some((7, 7)): 21/34 ≈ 0.618
      └── Some((7, 8)): 12/24 ≈ 0.500
├── Some((3, 0)): 5165/10046 ≈ 0.514
  ├── Some((0, 0)): 757/1431 ≈ 0.529
    ├── Some((0, 1)): 89/172 ≈ 0.517
      ├── Some((1, 0)): 12/21 ≈ 0.571
      ├── Some((1, 1)): 5/14 ≈ 0.357
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 3)): 6/15 ≈ 0.400
      ├── Some((1, 4)): 12/22 ≈ 0.545
      ├── Some((1, 5)): 8/17 ≈ 0.471
      ├── Some((1, 6)): 5/14 ≈ 0.357
      ├── Some((1, 7)): 8/17 ≈ 0.471
      └── Some((1, 8)): 23/33 ≈ 0.697
    ├── Some((0, 2)): 92/177 ≈ 0.520
      ├── Some((2, 0)): 10/20 ≈ 0.500
      ├── Some((2, 1)): 10/20 ≈ 0.500
      ├── Some((2, 2)): 7/16 ≈ 0.438
      ├── Some((2, 3)): 2/10 ≈ 0.200
      ├── Some((2, 4)): 12/22 ≈ 0.545
      ├── Some((2, 5)): 12/22 ≈ 0.545
      ├── Some((2, 6)): 8/17 ≈ 0.471
      ├── Some((2, 7)): 24/34 ≈ 0.706
      └── Some((2, 8)): 6/15 ≈ 0.400
    ├── Some((0, 3)): 153/265 ≈ 0.577
      ├── Some((3, 1)): 17/31 ≈ 0.548
      ├── Some((3, 2)): 8/21 ≈ 0.381
      ├── Some((3, 3)): 1/11 ≈ 0.091
      ├── Some((3, 4)): 26/41 ≈ 0.634
      ├── Some((3, 5)): 17/31 ≈ 0.548
      ├── Some((3, 6)): 28/43 ≈ 0.651
      ├── Some((3, 7)): 24/39 ≈ 0.615
      └── Some((3, 8)): 31/47 ≈ 0.660
    ├── Some((0, 4)): 108/200 ≈ 0.540
      ├── Some((4, 0)): 14/24 ≈ 0.583
      ├── Some((4, 1)): 7/17 ≈ 0.412
      ├── Some((4, 2)): 21/32 ≈ 0.656
      ├── Some((4, 3)): 17/28 ≈ 0.607
      ├── Some((4, 4)): 4/13 ≈ 0.308
      ├── Some((4, 5)): 8/18 ≈ 0.444
      ├── Some((4, 6)): 13/23 ≈ 0.565
      ├── Some((4, 7)): 19/30 ≈ 0.633
      └── Some((4, 8)): 5/14 ≈ 0.357
    ├── Some((0, 5)): 13/51 ≈ 0.255
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 4/8 ≈ 0.500
      ├── Some((5, 5)): 0/4 ≈ 0.000
      ├── Some((5, 6)): 3/8 ≈ 0.375
      ├── Some((5, 7)): 0/4 ≈ 0.000
      └── Some((5, 8)): 1/5 ≈ 0.200
    ├── Some((0, 6)): 73/148 ≈ 0.493
      ├── Some((6, 0)): 5/13 ≈ 0.385
      ├── Some((6, 1)): 8/16 ≈ 0.500
      ├── Some((6, 2)): 8/16 ≈ 0.500
      ├── Some((6, 3)): 13/22 ≈ 0.591
      ├── Some((6, 4)): 6/14 ≈ 0.429
      ├── Some((6, 5)): 4/12 ≈ 0.333
      ├── Some((6, 6)): 4/12 ≈ 0.333
      ├── Some((6, 7)): 11/20 ≈ 0.550
      └── Some((6, 8)): 13/22 ≈ 0.591
    ├── Some((0, 7)): 139/245 ≈ 0.567
      ├── Some((7, 0)): 11/23 ≈ 0.478
      ├── Some((7, 1)): 17/29 ≈ 0.586
      ├── Some((7, 2)): 21/33 ≈ 0.636
      ├── Some((7, 3)): 10/21 ≈ 0.476
      ├── Some((7, 4)): 17/29 ≈ 0.586
      ├── Some((7, 5)): 8/19 ≈ 0.421
      ├── Some((7, 6)): 21/33 ≈ 0.636
      ├── Some((7, 7)): 24/37 ≈ 0.649
      └── Some((7, 8)): 9/20 ≈ 0.450
    └── Some((0, 8)): 89/172 ≈ 0.517
      ├── Some((8, 0)): 18/28 ≈ 0.643
      ├── Some((8, 1)): 8/17 ≈ 0.471
      ├── Some((8, 2)): 10/19 ≈ 0.526
      ├── Some((8, 3)): 8/17 ≈ 0.471
      ├── Some((8, 4)): 6/15 ≈ 0.400
      ├── Some((8, 5)): 16/26 ≈ 0.615
      ├── Some((8, 6)): 10/19 ≈ 0.526
      ├── Some((8, 7)): 8/17 ≈ 0.471
      └── Some((8, 8)): 4/13 ≈ 0.308
  ├── Some((0, 1)): 634/1222 ≈ 0.519
    ├── Some((1, 0)): 48/103 ≈ 0.466
      ├── Some((0, 0)): 5/12 ≈ 0.417
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 5/12 ≈ 0.417
      ├── Some((0, 4)): 9/16 ≈ 0.562
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 6/13 ≈ 0.462
      └── Some((0, 8)): 8/15 ≈ 0.533
    ├── Some((1, 1)): 106/186 ≈ 0.570
      ├── Some((1, 0)): 15/25 ≈ 0.600
      ├── Some((1, 2)): 8/18 ≈ 0.444
      ├── Some((1, 3)): 11/21 ≈ 0.524
      ├── Some((1, 4)): 4/13 ≈ 0.308
      ├── Some((1, 5)): 20/30 ≈ 0.667
      ├── Some((1, 6)): 15/25 ≈ 0.600
      ├── Some((1, 7)): 20/31 ≈ 0.645
      └── Some((1, 8)): 12/22 ≈ 0.545
    ├── Some((1, 2)): 84/156 ≈ 0.538
      ├── Some((2, 0)): 12/20 ≈ 0.600
      ├── Some((2, 1)): 3/11 ≈ 0.273
      ├── Some((2, 2)): 19/27 ≈ 0.704
      ├── Some((2, 3)): 12/20 ≈ 0.600
      ├── Some((2, 4)): 4/12 ≈ 0.333
      ├── Some((2, 5)): 10/18 ≈ 0.556
      ├── Some((2, 6)): 9/17 ≈ 0.529
      ├── Some((2, 7)): 8/16 ≈ 0.500
      └── Some((2, 8)): 6/14 ≈ 0.429
    ├── Some((1, 3)): 37/86 ≈ 0.430
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 7/13 ≈ 0.538
      ├── Some((3, 3)): 2/8 ≈ 0.250
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 0/5 ≈ 0.000
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 7/13 ≈ 0.538
    ├── Some((1, 4)): 78/147 ≈ 0.531
      ├── Some((4, 0)): 10/18 ≈ 0.556
      ├── Some((4, 1)): 8/16 ≈ 0.500
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 11/19 ≈ 0.579
      ├── Some((4, 4)): 15/23 ≈ 0.652
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 8/16 ≈ 0.500
      ├── Some((4, 7)): 11/19 ≈ 0.579
      └── Some((4, 8)): 3/10 ≈ 0.300
    ├── Some((1, 5)): 50/106 ≈ 0.472
      ├── Some((5, 0)): 6/12 ≈ 0.500
      ├── Some((5, 1)): 2/8 ≈ 0.250
      ├── Some((5, 2)): 2/8 ≈ 0.250
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 10/16 ≈ 0.625
      ├── Some((5, 6)): 9/15 ≈ 0.600
      ├── Some((5, 7)): 8/15 ≈ 0.533
      └── Some((5, 8)): 3/9 ≈ 0.333
    ├── Some((1, 6)): 80/150 ≈ 0.533
      ├── Some((6, 0)): 10/18 ≈ 0.556
      ├── Some((6, 1)): 12/20 ≈ 0.600
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 12/20 ≈ 0.600
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 9/17 ≈ 0.529
      ├── Some((6, 6)): 5/12 ≈ 0.417
      ├── Some((6, 7)): 16/24 ≈ 0.667
      └── Some((6, 8)): 6/14 ≈ 0.429
    ├── Some((1, 7)): 89/163 ≈ 0.546
      ├── Some((7, 0)): 6/14 ≈ 0.429
      ├── Some((7, 1)): 10/18 ≈ 0.556
      ├── Some((7, 2)): 11/19 ≈ 0.579
      ├── Some((7, 3)): 7/15 ≈ 0.467
      ├── Some((7, 4)): 10/18 ≈ 0.556
      ├── Some((7, 5)): 11/19 ≈ 0.579
      ├── Some((7, 6)): 13/21 ≈ 0.619
      ├── Some((7, 7)): 8/16 ≈ 0.500
      └── Some((7, 8)): 13/22 ≈ 0.591
    └── Some((1, 8)): 62/124 ≈ 0.500
      ├── Some((8, 0)): 16/22 ≈ 0.727
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 4/11 ≈ 0.364
      ├── Some((8, 3)): 3/10 ≈ 0.300
      ├── Some((8, 4)): 7/14 ≈ 0.500
      ├── Some((8, 5)): 7/14 ≈ 0.500
      ├── Some((8, 6)): 6/13 ≈ 0.462
      ├── Some((8, 7)): 8/15 ≈ 0.533
      └── Some((8, 8)): 5/12 ≈ 0.417
  ├── Some((0, 2)): 438/883 ≈ 0.496
    ├── Some((2, 0)): 53/105 ≈ 0.505
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 10/16 ≈ 0.625
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 10/16 ≈ 0.625
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 9/16 ≈ 0.562
      ├── Some((0, 7)): 8/15 ≈ 0.533
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((2, 1)): 54/106 ≈ 0.509
      ├── Some((1, 0)): 2/7 ≈ 0.286
      ├── Some((1, 1)): 3/9 ≈ 0.333
      ├── Some((1, 2)): 8/13 ≈ 0.615
      ├── Some((1, 3)): 7/13 ≈ 0.538
      ├── Some((1, 4)): 7/13 ≈ 0.538
      ├── Some((1, 5)): 8/14 ≈ 0.571
      ├── Some((1, 6)): 9/14 ≈ 0.643
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 5/11 ≈ 0.455
    ├── Some((2, 2)): 15/48 ≈ 0.312
      ├── Some((2, 0)): 0/4 ≈ 0.000
      ├── Some((2, 1)): 2/6 ≈ 0.333
      ├── Some((2, 3)): 0/4 ≈ 0.000
      ├── Some((2, 4)): 4/8 ≈ 0.500
      ├── Some((2, 5)): 2/6 ≈ 0.333
      ├── Some((2, 6)): 1/5 ≈ 0.200
      ├── Some((2, 7)): 1/5 ≈ 0.200
      └── Some((2, 8)): 4/9 ≈ 0.444
    ├── Some((2, 3)): 43/91 ≈ 0.473
      ├── Some((3, 1)): 3/9 ≈ 0.333
      ├── Some((3, 2)): 7/13 ≈ 0.538
      ├── Some((3, 3)): 7/13 ≈ 0.538
      ├── Some((3, 4)): 6/12 ≈ 0.500
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 4/10 ≈ 0.400
      ├── Some((3, 7)): 8/14 ≈ 0.571
      └── Some((3, 8)): 6/12 ≈ 0.500
    ├── Some((2, 4)): 52/104 ≈ 0.500
      ├── Some((4, 0)): 7/13 ≈ 0.538
      ├── Some((4, 1)): 10/16 ≈ 0.625
      ├── Some((4, 2)): 7/13 ≈ 0.538
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 1/6 ≈ 0.167
      ├── Some((4, 5)): 11/17 ≈ 0.647
      ├── Some((4, 6)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 5/11 ≈ 0.455
    ├── Some((2, 5)): 34/77 ≈ 0.442
      ├── Some((5, 0)): 6/11 ≈ 0.545
      ├── Some((5, 1)): 5/10 ≈ 0.500
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 4/9 ≈ 0.444
      ├── Some((5, 5)): 0/4 ≈ 0.000
      ├── Some((5, 6)): 1/6 ≈ 0.167
      ├── Some((5, 7)): 7/11 ≈ 0.636
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((2, 6)): 63/119 ≈ 0.529
      ├── Some((6, 0)): 8/14 ≈ 0.571
      ├── Some((6, 1)): 6/12 ≈ 0.500
      ├── Some((6, 2)): 7/13 ≈ 0.538
      ├── Some((6, 3)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 9/15 ≈ 0.600
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 11/17 ≈ 0.647
      ├── Some((6, 7)): 8/14 ≈ 0.571
      └── Some((6, 8)): 1/7 ≈ 0.143
    ├── Some((2, 7)): 102/173 ≈ 0.590
      ├── Some((7, 0)): 12/20 ≈ 0.600
      ├── Some((7, 1)): 15/23 ≈ 0.652
      ├── Some((7, 2)): 1/8 ≈ 0.125
      ├── Some((7, 3)): 16/24 ≈ 0.667
      ├── Some((7, 4)): 10/18 ≈ 0.556
      ├── Some((7, 5)): 5/13 ≈ 0.385
      ├── Some((7, 6)): 12/20 ≈ 0.600
      ├── Some((7, 7)): 19/27 ≈ 0.704
      └── Some((7, 8)): 11/19 ≈ 0.579
    └── Some((2, 8)): 22/59 ≈ 0.373
      ├── Some((8, 0)): 1/5 ≈ 0.200
      ├── Some((8, 1)): 3/7 ≈ 0.429
      ├── Some((8, 2)): 0/4 ≈ 0.000
      ├── Some((8, 3)): 4/8 ≈ 0.500
      ├── Some((8, 4)): 4/8 ≈ 0.500
      ├── Some((8, 5)): 4/8 ≈ 0.500
      ├── Some((8, 6)): 0/4 ≈ 0.000
      ├── Some((8, 7)): 1/5 ≈ 0.200
      └── Some((8, 8)): 5/9 ≈ 0.556
  ├── Some((0, 3)): 320/675 ≈ 0.474
    ├── Some((3, 1)): 23/59 ≈ 0.390
      ├── Some((1, 0)): 1/5 ≈ 0.200
      ├── Some((1, 1)): 3/7 ≈ 0.429
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 4/8 ≈ 0.500
      ├── Some((1, 6)): 2/6 ≈ 0.333
      ├── Some((1, 7)): 5/8 ≈ 0.625
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((3, 2)): 40/85 ≈ 0.471
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 8/13 ≈ 0.615
      ├── Some((2, 2)): 6/11 ≈ 0.545
      ├── Some((2, 3)): 5/10 ≈ 0.500
      ├── Some((2, 4)): 6/11 ≈ 0.545
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 5/10 ≈ 0.500
      ├── Some((2, 7)): 0/5 ≈ 0.000
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((3, 3)): 50/99 ≈ 0.505
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 16/23 ≈ 0.696
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 4/11 ≈ 0.364
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 3/9 ≈ 0.333
    ├── Some((3, 4)): 37/80 ≈ 0.463
      ├── Some((4, 0)): 6/10 ≈ 0.600
      ├── Some((4, 1)): 5/10 ≈ 0.500
      ├── Some((4, 2)): 8/12 ≈ 0.667
      ├── Some((4, 3)): 5/10 ≈ 0.500
      ├── Some((4, 4)): 0/4 ≈ 0.000
      ├── Some((4, 5)): 4/9 ≈ 0.444
      ├── Some((4, 6)): 2/7 ≈ 0.286
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 6/11 ≈ 0.545
    ├── Some((3, 5)): 42/87 ≈ 0.483
      ├── Some((5, 0)): 1/6 ≈ 0.167
      ├── Some((5, 1)): 0/5 ≈ 0.000
      ├── Some((5, 2)): 7/12 ≈ 0.583
      ├── Some((5, 3)): 11/16 ≈ 0.688
      ├── Some((5, 4)): 6/11 ≈ 0.545
      ├── Some((5, 5)): 1/6 ≈ 0.167
      ├── Some((5, 6)): 6/11 ≈ 0.545
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 3/8 ≈ 0.375
    ├── Some((3, 6)): 41/86 ≈ 0.477
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 1/6 ≈ 0.167
      ├── Some((6, 2)): 8/13 ≈ 0.615
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 4)): 7/12 ≈ 0.583
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 6)): 9/13 ≈ 0.692
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 4/9 ≈ 0.444
    ├── Some((3, 7)): 41/86 ≈ 0.477
      ├── Some((7, 0)): 3/8 ≈ 0.375
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 2)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 11/15 ≈ 0.733
      └── Some((7, 8)): 2/7 ≈ 0.286
    └── Some((3, 8)): 45/92 ≈ 0.489
      ├── Some((8, 0)): 4/9 ≈ 0.444
      ├── Some((8, 1)): 4/9 ≈ 0.444
      ├── Some((8, 2)): 5/11 ≈ 0.455
      ├── Some((8, 3)): 7/12 ≈ 0.583
      ├── Some((8, 4)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 6/11 ≈ 0.545
      ├── Some((8, 6)): 6/11 ≈ 0.545
      ├── Some((8, 7)): 1/6 ≈ 0.167
      └── Some((8, 8)): 6/11 ≈ 0.545
  ├── Some((0, 4)): 541/1062 ≈ 0.509
    ├── Some((4, 0)): 63/122 ≈ 0.516
      ├── Some((0, 0)): 12/20 ≈ 0.600
      ├── Some((0, 1)): 4/11 ≈ 0.364
      ├── Some((0, 2)): 3/10 ≈ 0.300
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 10/18 ≈ 0.556
      ├── Some((0, 7)): 14/21 ≈ 0.667
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((4, 1)): 57/114 ≈ 0.500
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 7/14 ≈ 0.500
      ├── Some((1, 2)): 3/9 ≈ 0.333
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 9/15 ≈ 0.600
      ├── Some((1, 7)): 9/15 ≈ 0.600
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((4, 2)): 72/135 ≈ 0.533
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 1)): 12/19 ≈ 0.632
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 9/16 ≈ 0.562
      ├── Some((2, 5)): 7/14 ≈ 0.500
      ├── Some((2, 6)): 10/17 ≈ 0.588
      ├── Some((2, 7)): 2/9 ≈ 0.222
      └── Some((2, 8)): 15/22 ≈ 0.682
    ├── Some((4, 3)): 49/102 ≈ 0.480
      ├── Some((3, 1)): 2/8 ≈ 0.250
      ├── Some((3, 2)): 9/16 ≈ 0.562
      ├── Some((3, 3)): 6/13 ≈ 0.462
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 11/17 ≈ 0.647
      ├── Some((3, 7)): 2/8 ≈ 0.250
      └── Some((3, 8)): 7/14 ≈ 0.500
    ├── Some((4, 4)): 46/97 ≈ 0.474
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 6/13 ≈ 0.462
      ├── Some((4, 3)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 14/20 ≈ 0.700
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 5/12 ≈ 0.417
    ├── Some((4, 5)): 61/119 ≈ 0.513
      ├── Some((5, 0)): 10/17 ≈ 0.588
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 13/19 ≈ 0.684
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 8/15 ≈ 0.533
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 7/14 ≈ 0.500
      ├── Some((5, 7)): 2/8 ≈ 0.250
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((4, 6)): 66/127 ≈ 0.520
      ├── Some((6, 0)): 10/17 ≈ 0.588
      ├── Some((6, 1)): 1/7 ≈ 0.143
      ├── Some((6, 2)): 10/17 ≈ 0.588
      ├── Some((6, 3)): 9/16 ≈ 0.562
      ├── Some((6, 4)): 12/19 ≈ 0.632
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 9/16 ≈ 0.562
      └── Some((6, 8)): 3/9 ≈ 0.333
    ├── Some((4, 7)): 87/156 ≈ 0.558
      ├── Some((7, 0)): 7/15 ≈ 0.467
      ├── Some((7, 1)): 11/19 ≈ 0.579
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 19/27 ≈ 0.704
      ├── Some((7, 4)): 5/12 ≈ 0.417
      ├── Some((7, 5)): 14/22 ≈ 0.636
      ├── Some((7, 6)): 12/20 ≈ 0.600
      ├── Some((7, 7)): 5/12 ≈ 0.417
      └── Some((7, 8)): 10/18 ≈ 0.556
    └── Some((4, 8)): 40/89 ≈ 0.449
      ├── Some((8, 0)): 0/5 ≈ 0.000
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 10/15 ≈ 0.667
      ├── Some((8, 3)): 7/12 ≈ 0.583
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 7/12 ≈ 0.583
      ├── Some((8, 6)): 1/6 ≈ 0.167
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 4/10 ≈ 0.400
  ├── Some((0, 5)): 488/970 ≈ 0.503
    ├── Some((5, 0)): 54/108 ≈ 0.500
      ├── Some((0, 0)): 7/14 ≈ 0.500
      ├── Some((0, 1)): 11/18 ≈ 0.611
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 8/15 ≈ 0.533
      ├── Some((0, 4)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 3/10 ≈ 0.300
      ├── Some((0, 7)): 14/21 ≈ 0.667
      └── Some((0, 8)): 2/8 ≈ 0.250
    ├── Some((5, 1)): 53/106 ≈ 0.500
      ├── Some((1, 0)): 3/9 ≈ 0.333
      ├── Some((1, 1)): 9/15 ≈ 0.600
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 11/16 ≈ 0.688
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 4/10 ≈ 0.400
      ├── Some((1, 6)): 3/9 ≈ 0.333
      ├── Some((1, 7)): 8/14 ≈ 0.571
      └── Some((1, 8)): 5/11 ≈ 0.455
    ├── Some((5, 2)): 68/128 ≈ 0.531
      ├── Some((2, 0)): 4/11 ≈ 0.364
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 2)): 8/15 ≈ 0.533
      ├── Some((2, 3)): 10/17 ≈ 0.588
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 2/8 ≈ 0.250
      ├── Some((2, 7)): 14/21 ≈ 0.667
      └── Some((2, 8)): 19/25 ≈ 0.760
    ├── Some((5, 3)): 41/89 ≈ 0.461
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 7/13 ≈ 0.538
      ├── Some((3, 3)): 1/7 ≈ 0.143
      ├── Some((3, 4)): 10/16 ≈ 0.625
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 7/13 ≈ 0.538
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 6/12 ≈ 0.500
    ├── Some((5, 4)): 44/93 ≈ 0.473
      ├── Some((4, 0)): 6/11 ≈ 0.545
      ├── Some((4, 1)): 5/11 ≈ 0.455
      ├── Some((4, 2)): 11/16 ≈ 0.688
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((5, 5)): 56/111 ≈ 0.505
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 11/18 ≈ 0.611
      ├── Some((5, 2)): 11/18 ≈ 0.611
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 1/7 ≈ 0.143
      ├── Some((5, 6)): 13/20 ≈ 0.650
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 2/8 ≈ 0.250
    ├── Some((5, 6)): 38/84 ≈ 0.452
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 5/10 ≈ 0.500
      ├── Some((6, 3)): 9/14 ≈ 0.643
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 5/10 ≈ 0.500
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 6/11 ≈ 0.545
    ├── Some((5, 7)): 53/106 ≈ 0.500
      ├── Some((7, 0)): 7/13 ≈ 0.538
      ├── Some((7, 1)): 0/5 ≈ 0.000
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 8/14 ≈ 0.571
      ├── Some((7, 5)): 1/7 ≈ 0.143
      ├── Some((7, 6)): 16/22 ≈ 0.727
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 8/14 ≈ 0.571
    └── Some((5, 8)): 80/144 ≈ 0.556
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 15/22 ≈ 0.682
      ├── Some((8, 3)): 9/16 ≈ 0.562
      ├── Some((8, 4)): 6/13 ≈ 0.462
      ├── Some((8, 5)): 12/20 ≈ 0.600
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 8/15 ≈ 0.533
      └── Some((8, 8)): 7/14 ≈ 0.500
  ├── Some((0, 6)): 915/1699 ≈ 0.539
    ├── Some((6, 0)): 105/194 ≈ 0.541
      ├── Some((0, 0)): 16/27 ≈ 0.593
      ├── Some((0, 1)): 21/33 ≈ 0.636
      ├── Some((0, 2)): 10/21 ≈ 0.476
      ├── Some((0, 3)): 16/27 ≈ 0.593
      ├── Some((0, 4)): 12/23 ≈ 0.522
      ├── Some((0, 5)): 14/25 ≈ 0.560
      ├── Some((0, 7)): 8/18 ≈ 0.444
      └── Some((0, 8)): 8/19 ≈ 0.421
    ├── Some((6, 1)): 83/162 ≈ 0.512
      ├── Some((1, 0)): 2/10 ≈ 0.200
      ├── Some((1, 1)): 13/22 ≈ 0.591
      ├── Some((1, 2)): 5/13 ≈ 0.385
      ├── Some((1, 3)): 11/20 ≈ 0.550
      ├── Some((1, 4)): 6/15 ≈ 0.400
      ├── Some((1, 5)): 9/18 ≈ 0.500
      ├── Some((1, 6)): 17/26 ≈ 0.654
      ├── Some((1, 7)): 5/13 ≈ 0.385
      └── Some((1, 8)): 15/24 ≈ 0.625
    ├── Some((6, 2)): 82/161 ≈ 0.509
      ├── Some((2, 0)): 6/14 ≈ 0.429
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 8/17 ≈ 0.471
      ├── Some((2, 3)): 11/20 ≈ 0.550
      ├── Some((2, 4)): 9/18 ≈ 0.500
      ├── Some((2, 5)): 12/21 ≈ 0.571
      ├── Some((2, 6)): 7/15 ≈ 0.467
      ├── Some((2, 7)): 15/24 ≈ 0.625
      └── Some((2, 8)): 6/14 ≈ 0.429
    ├── Some((6, 3)): 57/123 ≈ 0.463
      ├── Some((3, 1)): 12/21 ≈ 0.571
      ├── Some((3, 2)): 5/13 ≈ 0.385
      ├── Some((3, 3)): 13/22 ≈ 0.591
      ├── Some((3, 4)): 9/18 ≈ 0.500
      ├── Some((3, 5)): 5/13 ≈ 0.385
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 2/9 ≈ 0.222
    ├── Some((6, 4)): 80/158 ≈ 0.506
      ├── Some((4, 0)): 13/22 ≈ 0.591
      ├── Some((4, 1)): 5/13 ≈ 0.385
      ├── Some((4, 2)): 16/25 ≈ 0.640
      ├── Some((4, 3)): 14/23 ≈ 0.609
      ├── Some((4, 4)): 7/16 ≈ 0.438
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 8/17 ≈ 0.471
      └── Some((4, 8)): 3/11 ≈ 0.273
    ├── Some((6, 5)): 176/295 ≈ 0.597
      ├── Some((5, 0)): 28/42 ≈ 0.667
      ├── Some((5, 1)): 24/38 ≈ 0.632
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 3)): 16/29 ≈ 0.552
      ├── Some((5, 4)): 28/42 ≈ 0.667
      ├── Some((5, 5)): 11/23 ≈ 0.478
      ├── Some((5, 6)): 31/45 ≈ 0.689
      ├── Some((5, 7)): 13/25 ≈ 0.520
      └── Some((5, 8)): 13/26 ≈ 0.500
    ├── Some((6, 6)): 79/156 ≈ 0.506
      ├── Some((6, 0)): 3/12 ≈ 0.250
      ├── Some((6, 1)): 9/19 ≈ 0.474
      ├── Some((6, 2)): 6/15 ≈ 0.400
      ├── Some((6, 3)): 12/22 ≈ 0.545
      ├── Some((6, 4)): 19/29 ≈ 0.655
      ├── Some((6, 5)): 6/15 ≈ 0.400
      ├── Some((6, 7)): 12/22 ≈ 0.545
      └── Some((6, 8)): 11/21 ≈ 0.524
    ├── Some((6, 7)): 134/236 ≈ 0.568
      ├── Some((7, 0)): 10/21 ≈ 0.476
      ├── Some((7, 1)): 13/24 ≈ 0.542
      ├── Some((7, 2)): 12/23 ≈ 0.522
      ├── Some((7, 3)): 7/17 ≈ 0.412
      ├── Some((7, 4)): 22/34 ≈ 0.647
      ├── Some((7, 5)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 24/36 ≈ 0.667
      ├── Some((7, 7)): 16/28 ≈ 0.571
      └── Some((7, 8)): 19/31 ≈ 0.613
    └── Some((6, 8)): 118/213 ≈ 0.554
      ├── Some((8, 0)): 16/27 ≈ 0.593
      ├── Some((8, 1)): 11/21 ≈ 0.524
      ├── Some((8, 2)): 15/26 ≈ 0.577
      ├── Some((8, 3)): 21/32 ≈ 0.656
      ├── Some((8, 4)): 6/16 ≈ 0.375
      ├── Some((8, 5)): 4/13 ≈ 0.308
      ├── Some((8, 6)): 17/28 ≈ 0.607
      ├── Some((8, 7)): 15/26 ≈ 0.577
      └── Some((8, 8)): 12/23 ≈ 0.522
  ├── Some((0, 7)): 648/1246 ≈ 0.520
    ├── Some((7, 0)): 88/162 ≈ 0.543
      ├── Some((0, 0)): 10/19 ≈ 0.526
      ├── Some((0, 1)): 11/20 ≈ 0.550
      ├── Some((0, 2)): 16/26 ≈ 0.615
      ├── Some((0, 3)): 11/20 ≈ 0.550
      ├── Some((0, 4)): 8/17 ≈ 0.471
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 20/30 ≈ 0.667
      └── Some((0, 8)): 3/11 ≈ 0.273
    ├── Some((7, 1)): 54/112 ≈ 0.482
      ├── Some((1, 0)): 11/18 ≈ 0.611
      ├── Some((1, 1)): 6/13 ≈ 0.462
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 2/8 ≈ 0.250
      ├── Some((1, 5)): 10/17 ≈ 0.588
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((7, 2)): 87/160 ≈ 0.544
      ├── Some((2, 0)): 14/23 ≈ 0.609
      ├── Some((2, 1)): 9/17 ≈ 0.529
      ├── Some((2, 2)): 16/25 ≈ 0.640
      ├── Some((2, 3)): 18/26 ≈ 0.692
      ├── Some((2, 4)): 0/7 ≈ 0.000
      ├── Some((2, 5)): 7/15 ≈ 0.467
      ├── Some((2, 6)): 6/14 ≈ 0.429
      ├── Some((2, 7)): 14/23 ≈ 0.609
      └── Some((2, 8)): 2/9 ≈ 0.222
    ├── Some((7, 3)): 86/159 ≈ 0.541
      ├── Some((3, 1)): 4/12 ≈ 0.333
      ├── Some((3, 2)): 17/27 ≈ 0.630
      ├── Some((3, 3)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 16/26 ≈ 0.615
      ├── Some((3, 5)): 4/12 ≈ 0.333
      ├── Some((3, 6)): 8/17 ≈ 0.471
      ├── Some((3, 7)): 20/30 ≈ 0.667
      └── Some((3, 8)): 8/17 ≈ 0.471
    ├── Some((7, 4)): 74/141 ≈ 0.525
      ├── Some((4, 0)): 3/10 ≈ 0.300
      ├── Some((4, 1)): 4/11 ≈ 0.364
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 9/17 ≈ 0.529
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 4/11 ≈ 0.364
      ├── Some((4, 7)): 10/18 ≈ 0.556
      └── Some((4, 8)): 19/26 ≈ 0.731
    ├── Some((7, 5)): 58/118 ≈ 0.492
      ├── Some((5, 0)): 5/12 ≈ 0.417
      ├── Some((5, 1)): 7/14 ≈ 0.500
      ├── Some((5, 2)): 10/17 ≈ 0.588
      ├── Some((5, 3)): 5/12 ≈ 0.417
      ├── Some((5, 4)): 8/15 ≈ 0.533
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 11/17 ≈ 0.647
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 4/10 ≈ 0.400
    ├── Some((7, 6)): 74/142 ≈ 0.521
      ├── Some((6, 0)): 4/11 ≈ 0.364
      ├── Some((6, 1)): 15/23 ≈ 0.652
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 3)): 0/6 ≈ 0.000
      ├── Some((6, 4)): 6/13 ≈ 0.462
      ├── Some((6, 5)): 7/15 ≈ 0.467
      ├── Some((6, 6)): 12/20 ≈ 0.600
      ├── Some((6, 7)): 15/23 ≈ 0.652
      └── Some((6, 8)): 8/16 ≈ 0.500
    ├── Some((7, 7)): 65/128 ≈ 0.508
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 20/28 ≈ 0.714
      ├── Some((7, 3)): 7/15 ≈ 0.467
      ├── Some((7, 4)): 5/13 ≈ 0.385
      ├── Some((7, 5)): 5/13 ≈ 0.385
      ├── Some((7, 6)): 3/10 ≈ 0.300
      └── Some((7, 8)): 12/20 ≈ 0.600
    └── Some((7, 8)): 61/123 ≈ 0.496
      ├── Some((8, 0)): 6/13 ≈ 0.462
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 4/11 ≈ 0.364
      ├── Some((8, 3)): 10/17 ≈ 0.588
      ├── Some((8, 4)): 8/15 ≈ 0.533
      ├── Some((8, 5)): 15/22 ≈ 0.682
      ├── Some((8, 6)): 2/8 ≈ 0.250
      ├── Some((8, 7)): 5/12 ≈ 0.417
      └── Some((8, 8)): 2/9 ≈ 0.222
  └── Some((0, 8)): 423/857 ≈ 0.494
    ├── Some((8, 0)): 56/108 ≈ 0.519
      ├── Some((0, 0)): 6/12 ≈ 0.500
      ├── Some((0, 1)): 10/16 ≈ 0.625
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 8/15 ≈ 0.533
      ├── Some((0, 4)): 1/7 ≈ 0.143
      ├── Some((0, 5)): 10/16 ≈ 0.625
      ├── Some((0, 6)): 5/11 ≈ 0.455
      └── Some((0, 7)): 10/17 ≈ 0.588
    ├── Some((8, 1)): 64/120 ≈ 0.533
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 3/9 ≈ 0.333
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 12/18 ≈ 0.667
      ├── Some((1, 4)): 8/15 ≈ 0.533
      ├── Some((1, 5)): 4/10 ≈ 0.400
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 9/16 ≈ 0.562
      └── Some((1, 8)): 11/17 ≈ 0.647
    ├── Some((8, 2)): 34/77 ≈ 0.442
      ├── Some((2, 0)): 0/4 ≈ 0.000
      ├── Some((2, 1)): 4/9 ≈ 0.444
      ├── Some((2, 2)): 4/9 ≈ 0.444
      ├── Some((2, 3)): 3/8 ≈ 0.375
      ├── Some((2, 4)): 7/11 ≈ 0.636
      ├── Some((2, 5)): 7/12 ≈ 0.583
      ├── Some((2, 6)): 5/10 ≈ 0.500
      ├── Some((2, 7)): 4/9 ≈ 0.444
      └── Some((2, 8)): 0/4 ≈ 0.000
    ├── Some((8, 3)): 44/91 ≈ 0.484
      ├── Some((3, 1)): 0/5 ≈ 0.000
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 6/12 ≈ 0.500
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 7/13 ≈ 0.538
      ├── Some((3, 6)): 8/14 ≈ 0.571
      ├── Some((3, 7)): 6/12 ≈ 0.500
      └── Some((3, 8)): 9/15 ≈ 0.600
    ├── Some((8, 4)): 58/111 ≈ 0.523
      ├── Some((4, 0)): 9/15 ≈ 0.600
      ├── Some((4, 1)): 10/15 ≈ 0.667
      ├── Some((4, 2)): 10/16 ≈ 0.625
      ├── Some((4, 3)): 7/13 ≈ 0.538
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 9/15 ≈ 0.600
      ├── Some((4, 6)): 3/9 ≈ 0.333
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 5/11 ≈ 0.455
    ├── Some((8, 5)): 56/108 ≈ 0.519
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 4/10 ≈ 0.400
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 3/9 ≈ 0.333
      ├── Some((5, 6)): 9/14 ≈ 0.643
      ├── Some((5, 7)): 9/14 ≈ 0.643
      └── Some((5, 8)): 12/17 ≈ 0.706
    ├── Some((8, 6)): 35/78 ≈ 0.449
      ├── Some((6, 0)): 5/9 ≈ 0.556
      ├── Some((6, 1)): 5/10 ≈ 0.500
      ├── Some((6, 2)): 5/10 ≈ 0.500
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 6)): 6/10 ≈ 0.600
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 4/9 ≈ 0.444
    ├── Some((8, 7)): 38/82 ≈ 0.463
      ├── Some((7, 0)): 8/13 ≈ 0.615
      ├── Some((7, 1)): 6/11 ≈ 0.545
      ├── Some((7, 2)): 1/6 ≈ 0.167
      ├── Some((7, 3)): 9/13 ≈ 0.692
      ├── Some((7, 4)): 1/6 ≈ 0.167
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 1/6 ≈ 0.167
      ├── Some((7, 7)): 1/6 ≈ 0.167
      └── Some((7, 8)): 8/13 ≈ 0.615
    └── Some((8, 8)): 37/81 ≈ 0.457
      ├── Some((8, 0)): 11/16 ≈ 0.688
      ├── Some((8, 1)): 2/7 ≈ 0.286
      ├── Some((8, 2)): 3/8 ≈ 0.375
      ├── Some((8, 3)): 8/14 ≈ 0.571
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 0/5 ≈ 0.000
      └── Some((8, 7)): 2/7 ≈ 0.286
├── Some((3, 1)): 3659/7260 ≈ 0.504
  ├── Some((1, 0)): 155/364 ≈ 0.426
    ├── Some((0, 0)): 21/46 ≈ 0.457
      ├── Some((0, 1)): 3/6 ≈ 0.500
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 5/8 ≈ 0.625
      ├── Some((0, 4)): 2/5 ≈ 0.400
      ├── Some((0, 5)): 3/6 ≈ 0.500
      ├── Some((0, 6)): 2/5 ≈ 0.400
      ├── Some((0, 7)): 2/5 ≈ 0.400
      └── Some((0, 8)): 2/5 ≈ 0.400
    ├── Some((0, 1)): 30/58 ≈ 0.517
      ├── Some((1, 1)): 3/7 ≈ 0.429
      ├── Some((1, 2)): 4/7 ≈ 0.571
      ├── Some((1, 3)): 4/7 ≈ 0.571
      ├── Some((1, 4)): 4/7 ≈ 0.571
      ├── Some((1, 5)): 2/6 ≈ 0.333
      ├── Some((1, 6)): 3/7 ≈ 0.429
      ├── Some((1, 7)): 6/9 ≈ 0.667
      └── Some((1, 8)): 3/7 ≈ 0.429
    ├── Some((0, 2)): 16/39 ≈ 0.410
      ├── Some((2, 0)): 0/3 ≈ 0.000
      ├── Some((2, 1)): 0/3 ≈ 0.000
      ├── Some((2, 2)): 0/3 ≈ 0.000
      ├── Some((2, 3)): 1/4 ≈ 0.250
      ├── Some((2, 4)): 5/7 ≈ 0.714
      ├── Some((2, 5)): 1/4 ≈ 0.250
      ├── Some((2, 6)): 2/4 ≈ 0.500
      ├── Some((2, 7)): 6/7 ≈ 0.857
      └── Some((2, 8)): 0/3 ≈ 0.000
    ├── Some((0, 3)): 17/40 ≈ 0.425
      ├── Some((3, 0)): 1/4 ≈ 0.250
      ├── Some((3, 2)): 2/5 ≈ 0.400
      ├── Some((3, 3)): 0/3 ≈ 0.000
      ├── Some((3, 4)): 3/6 ≈ 0.500
      ├── Some((3, 5)): 3/6 ≈ 0.500
      ├── Some((3, 6)): 0/3 ≈ 0.000
      ├── Some((3, 7)): 3/6 ≈ 0.500
      └── Some((3, 8)): 4/6 ≈ 0.667
    ├── Some((0, 4)): 7/26 ≈ 0.269
      ├── Some((4, 0)): 0/2 ≈ 0.000
      ├── Some((4, 1)): 1/3 ≈ 0.333
      ├── Some((4, 2)): 1/3 ≈ 0.333
      ├── Some((4, 3)): 0/2 ≈ 0.000
      ├── Some((4, 4)): 0/2 ≈ 0.000
      ├── Some((4, 5)): 1/3 ≈ 0.333
      ├── Some((4, 6)): 0/2 ≈ 0.000
      ├── Some((4, 7)): 2/4 ≈ 0.500
      └── Some((4, 8)): 2/4 ≈ 0.500
    ├── Some((0, 5)): 16/39 ≈ 0.410
      ├── Some((5, 0)): 3/5 ≈ 0.600
      ├── Some((5, 1)): 1/4 ≈ 0.250
      ├── Some((5, 2)): 1/4 ≈ 0.250
      ├── Some((5, 3)): 2/4 ≈ 0.500
      ├── Some((5, 4)): 3/5 ≈ 0.600
      ├── Some((5, 5)): 1/4 ≈ 0.250
      ├── Some((5, 6)): 1/4 ≈ 0.250
      ├── Some((5, 7)): 2/4 ≈ 0.500
      └── Some((5, 8)): 2/4 ≈ 0.500
    ├── Some((0, 6)): 12/33 ≈ 0.364
      ├── Some((6, 0)): 0/3 ≈ 0.000
      ├── Some((6, 1)): 3/5 ≈ 0.600
      ├── Some((6, 2)): 1/3 ≈ 0.333
      ├── Some((6, 3)): 1/3 ≈ 0.333
      ├── Some((6, 4)): 1/3 ≈ 0.333
      ├── Some((6, 5)): 0/3 ≈ 0.000
      ├── Some((6, 6)): 1/4 ≈ 0.250
      ├── Some((6, 7)): 2/4 ≈ 0.500
      └── Some((6, 8)): 2/4 ≈ 0.500
    ├── Some((0, 7)): 20/44 ≈ 0.455
      ├── Some((7, 0)): 2/5 ≈ 0.400
      ├── Some((7, 1)): 3/5 ≈ 0.600
      ├── Some((7, 2)): 3/5 ≈ 0.600
      ├── Some((7, 3)): 3/5 ≈ 0.600
      ├── Some((7, 4)): 2/5 ≈ 0.400
      ├── Some((7, 5)): 1/4 ≈ 0.250
      ├── Some((7, 6)): 2/5 ≈ 0.400
      ├── Some((7, 7)): 3/5 ≈ 0.600
      └── Some((7, 8)): 1/4 ≈ 0.250
    └── Some((0, 8)): 15/38 ≈ 0.395
      ├── Some((8, 0)): 0/3 ≈ 0.000
      ├── Some((8, 1)): 1/4 ≈ 0.250
      ├── Some((8, 2)): 3/5 ≈ 0.600
      ├── Some((8, 3)): 2/4 ≈ 0.500
      ├── Some((8, 4)): 2/4 ≈ 0.500
      ├── Some((8, 5)): 2/4 ≈ 0.500
      ├── Some((8, 6)): 1/4 ≈ 0.250
      ├── Some((8, 7)): 1/4 ≈ 0.250
      └── Some((8, 8)): 2/5 ≈ 0.400
  ├── Some((1, 1)): 372/749 ≈ 0.497
    ├── Some((1, 0)): 28/67 ≈ 0.418
      ├── Some((0, 0)): 0/4 ≈ 0.000
      ├── Some((0, 1)): 4/8 ≈ 0.500
      ├── Some((0, 2)): 6/10 ≈ 0.600
      ├── Some((0, 3)): 4/8 ≈ 0.500
      ├── Some((0, 4)): 5/9 ≈ 0.556
      ├── Some((0, 5)): 4/8 ≈ 0.500
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 0/4 ≈ 0.000
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((1, 2)): 86/149 ≈ 0.577
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 13/20 ≈ 0.650
      ├── Some((2, 2)): 3/10 ≈ 0.300
      ├── Some((2, 3)): 15/22 ≈ 0.682
      ├── Some((2, 4)): 11/18 ≈ 0.611
      ├── Some((2, 5)): 9/16 ≈ 0.562
      ├── Some((2, 6)): 10/17 ≈ 0.588
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 9/16 ≈ 0.562
    ├── Some((1, 3)): 56/108 ≈ 0.519
      ├── Some((3, 0)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 11/17 ≈ 0.647
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 6/12 ≈ 0.500
      └── Some((3, 8)): 8/15 ≈ 0.533
    ├── Some((1, 4)): 61/115 ≈ 0.530
      ├── Some((4, 0)): 10/16 ≈ 0.625
      ├── Some((4, 1)): 7/13 ≈ 0.538
      ├── Some((4, 2)): 9/15 ≈ 0.600
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 6/12 ≈ 0.500
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 8/14 ≈ 0.571
      ├── Some((4, 7)): 7/13 ≈ 0.538
      └── Some((4, 8)): 2/8 ≈ 0.250
    ├── Some((1, 5)): 61/115 ≈ 0.530
      ├── Some((5, 0)): 6/12 ≈ 0.500
      ├── Some((5, 1)): 2/8 ≈ 0.250
      ├── Some((5, 2)): 13/19 ≈ 0.684
      ├── Some((5, 3)): 3/9 ≈ 0.333
      ├── Some((5, 4)): 4/10 ≈ 0.400
      ├── Some((5, 5)): 3/9 ≈ 0.333
      ├── Some((5, 6)): 3/9 ≈ 0.333
      ├── Some((5, 7)): 8/14 ≈ 0.571
      └── Some((5, 8)): 18/24 ≈ 0.750
    ├── Some((1, 6)): 23/59 ≈ 0.390
      ├── Some((6, 0)): 3/7 ≈ 0.429
      ├── Some((6, 1)): 4/7 ≈ 0.571
      ├── Some((6, 2)): 2/6 ≈ 0.333
      ├── Some((6, 3)): 0/4 ≈ 0.000
      ├── Some((6, 4)): 2/6 ≈ 0.333
      ├── Some((6, 5)): 4/8 ≈ 0.500
      ├── Some((6, 6)): 0/4 ≈ 0.000
      ├── Some((6, 7)): 4/8 ≈ 0.500
      └── Some((6, 8)): 4/8 ≈ 0.500
    ├── Some((1, 7)): 39/84 ≈ 0.464
      ├── Some((7, 0)): 3/8 ≈ 0.375
      ├── Some((7, 1)): 7/12 ≈ 0.583
      ├── Some((7, 2)): 6/11 ≈ 0.545
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 1/6 ≈ 0.167
      ├── Some((7, 5)): 0/4 ≈ 0.000
      ├── Some((7, 6)): 8/13 ≈ 0.615
      ├── Some((7, 7)): 6/11 ≈ 0.545
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((1, 8)): 18/51 ≈ 0.353
      ├── Some((8, 0)): 4/7 ≈ 0.571
      ├── Some((8, 1)): 1/5 ≈ 0.200
      ├── Some((8, 2)): 4/7 ≈ 0.571
      ├── Some((8, 3)): 0/3 ≈ 0.000
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 0/4 ≈ 0.000
      ├── Some((8, 7)): 5/8 ≈ 0.625
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((1, 2)): 375/754 ≈ 0.497
    ├── Some((2, 0)): 12/40 ≈ 0.300
      ├── Some((0, 0)): 2/5 ≈ 0.400
      ├── Some((0, 1)): 0/3 ≈ 0.000
      ├── Some((0, 2)): 0/3 ≈ 0.000
      ├── Some((0, 3)): 1/4 ≈ 0.250
      ├── Some((0, 4)): 0/3 ≈ 0.000
      ├── Some((0, 5)): 4/7 ≈ 0.571
      ├── Some((0, 6)): 0/3 ≈ 0.000
      ├── Some((0, 7)): 0/3 ≈ 0.000
      └── Some((0, 8)): 5/8 ≈ 0.625
    ├── Some((2, 1)): 20/53 ≈ 0.377
      ├── Some((1, 0)): 1/5 ≈ 0.200
      ├── Some((1, 1)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 1/5 ≈ 0.200
      ├── Some((1, 4)): 1/5 ≈ 0.200
      ├── Some((1, 5)): 2/6 ≈ 0.333
      ├── Some((1, 6)): 4/8 ≈ 0.500
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 6/10 ≈ 0.600
    ├── Some((2, 2)): 30/68 ≈ 0.441
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 0/4 ≈ 0.000
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 6/10 ≈ 0.600
      ├── Some((2, 6)): 4/9 ≈ 0.444
      ├── Some((2, 7)): 7/11 ≈ 0.636
      └── Some((2, 8)): 6/11 ≈ 0.545
    ├── Some((2, 3)): 39/81 ≈ 0.481
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 9/14 ≈ 0.643
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 9/14 ≈ 0.643
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((2, 4)): 47/92 ≈ 0.511
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 7/12 ≈ 0.583
      ├── Some((4, 2)): 7/12 ≈ 0.583
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 5/10 ≈ 0.500
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 7/12 ≈ 0.583
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((2, 5)): 55/103 ≈ 0.534
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 16/21 ≈ 0.762
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 0/5 ≈ 0.000
      ├── Some((5, 4)): 6/11 ≈ 0.545
      ├── Some((5, 5)): 9/14 ≈ 0.643
      ├── Some((5, 6)): 6/11 ≈ 0.545
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((2, 6)): 78/134 ≈ 0.582
      ├── Some((6, 0)): 10/16 ≈ 0.625
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 14/20 ≈ 0.700
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 15/21 ≈ 0.714
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 11/17 ≈ 0.647
    ├── Some((2, 7)): 60/110 ≈ 0.545
      ├── Some((7, 0)): 9/14 ≈ 0.643
      ├── Some((7, 1)): 0/5 ≈ 0.000
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 7/13 ≈ 0.538
      ├── Some((7, 4)): 6/12 ≈ 0.500
      ├── Some((7, 5)): 2/8 ≈ 0.250
      ├── Some((7, 6)): 13/18 ≈ 0.722
      ├── Some((7, 7)): 8/14 ≈ 0.571
      └── Some((7, 8)): 9/14 ≈ 0.643
    └── Some((2, 8)): 33/72 ≈ 0.458
      ├── Some((8, 0)): 7/11 ≈ 0.636
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 7/11 ≈ 0.636
      ├── Some((8, 3)): 4/8 ≈ 0.500
      ├── Some((8, 4)): 0/4 ≈ 0.000
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 5/9 ≈ 0.556
      └── Some((8, 8)): 2/6 ≈ 0.333
  ├── Some((1, 3)): 407/809 ≈ 0.503
    ├── Some((3, 0)): 21/58 ≈ 0.362
      ├── Some((0, 0)): 2/6 ≈ 0.333
      ├── Some((0, 1)): 1/5 ≈ 0.200
      ├── Some((0, 2)): 2/6 ≈ 0.333
      ├── Some((0, 3)): 2/6 ≈ 0.333
      ├── Some((0, 4)): 1/5 ≈ 0.200
      ├── Some((0, 5)): 4/8 ≈ 0.500
      ├── Some((0, 6)): 4/8 ≈ 0.500
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((3, 2)): 133/216 ≈ 0.616
      ├── Some((2, 0)): 27/36 ≈ 0.750
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 7/16 ≈ 0.438
      ├── Some((2, 3)): 8/17 ≈ 0.471
      ├── Some((2, 4)): 19/29 ≈ 0.655
      ├── Some((2, 5)): 20/29 ≈ 0.690
      ├── Some((2, 6)): 17/27 ≈ 0.630
      ├── Some((2, 7)): 24/33 ≈ 0.727
      └── Some((2, 8)): 3/11 ≈ 0.273
    ├── Some((3, 3)): 51/103 ≈ 0.495
      ├── Some((3, 0)): 9/17 ≈ 0.529
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 4)): 7/14 ≈ 0.500
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 5/12 ≈ 0.417
      ├── Some((3, 7)): 4/11 ≈ 0.364
      └── Some((3, 8)): 10/18 ≈ 0.556
    ├── Some((3, 4)): 72/133 ≈ 0.541
      ├── Some((4, 0)): 4/11 ≈ 0.364
      ├── Some((4, 1)): 0/6 ≈ 0.000
      ├── Some((4, 2)): 7/14 ≈ 0.500
      ├── Some((4, 3)): 12/19 ≈ 0.632
      ├── Some((4, 4)): 1/7 ≈ 0.143
      ├── Some((4, 5)): 9/16 ≈ 0.562
      ├── Some((4, 6)): 9/16 ≈ 0.562
      ├── Some((4, 7)): 13/20 ≈ 0.650
      └── Some((4, 8)): 16/23 ≈ 0.696
    ├── Some((3, 5)): 33/76 ≈ 0.434
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 6/10 ≈ 0.600
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 3)): 3/8 ≈ 0.375
      ├── Some((5, 4)): 7/11 ≈ 0.636
      ├── Some((5, 5)): 5/10 ≈ 0.500
      ├── Some((5, 6)): 5/10 ≈ 0.500
      ├── Some((5, 7)): 1/6 ≈ 0.167
      └── Some((5, 8)): 1/6 ≈ 0.167
    ├── Some((3, 6)): 7/34 ≈ 0.206
      ├── Some((6, 0)): 2/4 ≈ 0.500
      ├── Some((6, 1)): 0/3 ≈ 0.000
      ├── Some((6, 2)): 2/5 ≈ 0.400
      ├── Some((6, 3)): 0/3 ≈ 0.000
      ├── Some((6, 4)): 0/3 ≈ 0.000
      ├── Some((6, 5)): 0/3 ≈ 0.000
      ├── Some((6, 6)): 0/3 ≈ 0.000
      ├── Some((6, 7)): 1/4 ≈ 0.250
      └── Some((6, 8)): 2/5 ≈ 0.400
    ├── Some((3, 7)): 35/79 ≈ 0.443
      ├── Some((7, 0)): 6/11 ≈ 0.545
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 2)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 8/13 ≈ 0.615
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 1/6 ≈ 0.167
      ├── Some((7, 6)): 2/7 ≈ 0.286
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 0/4 ≈ 0.000
    └── Some((3, 8)): 55/109 ≈ 0.505
      ├── Some((8, 0)): 2/8 ≈ 0.250
      ├── Some((8, 1)): 8/14 ≈ 0.571
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 7/13 ≈ 0.538
      ├── Some((8, 4)): 6/12 ≈ 0.500
      ├── Some((8, 5)): 9/14 ≈ 0.643
      ├── Some((8, 6)): 6/12 ≈ 0.500
      ├── Some((8, 7)): 8/14 ≈ 0.571
      └── Some((8, 8)): 6/12 ≈ 0.500
  ├── Some((1, 4)): 495/960 ≈ 0.516
    ├── Some((4, 0)): 53/104 ≈ 0.510
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 6/12 ≈ 0.500
      ├── Some((0, 2)): 6/12 ≈ 0.500
      ├── Some((0, 3)): 1/6 ≈ 0.167
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 11/16 ≈ 0.688
      ├── Some((0, 6)): 8/14 ≈ 0.571
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 6/12 ≈ 0.500
    ├── Some((4, 1)): 49/98 ≈ 0.500
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 3/9 ≈ 0.333
      ├── Some((1, 2)): 11/17 ≈ 0.647
      ├── Some((1, 3)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 10/16 ≈ 0.625
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 10/16 ≈ 0.625
    ├── Some((4, 2)): 70/128 ≈ 0.547
      ├── Some((2, 0)): 9/15 ≈ 0.600
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 9/16 ≈ 0.562
      ├── Some((2, 4)): 7/14 ≈ 0.500
      ├── Some((2, 5)): 9/16 ≈ 0.562
      ├── Some((2, 6)): 6/13 ≈ 0.462
      ├── Some((2, 7)): 12/18 ≈ 0.667
      └── Some((2, 8)): 10/16 ≈ 0.625
    ├── Some((4, 3)): 45/93 ≈ 0.484
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 8/14 ≈ 0.571
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 7/13 ≈ 0.538
      ├── Some((3, 6)): 6/12 ≈ 0.500
      ├── Some((3, 7)): 8/14 ≈ 0.571
      └── Some((3, 8)): 4/10 ≈ 0.400
    ├── Some((4, 4)): 88/152 ≈ 0.579
      ├── Some((4, 0)): 9/17 ≈ 0.529
      ├── Some((4, 1)): 20/28 ≈ 0.714
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 14/23 ≈ 0.609
      ├── Some((4, 5)): 11/19 ≈ 0.579
      ├── Some((4, 6)): 2/9 ≈ 0.222
      ├── Some((4, 7)): 16/24 ≈ 0.667
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((4, 5)): 47/96 ≈ 0.490
      ├── Some((5, 0)): 6/12 ≈ 0.500
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 1/6 ≈ 0.167
      ├── Some((5, 3)): 6/12 ≈ 0.500
      ├── Some((5, 4)): 10/15 ≈ 0.667
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 8/13 ≈ 0.615
      ├── Some((5, 7)): 7/13 ≈ 0.538
      └── Some((5, 8)): 1/6 ≈ 0.167
    ├── Some((4, 6)): 50/100 ≈ 0.500
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 9/14 ≈ 0.643
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 9/14 ≈ 0.643
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 8/13 ≈ 0.615
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((4, 7)): 46/94 ≈ 0.489
      ├── Some((7, 0)): 3/8 ≈ 0.375
      ├── Some((7, 1)): 9/14 ≈ 0.643
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 1/6 ≈ 0.167
      ├── Some((7, 6)): 8/13 ≈ 0.615
      ├── Some((7, 7)): 2/7 ≈ 0.286
      └── Some((7, 8)): 9/14 ≈ 0.643
    └── Some((4, 8)): 46/94 ≈ 0.489
      ├── Some((8, 0)): 4/9 ≈ 0.444
      ├── Some((8, 1)): 6/11 ≈ 0.545
      ├── Some((8, 2)): 6/11 ≈ 0.545
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 8/13 ≈ 0.615
      ├── Some((8, 5)): 6/11 ≈ 0.545
      ├── Some((8, 6)): 4/9 ≈ 0.444
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 5/11 ≈ 0.455
  ├── Some((1, 5)): 385/772 ≈ 0.499
    ├── Some((5, 0)): 23/58 ≈ 0.397
      ├── Some((0, 0)): 2/6 ≈ 0.333
      ├── Some((0, 1)): 0/4 ≈ 0.000
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 3/7 ≈ 0.429
      ├── Some((0, 4)): 2/6 ≈ 0.333
      ├── Some((0, 5)): 4/7 ≈ 0.571
      ├── Some((0, 6)): 4/7 ≈ 0.571
      ├── Some((0, 7)): 3/7 ≈ 0.429
      └── Some((0, 8)): 4/8 ≈ 0.500
    ├── Some((5, 1)): 19/51 ≈ 0.373
      ├── Some((1, 0)): 2/6 ≈ 0.333
      ├── Some((1, 1)): 1/5 ≈ 0.200
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 0/4 ≈ 0.000
      ├── Some((1, 4)): 7/10 ≈ 0.700
      ├── Some((1, 6)): 5/9 ≈ 0.556
      ├── Some((1, 7)): 1/5 ≈ 0.200
      └── Some((1, 8)): 1/5 ≈ 0.200
    ├── Some((5, 2)): 36/77 ≈ 0.468
      ├── Some((2, 0)): 4/8 ≈ 0.500
      ├── Some((2, 1)): 4/8 ≈ 0.500
      ├── Some((2, 2)): 10/14 ≈ 0.714
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 4/9 ≈ 0.444
      ├── Some((2, 7)): 4/9 ≈ 0.444
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((5, 3)): 44/88 ≈ 0.500
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 4/10 ≈ 0.400
      ├── Some((3, 4)): 9/14 ≈ 0.643
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 9/14 ≈ 0.643
      ├── Some((3, 7)): 6/12 ≈ 0.500
      └── Some((3, 8)): 7/12 ≈ 0.583
    ├── Some((5, 4)): 38/80 ≈ 0.475
      ├── Some((4, 0)): 0/4 ≈ 0.000
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 5/9 ≈ 0.556
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 4)): 6/10 ≈ 0.600
      ├── Some((4, 5)): 8/12 ≈ 0.667
      ├── Some((4, 6)): 4/9 ≈ 0.444
      ├── Some((4, 7)): 4/9 ≈ 0.444
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((5, 5)): 60/111 ≈ 0.541
      ├── Some((5, 0)): 7/13 ≈ 0.538
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 7/14 ≈ 0.500
      ├── Some((5, 3)): 3/9 ≈ 0.333
      ├── Some((5, 4)): 11/17 ≈ 0.647
      ├── Some((5, 6)): 8/15 ≈ 0.533
      ├── Some((5, 7)): 9/15 ≈ 0.600
      └── Some((5, 8)): 11/17 ≈ 0.647
    ├── Some((5, 6)): 57/106 ≈ 0.538
      ├── Some((6, 0)): 8/13 ≈ 0.615
      ├── Some((6, 1)): 6/12 ≈ 0.500
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 7/13 ≈ 0.538
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 15/20 ≈ 0.750
      ├── Some((6, 6)): 8/13 ≈ 0.615
      ├── Some((6, 7)): 2/7 ≈ 0.286
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((5, 7)): 85/144 ≈ 0.590
      ├── Some((7, 0)): 14/20 ≈ 0.700
      ├── Some((7, 1)): 12/18 ≈ 0.667
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 8/15 ≈ 0.533
      ├── Some((7, 4)): 13/19 ≈ 0.684
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 7/14 ≈ 0.500
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 13/19 ≈ 0.684
    └── Some((5, 8)): 22/56 ≈ 0.393
      ├── Some((8, 0)): 3/7 ≈ 0.429
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 4/7 ≈ 0.571
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 3/7 ≈ 0.429
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 4/7 ≈ 0.571
      ├── Some((8, 7)): 3/7 ≈ 0.429
      └── Some((8, 8)): 1/5 ≈ 0.200
  ├── Some((1, 6)): 542/1039 ≈ 0.522
    ├── Some((6, 0)): 35/79 ≈ 0.443
      ├── Some((0, 0)): 0/4 ≈ 0.000
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 6/11 ≈ 0.545
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 7/12 ≈ 0.583
      ├── Some((0, 6)): 8/12 ≈ 0.667
      ├── Some((0, 7)): 7/12 ≈ 0.583
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((6, 1)): 59/114 ≈ 0.518
      ├── Some((1, 0)): 15/22 ≈ 0.682
      ├── Some((1, 1)): 4/11 ≈ 0.364
      ├── Some((1, 2)): 4/11 ≈ 0.364
      ├── Some((1, 3)): 5/12 ≈ 0.417
      ├── Some((1, 4)): 2/8 ≈ 0.250
      ├── Some((1, 5)): 10/17 ≈ 0.588
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 10/17 ≈ 0.588
    ├── Some((6, 2)): 67/125 ≈ 0.536
      ├── Some((2, 0)): 9/15 ≈ 0.600
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 6/13 ≈ 0.462
      ├── Some((2, 5)): 15/21 ≈ 0.714
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 11/17 ≈ 0.647
    ├── Some((6, 3)): 62/118 ≈ 0.525
      ├── Some((3, 0)): 15/22 ≈ 0.682
      ├── Some((3, 2)): 5/12 ≈ 0.417
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 1/8 ≈ 0.125
      ├── Some((3, 5)): 5/12 ≈ 0.417
      ├── Some((3, 6)): 7/14 ≈ 0.500
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 15/22 ≈ 0.682
    ├── Some((6, 4)): 57/111 ≈ 0.514
      ├── Some((4, 0)): 12/18 ≈ 0.667
      ├── Some((4, 1)): 8/14 ≈ 0.571
      ├── Some((4, 2)): 1/7 ≈ 0.143
      ├── Some((4, 3)): 7/13 ≈ 0.538
      ├── Some((4, 4)): 5/11 ≈ 0.455
      ├── Some((4, 5)): 0/5 ≈ 0.000
      ├── Some((4, 6)): 8/14 ≈ 0.571
      ├── Some((4, 7)): 10/16 ≈ 0.625
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((6, 5)): 99/169 ≈ 0.586
      ├── Some((5, 0)): 10/18 ≈ 0.556
      ├── Some((5, 1)): 15/22 ≈ 0.682
      ├── Some((5, 2)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 11/19 ≈ 0.579
      ├── Some((5, 4)): 11/19 ≈ 0.579
      ├── Some((5, 5)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 21/28 ≈ 0.750
      └── Some((5, 8)): 9/17 ≈ 0.529
    ├── Some((6, 6)): 36/81 ≈ 0.444
      ├── Some((6, 0)): 6/12 ≈ 0.500
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 1/6 ≈ 0.167
      ├── Some((6, 4)): 4/10 ≈ 0.400
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 12/17 ≈ 0.706
      └── Some((6, 8)): 4/10 ≈ 0.400
    ├── Some((6, 7)): 54/107 ≈ 0.505
      ├── Some((7, 0)): 12/18 ≈ 0.667
      ├── Some((7, 1)): 12/18 ≈ 0.667
      ├── Some((7, 2)): 1/6 ≈ 0.167
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 9/15 ≈ 0.600
      ├── Some((7, 5)): 1/6 ≈ 0.167
      ├── Some((7, 6)): 7/13 ≈ 0.538
      ├── Some((7, 7)): 2/8 ≈ 0.250
      └── Some((7, 8)): 8/14 ≈ 0.571
    └── Some((6, 8)): 73/134 ≈ 0.545
      ├── Some((8, 0)): 5/12 ≈ 0.417
      ├── Some((8, 1)): 9/16 ≈ 0.562
      ├── Some((8, 2)): 16/22 ≈ 0.727
      ├── Some((8, 3)): 10/16 ≈ 0.625
      ├── Some((8, 4)): 8/15 ≈ 0.533
      ├── Some((8, 5)): 6/13 ≈ 0.462
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((1, 7)): 501/970 ≈ 0.516
    ├── Some((7, 0)): 41/87 ≈ 0.471
      ├── Some((0, 0)): 0/5 ≈ 0.000
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 7/12 ≈ 0.583
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 7/12 ≈ 0.583
      ├── Some((0, 5)): 4/9 ≈ 0.444
      ├── Some((0, 6)): 2/7 ≈ 0.286
      ├── Some((0, 7)): 0/5 ≈ 0.000
      └── Some((0, 8)): 12/17 ≈ 0.706
    ├── Some((7, 1)): 60/114 ≈ 0.526
      ├── Some((1, 0)): 1/7 ≈ 0.143
      ├── Some((1, 1)): 7/14 ≈ 0.500
      ├── Some((1, 2)): 14/21 ≈ 0.667
      ├── Some((1, 3)): 1/7 ≈ 0.143
      ├── Some((1, 4)): 4/11 ≈ 0.364
      ├── Some((1, 5)): 9/16 ≈ 0.562
      ├── Some((1, 6)): 7/14 ≈ 0.500
      └── Some((1, 8)): 16/23 ≈ 0.696
    ├── Some((7, 2)): 76/136 ≈ 0.559
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 5/12 ≈ 0.417
      ├── Some((2, 2)): 13/19 ≈ 0.684
      ├── Some((2, 3)): 3/9 ≈ 0.333
      ├── Some((2, 4)): 9/16 ≈ 0.562
      ├── Some((2, 5)): 12/18 ≈ 0.667
      ├── Some((2, 6)): 12/19 ≈ 0.632
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 8/15 ≈ 0.533
    ├── Some((7, 3)): 59/113 ≈ 0.522
      ├── Some((3, 0)): 16/22 ≈ 0.727
      ├── Some((3, 2)): 6/13 ≈ 0.462
      ├── Some((3, 3)): 2/8 ≈ 0.250
      ├── Some((3, 4)): 0/6 ≈ 0.000
      ├── Some((3, 5)): 5/12 ≈ 0.417
      ├── Some((3, 6)): 9/16 ≈ 0.562
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 15/22 ≈ 0.682
    ├── Some((7, 4)): 62/117 ≈ 0.530
      ├── Some((4, 0)): 15/21 ≈ 0.714
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 13/19 ≈ 0.684
      ├── Some((4, 3)): 8/14 ≈ 0.571
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 7/13 ≈ 0.538
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 7/14 ≈ 0.500
      └── Some((4, 8)): 3/9 ≈ 0.333
    ├── Some((7, 5)): 71/130 ≈ 0.546
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 6/12 ≈ 0.500
      ├── Some((5, 4)): 11/17 ≈ 0.647
      ├── Some((5, 5)): 9/15 ≈ 0.600
      ├── Some((5, 6)): 8/15 ≈ 0.533
      ├── Some((5, 7)): 8/15 ≈ 0.533
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((7, 6)): 35/78 ≈ 0.449
      ├── Some((6, 0)): 7/12 ≈ 0.583
      ├── Some((6, 1)): 7/12 ≈ 0.583
      ├── Some((6, 2)): 0/4 ≈ 0.000
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 4)): 0/4 ≈ 0.000
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 8/13 ≈ 0.615
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((7, 7)): 44/91 ≈ 0.484
      ├── Some((7, 0)): 7/13 ≈ 0.538
      ├── Some((7, 1)): 10/16 ≈ 0.625
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 10/16 ≈ 0.625
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 0/5 ≈ 0.000
      ├── Some((7, 6)): 3/9 ≈ 0.333
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((7, 8)): 52/103 ≈ 0.505
      ├── Some((8, 0)): 9/15 ≈ 0.600
      ├── Some((8, 1)): 7/13 ≈ 0.538
      ├── Some((8, 2)): 13/18 ≈ 0.722
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 1/6 ≈ 0.167
      ├── Some((8, 5)): 10/15 ≈ 0.667
      ├── Some((8, 6)): 2/8 ≈ 0.250
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 0/5 ≈ 0.000
  └── Some((1, 8)): 426/842 ≈ 0.506
    ├── Some((8, 0)): 48/95 ≈ 0.505
      ├── Some((0, 0)): 7/12 ≈ 0.583
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 5/10 ≈ 0.500
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 4/9 ≈ 0.444
      ├── Some((0, 5)): 6/11 ≈ 0.545
      ├── Some((0, 6)): 10/15 ≈ 0.667
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((8, 1)): 40/84 ≈ 0.476
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 1/6 ≈ 0.167
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 11/16 ≈ 0.688
      ├── Some((1, 6)): 7/13 ≈ 0.538
      └── Some((1, 7)): 8/13 ≈ 0.615
    ├── Some((8, 2)): 67/121 ≈ 0.554
      ├── Some((2, 0)): 9/15 ≈ 0.600
      ├── Some((2, 1)): 7/13 ≈ 0.538
      ├── Some((2, 2)): 10/16 ≈ 0.625
      ├── Some((2, 3)): 2/8 ≈ 0.250
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 11/17 ≈ 0.647
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 15/21 ≈ 0.714
    ├── Some((8, 3)): 19/52 ≈ 0.365
      ├── Some((3, 0)): 2/6 ≈ 0.333
      ├── Some((3, 2)): 1/5 ≈ 0.200
      ├── Some((3, 3)): 1/5 ≈ 0.200
      ├── Some((3, 4)): 1/5 ≈ 0.200
      ├── Some((3, 5)): 5/9 ≈ 0.556
      ├── Some((3, 6)): 1/5 ≈ 0.200
      ├── Some((3, 7)): 4/8 ≈ 0.500
      └── Some((3, 8)): 4/8 ≈ 0.500
    ├── Some((8, 4)): 48/95 ≈ 0.505
      ├── Some((4, 0)): 5/10 ≈ 0.500
      ├── Some((4, 1)): 6/11 ≈ 0.545
      ├── Some((4, 2)): 2/7 ≈ 0.286
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 1/6 ≈ 0.167
      ├── Some((4, 5)): 6/11 ≈ 0.545
      ├── Some((4, 6)): 9/14 ≈ 0.643
      ├── Some((4, 7)): 6/11 ≈ 0.545
      └── Some((4, 8)): 8/13 ≈ 0.615
    ├── Some((8, 5)): 67/121 ≈ 0.554
      ├── Some((5, 0)): 7/13 ≈ 0.538
      ├── Some((5, 1)): 2/8 ≈ 0.250
      ├── Some((5, 2)): 10/16 ≈ 0.625
      ├── Some((5, 3)): 11/17 ≈ 0.647
      ├── Some((5, 4)): 14/20 ≈ 0.700
      ├── Some((5, 5)): 6/12 ≈ 0.500
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 8/14 ≈ 0.571
    ├── Some((8, 6)): 21/55 ≈ 0.382
      ├── Some((6, 0)): 2/6 ≈ 0.333
      ├── Some((6, 1)): 5/8 ≈ 0.625
      ├── Some((6, 2)): 3/7 ≈ 0.429
      ├── Some((6, 3)): 1/5 ≈ 0.200
      ├── Some((6, 4)): 2/6 ≈ 0.333
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 1/5 ≈ 0.200
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 4/7 ≈ 0.571
    ├── Some((8, 7)): 43/88 ≈ 0.489
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 1/6 ≈ 0.167
      ├── Some((7, 3)): 5/10 ≈ 0.500
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 5/10 ≈ 0.500
      ├── Some((7, 6)): 8/13 ≈ 0.615
      ├── Some((7, 7)): 5/10 ≈ 0.500
      └── Some((7, 8)): 9/14 ≈ 0.643
    └── Some((8, 8)): 73/130 ≈ 0.562
      ├── Some((8, 0)): 4/11 ≈ 0.364
      ├── Some((8, 1)): 14/21 ≈ 0.667
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 15/22 ≈ 0.682
      ├── Some((8, 4)): 9/16 ≈ 0.562
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 6/13 ≈ 0.462
      └── Some((8, 7)): 9/17 ≈ 0.529
├── Some((3, 2)): 3914/7733 ≈ 0.506
  ├── Some((2, 0)): 410/817 ≈ 0.502
    ├── Some((0, 0)): 60/111 ≈ 0.541
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 17/23 ≈ 0.739
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 12/18 ≈ 0.667
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 7/14 ≈ 0.500
      └── Some((0, 8)): 11/18 ≈ 0.611
    ├── Some((0, 1)): 42/86 ≈ 0.488
      ├── Some((1, 0)): 8/12 ≈ 0.667
      ├── Some((1, 1)): 0/5 ≈ 0.000
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 7/12 ≈ 0.583
      ├── Some((1, 5)): 4/9 ≈ 0.444
      ├── Some((1, 6)): 9/13 ≈ 0.692
      ├── Some((1, 7)): 4/9 ≈ 0.444
      └── Some((1, 8)): 5/10 ≈ 0.500
    ├── Some((0, 2)): 32/72 ≈ 0.444
      ├── Some((2, 1)): 5/10 ≈ 0.500
      ├── Some((2, 2)): 4/9 ≈ 0.444
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 0/5 ≈ 0.000
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 4/9 ≈ 0.444
      ├── Some((2, 7)): 2/7 ≈ 0.286
      └── Some((2, 8)): 10/15 ≈ 0.667
    ├── Some((0, 3)): 38/80 ≈ 0.475
      ├── Some((3, 0)): 5/10 ≈ 0.500
      ├── Some((3, 1)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 9/14 ≈ 0.643
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((0, 4)): 60/111 ≈ 0.541
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 10/15 ≈ 0.667
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 10/16 ≈ 0.625
      ├── Some((4, 4)): 14/19 ≈ 0.737
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((0, 5)): 43/88 ≈ 0.489
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 5/10 ≈ 0.500
      ├── Some((5, 4)): 2/7 ≈ 0.286
      ├── Some((5, 5)): 7/12 ≈ 0.583
      ├── Some((5, 6)): 14/18 ≈ 0.778
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((0, 6)): 64/117 ≈ 0.547
      ├── Some((6, 0)): 11/16 ≈ 0.688
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 12/17 ≈ 0.706
      ├── Some((6, 4)): 9/15 ≈ 0.600
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 6/12 ≈ 0.500
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 9/15 ≈ 0.600
    ├── Some((0, 7)): 47/93 ≈ 0.505
      ├── Some((7, 0)): 6/11 ≈ 0.545
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 11/16 ≈ 0.688
      ├── Some((7, 4)): 1/6 ≈ 0.167
      ├── Some((7, 5)): 5/10 ≈ 0.500
      ├── Some((7, 6)): 6/11 ≈ 0.545
      ├── Some((7, 7)): 5/10 ≈ 0.500
      └── Some((7, 8)): 6/11 ≈ 0.545
    └── Some((0, 8)): 23/58 ≈ 0.397
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 3/7 ≈ 0.429
      ├── Some((8, 2)): 2/6 ≈ 0.333
      ├── Some((8, 3)): 3/7 ≈ 0.429
      ├── Some((8, 4)): 0/4 ≈ 0.000
      ├── Some((8, 5)): 4/7 ≈ 0.571
      ├── Some((8, 6)): 1/5 ≈ 0.200
      ├── Some((8, 7)): 3/7 ≈ 0.429
      └── Some((8, 8)): 5/8 ≈ 0.625
  ├── Some((2, 1)): 599/1139 ≈ 0.526
    ├── Some((1, 0)): 67/127 ≈ 0.528
      ├── Some((0, 0)): 9/16 ≈ 0.562
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 10/16 ≈ 0.625
      ├── Some((0, 5)): 11/17 ≈ 0.647
      ├── Some((0, 6)): 8/15 ≈ 0.533
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((1, 1)): 73/136 ≈ 0.537
      ├── Some((1, 0)): 10/18 ≈ 0.556
      ├── Some((1, 2)): 9/17 ≈ 0.529
      ├── Some((1, 3)): 8/15 ≈ 0.533
      ├── Some((1, 4)): 9/17 ≈ 0.529
      ├── Some((1, 5)): 10/18 ≈ 0.556
      ├── Some((1, 6)): 7/14 ≈ 0.500
      ├── Some((1, 7)): 9/17 ≈ 0.529
      └── Some((1, 8)): 11/19 ≈ 0.579
    ├── Some((1, 2)): 85/153 ≈ 0.556
      ├── Some((2, 0)): 4/12 ≈ 0.333
      ├── Some((2, 2)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 11/20 ≈ 0.550
      ├── Some((2, 4)): 19/28 ≈ 0.679
      ├── Some((2, 5)): 6/14 ≈ 0.429
      ├── Some((2, 6)): 21/29 ≈ 0.724
      ├── Some((2, 7)): 6/14 ≈ 0.429
      └── Some((2, 8)): 11/20 ≈ 0.550
    ├── Some((1, 3)): 68/129 ≈ 0.527
      ├── Some((3, 0)): 5/12 ≈ 0.417
      ├── Some((3, 1)): 13/21 ≈ 0.619
      ├── Some((3, 3)): 6/13 ≈ 0.462
      ├── Some((3, 4)): 8/15 ≈ 0.533
      ├── Some((3, 5)): 3/10 ≈ 0.300
      ├── Some((3, 6)): 11/19 ≈ 0.579
      ├── Some((3, 7)): 14/22 ≈ 0.636
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((1, 4)): 53/107 ≈ 0.495
      ├── Some((4, 0)): 6/12 ≈ 0.500
      ├── Some((4, 1)): 9/15 ≈ 0.600
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 12/18 ≈ 0.667
      ├── Some((4, 4)): 5/11 ≈ 0.455
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((1, 5)): 85/153 ≈ 0.556
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 3/10 ≈ 0.300
      ├── Some((5, 2)): 13/20 ≈ 0.650
      ├── Some((5, 3)): 12/20 ≈ 0.600
      ├── Some((5, 4)): 11/19 ≈ 0.579
      ├── Some((5, 5)): 10/18 ≈ 0.556
      ├── Some((5, 6)): 13/21 ≈ 0.619
      ├── Some((5, 7)): 2/9 ≈ 0.222
      └── Some((5, 8)): 13/21 ≈ 0.619
    ├── Some((1, 6)): 62/120 ≈ 0.517
      ├── Some((6, 0)): 10/17 ≈ 0.588
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 2/8 ≈ 0.250
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 14/20 ≈ 0.700
      ├── Some((6, 7)): 8/15 ≈ 0.533
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((1, 7)): 61/119 ≈ 0.513
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 6/12 ≈ 0.500
      ├── Some((7, 3)): 12/18 ≈ 0.667
      ├── Some((7, 4)): 6/13 ≈ 0.462
      ├── Some((7, 5)): 9/16 ≈ 0.562
      ├── Some((7, 6)): 3/9 ≈ 0.333
      ├── Some((7, 7)): 8/15 ≈ 0.533
      └── Some((7, 8)): 10/16 ≈ 0.625
    └── Some((1, 8)): 44/94 ≈ 0.468
      ├── Some((8, 0)): 6/12 ≈ 0.500
      ├── Some((8, 1)): 1/6 ≈ 0.167
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 6/12 ≈ 0.500
      ├── Some((8, 4)): 10/15 ≈ 0.667
      ├── Some((8, 5)): 8/14 ≈ 0.571
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 1/6 ≈ 0.167
      └── Some((8, 8)): 3/9 ≈ 0.333
  ├── Some((2, 2)): 478/934 ≈ 0.512
    ├── Some((2, 0)): 37/83 ≈ 0.446
      ├── Some((0, 0)): 4/9 ≈ 0.444
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 6/11 ≈ 0.545
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 8/13 ≈ 0.615
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((2, 1)): 71/133 ≈ 0.534
      ├── Some((1, 0)): 15/22 ≈ 0.682
      ├── Some((1, 1)): 0/6 ≈ 0.000
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 3)): 11/18 ≈ 0.611
      ├── Some((1, 4)): 11/18 ≈ 0.611
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 5/12 ≈ 0.417
    ├── Some((2, 3)): 71/133 ≈ 0.534
      ├── Some((3, 0)): 9/17 ≈ 0.529
      ├── Some((3, 1)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 17/25 ≈ 0.680
      ├── Some((3, 4)): 4/11 ≈ 0.364
      ├── Some((3, 5)): 4/11 ≈ 0.364
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 9/17 ≈ 0.529
      └── Some((3, 8)): 14/22 ≈ 0.636
    ├── Some((2, 4)): 73/136 ≈ 0.537
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 12/19 ≈ 0.632
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 14/21 ≈ 0.667
      ├── Some((4, 4)): 14/21 ≈ 0.667
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 6/13 ≈ 0.462
      ├── Some((4, 7)): 3/10 ≈ 0.300
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((2, 5)): 41/90 ≈ 0.456
      ├── Some((5, 0)): 11/16 ≈ 0.688
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 0/5 ≈ 0.000
      ├── Some((5, 4)): 4/10 ≈ 0.400
      ├── Some((5, 5)): 9/14 ≈ 0.643
      ├── Some((5, 6)): 3/9 ≈ 0.333
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 4/10 ≈ 0.400
    ├── Some((2, 6)): 54/109 ≈ 0.495
      ├── Some((6, 0)): 5/11 ≈ 0.455
      ├── Some((6, 1)): 8/14 ≈ 0.571
      ├── Some((6, 2)): 2/8 ≈ 0.250
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 8/15 ≈ 0.533
      ├── Some((6, 5)): 10/16 ≈ 0.625
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 7/13 ≈ 0.538
    ├── Some((2, 7)): 44/94 ≈ 0.468
      ├── Some((7, 0)): 14/19 ≈ 0.737
      ├── Some((7, 1)): 6/12 ≈ 0.500
      ├── Some((7, 2)): 7/13 ≈ 0.538
      ├── Some((7, 3)): 1/6 ≈ 0.167
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 1/6 ≈ 0.167
      ├── Some((7, 7)): 1/6 ≈ 0.167
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((2, 8)): 87/155 ≈ 0.561
      ├── Some((8, 0)): 18/26 ≈ 0.692
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 10/18 ≈ 0.556
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 4/11 ≈ 0.364
      ├── Some((8, 5)): 10/18 ≈ 0.556
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 19/26 ≈ 0.731
      └── Some((8, 8)): 9/17 ≈ 0.529
  ├── Some((2, 3)): 380/765 ≈ 0.497
    ├── Some((3, 0)): 43/90 ≈ 0.478
      ├── Some((0, 0)): 9/14 ≈ 0.643
      ├── Some((0, 1)): 1/6 ≈ 0.167
      ├── Some((0, 2)): 6/11 ≈ 0.545
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 4/9 ≈ 0.444
      ├── Some((0, 6)): 8/13 ≈ 0.615
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((3, 1)): 84/147 ≈ 0.571
      ├── Some((1, 0)): 10/17 ≈ 0.588
      ├── Some((1, 1)): 10/17 ≈ 0.588
      ├── Some((1, 2)): 15/22 ≈ 0.682
      ├── Some((1, 3)): 17/24 ≈ 0.708
      ├── Some((1, 4)): 4/11 ≈ 0.364
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 3/10 ≈ 0.300
      ├── Some((1, 7)): 12/19 ≈ 0.632
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((3, 3)): 38/82 ≈ 0.463
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 11/18 ≈ 0.611
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 4/10 ≈ 0.400
    ├── Some((3, 4)): 31/72 ≈ 0.431
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 1/5 ≈ 0.200
      ├── Some((4, 2)): 0/4 ≈ 0.000
      ├── Some((4, 3)): 9/13 ≈ 0.692
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 5/9 ≈ 0.556
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((3, 5)): 51/101 ≈ 0.505
      ├── Some((5, 0)): 8/13 ≈ 0.615
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 7/12 ≈ 0.583
      ├── Some((5, 3)): 7/13 ≈ 0.538
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 1/6 ≈ 0.167
      ├── Some((5, 7)): 8/13 ≈ 0.615
      └── Some((5, 8)): 1/6 ≈ 0.167
    ├── Some((3, 6)): 42/88 ≈ 0.477
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 4/9 ≈ 0.444
      ├── Some((6, 3)): 6/11 ≈ 0.545
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 7/12 ≈ 0.583
      ├── Some((6, 7)): 8/13 ≈ 0.615
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((3, 7)): 64/120 ≈ 0.533
      ├── Some((7, 0)): 10/16 ≈ 0.625
      ├── Some((7, 1)): 11/17 ≈ 0.647
      ├── Some((7, 2)): 17/23 ≈ 0.739
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 6/12 ≈ 0.500
      ├── Some((7, 5)): 8/15 ≈ 0.533
      ├── Some((7, 6)): 0/6 ≈ 0.000
      ├── Some((7, 7)): 6/12 ≈ 0.500
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((3, 8)): 26/64 ≈ 0.406
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 1/5 ≈ 0.200
      ├── Some((8, 2)): 0/4 ≈ 0.000
      ├── Some((8, 3)): 0/4 ≈ 0.000
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 5/9 ≈ 0.556
      ├── Some((8, 7)): 9/13 ≈ 0.692
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((2, 4)): 348/710 ≈ 0.490
    ├── Some((4, 0)): 46/89 ≈ 0.517
      ├── Some((0, 0)): 5/10 ≈ 0.500
      ├── Some((0, 1)): 9/13 ≈ 0.692
      ├── Some((0, 2)): 5/10 ≈ 0.500
      ├── Some((0, 3)): 7/11 ≈ 0.636
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 6/11 ≈ 0.545
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 7/12 ≈ 0.583
    ├── Some((4, 1)): 32/69 ≈ 0.464
      ├── Some((1, 0)): 2/7 ≈ 0.286
      ├── Some((1, 1)): 4/8 ≈ 0.500
      ├── Some((1, 2)): 4/8 ≈ 0.500
      ├── Some((1, 3)): 4/8 ≈ 0.500
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 4/8 ≈ 0.500
      ├── Some((1, 6)): 1/5 ≈ 0.200
      ├── Some((1, 7)): 7/11 ≈ 0.636
      └── Some((1, 8)): 1/5 ≈ 0.200
    ├── Some((4, 2)): 60/108 ≈ 0.556
      ├── Some((2, 0)): 10/16 ≈ 0.625
      ├── Some((2, 1)): 8/14 ≈ 0.571
      ├── Some((2, 2)): 16/22 ≈ 0.727
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 5)): 10/16 ≈ 0.625
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 0/6 ≈ 0.000
      └── Some((2, 8)): 5/11 ≈ 0.455
    ├── Some((4, 3)): 37/77 ≈ 0.481
      ├── Some((3, 0)): 10/14 ≈ 0.714
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 5/10 ≈ 0.500
      ├── Some((3, 6)): 0/5 ≈ 0.000
      ├── Some((3, 7)): 7/12 ≈ 0.583
      └── Some((3, 8)): 9/14 ≈ 0.643
    ├── Some((4, 4)): 38/78 ≈ 0.487
      ├── Some((4, 0)): 5/10 ≈ 0.500
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 10/15 ≈ 0.667
      ├── Some((4, 3)): 8/13 ≈ 0.615
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 0/5 ≈ 0.000
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 7/12 ≈ 0.583
    ├── Some((4, 5)): 27/62 ≈ 0.435
      ├── Some((5, 0)): 4/7 ≈ 0.571
      ├── Some((5, 1)): 3/7 ≈ 0.429
      ├── Some((5, 2)): 1/5 ≈ 0.200
      ├── Some((5, 3)): 4/8 ≈ 0.500
      ├── Some((5, 4)): 3/7 ≈ 0.429
      ├── Some((5, 5)): 3/7 ≈ 0.429
      ├── Some((5, 6)): 5/8 ≈ 0.625
      ├── Some((5, 7)): 2/6 ≈ 0.333
      └── Some((5, 8)): 2/6 ≈ 0.333
    ├── Some((4, 6)): 41/82 ≈ 0.500
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 5/9 ≈ 0.556
      ├── Some((6, 2)): 12/16 ≈ 0.750
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 5/9 ≈ 0.556
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 7/11 ≈ 0.636
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((4, 7)): 32/70 ≈ 0.457
      ├── Some((7, 0)): 1/5 ≈ 0.200
      ├── Some((7, 1)): 10/14 ≈ 0.714
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 4/8 ≈ 0.500
      ├── Some((7, 4)): 1/5 ≈ 0.200
      ├── Some((7, 5)): 3/8 ≈ 0.375
      ├── Some((7, 6)): 0/4 ≈ 0.000
      ├── Some((7, 7)): 8/12 ≈ 0.667
      └── Some((7, 8)): 1/5 ≈ 0.200
    └── Some((4, 8)): 35/74 ≈ 0.473
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 1/5 ≈ 0.200
      ├── Some((8, 2)): 0/4 ≈ 0.000
      ├── Some((8, 3)): 4/8 ≈ 0.500
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 7/11 ≈ 0.636
      ├── Some((8, 7)): 10/14 ≈ 0.714
      └── Some((8, 8)): 6/10 ≈ 0.600
  ├── Some((2, 5)): 337/691 ≈ 0.488
    ├── Some((5, 0)): 76/130 ≈ 0.585
      ├── Some((0, 0)): 14/20 ≈ 0.700
      ├── Some((0, 1)): 20/26 ≈ 0.769
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 6/12 ≈ 0.500
      ├── Some((0, 4)): 7/13 ≈ 0.538
      ├── Some((0, 5)): 10/16 ≈ 0.625
      ├── Some((0, 6)): 7/13 ≈ 0.538
      ├── Some((0, 7)): 6/12 ≈ 0.500
      └── Some((0, 8)): 2/8 ≈ 0.250
    ├── Some((5, 1)): 33/71 ≈ 0.465
      ├── Some((1, 0)): 8/12 ≈ 0.667
      ├── Some((1, 1)): 4/8 ≈ 0.500
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 5/9 ≈ 0.556
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 1/5 ≈ 0.200
      └── Some((1, 8)): 5/9 ≈ 0.556
    ├── Some((5, 2)): 49/93 ≈ 0.527
      ├── Some((2, 0)): 18/23 ≈ 0.783
      ├── Some((2, 1)): 6/12 ≈ 0.500
      ├── Some((2, 2)): 9/14 ≈ 0.643
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 0/5 ≈ 0.000
      └── Some((2, 8)): 8/14 ≈ 0.571
    ├── Some((5, 3)): 39/79 ≈ 0.494
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 7/12 ≈ 0.583
      ├── Some((3, 3)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 0/5 ≈ 0.000
      ├── Some((3, 5)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 8/13 ≈ 0.615
      ├── Some((3, 7)): 5/10 ≈ 0.500
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((5, 4)): 15/44 ≈ 0.341
      ├── Some((4, 0)): 0/3 ≈ 0.000
      ├── Some((4, 1)): 2/6 ≈ 0.333
      ├── Some((4, 2)): 3/6 ≈ 0.500
      ├── Some((4, 3)): 4/7 ≈ 0.571
      ├── Some((4, 4)): 0/3 ≈ 0.000
      ├── Some((4, 5)): 0/3 ≈ 0.000
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 4/7 ≈ 0.571
      └── Some((4, 8)): 0/3 ≈ 0.000
    ├── Some((5, 5)): 43/85 ≈ 0.506
      ├── Some((5, 0)): 8/13 ≈ 0.615
      ├── Some((5, 1)): 8/13 ≈ 0.615
      ├── Some((5, 2)): 5/10 ≈ 0.500
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 1/6 ≈ 0.167
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 7/12 ≈ 0.583
    ├── Some((5, 6)): 32/70 ≈ 0.457
      ├── Some((6, 0)): 2/6 ≈ 0.333
      ├── Some((6, 1)): 0/4 ≈ 0.000
      ├── Some((6, 2)): 6/10 ≈ 0.600
      ├── Some((6, 3)): 5/9 ≈ 0.556
      ├── Some((6, 4)): 4/8 ≈ 0.500
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 9/13 ≈ 0.692
      ├── Some((6, 7)): 2/6 ≈ 0.333
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((5, 7)): 27/62 ≈ 0.435
      ├── Some((7, 0)): 5/9 ≈ 0.556
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 2/6 ≈ 0.333
      ├── Some((7, 3)): 3/7 ≈ 0.429
      ├── Some((7, 4)): 0/4 ≈ 0.000
      ├── Some((7, 5)): 6/9 ≈ 0.667
      ├── Some((7, 6)): 2/6 ≈ 0.333
      ├── Some((7, 7)): 6/10 ≈ 0.600
      └── Some((7, 8)): 1/5 ≈ 0.200
    └── Some((5, 8)): 23/56 ≈ 0.411
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 2/6 ≈ 0.333
      ├── Some((8, 2)): 7/10 ≈ 0.700
      ├── Some((8, 3)): 3/6 ≈ 0.500
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 3/6 ≈ 0.500
      ├── Some((8, 6)): 3/6 ≈ 0.500
      ├── Some((8, 7)): 0/4 ≈ 0.000
      └── Some((8, 8)): 1/5 ≈ 0.200
  ├── Some((2, 6)): 430/852 ≈ 0.505
    ├── Some((6, 0)): 35/77 ≈ 0.455
      ├── Some((0, 0)): 0/4 ≈ 0.000
      ├── Some((0, 1)): 5/10 ≈ 0.500
      ├── Some((0, 2)): 6/10 ≈ 0.600
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 6/10 ≈ 0.600
      ├── Some((0, 5)): 4/9 ≈ 0.444
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 1/6 ≈ 0.167
    ├── Some((6, 1)): 65/119 ≈ 0.546
      ├── Some((1, 0)): 9/15 ≈ 0.600
      ├── Some((1, 1)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 1/7 ≈ 0.143
      ├── Some((1, 3)): 13/18 ≈ 0.722
      ├── Some((1, 4)): 4/10 ≈ 0.400
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 13/19 ≈ 0.684
      ├── Some((1, 7)): 11/17 ≈ 0.647
      └── Some((1, 8)): 5/11 ≈ 0.455
    ├── Some((6, 2)): 53/102 ≈ 0.520
      ├── Some((2, 0)): 12/18 ≈ 0.667
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 7/13 ≈ 0.538
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 7/13 ≈ 0.538
      ├── Some((2, 5)): 6/12 ≈ 0.500
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 9/15 ≈ 0.600
    ├── Some((6, 3)): 44/90 ≈ 0.489
      ├── Some((3, 0)): 3/8 ≈ 0.375
      ├── Some((3, 1)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 5/11 ≈ 0.455
      ├── Some((3, 4)): 7/13 ≈ 0.538
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 6/12 ≈ 0.500
      └── Some((3, 8)): 11/16 ≈ 0.688
    ├── Some((6, 4)): 46/92 ≈ 0.500
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 5/10 ≈ 0.500
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 6/11 ≈ 0.545
      ├── Some((4, 6)): 5/10 ≈ 0.500
      ├── Some((4, 7)): 7/12 ≈ 0.583
      └── Some((4, 8)): 7/12 ≈ 0.583
    ├── Some((6, 5)): 40/84 ≈ 0.476
      ├── Some((5, 0)): 0/4 ≈ 0.000
      ├── Some((5, 1)): 8/13 ≈ 0.615
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 5/10 ≈ 0.500
      ├── Some((5, 4)): 8/13 ≈ 0.615
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 0/4 ≈ 0.000
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 8/13 ≈ 0.615
    ├── Some((6, 6)): 41/85 ≈ 0.482
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 7/13 ≈ 0.538
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 5/11 ≈ 0.455
      └── Some((6, 8)): 9/14 ≈ 0.643
    ├── Some((6, 7)): 75/133 ≈ 0.564
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 3/9 ≈ 0.333
      ├── Some((7, 2)): 9/16 ≈ 0.562
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 4)): 15/21 ≈ 0.714
      ├── Some((7, 5)): 9/16 ≈ 0.562
      ├── Some((7, 6)): 12/18 ≈ 0.667
      ├── Some((7, 7)): 9/16 ≈ 0.562
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((6, 8)): 30/69 ≈ 0.435
      ├── Some((8, 0)): 7/11 ≈ 0.636
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 2/7 ≈ 0.286
      ├── Some((8, 4)): 4/8 ≈ 0.500
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 5/9 ≈ 0.556
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 4/8 ≈ 0.500
  ├── Some((2, 7)): 355/722 ≈ 0.492
    ├── Some((7, 0)): 46/90 ≈ 0.511
      ├── Some((0, 0)): 8/12 ≈ 0.667
      ├── Some((0, 1)): 7/12 ≈ 0.583
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 7/12 ≈ 0.583
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 8/12 ≈ 0.667
    ├── Some((7, 1)): 45/89 ≈ 0.506
      ├── Some((1, 0)): 8/12 ≈ 0.667
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 5/10 ≈ 0.500
      ├── Some((1, 3)): 8/13 ≈ 0.615
      ├── Some((1, 4)): 8/13 ≈ 0.615
      ├── Some((1, 5)): 0/5 ≈ 0.000
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 9/13 ≈ 0.692
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((7, 2)): 22/56 ≈ 0.393
      ├── Some((2, 0)): 5/9 ≈ 0.556
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 2/6 ≈ 0.333
      ├── Some((2, 3)): 1/5 ≈ 0.200
      ├── Some((2, 4)): 4/8 ≈ 0.500
      ├── Some((2, 5)): 6/10 ≈ 0.600
      ├── Some((2, 6)): 0/4 ≈ 0.000
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((7, 3)): 28/64 ≈ 0.438
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 5/9 ≈ 0.556
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 4)): 1/5 ≈ 0.200
      ├── Some((3, 5)): 5/10 ≈ 0.500
      ├── Some((3, 6)): 5/10 ≈ 0.500
      ├── Some((3, 7)): 2/7 ≈ 0.286
      └── Some((3, 8)): 3/8 ≈ 0.375
    ├── Some((7, 4)): 41/83 ≈ 0.494
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 5/9 ≈ 0.556
      ├── Some((4, 4)): 0/4 ≈ 0.000
      ├── Some((4, 5)): 9/13 ≈ 0.692
      ├── Some((4, 6)): 4/9 ≈ 0.444
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((7, 5)): 17/48 ≈ 0.354
      ├── Some((5, 0)): 5/8 ≈ 0.625
      ├── Some((5, 1)): 0/3 ≈ 0.000
      ├── Some((5, 2)): 0/3 ≈ 0.000
      ├── Some((5, 3)): 0/3 ≈ 0.000
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 2/5 ≈ 0.400
      ├── Some((5, 6)): 1/5 ≈ 0.200
      ├── Some((5, 7)): 6/9 ≈ 0.667
      └── Some((5, 8)): 2/6 ≈ 0.333
    ├── Some((7, 6)): 90/150 ≈ 0.600
      ├── Some((6, 0)): 10/16 ≈ 0.625
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 6/13 ≈ 0.462
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 6/13 ≈ 0.462
      ├── Some((6, 5)): 9/16 ≈ 0.562
      ├── Some((6, 6)): 20/26 ≈ 0.769
      ├── Some((6, 7)): 10/17 ≈ 0.588
      └── Some((6, 8)): 13/19 ≈ 0.684
    ├── Some((7, 7)): 15/45 ≈ 0.333
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 2/6 ≈ 0.333
      ├── Some((7, 5)): 3/6 ≈ 0.500
      ├── Some((7, 6)): 0/3 ≈ 0.000
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((7, 8)): 50/96 ≈ 0.521
      ├── Some((8, 0)): 6/11 ≈ 0.545
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 3/8 ≈ 0.375
      ├── Some((8, 3)): 11/16 ≈ 0.688
      ├── Some((8, 4)): 10/15 ≈ 0.667
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 4/9 ≈ 0.444
      ├── Some((8, 7)): 4/9 ≈ 0.444
      └── Some((8, 8)): 5/11 ≈ 0.455
  └── Some((2, 8)): 577/1102 ≈ 0.524
    ├── Some((8, 0)): 64/123 ≈ 0.520
      ├── Some((0, 0)): 12/18 ≈ 0.667
      ├── Some((0, 1)): 9/15 ≈ 0.600
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 9/16 ≈ 0.562
      ├── Some((0, 7)): 2/8 ≈ 0.250
      └── Some((0, 8)): 9/16 ≈ 0.562
    ├── Some((8, 1)): 44/94 ≈ 0.468
      ├── Some((1, 0)): 3/8 ≈ 0.375
      ├── Some((1, 1)): 1/6 ≈ 0.167
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 8/13 ≈ 0.615
      ├── Some((1, 4)): 6/12 ≈ 0.500
      ├── Some((1, 5)): 9/14 ≈ 0.643
      ├── Some((1, 6)): 3/9 ≈ 0.333
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((8, 2)): 83/149 ≈ 0.557
      ├── Some((2, 0)): 8/16 ≈ 0.500
      ├── Some((2, 1)): 16/25 ≈ 0.640
      ├── Some((2, 2)): 13/22 ≈ 0.591
      ├── Some((2, 3)): 4/12 ≈ 0.333
      ├── Some((2, 4)): 19/27 ≈ 0.704
      ├── Some((2, 5)): 7/15 ≈ 0.467
      ├── Some((2, 6)): 10/18 ≈ 0.556
      └── Some((2, 7)): 5/13 ≈ 0.385
    ├── Some((8, 3)): 58/114 ≈ 0.509
      ├── Some((3, 0)): 7/14 ≈ 0.500
      ├── Some((3, 1)): 13/20 ≈ 0.650
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 14/21 ≈ 0.667
      ├── Some((3, 6)): 5/12 ≈ 0.417
      ├── Some((3, 7)): 0/6 ≈ 0.000
      └── Some((3, 8)): 3/10 ≈ 0.300
    ├── Some((8, 4)): 73/135 ≈ 0.541
      ├── Some((4, 0)): 1/7 ≈ 0.143
      ├── Some((4, 1)): 16/23 ≈ 0.696
      ├── Some((4, 2)): 9/16 ≈ 0.562
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 4)): 10/17 ≈ 0.588
      ├── Some((4, 5)): 12/19 ≈ 0.632
      ├── Some((4, 6)): 1/7 ≈ 0.143
      ├── Some((4, 7)): 14/21 ≈ 0.667
      └── Some((4, 8)): 3/10 ≈ 0.300
    ├── Some((8, 5)): 82/148 ≈ 0.554
      ├── Some((5, 0)): 18/25 ≈ 0.720
      ├── Some((5, 1)): 12/20 ≈ 0.600
      ├── Some((5, 2)): 9/16 ≈ 0.562
      ├── Some((5, 3)): 9/16 ≈ 0.562
      ├── Some((5, 4)): 4/11 ≈ 0.364
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 4/11 ≈ 0.364
      ├── Some((5, 7)): 5/12 ≈ 0.417
      └── Some((5, 8)): 11/19 ≈ 0.579
    ├── Some((8, 6)): 56/111 ≈ 0.505
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 8/14 ≈ 0.571
      ├── Some((6, 2)): 1/7 ≈ 0.143
      ├── Some((6, 3)): 8/14 ≈ 0.571
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 8/14 ≈ 0.571
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 10/16 ≈ 0.625
    ├── Some((8, 7)): 31/74 ≈ 0.419
      ├── Some((7, 0)): 5/10 ≈ 0.500
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 7/11 ≈ 0.636
      ├── Some((7, 4)): 1/6 ≈ 0.167
      ├── Some((7, 5)): 0/4 ≈ 0.000
      ├── Some((7, 6)): 5/10 ≈ 0.500
      ├── Some((7, 7)): 5/10 ≈ 0.500
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((8, 8)): 86/153 ≈ 0.562
      ├── Some((8, 0)): 12/20 ≈ 0.600
      ├── Some((8, 1)): 8/16 ≈ 0.500
      ├── Some((8, 2)): 12/20 ≈ 0.600
      ├── Some((8, 3)): 15/24 ≈ 0.625
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 10/18 ≈ 0.556
      ├── Some((8, 6)): 8/16 ≈ 0.500
      └── Some((8, 7)): 16/25 ≈ 0.640
├── Some((3, 3)): 4861/9486 ≈ 0.512
  ├── Some((3, 0)): 754/1440 ≈ 0.524
    ├── Some((0, 0)): 72/143 ≈ 0.503
      ├── Some((0, 1)): 9/18 ≈ 0.500
      ├── Some((0, 2)): 3/11 ≈ 0.273
      ├── Some((0, 3)): 6/14 ≈ 0.429
      ├── Some((0, 4)): 7/16 ≈ 0.438
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 8/17 ≈ 0.471
      ├── Some((0, 7)): 10/19 ≈ 0.526
      └── Some((0, 8)): 20/29 ≈ 0.690
    ├── Some((0, 1)): 81/156 ≈ 0.519
      ├── Some((1, 0)): 3/11 ≈ 0.273
      ├── Some((1, 1)): 10/19 ≈ 0.526
      ├── Some((1, 2)): 3/11 ≈ 0.273
      ├── Some((1, 3)): 2/9 ≈ 0.222
      ├── Some((1, 4)): 22/30 ≈ 0.733
      ├── Some((1, 5)): 8/16 ≈ 0.500
      ├── Some((1, 6)): 13/22 ≈ 0.591
      ├── Some((1, 7)): 11/20 ≈ 0.550
      └── Some((1, 8)): 9/17 ≈ 0.529
    ├── Some((0, 2)): 55/117 ≈ 0.470
      ├── Some((2, 0)): 12/19 ≈ 0.632
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 2)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 7/14 ≈ 0.500
      ├── Some((2, 4)): 7/14 ≈ 0.500
      ├── Some((2, 5)): 4/11 ≈ 0.364
      ├── Some((2, 6)): 3/10 ≈ 0.300
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((0, 3)): 75/147 ≈ 0.510
      ├── Some((3, 1)): 5/14 ≈ 0.357
      ├── Some((3, 2)): 7/17 ≈ 0.412
      ├── Some((3, 4)): 11/21 ≈ 0.524
      ├── Some((3, 5)): 9/19 ≈ 0.474
      ├── Some((3, 6)): 13/24 ≈ 0.542
      ├── Some((3, 7)): 20/31 ≈ 0.645
      └── Some((3, 8)): 10/20 ≈ 0.500
    ├── Some((0, 4)): 116/207 ≈ 0.560
      ├── Some((4, 0)): 11/21 ≈ 0.524
      ├── Some((4, 1)): 18/28 ≈ 0.643
      ├── Some((4, 2)): 20/30 ≈ 0.667
      ├── Some((4, 3)): 8/18 ≈ 0.444
      ├── Some((4, 4)): 12/22 ≈ 0.545
      ├── Some((4, 5)): 15/25 ≈ 0.600
      ├── Some((4, 6)): 11/21 ≈ 0.524
      ├── Some((4, 7)): 10/20 ≈ 0.500
      └── Some((4, 8)): 11/21 ≈ 0.524
    ├── Some((0, 5)): 94/175 ≈ 0.537
      ├── Some((5, 0)): 8/17 ≈ 0.471
      ├── Some((5, 1)): 5/14 ≈ 0.357
      ├── Some((5, 2)): 13/22 ≈ 0.591
      ├── Some((5, 3)): 19/28 ≈ 0.679
      ├── Some((5, 4)): 15/24 ≈ 0.625
      ├── Some((5, 5)): 8/17 ≈ 0.471
      ├── Some((5, 6)): 13/22 ≈ 0.591
      ├── Some((5, 7)): 9/18 ≈ 0.500
      └── Some((5, 8)): 4/12 ≈ 0.333
    ├── Some((0, 6)): 99/182 ≈ 0.544
      ├── Some((6, 0)): 14/24 ≈ 0.583
      ├── Some((6, 1)): 13/22 ≈ 0.591
      ├── Some((6, 2)): 16/26 ≈ 0.615
      ├── Some((6, 3)): 7/16 ≈ 0.438
      ├── Some((6, 4)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 14/24 ≈ 0.583
      ├── Some((6, 6)): 4/12 ≈ 0.333
      ├── Some((6, 7)): 10/19 ≈ 0.526
      └── Some((6, 8)): 10/19 ≈ 0.526
    ├── Some((0, 7)): 77/150 ≈ 0.513
      ├── Some((7, 0)): 11/19 ≈ 0.579
      ├── Some((7, 1)): 14/22 ≈ 0.636
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 8/16 ≈ 0.500
      ├── Some((7, 4)): 6/14 ≈ 0.429
      ├── Some((7, 5)): 9/17 ≈ 0.529
      ├── Some((7, 6)): 4/12 ≈ 0.333
      ├── Some((7, 7)): 5/13 ≈ 0.385
      └── Some((7, 8)): 12/20 ≈ 0.600
    └── Some((0, 8)): 85/162 ≈ 0.525
      ├── Some((8, 0)): 9/18 ≈ 0.500
      ├── Some((8, 1)): 7/15 ≈ 0.467
      ├── Some((8, 2)): 12/21 ≈ 0.571
      ├── Some((8, 3)): 13/22 ≈ 0.591
      ├── Some((8, 4)): 6/14 ≈ 0.429
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 13/22 ≈ 0.591
      ├── Some((8, 7)): 8/16 ≈ 0.500
      └── Some((8, 8)): 9/18 ≈ 0.500
  ├── Some((3, 1)): 340/718 ≈ 0.474
    ├── Some((1, 0)): 51/99 ≈ 0.515
      ├── Some((0, 0)): 1/6 ≈ 0.167
      ├── Some((0, 1)): 7/12 ≈ 0.583
      ├── Some((0, 2)): 1/6 ≈ 0.167
      ├── Some((0, 3)): 0/5 ≈ 0.000
      ├── Some((0, 4)): 7/13 ≈ 0.538
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 14/19 ≈ 0.737
      ├── Some((0, 7)): 8/13 ≈ 0.615
      └── Some((0, 8)): 7/13 ≈ 0.538
    ├── Some((1, 1)): 51/99 ≈ 0.515
      ├── Some((1, 0)): 11/17 ≈ 0.647
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 5/11 ≈ 0.455
      ├── Some((1, 6)): 9/15 ≈ 0.600
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 7/13 ≈ 0.538
    ├── Some((1, 2)): 27/64 ≈ 0.422
      ├── Some((2, 0)): 4/8 ≈ 0.500
      ├── Some((2, 1)): 0/4 ≈ 0.000
      ├── Some((2, 2)): 6/10 ≈ 0.600
      ├── Some((2, 3)): 1/5 ≈ 0.200
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 0/4 ≈ 0.000
      ├── Some((2, 6)): 3/7 ≈ 0.429
      ├── Some((2, 7)): 4/8 ≈ 0.500
      └── Some((2, 8)): 8/12 ≈ 0.667
    ├── Some((1, 3)): 34/75 ≈ 0.453
      ├── Some((3, 0)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 5/11 ≈ 0.455
      ├── Some((3, 4)): 0/5 ≈ 0.000
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 9/15 ≈ 0.600
      ├── Some((3, 7)): 1/7 ≈ 0.143
      └── Some((3, 8)): 8/14 ≈ 0.571
    ├── Some((1, 4)): 62/115 ≈ 0.539
      ├── Some((4, 0)): 10/15 ≈ 0.667
      ├── Some((4, 1)): 10/16 ≈ 0.625
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 8/14 ≈ 0.571
      ├── Some((4, 4)): 0/5 ≈ 0.000
      ├── Some((4, 5)): 7/13 ≈ 0.538
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 10/16 ≈ 0.625
      └── Some((4, 8)): 7/13 ≈ 0.538
    ├── Some((1, 5)): 45/91 ≈ 0.495
      ├── Some((5, 0)): 8/13 ≈ 0.615
      ├── Some((5, 1)): 5/10 ≈ 0.500
      ├── Some((5, 2)): 0/5 ≈ 0.000
      ├── Some((5, 3)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 2/7 ≈ 0.286
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 9/14 ≈ 0.643
      ├── Some((5, 7)): 7/12 ≈ 0.583
      └── Some((5, 8)): 8/13 ≈ 0.615
    ├── Some((1, 6)): 15/46 ≈ 0.326
      ├── Some((6, 0)): 2/5 ≈ 0.400
      ├── Some((6, 1)): 0/3 ≈ 0.000
      ├── Some((6, 2)): 2/5 ≈ 0.400
      ├── Some((6, 3)): 3/6 ≈ 0.500
      ├── Some((6, 4)): 2/5 ≈ 0.400
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 2/5 ≈ 0.400
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 2/6 ≈ 0.333
    ├── Some((1, 7)): 25/61 ≈ 0.410
      ├── Some((7, 0)): 5/8 ≈ 0.625
      ├── Some((7, 1)): 4/8 ≈ 0.500
      ├── Some((7, 2)): 2/6 ≈ 0.333
      ├── Some((7, 3)): 4/8 ≈ 0.500
      ├── Some((7, 4)): 4/8 ≈ 0.500
      ├── Some((7, 5)): 0/4 ≈ 0.000
      ├── Some((7, 6)): 4/8 ≈ 0.500
      ├── Some((7, 7)): 0/4 ≈ 0.000
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((1, 8)): 29/67 ≈ 0.433
      ├── Some((8, 0)): 3/7 ≈ 0.429
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 2/6 ≈ 0.333
      ├── Some((8, 3)): 4/8 ≈ 0.500
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 4/8 ≈ 0.500
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 6/10 ≈ 0.600
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((3, 2)): 506/1012 ≈ 0.500
    ├── Some((2, 0)): 24/64 ≈ 0.375
      ├── Some((0, 0)): 0/4 ≈ 0.000
      ├── Some((0, 1)): 7/11 ≈ 0.636
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 1/5 ≈ 0.200
      ├── Some((0, 4)): 8/12 ≈ 0.667
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 1/6 ≈ 0.167
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((2, 1)): 49/103 ≈ 0.476
      ├── Some((1, 0)): 2/8 ≈ 0.250
      ├── Some((1, 1)): 8/14 ≈ 0.571
      ├── Some((1, 2)): 12/18 ≈ 0.667
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 6/12 ≈ 0.500
      ├── Some((1, 5)): 0/6 ≈ 0.000
      ├── Some((1, 6)): 1/7 ≈ 0.143
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 12/18 ≈ 0.667
    ├── Some((2, 2)): 110/189 ≈ 0.582
      ├── Some((2, 0)): 14/24 ≈ 0.583
      ├── Some((2, 1)): 26/36 ≈ 0.722
      ├── Some((2, 3)): 9/19 ≈ 0.474
      ├── Some((2, 4)): 15/25 ≈ 0.600
      ├── Some((2, 5)): 5/14 ≈ 0.357
      ├── Some((2, 6)): 7/17 ≈ 0.412
      ├── Some((2, 7)): 18/28 ≈ 0.643
      └── Some((2, 8)): 15/25 ≈ 0.600
    ├── Some((2, 3)): 37/85 ≈ 0.435
      ├── Some((3, 0)): 7/14 ≈ 0.500
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 2/9 ≈ 0.222
      ├── Some((3, 5)): 0/6 ≈ 0.000
      ├── Some((3, 6)): 11/19 ≈ 0.579
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 1/7 ≈ 0.143
    ├── Some((2, 4)): 93/166 ≈ 0.560
      ├── Some((4, 0)): 19/27 ≈ 0.704
      ├── Some((4, 1)): 16/24 ≈ 0.667
      ├── Some((4, 2)): 4/12 ≈ 0.333
      ├── Some((4, 3)): 14/23 ≈ 0.609
      ├── Some((4, 4)): 10/18 ≈ 0.556
      ├── Some((4, 5)): 7/15 ≈ 0.467
      ├── Some((4, 6)): 2/9 ≈ 0.222
      ├── Some((4, 7)): 10/18 ≈ 0.556
      └── Some((4, 8)): 11/19 ≈ 0.579
    ├── Some((2, 5)): 73/137 ≈ 0.533
      ├── Some((5, 0)): 11/19 ≈ 0.579
      ├── Some((5, 1)): 2/9 ≈ 0.222
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 3)): 19/26 ≈ 0.731
      ├── Some((5, 4)): 6/13 ≈ 0.462
      ├── Some((5, 5)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 5/12 ≈ 0.417
      ├── Some((5, 7)): 10/17 ≈ 0.588
      └── Some((5, 8)): 8/15 ≈ 0.533
    ├── Some((2, 6)): 51/105 ≈ 0.486
      ├── Some((6, 0)): 5/11 ≈ 0.455
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 10/16 ≈ 0.625
      ├── Some((6, 3)): 11/17 ≈ 0.647
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 4/10 ≈ 0.400
    ├── Some((2, 7)): 32/77 ≈ 0.416
      ├── Some((7, 0)): 1/6 ≈ 0.167
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 2)): 6/11 ≈ 0.545
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 5/10 ≈ 0.500
      ├── Some((7, 6)): 5/10 ≈ 0.500
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 0/4 ≈ 0.000
    └── Some((2, 8)): 37/85 ≈ 0.435
      ├── Some((8, 0)): 4/9 ≈ 0.444
      ├── Some((8, 1)): 0/5 ≈ 0.000
      ├── Some((8, 2)): 7/12 ≈ 0.583
      ├── Some((8, 3)): 6/12 ≈ 0.500
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 7/12 ≈ 0.583
      ├── Some((8, 6)): 4/10 ≈ 0.400
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 0/5 ≈ 0.000
  ├── Some((3, 4)): 746/1427 ≈ 0.523
    ├── Some((4, 0)): 88/166 ≈ 0.530
      ├── Some((0, 0)): 9/18 ≈ 0.500
      ├── Some((0, 1)): 14/23 ≈ 0.609
      ├── Some((0, 2)): 8/16 ≈ 0.500
      ├── Some((0, 3)): 7/15 ≈ 0.467
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 9/18 ≈ 0.500
      ├── Some((0, 7)): 13/22 ≈ 0.591
      └── Some((0, 8)): 13/22 ≈ 0.591
    ├── Some((4, 1)): 89/168 ≈ 0.530
      ├── Some((1, 0)): 6/14 ≈ 0.429
      ├── Some((1, 1)): 13/22 ≈ 0.591
      ├── Some((1, 2)): 11/20 ≈ 0.550
      ├── Some((1, 3)): 5/13 ≈ 0.385
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 15/24 ≈ 0.625
      ├── Some((1, 7)): 7/16 ≈ 0.438
      └── Some((1, 8)): 10/19 ≈ 0.526
    ├── Some((4, 2)): 53/114 ≈ 0.465
      ├── Some((2, 0)): 2/8 ≈ 0.250
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 9/16 ≈ 0.562
      ├── Some((2, 5)): 8/15 ≈ 0.533
      ├── Some((2, 6)): 3/10 ≈ 0.300
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 8/15 ≈ 0.533
    ├── Some((4, 3)): 76/149 ≈ 0.510
      ├── Some((3, 0)): 12/23 ≈ 0.522
      ├── Some((3, 1)): 4/13 ≈ 0.308
      ├── Some((3, 2)): 11/22 ≈ 0.500
      ├── Some((3, 5)): 7/17 ≈ 0.412
      ├── Some((3, 6)): 20/31 ≈ 0.645
      ├── Some((3, 7)): 5/15 ≈ 0.333
      └── Some((3, 8)): 16/27 ≈ 0.593
    ├── Some((4, 4)): 91/171 ≈ 0.532
      ├── Some((4, 0)): 10/20 ≈ 0.500
      ├── Some((4, 1)): 15/25 ≈ 0.600
      ├── Some((4, 2)): 11/21 ≈ 0.524
      ├── Some((4, 3)): 11/21 ≈ 0.524
      ├── Some((4, 5)): 13/23 ≈ 0.565
      ├── Some((4, 6)): 12/22 ≈ 0.545
      ├── Some((4, 7)): 11/21 ≈ 0.524
      └── Some((4, 8)): 7/17 ≈ 0.412
    ├── Some((4, 5)): 106/192 ≈ 0.552
      ├── Some((5, 0)): 8/17 ≈ 0.471
      ├── Some((5, 1)): 9/18 ≈ 0.500
      ├── Some((5, 2)): 22/32 ≈ 0.688
      ├── Some((5, 3)): 10/19 ≈ 0.526
      ├── Some((5, 4)): 9/18 ≈ 0.500
      ├── Some((5, 5)): 9/18 ≈ 0.500
      ├── Some((5, 6)): 18/28 ≈ 0.643
      ├── Some((5, 7)): 10/20 ≈ 0.500
      └── Some((5, 8)): 11/21 ≈ 0.524
    ├── Some((4, 6)): 104/189 ≈ 0.550
      ├── Some((6, 0)): 12/21 ≈ 0.571
      ├── Some((6, 1)): 16/26 ≈ 0.615
      ├── Some((6, 2)): 14/24 ≈ 0.583
      ├── Some((6, 3)): 9/18 ≈ 0.500
      ├── Some((6, 4)): 12/21 ≈ 0.571
      ├── Some((6, 5)): 3/11 ≈ 0.273
      ├── Some((6, 6)): 15/25 ≈ 0.600
      ├── Some((6, 7)): 15/25 ≈ 0.600
      └── Some((6, 8)): 8/17 ≈ 0.471
    ├── Some((4, 7)): 45/102 ≈ 0.441
      ├── Some((7, 0)): 2/8 ≈ 0.250
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 4/10 ≈ 0.400
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 9/16 ≈ 0.562
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 7/14 ≈ 0.500
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((4, 8)): 94/175 ≈ 0.537
      ├── Some((8, 0)): 13/23 ≈ 0.565
      ├── Some((8, 1)): 3/11 ≈ 0.273
      ├── Some((8, 2)): 4/12 ≈ 0.333
      ├── Some((8, 3)): 11/20 ≈ 0.550
      ├── Some((8, 4)): 11/20 ≈ 0.550
      ├── Some((8, 5)): 12/21 ≈ 0.571
      ├── Some((8, 6)): 23/33 ≈ 0.697
      ├── Some((8, 7)): 10/19 ≈ 0.526
      └── Some((8, 8)): 6/15 ≈ 0.400
  ├── Some((3, 5)): 482/969 ≈ 0.497
    ├── Some((5, 0)): 42/91 ≈ 0.462
      ├── Some((0, 0)): 8/13 ≈ 0.615
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 6/12 ≈ 0.500
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 3/8 ≈ 0.375
      ├── Some((0, 6)): 0/5 ≈ 0.000
      ├── Some((0, 7)): 7/12 ≈ 0.583
      └── Some((0, 8)): 6/12 ≈ 0.500
    ├── Some((5, 1)): 70/132 ≈ 0.530
      ├── Some((1, 0)): 2/8 ≈ 0.250
      ├── Some((1, 1)): 11/18 ≈ 0.611
      ├── Some((1, 2)): 3/9 ≈ 0.333
      ├── Some((1, 3)): 4/11 ≈ 0.364
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 10/17 ≈ 0.588
      ├── Some((1, 6)): 13/20 ≈ 0.650
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 12/19 ≈ 0.632
    ├── Some((5, 2)): 45/96 ≈ 0.469
      ├── Some((2, 0)): 7/13 ≈ 0.538
      ├── Some((2, 1)): 8/14 ≈ 0.571
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 7/13 ≈ 0.538
      ├── Some((2, 4)): 7/13 ≈ 0.538
      ├── Some((2, 5)): 6/12 ≈ 0.500
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 1/6 ≈ 0.167
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((5, 3)): 32/76 ≈ 0.421
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 6/12 ≈ 0.500
      ├── Some((3, 2)): 7/13 ≈ 0.538
      ├── Some((3, 4)): 2/8 ≈ 0.250
      ├── Some((3, 6)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((5, 4)): 79/144 ≈ 0.549
      ├── Some((4, 0)): 9/17 ≈ 0.529
      ├── Some((4, 1)): 13/20 ≈ 0.650
      ├── Some((4, 2)): 7/14 ≈ 0.500
      ├── Some((4, 3)): 15/22 ≈ 0.682
      ├── Some((4, 4)): 2/9 ≈ 0.222
      ├── Some((4, 5)): 15/22 ≈ 0.682
      ├── Some((4, 6)): 9/17 ≈ 0.529
      ├── Some((4, 7)): 6/13 ≈ 0.462
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((5, 5)): 38/85 ≈ 0.447
      ├── Some((5, 0)): 7/13 ≈ 0.538
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 2/7 ≈ 0.286
      ├── Some((5, 4)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 2/8 ≈ 0.250
    ├── Some((5, 6)): 71/133 ≈ 0.534
      ├── Some((6, 0)): 4/11 ≈ 0.364
      ├── Some((6, 1)): 17/23 ≈ 0.739
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 12/19 ≈ 0.632
      ├── Some((6, 5)): 11/18 ≈ 0.611
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 4/11 ≈ 0.364
    ├── Some((5, 7)): 53/107 ≈ 0.495
      ├── Some((7, 0)): 13/19 ≈ 0.684
      ├── Some((7, 1)): 5/11 ≈ 0.455
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 8/14 ≈ 0.571
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 6/12 ≈ 0.500
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 8/14 ≈ 0.571
    └── Some((5, 8)): 51/104 ≈ 0.490
      ├── Some((8, 0)): 10/16 ≈ 0.625
      ├── Some((8, 1)): 10/16 ≈ 0.625
      ├── Some((8, 2)): 8/14 ≈ 0.571
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 1/6 ≈ 0.167
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 11/17 ≈ 0.647
      ├── Some((8, 7)): 3/9 ≈ 0.333
      └── Some((8, 8)): 1/7 ≈ 0.143
  ├── Some((3, 6)): 390/807 ≈ 0.483
    ├── Some((6, 0)): 43/89 ≈ 0.483
      ├── Some((0, 0)): 4/9 ≈ 0.444
      ├── Some((0, 1)): 6/11 ≈ 0.545
      ├── Some((0, 2)): 6/11 ≈ 0.545
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 6/11 ≈ 0.545
      ├── Some((0, 5)): 3/8 ≈ 0.375
      ├── Some((0, 6)): 2/7 ≈ 0.286
      ├── Some((0, 7)): 8/13 ≈ 0.615
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((6, 1)): 27/66 ≈ 0.409
      ├── Some((1, 0)): 2/6 ≈ 0.333
      ├── Some((1, 1)): 5/9 ≈ 0.556
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 6/10 ≈ 0.600
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 2/6 ≈ 0.333
      ├── Some((1, 7)): 0/4 ≈ 0.000
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((6, 2)): 66/122 ≈ 0.541
      ├── Some((2, 0)): 9/15 ≈ 0.600
      ├── Some((2, 1)): 9/15 ≈ 0.600
      ├── Some((2, 2)): 2/8 ≈ 0.250
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 7/14 ≈ 0.500
      ├── Some((2, 6)): 7/14 ≈ 0.500
      ├── Some((2, 7)): 16/22 ≈ 0.727
      └── Some((2, 8)): 5/11 ≈ 0.455
    ├── Some((6, 3)): 36/79 ≈ 0.456
      ├── Some((3, 0)): 8/14 ≈ 0.571
      ├── Some((3, 1)): 2/8 ≈ 0.250
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 4)): 8/14 ≈ 0.571
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 7/13 ≈ 0.538
      └── Some((3, 8)): 4/10 ≈ 0.400
    ├── Some((6, 4)): 68/125 ≈ 0.544
      ├── Some((4, 0)): 1/7 ≈ 0.143
      ├── Some((4, 1)): 2/8 ≈ 0.250
      ├── Some((4, 2)): 9/15 ≈ 0.600
      ├── Some((4, 3)): 12/18 ≈ 0.667
      ├── Some((4, 4)): 8/15 ≈ 0.533
      ├── Some((4, 5)): 13/19 ≈ 0.684
      ├── Some((4, 6)): 9/16 ≈ 0.562
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 8/15 ≈ 0.533
    ├── Some((6, 5)): 54/105 ≈ 0.514
      ├── Some((5, 0)): 8/14 ≈ 0.571
      ├── Some((5, 1)): 7/13 ≈ 0.538
      ├── Some((5, 2)): 5/11 ≈ 0.455
      ├── Some((5, 3)): 6/12 ≈ 0.500
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 8/14 ≈ 0.571
      ├── Some((5, 7)): 1/6 ≈ 0.167
      └── Some((5, 8)): 11/16 ≈ 0.688
    ├── Some((6, 6)): 48/97 ≈ 0.495
      ├── Some((6, 0)): 9/16 ≈ 0.562
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 3/9 ≈ 0.333
      ├── Some((6, 3)): 13/19 ≈ 0.684
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 5)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 0/6 ≈ 0.000
    ├── Some((6, 7)): 23/60 ≈ 0.383
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 0/4 ≈ 0.000
      ├── Some((7, 2)): 4/8 ≈ 0.500
      ├── Some((7, 3)): 3/7 ≈ 0.429
      ├── Some((7, 4)): 0/4 ≈ 0.000
      ├── Some((7, 5)): 5/9 ≈ 0.556
      ├── Some((7, 6)): 2/6 ≈ 0.333
      ├── Some((7, 7)): 2/6 ≈ 0.333
      └── Some((7, 8)): 5/9 ≈ 0.556
    └── Some((6, 8)): 25/63 ≈ 0.397
      ├── Some((8, 0)): 4/8 ≈ 0.500
      ├── Some((8, 1)): 2/6 ≈ 0.333
      ├── Some((8, 2)): 2/6 ≈ 0.333
      ├── Some((8, 3)): 0/4 ≈ 0.000
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 6/10 ≈ 0.600
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 2/6 ≈ 0.333
  ├── Some((3, 7)): 853/1610 ≈ 0.530
    ├── Some((7, 0)): 127/226 ≈ 0.562
      ├── Some((0, 0)): 19/30 ≈ 0.633
      ├── Some((0, 1)): 21/32 ≈ 0.656
      ├── Some((0, 2)): 11/22 ≈ 0.500
      ├── Some((0, 3)): 6/16 ≈ 0.375
      ├── Some((0, 4)): 17/28 ≈ 0.607
      ├── Some((0, 5)): 17/28 ≈ 0.607
      ├── Some((0, 6)): 16/27 ≈ 0.593
      ├── Some((0, 7)): 10/21 ≈ 0.476
      └── Some((0, 8)): 10/21 ≈ 0.476
    ├── Some((7, 1)): 110/201 ≈ 0.547
      ├── Some((1, 0)): 9/19 ≈ 0.474
      ├── Some((1, 1)): 20/31 ≈ 0.645
      ├── Some((1, 2)): 6/16 ≈ 0.375
      ├── Some((1, 3)): 11/21 ≈ 0.524
      ├── Some((1, 4)): 13/23 ≈ 0.565
      ├── Some((1, 5)): 23/34 ≈ 0.676
      ├── Some((1, 6)): 5/14 ≈ 0.357
      ├── Some((1, 7)): 15/25 ≈ 0.600
      └── Some((1, 8)): 7/17 ≈ 0.412
    ├── Some((7, 2)): 63/132 ≈ 0.477
      ├── Some((2, 0)): 3/10 ≈ 0.300
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 9/17 ≈ 0.529
      ├── Some((2, 4)): 7/15 ≈ 0.467
      ├── Some((2, 5)): 3/10 ≈ 0.300
      ├── Some((2, 6)): 8/16 ≈ 0.500
      ├── Some((2, 7)): 14/22 ≈ 0.636
      └── Some((2, 8)): 11/19 ≈ 0.579
    ├── Some((7, 3)): 64/133 ≈ 0.481
      ├── Some((3, 0)): 3/12 ≈ 0.250
      ├── Some((3, 1)): 9/19 ≈ 0.474
      ├── Some((3, 2)): 7/17 ≈ 0.412
      ├── Some((3, 4)): 9/19 ≈ 0.474
      ├── Some((3, 5)): 13/23 ≈ 0.565
      ├── Some((3, 6)): 9/19 ≈ 0.474
      └── Some((3, 8)): 13/23 ≈ 0.565
    ├── Some((7, 4)): 92/175 ≈ 0.526
      ├── Some((4, 0)): 5/14 ≈ 0.357
      ├── Some((4, 1)): 10/19 ≈ 0.526
      ├── Some((4, 2)): 19/29 ≈ 0.655
      ├── Some((4, 3)): 12/21 ≈ 0.571
      ├── Some((4, 4)): 10/19 ≈ 0.526
      ├── Some((4, 5)): 12/21 ≈ 0.571
      ├── Some((4, 6)): 12/22 ≈ 0.545
      ├── Some((4, 7)): 6/15 ≈ 0.400
      └── Some((4, 8)): 5/14 ≈ 0.357
    ├── Some((7, 5)): 84/163 ≈ 0.515
      ├── Some((5, 0)): 8/17 ≈ 0.471
      ├── Some((5, 1)): 11/20 ≈ 0.550
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 11/20 ≈ 0.550
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 11/20 ≈ 0.550
      ├── Some((5, 6)): 9/18 ≈ 0.500
      ├── Some((5, 7)): 12/21 ≈ 0.571
      └── Some((5, 8)): 9/18 ≈ 0.500
    ├── Some((7, 6)): 95/180 ≈ 0.528
      ├── Some((6, 0)): 9/18 ≈ 0.500
      ├── Some((6, 1)): 10/20 ≈ 0.500
      ├── Some((6, 2)): 16/26 ≈ 0.615
      ├── Some((6, 3)): 21/31 ≈ 0.677
      ├── Some((6, 4)): 4/13 ≈ 0.308
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 11/21 ≈ 0.524
      ├── Some((6, 7)): 7/16 ≈ 0.438
      └── Some((6, 8)): 7/16 ≈ 0.438
    ├── Some((7, 7)): 118/213 ≈ 0.554
      ├── Some((7, 0)): 13/25 ≈ 0.520
      ├── Some((7, 1)): 11/22 ≈ 0.500
      ├── Some((7, 2)): 13/25 ≈ 0.520
      ├── Some((7, 3)): 8/19 ≈ 0.421
      ├── Some((7, 4)): 18/30 ≈ 0.600
      ├── Some((7, 5)): 25/38 ≈ 0.658
      ├── Some((7, 6)): 16/28 ≈ 0.571
      └── Some((7, 8)): 13/25 ≈ 0.520
    └── Some((7, 8)): 99/186 ≈ 0.532
      ├── Some((8, 0)): 15/25 ≈ 0.600
      ├── Some((8, 1)): 5/14 ≈ 0.357
      ├── Some((8, 2)): 17/27 ≈ 0.630
      ├── Some((8, 3)): 6/15 ≈ 0.400
      ├── Some((8, 4)): 8/17 ≈ 0.471
      ├── Some((8, 5)): 12/22 ≈ 0.545
      ├── Some((8, 6)): 11/21 ≈ 0.524
      ├── Some((8, 7)): 9/19 ≈ 0.474
      └── Some((8, 8)): 15/25 ≈ 0.600
  └── Some((3, 8)): 790/1502 ≈ 0.526
    ├── Some((8, 0)): 58/123 ≈ 0.472
      ├── Some((0, 0)): 5/12 ≈ 0.417
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 12/20 ≈ 0.600
      ├── Some((0, 6)): 4/11 ≈ 0.364
      ├── Some((0, 7)): 3/10 ≈ 0.300
      └── Some((0, 8)): 1/8 ≈ 0.125
    ├── Some((8, 1)): 116/209 ≈ 0.555
      ├── Some((1, 0)): 14/25 ≈ 0.560
      ├── Some((1, 1)): 9/19 ≈ 0.474
      ├── Some((1, 2)): 6/16 ≈ 0.375
      ├── Some((1, 3)): 10/20 ≈ 0.500
      ├── Some((1, 4)): 25/36 ≈ 0.694
      ├── Some((1, 5)): 11/21 ≈ 0.524
      ├── Some((1, 6)): 15/26 ≈ 0.577
      ├── Some((1, 7)): 12/22 ≈ 0.545
      └── Some((1, 8)): 13/23 ≈ 0.565
    ├── Some((8, 2)): 102/189 ≈ 0.540
      ├── Some((2, 0)): 5/14 ≈ 0.357
      ├── Some((2, 1)): 5/14 ≈ 0.357
      ├── Some((2, 2)): 16/26 ≈ 0.615
      ├── Some((2, 3)): 12/22 ≈ 0.545
      ├── Some((2, 4)): 17/27 ≈ 0.630
      ├── Some((2, 5)): 4/13 ≈ 0.308
      ├── Some((2, 6)): 21/31 ≈ 0.677
      ├── Some((2, 7)): 8/18 ≈ 0.444
      └── Some((2, 8)): 13/23 ≈ 0.565
    ├── Some((8, 3)): 29/78 ≈ 0.372
      ├── Some((3, 0)): 3/10 ≈ 0.300
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 0/6 ≈ 0.000
      ├── Some((3, 4)): 6/13 ≈ 0.462
      ├── Some((3, 5)): 4/11 ≈ 0.364
      ├── Some((3, 6)): 8/16 ≈ 0.500
      └── Some((3, 7)): 1/7 ≈ 0.143
    ├── Some((8, 4)): 134/234 ≈ 0.573
      ├── Some((4, 0)): 14/25 ≈ 0.560
      ├── Some((4, 1)): 23/35 ≈ 0.657
      ├── Some((4, 2)): 21/32 ≈ 0.656
      ├── Some((4, 3)): 16/27 ≈ 0.593
      ├── Some((4, 4)): 8/18 ≈ 0.444
      ├── Some((4, 5)): 14/25 ≈ 0.560
      ├── Some((4, 6)): 14/25 ≈ 0.560
      ├── Some((4, 7)): 10/21 ≈ 0.476
      └── Some((4, 8)): 14/25 ≈ 0.560
    ├── Some((8, 5)): 98/183 ≈ 0.536
      ├── Some((5, 0)): 9/18 ≈ 0.500
      ├── Some((5, 1)): 7/16 ≈ 0.438
      ├── Some((5, 2)): 16/26 ≈ 0.615
      ├── Some((5, 3)): 8/17 ≈ 0.471
      ├── Some((5, 4)): 7/16 ≈ 0.438
      ├── Some((5, 5)): 8/17 ≈ 0.471
      ├── Some((5, 6)): 9/19 ≈ 0.474
      ├── Some((5, 7)): 15/25 ≈ 0.600
      └── Some((5, 8)): 18/28 ≈ 0.643
    ├── Some((8, 6)): 132/231 ≈ 0.571
      ├── Some((6, 0)): 9/19 ≈ 0.474
      ├── Some((6, 1)): 13/24 ≈ 0.542
      ├── Some((6, 2)): 12/23 ≈ 0.522
      ├── Some((6, 3)): 23/35 ≈ 0.657
      ├── Some((6, 4)): 19/30 ≈ 0.633
      ├── Some((6, 5)): 11/22 ≈ 0.500
      ├── Some((6, 6)): 8/18 ≈ 0.444
      ├── Some((6, 7)): 23/35 ≈ 0.657
      └── Some((6, 8)): 13/24 ≈ 0.542
    ├── Some((8, 7)): 69/140 ≈ 0.493
      ├── Some((7, 0)): 13/21 ≈ 0.619
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 5/13 ≈ 0.385
      ├── Some((7, 4)): 9/17 ≈ 0.529
      ├── Some((7, 5)): 13/21 ≈ 0.619
      ├── Some((7, 6)): 1/8 ≈ 0.125
      ├── Some((7, 7)): 7/15 ≈ 0.467
      └── Some((7, 8)): 10/18 ≈ 0.556
    └── Some((8, 8)): 52/114 ≈ 0.456
      ├── Some((8, 0)): 3/10 ≈ 0.300
      ├── Some((8, 1)): 3/10 ≈ 0.300
      ├── Some((8, 2)): 6/14 ≈ 0.429
      ├── Some((8, 3)): 13/21 ≈ 0.619
      ├── Some((8, 4)): 9/17 ≈ 0.529
      ├── Some((8, 5)): 5/13 ≈ 0.385
      ├── Some((8, 6)): 9/17 ≈ 0.529
      └── Some((8, 7)): 3/11 ≈ 0.273
├── Some((3, 4)): 2944/5926 ≈ 0.497
  ├── Some((4, 0)): 310/630 ≈ 0.492
    ├── Some((0, 0)): 14/41 ≈ 0.341
      ├── Some((0, 1)): 2/5 ≈ 0.400
      ├── Some((0, 2)): 3/6 ≈ 0.500
      ├── Some((0, 3)): 2/5 ≈ 0.400
      ├── Some((0, 4)): 0/3 ≈ 0.000
      ├── Some((0, 5)): 1/5 ≈ 0.200
      ├── Some((0, 6)): 3/6 ≈ 0.500
      ├── Some((0, 7)): 1/5 ≈ 0.200
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((0, 1)): 38/75 ≈ 0.507
      ├── Some((1, 0)): 1/5 ≈ 0.200
      ├── Some((1, 1)): 4/8 ≈ 0.500
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 5/9 ≈ 0.556
      ├── Some((1, 6)): 2/6 ≈ 0.333
      ├── Some((1, 7)): 9/13 ≈ 0.692
      └── Some((1, 8)): 10/14 ≈ 0.714
    ├── Some((0, 2)): 58/102 ≈ 0.569
      ├── Some((2, 0)): 7/12 ≈ 0.583
      ├── Some((2, 1)): 8/12 ≈ 0.667
      ├── Some((2, 2)): 6/11 ≈ 0.545
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 5/10 ≈ 0.500
      ├── Some((2, 5)): 7/12 ≈ 0.583
      ├── Some((2, 6)): 8/12 ≈ 0.667
      ├── Some((2, 7)): 8/13 ≈ 0.615
      └── Some((2, 8)): 5/10 ≈ 0.500
    ├── Some((0, 3)): 26/58 ≈ 0.448
      ├── Some((3, 0)): 0/4 ≈ 0.000
      ├── Some((3, 1)): 4/8 ≈ 0.500
      ├── Some((3, 2)): 5/9 ≈ 0.556
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 5)): 4/8 ≈ 0.500
      ├── Some((3, 6)): 4/8 ≈ 0.500
      ├── Some((3, 7)): 6/9 ≈ 0.667
      └── Some((3, 8)): 3/7 ≈ 0.429
    ├── Some((0, 4)): 31/66 ≈ 0.470
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 4/8 ≈ 0.500
      ├── Some((4, 3)): 4/8 ≈ 0.500
      ├── Some((4, 4)): 4/8 ≈ 0.500
      ├── Some((4, 5)): 4/8 ≈ 0.500
      ├── Some((4, 6)): 0/4 ≈ 0.000
      ├── Some((4, 7)): 9/13 ≈ 0.692
      └── Some((4, 8)): 4/9 ≈ 0.444
    ├── Some((0, 5)): 28/61 ≈ 0.459
      ├── Some((5, 0)): 4/7 ≈ 0.571
      ├── Some((5, 1)): 3/7 ≈ 0.429
      ├── Some((5, 2)): 4/7 ≈ 0.571
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 6/9 ≈ 0.667
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 2/6 ≈ 0.333
      ├── Some((5, 7)): 2/6 ≈ 0.333
      └── Some((5, 8)): 4/8 ≈ 0.500
    ├── Some((0, 6)): 30/64 ≈ 0.469
      ├── Some((6, 0)): 9/12 ≈ 0.750
      ├── Some((6, 1)): 0/4 ≈ 0.000
      ├── Some((6, 2)): 5/8 ≈ 0.625
      ├── Some((6, 3)): 4/7 ≈ 0.571
      ├── Some((6, 4)): 4/8 ≈ 0.500
      ├── Some((6, 5)): 0/4 ≈ 0.000
      ├── Some((6, 6)): 3/7 ≈ 0.429
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 4/8 ≈ 0.500
    ├── Some((0, 7)): 38/75 ≈ 0.507
      ├── Some((7, 0)): 1/5 ≈ 0.200
      ├── Some((7, 1)): 8/12 ≈ 0.667
      ├── Some((7, 2)): 6/10 ≈ 0.600
      ├── Some((7, 3)): 6/10 ≈ 0.600
      ├── Some((7, 4)): 7/11 ≈ 0.636
      ├── Some((7, 5)): 7/11 ≈ 0.636
      ├── Some((7, 6)): 3/7 ≈ 0.429
      ├── Some((7, 7)): 0/4 ≈ 0.000
      └── Some((7, 8)): 0/4 ≈ 0.000
    └── Some((0, 8)): 47/87 ≈ 0.540
      ├── Some((8, 0)): 8/12 ≈ 0.667
      ├── Some((8, 1)): 9/13 ≈ 0.692
      ├── Some((8, 2)): 1/6 ≈ 0.167
      ├── Some((8, 3)): 8/12 ≈ 0.667
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 4/9 ≈ 0.444
      ├── Some((8, 7)): 6/10 ≈ 0.600
      └── Some((8, 8)): 5/9 ≈ 0.556
  ├── Some((4, 1)): 486/929 ≈ 0.523
    ├── Some((1, 0)): 55/105 ≈ 0.524
      ├── Some((0, 0)): 1/6 ≈ 0.167
      ├── Some((0, 1)): 12/17 ≈ 0.706
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 8/13 ≈ 0.615
      ├── Some((0, 4)): 8/13 ≈ 0.615
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 7/13 ≈ 0.538
      ├── Some((0, 7)): 4/10 ≈ 0.400
      └── Some((0, 8)): 6/12 ≈ 0.500
    ├── Some((1, 1)): 50/98 ≈ 0.510
      ├── Some((1, 0)): 10/16 ≈ 0.625
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 7/13 ≈ 0.538
      ├── Some((1, 5)): 6/12 ≈ 0.500
      ├── Some((1, 6)): 3/9 ≈ 0.333
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 8/14 ≈ 0.571
    ├── Some((1, 2)): 39/82 ≈ 0.476
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 0/4 ≈ 0.000
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 8/12 ≈ 0.667
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 5/10 ≈ 0.500
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 7/12 ≈ 0.583
    ├── Some((1, 3)): 34/75 ≈ 0.453
      ├── Some((3, 0)): 6/11 ≈ 0.545
      ├── Some((3, 1)): 5/10 ≈ 0.500
      ├── Some((3, 2)): 4/9 ≈ 0.444
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 3/8 ≈ 0.375
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((1, 4)): 96/160 ≈ 0.600
      ├── Some((4, 0)): 12/20 ≈ 0.600
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 10/18 ≈ 0.556
      ├── Some((4, 4)): 16/24 ≈ 0.667
      ├── Some((4, 5)): 15/23 ≈ 0.652
      ├── Some((4, 6)): 16/24 ≈ 0.667
      ├── Some((4, 7)): 14/22 ≈ 0.636
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((1, 5)): 52/101 ≈ 0.515
      ├── Some((5, 0)): 7/12 ≈ 0.583
      ├── Some((5, 1)): 9/14 ≈ 0.643
      ├── Some((5, 2)): 9/14 ≈ 0.643
      ├── Some((5, 3)): 0/5 ≈ 0.000
      ├── Some((5, 4)): 7/12 ≈ 0.583
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((1, 6)): 61/113 ≈ 0.540
      ├── Some((6, 0)): 8/14 ≈ 0.571
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 7/13 ≈ 0.538
      ├── Some((6, 3)): 9/14 ≈ 0.643
      ├── Some((6, 4)): 9/14 ≈ 0.643
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 7/13 ≈ 0.538
      └── Some((6, 8)): 9/15 ≈ 0.600
    ├── Some((1, 7)): 61/113 ≈ 0.540
      ├── Some((7, 0)): 10/15 ≈ 0.667
      ├── Some((7, 1)): 6/12 ≈ 0.500
      ├── Some((7, 2)): 9/14 ≈ 0.643
      ├── Some((7, 3)): 8/14 ≈ 0.571
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 8/14 ≈ 0.571
    └── Some((1, 8)): 38/81 ≈ 0.469
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 6/10 ≈ 0.600
      ├── Some((8, 2)): 6/11 ≈ 0.545
      ├── Some((8, 3)): 6/11 ≈ 0.545
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 5/10 ≈ 0.500
      ├── Some((8, 7)): 4/9 ≈ 0.444
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((4, 2)): 314/637 ≈ 0.493
    ├── Some((2, 0)): 31/66 ≈ 0.470
      ├── Some((0, 0)): 2/6 ≈ 0.333
      ├── Some((0, 1)): 4/8 ≈ 0.500
      ├── Some((0, 2)): 3/7 ≈ 0.429
      ├── Some((0, 3)): 4/8 ≈ 0.500
      ├── Some((0, 4)): 4/8 ≈ 0.500
      ├── Some((0, 5)): 3/7 ≈ 0.429
      ├── Some((0, 6)): 5/8 ≈ 0.625
      ├── Some((0, 7)): 5/8 ≈ 0.625
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((2, 1)): 25/57 ≈ 0.439
      ├── Some((1, 0)): 3/6 ≈ 0.500
      ├── Some((1, 1)): 0/4 ≈ 0.000
      ├── Some((1, 2)): 4/7 ≈ 0.571
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 6/9 ≈ 0.667
      ├── Some((1, 5)): 2/6 ≈ 0.333
      ├── Some((1, 6)): 2/6 ≈ 0.333
      ├── Some((1, 7)): 3/6 ≈ 0.500
      └── Some((1, 8)): 2/6 ≈ 0.333
    ├── Some((2, 2)): 25/57 ≈ 0.439
      ├── Some((2, 0)): 7/10 ≈ 0.700
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 3)): 1/5 ≈ 0.200
      ├── Some((2, 4)): 4/8 ≈ 0.500
      ├── Some((2, 5)): 2/6 ≈ 0.333
      ├── Some((2, 6)): 2/6 ≈ 0.333
      ├── Some((2, 7)): 4/8 ≈ 0.500
      └── Some((2, 8)): 4/8 ≈ 0.500
    ├── Some((2, 3)): 28/61 ≈ 0.459
      ├── Some((3, 0)): 1/5 ≈ 0.200
      ├── Some((3, 1)): 6/10 ≈ 0.600
      ├── Some((3, 2)): 7/11 ≈ 0.636
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 5)): 4/8 ≈ 0.500
      ├── Some((3, 6)): 3/7 ≈ 0.429
      ├── Some((3, 7)): 1/5 ≈ 0.200
      └── Some((3, 8)): 6/10 ≈ 0.600
    ├── Some((2, 4)): 41/79 ≈ 0.519
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 0/4 ≈ 0.000
      ├── Some((4, 3)): 6/11 ≈ 0.545
      ├── Some((4, 4)): 8/13 ≈ 0.615
      ├── Some((4, 5)): 9/13 ≈ 0.692
      ├── Some((4, 6)): 7/12 ≈ 0.583
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((2, 5)): 43/82 ≈ 0.524
      ├── Some((5, 0)): 5/9 ≈ 0.556
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 7/11 ≈ 0.636
      ├── Some((5, 3)): 10/14 ≈ 0.714
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 5/9 ≈ 0.556
      ├── Some((5, 7)): 6/10 ≈ 0.600
      └── Some((5, 8)): 2/7 ≈ 0.286
    ├── Some((2, 6)): 44/84 ≈ 0.524
      ├── Some((6, 0)): 5/9 ≈ 0.556
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 0/4 ≈ 0.000
      ├── Some((6, 3)): 8/12 ≈ 0.667
      ├── Some((6, 4)): 5/9 ≈ 0.556
      ├── Some((6, 5)): 9/13 ≈ 0.692
      ├── Some((6, 6)): 5/10 ≈ 0.500
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 5/10 ≈ 0.500
    ├── Some((2, 7)): 33/68 ≈ 0.485
      ├── Some((7, 0)): 4/8 ≈ 0.500
      ├── Some((7, 1)): 3/7 ≈ 0.429
      ├── Some((7, 2)): 0/4 ≈ 0.000
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 9/12 ≈ 0.750
      ├── Some((7, 5)): 4/8 ≈ 0.500
      ├── Some((7, 6)): 2/6 ≈ 0.333
      ├── Some((7, 7)): 4/8 ≈ 0.500
      └── Some((7, 8)): 4/8 ≈ 0.500
    └── Some((2, 8)): 43/82 ≈ 0.524
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 8/12 ≈ 0.667
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 10/14 ≈ 0.714
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 5/9 ≈ 0.556
      └── Some((8, 8)): 5/9 ≈ 0.556
  ├── Some((4, 3)): 375/742 ≈ 0.505
    ├── Some((3, 0)): 70/125 ≈ 0.560
      ├── Some((0, 0)): 9/15 ≈ 0.600
      ├── Some((0, 1)): 6/12 ≈ 0.500
      ├── Some((0, 2)): 10/16 ≈ 0.625
      ├── Some((0, 3)): 14/20 ≈ 0.700
      ├── Some((0, 4)): 10/16 ≈ 0.625
      ├── Some((0, 5)): 9/15 ≈ 0.600
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 1/7 ≈ 0.143
      └── Some((0, 8)): 8/15 ≈ 0.533
    ├── Some((3, 1)): 65/119 ≈ 0.546
      ├── Some((1, 0)): 7/13 ≈ 0.538
      ├── Some((1, 1)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 7/13 ≈ 0.538
      ├── Some((1, 4)): 8/14 ≈ 0.571
      ├── Some((1, 5)): 7/13 ≈ 0.538
      ├── Some((1, 6)): 8/14 ≈ 0.571
      ├── Some((1, 7)): 11/16 ≈ 0.688
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((3, 2)): 47/93 ≈ 0.505
      ├── Some((2, 0)): 1/6 ≈ 0.167
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 13/18 ≈ 0.722
      ├── Some((2, 3)): 7/12 ≈ 0.583
      ├── Some((2, 4)): 8/13 ≈ 0.615
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((3, 3)): 39/82 ≈ 0.476
      ├── Some((3, 0)): 1/7 ≈ 0.143
      ├── Some((3, 1)): 10/17 ≈ 0.588
      ├── Some((3, 2)): 12/19 ≈ 0.632
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 6/12 ≈ 0.500
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 0/5 ≈ 0.000
    ├── Some((3, 5)): 42/86 ≈ 0.488
      ├── Some((5, 0)): 2/7 ≈ 0.286
      ├── Some((5, 1)): 0/5 ≈ 0.000
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 5/10 ≈ 0.500
      ├── Some((5, 4)): 7/12 ≈ 0.583
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 9/13 ≈ 0.692
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 8/13 ≈ 0.615
    ├── Some((3, 6)): 40/83 ≈ 0.482
      ├── Some((6, 0)): 5/9 ≈ 0.556
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 2/7 ≈ 0.286
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 5/10 ≈ 0.500
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 7/11 ≈ 0.636
      └── Some((6, 8)): 7/11 ≈ 0.636
    ├── Some((3, 7)): 51/99 ≈ 0.515
      ├── Some((7, 0)): 1/6 ≈ 0.167
      ├── Some((7, 1)): 8/13 ≈ 0.615
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 6/11 ≈ 0.545
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 8/13 ≈ 0.615
      ├── Some((7, 6)): 11/16 ≈ 0.688
      ├── Some((7, 7)): 4/9 ≈ 0.444
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((3, 8)): 20/54 ≈ 0.370
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 1/5 ≈ 0.200
      ├── Some((8, 2)): 3/6 ≈ 0.500
      ├── Some((8, 3)): 2/6 ≈ 0.333
      ├── Some((8, 4)): 0/4 ≈ 0.000
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 3/7 ≈ 0.429
      ├── Some((8, 7)): 0/4 ≈ 0.000
      └── Some((8, 8)): 6/9 ≈ 0.667
  ├── Some((4, 4)): 212/459 ≈ 0.462
    ├── Some((4, 0)): 15/41 ≈ 0.366
      ├── Some((0, 0)): 2/5 ≈ 0.400
      ├── Some((0, 1)): 1/4 ≈ 0.250
      ├── Some((0, 2)): 0/3 ≈ 0.000
      ├── Some((0, 3)): 0/3 ≈ 0.000
      ├── Some((0, 4)): 1/4 ≈ 0.250
      ├── Some((0, 5)): 2/5 ≈ 0.400
      ├── Some((0, 6)): 1/4 ≈ 0.250
      ├── Some((0, 7)): 5/7 ≈ 0.714
      └── Some((0, 8)): 3/5 ≈ 0.600
    ├── Some((4, 1)): 16/42 ≈ 0.381
      ├── Some((1, 0)): 1/4 ≈ 0.250
      ├── Some((1, 1)): 3/6 ≈ 0.500
      ├── Some((1, 2)): 2/5 ≈ 0.400
      ├── Some((1, 3)): 0/3 ≈ 0.000
      ├── Some((1, 4)): 1/4 ≈ 0.250
      ├── Some((1, 5)): 1/4 ≈ 0.250
      ├── Some((1, 6)): 1/4 ≈ 0.250
      ├── Some((1, 7)): 4/6 ≈ 0.667
      └── Some((1, 8)): 2/5 ≈ 0.400
    ├── Some((4, 2)): 37/72 ≈ 0.514
      ├── Some((2, 0)): 3/7 ≈ 0.429
      ├── Some((2, 1)): 4/8 ≈ 0.500
      ├── Some((2, 2)): 8/11 ≈ 0.727
      ├── Some((2, 3)): 5/9 ≈ 0.556
      ├── Some((2, 4)): 3/7 ≈ 0.429
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 2/6 ≈ 0.333
      ├── Some((2, 7)): 6/9 ≈ 0.667
      └── Some((2, 8)): 5/9 ≈ 0.556
    ├── Some((4, 3)): 35/69 ≈ 0.507
      ├── Some((3, 0)): 3/8 ≈ 0.375
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 5/9 ≈ 0.556
      ├── Some((3, 3)): 5/9 ≈ 0.556
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 5/9 ≈ 0.556
      ├── Some((3, 7)): 5/9 ≈ 0.556
      └── Some((3, 8)): 8/12 ≈ 0.667
    ├── Some((4, 5)): 22/51 ≈ 0.431
      ├── Some((5, 0)): 3/6 ≈ 0.500
      ├── Some((5, 1)): 2/5 ≈ 0.400
      ├── Some((5, 2)): 3/6 ≈ 0.500
      ├── Some((5, 3)): 4/7 ≈ 0.571
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 4/7 ≈ 0.571
      ├── Some((5, 6)): 3/6 ≈ 0.500
      ├── Some((5, 7)): 0/3 ≈ 0.000
      └── Some((5, 8)): 2/5 ≈ 0.400
    ├── Some((4, 6)): 30/63 ≈ 0.476
      ├── Some((6, 0)): 4/8 ≈ 0.500
      ├── Some((6, 1)): 5/8 ≈ 0.625
      ├── Some((6, 2)): 0/4 ≈ 0.000
      ├── Some((6, 3)): 3/7 ≈ 0.429
      ├── Some((6, 4)): 5/8 ≈ 0.625
      ├── Some((6, 5)): 3/7 ≈ 0.429
      ├── Some((6, 6)): 5/8 ≈ 0.625
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 3/7 ≈ 0.429
    ├── Some((4, 7)): 20/48 ≈ 0.417
      ├── Some((7, 0)): 0/3 ≈ 0.000
      ├── Some((7, 1)): 3/6 ≈ 0.500
      ├── Some((7, 2)): 1/4 ≈ 0.250
      ├── Some((7, 3)): 0/3 ≈ 0.000
      ├── Some((7, 4)): 3/6 ≈ 0.500
      ├── Some((7, 5)): 2/5 ≈ 0.400
      ├── Some((7, 6)): 1/4 ≈ 0.250
      ├── Some((7, 7)): 3/6 ≈ 0.500
      └── Some((7, 8)): 7/10 ≈ 0.700
    └── Some((4, 8)): 37/72 ≈ 0.514
      ├── Some((8, 0)): 6/9 ≈ 0.667
      ├── Some((8, 1)): 4/8 ≈ 0.500
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 6/10 ≈ 0.600
      ├── Some((8, 4)): 5/9 ≈ 0.556
      ├── Some((8, 5)): 4/8 ≈ 0.500
      ├── Some((8, 6)): 7/10 ≈ 0.700
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((4, 5)): 409/799 ≈ 0.512
    ├── Some((5, 0)): 51/97 ≈ 0.526
      ├── Some((0, 0)): 7/12 ≈ 0.583
      ├── Some((0, 1)): 3/8 ≈ 0.375
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 6/11 ≈ 0.545
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 6/11 ≈ 0.545
      └── Some((0, 8)): 15/20 ≈ 0.750
    ├── Some((5, 1)): 59/108 ≈ 0.546
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 7/12 ≈ 0.583
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 10/15 ≈ 0.667
      ├── Some((1, 5)): 9/14 ≈ 0.643
      ├── Some((1, 6)): 9/14 ≈ 0.643
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 5/11 ≈ 0.455
    ├── Some((5, 2)): 65/116 ≈ 0.560
      ├── Some((2, 0)): 10/15 ≈ 0.667
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 9/15 ≈ 0.600
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 11/16 ≈ 0.688
      ├── Some((2, 5)): 1/6 ≈ 0.167
      ├── Some((2, 6)): 10/15 ≈ 0.667
      ├── Some((2, 7)): 7/13 ≈ 0.538
      └── Some((2, 8)): 7/13 ≈ 0.538
    ├── Some((5, 3)): 66/117 ≈ 0.564
      ├── Some((3, 0)): 9/15 ≈ 0.600
      ├── Some((3, 1)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 8/15 ≈ 0.533
      ├── Some((3, 3)): 8/15 ≈ 0.533
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 9/15 ≈ 0.600
      ├── Some((3, 7)): 12/18 ≈ 0.667
      └── Some((3, 8)): 10/16 ≈ 0.625
    ├── Some((5, 4)): 37/77 ≈ 0.481
      ├── Some((4, 0)): 7/12 ≈ 0.583
      ├── Some((4, 1)): 0/5 ≈ 0.000
      ├── Some((4, 2)): 4/9 ≈ 0.444
      ├── Some((4, 3)): 9/14 ≈ 0.643
      ├── Some((4, 4)): 5/10 ≈ 0.500
      ├── Some((4, 6)): 4/9 ≈ 0.444
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 4/9 ≈ 0.444
    ├── Some((5, 5)): 26/62 ≈ 0.419
      ├── Some((5, 0)): 8/12 ≈ 0.667
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 1/5 ≈ 0.200
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 7/11 ≈ 0.636
      ├── Some((5, 6)): 0/4 ≈ 0.000
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((5, 6)): 30/67 ≈ 0.448
      ├── Some((6, 0)): 4/8 ≈ 0.500
      ├── Some((6, 1)): 5/9 ≈ 0.556
      ├── Some((6, 2)): 0/4 ≈ 0.000
      ├── Some((6, 3)): 6/10 ≈ 0.600
      ├── Some((6, 4)): 2/6 ≈ 0.333
      ├── Some((6, 5)): 3/7 ≈ 0.429
      ├── Some((6, 6)): 4/8 ≈ 0.500
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 6/10 ≈ 0.600
    ├── Some((5, 7)): 46/90 ≈ 0.511
      ├── Some((7, 0)): 1/6 ≈ 0.167
      ├── Some((7, 1)): 13/17 ≈ 0.765
      ├── Some((7, 2)): 7/12 ≈ 0.583
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 5/10 ≈ 0.500
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 8/13 ≈ 0.615
      └── Some((7, 8)): 1/6 ≈ 0.167
    └── Some((5, 8)): 28/64 ≈ 0.438
      ├── Some((8, 0)): 4/8 ≈ 0.500
      ├── Some((8, 1)): 5/8 ≈ 0.625
      ├── Some((8, 2)): 5/9 ≈ 0.556
      ├── Some((8, 3)): 0/4 ≈ 0.000
      ├── Some((8, 4)): 4/8 ≈ 0.500
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 5/9 ≈ 0.556
      └── Some((8, 8)): 2/6 ≈ 0.333
  ├── Some((4, 6)): 230/491 ≈ 0.468
    ├── Some((6, 0)): 7/28 ≈ 0.250
      ├── Some((0, 0)): 0/3 ≈ 0.000
      ├── Some((0, 1)): 1/3 ≈ 0.333
      ├── Some((0, 2)): 0/3 ≈ 0.000
      ├── Some((0, 3)): 1/3 ≈ 0.333
      ├── Some((0, 4)): 1/3 ≈ 0.333
      ├── Some((0, 5)): 1/3 ≈ 0.333
      ├── Some((0, 6)): 1/3 ≈ 0.333
      ├── Some((0, 7)): 0/3 ≈ 0.000
      └── Some((0, 8)): 1/3 ≈ 0.333
    ├── Some((6, 1)): 20/47 ≈ 0.426
      ├── Some((1, 0)): 2/5 ≈ 0.400
      ├── Some((1, 1)): 0/3 ≈ 0.000
      ├── Some((1, 2)): 0/3 ≈ 0.000
      ├── Some((1, 3)): 4/7 ≈ 0.571
      ├── Some((1, 4)): 6/8 ≈ 0.750
      ├── Some((1, 5)): 1/4 ≈ 0.250
      ├── Some((1, 6)): 3/6 ≈ 0.500
      ├── Some((1, 7)): 2/5 ≈ 0.400
      └── Some((1, 8)): 2/5 ≈ 0.400
    ├── Some((6, 2)): 25/54 ≈ 0.463
      ├── Some((2, 0)): 2/5 ≈ 0.400
      ├── Some((2, 1)): 2/6 ≈ 0.333
      ├── Some((2, 2)): 4/7 ≈ 0.571
      ├── Some((2, 3)): 5/8 ≈ 0.625
      ├── Some((2, 4)): 4/7 ≈ 0.571
      ├── Some((2, 5)): 3/6 ≈ 0.500
      ├── Some((2, 6)): 3/6 ≈ 0.500
      ├── Some((2, 7)): 0/3 ≈ 0.000
      └── Some((2, 8)): 1/5 ≈ 0.200
    ├── Some((6, 3)): 25/54 ≈ 0.463
      ├── Some((3, 0)): 2/6 ≈ 0.333
      ├── Some((3, 1)): 4/7 ≈ 0.571
      ├── Some((3, 2)): 2/6 ≈ 0.333
      ├── Some((3, 3)): 2/6 ≈ 0.333
      ├── Some((3, 5)): 5/8 ≈ 0.625
      ├── Some((3, 6)): 3/7 ≈ 0.429
      ├── Some((3, 7)): 5/8 ≈ 0.625
      └── Some((3, 8)): 1/5 ≈ 0.200
    ├── Some((6, 4)): 38/72 ≈ 0.528
      ├── Some((4, 0)): 7/11 ≈ 0.636
      ├── Some((4, 1)): 4/8 ≈ 0.500
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 12/16 ≈ 0.750
      ├── Some((4, 5)): 4/9 ≈ 0.444
      ├── Some((4, 7)): 0/4 ≈ 0.000
      └── Some((4, 8)): 1/5 ≈ 0.200
    ├── Some((6, 5)): 18/44 ≈ 0.409
      ├── Some((5, 0)): 0/3 ≈ 0.000
      ├── Some((5, 1)): 5/7 ≈ 0.714
      ├── Some((5, 2)): 2/5 ≈ 0.400
      ├── Some((5, 3)): 2/5 ≈ 0.400
      ├── Some((5, 4)): 2/5 ≈ 0.400
      ├── Some((5, 5)): 3/5 ≈ 0.600
      ├── Some((5, 6)): 0/3 ≈ 0.000
      ├── Some((5, 7)): 2/5 ≈ 0.400
      └── Some((5, 8)): 2/5 ≈ 0.400
    ├── Some((6, 6)): 19/46 ≈ 0.413
      ├── Some((6, 0)): 3/6 ≈ 0.500
      ├── Some((6, 1)): 1/5 ≈ 0.200
      ├── Some((6, 2)): 6/9 ≈ 0.667
      ├── Some((6, 3)): 2/5 ≈ 0.400
      ├── Some((6, 4)): 2/5 ≈ 0.400
      ├── Some((6, 5)): 3/6 ≈ 0.500
      ├── Some((6, 7)): 0/3 ≈ 0.000
      └── Some((6, 8)): 2/6 ≈ 0.333
    ├── Some((6, 7)): 53/91 ≈ 0.582
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 5/9 ≈ 0.556
      ├── Some((7, 2)): 5/9 ≈ 0.556
      ├── Some((7, 3)): 5/9 ≈ 0.556
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 6/10 ≈ 0.600
      ├── Some((7, 6)): 5/10 ≈ 0.500
      ├── Some((7, 7)): 14/17 ≈ 0.824
      └── Some((7, 8)): 6/10 ≈ 0.600
    └── Some((6, 8)): 25/54 ≈ 0.463
      ├── Some((8, 0)): 0/3 ≈ 0.000
      ├── Some((8, 1)): 6/9 ≈ 0.667
      ├── Some((8, 2)): 4/7 ≈ 0.571
      ├── Some((8, 3)): 0/4 ≈ 0.000
      ├── Some((8, 4)): 3/6 ≈ 0.500
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 4/7 ≈ 0.571
      ├── Some((8, 7)): 3/6 ≈ 0.500
      └── Some((8, 8)): 4/7 ≈ 0.571
  ├── Some((4, 7)): 355/708 ≈ 0.501
    ├── Some((7, 0)): 33/70 ≈ 0.471
      ├── Some((0, 0)): 4/8 ≈ 0.500
      ├── Some((0, 1)): 3/7 ≈ 0.429
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 2/6 ≈ 0.333
      ├── Some((0, 4)): 1/5 ≈ 0.200
      ├── Some((0, 5)): 6/10 ≈ 0.600
      ├── Some((0, 6)): 6/10 ≈ 0.600
      ├── Some((0, 7)): 5/9 ≈ 0.556
      └── Some((0, 8)): 5/9 ≈ 0.556
    ├── Some((7, 1)): 85/140 ≈ 0.607
      ├── Some((1, 0)): 15/21 ≈ 0.714
      ├── Some((1, 1)): 4/10 ≈ 0.400
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 9/15 ≈ 0.600
      ├── Some((1, 4)): 6/12 ≈ 0.500
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 15/21 ≈ 0.714
      ├── Some((1, 7)): 9/15 ≈ 0.600
      └── Some((1, 8)): 12/18 ≈ 0.667
    ├── Some((7, 2)): 35/73 ≈ 0.479
      ├── Some((2, 0)): 1/5 ≈ 0.200
      ├── Some((2, 1)): 4/9 ≈ 0.444
      ├── Some((2, 2)): 6/10 ≈ 0.600
      ├── Some((2, 3)): 6/10 ≈ 0.600
      ├── Some((2, 4)): 4/9 ≈ 0.444
      ├── Some((2, 5)): 5/9 ≈ 0.556
      ├── Some((2, 6)): 1/5 ≈ 0.200
      ├── Some((2, 7)): 0/4 ≈ 0.000
      └── Some((2, 8)): 7/11 ≈ 0.636
    ├── Some((7, 3)): 33/70 ≈ 0.471
      ├── Some((3, 0)): 5/9 ≈ 0.556
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 0/4 ≈ 0.000
      ├── Some((3, 3)): 5/10 ≈ 0.500
      ├── Some((3, 5)): 7/11 ≈ 0.636
      ├── Some((3, 6)): 4/9 ≈ 0.444
      ├── Some((3, 7)): 5/10 ≈ 0.500
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((7, 4)): 32/68 ≈ 0.471
      ├── Some((4, 0)): 4/8 ≈ 0.500
      ├── Some((4, 1)): 4/8 ≈ 0.500
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 5/9 ≈ 0.556
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 5/9 ≈ 0.556
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((7, 5)): 43/84 ≈ 0.512
      ├── Some((5, 0)): 4/9 ≈ 0.444
      ├── Some((5, 1)): 5/9 ≈ 0.556
      ├── Some((5, 2)): 3/8 ≈ 0.375
      ├── Some((5, 3)): 7/11 ≈ 0.636
      ├── Some((5, 4)): 9/13 ≈ 0.692
      ├── Some((5, 5)): 1/6 ≈ 0.167
      ├── Some((5, 6)): 7/11 ≈ 0.636
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 3/8 ≈ 0.375
    ├── Some((7, 6)): 34/71 ≈ 0.479
      ├── Some((6, 0)): 3/7 ≈ 0.429
      ├── Some((6, 1)): 0/4 ≈ 0.000
      ├── Some((6, 2)): 2/6 ≈ 0.333
      ├── Some((6, 3)): 4/8 ≈ 0.500
      ├── Some((6, 4)): 0/4 ≈ 0.000
      ├── Some((6, 5)): 9/13 ≈ 0.692
      ├── Some((6, 6)): 7/11 ≈ 0.636
      ├── Some((6, 7)): 5/9 ≈ 0.556
      └── Some((6, 8)): 4/8 ≈ 0.500
    ├── Some((7, 7)): 19/50 ≈ 0.380
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 3/7 ≈ 0.429
      ├── Some((7, 2)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 4/7 ≈ 0.571
      ├── Some((7, 4)): 3/7 ≈ 0.429
      ├── Some((7, 5)): 2/6 ≈ 0.333
      ├── Some((7, 6)): 4/7 ≈ 0.571
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((7, 8)): 41/81 ≈ 0.506
      ├── Some((8, 0)): 8/12 ≈ 0.667
      ├── Some((8, 1)): 4/8 ≈ 0.500
      ├── Some((8, 2)): 6/10 ≈ 0.600
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 4/9 ≈ 0.444
      ├── Some((8, 6)): 0/4 ≈ 0.000
      ├── Some((8, 7)): 11/15 ≈ 0.733
      └── Some((8, 8)): 4/9 ≈ 0.444
  └── Some((4, 8)): 252/530 ≈ 0.475
    ├── Some((8, 0)): 23/52 ≈ 0.442
      ├── Some((0, 0)): 2/5 ≈ 0.400
      ├── Some((0, 1)): 3/6 ≈ 0.500
      ├── Some((0, 2)): 3/6 ≈ 0.500
      ├── Some((0, 3)): 3/6 ≈ 0.500
      ├── Some((0, 4)): 2/6 ≈ 0.333
      ├── Some((0, 5)): 0/3 ≈ 0.000
      ├── Some((0, 6)): 3/6 ≈ 0.500
      ├── Some((0, 7)): 3/6 ≈ 0.500
      └── Some((0, 8)): 4/7 ≈ 0.571
    ├── Some((8, 1)): 42/78 ≈ 0.538
      ├── Some((1, 0)): 4/8 ≈ 0.500
      ├── Some((1, 1)): 3/7 ≈ 0.429
      ├── Some((1, 2)): 7/11 ≈ 0.636
      ├── Some((1, 3)): 3/7 ≈ 0.429
      ├── Some((1, 4)): 2/6 ≈ 0.333
      ├── Some((1, 5)): 5/9 ≈ 0.556
      ├── Some((1, 6)): 3/7 ≈ 0.429
      ├── Some((1, 7)): 8/11 ≈ 0.727
      └── Some((1, 8)): 7/11 ≈ 0.636
    ├── Some((8, 2)): 24/53 ≈ 0.453
      ├── Some((2, 0)): 3/6 ≈ 0.500
      ├── Some((2, 1)): 0/3 ≈ 0.000
      ├── Some((2, 2)): 7/10 ≈ 0.700
      ├── Some((2, 3)): 5/8 ≈ 0.625
      ├── Some((2, 4)): 3/6 ≈ 0.500
      ├── Some((2, 5)): 5/8 ≈ 0.625
      ├── Some((2, 6)): 0/3 ≈ 0.000
      ├── Some((2, 7)): 0/3 ≈ 0.000
      └── Some((2, 8)): 1/5 ≈ 0.200
    ├── Some((8, 3)): 18/45 ≈ 0.400
      ├── Some((3, 0)): 1/5 ≈ 0.200
      ├── Some((3, 1)): 2/5 ≈ 0.400
      ├── Some((3, 2)): 2/6 ≈ 0.333
      ├── Some((3, 3)): 6/9 ≈ 0.667
      ├── Some((3, 5)): 4/7 ≈ 0.571
      ├── Some((3, 6)): 0/3 ≈ 0.000
      ├── Some((3, 7)): 0/3 ≈ 0.000
      └── Some((3, 8)): 3/6 ≈ 0.500
    ├── Some((8, 4)): 15/40 ≈ 0.375
      ├── Some((4, 0)): 2/5 ≈ 0.400
      ├── Some((4, 1)): 2/5 ≈ 0.400
      ├── Some((4, 2)): 4/7 ≈ 0.571
      ├── Some((4, 3)): 2/5 ≈ 0.400
      ├── Some((4, 4)): 1/4 ≈ 0.250
      ├── Some((4, 5)): 0/3 ≈ 0.000
      ├── Some((4, 6)): 2/5 ≈ 0.400
      └── Some((4, 7)): 1/5 ≈ 0.200
    ├── Some((8, 5)): 30/62 ≈ 0.484
      ├── Some((5, 0)): 3/6 ≈ 0.500
      ├── Some((5, 1)): 9/11 ≈ 0.818
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 3/6 ≈ 0.500
      ├── Some((5, 4)): 2/6 ≈ 0.333
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 4/7 ≈ 0.571
      ├── Some((5, 7)): 3/7 ≈ 0.429
      └── Some((5, 8)): 3/7 ≈ 0.429
    ├── Some((8, 6)): 31/63 ≈ 0.492
      ├── Some((6, 0)): 4/7 ≈ 0.571
      ├── Some((6, 1)): 6/9 ≈ 0.667
      ├── Some((6, 2)): 5/8 ≈ 0.625
      ├── Some((6, 3)): 3/7 ≈ 0.429
      ├── Some((6, 4)): 4/7 ≈ 0.571
      ├── Some((6, 5)): 3/7 ≈ 0.429
      ├── Some((6, 6)): 4/7 ≈ 0.571
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 1/5 ≈ 0.200
    ├── Some((8, 7)): 25/55 ≈ 0.455
      ├── Some((7, 0)): 1/4 ≈ 0.250
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 4/7 ≈ 0.571
      ├── Some((7, 3)): 6/9 ≈ 0.667
      ├── Some((7, 4)): 1/5 ≈ 0.200
      ├── Some((7, 5)): 0/3 ≈ 0.000
      ├── Some((7, 6)): 5/8 ≈ 0.625
      ├── Some((7, 7)): 5/8 ≈ 0.625
      └── Some((7, 8)): 2/5 ≈ 0.400
    └── Some((8, 8)): 44/81 ≈ 0.543
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 5/10 ≈ 0.500
      ├── Some((8, 3)): 2/7 ≈ 0.286
      ├── Some((8, 4)): 6/10 ≈ 0.600
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 11/15 ≈ 0.733
      └── Some((8, 7)): 6/10 ≈ 0.600
├── Some((3, 5)): 4714/9214 ≈ 0.512
  ├── Some((5, 0)): 557/1083 ≈ 0.514
    ├── Some((0, 0)): 48/101 ≈ 0.475
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 10/17 ≈ 0.588
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 9/16 ≈ 0.562
      ├── Some((0, 7)): 3/9 ≈ 0.333
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((0, 1)): 52/106 ≈ 0.491
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 13/18 ≈ 0.722
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 6/12 ≈ 0.500
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((0, 2)): 53/108 ≈ 0.491
      ├── Some((2, 0)): 14/20 ≈ 0.700
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 7/13 ≈ 0.538
      ├── Some((2, 5)): 10/16 ≈ 0.625
      ├── Some((2, 6)): 8/15 ≈ 0.533
      ├── Some((2, 7)): 1/7 ≈ 0.143
      └── Some((2, 8)): 2/8 ≈ 0.250
    ├── Some((0, 3)): 61/119 ≈ 0.513
      ├── Some((3, 0)): 10/17 ≈ 0.588
      ├── Some((3, 1)): 4/11 ≈ 0.364
      ├── Some((3, 2)): 5/12 ≈ 0.417
      ├── Some((3, 3)): 10/18 ≈ 0.556
      ├── Some((3, 4)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 9/16 ≈ 0.562
      ├── Some((3, 7)): 9/16 ≈ 0.562
      └── Some((3, 8)): 7/14 ≈ 0.500
    ├── Some((0, 4)): 99/173 ≈ 0.572
      ├── Some((4, 0)): 17/25 ≈ 0.680
      ├── Some((4, 1)): 6/14 ≈ 0.429
      ├── Some((4, 2)): 12/20 ≈ 0.600
      ├── Some((4, 3)): 9/17 ≈ 0.529
      ├── Some((4, 4)): 14/23 ≈ 0.609
      ├── Some((4, 5)): 3/11 ≈ 0.273
      ├── Some((4, 6)): 15/23 ≈ 0.652
      ├── Some((4, 7)): 6/14 ≈ 0.429
      └── Some((4, 8)): 17/25 ≈ 0.680
    ├── Some((0, 5)): 72/135 ≈ 0.533
      ├── Some((5, 1)): 11/19 ≈ 0.579
      ├── Some((5, 2)): 11/19 ≈ 0.579
      ├── Some((5, 3)): 8/16 ≈ 0.500
      ├── Some((5, 4)): 2/9 ≈ 0.222
      ├── Some((5, 5)): 5/13 ≈ 0.385
      ├── Some((5, 6)): 9/17 ≈ 0.529
      ├── Some((5, 7)): 13/21 ≈ 0.619
      └── Some((5, 8)): 12/20 ≈ 0.600
    ├── Some((0, 6)): 38/86 ≈ 0.442
      ├── Some((6, 0)): 5/10 ≈ 0.500
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 0/5 ≈ 0.000
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 6/11 ≈ 0.545
      └── Some((6, 8)): 8/13 ≈ 0.615
    ├── Some((0, 7)): 81/148 ≈ 0.547
      ├── Some((7, 0)): 5/12 ≈ 0.417
      ├── Some((7, 1)): 8/15 ≈ 0.533
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 3/10 ≈ 0.300
      ├── Some((7, 5)): 17/24 ≈ 0.708
      ├── Some((7, 6)): 13/21 ≈ 0.619
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 13/21 ≈ 0.619
    └── Some((0, 8)): 52/106 ≈ 0.491
      ├── Some((8, 0)): 10/16 ≈ 0.625
      ├── Some((8, 1)): 2/8 ≈ 0.250
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 6/12 ≈ 0.500
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 7/13 ≈ 0.538
      ├── Some((8, 6)): 1/6 ≈ 0.167
      ├── Some((8, 7)): 8/14 ≈ 0.571
      └── Some((8, 8)): 8/14 ≈ 0.571
  ├── Some((5, 1)): 355/732 ≈ 0.485
    ├── Some((1, 0)): 60/110 ≈ 0.545
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 8/13 ≈ 0.615
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 6/12 ≈ 0.500
      ├── Some((0, 7)): 9/14 ≈ 0.643
      └── Some((0, 8)): 10/15 ≈ 0.667
    ├── Some((1, 1)): 36/77 ≈ 0.468
      ├── Some((1, 0)): 5/10 ≈ 0.500
      ├── Some((1, 2)): 4/9 ≈ 0.444
      ├── Some((1, 3)): 6/11 ≈ 0.545
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 4/9 ≈ 0.444
      ├── Some((1, 6)): 5/10 ≈ 0.500
      ├── Some((1, 7)): 4/9 ≈ 0.444
      └── Some((1, 8)): 5/10 ≈ 0.500
    ├── Some((1, 2)): 55/103 ≈ 0.534
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 2/7 ≈ 0.286
      ├── Some((2, 2)): 7/12 ≈ 0.583
      ├── Some((2, 3)): 10/15 ≈ 0.667
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 9/14 ≈ 0.643
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 7/12 ≈ 0.583
    ├── Some((1, 3)): 37/78 ≈ 0.474
      ├── Some((3, 0)): 3/8 ≈ 0.375
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 7/12 ≈ 0.583
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 6/11 ≈ 0.545
      └── Some((3, 8)): 13/18 ≈ 0.722
    ├── Some((1, 4)): 34/74 ≈ 0.459
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 1/5 ≈ 0.200
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 7/11 ≈ 0.636
      ├── Some((4, 5)): 6/10 ≈ 0.600
      ├── Some((4, 6)): 2/7 ≈ 0.286
      ├── Some((4, 7)): 0/4 ≈ 0.000
      └── Some((4, 8)): 7/11 ≈ 0.636
    ├── Some((1, 5)): 33/72 ≈ 0.458
      ├── Some((5, 0)): 7/12 ≈ 0.583
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 3)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 4/9 ≈ 0.444
      ├── Some((5, 5)): 4/9 ≈ 0.444
      ├── Some((5, 6)): 6/11 ≈ 0.545
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 0/4 ≈ 0.000
    ├── Some((1, 6)): 31/69 ≈ 0.449
      ├── Some((6, 0)): 2/6 ≈ 0.333
      ├── Some((6, 1)): 5/9 ≈ 0.556
      ├── Some((6, 2)): 2/6 ≈ 0.333
      ├── Some((6, 3)): 1/5 ≈ 0.200
      ├── Some((6, 4)): 4/8 ≈ 0.500
      ├── Some((6, 5)): 6/10 ≈ 0.600
      ├── Some((6, 6)): 1/5 ≈ 0.200
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 7/11 ≈ 0.636
    ├── Some((1, 7)): 29/66 ≈ 0.439
      ├── Some((7, 0)): 3/7 ≈ 0.429
      ├── Some((7, 1)): 3/7 ≈ 0.429
      ├── Some((7, 2)): 2/6 ≈ 0.333
      ├── Some((7, 3)): 4/8 ≈ 0.500
      ├── Some((7, 4)): 6/10 ≈ 0.600
      ├── Some((7, 5)): 3/7 ≈ 0.429
      ├── Some((7, 6)): 4/8 ≈ 0.500
      ├── Some((7, 7)): 1/5 ≈ 0.200
      └── Some((7, 8)): 3/7 ≈ 0.429
    └── Some((1, 8)): 40/82 ≈ 0.488
      ├── Some((8, 0)): 7/11 ≈ 0.636
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 5/9 ≈ 0.556
      ├── Some((8, 3)): 1/6 ≈ 0.167
      ├── Some((8, 4)): 1/6 ≈ 0.167
      ├── Some((8, 5)): 5/10 ≈ 0.500
      ├── Some((8, 6)): 4/9 ≈ 0.444
      ├── Some((8, 7)): 9/13 ≈ 0.692
      └── Some((8, 8)): 4/9 ≈ 0.444
  ├── Some((5, 2)): 594/1146 ≈ 0.518
    ├── Some((2, 0)): 94/168 ≈ 0.560
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 8/16 ≈ 0.500
      ├── Some((0, 2)): 3/11 ≈ 0.273
      ├── Some((0, 3)): 14/23 ≈ 0.609
      ├── Some((0, 4)): 19/27 ≈ 0.704
      ├── Some((0, 5)): 15/24 ≈ 0.625
      ├── Some((0, 6)): 8/16 ≈ 0.500
      ├── Some((0, 7)): 9/17 ≈ 0.529
      └── Some((0, 8)): 10/18 ≈ 0.556
    ├── Some((2, 1)): 72/136 ≈ 0.529
      ├── Some((1, 0)): 15/22 ≈ 0.682
      ├── Some((1, 1)): 8/15 ≈ 0.533
      ├── Some((1, 2)): 9/16 ≈ 0.562
      ├── Some((1, 3)): 8/15 ≈ 0.533
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 5/12 ≈ 0.417
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 7/14 ≈ 0.500
    ├── Some((2, 2)): 83/152 ≈ 0.546
      ├── Some((2, 0)): 10/19 ≈ 0.526
      ├── Some((2, 1)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 6/14 ≈ 0.429
      ├── Some((2, 4)): 4/12 ≈ 0.333
      ├── Some((2, 5)): 21/30 ≈ 0.700
      ├── Some((2, 6)): 5/13 ≈ 0.385
      ├── Some((2, 7)): 17/26 ≈ 0.654
      └── Some((2, 8)): 13/22 ≈ 0.591
    ├── Some((2, 3)): 21/60 ≈ 0.350
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 4/9 ≈ 0.444
      ├── Some((3, 7)): 1/6 ≈ 0.167
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((2, 4)): 49/103 ≈ 0.476
      ├── Some((4, 0)): 6/12 ≈ 0.500
      ├── Some((4, 1)): 12/18 ≈ 0.667
      ├── Some((4, 2)): 0/5 ≈ 0.000
      ├── Some((4, 3)): 3/9 ≈ 0.333
      ├── Some((4, 4)): 6/12 ≈ 0.500
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 3/9 ≈ 0.333
      ├── Some((4, 7)): 10/16 ≈ 0.625
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((2, 5)): 65/126 ≈ 0.516
      ├── Some((5, 0)): 7/15 ≈ 0.467
      ├── Some((5, 1)): 11/19 ≈ 0.579
      ├── Some((5, 3)): 13/21 ≈ 0.619
      ├── Some((5, 4)): 3/10 ≈ 0.300
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 12/20 ≈ 0.600
      └── Some((5, 8)): 3/10 ≈ 0.300
    ├── Some((2, 6)): 56/113 ≈ 0.496
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 8/15 ≈ 0.533
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 8/15 ≈ 0.533
      ├── Some((6, 5)): 13/19 ≈ 0.684
      ├── Some((6, 6)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((2, 7)): 102/179 ≈ 0.570
      ├── Some((7, 0)): 13/22 ≈ 0.591
      ├── Some((7, 1)): 14/23 ≈ 0.609
      ├── Some((7, 2)): 11/20 ≈ 0.550
      ├── Some((7, 3)): 3/11 ≈ 0.273
      ├── Some((7, 4)): 12/21 ≈ 0.571
      ├── Some((7, 5)): 13/22 ≈ 0.591
      ├── Some((7, 6)): 4/12 ≈ 0.333
      ├── Some((7, 7)): 7/15 ≈ 0.467
      └── Some((7, 8)): 24/32 ≈ 0.750
    └── Some((2, 8)): 52/108 ≈ 0.481
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 3/9 ≈ 0.333
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 3/9 ≈ 0.333
      ├── Some((8, 4)): 9/15 ≈ 0.600
      ├── Some((8, 5)): 9/15 ≈ 0.600
      ├── Some((8, 6)): 3/9 ≈ 0.333
      ├── Some((8, 7)): 9/16 ≈ 0.562
      └── Some((8, 8)): 5/11 ≈ 0.455
  ├── Some((5, 3)): 676/1285 ≈ 0.526
    ├── Some((3, 0)): 88/166 ≈ 0.530
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 5/13 ≈ 0.385
      ├── Some((0, 2)): 8/17 ≈ 0.471
      ├── Some((0, 3)): 10/19 ≈ 0.526
      ├── Some((0, 4)): 16/25 ≈ 0.640
      ├── Some((0, 5)): 7/15 ≈ 0.467
      ├── Some((0, 6)): 10/19 ≈ 0.526
      ├── Some((0, 7)): 17/26 ≈ 0.654
      └── Some((0, 8)): 7/16 ≈ 0.438
    ├── Some((3, 1)): 89/167 ≈ 0.533
      ├── Some((1, 0)): 5/13 ≈ 0.385
      ├── Some((1, 1)): 4/12 ≈ 0.333
      ├── Some((1, 2)): 10/19 ≈ 0.526
      ├── Some((1, 3)): 15/24 ≈ 0.625
      ├── Some((1, 4)): 13/22 ≈ 0.591
      ├── Some((1, 5)): 18/27 ≈ 0.667
      ├── Some((1, 6)): 7/16 ≈ 0.438
      ├── Some((1, 7)): 17/26 ≈ 0.654
      └── Some((1, 8)): 0/7 ≈ 0.000
    ├── Some((3, 2)): 95/176 ≈ 0.540
      ├── Some((2, 0)): 2/10 ≈ 0.200
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 16/25 ≈ 0.640
      ├── Some((2, 3)): 7/16 ≈ 0.438
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 14/23 ≈ 0.609
      ├── Some((2, 6)): 6/15 ≈ 0.400
      ├── Some((2, 7)): 13/22 ≈ 0.591
      └── Some((2, 8)): 22/32 ≈ 0.688
    ├── Some((3, 3)): 73/144 ≈ 0.507
      ├── Some((3, 0)): 6/16 ≈ 0.375
      ├── Some((3, 1)): 16/27 ≈ 0.593
      ├── Some((3, 2)): 5/14 ≈ 0.357
      ├── Some((3, 4)): 9/19 ≈ 0.474
      ├── Some((3, 6)): 5/14 ≈ 0.357
      ├── Some((3, 7)): 13/24 ≈ 0.542
      └── Some((3, 8)): 18/29 ≈ 0.621
    ├── Some((3, 4)): 112/201 ≈ 0.557
      ├── Some((4, 0)): 4/13 ≈ 0.308
      ├── Some((4, 1)): 12/22 ≈ 0.545
      ├── Some((4, 2)): 19/29 ≈ 0.655
      ├── Some((4, 3)): 17/27 ≈ 0.630
      ├── Some((4, 4)): 12/22 ≈ 0.545
      ├── Some((4, 5)): 17/27 ≈ 0.630
      ├── Some((4, 6)): 11/21 ≈ 0.524
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 11/21 ≈ 0.524
    ├── Some((3, 6)): 69/138 ≈ 0.500
      ├── Some((6, 0)): 16/24 ≈ 0.667
      ├── Some((6, 1)): 5/12 ≈ 0.417
      ├── Some((6, 2)): 9/17 ≈ 0.529
      ├── Some((6, 3)): 14/22 ≈ 0.636
      ├── Some((6, 4)): 6/14 ≈ 0.429
      ├── Some((6, 5)): 1/8 ≈ 0.125
      ├── Some((6, 6)): 4/11 ≈ 0.364
      ├── Some((6, 7)): 7/15 ≈ 0.467
      └── Some((6, 8)): 6/14 ≈ 0.429
    ├── Some((3, 7)): 46/103 ≈ 0.447
      ├── Some((7, 0)): 5/11 ≈ 0.455
      ├── Some((7, 1)): 6/12 ≈ 0.500
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 8/15 ≈ 0.533
      ├── Some((7, 5)): 1/7 ≈ 0.143
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 10/17 ≈ 0.588
    └── Some((3, 8)): 104/189 ≈ 0.550
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 18/28 ≈ 0.643
      ├── Some((8, 3)): 12/22 ≈ 0.545
      ├── Some((8, 4)): 5/14 ≈ 0.357
      ├── Some((8, 5)): 3/11 ≈ 0.273
      ├── Some((8, 6)): 17/27 ≈ 0.630
      ├── Some((8, 7)): 25/35 ≈ 0.714
      └── Some((8, 8)): 8/17 ≈ 0.471
  ├── Some((5, 4)): 449/897 ≈ 0.501
    ├── Some((4, 0)): 54/106 ≈ 0.509
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 9/14 ≈ 0.643
      ├── Some((0, 3)): 6/12 ≈ 0.500
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 7/13 ≈ 0.538
      ├── Some((0, 6)): 8/14 ≈ 0.571
      ├── Some((0, 7)): 9/15 ≈ 0.600
      └── Some((0, 8)): 1/6 ≈ 0.167
    ├── Some((4, 1)): 34/77 ≈ 0.442
      ├── Some((1, 0)): 3/8 ≈ 0.375
      ├── Some((1, 1)): 1/5 ≈ 0.200
      ├── Some((1, 2)): 4/9 ≈ 0.444
      ├── Some((1, 3)): 5/10 ≈ 0.500
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 1/6 ≈ 0.167
      ├── Some((1, 7)): 6/10 ≈ 0.600
      └── Some((1, 8)): 6/10 ≈ 0.600
    ├── Some((4, 2)): 43/90 ≈ 0.478
      ├── Some((2, 0)): 7/12 ≈ 0.583
      ├── Some((2, 1)): 6/11 ≈ 0.545
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 8/13 ≈ 0.615
    ├── Some((4, 3)): 55/107 ≈ 0.514
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 3/9 ≈ 0.333
      ├── Some((3, 2)): 2/8 ≈ 0.250
      ├── Some((3, 3)): 9/16 ≈ 0.562
      ├── Some((3, 4)): 10/16 ≈ 0.625
      ├── Some((3, 6)): 9/16 ≈ 0.562
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 13/19 ≈ 0.684
    ├── Some((4, 4)): 52/103 ≈ 0.505
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 6/12 ≈ 0.500
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 8/15 ≈ 0.533
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 9/15 ≈ 0.600
    ├── Some((4, 5)): 66/122 ≈ 0.541
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 3/10 ≈ 0.300
      ├── Some((5, 2)): 13/20 ≈ 0.650
      ├── Some((5, 3)): 11/18 ≈ 0.611
      ├── Some((5, 5)): 13/20 ≈ 0.650
      ├── Some((5, 6)): 11/18 ≈ 0.611
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 1/7 ≈ 0.143
    ├── Some((4, 6)): 60/114 ≈ 0.526
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 8/14 ≈ 0.571
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 2/8 ≈ 0.250
      ├── Some((6, 5)): 8/14 ≈ 0.571
      ├── Some((6, 6)): 9/15 ≈ 0.600
      ├── Some((6, 7)): 12/18 ≈ 0.667
      └── Some((6, 8)): 6/12 ≈ 0.500
    ├── Some((4, 7)): 35/78 ≈ 0.449
      ├── Some((7, 0)): 5/10 ≈ 0.500
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 3)): 11/15 ≈ 0.733
      ├── Some((7, 4)): 0/4 ≈ 0.000
      ├── Some((7, 5)): 4/9 ≈ 0.444
      ├── Some((7, 6)): 4/9 ≈ 0.444
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 5/10 ≈ 0.500
    └── Some((4, 8)): 49/99 ≈ 0.495
      ├── Some((8, 0)): 7/13 ≈ 0.538
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 1/6 ≈ 0.167
      ├── Some((8, 3)): 8/13 ≈ 0.615
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 3/9 ≈ 0.333
      ├── Some((8, 6)): 8/13 ≈ 0.615
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 9/14 ≈ 0.643
  ├── Some((5, 5)): 470/933 ≈ 0.504
    ├── Some((5, 0)): 44/95 ≈ 0.463
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 1/6 ≈ 0.167
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 3/9 ≈ 0.333
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 13/18 ≈ 0.722
      ├── Some((0, 6)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 7/13 ≈ 0.538
    ├── Some((5, 1)): 81/149 ≈ 0.544
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 9/17 ≈ 0.529
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 3)): 4/11 ≈ 0.364
      ├── Some((1, 4)): 14/21 ≈ 0.667
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 14/22 ≈ 0.636
      ├── Some((1, 7)): 8/16 ≈ 0.500
      └── Some((1, 8)): 12/20 ≈ 0.600
    ├── Some((5, 2)): 53/109 ≈ 0.486
      ├── Some((2, 0)): 11/17 ≈ 0.647
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 7/13 ≈ 0.538
      ├── Some((2, 3)): 7/14 ≈ 0.500
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((5, 3)): 59/117 ≈ 0.504
      ├── Some((3, 0)): 6/13 ≈ 0.462
      ├── Some((3, 1)): 12/20 ≈ 0.600
      ├── Some((3, 2)): 13/21 ≈ 0.619
      ├── Some((3, 3)): 8/15 ≈ 0.533
      ├── Some((3, 4)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 1/7 ≈ 0.143
    ├── Some((5, 4)): 22/61 ≈ 0.361
      ├── Some((4, 0)): 1/5 ≈ 0.200
      ├── Some((4, 1)): 7/11 ≈ 0.636
      ├── Some((4, 2)): 2/6 ≈ 0.333
      ├── Some((4, 3)): 2/6 ≈ 0.333
      ├── Some((4, 4)): 1/5 ≈ 0.200
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 2/6 ≈ 0.333
      ├── Some((4, 7)): 4/9 ≈ 0.444
      └── Some((4, 8)): 0/4 ≈ 0.000
    ├── Some((5, 6)): 63/123 ≈ 0.512
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 9/16 ≈ 0.562
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 10/17 ≈ 0.588
      ├── Some((6, 4)): 6/13 ≈ 0.462
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 10/17 ≈ 0.588
      ├── Some((6, 7)): 11/18 ≈ 0.611
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((5, 7)): 75/140 ≈ 0.536
      ├── Some((7, 0)): 12/19 ≈ 0.632
      ├── Some((7, 1)): 10/17 ≈ 0.588
      ├── Some((7, 2)): 2/9 ≈ 0.222
      ├── Some((7, 3)): 2/9 ≈ 0.222
      ├── Some((7, 4)): 12/19 ≈ 0.632
      ├── Some((7, 5)): 11/19 ≈ 0.579
      ├── Some((7, 6)): 6/13 ≈ 0.462
      ├── Some((7, 7)): 16/23 ≈ 0.696
      └── Some((7, 8)): 4/11 ≈ 0.364
    └── Some((5, 8)): 73/138 ≈ 0.529
      ├── Some((8, 0)): 14/21 ≈ 0.667
      ├── Some((8, 1)): 4/11 ≈ 0.364
      ├── Some((8, 2)): 4/11 ≈ 0.364
      ├── Some((8, 3)): 7/14 ≈ 0.500
      ├── Some((8, 4)): 6/13 ≈ 0.462
      ├── Some((8, 5)): 2/9 ≈ 0.222
      ├── Some((8, 6)): 17/24 ≈ 0.708
      ├── Some((8, 7)): 10/18 ≈ 0.556
      └── Some((8, 8)): 9/16 ≈ 0.562
  ├── Some((5, 6)): 811/1514 ≈ 0.536
    ├── Some((6, 0)): 46/103 ≈ 0.447
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 13/19 ≈ 0.684
      ├── Some((0, 7)): 3/9 ≈ 0.333
      └── Some((0, 8)): 5/12 ≈ 0.417
    ├── Some((6, 1)): 81/155 ≈ 0.523
      ├── Some((1, 0)): 7/15 ≈ 0.467
      ├── Some((1, 1)): 9/17 ≈ 0.529
      ├── Some((1, 2)): 17/25 ≈ 0.680
      ├── Some((1, 3)): 18/26 ≈ 0.692
      ├── Some((1, 4)): 3/11 ≈ 0.273
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 4/12 ≈ 0.333
      ├── Some((1, 7)): 3/11 ≈ 0.273
      └── Some((1, 8)): 7/15 ≈ 0.467
    ├── Some((6, 2)): 94/174 ≈ 0.540
      ├── Some((2, 0)): 14/23 ≈ 0.609
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 16/25 ≈ 0.640
      ├── Some((2, 3)): 9/18 ≈ 0.500
      ├── Some((2, 4)): 11/20 ≈ 0.550
      ├── Some((2, 5)): 6/15 ≈ 0.400
      ├── Some((2, 6)): 14/23 ≈ 0.609
      ├── Some((2, 7)): 5/13 ≈ 0.385
      └── Some((2, 8)): 10/19 ≈ 0.526
    ├── Some((6, 3)): 90/169 ≈ 0.533
      ├── Some((3, 0)): 12/22 ≈ 0.545
      ├── Some((3, 1)): 12/22 ≈ 0.545
      ├── Some((3, 2)): 10/20 ≈ 0.500
      ├── Some((3, 3)): 7/16 ≈ 0.438
      ├── Some((3, 4)): 12/22 ≈ 0.545
      ├── Some((3, 6)): 12/22 ≈ 0.545
      ├── Some((3, 7)): 12/22 ≈ 0.545
      └── Some((3, 8)): 12/22 ≈ 0.545
    ├── Some((6, 4)): 106/192 ≈ 0.552
      ├── Some((4, 0)): 7/16 ≈ 0.438
      ├── Some((4, 1)): 24/34 ≈ 0.706
      ├── Some((4, 2)): 14/24 ≈ 0.583
      ├── Some((4, 3)): 7/16 ≈ 0.438
      ├── Some((4, 4)): 16/26 ≈ 0.615
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 8/17 ≈ 0.471
      ├── Some((4, 7)): 20/30 ≈ 0.667
      └── Some((4, 8)): 1/9 ≈ 0.111
    ├── Some((6, 5)): 130/225 ≈ 0.578
      ├── Some((5, 0)): 15/27 ≈ 0.556
      ├── Some((5, 1)): 8/19 ≈ 0.421
      ├── Some((5, 2)): 18/30 ≈ 0.600
      ├── Some((5, 3)): 13/25 ≈ 0.520
      ├── Some((5, 4)): 15/27 ≈ 0.556
      ├── Some((5, 5)): 32/45 ≈ 0.711
      ├── Some((5, 7)): 21/33 ≈ 0.636
      └── Some((5, 8)): 7/18 ≈ 0.389
    ├── Some((6, 6)): 97/179 ≈ 0.542
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 16/27 ≈ 0.593
      ├── Some((6, 2)): 4/13 ≈ 0.308
      ├── Some((6, 3)): 12/22 ≈ 0.545
      ├── Some((6, 4)): 2/10 ≈ 0.200
      ├── Some((6, 5)): 18/29 ≈ 0.621
      ├── Some((6, 7)): 17/28 ≈ 0.607
      └── Some((6, 8)): 21/32 ≈ 0.656
    ├── Some((6, 7)): 74/145 ≈ 0.510
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 10/18 ≈ 0.556
      ├── Some((7, 3)): 11/19 ≈ 0.579
      ├── Some((7, 4)): 6/14 ≈ 0.429
      ├── Some((7, 5)): 6/14 ≈ 0.429
      ├── Some((7, 6)): 14/22 ≈ 0.636
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 4/12 ≈ 0.333
    └── Some((6, 8)): 92/171 ≈ 0.538
      ├── Some((8, 0)): 18/27 ≈ 0.667
      ├── Some((8, 1)): 12/21 ≈ 0.571
      ├── Some((8, 2)): 7/15 ≈ 0.467
      ├── Some((8, 3)): 8/17 ≈ 0.471
      ├── Some((8, 4)): 4/12 ≈ 0.333
      ├── Some((8, 5)): 7/16 ≈ 0.438
      ├── Some((8, 6)): 3/11 ≈ 0.273
      ├── Some((8, 7)): 15/24 ≈ 0.625
      └── Some((8, 8)): 18/27 ≈ 0.667
  ├── Some((5, 7)): 332/692 ≈ 0.480
    ├── Some((7, 0)): 37/77 ≈ 0.481
      ├── Some((0, 0)): 4/8 ≈ 0.500
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 6/10 ≈ 0.600
      ├── Some((0, 4)): 7/11 ≈ 0.636
      ├── Some((0, 5)): 3/8 ≈ 0.375
      ├── Some((0, 6)): 4/8 ≈ 0.500
      ├── Some((0, 7)): 6/10 ≈ 0.600
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((7, 1)): 28/64 ≈ 0.438
      ├── Some((1, 0)): 4/8 ≈ 0.500
      ├── Some((1, 1)): 4/8 ≈ 0.500
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 5/8 ≈ 0.625
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 3/7 ≈ 0.429
      ├── Some((1, 6)): 1/5 ≈ 0.200
      ├── Some((1, 7)): 4/8 ≈ 0.500
      └── Some((1, 8)): 2/6 ≈ 0.333
    ├── Some((7, 2)): 38/79 ≈ 0.481
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 8/12 ≈ 0.667
      ├── Some((2, 2)): 5/9 ≈ 0.556
      ├── Some((2, 3)): 5/10 ≈ 0.500
      ├── Some((2, 4)): 2/7 ≈ 0.286
      ├── Some((2, 5)): 0/4 ≈ 0.000
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 6/10 ≈ 0.600
      └── Some((2, 8)): 5/10 ≈ 0.500
    ├── Some((7, 3)): 49/94 ≈ 0.521
      ├── Some((3, 0)): 8/13 ≈ 0.615
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 5/11 ≈ 0.455
      ├── Some((3, 3)): 7/13 ≈ 0.538
      ├── Some((3, 4)): 9/14 ≈ 0.643
      ├── Some((3, 6)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 8/14 ≈ 0.571
      └── Some((3, 8)): 7/13 ≈ 0.538
    ├── Some((7, 4)): 47/91 ≈ 0.516
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 7/12 ≈ 0.583
      ├── Some((4, 3)): 11/15 ≈ 0.733
      ├── Some((4, 4)): 1/6 ≈ 0.167
      ├── Some((4, 5)): 8/12 ≈ 0.667
      ├── Some((4, 6)): 0/5 ≈ 0.000
      ├── Some((4, 7)): 8/13 ≈ 0.615
      └── Some((4, 8)): 6/11 ≈ 0.545
    ├── Some((7, 5)): 27/63 ≈ 0.429
      ├── Some((5, 0)): 6/10 ≈ 0.600
      ├── Some((5, 1)): 4/8 ≈ 0.500
      ├── Some((5, 2)): 4/8 ≈ 0.500
      ├── Some((5, 3)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 4/9 ≈ 0.444
      └── Some((5, 8)): 1/5 ≈ 0.200
    ├── Some((7, 6)): 35/74 ≈ 0.473
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 2/6 ≈ 0.333
      ├── Some((6, 2)): 3/7 ≈ 0.429
      ├── Some((6, 3)): 3/7 ≈ 0.429
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 10/14 ≈ 0.714
      ├── Some((6, 7)): 8/12 ≈ 0.667
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((7, 7)): 24/58 ≈ 0.414
      ├── Some((7, 0)): 6/10 ≈ 0.600
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 2/6 ≈ 0.333
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 4/8 ≈ 0.500
      ├── Some((7, 5)): 4/8 ≈ 0.500
      ├── Some((7, 6)): 1/5 ≈ 0.200
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((7, 8)): 47/91 ≈ 0.516
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 8/12 ≈ 0.667
      ├── Some((8, 2)): 1/6 ≈ 0.167
      ├── Some((8, 3)): 4/9 ≈ 0.444
      ├── Some((8, 4)): 7/11 ≈ 0.636
      ├── Some((8, 5)): 7/12 ≈ 0.583
      ├── Some((8, 6)): 5/10 ≈ 0.500
      ├── Some((8, 7)): 5/10 ≈ 0.500
      └── Some((8, 8)): 7/12 ≈ 0.583
  └── Some((5, 8)): 469/931 ≈ 0.504
    ├── Some((8, 0)): 90/157 ≈ 0.573
      ├── Some((0, 0)): 11/19 ≈ 0.579
      ├── Some((0, 1)): 14/21 ≈ 0.667
      ├── Some((0, 2)): 18/25 ≈ 0.720
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 4/11 ≈ 0.364
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 6)): 14/22 ≈ 0.636
      ├── Some((0, 7)): 8/16 ≈ 0.500
      └── Some((0, 8)): 5/12 ≈ 0.417
    ├── Some((8, 1)): 37/82 ≈ 0.451
      ├── Some((1, 0)): 5/10 ≈ 0.500
      ├── Some((1, 1)): 8/13 ≈ 0.615
      ├── Some((1, 2)): 4/9 ≈ 0.444
      ├── Some((1, 3)): 0/5 ≈ 0.000
      ├── Some((1, 4)): 1/6 ≈ 0.167
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 7/12 ≈ 0.583
      ├── Some((1, 7)): 9/13 ≈ 0.692
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((8, 2)): 68/126 ≈ 0.540
      ├── Some((2, 0)): 2/8 ≈ 0.250
      ├── Some((2, 1)): 10/17 ≈ 0.588
      ├── Some((2, 2)): 8/15 ≈ 0.533
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 8/15 ≈ 0.533
      ├── Some((2, 6)): 23/29 ≈ 0.793
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 5/12 ≈ 0.417
    ├── Some((8, 3)): 53/105 ≈ 0.505
      ├── Some((3, 0)): 8/15 ≈ 0.533
      ├── Some((3, 1)): 6/12 ≈ 0.500
      ├── Some((3, 2)): 10/16 ≈ 0.625
      ├── Some((3, 3)): 1/7 ≈ 0.143
      ├── Some((3, 4)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 7/14 ≈ 0.500
      ├── Some((3, 7)): 9/15 ≈ 0.600
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((8, 4)): 36/80 ≈ 0.450
      ├── Some((4, 0)): 0/5 ≈ 0.000
      ├── Some((4, 1)): 10/14 ≈ 0.714
      ├── Some((4, 2)): 4/9 ≈ 0.444
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 5/10 ≈ 0.500
      ├── Some((4, 5)): 8/13 ≈ 0.615
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((8, 5)): 40/86 ≈ 0.465
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 8/13 ≈ 0.615
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 7/13 ≈ 0.538
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 6/12 ≈ 0.500
      └── Some((5, 7)): 5/11 ≈ 0.455
    ├── Some((8, 6)): 38/83 ≈ 0.458
      ├── Some((6, 0)): 8/13 ≈ 0.615
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 4/9 ≈ 0.444
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 5/10 ≈ 0.500
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 5/10 ≈ 0.500
    ├── Some((8, 7)): 46/95 ≈ 0.484
      ├── Some((7, 0)): 6/11 ≈ 0.545
      ├── Some((7, 1)): 7/12 ≈ 0.583
      ├── Some((7, 2)): 6/11 ≈ 0.545
      ├── Some((7, 3)): 6/11 ≈ 0.545
      ├── Some((7, 4)): 5/11 ≈ 0.455
      ├── Some((7, 5)): 0/5 ≈ 0.000
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 8/13 ≈ 0.615
    └── Some((8, 8)): 61/116 ≈ 0.526
      ├── Some((8, 0)): 14/21 ≈ 0.667
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 10/17 ≈ 0.588
      ├── Some((8, 3)): 5/12 ≈ 0.417
      ├── Some((8, 4)): 6/13 ≈ 0.462
      ├── Some((8, 5)): 2/8 ≈ 0.250
      ├── Some((8, 6)): 3/10 ≈ 0.300
      └── Some((8, 7)): 12/19 ≈ 0.632
├── Some((3, 6)): 4607/9017 ≈ 0.511
  ├── Some((6, 0)): 524/1025 ≈ 0.511
    ├── Some((0, 0)): 46/97 ≈ 0.474
      ├── Some((0, 1)): 1/7 ≈ 0.143
      ├── Some((0, 2)): 11/17 ≈ 0.647
      ├── Some((0, 3)): 8/15 ≈ 0.533
      ├── Some((0, 4)): 9/16 ≈ 0.562
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 0/6 ≈ 0.000
      └── Some((0, 8)): 10/16 ≈ 0.625
    ├── Some((0, 1)): 79/144 ≈ 0.549
      ├── Some((1, 0)): 15/22 ≈ 0.682
      ├── Some((1, 1)): 7/14 ≈ 0.500
      ├── Some((1, 2)): 2/9 ≈ 0.222
      ├── Some((1, 3)): 4/11 ≈ 0.364
      ├── Some((1, 4)): 9/17 ≈ 0.529
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 7/14 ≈ 0.500
      ├── Some((1, 7)): 14/21 ≈ 0.667
      └── Some((1, 8)): 15/22 ≈ 0.682
    ├── Some((0, 2)): 44/94 ≈ 0.468
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 6/11 ≈ 0.545
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 1/6 ≈ 0.167
      ├── Some((2, 6)): 5/11 ≈ 0.455
      ├── Some((2, 7)): 12/17 ≈ 0.706
      └── Some((2, 8)): 4/10 ≈ 0.400
    ├── Some((0, 3)): 81/147 ≈ 0.551
      ├── Some((3, 0)): 6/14 ≈ 0.429
      ├── Some((3, 1)): 20/29 ≈ 0.690
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 10/18 ≈ 0.556
      ├── Some((3, 4)): 7/15 ≈ 0.467
      ├── Some((3, 5)): 10/18 ≈ 0.556
      ├── Some((3, 7)): 11/20 ≈ 0.550
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((0, 4)): 67/127 ≈ 0.528
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 7/14 ≈ 0.500
      ├── Some((4, 2)): 2/8 ≈ 0.250
      ├── Some((4, 3)): 3/9 ≈ 0.333
      ├── Some((4, 4)): 14/20 ≈ 0.700
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 10/17 ≈ 0.588
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((0, 5)): 74/137 ≈ 0.540
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 10/17 ≈ 0.588
      ├── Some((5, 2)): 5/12 ≈ 0.417
      ├── Some((5, 3)): 8/15 ≈ 0.533
      ├── Some((5, 4)): 16/22 ≈ 0.727
      ├── Some((5, 5)): 9/16 ≈ 0.562
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 7/14 ≈ 0.500
      └── Some((5, 8)): 5/12 ≈ 0.417
    ├── Some((0, 6)): 24/63 ≈ 0.381
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 5/10 ≈ 0.500
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 6/11 ≈ 0.545
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((0, 7)): 31/74 ≈ 0.419
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 6/10 ≈ 0.600
      ├── Some((7, 3)): 1/6 ≈ 0.167
      ├── Some((7, 4)): 5/10 ≈ 0.500
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 4/9 ≈ 0.444
      ├── Some((7, 7)): 4/9 ≈ 0.444
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((0, 8)): 77/141 ≈ 0.546
      ├── Some((8, 0)): 3/10 ≈ 0.300
      ├── Some((8, 1)): 1/8 ≈ 0.125
      ├── Some((8, 2)): 9/16 ≈ 0.562
      ├── Some((8, 3)): 12/19 ≈ 0.632
      ├── Some((8, 4)): 13/20 ≈ 0.650
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 14/21 ≈ 0.667
      └── Some((8, 8)): 11/19 ≈ 0.579
  ├── Some((6, 1)): 923/1701 ≈ 0.543
    ├── Some((1, 0)): 78/153 ≈ 0.510
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 5/13 ≈ 0.385
      ├── Some((0, 2)): 11/20 ≈ 0.550
      ├── Some((0, 3)): 11/20 ≈ 0.550
      ├── Some((0, 4)): 7/15 ≈ 0.467
      ├── Some((0, 5)): 6/14 ≈ 0.429
      ├── Some((0, 6)): 12/21 ≈ 0.571
      ├── Some((0, 7)): 16/25 ≈ 0.640
      └── Some((0, 8)): 2/9 ≈ 0.222
    ├── Some((1, 1)): 140/243 ≈ 0.576
      ├── Some((1, 0)): 25/39 ≈ 0.641
      ├── Some((1, 2)): 23/37 ≈ 0.622
      ├── Some((1, 3)): 12/24 ≈ 0.500
      ├── Some((1, 4)): 9/21 ≈ 0.429
      ├── Some((1, 5)): 27/41 ≈ 0.659
      ├── Some((1, 6)): 4/15 ≈ 0.267
      ├── Some((1, 7)): 18/31 ≈ 0.581
      └── Some((1, 8)): 21/34 ≈ 0.618
    ├── Some((1, 2)): 89/170 ≈ 0.524
      ├── Some((2, 0)): 13/22 ≈ 0.591
      ├── Some((2, 1)): 15/24 ≈ 0.625
      ├── Some((2, 2)): 5/13 ≈ 0.385
      ├── Some((2, 3)): 5/14 ≈ 0.357
      ├── Some((2, 4)): 5/14 ≈ 0.357
      ├── Some((2, 5)): 8/17 ≈ 0.471
      ├── Some((2, 6)): 13/22 ≈ 0.591
      ├── Some((2, 7)): 14/23 ≈ 0.609
      └── Some((2, 8)): 11/20 ≈ 0.550
    ├── Some((1, 3)): 128/226 ≈ 0.566
      ├── Some((3, 0)): 18/30 ≈ 0.600
      ├── Some((3, 1)): 20/33 ≈ 0.606
      ├── Some((3, 2)): 13/25 ≈ 0.520
      ├── Some((3, 3)): 13/25 ≈ 0.520
      ├── Some((3, 4)): 21/34 ≈ 0.618
      ├── Some((3, 5)): 10/21 ≈ 0.476
      ├── Some((3, 7)): 19/32 ≈ 0.594
      └── Some((3, 8)): 13/25 ≈ 0.520
    ├── Some((1, 4)): 99/184 ≈ 0.538
      ├── Some((4, 0)): 18/28 ≈ 0.643
      ├── Some((4, 1)): 10/20 ≈ 0.500
      ├── Some((4, 2)): 3/11 ≈ 0.273
      ├── Some((4, 3)): 15/25 ≈ 0.600
      ├── Some((4, 4)): 5/14 ≈ 0.357
      ├── Some((4, 5)): 18/28 ≈ 0.643
      ├── Some((4, 6)): 3/11 ≈ 0.273
      ├── Some((4, 7)): 13/23 ≈ 0.565
      └── Some((4, 8)): 13/23 ≈ 0.565
    ├── Some((1, 5)): 60/126 ≈ 0.476
      ├── Some((5, 0)): 3/10 ≈ 0.300
      ├── Some((5, 1)): 1/8 ≈ 0.125
      ├── Some((5, 2)): 7/14 ≈ 0.500
      ├── Some((5, 3)): 3/10 ≈ 0.300
      ├── Some((5, 4)): 10/18 ≈ 0.556
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 6)): 10/18 ≈ 0.556
      ├── Some((5, 7)): 5/12 ≈ 0.417
      └── Some((5, 8)): 14/22 ≈ 0.636
    ├── Some((1, 6)): 105/193 ≈ 0.544
      ├── Some((6, 0)): 8/18 ≈ 0.444
      ├── Some((6, 2)): 11/22 ≈ 0.500
      ├── Some((6, 3)): 11/22 ≈ 0.500
      ├── Some((6, 4)): 29/41 ≈ 0.707
      ├── Some((6, 5)): 17/29 ≈ 0.586
      ├── Some((6, 6)): 5/15 ≈ 0.333
      ├── Some((6, 7)): 6/16 ≈ 0.375
      └── Some((6, 8)): 17/29 ≈ 0.586
    ├── Some((1, 7)): 100/185 ≈ 0.541
      ├── Some((7, 0)): 3/11 ≈ 0.273
      ├── Some((7, 1)): 13/23 ≈ 0.565
      ├── Some((7, 2)): 11/20 ≈ 0.550
      ├── Some((7, 3)): 19/29 ≈ 0.655
      ├── Some((7, 4)): 14/24 ≈ 0.583
      ├── Some((7, 5)): 12/22 ≈ 0.545
      ├── Some((7, 6)): 7/16 ≈ 0.438
      ├── Some((7, 7)): 8/17 ≈ 0.471
      └── Some((7, 8)): 12/22 ≈ 0.545
    └── Some((1, 8)): 124/220 ≈ 0.564
      ├── Some((8, 0)): 14/25 ≈ 0.560
      ├── Some((8, 1)): 14/25 ≈ 0.560
      ├── Some((8, 2)): 21/32 ≈ 0.656
      ├── Some((8, 3)): 10/20 ≈ 0.500
      ├── Some((8, 4)): 7/17 ≈ 0.412
      ├── Some((8, 5)): 23/34 ≈ 0.676
      ├── Some((8, 6)): 5/15 ≈ 0.333
      ├── Some((8, 7)): 11/22 ≈ 0.500
      └── Some((8, 8)): 18/29 ≈ 0.621
  ├── Some((6, 2)): 500/984 ≈ 0.508
    ├── Some((2, 0)): 49/101 ≈ 0.485
      ├── Some((0, 0)): 8/14 ≈ 0.571
      ├── Some((0, 1)): 1/6 ≈ 0.167
      ├── Some((0, 2)): 0/5 ≈ 0.000
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 9/15 ≈ 0.600
      ├── Some((0, 6)): 7/13 ≈ 0.538
      ├── Some((0, 7)): 11/16 ≈ 0.688
      └── Some((0, 8)): 6/12 ≈ 0.500
    ├── Some((2, 1)): 45/95 ≈ 0.474
      ├── Some((1, 0)): 8/14 ≈ 0.571
      ├── Some((1, 1)): 0/5 ≈ 0.000
      ├── Some((1, 2)): 7/13 ≈ 0.538
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 10/15 ≈ 0.667
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 6/12 ≈ 0.500
    ├── Some((2, 2)): 105/179 ≈ 0.587
      ├── Some((2, 0)): 9/18 ≈ 0.500
      ├── Some((2, 1)): 30/40 ≈ 0.750
      ├── Some((2, 3)): 2/10 ≈ 0.200
      ├── Some((2, 4)): 24/34 ≈ 0.706
      ├── Some((2, 5)): 7/16 ≈ 0.438
      ├── Some((2, 6)): 5/14 ≈ 0.357
      ├── Some((2, 7)): 10/19 ≈ 0.526
      └── Some((2, 8)): 17/27 ≈ 0.630
    ├── Some((2, 3)): 24/63 ≈ 0.381
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 1)): 6/11 ≈ 0.545
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 5/10 ≈ 0.500
      ├── Some((3, 7)): 1/6 ≈ 0.167
      └── Some((3, 8)): 5/10 ≈ 0.500
    ├── Some((2, 4)): 72/133 ≈ 0.541
      ├── Some((4, 0)): 1/7 ≈ 0.143
      ├── Some((4, 1)): 13/20 ≈ 0.650
      ├── Some((4, 2)): 9/16 ≈ 0.562
      ├── Some((4, 3)): 11/18 ≈ 0.611
      ├── Some((4, 4)): 11/18 ≈ 0.611
      ├── Some((4, 5)): 3/10 ≈ 0.300
      ├── Some((4, 6)): 4/11 ≈ 0.364
      ├── Some((4, 7)): 2/8 ≈ 0.250
      └── Some((4, 8)): 17/24 ≈ 0.708
    ├── Some((2, 5)): 38/84 ≈ 0.452
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 1/6 ≈ 0.167
      ├── Some((5, 2)): 1/6 ≈ 0.167
      ├── Some((5, 3)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 11/16 ≈ 0.688
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 3/8 ≈ 0.375
      ├── Some((5, 7)): 10/15 ≈ 0.667
      └── Some((5, 8)): 0/5 ≈ 0.000
    ├── Some((2, 6)): 32/75 ≈ 0.427
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 4/10 ≈ 0.400
      ├── Some((6, 7)): 11/16 ≈ 0.688
      └── Some((6, 8)): 4/10 ≈ 0.400
    ├── Some((2, 7)): 54/108 ≈ 0.500
      ├── Some((7, 0)): 8/14 ≈ 0.571
      ├── Some((7, 1)): 9/15 ≈ 0.600
      ├── Some((7, 2)): 1/6 ≈ 0.167
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 5/11 ≈ 0.455
      ├── Some((7, 5)): 7/13 ≈ 0.538
      ├── Some((7, 6)): 8/14 ≈ 0.571
      ├── Some((7, 7)): 10/16 ≈ 0.625
      └── Some((7, 8)): 1/7 ≈ 0.143
    └── Some((2, 8)): 80/145 ≈ 0.552
      ├── Some((8, 0)): 4/11 ≈ 0.364
      ├── Some((8, 1)): 11/19 ≈ 0.579
      ├── Some((8, 2)): 5/12 ≈ 0.417
      ├── Some((8, 3)): 14/21 ≈ 0.667
      ├── Some((8, 4)): 12/19 ≈ 0.632
      ├── Some((8, 5)): 13/20 ≈ 0.650
      ├── Some((8, 6)): 3/10 ≈ 0.300
      ├── Some((8, 7)): 3/10 ≈ 0.300
      └── Some((8, 8)): 15/22 ≈ 0.682
  ├── Some((6, 3)): 440/880 ≈ 0.500
    ├── Some((3, 0)): 66/126 ≈ 0.524
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 3/9 ≈ 0.333
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 13/19 ≈ 0.684
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 9/16 ≈ 0.562
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 13/20 ≈ 0.650
    ├── Some((3, 1)): 43/92 ≈ 0.467
      ├── Some((1, 0)): 8/13 ≈ 0.615
      ├── Some((1, 1)): 4/9 ≈ 0.444
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 1/6 ≈ 0.167
      ├── Some((1, 5)): 4/10 ≈ 0.400
      ├── Some((1, 6)): 7/12 ≈ 0.583
      ├── Some((1, 7)): 7/12 ≈ 0.583
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((3, 2)): 59/116 ≈ 0.509
      ├── Some((2, 0)): 12/18 ≈ 0.667
      ├── Some((2, 1)): 9/16 ≈ 0.562
      ├── Some((2, 2)): 10/16 ≈ 0.625
      ├── Some((2, 3)): 8/15 ≈ 0.533
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 2/8 ≈ 0.250
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 6/12 ≈ 0.500
    ├── Some((3, 3)): 82/149 ≈ 0.550
      ├── Some((3, 0)): 17/27 ≈ 0.630
      ├── Some((3, 1)): 18/28 ≈ 0.643
      ├── Some((3, 2)): 12/22 ≈ 0.545
      ├── Some((3, 4)): 9/18 ≈ 0.500
      ├── Some((3, 5)): 15/25 ≈ 0.600
      ├── Some((3, 7)): 7/16 ≈ 0.438
      └── Some((3, 8)): 4/12 ≈ 0.333
    ├── Some((3, 4)): 56/112 ≈ 0.500
      ├── Some((4, 0)): 14/20 ≈ 0.700
      ├── Some((4, 1)): 10/16 ≈ 0.625
      ├── Some((4, 2)): 0/6 ≈ 0.000
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 2/8 ≈ 0.250
      ├── Some((4, 6)): 10/16 ≈ 0.625
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((3, 5)): 38/85 ≈ 0.447
      ├── Some((5, 0)): 7/12 ≈ 0.583
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 3/8 ≈ 0.375
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 6/12 ≈ 0.500
      ├── Some((5, 6)): 4/9 ≈ 0.444
      ├── Some((5, 7)): 7/12 ≈ 0.583
      └── Some((5, 8)): 1/6 ≈ 0.167
    ├── Some((3, 7)): 52/106 ≈ 0.491
      ├── Some((7, 0)): 9/15 ≈ 0.600
      ├── Some((7, 1)): 7/13 ≈ 0.538
      ├── Some((7, 2)): 4/10 ≈ 0.400
      ├── Some((7, 3)): 0/6 ≈ 0.000
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 9/15 ≈ 0.600
      ├── Some((7, 7)): 7/13 ≈ 0.538
      └── Some((7, 8)): 3/9 ≈ 0.333
    └── Some((3, 8)): 43/93 ≈ 0.462
      ├── Some((8, 0)): 7/12 ≈ 0.583
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 6/12 ≈ 0.500
      ├── Some((8, 5)): 8/13 ≈ 0.615
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 1/6 ≈ 0.167
  ├── Some((6, 4)): 433/868 ≈ 0.499
    ├── Some((4, 0)): 21/56 ≈ 0.375
      ├── Some((0, 0)): 8/11 ≈ 0.727
      ├── Some((0, 1)): 3/7 ≈ 0.429
      ├── Some((0, 2)): 3/7 ≈ 0.429
      ├── Some((0, 3)): 0/4 ≈ 0.000
      ├── Some((0, 4)): 0/4 ≈ 0.000
      ├── Some((0, 5)): 0/4 ≈ 0.000
      ├── Some((0, 6)): 4/7 ≈ 0.571
      ├── Some((0, 7)): 1/5 ≈ 0.200
      └── Some((0, 8)): 2/6 ≈ 0.333
    ├── Some((4, 1)): 68/125 ≈ 0.544
      ├── Some((1, 0)): 8/15 ≈ 0.533
      ├── Some((1, 1)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 8/15 ≈ 0.533
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 9/15 ≈ 0.600
      ├── Some((1, 5)): 6/12 ≈ 0.500
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 11/17 ≈ 0.647
      └── Some((1, 8)): 10/16 ≈ 0.625
    ├── Some((4, 2)): 65/121 ≈ 0.537
      ├── Some((2, 0)): 11/17 ≈ 0.647
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 17/23 ≈ 0.739
      ├── Some((2, 3)): 2/8 ≈ 0.250
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 11/17 ≈ 0.647
    ├── Some((4, 3)): 65/121 ≈ 0.537
      ├── Some((3, 0)): 10/17 ≈ 0.588
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 12/19 ≈ 0.632
      ├── Some((3, 3)): 14/20 ≈ 0.700
      ├── Some((3, 4)): 4/11 ≈ 0.364
      ├── Some((3, 5)): 5/12 ≈ 0.417
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((4, 4)): 22/58 ≈ 0.379
      ├── Some((4, 0)): 5/9 ≈ 0.556
      ├── Some((4, 1)): 1/5 ≈ 0.200
      ├── Some((4, 2)): 3/8 ≈ 0.375
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 1/5 ≈ 0.200
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((4, 5)): 51/101 ≈ 0.505
      ├── Some((5, 0)): 8/13 ≈ 0.615
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 7/13 ≈ 0.538
      ├── Some((5, 3)): 8/13 ≈ 0.615
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 5/11 ≈ 0.455
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 8/13 ≈ 0.615
      └── Some((5, 8)): 8/14 ≈ 0.571
    ├── Some((4, 6)): 37/81 ≈ 0.457
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 2/7 ≈ 0.286
      └── Some((6, 8)): 8/13 ≈ 0.615
    ├── Some((4, 7)): 45/92 ≈ 0.489
      ├── Some((7, 0)): 9/14 ≈ 0.643
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 3)): 13/18 ≈ 0.722
      ├── Some((7, 4)): 6/11 ≈ 0.545
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 5/10 ≈ 0.500
      ├── Some((7, 7)): 0/5 ≈ 0.000
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((4, 8)): 59/112 ≈ 0.527
      ├── Some((8, 0)): 11/17 ≈ 0.647
      ├── Some((8, 1)): 3/9 ≈ 0.333
      ├── Some((8, 2)): 8/14 ≈ 0.571
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 6/12 ≈ 0.500
      ├── Some((8, 5)): 2/8 ≈ 0.250
      ├── Some((8, 6)): 6/12 ≈ 0.500
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 12/17 ≈ 0.706
  ├── Some((6, 5)): 282/603 ≈ 0.468
    ├── Some((5, 0)): 47/89 ≈ 0.528
      ├── Some((0, 0)): 9/13 ≈ 0.692
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 5/9 ≈ 0.556
      ├── Some((0, 3)): 5/9 ≈ 0.556
      ├── Some((0, 4)): 4/9 ≈ 0.444
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 5/10 ≈ 0.500
      ├── Some((0, 7)): 8/12 ≈ 0.667
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((5, 1)): 21/52 ≈ 0.404
      ├── Some((1, 0)): 2/5 ≈ 0.400
      ├── Some((1, 1)): 2/5 ≈ 0.400
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 4/7 ≈ 0.571
      ├── Some((1, 4)): 4/7 ≈ 0.571
      ├── Some((1, 5)): 3/6 ≈ 0.500
      ├── Some((1, 6)): 2/6 ≈ 0.333
      ├── Some((1, 7)): 1/5 ≈ 0.200
      └── Some((1, 8)): 1/5 ≈ 0.200
    ├── Some((5, 2)): 37/75 ≈ 0.493
      ├── Some((2, 0)): 5/9 ≈ 0.556
      ├── Some((2, 1)): 4/8 ≈ 0.500
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 5/9 ≈ 0.556
      ├── Some((2, 4)): 4/8 ≈ 0.500
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 5/9 ≈ 0.556
      ├── Some((2, 7)): 4/8 ≈ 0.500
      └── Some((2, 8)): 4/8 ≈ 0.500
    ├── Some((5, 3)): 20/51 ≈ 0.392
      ├── Some((3, 0)): 5/8 ≈ 0.625
      ├── Some((3, 1)): 0/4 ≈ 0.000
      ├── Some((3, 2)): 3/7 ≈ 0.429
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 4)): 2/6 ≈ 0.333
      ├── Some((3, 5)): 2/6 ≈ 0.333
      ├── Some((3, 7)): 5/9 ≈ 0.556
      └── Some((3, 8)): 2/6 ≈ 0.333
    ├── Some((5, 4)): 27/61 ≈ 0.443
      ├── Some((4, 0)): 4/7 ≈ 0.571
      ├── Some((4, 1)): 1/5 ≈ 0.200
      ├── Some((4, 2)): 4/7 ≈ 0.571
      ├── Some((4, 3)): 3/7 ≈ 0.429
      ├── Some((4, 4)): 4/8 ≈ 0.500
      ├── Some((4, 5)): 4/8 ≈ 0.500
      ├── Some((4, 6)): 2/6 ≈ 0.333
      ├── Some((4, 7)): 0/4 ≈ 0.000
      └── Some((4, 8)): 5/8 ≈ 0.625
    ├── Some((5, 5)): 23/55 ≈ 0.418
      ├── Some((5, 0)): 0/4 ≈ 0.000
      ├── Some((5, 1)): 2/6 ≈ 0.333
      ├── Some((5, 2)): 6/10 ≈ 0.600
      ├── Some((5, 3)): 4/8 ≈ 0.500
      ├── Some((5, 4)): 3/7 ≈ 0.429
      ├── Some((5, 6)): 1/5 ≈ 0.200
      ├── Some((5, 7)): 1/5 ≈ 0.200
      └── Some((5, 8)): 5/9 ≈ 0.556
    ├── Some((5, 6)): 33/70 ≈ 0.471
      ├── Some((6, 0)): 7/11 ≈ 0.636
      ├── Some((6, 1)): 4/8 ≈ 0.500
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 5/9 ≈ 0.556
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 4/9 ≈ 0.444
    ├── Some((5, 7)): 20/51 ≈ 0.392
      ├── Some((7, 0)): 2/5 ≈ 0.400
      ├── Some((7, 1)): 3/6 ≈ 0.500
      ├── Some((7, 2)): 3/6 ≈ 0.500
      ├── Some((7, 3)): 1/5 ≈ 0.200
      ├── Some((7, 4)): 2/5 ≈ 0.400
      ├── Some((7, 5)): 2/5 ≈ 0.400
      ├── Some((7, 6)): 2/6 ≈ 0.333
      ├── Some((7, 7)): 2/6 ≈ 0.333
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((5, 8)): 54/98 ≈ 0.551
      ├── Some((8, 0)): 7/12 ≈ 0.583
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 6/11 ≈ 0.545
      ├── Some((8, 3)): 12/16 ≈ 0.750
      ├── Some((8, 4)): 5/10 ≈ 0.500
      ├── Some((8, 5)): 8/13 ≈ 0.615
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 4/9 ≈ 0.444
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((6, 6)): 683/1297 ≈ 0.527
    ├── Some((6, 0)): 47/106 ≈ 0.443
      ├── Some((0, 0)): 13/19 ≈ 0.684
      ├── Some((0, 1)): 7/14 ≈ 0.500
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 3/9 ≈ 0.333
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 6/13 ≈ 0.462
      ├── Some((0, 7)): 2/8 ≈ 0.250
      └── Some((0, 8)): 2/8 ≈ 0.250
    ├── Some((6, 1)): 110/199 ≈ 0.553
      ├── Some((1, 0)): 16/26 ≈ 0.615
      ├── Some((1, 1)): 2/10 ≈ 0.200
      ├── Some((1, 2)): 23/33 ≈ 0.697
      ├── Some((1, 3)): 7/17 ≈ 0.412
      ├── Some((1, 4)): 16/26 ≈ 0.615
      ├── Some((1, 5)): 11/21 ≈ 0.524
      ├── Some((1, 6)): 17/27 ≈ 0.630
      ├── Some((1, 7)): 8/18 ≈ 0.444
      └── Some((1, 8)): 10/20 ≈ 0.500
    ├── Some((6, 2)): 54/116 ≈ 0.466
      ├── Some((2, 0)): 4/11 ≈ 0.364
      ├── Some((2, 1)): 8/15 ≈ 0.533
      ├── Some((2, 2)): 4/11 ≈ 0.364
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 2/8 ≈ 0.250
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 11/18 ≈ 0.611
      ├── Some((2, 7)): 4/11 ≈ 0.364
      └── Some((2, 8)): 9/16 ≈ 0.562
    ├── Some((6, 3)): 43/99 ≈ 0.434
      ├── Some((3, 0)): 6/13 ≈ 0.462
      ├── Some((3, 1)): 2/9 ≈ 0.222
      ├── Some((3, 2)): 5/12 ≈ 0.417
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 4/11 ≈ 0.364
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 7/14 ≈ 0.500
    ├── Some((6, 4)): 177/294 ≈ 0.602
      ├── Some((4, 0)): 18/31 ≈ 0.581
      ├── Some((4, 1)): 32/46 ≈ 0.696
      ├── Some((4, 2)): 13/25 ≈ 0.520
      ├── Some((4, 3)): 17/30 ≈ 0.567
      ├── Some((4, 4)): 18/31 ≈ 0.581
      ├── Some((4, 5)): 19/32 ≈ 0.594
      ├── Some((4, 6)): 19/32 ≈ 0.594
      ├── Some((4, 7)): 27/41 ≈ 0.659
      └── Some((4, 8)): 13/25 ≈ 0.520
    ├── Some((6, 5)): 83/160 ≈ 0.519
      ├── Some((5, 0)): 19/28 ≈ 0.679
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 1/8 ≈ 0.125
      ├── Some((5, 3)): 20/29 ≈ 0.690
      ├── Some((5, 4)): 6/15 ≈ 0.400
      ├── Some((5, 5)): 11/20 ≈ 0.550
      ├── Some((5, 6)): 8/17 ≈ 0.471
      ├── Some((5, 7)): 9/18 ≈ 0.500
      └── Some((5, 8)): 4/12 ≈ 0.333
    ├── Some((6, 7)): 49/109 ≈ 0.450
      ├── Some((7, 0)): 1/7 ≈ 0.143
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 3/9 ≈ 0.333
      ├── Some((7, 4)): 2/8 ≈ 0.250
      ├── Some((7, 5)): 9/16 ≈ 0.562
      ├── Some((7, 6)): 4/11 ≈ 0.364
      ├── Some((7, 7)): 11/18 ≈ 0.611
      └── Some((7, 8)): 7/14 ≈ 0.500
    └── Some((6, 8)): 120/213 ≈ 0.563
      ├── Some((8, 0)): 13/23 ≈ 0.565
      ├── Some((8, 1)): 20/31 ≈ 0.645
      ├── Some((8, 2)): 8/18 ≈ 0.444
      ├── Some((8, 3)): 12/22 ≈ 0.545
      ├── Some((8, 4)): 10/20 ≈ 0.500
      ├── Some((8, 5)): 17/28 ≈ 0.607
      ├── Some((8, 6)): 13/23 ≈ 0.565
      ├── Some((8, 7)): 12/22 ≈ 0.545
      └── Some((8, 8)): 15/25 ≈ 0.600
  ├── Some((6, 7)): 425/854 ≈ 0.498
    ├── Some((7, 0)): 48/97 ≈ 0.495
      ├── Some((0, 0)): 8/13 ≈ 0.615
      ├── Some((0, 1)): 6/11 ≈ 0.545
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 4/9 ≈ 0.444
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 7/12 ≈ 0.583
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((7, 1)): 54/105 ≈ 0.514
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 4/10 ≈ 0.400
      ├── Some((1, 2)): 2/8 ≈ 0.250
      ├── Some((1, 3)): 3/9 ≈ 0.333
      ├── Some((1, 4)): 11/16 ≈ 0.688
      ├── Some((1, 5)): 8/14 ≈ 0.571
      ├── Some((1, 6)): 10/15 ≈ 0.667
      ├── Some((1, 7)): 8/14 ≈ 0.571
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((7, 2)): 94/160 ≈ 0.587
      ├── Some((2, 0)): 11/19 ≈ 0.579
      ├── Some((2, 1)): 14/21 ≈ 0.667
      ├── Some((2, 2)): 14/22 ≈ 0.636
      ├── Some((2, 3)): 19/26 ≈ 0.731
      ├── Some((2, 4)): 4/11 ≈ 0.364
      ├── Some((2, 5)): 7/14 ≈ 0.500
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 12/20 ≈ 0.600
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((7, 3)): 44/91 ≈ 0.484
      ├── Some((3, 0)): 6/12 ≈ 0.500
      ├── Some((3, 1)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 6/12 ≈ 0.500
      ├── Some((3, 4)): 7/12 ≈ 0.583
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 6/12 ≈ 0.500
    ├── Some((7, 4)): 50/100 ≈ 0.500
      ├── Some((4, 0)): 1/6 ≈ 0.167
      ├── Some((4, 1)): 9/14 ≈ 0.643
      ├── Some((4, 2)): 2/7 ≈ 0.286
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 9/14 ≈ 0.643
      ├── Some((4, 5)): 9/15 ≈ 0.600
      ├── Some((4, 6)): 0/5 ≈ 0.000
      ├── Some((4, 7)): 9/15 ≈ 0.600
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((7, 5)): 22/58 ≈ 0.379
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 2/6 ≈ 0.333
      ├── Some((5, 2)): 1/5 ≈ 0.200
      ├── Some((5, 3)): 3/7 ≈ 0.429
      ├── Some((5, 4)): 4/8 ≈ 0.500
      ├── Some((5, 5)): 2/6 ≈ 0.333
      ├── Some((5, 6)): 2/6 ≈ 0.333
      ├── Some((5, 7)): 0/4 ≈ 0.000
      └── Some((5, 8)): 7/10 ≈ 0.700
    ├── Some((7, 6)): 52/102 ≈ 0.510
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 8/14 ≈ 0.571
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 10/16 ≈ 0.625
      ├── Some((6, 5)): 8/15 ≈ 0.533
      ├── Some((6, 6)): 11/17 ≈ 0.647
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((7, 7)): 36/79 ≈ 0.456
      ├── Some((7, 0)): 6/12 ≈ 0.500
      ├── Some((7, 1)): 7/12 ≈ 0.583
      ├── Some((7, 2)): 7/12 ≈ 0.583
      ├── Some((7, 3)): 7/13 ≈ 0.538
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 0/5 ≈ 0.000
      ├── Some((7, 6)): 3/8 ≈ 0.375
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((7, 8)): 24/61 ≈ 0.393
      ├── Some((8, 0)): 1/5 ≈ 0.200
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 4/8 ≈ 0.500
      ├── Some((8, 3)): 0/4 ≈ 0.000
      ├── Some((8, 4)): 4/8 ≈ 0.500
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 4/8 ≈ 0.500
      ├── Some((8, 7)): 6/10 ≈ 0.600
      └── Some((8, 8)): 1/5 ≈ 0.200
  └── Some((6, 8)): 396/804 ≈ 0.493
    ├── Some((8, 0)): 52/101 ≈ 0.515
      ├── Some((0, 0)): 13/18 ≈ 0.722
      ├── Some((0, 1)): 3/8 ≈ 0.375
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 7/12 ≈ 0.583
      ├── Some((0, 6)): 6/11 ≈ 0.545
      ├── Some((0, 7)): 6/12 ≈ 0.500
      └── Some((0, 8)): 7/12 ≈ 0.583
    ├── Some((8, 1)): 27/65 ≈ 0.415
      ├── Some((1, 0)): 1/5 ≈ 0.200
      ├── Some((1, 1)): 0/4 ≈ 0.000
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 6/10 ≈ 0.600
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 6/10 ≈ 0.600
      ├── Some((1, 6)): 4/8 ≈ 0.500
      ├── Some((1, 7)): 4/8 ≈ 0.500
      └── Some((1, 8)): 2/6 ≈ 0.333
    ├── Some((8, 2)): 43/88 ≈ 0.489
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 0/5 ≈ 0.000
      ├── Some((2, 2)): 4/9 ≈ 0.444
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 7/12 ≈ 0.583
      ├── Some((2, 5)): 5/10 ≈ 0.500
      ├── Some((2, 6)): 9/14 ≈ 0.643
      ├── Some((2, 7)): 5/10 ≈ 0.500
      └── Some((2, 8)): 5/10 ≈ 0.500
    ├── Some((8, 3)): 33/73 ≈ 0.452
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 1)): 4/9 ≈ 0.444
      ├── Some((3, 2)): 4/9 ≈ 0.444
      ├── Some((3, 3)): 10/14 ≈ 0.714
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 7)): 1/6 ≈ 0.167
      └── Some((3, 8)): 3/8 ≈ 0.375
    ├── Some((8, 4)): 48/95 ≈ 0.505
      ├── Some((4, 0)): 7/12 ≈ 0.583
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 3/8 ≈ 0.375
      ├── Some((4, 3)): 6/11 ≈ 0.545
      ├── Some((4, 4)): 8/13 ≈ 0.615
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 6/11 ≈ 0.545
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((8, 5)): 43/88 ≈ 0.489
      ├── Some((5, 0)): 4/9 ≈ 0.444
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 5/10 ≈ 0.500
      ├── Some((5, 3)): 7/12 ≈ 0.583
      ├── Some((5, 4)): 4/9 ≈ 0.444
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 4/9 ≈ 0.444
      ├── Some((5, 7)): 5/10 ≈ 0.500
      └── Some((5, 8)): 7/12 ≈ 0.583
    ├── Some((8, 6)): 47/94 ≈ 0.500
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 9/15 ≈ 0.600
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 2/8 ≈ 0.250
      ├── Some((6, 4)): 11/17 ≈ 0.647
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 11/17 ≈ 0.647
      └── Some((6, 7)): 1/6 ≈ 0.167
    ├── Some((8, 7)): 53/102 ≈ 0.520
      ├── Some((7, 0)): 9/14 ≈ 0.643
      ├── Some((7, 1)): 9/14 ≈ 0.643
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 8/13 ≈ 0.615
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 9/14 ≈ 0.643
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 1/6 ≈ 0.167
    └── Some((8, 8)): 49/97 ≈ 0.505
      ├── Some((8, 0)): 6/12 ≈ 0.500
      ├── Some((8, 1)): 0/5 ≈ 0.000
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 0/6 ≈ 0.000
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 11/17 ≈ 0.647
      ├── Some((8, 6)): 14/20 ≈ 0.700
      └── Some((8, 7)): 5/11 ≈ 0.455
├── Some((3, 7)): 5956/11501 ≈ 0.518
  ├── Some((7, 0)): 481/966 ≈ 0.498
    ├── Some((0, 0)): 63/121 ≈ 0.521
      ├── Some((0, 1)): 5/12 ≈ 0.417
      ├── Some((0, 2)): 11/19 ≈ 0.579
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 3/10 ≈ 0.300
      ├── Some((0, 7)): 14/21 ≈ 0.667
      └── Some((0, 8)): 8/15 ≈ 0.533
    ├── Some((0, 1)): 61/118 ≈ 0.517
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 5/11 ≈ 0.455
      ├── Some((1, 2)): 10/16 ≈ 0.625
      ├── Some((1, 3)): 2/8 ≈ 0.250
      ├── Some((1, 4)): 9/16 ≈ 0.562
      ├── Some((1, 5)): 5/11 ≈ 0.455
      ├── Some((1, 6)): 10/17 ≈ 0.588
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 10/17 ≈ 0.588
    ├── Some((0, 2)): 41/89 ≈ 0.461
      ├── Some((2, 0)): 8/13 ≈ 0.615
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 1/6 ≈ 0.167
      ├── Some((2, 3)): 8/13 ≈ 0.615
      ├── Some((2, 4)): 8/14 ≈ 0.571
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 0/5 ≈ 0.000
      ├── Some((2, 7)): 1/6 ≈ 0.167
      └── Some((2, 8)): 7/13 ≈ 0.538
    ├── Some((0, 3)): 46/97 ≈ 0.474
      ├── Some((3, 0)): 10/17 ≈ 0.588
      ├── Some((3, 1)): 11/17 ≈ 0.647
      ├── Some((3, 2)): 10/17 ≈ 0.588
      ├── Some((3, 3)): 6/12 ≈ 0.500
      ├── Some((3, 4)): 3/9 ≈ 0.333
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 2/8 ≈ 0.250
      └── Some((3, 8)): 1/7 ≈ 0.143
    ├── Some((0, 4)): 43/92 ≈ 0.467
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 1)): 10/15 ≈ 0.667
      ├── Some((4, 2)): 1/6 ≈ 0.167
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 5/11 ≈ 0.455
      ├── Some((4, 5)): 11/16 ≈ 0.688
      ├── Some((4, 6)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((0, 5)): 58/114 ≈ 0.509
      ├── Some((5, 0)): 10/16 ≈ 0.625
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 9/15 ≈ 0.600
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 1/7 ≈ 0.143
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 8/15 ≈ 0.533
      ├── Some((5, 7)): 8/15 ≈ 0.533
      └── Some((5, 8)): 9/15 ≈ 0.600
    ├── Some((0, 6)): 54/108 ≈ 0.500
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 10/16 ≈ 0.625
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 6/12 ≈ 0.500
      ├── Some((6, 7)): 2/8 ≈ 0.250
      └── Some((6, 8)): 9/15 ≈ 0.600
    ├── Some((0, 7)): 64/123 ≈ 0.520
      ├── Some((7, 1)): 4/11 ≈ 0.364
      ├── Some((7, 2)): 14/22 ≈ 0.636
      ├── Some((7, 3)): 15/23 ≈ 0.652
      ├── Some((7, 4)): 1/8 ≈ 0.125
      ├── Some((7, 5)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 15/23 ≈ 0.652
      ├── Some((7, 7)): 5/12 ≈ 0.417
      └── Some((7, 8)): 4/11 ≈ 0.364
    └── Some((0, 8)): 50/103 ≈ 0.485
      ├── Some((8, 0)): 6/12 ≈ 0.500
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 7/13 ≈ 0.538
      ├── Some((8, 3)): 8/14 ≈ 0.571
      ├── Some((8, 4)): 9/15 ≈ 0.600
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 6/12 ≈ 0.500
      ├── Some((8, 7)): 2/8 ≈ 0.250
      └── Some((8, 8)): 6/12 ≈ 0.500
  ├── Some((7, 1)): 568/1117 ≈ 0.509
    ├── Some((1, 0)): 28/72 ≈ 0.389
      ├── Some((0, 0)): 1/6 ≈ 0.167
      ├── Some((0, 1)): 6/10 ≈ 0.600
      ├── Some((0, 2)): 6/11 ≈ 0.545
      ├── Some((0, 3)): 6/11 ≈ 0.545
      ├── Some((0, 4)): 5/10 ≈ 0.500
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 0/4 ≈ 0.000
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((1, 1)): 92/166 ≈ 0.554
      ├── Some((1, 0)): 8/17 ≈ 0.471
      ├── Some((1, 2)): 7/16 ≈ 0.438
      ├── Some((1, 3)): 8/17 ≈ 0.471
      ├── Some((1, 4)): 13/22 ≈ 0.591
      ├── Some((1, 5)): 15/24 ≈ 0.625
      ├── Some((1, 6)): 23/33 ≈ 0.697
      ├── Some((1, 7)): 7/16 ≈ 0.438
      └── Some((1, 8)): 11/20 ≈ 0.550
    ├── Some((1, 2)): 50/105 ≈ 0.476
      ├── Some((2, 0)): 10/16 ≈ 0.625
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 0/6 ≈ 0.000
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 2/8 ≈ 0.250
      ├── Some((2, 6)): 12/18 ≈ 0.667
      ├── Some((2, 7)): 8/15 ≈ 0.533
      └── Some((2, 8)): 4/10 ≈ 0.400
    ├── Some((1, 3)): 98/174 ≈ 0.563
      ├── Some((3, 0)): 13/23 ≈ 0.565
      ├── Some((3, 1)): 10/19 ≈ 0.526
      ├── Some((3, 2)): 11/20 ≈ 0.550
      ├── Some((3, 3)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 17/27 ≈ 0.630
      ├── Some((3, 5)): 15/25 ≈ 0.600
      ├── Some((3, 6)): 12/22 ≈ 0.545
      └── Some((3, 8)): 11/20 ≈ 0.550
    ├── Some((1, 4)): 63/125 ≈ 0.504
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 11/18 ≈ 0.611
      ├── Some((4, 3)): 8/15 ≈ 0.533
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 0/6 ≈ 0.000
      └── Some((4, 8)): 13/19 ≈ 0.684
    ├── Some((1, 5)): 61/122 ≈ 0.500
      ├── Some((5, 0)): 2/8 ≈ 0.250
      ├── Some((5, 1)): 9/16 ≈ 0.562
      ├── Some((5, 2)): 9/16 ≈ 0.562
      ├── Some((5, 3)): 10/17 ≈ 0.588
      ├── Some((5, 4)): 4/10 ≈ 0.400
      ├── Some((5, 5)): 2/8 ≈ 0.250
      ├── Some((5, 6)): 11/18 ≈ 0.611
      ├── Some((5, 7)): 10/17 ≈ 0.588
      └── Some((5, 8)): 4/11 ≈ 0.364
    ├── Some((1, 6)): 49/104 ≈ 0.471
      ├── Some((6, 0)): 10/16 ≈ 0.625
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 0/6 ≈ 0.000
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 11/17 ≈ 0.647
    ├── Some((1, 7)): 48/102 ≈ 0.471
      ├── Some((7, 0)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 4/10 ≈ 0.400
      ├── Some((7, 3)): 4/11 ≈ 0.364
      ├── Some((7, 4)): 11/18 ≈ 0.611
      ├── Some((7, 5)): 11/18 ≈ 0.611
      ├── Some((7, 6)): 5/12 ≈ 0.417
      ├── Some((7, 7)): 6/13 ≈ 0.462
      └── Some((7, 8)): 1/7 ≈ 0.143
    └── Some((1, 8)): 78/146 ≈ 0.534
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 10/18 ≈ 0.556
      ├── Some((8, 2)): 10/18 ≈ 0.556
      ├── Some((8, 3)): 10/18 ≈ 0.556
      ├── Some((8, 4)): 10/18 ≈ 0.556
      ├── Some((8, 5)): 13/20 ≈ 0.650
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 10/18 ≈ 0.556
      └── Some((8, 8)): 3/10 ≈ 0.300
  ├── Some((7, 2)): 857/1613 ≈ 0.531
    ├── Some((2, 0)): 107/197 ≈ 0.543
      ├── Some((0, 0)): 12/22 ≈ 0.545
      ├── Some((0, 1)): 11/21 ≈ 0.524
      ├── Some((0, 2)): 4/13 ≈ 0.308
      ├── Some((0, 3)): 1/9 ≈ 0.111
      ├── Some((0, 4)): 18/28 ≈ 0.643
      ├── Some((0, 5)): 12/22 ≈ 0.545
      ├── Some((0, 6)): 8/18 ≈ 0.444
      ├── Some((0, 7)): 23/34 ≈ 0.676
      └── Some((0, 8)): 18/29 ≈ 0.621
    ├── Some((2, 1)): 82/161 ≈ 0.509
      ├── Some((1, 0)): 15/24 ≈ 0.625
      ├── Some((1, 1)): 6/14 ≈ 0.429
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 3)): 10/19 ≈ 0.526
      ├── Some((1, 4)): 10/19 ≈ 0.526
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 11/20 ≈ 0.550
      ├── Some((1, 7)): 3/11 ≈ 0.273
      └── Some((1, 8)): 6/14 ≈ 0.429
    ├── Some((2, 2)): 68/140 ≈ 0.486
      ├── Some((2, 0)): 12/21 ≈ 0.571
      ├── Some((2, 1)): 10/19 ≈ 0.526
      ├── Some((2, 3)): 8/17 ≈ 0.471
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 10/19 ≈ 0.526
      ├── Some((2, 6)): 1/9 ≈ 0.111
      ├── Some((2, 7)): 17/27 ≈ 0.630
      └── Some((2, 8)): 4/12 ≈ 0.333
    ├── Some((2, 3)): 142/247 ≈ 0.575
      ├── Some((3, 0)): 23/37 ≈ 0.622
      ├── Some((3, 1)): 12/24 ≈ 0.500
      ├── Some((3, 2)): 18/31 ≈ 0.581
      ├── Some((3, 3)): 22/36 ≈ 0.611
      ├── Some((3, 4)): 14/27 ≈ 0.519
      ├── Some((3, 5)): 16/29 ≈ 0.552
      ├── Some((3, 6)): 25/39 ≈ 0.641
      └── Some((3, 8)): 11/23 ≈ 0.478
    ├── Some((2, 4)): 59/126 ≈ 0.468
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 6/13 ≈ 0.462
      ├── Some((4, 2)): 7/14 ≈ 0.500
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 8/16 ≈ 0.500
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 13/21 ≈ 0.619
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((2, 5)): 129/229 ≈ 0.563
      ├── Some((5, 0)): 28/40 ≈ 0.700
      ├── Some((5, 1)): 17/29 ≈ 0.586
      ├── Some((5, 2)): 15/26 ≈ 0.577
      ├── Some((5, 3)): 14/25 ≈ 0.560
      ├── Some((5, 4)): 18/30 ≈ 0.600
      ├── Some((5, 5)): 3/12 ≈ 0.250
      ├── Some((5, 6)): 6/16 ≈ 0.375
      ├── Some((5, 7)): 14/25 ≈ 0.560
      └── Some((5, 8)): 14/25 ≈ 0.560
    ├── Some((2, 6)): 140/245 ≈ 0.571
      ├── Some((6, 0)): 26/39 ≈ 0.667
      ├── Some((6, 1)): 14/26 ≈ 0.538
      ├── Some((6, 2)): 13/25 ≈ 0.520
      ├── Some((6, 3)): 29/42 ≈ 0.690
      ├── Some((6, 4)): 10/21 ≈ 0.476
      ├── Some((6, 5)): 8/19 ≈ 0.421
      ├── Some((6, 6)): 30/43 ≈ 0.698
      ├── Some((6, 7)): 5/15 ≈ 0.333
      └── Some((6, 8)): 4/14 ≈ 0.286
    ├── Some((2, 7)): 101/189 ≈ 0.534
      ├── Some((7, 0)): 11/22 ≈ 0.500
      ├── Some((7, 1)): 3/12 ≈ 0.250
      ├── Some((7, 3)): 13/24 ≈ 0.542
      ├── Some((7, 4)): 20/32 ≈ 0.625
      ├── Some((7, 5)): 14/25 ≈ 0.560
      ├── Some((7, 6)): 12/23 ≈ 0.522
      ├── Some((7, 7)): 16/27 ≈ 0.593
      └── Some((7, 8)): 12/23 ≈ 0.522
    └── Some((2, 8)): 29/78 ≈ 0.372
      ├── Some((8, 0)): 6/12 ≈ 0.500
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 7/13 ≈ 0.538
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 2/7 ≈ 0.286
      └── Some((8, 8)): 1/6 ≈ 0.167
  ├── Some((7, 3)): 560/1104 ≈ 0.507
    ├── Some((3, 0)): 58/120 ≈ 0.483
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 2)): 11/18 ≈ 0.611
      ├── Some((0, 3)): 4/11 ≈ 0.364
      ├── Some((0, 4)): 10/17 ≈ 0.588
      ├── Some((0, 5)): 4/11 ≈ 0.364
      ├── Some((0, 6)): 1/7 ≈ 0.143
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 9/16 ≈ 0.562
    ├── Some((3, 1)): 89/166 ≈ 0.536
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 1)): 22/31 ≈ 0.710
      ├── Some((1, 2)): 6/14 ≈ 0.429
      ├── Some((1, 3)): 4/12 ≈ 0.333
      ├── Some((1, 4)): 14/23 ≈ 0.609
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 5/13 ≈ 0.385
      ├── Some((1, 7)): 2/10 ≈ 0.200
      └── Some((1, 8)): 13/22 ≈ 0.591
    ├── Some((3, 2)): 51/110 ≈ 0.464
      ├── Some((2, 0)): 12/19 ≈ 0.632
      ├── Some((2, 1)): 4/11 ≈ 0.364
      ├── Some((2, 2)): 12/19 ≈ 0.632
      ├── Some((2, 3)): 1/7 ≈ 0.143
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 1/7 ≈ 0.143
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((3, 3)): 72/141 ≈ 0.511
      ├── Some((3, 0)): 12/22 ≈ 0.545
      ├── Some((3, 1)): 11/21 ≈ 0.524
      ├── Some((3, 2)): 11/21 ≈ 0.524
      ├── Some((3, 4)): 12/22 ≈ 0.545
      ├── Some((3, 5)): 2/10 ≈ 0.200
      ├── Some((3, 6)): 7/17 ≈ 0.412
      └── Some((3, 8)): 16/27 ≈ 0.593
    ├── Some((3, 4)): 51/110 ≈ 0.464
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 1)): 2/8 ≈ 0.250
      ├── Some((4, 2)): 6/13 ≈ 0.462
      ├── Some((4, 3)): 2/8 ≈ 0.250
      ├── Some((4, 4)): 11/18 ≈ 0.611
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 13/20 ≈ 0.650
      └── Some((4, 8)): 8/15 ≈ 0.533
    ├── Some((3, 5)): 80/153 ≈ 0.523
      ├── Some((5, 0)): 8/16 ≈ 0.500
      ├── Some((5, 1)): 3/11 ≈ 0.273
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 12/20 ≈ 0.600
      ├── Some((5, 4)): 10/18 ≈ 0.556
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 15/24 ≈ 0.625
    ├── Some((3, 6)): 86/162 ≈ 0.531
      ├── Some((6, 0)): 13/22 ≈ 0.591
      ├── Some((6, 1)): 16/25 ≈ 0.640
      ├── Some((6, 2)): 5/13 ≈ 0.385
      ├── Some((6, 3)): 6/14 ≈ 0.429
      ├── Some((6, 4)): 4/12 ≈ 0.333
      ├── Some((6, 5)): 8/16 ≈ 0.500
      ├── Some((6, 6)): 10/19 ≈ 0.526
      ├── Some((6, 7)): 14/23 ≈ 0.609
      └── Some((6, 8)): 9/17 ≈ 0.529
    └── Some((3, 8)): 72/141 ≈ 0.511
      ├── Some((8, 0)): 12/20 ≈ 0.600
      ├── Some((8, 1)): 0/6 ≈ 0.000
      ├── Some((8, 2)): 13/21 ≈ 0.619
      ├── Some((8, 3)): 4/11 ≈ 0.364
      ├── Some((8, 4)): 11/19 ≈ 0.579
      ├── Some((8, 5)): 5/13 ≈ 0.385
      ├── Some((8, 6)): 14/22 ≈ 0.636
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 6/14 ≈ 0.429
  ├── Some((7, 4)): 954/1777 ≈ 0.537
    ├── Some((4, 0)): 75/152 ≈ 0.493
      ├── Some((0, 0)): 4/12 ≈ 0.333
      ├── Some((0, 1)): 13/22 ≈ 0.591
      ├── Some((0, 2)): 8/16 ≈ 0.500
      ├── Some((0, 3)): 3/11 ≈ 0.273
      ├── Some((0, 4)): 11/20 ≈ 0.550
      ├── Some((0, 5)): 11/20 ≈ 0.550
      ├── Some((0, 6)): 5/13 ≈ 0.385
      ├── Some((0, 7)): 11/20 ≈ 0.550
      └── Some((0, 8)): 8/17 ≈ 0.471
    ├── Some((4, 1)): 116/212 ≈ 0.547
      ├── Some((1, 0)): 20/31 ≈ 0.645
      ├── Some((1, 1)): 9/19 ≈ 0.474
      ├── Some((1, 2)): 14/25 ≈ 0.560
      ├── Some((1, 3)): 10/20 ≈ 0.500
      ├── Some((1, 4)): 13/24 ≈ 0.542
      ├── Some((1, 5)): 11/21 ≈ 0.524
      ├── Some((1, 6)): 19/30 ≈ 0.633
      ├── Some((1, 7)): 6/16 ≈ 0.375
      └── Some((1, 8)): 14/25 ≈ 0.560
    ├── Some((4, 2)): 146/256 ≈ 0.570
      ├── Some((2, 0)): 13/25 ≈ 0.520
      ├── Some((2, 1)): 8/19 ≈ 0.421
      ├── Some((2, 2)): 28/42 ≈ 0.667
      ├── Some((2, 3)): 14/26 ≈ 0.538
      ├── Some((2, 4)): 12/24 ≈ 0.500
      ├── Some((2, 5)): 23/36 ≈ 0.639
      ├── Some((2, 6)): 22/35 ≈ 0.629
      ├── Some((2, 7)): 21/34 ≈ 0.618
      └── Some((2, 8)): 4/14 ≈ 0.286
    ├── Some((4, 3)): 52/117 ≈ 0.444
      ├── Some((3, 0)): 10/19 ≈ 0.526
      ├── Some((3, 1)): 7/15 ≈ 0.467
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 2/9 ≈ 0.222
      ├── Some((3, 4)): 7/15 ≈ 0.467
      ├── Some((3, 5)): 4/12 ≈ 0.333
      ├── Some((3, 6)): 7/15 ≈ 0.467
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((4, 4)): 87/170 ≈ 0.512
      ├── Some((4, 0)): 17/28 ≈ 0.607
      ├── Some((4, 1)): 11/21 ≈ 0.524
      ├── Some((4, 2)): 14/25 ≈ 0.560
      ├── Some((4, 3)): 14/25 ≈ 0.560
      ├── Some((4, 5)): 8/18 ≈ 0.444
      ├── Some((4, 6)): 8/18 ≈ 0.444
      ├── Some((4, 7)): 15/26 ≈ 0.577
      └── Some((4, 8)): 0/8 ≈ 0.000
    ├── Some((4, 5)): 111/205 ≈ 0.541
      ├── Some((5, 0)): 24/35 ≈ 0.686
      ├── Some((5, 1)): 16/27 ≈ 0.593
      ├── Some((5, 2)): 4/13 ≈ 0.308
      ├── Some((5, 3)): 14/25 ≈ 0.560
      ├── Some((5, 4)): 10/20 ≈ 0.500
      ├── Some((5, 5)): 9/19 ≈ 0.474
      ├── Some((5, 6)): 16/27 ≈ 0.593
      ├── Some((5, 7)): 9/19 ≈ 0.474
      └── Some((5, 8)): 9/19 ≈ 0.474
    ├── Some((4, 6)): 135/240 ≈ 0.562
      ├── Some((6, 0)): 16/28 ≈ 0.571
      ├── Some((6, 1)): 11/22 ≈ 0.500
      ├── Some((6, 2)): 15/27 ≈ 0.556
      ├── Some((6, 3)): 19/31 ≈ 0.613
      ├── Some((6, 4)): 12/23 ≈ 0.522
      ├── Some((6, 5)): 14/25 ≈ 0.560
      ├── Some((6, 6)): 16/28 ≈ 0.571
      ├── Some((6, 7)): 21/33 ≈ 0.636
      └── Some((6, 8)): 11/22 ≈ 0.500
    ├── Some((4, 7)): 94/180 ≈ 0.522
      ├── Some((7, 0)): 7/17 ≈ 0.412
      ├── Some((7, 1)): 19/31 ≈ 0.613
      ├── Some((7, 2)): 8/18 ≈ 0.444
      ├── Some((7, 3)): 14/25 ≈ 0.560
      ├── Some((7, 5)): 7/17 ≈ 0.412
      ├── Some((7, 6)): 8/18 ≈ 0.444
      ├── Some((7, 7)): 17/29 ≈ 0.586
      └── Some((7, 8)): 13/24 ≈ 0.542
    └── Some((4, 8)): 138/244 ≈ 0.566
      ├── Some((8, 0)): 7/18 ≈ 0.389
      ├── Some((8, 1)): 20/32 ≈ 0.625
      ├── Some((8, 2)): 16/28 ≈ 0.571
      ├── Some((8, 3)): 10/21 ≈ 0.476
      ├── Some((8, 4)): 18/30 ≈ 0.600
      ├── Some((8, 5)): 11/22 ≈ 0.500
      ├── Some((8, 6)): 18/30 ≈ 0.600
      ├── Some((8, 7)): 16/28 ≈ 0.571
      └── Some((8, 8)): 22/34 ≈ 0.647
  ├── Some((7, 5)): 766/1458 ≈ 0.525
    ├── Some((5, 0)): 149/254 ≈ 0.587
      ├── Some((0, 0)): 12/24 ≈ 0.500
      ├── Some((0, 1)): 19/31 ≈ 0.613
      ├── Some((0, 2)): 6/16 ≈ 0.375
      ├── Some((0, 3)): 20/32 ≈ 0.625
      ├── Some((0, 4)): 25/37 ≈ 0.676
      ├── Some((0, 5)): 16/28 ≈ 0.571
      ├── Some((0, 6)): 20/32 ≈ 0.625
      ├── Some((0, 7)): 22/34 ≈ 0.647
      └── Some((0, 8)): 8/19 ≈ 0.421
    ├── Some((5, 1)): 66/134 ≈ 0.493
      ├── Some((1, 0)): 2/9 ≈ 0.222
      ├── Some((1, 1)): 4/11 ≈ 0.364
      ├── Some((1, 2)): 7/15 ≈ 0.467
      ├── Some((1, 3)): 16/24 ≈ 0.667
      ├── Some((1, 4)): 10/18 ≈ 0.556
      ├── Some((1, 5)): 11/19 ≈ 0.579
      ├── Some((1, 6)): 5/12 ≈ 0.417
      ├── Some((1, 7)): 7/15 ≈ 0.467
      └── Some((1, 8)): 3/10 ≈ 0.300
    ├── Some((5, 2)): 54/116 ≈ 0.466
      ├── Some((2, 0)): 2/8 ≈ 0.250
      ├── Some((2, 1)): 4/11 ≈ 0.364
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 4/11 ≈ 0.364
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 12/19 ≈ 0.632
      ├── Some((2, 6)): 3/10 ≈ 0.300
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 11/18 ≈ 0.611
    ├── Some((5, 3)): 82/158 ≈ 0.519
      ├── Some((3, 0)): 12/22 ≈ 0.545
      ├── Some((3, 1)): 7/16 ≈ 0.438
      ├── Some((3, 2)): 9/18 ≈ 0.500
      ├── Some((3, 3)): 5/14 ≈ 0.357
      ├── Some((3, 4)): 14/24 ≈ 0.583
      ├── Some((3, 5)): 12/22 ≈ 0.545
      ├── Some((3, 6)): 8/17 ≈ 0.471
      └── Some((3, 8)): 14/24 ≈ 0.583
    ├── Some((5, 4)): 56/119 ≈ 0.471
      ├── Some((4, 0)): 12/19 ≈ 0.632
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 0/6 ≈ 0.000
      ├── Some((4, 3)): 0/6 ≈ 0.000
      ├── Some((4, 4)): 9/16 ≈ 0.562
      ├── Some((4, 5)): 11/19 ≈ 0.579
      ├── Some((4, 6)): 8/15 ≈ 0.533
      ├── Some((4, 7)): 4/11 ≈ 0.364
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((5, 5)): 114/205 ≈ 0.556
      ├── Some((5, 0)): 22/34 ≈ 0.647
      ├── Some((5, 1)): 8/18 ≈ 0.444
      ├── Some((5, 2)): 18/30 ≈ 0.600
      ├── Some((5, 3)): 8/19 ≈ 0.421
      ├── Some((5, 4)): 19/31 ≈ 0.613
      ├── Some((5, 6)): 14/25 ≈ 0.560
      ├── Some((5, 7)): 13/24 ≈ 0.542
      └── Some((5, 8)): 12/23 ≈ 0.522
    ├── Some((5, 6)): 87/166 ≈ 0.524
      ├── Some((6, 0)): 12/21 ≈ 0.571
      ├── Some((6, 1)): 14/23 ≈ 0.609
      ├── Some((6, 2)): 12/21 ≈ 0.571
      ├── Some((6, 3)): 4/12 ≈ 0.333
      ├── Some((6, 4)): 4/12 ≈ 0.333
      ├── Some((6, 5)): 10/19 ≈ 0.526
      ├── Some((6, 6)): 10/19 ≈ 0.526
      ├── Some((6, 7)): 13/22 ≈ 0.591
      └── Some((6, 8)): 7/16 ≈ 0.438
    ├── Some((5, 7)): 51/112 ≈ 0.455
      ├── Some((7, 0)): 5/12 ≈ 0.417
      ├── Some((7, 1)): 17/25 ≈ 0.680
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 5/12 ≈ 0.417
      ├── Some((7, 4)): 7/15 ≈ 0.467
      ├── Some((7, 6)): 5/13 ≈ 0.385
      ├── Some((7, 7)): 3/10 ≈ 0.300
      └── Some((7, 8)): 6/14 ≈ 0.429
    └── Some((5, 8)): 106/193 ≈ 0.549
      ├── Some((8, 0)): 14/24 ≈ 0.583
      ├── Some((8, 1)): 13/23 ≈ 0.565
      ├── Some((8, 2)): 13/23 ≈ 0.565
      ├── Some((8, 3)): 6/15 ≈ 0.400
      ├── Some((8, 4)): 10/19 ≈ 0.526
      ├── Some((8, 5)): 13/23 ≈ 0.565
      ├── Some((8, 6)): 10/19 ≈ 0.526
      ├── Some((8, 7)): 13/23 ≈ 0.565
      └── Some((8, 8)): 13/23 ≈ 0.565
  ├── Some((7, 6)): 511/1018 ≈ 0.502
    ├── Some((6, 0)): 15/49 ≈ 0.306
      ├── Some((0, 0)): 3/7 ≈ 0.429
      ├── Some((0, 1)): 1/5 ≈ 0.200
      ├── Some((0, 2)): 2/6 ≈ 0.333
      ├── Some((0, 3)): 3/7 ≈ 0.429
      ├── Some((0, 4)): 0/3 ≈ 0.000
      ├── Some((0, 5)): 4/7 ≈ 0.571
      ├── Some((0, 6)): 0/3 ≈ 0.000
      ├── Some((0, 7)): 2/6 ≈ 0.333
      └── Some((0, 8)): 0/4 ≈ 0.000
    ├── Some((6, 1)): 56/112 ≈ 0.500
      ├── Some((1, 0)): 13/19 ≈ 0.684
      ├── Some((1, 1)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 8/15 ≈ 0.533
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 11/17 ≈ 0.647
      ├── Some((1, 5)): 5/11 ≈ 0.455
      ├── Some((1, 6)): 3/9 ≈ 0.333
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((6, 2)): 63/123 ≈ 0.512
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 11/18 ≈ 0.611
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 9/16 ≈ 0.562
      ├── Some((2, 6)): 14/20 ≈ 0.700
      ├── Some((2, 7)): 5/12 ≈ 0.417
      └── Some((2, 8)): 4/10 ≈ 0.400
    ├── Some((6, 3)): 51/105 ≈ 0.486
      ├── Some((3, 0)): 13/20 ≈ 0.650
      ├── Some((3, 1)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 7/14 ≈ 0.500
      ├── Some((3, 3)): 5/12 ≈ 0.417
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 1/7 ≈ 0.143
      ├── Some((3, 6)): 4/10 ≈ 0.400
      └── Some((3, 8)): 8/15 ≈ 0.533
    ├── Some((6, 4)): 66/127 ≈ 0.520
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 12/19 ≈ 0.632
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 0/6 ≈ 0.000
      ├── Some((4, 5)): 11/18 ≈ 0.611
      ├── Some((4, 6)): 11/18 ≈ 0.611
      ├── Some((4, 7)): 12/19 ≈ 0.632
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((6, 5)): 83/151 ≈ 0.550
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 5)): 12/20 ≈ 0.600
      ├── Some((5, 6)): 11/19 ≈ 0.579
      ├── Some((5, 7)): 13/21 ≈ 0.619
      └── Some((5, 8)): 14/21 ≈ 0.667
    ├── Some((6, 6)): 71/134 ≈ 0.530
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 13/21 ≈ 0.619
      ├── Some((6, 2)): 5/13 ≈ 0.385
      ├── Some((6, 3)): 6/14 ≈ 0.429
      ├── Some((6, 4)): 2/9 ≈ 0.222
      ├── Some((6, 5)): 14/22 ≈ 0.636
      ├── Some((6, 7)): 11/19 ≈ 0.579
      └── Some((6, 8)): 12/20 ≈ 0.600
    ├── Some((6, 7)): 53/108 ≈ 0.491
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 3/10 ≈ 0.300
      ├── Some((7, 4)): 10/17 ≈ 0.588
      ├── Some((7, 5)): 2/8 ≈ 0.250
      ├── Some((7, 7)): 16/23 ≈ 0.696
      └── Some((7, 8)): 6/13 ≈ 0.462
    └── Some((6, 8)): 53/108 ≈ 0.491
      ├── Some((8, 0)): 14/20 ≈ 0.700
      ├── Some((8, 1)): 3/9 ≈ 0.333
      ├── Some((8, 2)): 8/14 ≈ 0.571
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 12/18 ≈ 0.667
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 2/8 ≈ 0.250
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((7, 7)): 605/1181 ≈ 0.512
    ├── Some((7, 0)): 92/172 ≈ 0.535
      ├── Some((0, 0)): 8/17 ≈ 0.471
      ├── Some((0, 1)): 11/20 ≈ 0.550
      ├── Some((0, 2)): 11/20 ≈ 0.550
      ├── Some((0, 3)): 12/21 ≈ 0.571
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 15/24 ≈ 0.625
      ├── Some((0, 7)): 15/24 ≈ 0.625
      └── Some((0, 8)): 6/14 ≈ 0.429
    ├── Some((7, 1)): 58/121 ≈ 0.479
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 4/11 ≈ 0.364
      ├── Some((1, 2)): 4/11 ≈ 0.364
      ├── Some((1, 3)): 17/24 ≈ 0.708
      ├── Some((1, 4)): 0/6 ≈ 0.000
      ├── Some((1, 5)): 3/10 ≈ 0.300
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 6/13 ≈ 0.462
      └── Some((1, 8)): 11/18 ≈ 0.611
    ├── Some((7, 2)): 79/153 ≈ 0.516
      ├── Some((2, 0)): 15/23 ≈ 0.652
      ├── Some((2, 1)): 6/14 ≈ 0.429
      ├── Some((2, 2)): 3/11 ≈ 0.273
      ├── Some((2, 3)): 7/15 ≈ 0.467
      ├── Some((2, 4)): 15/24 ≈ 0.625
      ├── Some((2, 5)): 4/12 ≈ 0.333
      ├── Some((2, 6)): 11/19 ≈ 0.579
      ├── Some((2, 7)): 12/20 ≈ 0.600
      └── Some((2, 8)): 6/14 ≈ 0.429
    ├── Some((7, 3)): 54/115 ≈ 0.470
      ├── Some((3, 0)): 11/19 ≈ 0.579
      ├── Some((3, 1)): 6/13 ≈ 0.462
      ├── Some((3, 2)): 11/19 ≈ 0.579
      ├── Some((3, 3)): 2/9 ≈ 0.222
      ├── Some((3, 4)): 10/18 ≈ 0.556
      ├── Some((3, 5)): 3/10 ≈ 0.300
      ├── Some((3, 6)): 9/17 ≈ 0.529
      └── Some((3, 8)): 2/9 ≈ 0.222
    ├── Some((7, 4)): 110/198 ≈ 0.556
      ├── Some((4, 0)): 24/34 ≈ 0.706
      ├── Some((4, 1)): 15/25 ≈ 0.600
      ├── Some((4, 2)): 9/19 ≈ 0.474
      ├── Some((4, 3)): 13/23 ≈ 0.565
      ├── Some((4, 4)): 2/10 ≈ 0.200
      ├── Some((4, 5)): 10/20 ≈ 0.500
      ├── Some((4, 6)): 7/17 ≈ 0.412
      ├── Some((4, 7)): 15/25 ≈ 0.600
      └── Some((4, 8)): 14/24 ≈ 0.583
    ├── Some((7, 5)): 59/123 ≈ 0.480
      ├── Some((5, 0)): 4/11 ≈ 0.364
      ├── Some((5, 1)): 15/22 ≈ 0.682
      ├── Some((5, 2)): 7/14 ≈ 0.500
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 6/13 ≈ 0.462
      ├── Some((5, 5)): 4/11 ≈ 0.364
      ├── Some((5, 6)): 5/12 ≈ 0.417
      ├── Some((5, 7)): 9/16 ≈ 0.562
      └── Some((5, 8)): 3/10 ≈ 0.300
    ├── Some((7, 6)): 96/178 ≈ 0.539
      ├── Some((6, 0)): 18/28 ≈ 0.643
      ├── Some((6, 1)): 12/21 ≈ 0.571
      ├── Some((6, 2)): 6/15 ≈ 0.400
      ├── Some((6, 3)): 12/21 ≈ 0.571
      ├── Some((6, 4)): 9/18 ≈ 0.500
      ├── Some((6, 5)): 10/19 ≈ 0.526
      ├── Some((6, 6)): 12/21 ≈ 0.571
      ├── Some((6, 7)): 4/12 ≈ 0.333
      └── Some((6, 8)): 13/22 ≈ 0.591
    └── Some((7, 8)): 57/120 ≈ 0.475
      ├── Some((8, 0)): 11/18 ≈ 0.611
      ├── Some((8, 1)): 2/9 ≈ 0.222
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 7/14 ≈ 0.500
      ├── Some((8, 4)): 2/9 ≈ 0.222
      ├── Some((8, 5)): 7/14 ≈ 0.500
      ├── Some((8, 6)): 6/13 ≈ 0.462
      ├── Some((8, 7)): 12/19 ≈ 0.632
      └── Some((8, 8)): 6/13 ≈ 0.462
  └── Some((7, 8)): 654/1266 ≈ 0.517
    ├── Some((8, 0)): 63/127 ≈ 0.496
      ├── Some((0, 0)): 2/9 ≈ 0.222
      ├── Some((0, 1)): 17/24 ≈ 0.708
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 3/10 ≈ 0.300
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 1/8 ≈ 0.125
      ├── Some((0, 7)): 9/16 ≈ 0.562
      └── Some((0, 8)): 8/15 ≈ 0.533
    ├── Some((8, 1)): 51/109 ≈ 0.468
      ├── Some((1, 0)): 3/9 ≈ 0.333
      ├── Some((1, 1)): 13/20 ≈ 0.650
      ├── Some((1, 2)): 9/16 ≈ 0.562
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 4/10 ≈ 0.400
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 4/11 ≈ 0.364
    ├── Some((8, 2)): 132/226 ≈ 0.584
      ├── Some((2, 0)): 11/21 ≈ 0.524
      ├── Some((2, 1)): 16/26 ≈ 0.615
      ├── Some((2, 2)): 22/33 ≈ 0.667
      ├── Some((2, 3)): 18/29 ≈ 0.621
      ├── Some((2, 4)): 18/29 ≈ 0.621
      ├── Some((2, 5)): 12/22 ≈ 0.545
      ├── Some((2, 6)): 22/33 ≈ 0.667
      ├── Some((2, 7)): 7/17 ≈ 0.412
      └── Some((2, 8)): 6/15 ≈ 0.400
    ├── Some((8, 3)): 76/146 ≈ 0.521
      ├── Some((3, 0)): 11/20 ≈ 0.550
      ├── Some((3, 1)): 4/12 ≈ 0.333
      ├── Some((3, 2)): 9/18 ≈ 0.500
      ├── Some((3, 3)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 6/14 ≈ 0.429
      ├── Some((3, 5)): 13/22 ≈ 0.591
      ├── Some((3, 6)): 18/27 ≈ 0.667
      └── Some((3, 8)): 6/15 ≈ 0.400
    ├── Some((8, 4)): 81/153 ≈ 0.529
      ├── Some((4, 0)): 8/16 ≈ 0.500
      ├── Some((4, 1)): 7/15 ≈ 0.467
      ├── Some((4, 2)): 4/12 ≈ 0.333
      ├── Some((4, 3)): 18/26 ≈ 0.692
      ├── Some((4, 4)): 4/12 ≈ 0.333
      ├── Some((4, 5)): 15/23 ≈ 0.652
      ├── Some((4, 6)): 10/18 ≈ 0.556
      ├── Some((4, 7)): 5/13 ≈ 0.385
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((8, 5)): 68/134 ≈ 0.507
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 9/17 ≈ 0.529
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 8/15 ≈ 0.533
      ├── Some((5, 4)): 3/10 ≈ 0.300
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 6)): 14/22 ≈ 0.636
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 8/15 ≈ 0.533
    ├── Some((8, 6)): 51/109 ≈ 0.468
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 2/8 ≈ 0.250
      ├── Some((6, 2)): 12/19 ≈ 0.632
      ├── Some((6, 3)): 2/8 ≈ 0.250
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 11/18 ≈ 0.611
    ├── Some((8, 7)): 61/124 ≈ 0.492
      ├── Some((7, 0)): 7/15 ≈ 0.467
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 17/25 ≈ 0.680
      ├── Some((7, 4)): 9/17 ≈ 0.529
      ├── Some((7, 5)): 6/14 ≈ 0.429
      ├── Some((7, 6)): 3/10 ≈ 0.300
      └── Some((7, 7)): 8/16 ≈ 0.500
    └── Some((8, 8)): 70/137 ≈ 0.511
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 1)): 5/13 ≈ 0.385
      ├── Some((8, 2)): 11/20 ≈ 0.550
      ├── Some((8, 3)): 9/17 ≈ 0.529
      ├── Some((8, 4)): 8/16 ≈ 0.500
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 9/17 ≈ 0.529
      └── Some((8, 7)): 10/19 ≈ 0.526
├── Some((3, 8)): 5271/10242 ≈ 0.515
  ├── Some((8, 0)): 369/762 ≈ 0.484
    ├── Some((0, 0)): 34/75 ≈ 0.453
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 6/11 ≈ 0.545
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 6/11 ≈ 0.545
    ├── Some((0, 1)): 41/85 ≈ 0.482
      ├── Some((1, 0)): 5/10 ≈ 0.500
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 4/9 ≈ 0.444
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 6/10 ≈ 0.600
      ├── Some((1, 7)): 5/10 ≈ 0.500
      └── Some((1, 8)): 7/11 ≈ 0.636
    ├── Some((0, 2)): 20/54 ≈ 0.370
      ├── Some((2, 0)): 0/4 ≈ 0.000
      ├── Some((2, 1)): 0/4 ≈ 0.000
      ├── Some((2, 2)): 3/7 ≈ 0.429
      ├── Some((2, 3)): 1/5 ≈ 0.200
      ├── Some((2, 4)): 3/6 ≈ 0.500
      ├── Some((2, 5)): 4/7 ≈ 0.571
      ├── Some((2, 6)): 4/7 ≈ 0.571
      ├── Some((2, 7)): 3/7 ≈ 0.429
      └── Some((2, 8)): 2/6 ≈ 0.333
    ├── Some((0, 3)): 31/71 ≈ 0.437
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 1)): 4/9 ≈ 0.444
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 6/10 ≈ 0.600
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 6/11 ≈ 0.545
      ├── Some((3, 6)): 3/8 ≈ 0.375
      └── Some((3, 7)): 6/11 ≈ 0.545
    ├── Some((0, 4)): 67/122 ≈ 0.549
      ├── Some((4, 0)): 12/18 ≈ 0.667
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 8/14 ≈ 0.571
      ├── Some((4, 4)): 7/13 ≈ 0.538
      ├── Some((4, 5)): 8/14 ≈ 0.571
      ├── Some((4, 6)): 12/18 ≈ 0.667
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 7/13 ≈ 0.538
    ├── Some((0, 5)): 67/122 ≈ 0.549
      ├── Some((5, 0)): 9/15 ≈ 0.600
      ├── Some((5, 1)): 7/13 ≈ 0.538
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 13/19 ≈ 0.684
      ├── Some((5, 5)): 2/8 ≈ 0.250
      ├── Some((5, 6)): 11/17 ≈ 0.647
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 12/18 ≈ 0.667
    ├── Some((0, 6)): 8/34 ≈ 0.235
      ├── Some((6, 0)): 1/3 ≈ 0.333
      ├── Some((6, 1)): 1/4 ≈ 0.250
      ├── Some((6, 2)): 1/4 ≈ 0.250
      ├── Some((6, 3)): 2/4 ≈ 0.500
      ├── Some((6, 4)): 1/4 ≈ 0.250
      ├── Some((6, 5)): 0/3 ≈ 0.000
      ├── Some((6, 6)): 1/4 ≈ 0.250
      ├── Some((6, 7)): 1/4 ≈ 0.250
      └── Some((6, 8)): 0/3 ≈ 0.000
    ├── Some((0, 7)): 55/105 ≈ 0.524
      ├── Some((7, 0)): 4/10 ≈ 0.400
      ├── Some((7, 1)): 7/12 ≈ 0.583
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 7/12 ≈ 0.583
      ├── Some((7, 4)): 8/13 ≈ 0.615
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 9/14 ≈ 0.643
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 7/13 ≈ 0.538
    └── Some((0, 8)): 46/93 ≈ 0.495
      ├── Some((8, 1)): 6/12 ≈ 0.500
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 3/9 ≈ 0.333
      ├── Some((8, 6)): 12/17 ≈ 0.706
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 6/12 ≈ 0.500
  ├── Some((8, 1)): 626/1208 ≈ 0.518
    ├── Some((1, 0)): 38/88 ≈ 0.432
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 6/12 ≈ 0.500
      ├── Some((0, 2)): 6/12 ≈ 0.500
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 0/5 ≈ 0.000
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 0/5 ≈ 0.000
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 7/13 ≈ 0.538
    ├── Some((1, 1)): 103/183 ≈ 0.563
      ├── Some((1, 0)): 12/22 ≈ 0.545
      ├── Some((1, 2)): 12/22 ≈ 0.545
      ├── Some((1, 3)): 6/15 ≈ 0.400
      ├── Some((1, 4)): 12/22 ≈ 0.545
      ├── Some((1, 5)): 24/35 ≈ 0.686
      ├── Some((1, 6)): 12/22 ≈ 0.545
      ├── Some((1, 7)): 10/20 ≈ 0.500
      └── Some((1, 8)): 14/24 ≈ 0.583
    ├── Some((1, 2)): 53/111 ≈ 0.477
      ├── Some((2, 0)): 3/9 ≈ 0.333
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 1/7 ≈ 0.143
      ├── Some((2, 3)): 9/16 ≈ 0.562
      ├── Some((2, 4)): 9/16 ≈ 0.562
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 12/18 ≈ 0.667
    ├── Some((1, 3)): 90/164 ≈ 0.549
      ├── Some((3, 0)): 8/17 ≈ 0.471
      ├── Some((3, 1)): 4/12 ≈ 0.333
      ├── Some((3, 2)): 8/17 ≈ 0.471
      ├── Some((3, 3)): 12/21 ≈ 0.571
      ├── Some((3, 4)): 11/20 ≈ 0.550
      ├── Some((3, 5)): 20/30 ≈ 0.667
      ├── Some((3, 6)): 14/24 ≈ 0.583
      └── Some((3, 7)): 13/22 ≈ 0.591
    ├── Some((1, 4)): 54/112 ≈ 0.482
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 1/7 ≈ 0.143
      ├── Some((4, 2)): 12/18 ≈ 0.667
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 5/12 ≈ 0.417
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 12/19 ≈ 0.632
    ├── Some((1, 5)): 58/118 ≈ 0.492
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 11/18 ≈ 0.611
      ├── Some((5, 2)): 2/8 ≈ 0.250
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 15/21 ≈ 0.714
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 6)): 0/6 ≈ 0.000
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((1, 6)): 29/74 ≈ 0.392
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 6/11 ≈ 0.545
      ├── Some((6, 3)): 1/6 ≈ 0.167
      ├── Some((6, 4)): 8/13 ≈ 0.615
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 0/5 ≈ 0.000
    ├── Some((1, 7)): 110/193 ≈ 0.570
      ├── Some((7, 0)): 7/16 ≈ 0.438
      ├── Some((7, 1)): 4/13 ≈ 0.308
      ├── Some((7, 2)): 16/26 ≈ 0.615
      ├── Some((7, 3)): 12/21 ≈ 0.571
      ├── Some((7, 4)): 11/20 ≈ 0.550
      ├── Some((7, 5)): 24/34 ≈ 0.706
      ├── Some((7, 6)): 14/23 ≈ 0.609
      ├── Some((7, 7)): 13/22 ≈ 0.591
      └── Some((7, 8)): 8/17 ≈ 0.471
    └── Some((1, 8)): 90/164 ≈ 0.549
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 2)): 13/23 ≈ 0.565
      ├── Some((8, 3)): 9/18 ≈ 0.500
      ├── Some((8, 4)): 11/20 ≈ 0.550
      ├── Some((8, 5)): 12/21 ≈ 0.571
      ├── Some((8, 6)): 10/19 ≈ 0.526
      ├── Some((8, 7)): 4/13 ≈ 0.308
      └── Some((8, 8)): 20/30 ≈ 0.667
  ├── Some((8, 2)): 730/1386 ≈ 0.527
    ├── Some((2, 0)): 96/175 ≈ 0.549
      ├── Some((0, 0)): 11/20 ≈ 0.550
      ├── Some((0, 1)): 20/29 ≈ 0.690
      ├── Some((0, 2)): 11/20 ≈ 0.550
      ├── Some((0, 3)): 14/23 ≈ 0.609
      ├── Some((0, 4)): 16/25 ≈ 0.640
      ├── Some((0, 5)): 7/16 ≈ 0.438
      ├── Some((0, 6)): 5/13 ≈ 0.385
      ├── Some((0, 7)): 7/16 ≈ 0.438
      └── Some((0, 8)): 4/12 ≈ 0.333
    ├── Some((2, 1)): 77/148 ≈ 0.520
      ├── Some((1, 0)): 12/20 ≈ 0.600
      ├── Some((1, 1)): 12/20 ≈ 0.600
      ├── Some((1, 2)): 11/19 ≈ 0.579
      ├── Some((1, 3)): 11/19 ≈ 0.579
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 6/14 ≈ 0.429
      ├── Some((1, 6)): 7/15 ≈ 0.467
      ├── Some((1, 7)): 4/11 ≈ 0.364
      └── Some((1, 8)): 8/16 ≈ 0.500
    ├── Some((2, 2)): 72/141 ≈ 0.511
      ├── Some((2, 0)): 9/18 ≈ 0.500
      ├── Some((2, 1)): 8/16 ≈ 0.500
      ├── Some((2, 3)): 2/9 ≈ 0.222
      ├── Some((2, 4)): 18/27 ≈ 0.667
      ├── Some((2, 5)): 5/13 ≈ 0.385
      ├── Some((2, 6)): 11/20 ≈ 0.550
      ├── Some((2, 7)): 10/19 ≈ 0.526
      └── Some((2, 8)): 9/18 ≈ 0.500
    ├── Some((2, 3)): 96/176 ≈ 0.545
      ├── Some((3, 0)): 6/15 ≈ 0.400
      ├── Some((3, 1)): 14/24 ≈ 0.583
      ├── Some((3, 2)): 16/26 ≈ 0.615
      ├── Some((3, 3)): 22/33 ≈ 0.667
      ├── Some((3, 4)): 7/17 ≈ 0.412
      ├── Some((3, 5)): 8/18 ≈ 0.444
      ├── Some((3, 6)): 7/17 ≈ 0.412
      └── Some((3, 7)): 15/25 ≈ 0.600
    ├── Some((2, 4)): 63/128 ≈ 0.492
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 8/15 ≈ 0.533
      ├── Some((4, 4)): 9/17 ≈ 0.529
      ├── Some((4, 5)): 2/9 ≈ 0.222
      ├── Some((4, 6)): 8/15 ≈ 0.533
      ├── Some((4, 7)): 13/21 ≈ 0.619
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((2, 5)): 77/148 ≈ 0.520
      ├── Some((5, 0)): 12/20 ≈ 0.600
      ├── Some((5, 1)): 16/24 ≈ 0.667
      ├── Some((5, 2)): 6/14 ≈ 0.429
      ├── Some((5, 3)): 2/9 ≈ 0.222
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 3/11 ≈ 0.273
      ├── Some((5, 7)): 6/14 ≈ 0.429
      └── Some((5, 8)): 13/21 ≈ 0.619
    ├── Some((2, 6)): 84/158 ≈ 0.532
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 10/19 ≈ 0.526
      ├── Some((6, 2)): 17/26 ≈ 0.654
      ├── Some((6, 3)): 1/8 ≈ 0.125
      ├── Some((6, 4)): 24/32 ≈ 0.750
      ├── Some((6, 5)): 11/20 ≈ 0.550
      ├── Some((6, 6)): 7/15 ≈ 0.467
      ├── Some((6, 7)): 6/14 ≈ 0.429
      └── Some((6, 8)): 1/8 ≈ 0.125
    ├── Some((2, 7)): 85/160 ≈ 0.531
      ├── Some((7, 0)): 5/13 ≈ 0.385
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 7/15 ≈ 0.467
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 11/20 ≈ 0.550
      ├── Some((7, 5)): 8/16 ≈ 0.500
      ├── Some((7, 6)): 15/24 ≈ 0.625
      ├── Some((7, 7)): 11/20 ≈ 0.550
      └── Some((7, 8)): 10/18 ≈ 0.556
    └── Some((2, 8)): 79/151 ≈ 0.523
      ├── Some((8, 0)): 17/26 ≈ 0.654
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 3)): 4/12 ≈ 0.333
      ├── Some((8, 4)): 11/20 ≈ 0.550
      ├── Some((8, 5)): 11/20 ≈ 0.550
      ├── Some((8, 6)): 10/19 ≈ 0.526
      ├── Some((8, 7)): 14/23 ≈ 0.609
      └── Some((8, 8)): 6/15 ≈ 0.400
  ├── Some((8, 3)): 520/1026 ≈ 0.507
    ├── Some((3, 0)): 86/160 ≈ 0.538
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 6/14 ≈ 0.429
      ├── Some((0, 2)): 16/25 ≈ 0.640
      ├── Some((0, 3)): 11/19 ≈ 0.579
      ├── Some((0, 4)): 9/17 ≈ 0.529
      ├── Some((0, 5)): 17/26 ≈ 0.654
      ├── Some((0, 6)): 10/18 ≈ 0.556
      ├── Some((0, 7)): 5/13 ≈ 0.385
      └── Some((0, 8)): 4/12 ≈ 0.333
    ├── Some((3, 1)): 93/170 ≈ 0.547
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 1)): 19/28 ≈ 0.679
      ├── Some((1, 2)): 22/31 ≈ 0.710
      ├── Some((1, 3)): 3/11 ≈ 0.273
      ├── Some((1, 4)): 14/23 ≈ 0.609
      ├── Some((1, 5)): 4/12 ≈ 0.333
      ├── Some((1, 6)): 9/17 ≈ 0.529
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 6/14 ≈ 0.429
    ├── Some((3, 2)): 82/154 ≈ 0.532
      ├── Some((2, 0)): 9/17 ≈ 0.529
      ├── Some((2, 1)): 9/17 ≈ 0.529
      ├── Some((2, 2)): 4/11 ≈ 0.364
      ├── Some((2, 3)): 9/17 ≈ 0.529
      ├── Some((2, 4)): 9/17 ≈ 0.529
      ├── Some((2, 5)): 14/22 ≈ 0.636
      ├── Some((2, 6)): 13/21 ≈ 0.619
      ├── Some((2, 7)): 6/14 ≈ 0.429
      └── Some((2, 8)): 9/17 ≈ 0.529
    ├── Some((3, 3)): 17/55 ≈ 0.309
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 0/5 ≈ 0.000
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 4/10 ≈ 0.400
      └── Some((3, 7)): 3/8 ≈ 0.375
    ├── Some((3, 4)): 63/127 ≈ 0.496
      ├── Some((4, 0)): 10/17 ≈ 0.588
      ├── Some((4, 1)): 3/10 ≈ 0.300
      ├── Some((4, 2)): 2/9 ≈ 0.222
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 12/19 ≈ 0.632
      ├── Some((4, 5)): 2/9 ≈ 0.222
      ├── Some((4, 6)): 5/12 ≈ 0.417
      ├── Some((4, 7)): 11/19 ≈ 0.579
      └── Some((4, 8)): 14/21 ≈ 0.667
    ├── Some((3, 5)): 67/132 ≈ 0.508
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 3/10 ≈ 0.300
      ├── Some((5, 2)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 7/14 ≈ 0.500
      ├── Some((5, 4)): 6/13 ≈ 0.462
      ├── Some((5, 5)): 14/22 ≈ 0.636
      ├── Some((5, 6)): 5/12 ≈ 0.417
      ├── Some((5, 7)): 5/12 ≈ 0.417
      └── Some((5, 8)): 8/15 ≈ 0.533
    ├── Some((3, 6)): 94/171 ≈ 0.550
      ├── Some((6, 0)): 17/26 ≈ 0.654
      ├── Some((6, 1)): 7/15 ≈ 0.467
      ├── Some((6, 2)): 9/18 ≈ 0.500
      ├── Some((6, 3)): 3/11 ≈ 0.273
      ├── Some((6, 4)): 27/36 ≈ 0.750
      ├── Some((6, 5)): 11/20 ≈ 0.550
      ├── Some((6, 6)): 6/14 ≈ 0.429
      ├── Some((6, 7)): 7/16 ≈ 0.438
      └── Some((6, 8)): 6/14 ≈ 0.429
    └── Some((3, 7)): 18/56 ≈ 0.321
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 4/8 ≈ 0.500
      ├── Some((7, 2)): 0/4 ≈ 0.000
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 2/6 ≈ 0.333
      ├── Some((7, 5)): 4/8 ≈ 0.500
      ├── Some((7, 6)): 3/7 ≈ 0.429
      ├── Some((7, 7)): 0/4 ≈ 0.000
      └── Some((7, 8)): 3/8 ≈ 0.375
  ├── Some((8, 4)): 491/976 ≈ 0.503
    ├── Some((4, 0)): 21/59 ≈ 0.356
      ├── Some((0, 0)): 1/5 ≈ 0.200
      ├── Some((0, 1)): 4/8 ≈ 0.500
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 4/8 ≈ 0.500
      ├── Some((0, 4)): 0/4 ≈ 0.000
      ├── Some((0, 5)): 4/8 ≈ 0.500
      ├── Some((0, 6)): 1/5 ≈ 0.200
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 2/6 ≈ 0.333
    ├── Some((4, 1)): 56/111 ≈ 0.505
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 9/15 ≈ 0.600
      ├── Some((1, 2)): 1/7 ≈ 0.143
      ├── Some((1, 3)): 10/16 ≈ 0.625
      ├── Some((1, 4)): 12/18 ≈ 0.667
      ├── Some((1, 5)): 3/9 ≈ 0.333
      ├── Some((1, 6)): 7/14 ≈ 0.500
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((4, 2)): 47/98 ≈ 0.480
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 3/8 ≈ 0.375
      ├── Some((2, 4)): 8/13 ≈ 0.615
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 10/15 ≈ 0.667
    ├── Some((4, 3)): 56/111 ≈ 0.505
      ├── Some((3, 0)): 4/10 ≈ 0.400
      ├── Some((3, 1)): 0/6 ≈ 0.000
      ├── Some((3, 2)): 11/18 ≈ 0.611
      ├── Some((3, 3)): 5/12 ≈ 0.417
      ├── Some((3, 4)): 12/19 ≈ 0.632
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 8/15 ≈ 0.533
      └── Some((3, 7)): 10/17 ≈ 0.588
    ├── Some((4, 4)): 103/177 ≈ 0.582
      ├── Some((4, 0)): 7/16 ≈ 0.438
      ├── Some((4, 1)): 14/23 ≈ 0.609
      ├── Some((4, 2)): 13/22 ≈ 0.591
      ├── Some((4, 3)): 14/23 ≈ 0.609
      ├── Some((4, 5)): 20/30 ≈ 0.667
      ├── Some((4, 6)): 19/29 ≈ 0.655
      ├── Some((4, 7)): 12/21 ≈ 0.571
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((4, 5)): 45/95 ≈ 0.474
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 8/13 ≈ 0.615
      ├── Some((5, 2)): 5/11 ≈ 0.455
      ├── Some((5, 3)): 2/7 ≈ 0.286
      ├── Some((5, 4)): 2/7 ≈ 0.286
      ├── Some((5, 5)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 3/8 ≈ 0.375
      ├── Some((5, 7)): 6/12 ≈ 0.500
      └── Some((5, 8)): 8/13 ≈ 0.615
    ├── Some((4, 6)): 32/76 ≈ 0.421
      ├── Some((6, 0)): 5/10 ≈ 0.500
      ├── Some((6, 1)): 5/10 ≈ 0.500
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 6/10 ≈ 0.600
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 3/8 ≈ 0.375
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 6/11 ≈ 0.545
    ├── Some((4, 7)): 56/111 ≈ 0.505
      ├── Some((7, 0)): 9/15 ≈ 0.600
      ├── Some((7, 1)): 7/13 ≈ 0.538
      ├── Some((7, 2)): 6/12 ≈ 0.500
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 3/9 ≈ 0.333
      ├── Some((7, 5)): 9/15 ≈ 0.600
      ├── Some((7, 6)): 6/12 ≈ 0.500
      ├── Some((7, 7)): 7/13 ≈ 0.538
      └── Some((7, 8)): 7/13 ≈ 0.538
    └── Some((4, 8)): 74/137 ≈ 0.540
      ├── Some((8, 0)): 16/24 ≈ 0.667
      ├── Some((8, 1)): 13/21 ≈ 0.619
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 12/20 ≈ 0.600
      ├── Some((8, 7)): 3/10 ≈ 0.300
      └── Some((8, 8)): 9/17 ≈ 0.529
  ├── Some((8, 5)): 708/1348 ≈ 0.525
    ├── Some((5, 0)): 92/169 ≈ 0.544
      ├── Some((0, 0)): 12/21 ≈ 0.571
      ├── Some((0, 1)): 2/10 ≈ 0.200
      ├── Some((0, 2)): 16/25 ≈ 0.640
      ├── Some((0, 3)): 23/32 ≈ 0.719
      ├── Some((0, 4)): 13/22 ≈ 0.591
      ├── Some((0, 5)): 2/10 ≈ 0.200
      ├── Some((0, 6)): 15/24 ≈ 0.625
      ├── Some((0, 7)): 8/16 ≈ 0.500
      └── Some((0, 8)): 1/8 ≈ 0.125
    ├── Some((5, 1)): 78/149 ≈ 0.523
      ├── Some((1, 0)): 3/10 ≈ 0.300
      ├── Some((1, 1)): 3/10 ≈ 0.300
      ├── Some((1, 2)): 9/17 ≈ 0.529
      ├── Some((1, 3)): 12/20 ≈ 0.600
      ├── Some((1, 4)): 8/16 ≈ 0.500
      ├── Some((1, 5)): 6/14 ≈ 0.429
      ├── Some((1, 6)): 15/23 ≈ 0.652
      ├── Some((1, 7)): 14/22 ≈ 0.636
      └── Some((1, 8)): 8/16 ≈ 0.500
    ├── Some((5, 2)): 96/175 ≈ 0.549
      ├── Some((2, 0)): 13/22 ≈ 0.591
      ├── Some((2, 1)): 20/29 ≈ 0.690
      ├── Some((2, 2)): 11/20 ≈ 0.550
      ├── Some((2, 3)): 6/14 ≈ 0.429
      ├── Some((2, 4)): 12/21 ≈ 0.571
      ├── Some((2, 5)): 6/14 ≈ 0.429
      ├── Some((2, 6)): 9/18 ≈ 0.500
      ├── Some((2, 7)): 8/16 ≈ 0.500
      └── Some((2, 8)): 11/20 ≈ 0.550
    ├── Some((5, 3)): 88/164 ≈ 0.537
      ├── Some((3, 0)): 13/23 ≈ 0.565
      ├── Some((3, 1)): 10/19 ≈ 0.526
      ├── Some((3, 2)): 9/18 ≈ 0.500
      ├── Some((3, 3)): 12/21 ≈ 0.571
      ├── Some((3, 4)): 12/22 ≈ 0.545
      ├── Some((3, 5)): 16/26 ≈ 0.615
      ├── Some((3, 6)): 6/15 ≈ 0.400
      └── Some((3, 7)): 10/19 ≈ 0.526
    ├── Some((5, 4)): 50/108 ≈ 0.463
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 10/17 ≈ 0.588
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 11/18 ≈ 0.611
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 0/6 ≈ 0.000
    ├── Some((5, 5)): 50/108 ≈ 0.463
      ├── Some((5, 0)): 4/11 ≈ 0.364
      ├── Some((5, 1)): 11/19 ≈ 0.579
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 4/11 ≈ 0.364
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 4/11 ≈ 0.364
    ├── Some((5, 6)): 77/148 ≈ 0.520
      ├── Some((6, 0)): 0/6 ≈ 0.000
      ├── Some((6, 1)): 11/19 ≈ 0.579
      ├── Some((6, 2)): 9/17 ≈ 0.529
      ├── Some((6, 3)): 10/18 ≈ 0.556
      ├── Some((6, 4)): 8/16 ≈ 0.500
      ├── Some((6, 5)): 8/16 ≈ 0.500
      ├── Some((6, 6)): 6/14 ≈ 0.429
      ├── Some((6, 7)): 6/14 ≈ 0.429
      └── Some((6, 8)): 19/27 ≈ 0.704
    ├── Some((5, 7)): 114/200 ≈ 0.570
      ├── Some((7, 0)): 11/21 ≈ 0.524
      ├── Some((7, 1)): 11/21 ≈ 0.524
      ├── Some((7, 2)): 25/35 ≈ 0.714
      ├── Some((7, 3)): 5/14 ≈ 0.357
      ├── Some((7, 4)): 22/32 ≈ 0.688
      ├── Some((7, 5)): 8/17 ≈ 0.471
      ├── Some((7, 6)): 15/25 ≈ 0.600
      ├── Some((7, 7)): 7/16 ≈ 0.438
      └── Some((7, 8)): 9/18 ≈ 0.500
    └── Some((5, 8)): 62/126 ≈ 0.492
      ├── Some((8, 0)): 9/17 ≈ 0.529
      ├── Some((8, 1)): 5/13 ≈ 0.385
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 4/12 ≈ 0.333
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 6)): 7/15 ≈ 0.467
      ├── Some((8, 7)): 9/17 ≈ 0.529
      └── Some((8, 8)): 14/22 ≈ 0.636
  ├── Some((8, 6)): 580/1129 ≈ 0.514
    ├── Some((6, 0)): 31/76 ≈ 0.408
      ├── Some((0, 0)): 6/11 ≈ 0.545
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 2/7 ≈ 0.286
      ├── Some((0, 3)): 6/11 ≈ 0.545
      ├── Some((0, 4)): 6/11 ≈ 0.545
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((6, 1)): 63/124 ≈ 0.508
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 1)): 4/10 ≈ 0.400
      ├── Some((1, 2)): 11/18 ≈ 0.611
      ├── Some((1, 3)): 9/16 ≈ 0.562
      ├── Some((1, 4)): 1/7 ≈ 0.143
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 12/18 ≈ 0.667
      ├── Some((1, 7)): 9/16 ≈ 0.562
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((6, 2)): 58/117 ≈ 0.496
      ├── Some((2, 0)): 4/10 ≈ 0.400
      ├── Some((2, 1)): 12/18 ≈ 0.667
      ├── Some((2, 2)): 1/7 ≈ 0.143
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 9/16 ≈ 0.562
      ├── Some((2, 5)): 2/8 ≈ 0.250
      ├── Some((2, 6)): 12/18 ≈ 0.667
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 5/12 ≈ 0.417
    ├── Some((6, 3)): 80/148 ≈ 0.541
      ├── Some((3, 0)): 17/26 ≈ 0.654
      ├── Some((3, 1)): 9/18 ≈ 0.500
      ├── Some((3, 2)): 4/12 ≈ 0.333
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 8/16 ≈ 0.500
      ├── Some((3, 5)): 15/24 ≈ 0.625
      ├── Some((3, 6)): 4/12 ≈ 0.333
      └── Some((3, 7)): 15/24 ≈ 0.625
    ├── Some((6, 4)): 43/94 ≈ 0.457
      ├── Some((4, 0)): 1/6 ≈ 0.167
      ├── Some((4, 1)): 9/15 ≈ 0.600
      ├── Some((4, 2)): 12/18 ≈ 0.667
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 6/12 ≈ 0.500
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 0/5 ≈ 0.000
      ├── Some((4, 7)): 2/8 ≈ 0.250
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((6, 5)): 108/187 ≈ 0.578
      ├── Some((5, 0)): 6/15 ≈ 0.400
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 13/22 ≈ 0.591
      ├── Some((5, 3)): 12/21 ≈ 0.571
      ├── Some((5, 4)): 22/31 ≈ 0.710
      ├── Some((5, 5)): 23/32 ≈ 0.719
      ├── Some((5, 6)): 11/20 ≈ 0.550
      ├── Some((5, 7)): 13/22 ≈ 0.591
      └── Some((5, 8)): 3/11 ≈ 0.273
    ├── Some((6, 6)): 48/102 ≈ 0.471
      ├── Some((6, 0)): 8/15 ≈ 0.533
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 3)): 9/16 ≈ 0.562
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 9/16 ≈ 0.562
    ├── Some((6, 7)): 78/145 ≈ 0.538
      ├── Some((7, 0)): 7/14 ≈ 0.500
      ├── Some((7, 1)): 17/24 ≈ 0.708
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 7/15 ≈ 0.467
      ├── Some((7, 4)): 11/19 ≈ 0.579
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 8/16 ≈ 0.500
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 14/22 ≈ 0.636
    └── Some((6, 8)): 71/135 ≈ 0.526
      ├── Some((8, 0)): 4/12 ≈ 0.333
      ├── Some((8, 1)): 12/20 ≈ 0.600
      ├── Some((8, 2)): 7/15 ≈ 0.467
      ├── Some((8, 3)): 9/17 ≈ 0.529
      ├── Some((8, 4)): 8/16 ≈ 0.500
      ├── Some((8, 5)): 12/20 ≈ 0.600
      ├── Some((8, 7)): 7/15 ≈ 0.467
      └── Some((8, 8)): 11/19 ≈ 0.579
  ├── Some((8, 7)): 529/1042 ≈ 0.508
    ├── Some((7, 0)): 46/97 ≈ 0.474
      ├── Some((0, 0)): 6/12 ≈ 0.500
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 10/15 ≈ 0.667
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 8/14 ≈ 0.571
      ├── Some((0, 5)): 7/13 ≈ 0.538
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 6/12 ≈ 0.500
      └── Some((0, 8)): 4/10 ≈ 0.400
    ├── Some((7, 1)): 39/87 ≈ 0.448
      ├── Some((1, 0)): 6/11 ≈ 0.545
      ├── Some((1, 1)): 1/6 ≈ 0.167
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 1/6 ≈ 0.167
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 8/13 ≈ 0.615
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 6/11 ≈ 0.545
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((7, 2)): 78/144 ≈ 0.542
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 2)): 8/15 ≈ 0.533
      ├── Some((2, 3)): 14/21 ≈ 0.667
      ├── Some((2, 4)): 8/15 ≈ 0.533
      ├── Some((2, 5)): 8/15 ≈ 0.533
      ├── Some((2, 6)): 9/17 ≈ 0.529
      ├── Some((2, 7)): 11/19 ≈ 0.579
      └── Some((2, 8)): 11/19 ≈ 0.579
    ├── Some((7, 3)): 49/102 ≈ 0.480
      ├── Some((3, 0)): 4/10 ≈ 0.400
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 7/14 ≈ 0.500
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 1/7 ≈ 0.143
      └── Some((3, 7)): 14/20 ≈ 0.700
    ├── Some((7, 4)): 59/116 ≈ 0.509
      ├── Some((4, 0)): 6/12 ≈ 0.500
      ├── Some((4, 1)): 11/17 ≈ 0.647
      ├── Some((4, 2)): 2/8 ≈ 0.250
      ├── Some((4, 3)): 11/17 ≈ 0.647
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 10/16 ≈ 0.625
      ├── Some((4, 7)): 6/13 ≈ 0.462
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((7, 5)): 77/142 ≈ 0.542
      ├── Some((5, 0)): 11/19 ≈ 0.579
      ├── Some((5, 1)): 10/17 ≈ 0.588
      ├── Some((5, 2)): 7/14 ≈ 0.500
      ├── Some((5, 3)): 13/20 ≈ 0.650
      ├── Some((5, 4)): 8/15 ≈ 0.533
      ├── Some((5, 5)): 4/11 ≈ 0.364
      ├── Some((5, 6)): 11/19 ≈ 0.579
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((7, 6)): 55/111 ≈ 0.495
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 12/18 ≈ 0.667
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 9/15 ≈ 0.600
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((7, 7)): 77/142 ≈ 0.542
      ├── Some((7, 0)): 6/14 ≈ 0.429
      ├── Some((7, 1)): 4/12 ≈ 0.333
      ├── Some((7, 2)): 15/24 ≈ 0.625
      ├── Some((7, 3)): 7/15 ≈ 0.467
      ├── Some((7, 4)): 10/18 ≈ 0.556
      ├── Some((7, 5)): 11/19 ≈ 0.579
      ├── Some((7, 6)): 18/26 ≈ 0.692
      └── Some((7, 8)): 5/13 ≈ 0.385
    └── Some((7, 8)): 48/100 ≈ 0.480
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 5/11 ≈ 0.455
      ├── Some((8, 3)): 8/15 ≈ 0.533
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 10/17 ≈ 0.588
      ├── Some((8, 6)): 9/16 ≈ 0.562
      └── Some((8, 8)): 1/7 ≈ 0.143
  └── Some((8, 8)): 717/1364 ≈ 0.526
    ├── Some((8, 0)): 98/183 ≈ 0.536
      ├── Some((0, 0)): 13/23 ≈ 0.565
      ├── Some((0, 1)): 8/17 ≈ 0.471
      ├── Some((0, 2)): 4/13 ≈ 0.308
      ├── Some((0, 3)): 11/20 ≈ 0.550
      ├── Some((0, 4)): 10/19 ≈ 0.526
      ├── Some((0, 5)): 11/21 ≈ 0.524
      ├── Some((0, 6)): 10/19 ≈ 0.526
      ├── Some((0, 7)): 18/28 ≈ 0.643
      └── Some((0, 8)): 12/22 ≈ 0.545
    ├── Some((8, 1)): 88/168 ≈ 0.524
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 1)): 4/12 ≈ 0.333
      ├── Some((1, 2)): 22/32 ≈ 0.688
      ├── Some((1, 3)): 4/12 ≈ 0.333
      ├── Some((1, 4)): 3/11 ≈ 0.273
      ├── Some((1, 5)): 6/15 ≈ 0.400
      ├── Some((1, 6)): 8/17 ≈ 0.471
      ├── Some((1, 7)): 10/19 ≈ 0.526
      └── Some((1, 8)): 20/30 ≈ 0.667
    ├── Some((8, 2)): 99/184 ≈ 0.538
      ├── Some((2, 0)): 8/17 ≈ 0.471
      ├── Some((2, 1)): 13/22 ≈ 0.591
      ├── Some((2, 2)): 13/23 ≈ 0.565
      ├── Some((2, 3)): 15/25 ≈ 0.600
      ├── Some((2, 4)): 7/16 ≈ 0.438
      ├── Some((2, 5)): 15/25 ≈ 0.600
      ├── Some((2, 6)): 17/27 ≈ 0.630
      ├── Some((2, 7)): 2/10 ≈ 0.200
      └── Some((2, 8)): 9/18 ≈ 0.500
    ├── Some((8, 3)): 70/142 ≈ 0.493
      ├── Some((3, 0)): 10/19 ≈ 0.526
      ├── Some((3, 1)): 11/20 ≈ 0.550
      ├── Some((3, 2)): 12/22 ≈ 0.545
      ├── Some((3, 3)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 8/17 ≈ 0.471
      ├── Some((3, 5)): 3/11 ≈ 0.273
      ├── Some((3, 6)): 13/23 ≈ 0.565
      └── Some((3, 7)): 4/12 ≈ 0.333
    ├── Some((8, 4)): 76/150 ≈ 0.507
      ├── Some((4, 0)): 8/16 ≈ 0.500
      ├── Some((4, 1)): 12/20 ≈ 0.600
      ├── Some((4, 2)): 4/12 ≈ 0.333
      ├── Some((4, 3)): 13/22 ≈ 0.591
      ├── Some((4, 4)): 12/20 ≈ 0.600
      ├── Some((4, 5)): 5/13 ≈ 0.385
      ├── Some((4, 6)): 10/18 ≈ 0.556
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 5/13 ≈ 0.385
    ├── Some((8, 5)): 91/173 ≈ 0.526
      ├── Some((5, 0)): 16/26 ≈ 0.615
      ├── Some((5, 1)): 6/15 ≈ 0.400
      ├── Some((5, 2)): 9/18 ≈ 0.500
      ├── Some((5, 3)): 17/27 ≈ 0.630
      ├── Some((5, 4)): 4/12 ≈ 0.333
      ├── Some((5, 5)): 2/10 ≈ 0.200
      ├── Some((5, 6)): 15/24 ≈ 0.625
      ├── Some((5, 7)): 12/21 ≈ 0.571
      └── Some((5, 8)): 10/19 ≈ 0.526
    ├── Some((8, 6)): 128/226 ≈ 0.566
      ├── Some((6, 0)): 13/24 ≈ 0.542
      ├── Some((6, 1)): 29/41 ≈ 0.707
      ├── Some((6, 2)): 13/24 ≈ 0.542
      ├── Some((6, 3)): 22/34 ≈ 0.647
      ├── Some((6, 4)): 23/35 ≈ 0.657
      ├── Some((6, 5)): 2/11 ≈ 0.182
      ├── Some((6, 6)): 18/29 ≈ 0.621
      ├── Some((6, 7)): 7/17 ≈ 0.412
      └── Some((6, 8)): 1/10 ≈ 0.100
    └── Some((8, 7)): 67/137 ≈ 0.489
      ├── Some((7, 0)): 7/15 ≈ 0.467
      ├── Some((7, 1)): 6/14 ≈ 0.429
      ├── Some((7, 2)): 4/11 ≈ 0.364
      ├── Some((7, 3)): 5/13 ≈ 0.385
      ├── Some((7, 4)): 12/20 ≈ 0.600
      ├── Some((7, 5)): 13/21 ≈ 0.619
      ├── Some((7, 6)): 10/18 ≈ 0.556
      ├── Some((7, 7)): 3/10 ≈ 0.300
      └── Some((7, 8)): 6/14 ≈ 0.429
├── Some((4, 0)): 39437/71712 ≈ 0.550
  ├── Some((0, 0)): 4251/7744 ≈ 0.549
    ├── Some((0, 1)): 458/852 ≈ 0.538
      ├── Some((1, 0)): 27/62 ≈ 0.435
      ├── Some((1, 1)): 43/85 ≈ 0.506
      ├── Some((1, 2)): 65/114 ≈ 0.570
      ├── Some((1, 3)): 42/83 ≈ 0.506
      ├── Some((1, 4)): 27/62 ≈ 0.435
      ├── Some((1, 5)): 59/106 ≈ 0.557
      ├── Some((1, 6)): 34/72 ≈ 0.472
      ├── Some((1, 7)): 85/140 ≈ 0.607
      └── Some((1, 8)): 75/127 ≈ 0.591
    ├── Some((0, 2)): 335/650 ≈ 0.515
      ├── Some((2, 0)): 49/88 ≈ 0.557
      ├── Some((2, 1)): 28/60 ≈ 0.467
      ├── Some((2, 2)): 49/88 ≈ 0.557
      ├── Some((2, 3)): 39/75 ≈ 0.520
      ├── Some((2, 4)): 24/54 ≈ 0.444
      ├── Some((2, 5)): 44/82 ≈ 0.537
      ├── Some((2, 6)): 45/83 ≈ 0.542
      ├── Some((2, 7)): 34/68 ≈ 0.500
      └── Some((2, 8)): 22/51 ≈ 0.431
    ├── Some((0, 3)): 523/957 ≈ 0.546
      ├── Some((3, 0)): 40/82 ≈ 0.488
      ├── Some((3, 1)): 63/113 ≈ 0.558
      ├── Some((3, 2)): 49/94 ≈ 0.521
      ├── Some((3, 3)): 58/106 ≈ 0.547
      ├── Some((3, 4)): 84/141 ≈ 0.596
      ├── Some((3, 5)): 63/113 ≈ 0.558
      ├── Some((3, 6)): 48/93 ≈ 0.516
      ├── Some((3, 7)): 57/105 ≈ 0.543
      └── Some((3, 8)): 60/109 ≈ 0.550
    ├── Some((0, 4)): 851/1480 ≈ 0.575
      ├── Some((4, 1)): 132/221 ≈ 0.597
      ├── Some((4, 2)): 117/200 ≈ 0.585
      ├── Some((4, 3)): 122/207 ≈ 0.589
      ├── Some((4, 4)): 59/118 ≈ 0.500
      ├── Some((4, 5)): 102/179 ≈ 0.570
      ├── Some((4, 6)): 132/221 ≈ 0.597
      ├── Some((4, 7)): 65/127 ≈ 0.512
      └── Some((4, 8)): 121/206 ≈ 0.587
    ├── Some((0, 5)): 516/945 ≈ 0.546
      ├── Some((5, 0)): 88/146 ≈ 0.603
      ├── Some((5, 1)): 65/116 ≈ 0.560
      ├── Some((5, 2)): 80/135 ≈ 0.593
      ├── Some((5, 3)): 50/95 ≈ 0.526
      ├── Some((5, 4)): 42/84 ≈ 0.500
      ├── Some((5, 5)): 48/92 ≈ 0.522
      ├── Some((5, 6)): 53/99 ≈ 0.535
      ├── Some((5, 7)): 39/80 ≈ 0.488
      └── Some((5, 8)): 51/97 ≈ 0.526
    ├── Some((0, 6)): 734/1294 ≈ 0.567
      ├── Some((6, 0)): 101/170 ≈ 0.594
      ├── Some((6, 1)): 55/107 ≈ 0.514
      ├── Some((6, 2)): 73/132 ≈ 0.553
      ├── Some((6, 3)): 91/157 ≈ 0.580
      ├── Some((6, 4)): 76/137 ≈ 0.555
      ├── Some((6, 5)): 100/169 ≈ 0.592
      ├── Some((6, 6)): 106/177 ≈ 0.599
      ├── Some((6, 7)): 57/110 ≈ 0.518
      └── Some((6, 8)): 74/134 ≈ 0.552
    ├── Some((0, 7)): 317/620 ≈ 0.511
      ├── Some((7, 0)): 24/54 ≈ 0.444
      ├── Some((7, 1)): 24/54 ≈ 0.444
      ├── Some((7, 2)): 26/57 ≈ 0.456
      ├── Some((7, 3)): 35/69 ≈ 0.507
      ├── Some((7, 4)): 91/140 ≈ 0.650
      ├── Some((7, 5)): 35/69 ≈ 0.507
      ├── Some((7, 6)): 37/72 ≈ 0.514
      ├── Some((7, 7)): 24/54 ≈ 0.444
      └── Some((7, 8)): 21/50 ≈ 0.420
    └── Some((0, 8)): 516/945 ≈ 0.546
      ├── Some((8, 0)): 53/99 ≈ 0.535
      ├── Some((8, 1)): 34/73 ≈ 0.466
      ├── Some((8, 2)): 56/104 ≈ 0.538
      ├── Some((8, 3)): 50/95 ≈ 0.526
      ├── Some((8, 4)): 66/117 ≈ 0.564
      ├── Some((8, 5)): 85/142 ≈ 0.599
      ├── Some((8, 6)): 45/88 ≈ 0.511
      ├── Some((8, 7)): 64/114 ≈ 0.561
      └── Some((8, 8)): 62/112 ≈ 0.554
  ├── Some((0, 1)): 4944/8941 ≈ 0.553
    ├── Some((1, 0)): 465/858 ≈ 0.542
      ├── Some((0, 0)): 55/103 ≈ 0.534
      ├── Some((0, 2)): 24/59 ≈ 0.407
      ├── Some((0, 3)): 79/136 ≈ 0.581
      ├── Some((0, 4)): 59/109 ≈ 0.541
      ├── Some((0, 5)): 62/113 ≈ 0.549
      ├── Some((0, 6)): 60/110 ≈ 0.545
      ├── Some((0, 7)): 84/142 ≈ 0.592
      └── Some((0, 8)): 42/85 ≈ 0.494
    ├── Some((1, 1)): 613/1095 ≈ 0.560
      ├── Some((1, 0)): 65/121 ≈ 0.537
      ├── Some((1, 2)): 61/116 ≈ 0.526
      ├── Some((1, 3)): 49/99 ≈ 0.495
      ├── Some((1, 4)): 91/157 ≈ 0.580
      ├── Some((1, 5)): 84/147 ≈ 0.571
      ├── Some((1, 6)): 73/132 ≈ 0.553
      ├── Some((1, 7)): 51/102 ≈ 0.500
      └── Some((1, 8)): 139/220 ≈ 0.632
    ├── Some((1, 2)): 575/1035 ≈ 0.556
      ├── Some((2, 0)): 49/95 ≈ 0.516
      ├── Some((2, 1)): 96/158 ≈ 0.608
      ├── Some((2, 2)): 79/136 ≈ 0.581
      ├── Some((2, 3)): 74/129 ≈ 0.574
      ├── Some((2, 4)): 50/96 ≈ 0.521
      ├── Some((2, 5)): 71/125 ≈ 0.568
      ├── Some((2, 6)): 25/61 ≈ 0.410
      ├── Some((2, 7)): 78/134 ≈ 0.582
      └── Some((2, 8)): 53/100 ≈ 0.530
    ├── Some((1, 3)): 524/953 ≈ 0.550
      ├── Some((3, 0)): 69/120 ≈ 0.575
      ├── Some((3, 1)): 63/112 ≈ 0.562
      ├── Some((3, 2)): 59/107 ≈ 0.551
      ├── Some((3, 3)): 51/96 ≈ 0.531
      ├── Some((3, 4)): 66/117 ≈ 0.564
      ├── Some((3, 5)): 40/81 ≈ 0.494
      ├── Some((3, 6)): 47/91 ≈ 0.516
      ├── Some((3, 7)): 51/96 ≈ 0.531
      └── Some((3, 8)): 78/132 ≈ 0.591
    ├── Some((1, 4)): 694/1224 ≈ 0.567
      ├── Some((4, 1)): 73/134 ≈ 0.545
      ├── Some((4, 2)): 71/131 ≈ 0.542
      ├── Some((4, 3)): 107/181 ≈ 0.591
      ├── Some((4, 4)): 83/148 ≈ 0.561
      ├── Some((4, 5)): 101/172 ≈ 0.587
      ├── Some((4, 6)): 81/145 ≈ 0.559
      ├── Some((4, 7)): 101/172 ≈ 0.587
      └── Some((4, 8)): 77/140 ≈ 0.550
    ├── Some((1, 5)): 493/903 ≈ 0.546
      ├── Some((5, 0)): 41/82 ≈ 0.500
      ├── Some((5, 1)): 72/124 ≈ 0.581
      ├── Some((5, 2)): 47/90 ≈ 0.522
      ├── Some((5, 3)): 106/168 ≈ 0.631
      ├── Some((5, 4)): 45/87 ≈ 0.517
      ├── Some((5, 5)): 46/89 ≈ 0.517
      ├── Some((5, 6)): 37/76 ≈ 0.487
      ├── Some((5, 7)): 65/114 ≈ 0.570
      └── Some((5, 8)): 34/72 ≈ 0.472
    ├── Some((1, 6)): 565/1019 ≈ 0.554
      ├── Some((6, 0)): 44/88 ≈ 0.500
      ├── Some((6, 1)): 76/131 ≈ 0.580
      ├── Some((6, 2)): 92/153 ≈ 0.601
      ├── Some((6, 3)): 67/119 ≈ 0.563
      ├── Some((6, 4)): 33/72 ≈ 0.458
      ├── Some((6, 5)): 69/122 ≈ 0.566
      ├── Some((6, 6)): 72/126 ≈ 0.571
      ├── Some((6, 7)): 53/100 ≈ 0.530
      └── Some((6, 8)): 58/107 ≈ 0.542
    ├── Some((1, 7)): 566/1021 ≈ 0.554
      ├── Some((7, 0)): 100/163 ≈ 0.613
      ├── Some((7, 1)): 46/91 ≈ 0.505
      ├── Some((7, 2)): 54/102 ≈ 0.529
      ├── Some((7, 3)): 40/82 ≈ 0.488
      ├── Some((7, 4)): 60/110 ≈ 0.545
      ├── Some((7, 5)): 37/78 ≈ 0.474
      ├── Some((7, 6)): 106/171 ≈ 0.620
      ├── Some((7, 7)): 58/107 ≈ 0.542
      └── Some((7, 8)): 64/116 ≈ 0.552
    └── Some((1, 8)): 449/832 ≈ 0.540
      ├── Some((8, 0)): 46/88 ≈ 0.523
      ├── Some((8, 1)): 61/108 ≈ 0.565
      ├── Some((8, 2)): 96/153 ≈ 0.627
      ├── Some((8, 3)): 25/58 ≈ 0.431
      ├── Some((8, 4)): 40/80 ≈ 0.500
      ├── Some((8, 5)): 33/70 ≈ 0.471
      ├── Some((8, 6)): 51/94 ≈ 0.543
      ├── Some((8, 7)): 42/82 ≈ 0.512
      └── Some((8, 8)): 54/98 ≈ 0.551
  ├── Some((0, 2)): 4042/7381 ≈ 0.548
    ├── Some((2, 0)): 606/1071 ≈ 0.566
      ├── Some((0, 0)): 94/159 ≈ 0.591
      ├── Some((0, 1)): 35/77 ≈ 0.455
      ├── Some((0, 3)): 49/97 ≈ 0.505
      ├── Some((0, 4)): 131/208 ≈ 0.630
      ├── Some((0, 5)): 68/124 ≈ 0.548
      ├── Some((0, 6)): 88/151 ≈ 0.583
      ├── Some((0, 7)): 42/88 ≈ 0.477
      └── Some((0, 8)): 99/166 ≈ 0.596
    ├── Some((2, 1)): 530/950 ≈ 0.558
      ├── Some((1, 0)): 87/143 ≈ 0.608
      ├── Some((1, 1)): 69/119 ≈ 0.580
      ├── Some((1, 2)): 66/116 ≈ 0.569
      ├── Some((1, 3)): 30/66 ≈ 0.455
      ├── Some((1, 4)): 40/80 ≈ 0.500
      ├── Some((1, 5)): 90/147 ≈ 0.612
      ├── Some((1, 6)): 50/94 ≈ 0.532
      ├── Some((1, 7)): 53/98 ≈ 0.541
      └── Some((1, 8)): 44/86 ≈ 0.512
    ├── Some((2, 2)): 352/665 ≈ 0.529
      ├── Some((2, 0)): 51/93 ≈ 0.548
      ├── Some((2, 1)): 19/49 ≈ 0.388
      ├── Some((2, 3)): 21/51 ≈ 0.412
      ├── Some((2, 4)): 41/80 ≈ 0.512
      ├── Some((2, 5)): 26/59 ≈ 0.441
      ├── Some((2, 6)): 53/96 ≈ 0.552
      ├── Some((2, 7)): 60/105 ≈ 0.571
      └── Some((2, 8)): 80/131 ≈ 0.611
    ├── Some((2, 3)): 513/924 ≈ 0.555
      ├── Some((3, 0)): 69/119 ≈ 0.580
      ├── Some((3, 1)): 71/122 ≈ 0.582
      ├── Some((3, 2)): 76/128 ≈ 0.594
      ├── Some((3, 3)): 30/66 ≈ 0.455
      ├── Some((3, 4)): 64/113 ≈ 0.566
      ├── Some((3, 5)): 69/119 ≈ 0.580
      ├── Some((3, 6)): 38/77 ≈ 0.494
      ├── Some((3, 7)): 69/119 ≈ 0.580
      └── Some((3, 8)): 26/60 ≈ 0.433
    ├── Some((2, 4)): 477/866 ≈ 0.551
      ├── Some((4, 1)): 89/148 ≈ 0.601
      ├── Some((4, 2)): 66/117 ≈ 0.564
      ├── Some((4, 3)): 74/128 ≈ 0.578
      ├── Some((4, 4)): 36/76 ≈ 0.474
      ├── Some((4, 5)): 59/108 ≈ 0.546
      ├── Some((4, 6)): 78/133 ≈ 0.586
      ├── Some((4, 7)): 50/95 ≈ 0.526
      └── Some((4, 8)): 25/60 ≈ 0.417
    ├── Some((2, 5)): 358/675 ≈ 0.530
      ├── Some((5, 0)): 38/73 ≈ 0.521
      ├── Some((5, 1)): 65/108 ≈ 0.602
      ├── Some((5, 2)): 35/69 ≈ 0.507
      ├── Some((5, 3)): 52/92 ≈ 0.565
      ├── Some((5, 4)): 36/70 ≈ 0.514
      ├── Some((5, 5)): 43/80 ≈ 0.538
      ├── Some((5, 6)): 11/35 ≈ 0.314
      ├── Some((5, 7)): 30/62 ≈ 0.484
      └── Some((5, 8)): 47/85 ≈ 0.553
    ├── Some((2, 6)): 600/1061 ≈ 0.566
      ├── Some((6, 0)): 52/99 ≈ 0.525
      ├── Some((6, 1)): 66/117 ≈ 0.564
      ├── Some((6, 2)): 42/85 ≈ 0.494
      ├── Some((6, 3)): 81/137 ≈ 0.591
      ├── Some((6, 4)): 90/149 ≈ 0.604
      ├── Some((6, 5)): 49/94 ≈ 0.521
      ├── Some((6, 6)): 44/87 ≈ 0.506
      ├── Some((6, 7)): 68/120 ≈ 0.567
      └── Some((6, 8)): 108/172 ≈ 0.628
    ├── Some((2, 7)): 269/529 ≈ 0.509
      ├── Some((7, 0)): 13/36 ≈ 0.361
      ├── Some((7, 1)): 47/81 ≈ 0.580
      ├── Some((7, 2)): 45/79 ≈ 0.570
      ├── Some((7, 3)): 47/81 ≈ 0.580
      ├── Some((7, 4)): 22/49 ≈ 0.449
      ├── Some((7, 5)): 31/61 ≈ 0.508
      ├── Some((7, 6)): 29/58 ≈ 0.500
      ├── Some((7, 7)): 13/36 ≈ 0.361
      └── Some((7, 8)): 21/47 ≈ 0.447
    └── Some((2, 8)): 336/639 ≈ 0.526
      ├── Some((8, 0)): 28/59 ≈ 0.475
      ├── Some((8, 1)): 39/73 ≈ 0.534
      ├── Some((8, 2)): 36/70 ≈ 0.514
      ├── Some((8, 3)): 52/90 ≈ 0.578
      ├── Some((8, 4)): 50/88 ≈ 0.568
      ├── Some((8, 5)): 33/65 ≈ 0.508
      ├── Some((8, 6)): 17/43 ≈ 0.395
      ├── Some((8, 7)): 44/80 ≈ 0.550
      └── Some((8, 8)): 36/70 ≈ 0.514
  ├── Some((0, 3)): 4725/8563 ≈ 0.552
    ├── Some((3, 0)): 616/1098 ≈ 0.561
      ├── Some((0, 0)): 68/125 ≈ 0.544
      ├── Some((0, 1)): 98/166 ≈ 0.590
      ├── Some((0, 2)): 63/118 ≈ 0.534
      ├── Some((0, 4)): 57/110 ≈ 0.518
      ├── Some((0, 5)): 72/130 ≈ 0.554
      ├── Some((0, 6)): 87/151 ≈ 0.576
      ├── Some((0, 7)): 88/152 ≈ 0.579
      └── Some((0, 8)): 83/145 ≈ 0.572
    ├── Some((3, 1)): 568/1021 ≈ 0.556
      ├── Some((1, 0)): 88/147 ≈ 0.599
      ├── Some((1, 1)): 51/97 ≈ 0.526
      ├── Some((1, 2)): 35/75 ≈ 0.467
      ├── Some((1, 3)): 96/157 ≈ 0.611
      ├── Some((1, 4)): 91/151 ≈ 0.603
      ├── Some((1, 5)): 72/126 ≈ 0.571
      ├── Some((1, 6)): 35/75 ≈ 0.467
      ├── Some((1, 7)): 41/84 ≈ 0.488
      └── Some((1, 8)): 59/108 ≈ 0.546
    ├── Some((3, 2)): 495/905 ≈ 0.547
      ├── Some((2, 0)): 62/110 ≈ 0.564
      ├── Some((2, 1)): 52/97 ≈ 0.536
      ├── Some((2, 2)): 44/86 ≈ 0.512
      ├── Some((2, 3)): 51/96 ≈ 0.531
      ├── Some((2, 4)): 61/109 ≈ 0.560
      ├── Some((2, 5)): 68/118 ≈ 0.576
      ├── Some((2, 6)): 32/69 ≈ 0.464
      ├── Some((2, 7)): 90/147 ≈ 0.612
      └── Some((2, 8)): 34/72 ≈ 0.472
    ├── Some((3, 3)): 387/730 ≈ 0.530
      ├── Some((3, 0)): 57/103 ≈ 0.553
      ├── Some((3, 1)): 70/120 ≈ 0.583
      ├── Some((3, 2)): 37/76 ≈ 0.487
      ├── Some((3, 4)): 57/103 ≈ 0.553
      ├── Some((3, 5)): 46/88 ≈ 0.523
      ├── Some((3, 6)): 32/69 ≈ 0.464
      ├── Some((3, 7)): 36/74 ≈ 0.486
      └── Some((3, 8)): 52/96 ≈ 0.542
    ├── Some((3, 4)): 622/1107 ≈ 0.562
      ├── Some((4, 1)): 71/129 ≈ 0.550
      ├── Some((4, 2)): 76/136 ≈ 0.559
      ├── Some((4, 3)): 93/159 ≈ 0.585
      ├── Some((4, 4)): 49/99 ≈ 0.495
      ├── Some((4, 5)): 61/116 ≈ 0.526
      ├── Some((4, 6)): 65/121 ≈ 0.537
      ├── Some((4, 7)): 118/193 ≈ 0.611
      └── Some((4, 8)): 88/153 ≈ 0.575
    ├── Some((3, 5)): 413/772 ≈ 0.535
      ├── Some((5, 0)): 63/109 ≈ 0.578
      ├── Some((5, 1)): 33/69 ≈ 0.478
      ├── Some((5, 2)): 30/64 ≈ 0.469
      ├── Some((5, 3)): 55/98 ≈ 0.561
      ├── Some((5, 4)): 37/74 ≈ 0.500
      ├── Some((5, 5)): 64/110 ≈ 0.582
      ├── Some((5, 6)): 63/109 ≈ 0.578
      ├── Some((5, 7)): 25/57 ≈ 0.439
      └── Some((5, 8)): 42/81 ≈ 0.519
    ├── Some((3, 6)): 558/1006 ≈ 0.555
      ├── Some((6, 0)): 88/147 ≈ 0.599
      ├── Some((6, 1)): 65/116 ≈ 0.560
      ├── Some((6, 2)): 62/112 ≈ 0.554
      ├── Some((6, 3)): 43/86 ≈ 0.500
      ├── Some((6, 4)): 74/128 ≈ 0.578
      ├── Some((6, 5)): 85/143 ≈ 0.594
      ├── Some((6, 6)): 56/104 ≈ 0.538
      ├── Some((6, 7)): 31/69 ≈ 0.449
      └── Some((6, 8)): 53/100 ≈ 0.530
    ├── Some((3, 7)): 337/648 ≈ 0.520
      ├── Some((7, 0)): 45/82 ≈ 0.549
      ├── Some((7, 1)): 32/65 ≈ 0.492
      ├── Some((7, 2)): 29/61 ≈ 0.475
      ├── Some((7, 3)): 13/38 ≈ 0.342
      ├── Some((7, 4)): 47/85 ≈ 0.553
      ├── Some((7, 5)): 53/93 ≈ 0.570
      ├── Some((7, 6)): 66/110 ≈ 0.600
      ├── Some((7, 7)): 25/55 ≈ 0.455
      └── Some((7, 8)): 27/58 ≈ 0.466
    └── Some((3, 8)): 728/1275 ≈ 0.571
      ├── Some((8, 0)): 108/178 ≈ 0.607
      ├── Some((8, 1)): 91/156 ≈ 0.583
      ├── Some((8, 2)): 78/138 ≈ 0.565
      ├── Some((8, 3)): 66/122 ≈ 0.541
      ├── Some((8, 4)): 102/170 ≈ 0.600
      ├── Some((8, 5)): 81/142 ≈ 0.570
      ├── Some((8, 6)): 57/109 ≈ 0.523
      ├── Some((8, 7)): 98/165 ≈ 0.594
      └── Some((8, 8)): 46/94 ≈ 0.489
  ├── Some((0, 4)): 5659/10174 ≈ 0.556
    ├── Some((4, 1)): 502/940 ≈ 0.534
      ├── Some((1, 0)): 100/164 ≈ 0.610
      ├── Some((1, 1)): 79/137 ≈ 0.577
      ├── Some((1, 2)): 55/104 ≈ 0.529
      ├── Some((1, 3)): 81/139 ≈ 0.583
      ├── Some((1, 4)): 38/80 ≈ 0.475
      ├── Some((1, 5)): 31/70 ≈ 0.443
      ├── Some((1, 6)): 30/68 ≈ 0.441
      ├── Some((1, 7)): 54/103 ≈ 0.524
      └── Some((1, 8)): 34/74 ≈ 0.459
    ├── Some((4, 2)): 932/1635 ≈ 0.570
      ├── Some((2, 0)): 49/104 ≈ 0.471
      ├── Some((2, 1)): 110/191 ≈ 0.576
      ├── Some((2, 2)): 132/221 ≈ 0.597
      ├── Some((2, 3)): 92/166 ≈ 0.554
      ├── Some((2, 4)): 116/199 ≈ 0.583
      ├── Some((2, 5)): 99/176 ≈ 0.562
      ├── Some((2, 6)): 71/136 ≈ 0.522
      ├── Some((2, 7)): 112/194 ≈ 0.577
      └── Some((2, 8)): 151/247 ≈ 0.611
    ├── Some((4, 3)): 540/1002 ≈ 0.539
      ├── Some((3, 0)): 34/75 ≈ 0.453
      ├── Some((3, 1)): 63/116 ≈ 0.543
      ├── Some((3, 2)): 63/116 ≈ 0.543
      ├── Some((3, 3)): 45/91 ≈ 0.495
      ├── Some((3, 4)): 49/96 ≈ 0.510
      ├── Some((3, 5)): 113/183 ≈ 0.617
      ├── Some((3, 6)): 73/129 ≈ 0.566
      ├── Some((3, 7)): 51/99 ≈ 0.515
      └── Some((3, 8)): 49/96 ≈ 0.510
    ├── Some((4, 4)): 1260/2155 ≈ 0.585
      ├── Some((4, 1)): 200/337 ≈ 0.593
      ├── Some((4, 2)): 177/305 ≈ 0.580
      ├── Some((4, 3)): 253/411 ≈ 0.616
      ├── Some((4, 5)): 108/204 ≈ 0.529
      ├── Some((4, 6)): 220/365 ≈ 0.603
      ├── Some((4, 7)): 207/347 ≈ 0.597
      └── Some((4, 8)): 95/185 ≈ 0.514
    ├── Some((4, 5)): 582/1071 ≈ 0.543
      ├── Some((5, 0)): 66/121 ≈ 0.545
      ├── Some((5, 1)): 61/115 ≈ 0.530
      ├── Some((5, 2)): 41/86 ≈ 0.477
      ├── Some((5, 3)): 56/108 ≈ 0.519
      ├── Some((5, 4)): 85/147 ≈ 0.578
      ├── Some((5, 5)): 71/128 ≈ 0.555
      ├── Some((5, 6)): 84/146 ≈ 0.575
      ├── Some((5, 7)): 22/58 ≈ 0.379
      └── Some((5, 8)): 95/161 ≈ 0.590
    ├── Some((4, 6)): 565/1043 ≈ 0.542
      ├── Some((6, 0)): 30/70 ≈ 0.429
      ├── Some((6, 1)): 95/160 ≈ 0.594
      ├── Some((6, 2)): 59/112 ≈ 0.527
      ├── Some((6, 3)): 45/92 ≈ 0.489
      ├── Some((6, 4)): 48/96 ≈ 0.500
      ├── Some((6, 5)): 120/194 ≈ 0.619
      ├── Some((6, 6)): 77/136 ≈ 0.566
      ├── Some((6, 7)): 27/65 ≈ 0.415
      └── Some((6, 8)): 63/117 ≈ 0.538
    ├── Some((4, 7)): 728/1308 ≈ 0.557
      ├── Some((7, 0)): 80/144 ≈ 0.556
      ├── Some((7, 1)): 80/144 ≈ 0.556
      ├── Some((7, 2)): 51/104 ≈ 0.490
      ├── Some((7, 3)): 98/169 ≈ 0.580
      ├── Some((7, 4)): 60/116 ≈ 0.517
      ├── Some((7, 5)): 95/165 ≈ 0.576
      ├── Some((7, 6)): 76/139 ≈ 0.547
      ├── Some((7, 7)): 75/138 ≈ 0.543
      └── Some((7, 8)): 112/188 ≈ 0.596
    └── Some((4, 8)): 550/1019 ≈ 0.540
      ├── Some((8, 0)): 55/105 ≈ 0.524
      ├── Some((8, 1)): 66/120 ≈ 0.550
      ├── Some((8, 2)): 58/109 ≈ 0.532
      ├── Some((8, 3)): 24/60 ≈ 0.400
      ├── Some((8, 4)): 57/108 ≈ 0.528
      ├── Some((8, 5)): 86/148 ≈ 0.581
      ├── Some((8, 6)): 83/143 ≈ 0.580
      ├── Some((8, 7)): 56/107 ≈ 0.523
      └── Some((8, 8)): 64/118 ≈ 0.542
  ├── Some((0, 5)): 4458/8102 ≈ 0.550
    ├── Some((5, 0)): 598/1065 ≈ 0.562
      ├── Some((0, 0)): 73/132 ≈ 0.553
      ├── Some((0, 1)): 30/71 ≈ 0.423
      ├── Some((0, 2)): 134/213 ≈ 0.629
      ├── Some((0, 3)): 116/190 ≈ 0.611
      ├── Some((0, 4)): 28/67 ≈ 0.418
      ├── Some((0, 6)): 85/148 ≈ 0.574
      ├── Some((0, 7)): 86/149 ≈ 0.577
      └── Some((0, 8)): 46/94 ≈ 0.489
    ├── Some((5, 1)): 528/954 ≈ 0.553
      ├── Some((1, 0)): 69/120 ≈ 0.575
      ├── Some((1, 1)): 48/92 ≈ 0.522
      ├── Some((1, 2)): 47/91 ≈ 0.516
      ├── Some((1, 3)): 60/108 ≈ 0.556
      ├── Some((1, 4)): 70/121 ≈ 0.579
      ├── Some((1, 5)): 82/137 ≈ 0.599
      ├── Some((1, 6)): 48/92 ≈ 0.522
      ├── Some((1, 7)): 36/75 ≈ 0.480
      └── Some((1, 8)): 67/117 ≈ 0.573
    ├── Some((5, 2)): 507/920 ≈ 0.551
      ├── Some((2, 0)): 25/59 ≈ 0.424
      ├── Some((2, 1)): 96/154 ≈ 0.623
      ├── Some((2, 2)): 59/106 ≈ 0.557
      ├── Some((2, 3)): 74/126 ≈ 0.587
      ├── Some((2, 4)): 60/108 ≈ 0.556
      ├── Some((2, 5)): 53/98 ≈ 0.541
      ├── Some((2, 6)): 49/93 ≈ 0.527
      ├── Some((2, 7)): 44/86 ≈ 0.512
      └── Some((2, 8)): 46/89 ≈ 0.517
    ├── Some((5, 3)): 391/734 ≈ 0.533
      ├── Some((3, 0)): 50/91 ≈ 0.549
      ├── Some((3, 1)): 31/65 ≈ 0.477
      ├── Some((3, 2)): 43/81 ≈ 0.531
      ├── Some((3, 3)): 68/114 ≈ 0.596
      ├── Some((3, 4)): 38/74 ≈ 0.514
      ├── Some((3, 5)): 32/66 ≈ 0.485
      ├── Some((3, 6)): 43/81 ≈ 0.531
      ├── Some((3, 7)): 40/77 ≈ 0.519
      └── Some((3, 8)): 45/84 ≈ 0.536
    ├── Some((5, 4)): 269/534 ≈ 0.504
      ├── Some((4, 1)): 31/64 ≈ 0.484
      ├── Some((4, 2)): 21/49 ≈ 0.429
      ├── Some((4, 3)): 59/101 ≈ 0.584
      ├── Some((4, 4)): 40/76 ≈ 0.526
      ├── Some((4, 5)): 13/38 ≈ 0.342
      ├── Some((4, 6)): 36/70 ≈ 0.514
      ├── Some((4, 7)): 41/77 ≈ 0.532
      └── Some((4, 8)): 27/58 ≈ 0.466
    ├── Some((5, 5)): 389/730 ≈ 0.533
      ├── Some((5, 0)): 53/97 ≈ 0.546
      ├── Some((5, 1)): 32/69 ≈ 0.464
      ├── Some((5, 2)): 75/127 ≈ 0.591
      ├── Some((5, 3)): 41/81 ≈ 0.506
      ├── Some((5, 4)): 41/81 ≈ 0.506
      ├── Some((5, 6)): 34/71 ≈ 0.479
      ├── Some((5, 7)): 52/96 ≈ 0.542
      └── Some((5, 8)): 60/107 ≈ 0.561
    ├── Some((5, 6)): 489/891 ≈ 0.549
      ├── Some((6, 0)): 41/82 ≈ 0.500
      ├── Some((6, 1)): 69/119 ≈ 0.580
      ├── Some((6, 2)): 9/34 ≈ 0.265
      ├── Some((6, 3)): 55/101 ≈ 0.545
      ├── Some((6, 4)): 96/154 ≈ 0.623
      ├── Some((6, 5)): 65/114 ≈ 0.570
      ├── Some((6, 6)): 46/88 ≈ 0.523
      ├── Some((6, 7)): 49/92 ≈ 0.533
      └── Some((6, 8)): 59/106 ≈ 0.557
    ├── Some((5, 7)): 726/1267 ≈ 0.573
      ├── Some((7, 0)): 124/199 ≈ 0.623
      ├── Some((7, 1)): 47/95 ≈ 0.495
      ├── Some((7, 2)): 63/117 ≈ 0.538
      ├── Some((7, 3)): 43/89 ≈ 0.483
      ├── Some((7, 4)): 60/113 ≈ 0.531
      ├── Some((7, 5)): 108/178 ≈ 0.607
      ├── Some((7, 6)): 61/115 ≈ 0.530
      ├── Some((7, 7)): 69/126 ≈ 0.548
      └── Some((7, 8)): 151/234 ≈ 0.645
    └── Some((5, 8)): 561/1006 ≈ 0.558
      ├── Some((8, 0)): 55/102 ≈ 0.539
      ├── Some((8, 1)): 53/99 ≈ 0.535
      ├── Some((8, 2)): 55/102 ≈ 0.539
      ├── Some((8, 3)): 52/98 ≈ 0.531
      ├── Some((8, 4)): 87/144 ≈ 0.604
      ├── Some((8, 5)): 53/99 ≈ 0.535
      ├── Some((8, 6)): 57/105 ≈ 0.543
      ├── Some((8, 7)): 74/127 ≈ 0.583
      └── Some((8, 8)): 75/129 ≈ 0.581
  ├── Some((0, 6)): 4259/7757 ≈ 0.549
    ├── Some((6, 0)): 479/872 ≈ 0.549
      ├── Some((0, 0)): 63/114 ≈ 0.553
      ├── Some((0, 1)): 48/93 ≈ 0.516
      ├── Some((0, 2)): 39/80 ≈ 0.488
      ├── Some((0, 3)): 69/122 ≈ 0.566
      ├── Some((0, 4)): 74/128 ≈ 0.578
      ├── Some((0, 5)): 60/109 ≈ 0.550
      ├── Some((0, 7)): 77/132 ≈ 0.583
      └── Some((0, 8)): 48/93 ≈ 0.516
    ├── Some((6, 1)): 391/730 ≈ 0.536
      ├── Some((1, 0)): 51/91 ≈ 0.560
      ├── Some((1, 1)): 31/64 ≈ 0.484
      ├── Some((1, 2)): 40/77 ≈ 0.519
      ├── Some((1, 3)): 45/83 ≈ 0.542
      ├── Some((1, 4)): 53/94 ≈ 0.564
      ├── Some((1, 5)): 25/56 ≈ 0.446
      ├── Some((1, 6)): 60/103 ≈ 0.583
      ├── Some((1, 7)): 34/69 ≈ 0.493
      └── Some((1, 8)): 52/92 ≈ 0.565
    ├── Some((6, 2)): 429/791 ≈ 0.542
      ├── Some((2, 0)): 34/70 ≈ 0.486
      ├── Some((2, 1)): 50/91 ≈ 0.549
      ├── Some((2, 2)): 35/71 ≈ 0.493
      ├── Some((2, 3)): 28/61 ≈ 0.459
      ├── Some((2, 4)): 55/98 ≈ 0.561
      ├── Some((2, 5)): 67/113 ≈ 0.593
      ├── Some((2, 6)): 43/82 ≈ 0.524
      ├── Some((2, 7)): 58/102 ≈ 0.569
      └── Some((2, 8)): 58/102 ≈ 0.569
    ├── Some((6, 3)): 477/868 ≈ 0.550
      ├── Some((3, 0)): 41/80 ≈ 0.512
      ├── Some((3, 1)): 41/80 ≈ 0.512
      ├── Some((3, 2)): 48/90 ≈ 0.533
      ├── Some((3, 3)): 59/105 ≈ 0.562
      ├── Some((3, 4)): 78/129 ≈ 0.605
      ├── Some((3, 5)): 29/64 ≈ 0.453
      ├── Some((3, 6)): 57/102 ≈ 0.559
      ├── Some((3, 7)): 75/126 ≈ 0.595
      └── Some((3, 8)): 49/91 ≈ 0.538
    ├── Some((6, 4)): 469/856 ≈ 0.548
      ├── Some((4, 1)): 56/104 ≈ 0.538
      ├── Some((4, 2)): 72/126 ≈ 0.571
      ├── Some((4, 3)): 82/139 ≈ 0.590
      ├── Some((4, 4)): 48/93 ≈ 0.516
      ├── Some((4, 5)): 59/108 ≈ 0.546
      ├── Some((4, 6)): 63/113 ≈ 0.558
      ├── Some((4, 7)): 14/43 ≈ 0.326
      └── Some((4, 8)): 75/129 ≈ 0.581
    ├── Some((6, 5)): 507/916 ≈ 0.553
      ├── Some((5, 0)): 51/95 ≈ 0.537
      ├── Some((5, 1)): 50/94 ≈ 0.532
      ├── Some((5, 2)): 51/95 ≈ 0.537
      ├── Some((5, 3)): 48/91 ≈ 0.527
      ├── Some((5, 4)): 59/106 ≈ 0.557
      ├── Some((5, 5)): 29/64 ≈ 0.453
      ├── Some((5, 6)): 89/145 ≈ 0.614
      ├── Some((5, 7)): 65/113 ≈ 0.575
      └── Some((5, 8)): 64/112 ≈ 0.571
    ├── Some((6, 6)): 409/759 ≈ 0.539
      ├── Some((6, 0)): 65/114 ≈ 0.570
      ├── Some((6, 1)): 11/37 ≈ 0.297
      ├── Some((6, 2)): 51/96 ≈ 0.531
      ├── Some((6, 3)): 39/79 ≈ 0.494
      ├── Some((6, 4)): 55/101 ≈ 0.545
      ├── Some((6, 5)): 80/134 ≈ 0.597
      ├── Some((6, 7)): 42/83 ≈ 0.506
      └── Some((6, 8)): 65/114 ≈ 0.570
    ├── Some((6, 7)): 532/956 ≈ 0.556
      ├── Some((7, 0)): 64/113 ≈ 0.566
      ├── Some((7, 1)): 68/118 ≈ 0.576
      ├── Some((7, 2)): 58/105 ≈ 0.552
      ├── Some((7, 3)): 66/116 ≈ 0.569
      ├── Some((7, 4)): 82/137 ≈ 0.599
      ├── Some((7, 5)): 46/89 ≈ 0.517
      ├── Some((7, 6)): 27/62 ≈ 0.435
      ├── Some((7, 7)): 73/125 ≈ 0.584
      └── Some((7, 8)): 47/90 ≈ 0.522
    └── Some((6, 8)): 565/1008 ≈ 0.561
      ├── Some((8, 0)): 41/83 ≈ 0.494
      ├── Some((8, 1)): 59/107 ≈ 0.551
      ├── Some((8, 2)): 45/88 ≈ 0.511
      ├── Some((8, 3)): 76/130 ≈ 0.585
      ├── Some((8, 4)): 74/127 ≈ 0.583
      ├── Some((8, 5)): 65/115 ≈ 0.565
      ├── Some((8, 6)): 75/128 ≈ 0.586
      ├── Some((8, 7)): 71/123 ≈ 0.577
      └── Some((8, 8)): 58/106 ≈ 0.547
  ├── Some((0, 7)): 3957/7234 ≈ 0.547
    ├── Some((7, 0)): 278/543 ≈ 0.512
      ├── Some((0, 0)): 54/94 ≈ 0.574
      ├── Some((0, 1)): 40/75 ≈ 0.533
      ├── Some((0, 2)): 31/63 ≈ 0.492
      ├── Some((0, 3)): 33/66 ≈ 0.500
      ├── Some((0, 4)): 29/60 ≈ 0.483
      ├── Some((0, 5)): 40/75 ≈ 0.533
      ├── Some((0, 6)): 29/60 ≈ 0.483
      └── Some((0, 8)): 21/49 ≈ 0.429
    ├── Some((7, 1)): 537/960 ≈ 0.559
      ├── Some((1, 0)): 74/126 ≈ 0.587
      ├── Some((1, 1)): 79/132 ≈ 0.598
      ├── Some((1, 2)): 94/152 ≈ 0.618
      ├── Some((1, 3)): 64/113 ≈ 0.566
      ├── Some((1, 4)): 24/58 ≈ 0.414
      ├── Some((1, 5)): 38/78 ≈ 0.487
      ├── Some((1, 6)): 49/93 ≈ 0.527
      ├── Some((1, 7)): 61/109 ≈ 0.560
      └── Some((1, 8)): 53/98 ≈ 0.541
    ├── Some((7, 2)): 468/851 ≈ 0.550
      ├── Some((2, 0)): 53/96 ≈ 0.552
      ├── Some((2, 1)): 44/84 ≈ 0.524
      ├── Some((2, 2)): 53/96 ≈ 0.552
      ├── Some((2, 3)): 61/107 ≈ 0.570
      ├── Some((2, 4)): 66/113 ≈ 0.584
      ├── Some((2, 5)): 51/93 ≈ 0.548
      ├── Some((2, 6)): 74/124 ≈ 0.597
      ├── Some((2, 7)): 42/81 ≈ 0.519
      └── Some((2, 8)): 24/56 ≈ 0.429
    ├── Some((7, 3)): 508/914 ≈ 0.556
      ├── Some((3, 0)): 79/131 ≈ 0.603
      ├── Some((3, 1)): 50/93 ≈ 0.538
      ├── Some((3, 2)): 68/117 ≈ 0.581
      ├── Some((3, 3)): 54/98 ≈ 0.551
      ├── Some((3, 4)): 57/102 ≈ 0.559
      ├── Some((3, 5)): 47/89 ≈ 0.528
      ├── Some((3, 6)): 39/78 ≈ 0.500
      ├── Some((3, 7)): 40/80 ≈ 0.500
      └── Some((3, 8)): 74/125 ≈ 0.592
    ├── Some((7, 4)): 395/734 ≈ 0.538
      ├── Some((4, 1)): 50/93 ≈ 0.538
      ├── Some((4, 2)): 54/98 ≈ 0.551
      ├── Some((4, 3)): 61/107 ≈ 0.570
      ├── Some((4, 4)): 70/119 ≈ 0.588
      ├── Some((4, 5)): 43/83 ≈ 0.518
      ├── Some((4, 6)): 36/74 ≈ 0.486
      ├── Some((4, 7)): 38/76 ≈ 0.500
      └── Some((4, 8)): 43/83 ≈ 0.518
    ├── Some((7, 5)): 549/979 ≈ 0.561
      ├── Some((5, 0)): 53/98 ≈ 0.541
      ├── Some((5, 1)): 88/144 ≈ 0.611
      ├── Some((5, 2)): 64/113 ≈ 0.566
      ├── Some((5, 3)): 63/112 ≈ 0.562
      ├── Some((5, 4)): 93/151 ≈ 0.616
      ├── Some((5, 5)): 46/89 ≈ 0.517
      ├── Some((5, 6)): 31/68 ≈ 0.456
      ├── Some((5, 7)): 63/112 ≈ 0.562
      └── Some((5, 8)): 48/91 ≈ 0.527
    ├── Some((7, 6)): 321/614 ≈ 0.523
      ├── Some((6, 0)): 20/47 ≈ 0.426
      ├── Some((6, 1)): 33/65 ≈ 0.508
      ├── Some((6, 2)): 33/65 ≈ 0.508
      ├── Some((6, 3)): 47/83 ≈ 0.566
      ├── Some((6, 4)): 18/44 ≈ 0.409
      ├── Some((6, 5)): 57/96 ≈ 0.594
      ├── Some((6, 6)): 41/76 ≈ 0.539
      ├── Some((6, 7)): 27/57 ≈ 0.474
      └── Some((6, 8)): 44/80 ≈ 0.550
    ├── Some((7, 7)): 633/1111 ≈ 0.570
      ├── Some((7, 0)): 88/151 ≈ 0.583
      ├── Some((7, 1)): 101/168 ≈ 0.601
      ├── Some((7, 2)): 115/187 ≈ 0.615
      ├── Some((7, 3)): 56/107 ≈ 0.523
      ├── Some((7, 4)): 54/105 ≈ 0.514
      ├── Some((7, 5)): 57/109 ≈ 0.523
      ├── Some((7, 6)): 68/124 ≈ 0.548
      └── Some((7, 8)): 94/159 ≈ 0.591
    └── Some((7, 8)): 268/527 ≈ 0.509
      ├── Some((8, 0)): 21/47 ≈ 0.447
      ├── Some((8, 1)): 51/86 ≈ 0.593
      ├── Some((8, 2)): 17/42 ≈ 0.405
      ├── Some((8, 3)): 11/33 ≈ 0.333
      ├── Some((8, 4)): 41/74 ≈ 0.554
      ├── Some((8, 5)): 36/67 ≈ 0.537
      ├── Some((8, 6)): 21/47 ≈ 0.447
      ├── Some((8, 7)): 33/63 ≈ 0.524
      └── Some((8, 8)): 36/67 ≈ 0.537
  └── Some((0, 8)): 3141/5815 ≈ 0.540
    ├── Some((8, 0)): 378/693 ≈ 0.545
      ├── Some((0, 0)): 27/59 ≈ 0.458
      ├── Some((0, 1)): 47/87 ≈ 0.540
      ├── Some((0, 2)): 31/65 ≈ 0.477
      ├── Some((0, 3)): 82/132 ≈ 0.621
      ├── Some((0, 4)): 22/52 ≈ 0.423
      ├── Some((0, 5)): 64/109 ≈ 0.587
      ├── Some((0, 6)): 51/92 ≈ 0.554
      └── Some((0, 7)): 54/96 ≈ 0.562
    ├── Some((8, 1)): 246/481 ≈ 0.511
      ├── Some((1, 0)): 36/65 ≈ 0.554
      ├── Some((1, 1)): 46/77 ≈ 0.597
      ├── Some((1, 2)): 40/70 ≈ 0.571
      ├── Some((1, 3)): 18/41 ≈ 0.439
      ├── Some((1, 4)): 30/57 ≈ 0.526
      ├── Some((1, 5)): 24/50 ≈ 0.480
      ├── Some((1, 6)): 15/37 ≈ 0.405
      ├── Some((1, 7)): 17/40 ≈ 0.425
      └── Some((1, 8)): 19/43 ≈ 0.442
    ├── Some((8, 2)): 248/484 ≈ 0.512
      ├── Some((2, 0)): 31/58 ≈ 0.534
      ├── Some((2, 1)): 12/33 ≈ 0.364
      ├── Some((2, 2)): 31/58 ≈ 0.534
      ├── Some((2, 3)): 26/52 ≈ 0.500
      ├── Some((2, 4)): 31/59 ≈ 0.525
      ├── Some((2, 5)): 26/52 ≈ 0.500
      ├── Some((2, 6)): 33/61 ≈ 0.541
      ├── Some((2, 7)): 18/41 ≈ 0.439
      └── Some((2, 8)): 39/69 ≈ 0.565
    ├── Some((8, 3)): 456/817 ≈ 0.558
      ├── Some((3, 0)): 72/119 ≈ 0.605
      ├── Some((3, 1)): 65/110 ≈ 0.591
      ├── Some((3, 2)): 63/107 ≈ 0.589
      ├── Some((3, 3)): 32/66 ≈ 0.485
      ├── Some((3, 4)): 22/52 ≈ 0.423
      ├── Some((3, 5)): 44/83 ≈ 0.530
      ├── Some((3, 6)): 47/86 ≈ 0.547
      ├── Some((3, 7)): 72/119 ≈ 0.605
      └── Some((3, 8)): 38/74 ≈ 0.514
    ├── Some((8, 4)): 431/777 ≈ 0.555
      ├── Some((4, 1)): 34/70 ≈ 0.486
      ├── Some((4, 2)): 54/98 ≈ 0.551
      ├── Some((4, 3)): 27/60 ≈ 0.450
      ├── Some((4, 4)): 58/103 ≈ 0.563
      ├── Some((4, 5)): 72/121 ≈ 0.595
      ├── Some((4, 6)): 50/92 ≈ 0.543
      ├── Some((4, 7)): 55/99 ≈ 0.556
      └── Some((4, 8)): 81/133 ≈ 0.609
    ├── Some((8, 5)): 239/470 ≈ 0.509
      ├── Some((5, 0)): 21/45 ≈ 0.467
      ├── Some((5, 1)): 26/51 ≈ 0.510
      ├── Some((5, 2)): 25/50 ≈ 0.500
      ├── Some((5, 3)): 23/47 ≈ 0.489
      ├── Some((5, 4)): 28/54 ≈ 0.519
      ├── Some((5, 5)): 27/53 ≈ 0.509
      ├── Some((5, 6)): 30/57 ≈ 0.526
      ├── Some((5, 7)): 29/55 ≈ 0.527
      └── Some((5, 8)): 30/57 ≈ 0.526
    ├── Some((8, 6)): 424/766 ≈ 0.554
      ├── Some((6, 0)): 46/84 ≈ 0.548
      ├── Some((6, 1)): 75/121 ≈ 0.620
      ├── Some((6, 2)): 50/89 ≈ 0.562
      ├── Some((6, 3)): 35/69 ≈ 0.507
      ├── Some((6, 4)): 24/54 ≈ 0.444
      ├── Some((6, 5)): 39/75 ≈ 0.520
      ├── Some((6, 6)): 40/76 ≈ 0.526
      ├── Some((6, 7)): 69/114 ≈ 0.605
      └── Some((6, 8)): 45/83 ≈ 0.542
    ├── Some((8, 7)): 298/566 ≈ 0.527
      ├── Some((7, 0)): 30/59 ≈ 0.508
      ├── Some((7, 1)): 43/76 ≈ 0.566
      ├── Some((7, 2)): 33/63 ≈ 0.524
      ├── Some((7, 3)): 17/42 ≈ 0.405
      ├── Some((7, 4)): 18/43 ≈ 0.419
      ├── Some((7, 5)): 39/71 ≈ 0.549
      ├── Some((7, 6)): 43/76 ≈ 0.566
      ├── Some((7, 7)): 12/34 ≈ 0.353
      └── Some((7, 8)): 63/101 ≈ 0.624
    └── Some((8, 8)): 420/760 ≈ 0.553
      ├── Some((8, 0)): 38/76 ≈ 0.500
      ├── Some((8, 1)): 63/109 ≈ 0.578
      ├── Some((8, 2)): 32/68 ≈ 0.471
      ├── Some((8, 3)): 69/117 ≈ 0.590
      ├── Some((8, 4)): 57/101 ≈ 0.564
      ├── Some((8, 5)): 76/126 ≈ 0.603
      ├── Some((8, 6)): 53/96 ≈ 0.552
      └── Some((8, 7)): 31/66 ≈ 0.470
├── Some((4, 1)): 17885/33130 ≈ 0.540
  ├── Some((1, 0)): 2841/5153 ≈ 0.551
    ├── Some((0, 0)): 385/681 ≈ 0.565
      ├── Some((0, 1)): 26/56 ≈ 0.464
      ├── Some((0, 2)): 41/76 ≈ 0.539
      ├── Some((0, 3)): 66/108 ≈ 0.611
      ├── Some((0, 4)): 47/84 ≈ 0.560
      ├── Some((0, 5)): 50/88 ≈ 0.568
      ├── Some((0, 6)): 29/60 ≈ 0.483
      ├── Some((0, 7)): 79/124 ≈ 0.637
      └── Some((0, 8)): 47/84 ≈ 0.560
    ├── Some((0, 1)): 410/720 ≈ 0.569
      ├── Some((1, 1)): 53/92 ≈ 0.576
      ├── Some((1, 2)): 63/105 ≈ 0.600
      ├── Some((1, 3)): 58/99 ≈ 0.586
      ├── Some((1, 4)): 30/62 ≈ 0.484
      ├── Some((1, 5)): 48/86 ≈ 0.558
      ├── Some((1, 6)): 34/68 ≈ 0.500
      ├── Some((1, 7)): 64/107 ≈ 0.598
      └── Some((1, 8)): 59/100 ≈ 0.590
    ├── Some((0, 2)): 326/590 ≈ 0.553
      ├── Some((2, 0)): 38/68 ≈ 0.559
      ├── Some((2, 1)): 38/68 ≈ 0.559
      ├── Some((2, 2)): 42/73 ≈ 0.575
      ├── Some((2, 3)): 23/49 ≈ 0.469
      ├── Some((2, 4)): 44/75 ≈ 0.587
      ├── Some((2, 5)): 26/52 ≈ 0.500
      ├── Some((2, 6)): 41/72 ≈ 0.569
      ├── Some((2, 7)): 26/53 ≈ 0.491
      └── Some((2, 8)): 47/79 ≈ 0.595
    ├── Some((0, 3)): 263/491 ≈ 0.536
      ├── Some((3, 0)): 42/71 ≈ 0.592
      ├── Some((3, 1)): 17/39 ≈ 0.436
      ├── Some((3, 2)): 22/46 ≈ 0.478
      ├── Some((3, 3)): 38/66 ≈ 0.576
      ├── Some((3, 4)): 18/41 ≈ 0.439
      ├── Some((3, 5)): 17/39 ≈ 0.436
      ├── Some((3, 6)): 38/66 ≈ 0.576
      ├── Some((3, 7)): 8/27 ≈ 0.296
      └── Some((3, 8)): 62/95 ≈ 0.653
    ├── Some((0, 4)): 235/447 ≈ 0.526
      ├── Some((4, 0)): 37/66 ≈ 0.561
      ├── Some((4, 2)): 23/48 ≈ 0.479
      ├── Some((4, 3)): 39/68 ≈ 0.574
      ├── Some((4, 4)): 23/48 ≈ 0.479
      ├── Some((4, 5)): 35/63 ≈ 0.556
      ├── Some((4, 6)): 25/50 ≈ 0.500
      ├── Some((4, 7)): 10/30 ≈ 0.333
      └── Some((4, 8)): 43/73 ≈ 0.589
    ├── Some((0, 5)): 279/517 ≈ 0.540
      ├── Some((5, 0)): 30/56 ≈ 0.536
      ├── Some((5, 1)): 29/55 ≈ 0.527
      ├── Some((5, 2)): 48/79 ≈ 0.608
      ├── Some((5, 3)): 32/59 ≈ 0.542
      ├── Some((5, 4)): 34/61 ≈ 0.557
      ├── Some((5, 5)): 31/58 ≈ 0.534
      ├── Some((5, 6)): 20/43 ≈ 0.465
      ├── Some((5, 7)): 15/37 ≈ 0.405
      └── Some((5, 8)): 39/68 ≈ 0.574
    ├── Some((0, 6)): 343/616 ≈ 0.557
      ├── Some((6, 0)): 22/48 ≈ 0.458
      ├── Some((6, 1)): 28/56 ≈ 0.500
      ├── Some((6, 2)): 56/91 ≈ 0.615
      ├── Some((6, 3)): 31/60 ≈ 0.517
      ├── Some((6, 4)): 50/83 ≈ 0.602
      ├── Some((6, 5)): 35/65 ≈ 0.538
      ├── Some((6, 6)): 46/79 ≈ 0.582
      ├── Some((6, 7)): 50/83 ≈ 0.602
      └── Some((6, 8)): 24/50 ≈ 0.480
    ├── Some((0, 7)): 441/767 ≈ 0.575
      ├── Some((7, 0)): 54/92 ≈ 0.587
      ├── Some((7, 1)): 65/106 ≈ 0.613
      ├── Some((7, 2)): 31/62 ≈ 0.500
      ├── Some((7, 3)): 57/96 ≈ 0.594
      ├── Some((7, 4)): 64/105 ≈ 0.610
      ├── Some((7, 5)): 80/124 ≈ 0.645
      ├── Some((7, 6)): 27/57 ≈ 0.474
      ├── Some((7, 7)): 42/77 ≈ 0.545
      └── Some((7, 8)): 20/47 ≈ 0.426
    └── Some((0, 8)): 158/323 ≈ 0.489
      ├── Some((8, 0)): 8/24 ≈ 0.333
      ├── Some((8, 1)): 15/33 ≈ 0.455
      ├── Some((8, 2)): 16/34 ≈ 0.471
      ├── Some((8, 3)): 9/25 ≈ 0.360
      ├── Some((8, 4)): 25/45 ≈ 0.556
      ├── Some((8, 5)): 32/54 ≈ 0.593
      ├── Some((8, 6)): 19/38 ≈ 0.500
      ├── Some((8, 7)): 9/25 ≈ 0.360
      └── Some((8, 8)): 24/44 ≈ 0.545
  ├── Some((1, 1)): 1254/2411 ≈ 0.520
    ├── Some((1, 0)): 114/235 ≈ 0.485
      ├── Some((0, 0)): 15/29 ≈ 0.517
      ├── Some((0, 1)): 5/17 ≈ 0.294
      ├── Some((0, 2)): 11/24 ≈ 0.458
      ├── Some((0, 3)): 17/31 ≈ 0.548
      ├── Some((0, 4)): 14/28 ≈ 0.500
      ├── Some((0, 5)): 17/32 ≈ 0.531
      ├── Some((0, 6)): 11/24 ≈ 0.458
      ├── Some((0, 7)): 16/30 ≈ 0.533
      └── Some((0, 8)): 7/19 ≈ 0.368
    ├── Some((1, 2)): 270/477 ≈ 0.566
      ├── Some((2, 0)): 38/63 ≈ 0.603
      ├── Some((2, 1)): 18/38 ≈ 0.474
      ├── Some((2, 2)): 35/59 ≈ 0.593
      ├── Some((2, 3)): 50/77 ≈ 0.649
      ├── Some((2, 4)): 25/47 ≈ 0.532
      ├── Some((2, 5)): 35/59 ≈ 0.593
      ├── Some((2, 6)): 22/43 ≈ 0.512
      ├── Some((2, 7)): 21/42 ≈ 0.500
      └── Some((2, 8)): 26/48 ≈ 0.542
    ├── Some((1, 3)): 94/203 ≈ 0.463
      ├── Some((3, 0)): 21/35 ≈ 0.600
      ├── Some((3, 1)): 8/20 ≈ 0.400
      ├── Some((3, 2)): 9/21 ≈ 0.429
      ├── Some((3, 3)): 5/16 ≈ 0.312
      ├── Some((3, 4)): 16/29 ≈ 0.552
      ├── Some((3, 5)): 1/10 ≈ 0.100
      ├── Some((3, 6)): 11/24 ≈ 0.458
      ├── Some((3, 7)): 10/22 ≈ 0.455
      └── Some((3, 8)): 12/25 ≈ 0.480
    ├── Some((1, 4)): 96/206 ≈ 0.466
      ├── Some((4, 0)): 14/28 ≈ 0.500
      ├── Some((4, 2)): 7/20 ≈ 0.350
      ├── Some((4, 3)): 14/28 ≈ 0.500
      ├── Some((4, 4)): 10/23 ≈ 0.435
      ├── Some((4, 5)): 16/31 ≈ 0.516
      ├── Some((4, 6)): 14/28 ≈ 0.500
      ├── Some((4, 7)): 15/29 ≈ 0.517
      └── Some((4, 8)): 6/18 ≈ 0.333
    ├── Some((1, 5)): 218/398 ≈ 0.548
      ├── Some((5, 0)): 12/29 ≈ 0.414
      ├── Some((5, 1)): 28/49 ≈ 0.571
      ├── Some((5, 2)): 34/56 ≈ 0.607
      ├── Some((5, 3)): 17/35 ≈ 0.486
      ├── Some((5, 4)): 45/69 ≈ 0.652
      ├── Some((5, 5)): 16/34 ≈ 0.471
      ├── Some((5, 6)): 17/36 ≈ 0.472
      ├── Some((5, 7)): 29/50 ≈ 0.580
      └── Some((5, 8)): 20/39 ≈ 0.513
    ├── Some((1, 6)): 157/303 ≈ 0.518
      ├── Some((6, 0)): 31/50 ≈ 0.620
      ├── Some((6, 1)): 18/35 ≈ 0.514
      ├── Some((6, 2)): 16/32 ≈ 0.500
      ├── Some((6, 3)): 20/37 ≈ 0.541
      ├── Some((6, 4)): 11/26 ≈ 0.423
      ├── Some((6, 5)): 16/32 ≈ 0.500
      ├── Some((6, 6)): 12/27 ≈ 0.444
      ├── Some((6, 7)): 26/44 ≈ 0.591
      └── Some((6, 8)): 6/19 ≈ 0.316
    ├── Some((1, 7)): 209/384 ≈ 0.544
      ├── Some((7, 0)): 10/26 ≈ 0.385
      ├── Some((7, 1)): 23/43 ≈ 0.535
      ├── Some((7, 2)): 41/64 ≈ 0.641
      ├── Some((7, 3)): 26/46 ≈ 0.565
      ├── Some((7, 4)): 16/34 ≈ 0.471
      ├── Some((7, 5)): 22/41 ≈ 0.537
      ├── Some((7, 6)): 31/52 ≈ 0.596
      ├── Some((7, 7)): 18/36 ≈ 0.500
      └── Some((7, 8)): 22/41 ≈ 0.537
    └── Some((1, 8)): 95/204 ≈ 0.466
      ├── Some((8, 0)): 18/31 ≈ 0.581
      ├── Some((8, 1)): 7/18 ≈ 0.389
      ├── Some((8, 2)): 14/27 ≈ 0.519
      ├── Some((8, 3)): 8/20 ≈ 0.400
      ├── Some((8, 4)): 13/26 ≈ 0.500
      ├── Some((8, 5)): 4/14 ≈ 0.286
      ├── Some((8, 6)): 12/24 ≈ 0.500
      ├── Some((8, 7)): 9/21 ≈ 0.429
      └── Some((8, 8)): 10/22 ≈ 0.455
  ├── Some((1, 2)): 1732/3245 ≈ 0.534
    ├── Some((2, 0)): 77/177 ≈ 0.435
      ├── Some((0, 0)): 10/21 ≈ 0.476
      ├── Some((0, 1)): 4/14 ≈ 0.286
      ├── Some((0, 2)): 7/18 ≈ 0.389
      ├── Some((0, 3)): 8/19 ≈ 0.421
      ├── Some((0, 4)): 7/18 ≈ 0.389
      ├── Some((0, 5)): 10/21 ≈ 0.476
      ├── Some((0, 6)): 4/14 ≈ 0.286
      ├── Some((0, 7)): 16/28 ≈ 0.571
      └── Some((0, 8)): 11/23 ≈ 0.478
    ├── Some((2, 1)): 133/268 ≈ 0.496
      ├── Some((1, 0)): 21/39 ≈ 0.538
      ├── Some((1, 1)): 13/29 ≈ 0.448
      ├── Some((1, 3)): 10/25 ≈ 0.400
      ├── Some((1, 4)): 23/42 ≈ 0.548
      ├── Some((1, 5)): 5/19 ≈ 0.263
      ├── Some((1, 6)): 26/45 ≈ 0.578
      ├── Some((1, 7)): 17/34 ≈ 0.500
      └── Some((1, 8)): 17/34 ≈ 0.500
    ├── Some((2, 2)): 210/389 ≈ 0.540
      ├── Some((2, 0)): 39/65 ≈ 0.600
      ├── Some((2, 1)): 29/52 ≈ 0.558
      ├── Some((2, 3)): 14/33 ≈ 0.424
      ├── Some((2, 4)): 16/36 ≈ 0.444
      ├── Some((2, 5)): 21/42 ≈ 0.500
      ├── Some((2, 6)): 24/46 ≈ 0.522
      ├── Some((2, 7)): 38/63 ≈ 0.603
      └── Some((2, 8)): 28/51 ≈ 0.549
    ├── Some((2, 3)): 283/500 ≈ 0.566
      ├── Some((3, 0)): 21/43 ≈ 0.488
      ├── Some((3, 1)): 40/66 ≈ 0.606
      ├── Some((3, 2)): 56/85 ≈ 0.659
      ├── Some((3, 3)): 30/54 ≈ 0.556
      ├── Some((3, 4)): 45/72 ≈ 0.625
      ├── Some((3, 5)): 18/39 ≈ 0.462
      ├── Some((3, 6)): 19/40 ≈ 0.475
      ├── Some((3, 7)): 28/51 ≈ 0.549
      └── Some((3, 8)): 26/49 ≈ 0.531
    ├── Some((2, 4)): 185/350 ≈ 0.529
      ├── Some((4, 0)): 21/41 ≈ 0.512
      ├── Some((4, 2)): 29/51 ≈ 0.569
      ├── Some((4, 3)): 21/41 ≈ 0.512
      ├── Some((4, 4)): 17/36 ≈ 0.472
      ├── Some((4, 5)): 28/50 ≈ 0.560
      ├── Some((4, 6)): 24/45 ≈ 0.533
      ├── Some((4, 7)): 29/51 ≈ 0.569
      └── Some((4, 8)): 15/34 ≈ 0.441
    ├── Some((2, 5)): 214/395 ≈ 0.542
      ├── Some((5, 0)): 29/50 ≈ 0.580
      ├── Some((5, 1)): 23/43 ≈ 0.535
      ├── Some((5, 2)): 19/38 ≈ 0.500
      ├── Some((5, 3)): 28/49 ≈ 0.571
      ├── Some((5, 4)): 33/55 ≈ 0.600
      ├── Some((5, 5)): 21/41 ≈ 0.512
      ├── Some((5, 6)): 20/39 ≈ 0.513
      ├── Some((5, 7)): 16/34 ≈ 0.471
      └── Some((5, 8)): 25/45 ≈ 0.556
    ├── Some((2, 6)): 207/384 ≈ 0.539
      ├── Some((6, 0)): 12/29 ≈ 0.414
      ├── Some((6, 1)): 24/44 ≈ 0.545
      ├── Some((6, 2)): 26/46 ≈ 0.565
      ├── Some((6, 3)): 14/32 ≈ 0.438
      ├── Some((6, 4)): 21/40 ≈ 0.525
      ├── Some((6, 5)): 25/45 ≈ 0.556
      ├── Some((6, 6)): 29/50 ≈ 0.580
      ├── Some((6, 7)): 16/34 ≈ 0.471
      └── Some((6, 8)): 40/63 ≈ 0.635
    ├── Some((2, 7)): 200/374 ≈ 0.535
      ├── Some((7, 0)): 24/44 ≈ 0.545
      ├── Some((7, 1)): 23/43 ≈ 0.535
      ├── Some((7, 2)): 15/33 ≈ 0.455
      ├── Some((7, 3)): 27/47 ≈ 0.574
      ├── Some((7, 4)): 15/33 ≈ 0.455
      ├── Some((7, 5)): 26/46 ≈ 0.565
      ├── Some((7, 6)): 18/36 ≈ 0.500
      ├── Some((7, 7)): 30/51 ≈ 0.588
      └── Some((7, 8)): 21/40 ≈ 0.525
    └── Some((2, 8)): 222/407 ≈ 0.545
      ├── Some((8, 0)): 27/48 ≈ 0.562
      ├── Some((8, 1)): 24/44 ≈ 0.545
      ├── Some((8, 2)): 21/41 ≈ 0.512
      ├── Some((8, 3)): 15/33 ≈ 0.455
      ├── Some((8, 4)): 30/52 ≈ 0.577
      ├── Some((8, 5)): 31/53 ≈ 0.585
      ├── Some((8, 6)): 24/44 ≈ 0.545
      ├── Some((8, 7)): 27/48 ≈ 0.562
      └── Some((8, 8)): 23/43 ≈ 0.535
  ├── Some((1, 3)): 2536/4631 ≈ 0.548
    ├── Some((3, 0)): 305/551 ≈ 0.554
      ├── Some((0, 0)): 25/50 ≈ 0.500
      ├── Some((0, 1)): 29/55 ≈ 0.527
      ├── Some((0, 2)): 32/59 ≈ 0.542
      ├── Some((0, 3)): 32/59 ≈ 0.542
      ├── Some((0, 4)): 47/77 ≈ 0.610
      ├── Some((0, 5)): 34/61 ≈ 0.557
      ├── Some((0, 6)): 29/55 ≈ 0.527
      ├── Some((0, 7)): 24/49 ≈ 0.490
      └── Some((0, 8)): 53/85 ≈ 0.624
    ├── Some((3, 1)): 194/377 ≈ 0.515
      ├── Some((1, 0)): 26/50 ≈ 0.520
      ├── Some((1, 1)): 14/34 ≈ 0.412
      ├── Some((1, 2)): 18/39 ≈ 0.462
      ├── Some((1, 4)): 34/59 ≈ 0.576
      ├── Some((1, 5)): 34/59 ≈ 0.576
      ├── Some((1, 6)): 34/60 ≈ 0.567
      ├── Some((1, 7)): 24/47 ≈ 0.511
      └── Some((1, 8)): 10/28 ≈ 0.357
    ├── Some((3, 2)): 336/599 ≈ 0.561
      ├── Some((2, 0)): 40/70 ≈ 0.571
      ├── Some((2, 1)): 41/71 ≈ 0.577
      ├── Some((2, 2)): 41/71 ≈ 0.577
      ├── Some((2, 3)): 49/81 ≈ 0.605
      ├── Some((2, 4)): 27/53 ≈ 0.509
      ├── Some((2, 5)): 51/84 ≈ 0.607
      ├── Some((2, 6)): 30/57 ≈ 0.526
      ├── Some((2, 7)): 31/59 ≈ 0.525
      └── Some((2, 8)): 26/52 ≈ 0.500
    ├── Some((3, 3)): 225/427 ≈ 0.527
      ├── Some((3, 0)): 37/65 ≈ 0.569
      ├── Some((3, 1)): 13/34 ≈ 0.382
      ├── Some((3, 2)): 36/64 ≈ 0.562
      ├── Some((3, 4)): 24/48 ≈ 0.500
      ├── Some((3, 5)): 42/71 ≈ 0.592
      ├── Some((3, 6)): 21/44 ≈ 0.477
      ├── Some((3, 7)): 28/53 ≈ 0.528
      └── Some((3, 8)): 23/47 ≈ 0.489
    ├── Some((3, 4)): 192/374 ≈ 0.513
      ├── Some((4, 0)): 33/58 ≈ 0.569
      ├── Some((4, 2)): 25/48 ≈ 0.521
      ├── Some((4, 3)): 35/61 ≈ 0.574
      ├── Some((4, 4)): 28/52 ≈ 0.538
      ├── Some((4, 5)): 14/34 ≈ 0.412
      ├── Some((4, 6)): 30/55 ≈ 0.545
      ├── Some((4, 7)): 15/35 ≈ 0.429
      └── Some((4, 8)): 11/30 ≈ 0.367
    ├── Some((3, 5)): 253/471 ≈ 0.537
      ├── Some((5, 0)): 20/42 ≈ 0.476
      ├── Some((5, 1)): 32/57 ≈ 0.561
      ├── Some((5, 2)): 30/55 ≈ 0.545
      ├── Some((5, 3)): 5/21 ≈ 0.238
      ├── Some((5, 4)): 32/58 ≈ 0.552
      ├── Some((5, 5)): 32/58 ≈ 0.552
      ├── Some((5, 6)): 37/64 ≈ 0.578
      ├── Some((5, 7)): 31/56 ≈ 0.554
      └── Some((5, 8)): 33/59 ≈ 0.559
    ├── Some((3, 6)): 303/548 ≈ 0.553
      ├── Some((6, 0)): 36/64 ≈ 0.562
      ├── Some((6, 1)): 45/75 ≈ 0.600
      ├── Some((6, 2)): 34/62 ≈ 0.548
      ├── Some((6, 3)): 39/68 ≈ 0.574
      ├── Some((6, 4)): 17/39 ≈ 0.436
      ├── Some((6, 5)): 38/66 ≈ 0.576
      ├── Some((6, 6)): 26/51 ≈ 0.510
      ├── Some((6, 7)): 32/59 ≈ 0.542
      └── Some((6, 8)): 35/63 ≈ 0.556
    ├── Some((3, 7)): 346/615 ≈ 0.563
      ├── Some((7, 0)): 42/73 ≈ 0.575
      ├── Some((7, 1)): 29/57 ≈ 0.509
      ├── Some((7, 2)): 19/43 ≈ 0.442
      ├── Some((7, 3)): 29/57 ≈ 0.509
      ├── Some((7, 4)): 34/63 ≈ 0.540
      ├── Some((7, 5)): 36/65 ≈ 0.554
      ├── Some((7, 6)): 56/90 ≈ 0.622
      ├── Some((7, 7)): 56/90 ≈ 0.622
      └── Some((7, 8)): 44/76 ≈ 0.579
    └── Some((3, 8)): 381/668 ≈ 0.570
      ├── Some((8, 0)): 66/104 ≈ 0.635
      ├── Some((8, 1)): 40/71 ≈ 0.563
      ├── Some((8, 2)): 48/81 ≈ 0.593
      ├── Some((8, 3)): 29/57 ≈ 0.509
      ├── Some((8, 4)): 42/74 ≈ 0.568
      ├── Some((8, 5)): 42/74 ≈ 0.568
      ├── Some((8, 6)): 31/60 ≈ 0.517
      ├── Some((8, 7)): 48/81 ≈ 0.593
      └── Some((8, 8)): 35/65 ≈ 0.538
  ├── Some((1, 4)): 1850/3450 ≈ 0.536
    ├── Some((4, 0)): 323/575 ≈ 0.562
      ├── Some((0, 0)): 18/42 ≈ 0.429
      ├── Some((0, 1)): 49/81 ≈ 0.605
      ├── Some((0, 2)): 20/44 ≈ 0.455
      ├── Some((0, 3)): 23/48 ≈ 0.479
      ├── Some((0, 4)): 30/57 ≈ 0.526
      ├── Some((0, 5)): 82/120 ≈ 0.683
      ├── Some((0, 6)): 25/51 ≈ 0.490
      ├── Some((0, 7)): 11/32 ≈ 0.344
      └── Some((0, 8)): 64/99 ≈ 0.646
    ├── Some((4, 2)): 227/426 ≈ 0.533
      ├── Some((2, 0)): 31/55 ≈ 0.564
      ├── Some((2, 1)): 10/28 ≈ 0.357
      ├── Some((2, 2)): 25/47 ≈ 0.532
      ├── Some((2, 3)): 48/75 ≈ 0.640
      ├── Some((2, 4)): 23/45 ≈ 0.511
      ├── Some((2, 5)): 10/28 ≈ 0.357
      ├── Some((2, 6)): 20/41 ≈ 0.488
      ├── Some((2, 7)): 24/46 ≈ 0.522
      └── Some((2, 8)): 35/60 ≈ 0.583
    ├── Some((4, 3)): 163/324 ≈ 0.503
      ├── Some((3, 0)): 14/31 ≈ 0.452
      ├── Some((3, 1)): 10/26 ≈ 0.385
      ├── Some((3, 2)): 24/43 ≈ 0.558
      ├── Some((3, 3)): 19/37 ≈ 0.514
      ├── Some((3, 4)): 23/42 ≈ 0.548
      ├── Some((3, 5)): 11/27 ≈ 0.407
      ├── Some((3, 6)): 20/39 ≈ 0.513
      ├── Some((3, 7)): 11/27 ≈ 0.407
      └── Some((3, 8)): 30/51 ≈ 0.588
    ├── Some((4, 4)): 294/530 ≈ 0.555
      ├── Some((4, 0)): 30/60 ≈ 0.500
      ├── Some((4, 2)): 43/77 ≈ 0.558
      ├── Some((4, 3)): 41/75 ≈ 0.547
      ├── Some((4, 5)): 21/48 ≈ 0.438
      ├── Some((4, 6)): 60/99 ≈ 0.606
      ├── Some((4, 7)): 28/57 ≈ 0.491
      └── Some((4, 8)): 71/113 ≈ 0.628
    ├── Some((4, 5)): 262/480 ≈ 0.546
      ├── Some((5, 0)): 32/57 ≈ 0.561
      ├── Some((5, 1)): 38/64 ≈ 0.594
      ├── Some((5, 2)): 27/51 ≈ 0.529
      ├── Some((5, 3)): 31/56 ≈ 0.554
      ├── Some((5, 4)): 22/44 ≈ 0.500
      ├── Some((5, 5)): 25/48 ≈ 0.521
      ├── Some((5, 6)): 15/35 ≈ 0.429
      ├── Some((5, 7)): 39/66 ≈ 0.591
      └── Some((5, 8)): 33/58 ≈ 0.569
    ├── Some((4, 6)): 284/515 ≈ 0.551
      ├── Some((6, 0)): 27/52 ≈ 0.519
      ├── Some((6, 1)): 28/53 ≈ 0.528
      ├── Some((6, 2)): 25/49 ≈ 0.510
      ├── Some((6, 3)): 36/63 ≈ 0.571
      ├── Some((6, 4)): 24/48 ≈ 0.500
      ├── Some((6, 5)): 60/92 ≈ 0.652
      ├── Some((6, 6)): 54/85 ≈ 0.635
      ├── Some((6, 7)): 25/50 ≈ 0.500
      └── Some((6, 8)): 5/22 ≈ 0.227
    ├── Some((4, 7)): 131/272 ≈ 0.482
      ├── Some((7, 0)): 17/33 ≈ 0.515
      ├── Some((7, 1)): 10/25 ≈ 0.400
      ├── Some((7, 2)): 15/31 ≈ 0.484
      ├── Some((7, 3)): 9/23 ≈ 0.391
      ├── Some((7, 4)): 16/32 ≈ 0.500
      ├── Some((7, 5)): 21/38 ≈ 0.553
      ├── Some((7, 6)): 16/32 ≈ 0.500
      ├── Some((7, 7)): 7/21 ≈ 0.333
      └── Some((7, 8)): 19/36 ≈ 0.528
    └── Some((4, 8)): 165/327 ≈ 0.505
      ├── Some((8, 0)): 13/30 ≈ 0.433
      ├── Some((8, 1)): 23/42 ≈ 0.548
      ├── Some((8, 2)): 32/53 ≈ 0.604
      ├── Some((8, 3)): 5/19 ≈ 0.263
      ├── Some((8, 4)): 25/45 ≈ 0.556
      ├── Some((8, 5)): 6/20 ≈ 0.300
      ├── Some((8, 6)): 37/59 ≈ 0.627
      ├── Some((8, 7)): 12/29 ≈ 0.414
      └── Some((8, 8)): 12/29 ≈ 0.414
  ├── Some((1, 5)): 1145/2219 ≈ 0.516
    ├── Some((5, 0)): 117/231 ≈ 0.506
      ├── Some((0, 0)): 12/25 ≈ 0.480
      ├── Some((0, 1)): 13/26 ≈ 0.500
      ├── Some((0, 2)): 3/13 ≈ 0.231
      ├── Some((0, 3)): 15/28 ≈ 0.536
      ├── Some((0, 4)): 33/48 ≈ 0.688
      ├── Some((0, 5)): 15/28 ≈ 0.536
      ├── Some((0, 6)): 10/22 ≈ 0.455
      ├── Some((0, 7)): 12/25 ≈ 0.480
      └── Some((0, 8)): 4/15 ≈ 0.267
    ├── Some((5, 1)): 142/270 ≈ 0.526
      ├── Some((1, 0)): 25/42 ≈ 0.595
      ├── Some((1, 1)): 12/27 ≈ 0.444
      ├── Some((1, 2)): 26/44 ≈ 0.591
      ├── Some((1, 3)): 22/39 ≈ 0.564
      ├── Some((1, 4)): 16/32 ≈ 0.500
      ├── Some((1, 6)): 13/28 ≈ 0.464
      ├── Some((1, 7)): 9/23 ≈ 0.391
      └── Some((1, 8)): 18/34 ≈ 0.529
    ├── Some((5, 2)): 80/173 ≈ 0.462
      ├── Some((2, 0)): 17/28 ≈ 0.607
      ├── Some((2, 1)): 7/17 ≈ 0.412
      ├── Some((2, 2)): 15/26 ≈ 0.577
      ├── Some((2, 3)): 4/13 ≈ 0.308
      ├── Some((2, 4)): 7/17 ≈ 0.412
      ├── Some((2, 5)): 12/23 ≈ 0.522
      ├── Some((2, 6)): 10/21 ≈ 0.476
      ├── Some((2, 7)): 6/16 ≈ 0.375
      └── Some((2, 8)): 2/11 ≈ 0.182
    ├── Some((5, 3)): 84/179 ≈ 0.469
      ├── Some((3, 0)): 8/18 ≈ 0.444
      ├── Some((3, 1)): 7/17 ≈ 0.412
      ├── Some((3, 2)): 6/16 ≈ 0.375
      ├── Some((3, 3)): 9/19 ≈ 0.474
      ├── Some((3, 4)): 10/21 ≈ 0.476
      ├── Some((3, 5)): 12/23 ≈ 0.522
      ├── Some((3, 6)): 11/22 ≈ 0.500
      ├── Some((3, 7)): 11/22 ≈ 0.500
      └── Some((3, 8)): 9/20 ≈ 0.450
    ├── Some((5, 4)): 168/309 ≈ 0.544
      ├── Some((4, 0)): 24/43 ≈ 0.558
      ├── Some((4, 2)): 20/38 ≈ 0.526
      ├── Some((4, 3)): 23/41 ≈ 0.561
      ├── Some((4, 4)): 10/25 ≈ 0.400
      ├── Some((4, 5)): 12/28 ≈ 0.429
      ├── Some((4, 6)): 10/25 ≈ 0.400
      ├── Some((4, 7)): 35/55 ≈ 0.636
      └── Some((4, 8)): 33/53 ≈ 0.623
    ├── Some((5, 5)): 123/241 ≈ 0.510
      ├── Some((5, 0)): 17/32 ≈ 0.531
      ├── Some((5, 1)): 10/24 ≈ 0.417
      ├── Some((5, 2)): 12/26 ≈ 0.462
      ├── Some((5, 3)): 14/28 ≈ 0.500
      ├── Some((5, 4)): 12/26 ≈ 0.462
      ├── Some((5, 6)): 14/29 ≈ 0.483
      ├── Some((5, 7)): 22/38 ≈ 0.579
      └── Some((5, 8)): 21/37 ≈ 0.568
    ├── Some((5, 6)): 162/300 ≈ 0.540
      ├── Some((6, 0)): 22/38 ≈ 0.579
      ├── Some((6, 1)): 16/31 ≈ 0.516
      ├── Some((6, 2)): 24/41 ≈ 0.585
      ├── Some((6, 3)): 16/31 ≈ 0.516
      ├── Some((6, 4)): 26/43 ≈ 0.605
      ├── Some((6, 5)): 15/30 ≈ 0.500
      ├── Some((6, 6)): 7/20 ≈ 0.350
      ├── Some((6, 7)): 12/26 ≈ 0.462
      └── Some((6, 8)): 23/39 ≈ 0.590
    ├── Some((5, 7)): 92/192 ≈ 0.479
      ├── Some((7, 0)): 20/33 ≈ 0.606
      ├── Some((7, 1)): 9/20 ≈ 0.450
      ├── Some((7, 2)): 0/8 ≈ 0.000
      ├── Some((7, 3)): 2/11 ≈ 0.182
      ├── Some((7, 4)): 13/25 ≈ 0.520
      ├── Some((7, 5)): 19/32 ≈ 0.594
      ├── Some((7, 6)): 16/29 ≈ 0.552
      ├── Some((7, 7)): 4/14 ≈ 0.286
      └── Some((7, 8)): 8/19 ≈ 0.421
    └── Some((5, 8)): 177/323 ≈ 0.548
      ├── Some((8, 0)): 19/35 ≈ 0.543
      ├── Some((8, 1)): 9/23 ≈ 0.391
      ├── Some((8, 2)): 26/43 ≈ 0.605
      ├── Some((8, 3)): 30/48 ≈ 0.625
      ├── Some((8, 4)): 20/36 ≈ 0.556
      ├── Some((8, 5)): 28/46 ≈ 0.609
      ├── Some((8, 6)): 12/27 ≈ 0.444
      ├── Some((8, 7)): 16/32 ≈ 0.500
      └── Some((8, 8)): 16/32 ≈ 0.500
  ├── Some((1, 6)): 2765/5024 ≈ 0.550
    ├── Some((6, 0)): 226/431 ≈ 0.524
      ├── Some((0, 0)): 12/31 ≈ 0.387
      ├── Some((0, 1)): 28/52 ≈ 0.538
      ├── Some((0, 2)): 39/65 ≈ 0.600
      ├── Some((0, 3)): 19/40 ≈ 0.475
      ├── Some((0, 4)): 44/71 ≈ 0.620
      ├── Some((0, 5)): 16/37 ≈ 0.432
      ├── Some((0, 6)): 19/40 ≈ 0.475
      ├── Some((0, 7)): 30/54 ≈ 0.556
      └── Some((0, 8)): 19/40 ≈ 0.475
    ├── Some((6, 1)): 305/555 ≈ 0.550
      ├── Some((1, 0)): 39/71 ≈ 0.549
      ├── Some((1, 1)): 44/77 ≈ 0.571
      ├── Some((1, 2)): 48/82 ≈ 0.585
      ├── Some((1, 3)): 31/60 ≈ 0.517
      ├── Some((1, 4)): 22/48 ≈ 0.458
      ├── Some((1, 5)): 53/89 ≈ 0.596
      ├── Some((1, 7)): 51/86 ≈ 0.593
      └── Some((1, 8)): 17/41 ≈ 0.415
    ├── Some((6, 2)): 346/619 ≈ 0.559
      ├── Some((2, 0)): 25/52 ≈ 0.481
      ├── Some((2, 1)): 35/65 ≈ 0.538
      ├── Some((2, 2)): 29/57 ≈ 0.509
      ├── Some((2, 3)): 73/111 ≈ 0.658
      ├── Some((2, 4)): 28/56 ≈ 0.500
      ├── Some((2, 5)): 42/73 ≈ 0.575
      ├── Some((2, 6)): 39/70 ≈ 0.557
      ├── Some((2, 7)): 37/67 ≈ 0.552
      └── Some((2, 8)): 37/67 ≈ 0.552
    ├── Some((6, 3)): 278/513 ≈ 0.542
      ├── Some((3, 0)): 22/46 ≈ 0.478
      ├── Some((3, 1)): 14/35 ≈ 0.400
      ├── Some((3, 2)): 33/60 ≈ 0.550
      ├── Some((3, 3)): 42/71 ≈ 0.592
      ├── Some((3, 4)): 36/64 ≈ 0.562
      ├── Some((3, 5)): 66/100 ≈ 0.660
      ├── Some((3, 6)): 13/34 ≈ 0.382
      ├── Some((3, 7)): 20/44 ≈ 0.455
      └── Some((3, 8)): 31/58 ≈ 0.534
    ├── Some((6, 4)): 459/792 ≈ 0.580
      ├── Some((4, 0)): 80/128 ≈ 0.625
      ├── Some((4, 2)): 58/100 ≈ 0.580
      ├── Some((4, 3)): 60/103 ≈ 0.583
      ├── Some((4, 4)): 30/63 ≈ 0.476
      ├── Some((4, 5)): 42/79 ≈ 0.532
      ├── Some((4, 6)): 59/101 ≈ 0.584
      ├── Some((4, 7)): 63/107 ≈ 0.589
      └── Some((4, 8)): 66/110 ≈ 0.600
    ├── Some((6, 5)): 307/558 ≈ 0.550
      ├── Some((5, 0)): 27/53 ≈ 0.509
      ├── Some((5, 1)): 28/55 ≈ 0.509
      ├── Some((5, 2)): 42/72 ≈ 0.583
      ├── Some((5, 3)): 28/55 ≈ 0.509
      ├── Some((5, 4)): 21/45 ≈ 0.467
      ├── Some((5, 5)): 37/66 ≈ 0.561
      ├── Some((5, 6)): 27/53 ≈ 0.509
      ├── Some((5, 7)): 57/90 ≈ 0.633
      └── Some((5, 8)): 39/68 ≈ 0.574
    ├── Some((6, 6)): 270/501 ≈ 0.539
      ├── Some((6, 0)): 48/81 ≈ 0.593
      ├── Some((6, 1)): 15/38 ≈ 0.395
      ├── Some((6, 2)): 43/75 ≈ 0.573
      ├── Some((6, 3)): 18/42 ≈ 0.429
      ├── Some((6, 4)): 38/68 ≈ 0.559
      ├── Some((6, 5)): 38/69 ≈ 0.551
      ├── Some((6, 7)): 24/50 ≈ 0.480
      └── Some((6, 8)): 45/77 ≈ 0.584
    ├── Some((6, 7)): 268/497 ≈ 0.539
      ├── Some((7, 0)): 18/40 ≈ 0.450
      ├── Some((7, 1)): 26/51 ≈ 0.510
      ├── Some((7, 2)): 27/52 ≈ 0.519
      ├── Some((7, 3)): 27/52 ≈ 0.519
      ├── Some((7, 4)): 24/48 ≈ 0.500
      ├── Some((7, 5)): 14/35 ≈ 0.400
      ├── Some((7, 6)): 46/76 ≈ 0.605
      ├── Some((7, 7)): 35/62 ≈ 0.565
      └── Some((7, 8)): 50/80 ≈ 0.625
    └── Some((6, 8)): 306/557 ≈ 0.549
      ├── Some((8, 0)): 33/61 ≈ 0.541
      ├── Some((8, 1)): 52/84 ≈ 0.619
      ├── Some((8, 2)): 17/40 ≈ 0.425
      ├── Some((8, 3)): 46/77 ≈ 0.597
      ├── Some((8, 4)): 32/59 ≈ 0.542
      ├── Some((8, 5)): 26/52 ≈ 0.500
      ├── Some((8, 6)): 35/63 ≈ 0.556
      ├── Some((8, 7)): 30/57 ≈ 0.526
      └── Some((8, 8)): 35/63 ≈ 0.556
  ├── Some((1, 7)): 2423/4437 ≈ 0.546
    ├── Some((7, 0)): 364/640 ≈ 0.569
      ├── Some((0, 0)): 23/49 ≈ 0.469
      ├── Some((0, 1)): 47/79 ≈ 0.595
      ├── Some((0, 2)): 38/68 ≈ 0.559
      ├── Some((0, 3)): 38/68 ≈ 0.559
      ├── Some((0, 4)): 48/81 ≈ 0.593
      ├── Some((0, 5)): 57/92 ≈ 0.620
      ├── Some((0, 6)): 35/64 ≈ 0.547
      ├── Some((0, 7)): 35/64 ≈ 0.547
      └── Some((0, 8)): 43/74 ≈ 0.581
    ├── Some((7, 1)): 245/456 ≈ 0.537
      ├── Some((1, 0)): 31/58 ≈ 0.534
      ├── Some((1, 1)): 35/63 ≈ 0.556
      ├── Some((1, 2)): 27/52 ≈ 0.519
      ├── Some((1, 3)): 20/43 ≈ 0.465
      ├── Some((1, 4)): 24/49 ≈ 0.490
      ├── Some((1, 5)): 46/76 ≈ 0.605
      ├── Some((1, 6)): 27/53 ≈ 0.509
      └── Some((1, 8)): 34/61 ≈ 0.557
    ├── Some((7, 2)): 258/477 ≈ 0.541
      ├── Some((2, 0)): 23/46 ≈ 0.500
      ├── Some((2, 1)): 22/45 ≈ 0.489
      ├── Some((2, 2)): 34/60 ≈ 0.567
      ├── Some((2, 3)): 40/68 ≈ 0.588
      ├── Some((2, 4)): 38/65 ≈ 0.585
      ├── Some((2, 5)): 27/51 ≈ 0.529
      ├── Some((2, 6)): 38/65 ≈ 0.585
      ├── Some((2, 7)): 32/58 ≈ 0.552
      └── Some((2, 8)): 3/18 ≈ 0.167
    ├── Some((7, 3)): 317/568 ≈ 0.558
      ├── Some((3, 0)): 39/68 ≈ 0.574
      ├── Some((3, 1)): 29/55 ≈ 0.527
      ├── Some((3, 2)): 43/73 ≈ 0.589
      ├── Some((3, 3)): 34/62 ≈ 0.548
      ├── Some((3, 4)): 11/31 ≈ 0.355
      ├── Some((3, 5)): 18/41 ≈ 0.439
      ├── Some((3, 6)): 41/71 ≈ 0.577
      ├── Some((3, 7)): 50/82 ≈ 0.610
      └── Some((3, 8)): 52/84 ≈ 0.619
    ├── Some((7, 4)): 314/563 ≈ 0.558
      ├── Some((4, 0)): 25/52 ≈ 0.481
      ├── Some((4, 2)): 33/63 ≈ 0.524
      ├── Some((4, 3)): 32/61 ≈ 0.525
      ├── Some((4, 4)): 62/99 ≈ 0.626
      ├── Some((4, 5)): 45/78 ≈ 0.577
      ├── Some((4, 6)): 23/50 ≈ 0.460
      ├── Some((4, 7)): 54/89 ≈ 0.607
      └── Some((4, 8)): 39/70 ≈ 0.557
    ├── Some((7, 5)): 148/302 ≈ 0.490
      ├── Some((5, 0)): 24/43 ≈ 0.558
      ├── Some((5, 1)): 8/23 ≈ 0.348
      ├── Some((5, 2)): 22/41 ≈ 0.537
      ├── Some((5, 3)): 13/30 ≈ 0.433
      ├── Some((5, 4)): 25/44 ≈ 0.568
      ├── Some((5, 5)): 20/38 ≈ 0.526
      ├── Some((5, 6)): 1/13 ≈ 0.077
      ├── Some((5, 7)): 16/33 ≈ 0.485
      └── Some((5, 8)): 18/36 ≈ 0.500
    ├── Some((7, 6)): 205/393 ≈ 0.522
      ├── Some((6, 0)): 18/38 ≈ 0.474
      ├── Some((6, 1)): 15/34 ≈ 0.441
      ├── Some((6, 2)): 29/52 ≈ 0.558
      ├── Some((6, 3)): 42/67 ≈ 0.627
      ├── Some((6, 4)): 31/54 ≈ 0.574
      ├── Some((6, 5)): 19/39 ≈ 0.487
      ├── Some((6, 6)): 14/33 ≈ 0.424
      ├── Some((6, 7)): 23/44 ≈ 0.523
      └── Some((6, 8)): 13/31 ≈ 0.419
    ├── Some((7, 7)): 240/448 ≈ 0.536
      ├── Some((7, 0)): 29/55 ≈ 0.527
      ├── Some((7, 1)): 12/32 ≈ 0.375
      ├── Some((7, 2)): 26/51 ≈ 0.510
      ├── Some((7, 3)): 33/60 ≈ 0.550
      ├── Some((7, 4)): 45/75 ≈ 0.600
      ├── Some((7, 5)): 20/43 ≈ 0.465
      ├── Some((7, 6)): 31/58 ≈ 0.534
      └── Some((7, 8)): 43/73 ≈ 0.589
    └── Some((7, 8)): 331/589 ≈ 0.562
      ├── Some((8, 0)): 36/65 ≈ 0.554
      ├── Some((8, 1)): 40/70 ≈ 0.571
      ├── Some((8, 2)): 22/47 ≈ 0.468
      ├── Some((8, 3)): 42/72 ≈ 0.583
      ├── Some((8, 4)): 43/73 ≈ 0.589
      ├── Some((8, 5)): 18/41 ≈ 0.439
      ├── Some((8, 6)): 30/57 ≈ 0.526
      ├── Some((8, 7)): 67/102 ≈ 0.657
      └── Some((8, 8)): 33/61 ≈ 0.541
  └── Some((1, 8)): 1338/2559 ≈ 0.523
    ├── Some((8, 0)): 111/226 ≈ 0.491
      ├── Some((0, 0)): 24/38 ≈ 0.632
      ├── Some((0, 1)): 4/15 ≈ 0.267
      ├── Some((0, 2)): 17/31 ≈ 0.548
      ├── Some((0, 3)): 15/28 ≈ 0.536
      ├── Some((0, 4)): 9/21 ≈ 0.429
      ├── Some((0, 5)): 11/24 ≈ 0.458
      ├── Some((0, 6)): 12/25 ≈ 0.480
      ├── Some((0, 7)): 6/17 ≈ 0.353
      └── Some((0, 8)): 13/26 ≈ 0.500
    ├── Some((8, 1)): 105/217 ≈ 0.484
      ├── Some((1, 0)): 8/21 ≈ 0.381
      ├── Some((1, 1)): 19/35 ≈ 0.543
      ├── Some((1, 2)): 6/18 ≈ 0.333
      ├── Some((1, 3)): 18/33 ≈ 0.545
      ├── Some((1, 4)): 28/45 ≈ 0.622
      ├── Some((1, 5)): 8/21 ≈ 0.381
      ├── Some((1, 6)): 3/14 ≈ 0.214
      └── Some((1, 7)): 14/29 ≈ 0.483
    ├── Some((8, 2)): 256/447 ≈ 0.573
      ├── Some((2, 0)): 33/55 ≈ 0.600
      ├── Some((2, 1)): 19/39 ≈ 0.487
      ├── Some((2, 2)): 27/48 ≈ 0.562
      ├── Some((2, 3)): 46/70 ≈ 0.657
      ├── Some((2, 4)): 14/32 ≈ 0.438
      ├── Some((2, 5)): 25/46 ≈ 0.543
      ├── Some((2, 6)): 36/59 ≈ 0.610
      ├── Some((2, 7)): 22/42 ≈ 0.524
      └── Some((2, 8)): 33/55 ≈ 0.600
    ├── Some((8, 3)): 147/282 ≈ 0.521
      ├── Some((3, 0)): 16/31 ≈ 0.516
      ├── Some((3, 1)): 13/27 ≈ 0.481
      ├── Some((3, 2)): 23/39 ≈ 0.590
      ├── Some((3, 3)): 17/32 ≈ 0.531
      ├── Some((3, 4)): 13/27 ≈ 0.481
      ├── Some((3, 5)): 18/33 ≈ 0.545
      ├── Some((3, 6)): 17/32 ≈ 0.531
      ├── Some((3, 7)): 19/35 ≈ 0.543
      └── Some((3, 8)): 11/25 ≈ 0.440
    ├── Some((8, 4)): 147/282 ≈ 0.521
      ├── Some((4, 0)): 29/48 ≈ 0.604
      ├── Some((4, 2)): 7/21 ≈ 0.333
      ├── Some((4, 3)): 17/34 ≈ 0.500
      ├── Some((4, 4)): 25/43 ≈ 0.581
      ├── Some((4, 5)): 32/51 ≈ 0.627
      ├── Some((4, 6)): 11/26 ≈ 0.423
      ├── Some((4, 7)): 16/33 ≈ 0.485
      └── Some((4, 8)): 10/25 ≈ 0.400
    ├── Some((8, 5)): 200/364 ≈ 0.549
      ├── Some((5, 0)): 28/48 ≈ 0.583
      ├── Some((5, 1)): 17/34 ≈ 0.500
      ├── Some((5, 2)): 20/38 ≈ 0.526
      ├── Some((5, 3)): 16/33 ≈ 0.485
      ├── Some((5, 4)): 20/38 ≈ 0.526
      ├── Some((5, 5)): 26/45 ≈ 0.578
      ├── Some((5, 6)): 12/28 ≈ 0.429
      ├── Some((5, 7)): 20/38 ≈ 0.526
      └── Some((5, 8)): 40/61 ≈ 0.656
    ├── Some((8, 6)): 122/244 ≈ 0.500
      ├── Some((6, 0)): 13/27 ≈ 0.481
      ├── Some((6, 1)): 11/24 ≈ 0.458
      ├── Some((6, 2)): 14/28 ≈ 0.500
      ├── Some((6, 3)): 16/30 ≈ 0.533
      ├── Some((6, 4)): 10/23 ≈ 0.435
      ├── Some((6, 5)): 20/35 ≈ 0.571
      ├── Some((6, 6)): 7/19 ≈ 0.368
      ├── Some((6, 7)): 18/32 ≈ 0.562
      └── Some((6, 8)): 12/25 ≈ 0.480
    ├── Some((8, 7)): 127/251 ≈ 0.506
      ├── Some((7, 0)): 15/29 ≈ 0.517
      ├── Some((7, 1)): 10/23 ≈ 0.435
      ├── Some((7, 2)): 28/44 ≈ 0.636
      ├── Some((7, 3)): 11/24 ≈ 0.458
      ├── Some((7, 4)): 9/22 ≈ 0.409
      ├── Some((7, 5)): 17/32 ≈ 0.531
      ├── Some((7, 6)): 14/28 ≈ 0.500
      ├── Some((7, 7)): 7/19 ≈ 0.368
      └── Some((7, 8)): 15/29 ≈ 0.517
    └── Some((8, 8)): 123/245 ≈ 0.502
      ├── Some((8, 0)): 2/13 ≈ 0.154
      ├── Some((8, 1)): 25/43 ≈ 0.581
      ├── Some((8, 2)): 34/53 ≈ 0.642
      ├── Some((8, 3)): 19/35 ≈ 0.543
      ├── Some((8, 4)): 17/33 ≈ 0.515
      ├── Some((8, 5)): 7/20 ≈ 0.350
      ├── Some((8, 6)): 12/27 ≈ 0.444
      └── Some((8, 7)): 7/20 ≈ 0.350
├── Some((4, 2)): 35166/64090 ≈ 0.549
  ├── Some((2, 0)): 4437/8039 ≈ 0.552
    ├── Some((0, 0)): 635/1120 ≈ 0.567
      ├── Some((0, 1)): 99/168 ≈ 0.589
      ├── Some((0, 2)): 26/65 ≈ 0.400
      ├── Some((0, 3)): 50/100 ≈ 0.500
      ├── Some((0, 4)): 114/187 ≈ 0.610
      ├── Some((0, 5)): 58/111 ≈ 0.523
      ├── Some((0, 6)): 113/186 ≈ 0.608
      ├── Some((0, 7)): 96/163 ≈ 0.589
      └── Some((0, 8)): 78/139 ≈ 0.561
    ├── Some((0, 1)): 374/703 ≈ 0.532
      ├── Some((1, 0)): 59/101 ≈ 0.584
      ├── Some((1, 1)): 32/65 ≈ 0.492
      ├── Some((1, 2)): 31/64 ≈ 0.484
      ├── Some((1, 3)): 41/78 ≈ 0.526
      ├── Some((1, 4)): 43/80 ≈ 0.538
      ├── Some((1, 5)): 39/75 ≈ 0.520
      ├── Some((1, 6)): 43/80 ≈ 0.538
      ├── Some((1, 7)): 47/85 ≈ 0.553
      └── Some((1, 8)): 38/74 ≈ 0.514
    ├── Some((0, 2)): 636/1121 ≈ 0.567
      ├── Some((2, 1)): 89/153 ≈ 0.582
      ├── Some((2, 2)): 80/141 ≈ 0.567
      ├── Some((2, 3)): 111/183 ≈ 0.607
      ├── Some((2, 4)): 42/88 ≈ 0.477
      ├── Some((2, 5)): 56/108 ≈ 0.519
      ├── Some((2, 6)): 77/137 ≈ 0.562
      ├── Some((2, 7)): 115/188 ≈ 0.612
      └── Some((2, 8)): 66/122 ≈ 0.541
    ├── Some((0, 3)): 481/876 ≈ 0.549
      ├── Some((3, 0)): 44/85 ≈ 0.518
      ├── Some((3, 1)): 73/123 ≈ 0.593
      ├── Some((3, 2)): 55/100 ≈ 0.550
      ├── Some((3, 3)): 19/49 ≈ 0.388
      ├── Some((3, 4)): 43/83 ≈ 0.518
      ├── Some((3, 5)): 43/84 ≈ 0.512
      ├── Some((3, 6)): 84/138 ≈ 0.609
      ├── Some((3, 7)): 74/125 ≈ 0.592
      └── Some((3, 8)): 46/88 ≈ 0.523
    ├── Some((0, 4)): 736/1279 ≈ 0.575
      ├── Some((4, 0)): 118/195 ≈ 0.605
      ├── Some((4, 1)): 127/207 ≈ 0.614
      ├── Some((4, 3)): 93/162 ≈ 0.574
      ├── Some((4, 4)): 86/152 ≈ 0.566
      ├── Some((4, 5)): 47/97 ≈ 0.485
      ├── Some((4, 6)): 85/151 ≈ 0.563
      ├── Some((4, 7)): 92/160 ≈ 0.575
      └── Some((4, 8)): 87/154 ≈ 0.565
    ├── Some((0, 5)): 437/805 ≈ 0.543
      ├── Some((5, 0)): 47/88 ≈ 0.534
      ├── Some((5, 1)): 57/101 ≈ 0.564
      ├── Some((5, 2)): 67/114 ≈ 0.588
      ├── Some((5, 3)): 29/63 ≈ 0.460
      ├── Some((5, 4)): 71/119 ≈ 0.597
      ├── Some((5, 5)): 33/68 ≈ 0.485
      ├── Some((5, 6)): 26/59 ≈ 0.441
      ├── Some((5, 7)): 68/115 ≈ 0.591
      └── Some((5, 8)): 39/77 ≈ 0.506
    ├── Some((0, 6)): 426/787 ≈ 0.541
      ├── Some((6, 0)): 57/101 ≈ 0.564
      ├── Some((6, 1)): 35/71 ≈ 0.493
      ├── Some((6, 2)): 59/104 ≈ 0.567
      ├── Some((6, 3)): 18/47 ≈ 0.383
      ├── Some((6, 4)): 23/54 ≈ 0.426
      ├── Some((6, 5)): 81/132 ≈ 0.614
      ├── Some((6, 6)): 43/82 ≈ 0.524
      ├── Some((6, 7)): 64/110 ≈ 0.582
      └── Some((6, 8)): 45/85 ≈ 0.529
    ├── Some((0, 7)): 413/766 ≈ 0.539
      ├── Some((7, 0)): 42/80 ≈ 0.525
      ├── Some((7, 1)): 48/88 ≈ 0.545
      ├── Some((7, 2)): 72/120 ≈ 0.600
      ├── Some((7, 3)): 31/65 ≈ 0.477
      ├── Some((7, 4)): 56/99 ≈ 0.566
      ├── Some((7, 5)): 23/54 ≈ 0.426
      ├── Some((7, 6)): 78/127 ≈ 0.614
      ├── Some((7, 7)): 41/79 ≈ 0.519
      └── Some((7, 8)): 22/53 ≈ 0.415
    └── Some((0, 8)): 299/581 ≈ 0.515
      ├── Some((8, 0)): 50/87 ≈ 0.575
      ├── Some((8, 1)): 43/78 ≈ 0.551
      ├── Some((8, 2)): 9/31 ≈ 0.290
      ├── Some((8, 3)): 23/51 ≈ 0.451
      ├── Some((8, 4)): 48/84 ≈ 0.571
      ├── Some((8, 5)): 44/79 ≈ 0.557
      ├── Some((8, 6)): 35/68 ≈ 0.515
      ├── Some((8, 7)): 35/68 ≈ 0.515
      └── Some((8, 8)): 11/34 ≈ 0.324
  ├── Some((2, 1)): 4598/8317 ≈ 0.553
    ├── Some((1, 0)): 689/1207 ≈ 0.571
      ├── Some((0, 0)): 42/87 ≈ 0.483
      ├── Some((0, 1)): 126/200 ≈ 0.630
      ├── Some((0, 2)): 139/217 ≈ 0.641
      ├── Some((0, 3)): 24/61 ≈ 0.393
      ├── Some((0, 4)): 85/146 ≈ 0.582
      ├── Some((0, 5)): 57/108 ≈ 0.528
      ├── Some((0, 6)): 71/128 ≈ 0.555
      ├── Some((0, 7)): 70/126 ≈ 0.556
      └── Some((0, 8)): 75/133 ≈ 0.564
    ├── Some((1, 1)): 320/617 ≈ 0.519
      ├── Some((1, 0)): 43/81 ≈ 0.531
      ├── Some((1, 2)): 34/69 ≈ 0.493
      ├── Some((1, 3)): 32/66 ≈ 0.485
      ├── Some((1, 4)): 36/72 ≈ 0.500
      ├── Some((1, 5)): 23/54 ≈ 0.426
      ├── Some((1, 6)): 48/88 ≈ 0.545
      ├── Some((1, 7)): 43/81 ≈ 0.531
      └── Some((1, 8)): 61/105 ≈ 0.581
    ├── Some((1, 2)): 445/820 ≈ 0.543
      ├── Some((2, 0)): 58/106 ≈ 0.547
      ├── Some((2, 2)): 46/89 ≈ 0.517
      ├── Some((2, 3)): 52/97 ≈ 0.536
      ├── Some((2, 4)): 58/106 ≈ 0.547
      ├── Some((2, 5)): 64/114 ≈ 0.561
      ├── Some((2, 6)): 45/88 ≈ 0.511
      ├── Some((2, 7)): 60/108 ≈ 0.556
      └── Some((2, 8)): 62/111 ≈ 0.559
    ├── Some((1, 3)): 467/855 ≈ 0.546
      ├── Some((3, 0)): 29/64 ≈ 0.453
      ├── Some((3, 1)): 68/117 ≈ 0.581
      ├── Some((3, 2)): 53/97 ≈ 0.546
      ├── Some((3, 3)): 61/108 ≈ 0.565
      ├── Some((3, 4)): 57/102 ≈ 0.559
      ├── Some((3, 5)): 28/63 ≈ 0.444
      ├── Some((3, 6)): 54/98 ≈ 0.551
      ├── Some((3, 7)): 95/151 ≈ 0.629
      └── Some((3, 8)): 22/54 ≈ 0.407
    ├── Some((1, 4)): 427/791 ≈ 0.540
      ├── Some((4, 0)): 37/77 ≈ 0.481
      ├── Some((4, 1)): 52/98 ≈ 0.531
      ├── Some((4, 3)): 104/166 ≈ 0.627
      ├── Some((4, 4)): 53/99 ≈ 0.535
      ├── Some((4, 5)): 31/68 ≈ 0.456
      ├── Some((4, 6)): 31/68 ≈ 0.456
      ├── Some((4, 7)): 79/134 ≈ 0.590
      └── Some((4, 8)): 39/80 ≈ 0.488
    ├── Some((1, 5)): 473/864 ≈ 0.547
      ├── Some((5, 0)): 29/64 ≈ 0.453
      ├── Some((5, 1)): 72/122 ≈ 0.590
      ├── Some((5, 2)): 66/114 ≈ 0.579
      ├── Some((5, 3)): 25/58 ≈ 0.431
      ├── Some((5, 4)): 44/85 ≈ 0.518
      ├── Some((5, 5)): 53/97 ≈ 0.546
      ├── Some((5, 6)): 52/96 ≈ 0.542
      ├── Some((5, 7)): 71/121 ≈ 0.587
      └── Some((5, 8)): 60/106 ≈ 0.566
    ├── Some((1, 6)): 535/963 ≈ 0.556
      ├── Some((6, 0)): 51/96 ≈ 0.531
      ├── Some((6, 1)): 105/167 ≈ 0.629
      ├── Some((6, 2)): 24/58 ≈ 0.414
      ├── Some((6, 3)): 49/93 ≈ 0.527
      ├── Some((6, 4)): 51/96 ≈ 0.531
      ├── Some((6, 5)): 54/100 ≈ 0.540
      ├── Some((6, 6)): 52/98 ≈ 0.531
      ├── Some((6, 7)): 78/132 ≈ 0.591
      └── Some((6, 8)): 70/122 ≈ 0.574
    ├── Some((1, 7)): 718/1253 ≈ 0.573
      ├── Some((7, 0)): 143/223 ≈ 0.641
      ├── Some((7, 1)): 81/141 ≈ 0.574
      ├── Some((7, 2)): 87/149 ≈ 0.584
      ├── Some((7, 3)): 72/129 ≈ 0.558
      ├── Some((7, 4)): 55/106 ≈ 0.519
      ├── Some((7, 5)): 65/120 ≈ 0.542
      ├── Some((7, 6)): 40/85 ≈ 0.471
      ├── Some((7, 7)): 104/172 ≈ 0.605
      └── Some((7, 8)): 70/127 ≈ 0.551
    └── Some((1, 8)): 524/946 ≈ 0.554
      ├── Some((8, 0)): 127/195 ≈ 0.651
      ├── Some((8, 1)): 67/118 ≈ 0.568
      ├── Some((8, 2)): 52/97 ≈ 0.536
      ├── Some((8, 3)): 62/111 ≈ 0.559
      ├── Some((8, 4)): 63/112 ≈ 0.562
      ├── Some((8, 5)): 60/108 ≈ 0.556
      ├── Some((8, 6)): 34/73 ≈ 0.466
      ├── Some((8, 7)): 32/70 ≈ 0.457
      └── Some((8, 8)): 26/61 ≈ 0.426
  ├── Some((2, 2)): 3351/6160 ≈ 0.544
    ├── Some((2, 0)): 308/591 ≈ 0.521
      ├── Some((0, 0)): 55/93 ≈ 0.591
      ├── Some((0, 1)): 49/85 ≈ 0.576
      ├── Some((0, 2)): 24/52 ≈ 0.462
      ├── Some((0, 3)): 40/74 ≈ 0.541
      ├── Some((0, 4)): 14/38 ≈ 0.368
      ├── Some((0, 5)): 34/66 ≈ 0.515
      ├── Some((0, 6)): 16/41 ≈ 0.390
      ├── Some((0, 7)): 57/96 ≈ 0.594
      └── Some((0, 8)): 19/45 ≈ 0.422
    ├── Some((2, 1)): 469/851 ≈ 0.551
      ├── Some((1, 0)): 60/105 ≈ 0.571
      ├── Some((1, 1)): 64/110 ≈ 0.582
      ├── Some((1, 2)): 24/56 ≈ 0.429
      ├── Some((1, 3)): 54/97 ≈ 0.557
      ├── Some((1, 4)): 38/76 ≈ 0.500
      ├── Some((1, 5)): 47/88 ≈ 0.534
      ├── Some((1, 6)): 51/93 ≈ 0.548
      ├── Some((1, 7)): 73/122 ≈ 0.598
      └── Some((1, 8)): 58/103 ≈ 0.563
    ├── Some((2, 3)): 315/603 ≈ 0.522
      ├── Some((3, 0)): 54/92 ≈ 0.587
      ├── Some((3, 1)): 51/88 ≈ 0.580
      ├── Some((3, 2)): 32/64 ≈ 0.500
      ├── Some((3, 3)): 41/75 ≈ 0.547
      ├── Some((3, 4)): 38/71 ≈ 0.535
      ├── Some((3, 5)): 18/44 ≈ 0.409
      ├── Some((3, 6)): 37/70 ≈ 0.529
      ├── Some((3, 7)): 27/57 ≈ 0.474
      └── Some((3, 8)): 16/41 ≈ 0.390
    ├── Some((2, 4)): 509/915 ≈ 0.556
      ├── Some((4, 0)): 80/136 ≈ 0.588
      ├── Some((4, 1)): 84/142 ≈ 0.592
      ├── Some((4, 3)): 60/110 ≈ 0.545
      ├── Some((4, 4)): 38/79 ≈ 0.481
      ├── Some((4, 5)): 58/107 ≈ 0.542
      ├── Some((4, 6)): 69/122 ≈ 0.566
      ├── Some((4, 7)): 60/110 ≈ 0.545
      └── Some((4, 8)): 59/108 ≈ 0.546
    ├── Some((2, 5)): 563/1000 ≈ 0.563
      ├── Some((5, 0)): 62/111 ≈ 0.559
      ├── Some((5, 1)): 70/121 ≈ 0.579
      ├── Some((5, 2)): 52/97 ≈ 0.536
      ├── Some((5, 3)): 80/135 ≈ 0.593
      ├── Some((5, 4)): 70/121 ≈ 0.579
      ├── Some((5, 5)): 26/61 ≈ 0.426
      ├── Some((5, 6)): 66/116 ≈ 0.569
      ├── Some((5, 7)): 75/128 ≈ 0.586
      └── Some((5, 8)): 61/109 ≈ 0.560
    ├── Some((2, 6)): 383/713 ≈ 0.537
      ├── Some((6, 0)): 33/67 ≈ 0.493
      ├── Some((6, 1)): 31/64 ≈ 0.484
      ├── Some((6, 2)): 25/56 ≈ 0.446
      ├── Some((6, 3)): 58/100 ≈ 0.580
      ├── Some((6, 4)): 57/99 ≈ 0.576
      ├── Some((6, 5)): 63/106 ≈ 0.594
      ├── Some((6, 6)): 36/71 ≈ 0.507
      ├── Some((6, 7)): 19/47 ≈ 0.404
      └── Some((6, 8)): 60/102 ≈ 0.588
    ├── Some((2, 7)): 421/774 ≈ 0.544
      ├── Some((7, 0)): 77/126 ≈ 0.611
      ├── Some((7, 1)): 35/71 ≈ 0.493
      ├── Some((7, 2)): 55/97 ≈ 0.567
      ├── Some((7, 3)): 71/118 ≈ 0.602
      ├── Some((7, 4)): 43/81 ≈ 0.531
      ├── Some((7, 5)): 42/80 ≈ 0.525
      ├── Some((7, 6)): 33/68 ≈ 0.485
      ├── Some((7, 7)): 42/80 ≈ 0.525
      └── Some((7, 8)): 22/52 ≈ 0.423
    └── Some((2, 8)): 382/712 ≈ 0.537
      ├── Some((8, 0)): 28/60 ≈ 0.467
      ├── Some((8, 1)): 76/123 ≈ 0.618
      ├── Some((8, 2)): 38/74 ≈ 0.514
      ├── Some((8, 3)): 25/56 ≈ 0.446
      ├── Some((8, 4)): 30/63 ≈ 0.476
      ├── Some((8, 5)): 56/97 ≈ 0.577
      ├── Some((8, 6)): 19/47 ≈ 0.404
      ├── Some((8, 7)): 64/108 ≈ 0.593
      └── Some((8, 8)): 45/83 ≈ 0.542
  ├── Some((2, 3)): 2685/5000 ≈ 0.537
    ├── Some((3, 0)): 374/675 ≈ 0.554
      ├── Some((0, 0)): 17/42 ≈ 0.405
      ├── Some((0, 1)): 69/110 ≈ 0.627
      ├── Some((0, 2)): 47/82 ≈ 0.573
      ├── Some((0, 3)): 24/52 ≈ 0.462
      ├── Some((0, 4)): 53/90 ≈ 0.589
      ├── Some((0, 5)): 48/84 ≈ 0.571
      ├── Some((0, 6)): 29/59 ≈ 0.492
      ├── Some((0, 7)): 41/75 ≈ 0.547
      └── Some((0, 8)): 45/80 ≈ 0.562
    ├── Some((3, 1)): 293/548 ≈ 0.535
      ├── Some((1, 0)): 26/52 ≈ 0.500
      ├── Some((1, 1)): 45/77 ≈ 0.584
      ├── Some((1, 2)): 21/46 ≈ 0.457
      ├── Some((1, 3)): 29/56 ≈ 0.518
      ├── Some((1, 4)): 35/64 ≈ 0.547
      ├── Some((1, 5)): 28/55 ≈ 0.509
      ├── Some((1, 6)): 26/53 ≈ 0.491
      ├── Some((1, 7)): 35/64 ≈ 0.547
      └── Some((1, 8)): 48/80 ≈ 0.600
    ├── Some((3, 2)): 325/598 ≈ 0.543
      ├── Some((2, 0)): 30/61 ≈ 0.492
      ├── Some((2, 1)): 66/107 ≈ 0.617
      ├── Some((2, 2)): 41/75 ≈ 0.547
      ├── Some((2, 4)): 35/68 ≈ 0.515
      ├── Some((2, 5)): 28/58 ≈ 0.483
      ├── Some((2, 6)): 41/75 ≈ 0.547
      ├── Some((2, 7)): 47/83 ≈ 0.566
      └── Some((2, 8)): 37/70 ≈ 0.529
    ├── Some((3, 3)): 362/656 ≈ 0.552
      ├── Some((3, 0)): 69/113 ≈ 0.611
      ├── Some((3, 1)): 22/51 ≈ 0.431
      ├── Some((3, 2)): 27/58 ≈ 0.466
      ├── Some((3, 4)): 55/95 ≈ 0.579
      ├── Some((3, 5)): 45/82 ≈ 0.549
      ├── Some((3, 6)): 32/65 ≈ 0.492
      ├── Some((3, 7)): 38/73 ≈ 0.521
      └── Some((3, 8)): 73/118 ≈ 0.619
    ├── Some((3, 4)): 329/605 ≈ 0.544
      ├── Some((4, 0)): 52/90 ≈ 0.578
      ├── Some((4, 1)): 48/85 ≈ 0.565
      ├── Some((4, 3)): 36/69 ≈ 0.522
      ├── Some((4, 4)): 41/75 ≈ 0.547
      ├── Some((4, 5)): 29/60 ≈ 0.483
      ├── Some((4, 6)): 59/98 ≈ 0.602
      ├── Some((4, 7)): 31/62 ≈ 0.500
      └── Some((4, 8)): 33/65 ≈ 0.508
    ├── Some((3, 5)): 241/464 ≈ 0.519
      ├── Some((5, 0)): 43/72 ≈ 0.597
      ├── Some((5, 1)): 17/39 ≈ 0.436
      ├── Some((5, 2)): 11/31 ≈ 0.355
      ├── Some((5, 3)): 25/50 ≈ 0.500
      ├── Some((5, 4)): 26/51 ≈ 0.510
      ├── Some((5, 5)): 33/60 ≈ 0.550
      ├── Some((5, 6)): 50/80 ≈ 0.625
      ├── Some((5, 7)): 15/36 ≈ 0.417
      └── Some((5, 8)): 21/44 ≈ 0.477
    ├── Some((3, 6)): 262/498 ≈ 0.526
      ├── Some((6, 0)): 27/53 ≈ 0.509
      ├── Some((6, 1)): 42/72 ≈ 0.583
      ├── Some((6, 2)): 16/38 ≈ 0.421
      ├── Some((6, 3)): 31/58 ≈ 0.534
      ├── Some((6, 4)): 22/46 ≈ 0.478
      ├── Some((6, 5)): 24/49 ≈ 0.490
      ├── Some((6, 6)): 30/57 ≈ 0.526
      ├── Some((6, 7)): 20/43 ≈ 0.465
      └── Some((6, 8)): 50/81 ≈ 0.617
    ├── Some((3, 7)): 271/513 ≈ 0.528
      ├── Some((7, 0)): 38/67 ≈ 0.567
      ├── Some((7, 1)): 42/72 ≈ 0.583
      ├── Some((7, 2)): 19/43 ≈ 0.442
      ├── Some((7, 3)): 22/47 ≈ 0.468
      ├── Some((7, 4)): 14/36 ≈ 0.389
      ├── Some((7, 5)): 29/56 ≈ 0.518
      ├── Some((7, 6)): 37/66 ≈ 0.561
      ├── Some((7, 7)): 28/54 ≈ 0.519
      └── Some((7, 8)): 41/71 ≈ 0.577
    └── Some((3, 8)): 227/442 ≈ 0.514
      ├── Some((8, 0)): 23/46 ≈ 0.500
      ├── Some((8, 1)): 32/58 ≈ 0.552
      ├── Some((8, 2)): 27/51 ≈ 0.529
      ├── Some((8, 3)): 12/32 ≈ 0.375
      ├── Some((8, 4)): 24/48 ≈ 0.500
      ├── Some((8, 5)): 45/74 ≈ 0.608
      ├── Some((8, 6)): 17/38 ≈ 0.447
      ├── Some((8, 7)): 15/36 ≈ 0.417
      └── Some((8, 8)): 32/58 ≈ 0.552
  ├── Some((2, 4)): 4045/7363 ≈ 0.549
    ├── Some((4, 0)): 600/1072 ≈ 0.560
      ├── Some((0, 0)): 92/153 ≈ 0.601
      ├── Some((0, 1)): 75/131 ≈ 0.573
      ├── Some((0, 2)): 46/91 ≈ 0.505
      ├── Some((0, 3)): 68/121 ≈ 0.562
      ├── Some((0, 4)): 45/90 ≈ 0.500
      ├── Some((0, 5)): 62/113 ≈ 0.549
      ├── Some((0, 6)): 74/130 ≈ 0.569
      ├── Some((0, 7)): 109/175 ≈ 0.623
      └── Some((0, 8)): 29/67 ≈ 0.433
    ├── Some((4, 1)): 427/794 ≈ 0.538
      ├── Some((1, 0)): 32/67 ≈ 0.478
      ├── Some((1, 1)): 70/118 ≈ 0.593
      ├── Some((1, 2)): 52/95 ≈ 0.547
      ├── Some((1, 3)): 30/65 ≈ 0.462
      ├── Some((1, 4)): 48/89 ≈ 0.539
      ├── Some((1, 5)): 30/65 ≈ 0.462
      ├── Some((1, 6)): 81/132 ≈ 0.614
      ├── Some((1, 7)): 50/92 ≈ 0.543
      └── Some((1, 8)): 34/70 ≈ 0.486
    ├── Some((4, 3)): 371/703 ≈ 0.528
      ├── Some((3, 0)): 56/98 ≈ 0.571
      ├── Some((3, 1)): 19/48 ≈ 0.396
      ├── Some((3, 2)): 38/74 ≈ 0.514
      ├── Some((3, 3)): 54/96 ≈ 0.562
      ├── Some((3, 4)): 49/89 ≈ 0.551
      ├── Some((3, 5)): 29/62 ≈ 0.468
      ├── Some((3, 6)): 16/43 ≈ 0.372
      ├── Some((3, 7)): 36/72 ≈ 0.500
      └── Some((3, 8)): 73/120 ≈ 0.608
    ├── Some((4, 4)): 568/1021 ≈ 0.556
      ├── Some((4, 0)): 63/120 ≈ 0.525
      ├── Some((4, 1)): 103/176 ≈ 0.585
      ├── Some((4, 3)): 86/152 ≈ 0.566
      ├── Some((4, 5)): 67/126 ≈ 0.532
      ├── Some((4, 6)): 81/146 ≈ 0.555
      ├── Some((4, 7)): 71/132 ≈ 0.538
      └── Some((4, 8)): 97/168 ≈ 0.577
    ├── Some((4, 5)): 562/1011 ≈ 0.556
      ├── Some((5, 0)): 86/144 ≈ 0.597
      ├── Some((5, 1)): 58/107 ≈ 0.542
      ├── Some((5, 2)): 31/69 ≈ 0.449
      ├── Some((5, 3)): 23/57 ≈ 0.404
      ├── Some((5, 4)): 65/116 ≈ 0.560
      ├── Some((5, 5)): 79/135 ≈ 0.585
      ├── Some((5, 6)): 67/119 ≈ 0.563
      ├── Some((5, 7)): 65/117 ≈ 0.556
      └── Some((5, 8)): 87/146 ≈ 0.596
    ├── Some((4, 6)): 616/1097 ≈ 0.562
      ├── Some((6, 0)): 118/187 ≈ 0.631
      ├── Some((6, 1)): 55/104 ≈ 0.529
      ├── Some((6, 2)): 60/111 ≈ 0.541
      ├── Some((6, 3)): 58/108 ≈ 0.537
      ├── Some((6, 4)): 51/99 ≈ 0.515
      ├── Some((6, 5)): 77/134 ≈ 0.575
      ├── Some((6, 6)): 53/101 ≈ 0.525
      ├── Some((6, 7)): 103/168 ≈ 0.613
      └── Some((6, 8)): 41/84 ≈ 0.488
    ├── Some((4, 7)): 399/749 ≈ 0.533
      ├── Some((7, 0)): 32/67 ≈ 0.478
      ├── Some((7, 1)): 37/74 ≈ 0.500
      ├── Some((7, 2)): 53/95 ≈ 0.558
      ├── Some((7, 3)): 24/55 ≈ 0.436
      ├── Some((7, 4)): 44/83 ≈ 0.530
      ├── Some((7, 5)): 36/72 ≈ 0.500
      ├── Some((7, 6)): 55/98 ≈ 0.561
      ├── Some((7, 7)): 39/76 ≈ 0.513
      └── Some((7, 8)): 79/128 ≈ 0.617
    └── Some((4, 8)): 502/915 ≈ 0.549
      ├── Some((8, 0)): 35/73 ≈ 0.479
      ├── Some((8, 1)): 58/105 ≈ 0.552
      ├── Some((8, 2)): 54/99 ≈ 0.545
      ├── Some((8, 3)): 70/121 ≈ 0.579
      ├── Some((8, 4)): 55/101 ≈ 0.545
      ├── Some((8, 5)): 41/82 ≈ 0.500
      ├── Some((8, 6)): 58/105 ≈ 0.552
      ├── Some((8, 7)): 85/140 ≈ 0.607
      └── Some((8, 8)): 46/88 ≈ 0.523
  ├── Some((2, 5)): 4340/7872 ≈ 0.551
    ├── Some((5, 0)): 668/1170 ≈ 0.571
      ├── Some((0, 0)): 122/193 ≈ 0.632
      ├── Some((0, 1)): 49/96 ≈ 0.510
      ├── Some((0, 2)): 93/155 ≈ 0.600
      ├── Some((0, 3)): 54/103 ≈ 0.524
      ├── Some((0, 4)): 87/147 ≈ 0.592
      ├── Some((0, 5)): 92/154 ≈ 0.597
      ├── Some((0, 6)): 57/107 ≈ 0.533
      ├── Some((0, 7)): 62/114 ≈ 0.544
      └── Some((0, 8)): 52/100 ≈ 0.520
    ├── Some((5, 1)): 336/641 ≈ 0.524
      ├── Some((1, 0)): 69/112 ≈ 0.616
      ├── Some((1, 1)): 40/75 ≈ 0.533
      ├── Some((1, 2)): 33/66 ≈ 0.500
      ├── Some((1, 3)): 36/70 ≈ 0.514
      ├── Some((1, 4)): 29/60 ≈ 0.483
      ├── Some((1, 5)): 34/67 ≈ 0.507
      ├── Some((1, 6)): 34/67 ≈ 0.507
      ├── Some((1, 7)): 25/55 ≈ 0.455
      └── Some((1, 8)): 35/68 ≈ 0.515
    ├── Some((5, 2)): 672/1177 ≈ 0.571
      ├── Some((2, 0)): 71/130 ≈ 0.546
      ├── Some((2, 1)): 92/158 ≈ 0.582
      ├── Some((2, 2)): 82/145 ≈ 0.566
      ├── Some((2, 3)): 60/115 ≈ 0.522
      ├── Some((2, 4)): 124/201 ≈ 0.617
      ├── Some((2, 6)): 70/128 ≈ 0.547
      ├── Some((2, 7)): 125/202 ≈ 0.619
      └── Some((2, 8)): 48/97 ≈ 0.495
    ├── Some((5, 3)): 481/874 ≈ 0.550
      ├── Some((3, 0)): 35/72 ≈ 0.486
      ├── Some((3, 1)): 74/125 ≈ 0.592
      ├── Some((3, 2)): 61/108 ≈ 0.565
      ├── Some((3, 3)): 26/60 ≈ 0.433
      ├── Some((3, 4)): 36/74 ≈ 0.486
      ├── Some((3, 5)): 70/119 ≈ 0.588
      ├── Some((3, 6)): 48/90 ≈ 0.533
      ├── Some((3, 7)): 80/132 ≈ 0.606
      └── Some((3, 8)): 50/93 ≈ 0.538
    ├── Some((5, 4)): 380/712 ≈ 0.534
      ├── Some((4, 0)): 35/72 ≈ 0.486
      ├── Some((4, 1)): 34/71 ≈ 0.479
      ├── Some((4, 3)): 60/106 ≈ 0.566
      ├── Some((4, 4)): 48/90 ≈ 0.533
      ├── Some((4, 5)): 31/67 ≈ 0.463
      ├── Some((4, 6)): 60/106 ≈ 0.566
      ├── Some((4, 7)): 35/72 ≈ 0.486
      └── Some((4, 8)): 76/127 ≈ 0.598
    ├── Some((5, 5)): 364/686 ≈ 0.531
      ├── Some((5, 0)): 47/88 ≈ 0.534
      ├── Some((5, 1)): 45/85 ≈ 0.529
      ├── Some((5, 2)): 51/93 ≈ 0.548
      ├── Some((5, 3)): 31/66 ≈ 0.470
      ├── Some((5, 4)): 55/99 ≈ 0.556
      ├── Some((5, 6)): 45/85 ≈ 0.529
      ├── Some((5, 7)): 58/103 ≈ 0.563
      └── Some((5, 8)): 31/66 ≈ 0.470
    ├── Some((5, 6)): 388/725 ≈ 0.535
      ├── Some((6, 0)): 18/46 ≈ 0.391
      ├── Some((6, 1)): 43/81 ≈ 0.531
      ├── Some((6, 2)): 40/77 ≈ 0.519
      ├── Some((6, 3)): 67/112 ≈ 0.598
      ├── Some((6, 4)): 68/113 ≈ 0.602
      ├── Some((6, 5)): 29/62 ≈ 0.468
      ├── Some((6, 6)): 35/70 ≈ 0.500
      ├── Some((6, 7)): 36/71 ≈ 0.507
      └── Some((6, 8)): 52/92 ≈ 0.565
    ├── Some((5, 7)): 671/1175 ≈ 0.571
      ├── Some((7, 0)): 99/163 ≈ 0.607
      ├── Some((7, 1)): 77/134 ≈ 0.575
      ├── Some((7, 2)): 40/83 ≈ 0.482
      ├── Some((7, 3)): 93/155 ≈ 0.600
      ├── Some((7, 4)): 87/147 ≈ 0.592
      ├── Some((7, 5)): 60/111 ≈ 0.541
      ├── Some((7, 6)): 73/129 ≈ 0.566
      ├── Some((7, 7)): 84/144 ≈ 0.583
      └── Some((7, 8)): 58/108 ≈ 0.537
    └── Some((5, 8)): 379/711 ≈ 0.533
      ├── Some((8, 0)): 28/60 ≈ 0.467
      ├── Some((8, 1)): 32/66 ≈ 0.485
      ├── Some((8, 2)): 27/59 ≈ 0.458
      ├── Some((8, 3)): 46/84 ≈ 0.548
      ├── Some((8, 4)): 49/88 ≈ 0.557
      ├── Some((8, 5)): 51/91 ≈ 0.560
      ├── Some((8, 6)): 71/116 ≈ 0.612
      ├── Some((8, 7)): 35/70 ≈ 0.500
      └── Some((8, 8)): 40/76 ≈ 0.526
  ├── Some((2, 6)): 3677/6726 ≈ 0.547
    ├── Some((6, 0)): 452/817 ≈ 0.553
      ├── Some((0, 0)): 29/63 ≈ 0.460
      ├── Some((0, 1)): 42/80 ≈ 0.525
      ├── Some((0, 2)): 72/120 ≈ 0.600
      ├── Some((0, 3)): 39/76 ≈ 0.513
      ├── Some((0, 4)): 53/95 ≈ 0.558
      ├── Some((0, 5)): 45/84 ≈ 0.536
      ├── Some((0, 6)): 48/88 ≈ 0.545
      ├── Some((0, 7)): 89/141 ≈ 0.631
      └── Some((0, 8)): 34/69 ≈ 0.493
    ├── Some((6, 1)): 482/864 ≈ 0.558
      ├── Some((1, 0)): 94/149 ≈ 0.631
      ├── Some((1, 1)): 45/85 ≈ 0.529
      ├── Some((1, 2)): 51/93 ≈ 0.548
      ├── Some((1, 3)): 66/113 ≈ 0.584
      ├── Some((1, 4)): 36/73 ≈ 0.493
      ├── Some((1, 5)): 46/86 ≈ 0.535
      ├── Some((1, 6)): 58/102 ≈ 0.569
      ├── Some((1, 7)): 24/56 ≈ 0.429
      └── Some((1, 8)): 61/106 ≈ 0.575
    ├── Some((6, 2)): 416/760 ≈ 0.547
      ├── Some((2, 0)): 55/99 ≈ 0.556
      ├── Some((2, 1)): 69/118 ≈ 0.585
      ├── Some((2, 2)): 45/86 ≈ 0.523
      ├── Some((2, 3)): 23/55 ≈ 0.418
      ├── Some((2, 4)): 42/82 ≈ 0.512
      ├── Some((2, 5)): 81/134 ≈ 0.604
      ├── Some((2, 7)): 48/90 ≈ 0.533
      └── Some((2, 8)): 52/95 ≈ 0.547
    ├── Some((6, 3)): 438/795 ≈ 0.551
      ├── Some((3, 0)): 55/97 ≈ 0.567
      ├── Some((3, 1)): 70/116 ≈ 0.603
      ├── Some((3, 2)): 30/63 ≈ 0.476
      ├── Some((3, 3)): 42/80 ≈ 0.525
      ├── Some((3, 4)): 74/121 ≈ 0.612
      ├── Some((3, 5)): 27/59 ≈ 0.458
      ├── Some((3, 6)): 48/88 ≈ 0.545
      ├── Some((3, 7)): 30/64 ≈ 0.469
      └── Some((3, 8)): 62/106 ≈ 0.585
    ├── Some((6, 4)): 344/644 ≈ 0.534
      ├── Some((4, 0)): 73/120 ≈ 0.608
      ├── Some((4, 1)): 34/69 ≈ 0.493
      ├── Some((4, 3)): 47/86 ≈ 0.547
      ├── Some((4, 4)): 37/73 ≈ 0.507
      ├── Some((4, 5)): 53/94 ≈ 0.564
      ├── Some((4, 6)): 23/53 ≈ 0.434
      ├── Some((4, 7)): 50/90 ≈ 0.556
      └── Some((4, 8)): 26/58 ≈ 0.448
    ├── Some((6, 5)): 475/853 ≈ 0.557
      ├── Some((5, 0)): 68/115 ≈ 0.591
      ├── Some((5, 1)): 33/69 ≈ 0.478
      ├── Some((5, 2)): 40/78 ≈ 0.513
      ├── Some((5, 3)): 73/121 ≈ 0.603
      ├── Some((5, 4)): 58/102 ≈ 0.569
      ├── Some((5, 5)): 66/112 ≈ 0.589
      ├── Some((5, 6)): 35/71 ≈ 0.493
      ├── Some((5, 7)): 40/78 ≈ 0.513
      └── Some((5, 8)): 61/106 ≈ 0.575
    ├── Some((6, 6)): 334/628 ≈ 0.532
      ├── Some((6, 0)): 64/108 ≈ 0.593
      ├── Some((6, 1)): 53/94 ≈ 0.564
      ├── Some((6, 2)): 30/63 ≈ 0.476
      ├── Some((6, 3)): 39/75 ≈ 0.520
      ├── Some((6, 4)): 26/57 ≈ 0.456
      ├── Some((6, 5)): 43/80 ≈ 0.538
      ├── Some((6, 7)): 28/60 ≈ 0.467
      └── Some((6, 8)): 50/90 ≈ 0.556
    ├── Some((6, 7)): 274/531 ≈ 0.516
      ├── Some((7, 0)): 19/44 ≈ 0.432
      ├── Some((7, 1)): 30/58 ≈ 0.517
      ├── Some((7, 2)): 28/56 ≈ 0.500
      ├── Some((7, 3)): 23/49 ≈ 0.469
      ├── Some((7, 4)): 39/70 ≈ 0.557
      ├── Some((7, 5)): 29/57 ≈ 0.509
      ├── Some((7, 6)): 37/67 ≈ 0.552
      ├── Some((7, 7)): 38/69 ≈ 0.551
      └── Some((7, 8)): 31/60 ≈ 0.517
    └── Some((6, 8)): 462/833 ≈ 0.555
      ├── Some((8, 0)): 69/116 ≈ 0.595
      ├── Some((8, 1)): 27/60 ≈ 0.450
      ├── Some((8, 2)): 38/75 ≈ 0.507
      ├── Some((8, 3)): 63/108 ≈ 0.583
      ├── Some((8, 4)): 45/85 ≈ 0.529
      ├── Some((8, 5)): 24/56 ≈ 0.429
      ├── Some((8, 6)): 36/72 ≈ 0.500
      ├── Some((8, 7)): 59/103 ≈ 0.573
      └── Some((8, 8)): 101/157 ≈ 0.643
  ├── Some((2, 7)): 5194/9343 ≈ 0.556
    ├── Some((7, 0)): 623/1112 ≈ 0.560
      ├── Some((0, 0)): 87/148 ≈ 0.588
      ├── Some((0, 1)): 76/133 ≈ 0.571
      ├── Some((0, 2)): 76/133 ≈ 0.571
      ├── Some((0, 3)): 64/117 ≈ 0.547
      ├── Some((0, 4)): 78/136 ≈ 0.574
      ├── Some((0, 5)): 27/64 ≈ 0.422
      ├── Some((0, 6)): 47/93 ≈ 0.505
      ├── Some((0, 7)): 75/132 ≈ 0.568
      └── Some((0, 8)): 93/155 ≈ 0.600
    ├── Some((7, 1)): 636/1132 ≈ 0.562
      ├── Some((1, 0)): 49/97 ≈ 0.505
      ├── Some((1, 1)): 135/211 ≈ 0.640
      ├── Some((1, 2)): 111/180 ≈ 0.617
      ├── Some((1, 3)): 81/140 ≈ 0.579
      ├── Some((1, 4)): 88/150 ≈ 0.587
      ├── Some((1, 5)): 39/83 ≈ 0.470
      ├── Some((1, 6)): 31/71 ≈ 0.437
      ├── Some((1, 7)): 49/97 ≈ 0.505
      └── Some((1, 8)): 53/102 ≈ 0.520
    ├── Some((7, 2)): 514/938 ≈ 0.548
      ├── Some((2, 0)): 73/129 ≈ 0.566
      ├── Some((2, 1)): 59/110 ≈ 0.536
      ├── Some((2, 2)): 88/149 ≈ 0.591
      ├── Some((2, 3)): 52/101 ≈ 0.515
      ├── Some((2, 4)): 43/88 ≈ 0.489
      ├── Some((2, 5)): 68/123 ≈ 0.553
      ├── Some((2, 6)): 55/105 ≈ 0.524
      └── Some((2, 8)): 75/132 ≈ 0.568
    ├── Some((7, 3)): 552/998 ≈ 0.553
      ├── Some((3, 0)): 70/123 ≈ 0.569
      ├── Some((3, 1)): 44/87 ≈ 0.506
      ├── Some((3, 2)): 82/138 ≈ 0.594
      ├── Some((3, 3)): 59/108 ≈ 0.546
      ├── Some((3, 4)): 65/116 ≈ 0.560
      ├── Some((3, 5)): 79/135 ≈ 0.585
      ├── Some((3, 6)): 61/111 ≈ 0.550
      ├── Some((3, 7)): 66/117 ≈ 0.564
      └── Some((3, 8)): 26/62 ≈ 0.419
    ├── Some((7, 4)): 597/1070 ≈ 0.558
      ├── Some((4, 0)): 48/97 ≈ 0.495
      ├── Some((4, 1)): 111/183 ≈ 0.607
      ├── Some((4, 3)): 53/104 ≈ 0.510
      ├── Some((4, 4)): 95/162 ≈ 0.586
      ├── Some((4, 5)): 74/133 ≈ 0.556
      ├── Some((4, 6)): 90/155 ≈ 0.581
      ├── Some((4, 7)): 62/117 ≈ 0.530
      └── Some((4, 8)): 63/118 ≈ 0.534
    ├── Some((7, 5)): 599/1073 ≈ 0.558
      ├── Some((5, 0)): 84/143 ≈ 0.587
      ├── Some((5, 1)): 68/121 ≈ 0.562
      ├── Some((5, 2)): 63/115 ≈ 0.548
      ├── Some((5, 3)): 37/79 ≈ 0.468
      ├── Some((5, 4)): 56/105 ≈ 0.533
      ├── Some((5, 5)): 46/91 ≈ 0.505
      ├── Some((5, 6)): 94/156 ≈ 0.603
      ├── Some((5, 7)): 51/98 ≈ 0.520
      └── Some((5, 8)): 100/164 ≈ 0.610
    ├── Some((7, 6)): 493/904 ≈ 0.545
      ├── Some((6, 0)): 49/93 ≈ 0.527
      ├── Some((6, 1)): 43/85 ≈ 0.506
      ├── Some((6, 2)): 84/139 ≈ 0.604
      ├── Some((6, 3)): 67/117 ≈ 0.573
      ├── Some((6, 4)): 49/93 ≈ 0.527
      ├── Some((6, 5)): 26/61 ≈ 0.426
      ├── Some((6, 6)): 51/95 ≈ 0.537
      ├── Some((6, 7)): 72/123 ≈ 0.585
      └── Some((6, 8)): 52/97 ≈ 0.536
    ├── Some((7, 7)): 693/1223 ≈ 0.567
      ├── Some((7, 0)): 99/170 ≈ 0.582
      ├── Some((7, 1)): 113/189 ≈ 0.598
      ├── Some((7, 2)): 77/140 ≈ 0.550
      ├── Some((7, 3)): 56/110 ≈ 0.509
      ├── Some((7, 4)): 61/118 ≈ 0.517
      ├── Some((7, 5)): 108/182 ≈ 0.593
      ├── Some((7, 6)): 94/163 ≈ 0.577
      └── Some((7, 8)): 84/150 ≈ 0.560
    └── Some((7, 8)): 486/892 ≈ 0.545
      ├── Some((8, 0)): 25/59 ≈ 0.424
      ├── Some((8, 1)): 54/99 ≈ 0.545
      ├── Some((8, 2)): 74/126 ≈ 0.587
      ├── Some((8, 3)): 40/80 ≈ 0.500
      ├── Some((8, 4)): 49/93 ≈ 0.527
      ├── Some((8, 5)): 57/103 ≈ 0.553
      ├── Some((8, 6)): 61/109 ≈ 0.560
      ├── Some((8, 7)): 65/114 ≈ 0.570
      └── Some((8, 8)): 60/108 ≈ 0.556
  └── Some((2, 8)): 2839/5269 ≈ 0.539
    ├── Some((8, 0)): 412/739 ≈ 0.558
      ├── Some((0, 0)): 70/113 ≈ 0.619
      ├── Some((0, 1)): 59/99 ≈ 0.596
      ├── Some((0, 2)): 24/53 ≈ 0.453
      ├── Some((0, 3)): 59/100 ≈ 0.590
      ├── Some((0, 4)): 18/45 ≈ 0.400
      ├── Some((0, 5)): 44/80 ≈ 0.550
      ├── Some((0, 6)): 60/101 ≈ 0.594
      ├── Some((0, 7)): 51/89 ≈ 0.573
      └── Some((0, 8)): 27/58 ≈ 0.466
    ├── Some((8, 1)): 343/630 ≈ 0.544
      ├── Some((1, 0)): 29/58 ≈ 0.500
      ├── Some((1, 1)): 25/53 ≈ 0.472
      ├── Some((1, 2)): 65/104 ≈ 0.625
      ├── Some((1, 3)): 51/87 ≈ 0.586
      ├── Some((1, 4)): 24/52 ≈ 0.462
      ├── Some((1, 5)): 28/57 ≈ 0.491
      ├── Some((1, 6)): 39/71 ≈ 0.549
      ├── Some((1, 7)): 35/66 ≈ 0.530
      └── Some((1, 8)): 47/81 ≈ 0.580
    ├── Some((8, 2)): 144/308 ≈ 0.468
      ├── Some((2, 0)): 16/36 ≈ 0.444
      ├── Some((2, 1)): 25/48 ≈ 0.521
      ├── Some((2, 2)): 6/22 ≈ 0.273
      ├── Some((2, 3)): 31/55 ≈ 0.564
      ├── Some((2, 4)): 14/33 ≈ 0.424
      ├── Some((2, 5)): 14/34 ≈ 0.412
      ├── Some((2, 6)): 27/50 ≈ 0.540
      └── Some((2, 7)): 11/29 ≈ 0.379
    ├── Some((8, 3)): 411/737 ≈ 0.558
      ├── Some((3, 0)): 54/93 ≈ 0.581
      ├── Some((3, 1)): 33/65 ≈ 0.508
      ├── Some((3, 2)): 39/73 ≈ 0.534
      ├── Some((3, 3)): 34/67 ≈ 0.507
      ├── Some((3, 4)): 57/97 ≈ 0.588
      ├── Some((3, 5)): 49/86 ≈ 0.570
      ├── Some((3, 6)): 44/80 ≈ 0.550
      ├── Some((3, 7)): 34/67 ≈ 0.507
      └── Some((3, 8)): 66/108 ≈ 0.611
    ├── Some((8, 4)): 271/516 ≈ 0.525
      ├── Some((4, 0)): 45/79 ≈ 0.570
      ├── Some((4, 1)): 39/71 ≈ 0.549
      ├── Some((4, 3)): 23/50 ≈ 0.460
      ├── Some((4, 4)): 28/57 ≈ 0.491
      ├── Some((4, 5)): 54/91 ≈ 0.593
      ├── Some((4, 6)): 26/54 ≈ 0.481
      ├── Some((4, 7)): 27/56 ≈ 0.482
      └── Some((4, 8)): 28/57 ≈ 0.491
    ├── Some((8, 5)): 289/544 ≈ 0.531
      ├── Some((5, 0)): 30/58 ≈ 0.517
      ├── Some((5, 1)): 39/69 ≈ 0.565
      ├── Some((5, 2)): 28/55 ≈ 0.509
      ├── Some((5, 3)): 36/65 ≈ 0.554
      ├── Some((5, 4)): 33/62 ≈ 0.532
      ├── Some((5, 5)): 27/54 ≈ 0.500
      ├── Some((5, 6)): 35/64 ≈ 0.547
      ├── Some((5, 7)): 24/50 ≈ 0.480
      └── Some((5, 8)): 36/66 ≈ 0.545
    ├── Some((8, 6)): 308/575 ≈ 0.536
      ├── Some((6, 0)): 16/40 ≈ 0.400
      ├── Some((6, 1)): 33/63 ≈ 0.524
      ├── Some((6, 2)): 34/64 ≈ 0.531
      ├── Some((6, 3)): 33/63 ≈ 0.524
      ├── Some((6, 4)): 59/95 ≈ 0.621
      ├── Some((6, 5)): 54/89 ≈ 0.607
      ├── Some((6, 6)): 34/64 ≈ 0.531
      ├── Some((6, 7)): 25/52 ≈ 0.481
      └── Some((6, 8)): 19/44 ≈ 0.432
    ├── Some((8, 7)): 350/641 ≈ 0.546
      ├── Some((7, 0)): 41/74 ≈ 0.554
      ├── Some((7, 1)): 29/59 ≈ 0.492
      ├── Some((7, 2)): 25/53 ≈ 0.472
      ├── Some((7, 3)): 30/60 ≈ 0.500
      ├── Some((7, 4)): 60/98 ≈ 0.612
      ├── Some((7, 5)): 44/78 ≈ 0.564
      ├── Some((7, 6)): 36/68 ≈ 0.529
      ├── Some((7, 7)): 53/89 ≈ 0.596
      └── Some((7, 8)): 31/61 ≈ 0.508
    └── Some((8, 8)): 310/578 ≈ 0.536
      ├── Some((8, 0)): 27/57 ≈ 0.474
      ├── Some((8, 1)): 36/69 ≈ 0.522
      ├── Some((8, 2)): 56/94 ≈ 0.596
      ├── Some((8, 3)): 27/57 ≈ 0.474
      ├── Some((8, 4)): 64/104 ≈ 0.615
      ├── Some((8, 5)): 40/74 ≈ 0.541
      ├── Some((8, 6)): 30/61 ≈ 0.492
      └── Some((8, 7)): 30/61 ≈ 0.492
├── Some((4, 3)): 17992/33323 ≈ 0.540
  ├── Some((3, 0)): 2208/4066 ≈ 0.543
    ├── Some((0, 0)): 284/512 ≈ 0.555
      ├── Some((0, 1)): 49/81 ≈ 0.605
      ├── Some((0, 2)): 36/65 ≈ 0.554
      ├── Some((0, 3)): 51/84 ≈ 0.607
      ├── Some((0, 4)): 38/67 ≈ 0.567
      ├── Some((0, 5)): 24/49 ≈ 0.490
      ├── Some((0, 6)): 24/50 ≈ 0.480
      ├── Some((0, 7)): 23/48 ≈ 0.479
      └── Some((0, 8)): 38/67 ≈ 0.567
    ├── Some((0, 1)): 312/555 ≈ 0.562
      ├── Some((1, 0)): 26/51 ≈ 0.510
      ├── Some((1, 1)): 45/74 ≈ 0.608
      ├── Some((1, 2)): 33/60 ≈ 0.550
      ├── Some((1, 3)): 40/68 ≈ 0.588
      ├── Some((1, 4)): 22/46 ≈ 0.478
      ├── Some((1, 5)): 32/58 ≈ 0.552
      ├── Some((1, 6)): 38/66 ≈ 0.576
      ├── Some((1, 7)): 37/64 ≈ 0.578
      └── Some((1, 8)): 39/67 ≈ 0.582
    ├── Some((0, 2)): 146/296 ≈ 0.493
      ├── Some((2, 0)): 15/31 ≈ 0.484
      ├── Some((2, 1)): 20/38 ≈ 0.526
      ├── Some((2, 2)): 17/34 ≈ 0.500
      ├── Some((2, 3)): 14/30 ≈ 0.467
      ├── Some((2, 4)): 15/31 ≈ 0.484
      ├── Some((2, 5)): 23/41 ≈ 0.561
      ├── Some((2, 6)): 7/21 ≈ 0.333
      ├── Some((2, 7)): 17/34 ≈ 0.500
      └── Some((2, 8)): 18/35 ≈ 0.514
    ├── Some((0, 3)): 255/468 ≈ 0.545
      ├── Some((3, 1)): 17/39 ≈ 0.436
      ├── Some((3, 2)): 31/58 ≈ 0.534
      ├── Some((3, 3)): 38/66 ≈ 0.576
      ├── Some((3, 4)): 29/55 ≈ 0.527
      ├── Some((3, 5)): 48/79 ≈ 0.608
      ├── Some((3, 6)): 31/58 ≈ 0.534
      ├── Some((3, 7)): 30/56 ≈ 0.536
      └── Some((3, 8)): 30/56 ≈ 0.536
    ├── Some((0, 4)): 148/299 ≈ 0.495
      ├── Some((4, 0)): 18/37 ≈ 0.486
      ├── Some((4, 1)): 10/27 ≈ 0.370
      ├── Some((4, 2)): 26/47 ≈ 0.553
      ├── Some((4, 4)): 28/49 ≈ 0.571
      ├── Some((4, 5)): 22/42 ≈ 0.524
      ├── Some((4, 6)): 15/33 ≈ 0.455
      ├── Some((4, 7)): 12/29 ≈ 0.414
      └── Some((4, 8)): 16/34 ≈ 0.471
    ├── Some((0, 5)): 319/566 ≈ 0.564
      ├── Some((5, 0)): 31/58 ≈ 0.534
      ├── Some((5, 1)): 51/82 ≈ 0.622
      ├── Some((5, 2)): 53/84 ≈ 0.631
      ├── Some((5, 3)): 23/47 ≈ 0.489
      ├── Some((5, 4)): 23/47 ≈ 0.489
      ├── Some((5, 5)): 33/60 ≈ 0.550
      ├── Some((5, 6)): 43/72 ≈ 0.597
      ├── Some((5, 7)): 40/69 ≈ 0.580
      └── Some((5, 8)): 22/46 ≈ 0.478
    ├── Some((0, 6)): 243/449 ≈ 0.541
      ├── Some((6, 0)): 26/49 ≈ 0.531
      ├── Some((6, 1)): 33/57 ≈ 0.579
      ├── Some((6, 2)): 24/46 ≈ 0.522
      ├── Some((6, 3)): 43/69 ≈ 0.623
      ├── Some((6, 4)): 33/58 ≈ 0.569
      ├── Some((6, 5)): 20/41 ≈ 0.488
      ├── Some((6, 6)): 32/56 ≈ 0.571
      ├── Some((6, 7)): 19/40 ≈ 0.475
      └── Some((6, 8)): 13/32 ≈ 0.406
    ├── Some((0, 7)): 266/485 ≈ 0.548
      ├── Some((7, 0)): 24/47 ≈ 0.511
      ├── Some((7, 1)): 33/59 ≈ 0.559
      ├── Some((7, 2)): 9/27 ≈ 0.333
      ├── Some((7, 3)): 43/71 ≈ 0.606
      ├── Some((7, 4)): 20/42 ≈ 0.476
      ├── Some((7, 5)): 37/63 ≈ 0.587
      ├── Some((7, 6)): 21/43 ≈ 0.488
      ├── Some((7, 7)): 24/47 ≈ 0.511
      └── Some((7, 8)): 55/85 ≈ 0.647
    └── Some((0, 8)): 234/435 ≈ 0.538
      ├── Some((8, 0)): 34/58 ≈ 0.586
      ├── Some((8, 1)): 28/51 ≈ 0.549
      ├── Some((8, 2)): 12/30 ≈ 0.400
      ├── Some((8, 3)): 30/53 ≈ 0.566
      ├── Some((8, 4)): 26/49 ≈ 0.531
      ├── Some((8, 5)): 35/59 ≈ 0.593
      ├── Some((8, 6)): 23/45 ≈ 0.511
      ├── Some((8, 7)): 28/51 ≈ 0.549
      └── Some((8, 8)): 18/38 ≈ 0.474
  ├── Some((3, 1)): 2326/4269 ≈ 0.545
    ├── Some((1, 0)): 223/420 ≈ 0.531
      ├── Some((0, 0)): 9/26 ≈ 0.346
      ├── Some((0, 1)): 41/67 ≈ 0.612
      ├── Some((0, 2)): 29/52 ≈ 0.558
      ├── Some((0, 3)): 19/40 ≈ 0.475
      ├── Some((0, 4)): 26/49 ≈ 0.531
      ├── Some((0, 5)): 17/37 ≈ 0.459
      ├── Some((0, 6)): 42/68 ≈ 0.618
      ├── Some((0, 7)): 27/50 ≈ 0.540
      └── Some((0, 8)): 12/30 ≈ 0.400
    ├── Some((1, 1)): 114/245 ≈ 0.465
      ├── Some((1, 0)): 4/17 ≈ 0.235
      ├── Some((1, 2)): 7/21 ≈ 0.333
      ├── Some((1, 3)): 31/51 ≈ 0.608
      ├── Some((1, 4)): 20/38 ≈ 0.526
      ├── Some((1, 5)): 15/32 ≈ 0.469
      ├── Some((1, 6)): 13/30 ≈ 0.433
      ├── Some((1, 7)): 8/23 ≈ 0.348
      └── Some((1, 8)): 15/32 ≈ 0.469
    ├── Some((1, 2)): 301/541 ≈ 0.556
      ├── Some((2, 0)): 48/78 ≈ 0.615
      ├── Some((2, 1)): 32/59 ≈ 0.542
      ├── Some((2, 2)): 29/55 ≈ 0.527
      ├── Some((2, 3)): 35/62 ≈ 0.565
      ├── Some((2, 4)): 44/73 ≈ 0.603
      ├── Some((2, 5)): 49/79 ≈ 0.620
      ├── Some((2, 6)): 23/47 ≈ 0.489
      ├── Some((2, 7)): 22/46 ≈ 0.478
      └── Some((2, 8)): 18/41 ≈ 0.439
    ├── Some((1, 3)): 230/431 ≈ 0.534
      ├── Some((3, 0)): 44/73 ≈ 0.603
      ├── Some((3, 2)): 16/37 ≈ 0.432
      ├── Some((3, 3)): 22/45 ≈ 0.489
      ├── Some((3, 4)): 32/58 ≈ 0.552
      ├── Some((3, 5)): 35/62 ≈ 0.565
      ├── Some((3, 6)): 37/65 ≈ 0.569
      ├── Some((3, 7)): 26/51 ≈ 0.510
      └── Some((3, 8)): 17/39 ≈ 0.436
    ├── Some((1, 4)): 289/523 ≈ 0.553
      ├── Some((4, 0)): 28/55 ≈ 0.509
      ├── Some((4, 1)): 49/82 ≈ 0.598
      ├── Some((4, 2)): 26/53 ≈ 0.491
      ├── Some((4, 4)): 61/96 ≈ 0.635
      ├── Some((4, 5)): 31/59 ≈ 0.525
      ├── Some((4, 6)): 42/73 ≈ 0.575
      ├── Some((4, 7)): 25/51 ≈ 0.490
      └── Some((4, 8)): 26/53 ≈ 0.491
    ├── Some((1, 5)): 341/602 ≈ 0.566
      ├── Some((5, 0)): 29/56 ≈ 0.518
      ├── Some((5, 1)): 24/49 ≈ 0.490
      ├── Some((5, 2)): 13/35 ≈ 0.371
      ├── Some((5, 3)): 58/92 ≈ 0.630
      ├── Some((5, 4)): 54/87 ≈ 0.621
      ├── Some((5, 5)): 53/86 ≈ 0.616
      ├── Some((5, 6)): 44/75 ≈ 0.587
      ├── Some((5, 7)): 32/60 ≈ 0.533
      └── Some((5, 8)): 33/61 ≈ 0.541
    ├── Some((1, 6)): 345/608 ≈ 0.567
      ├── Some((6, 0)): 37/66 ≈ 0.561
      ├── Some((6, 1)): 21/46 ≈ 0.457
      ├── Some((6, 2)): 35/64 ≈ 0.547
      ├── Some((6, 3)): 35/64 ≈ 0.547
      ├── Some((6, 4)): 44/75 ≈ 0.587
      ├── Some((6, 5)): 62/97 ≈ 0.639
      ├── Some((6, 6)): 32/60 ≈ 0.533
      ├── Some((6, 7)): 18/41 ≈ 0.439
      └── Some((6, 8)): 60/94 ≈ 0.638
    ├── Some((1, 7)): 240/447 ≈ 0.537
      ├── Some((7, 0)): 23/45 ≈ 0.511
      ├── Some((7, 1)): 54/82 ≈ 0.659
      ├── Some((7, 2)): 14/34 ≈ 0.412
      ├── Some((7, 3)): 28/51 ≈ 0.549
      ├── Some((7, 4)): 26/49 ≈ 0.531
      ├── Some((7, 5)): 27/50 ≈ 0.540
      ├── Some((7, 6)): 21/43 ≈ 0.488
      ├── Some((7, 7)): 23/45 ≈ 0.511
      └── Some((7, 8)): 24/47 ≈ 0.511
    └── Some((1, 8)): 243/451 ≈ 0.539
      ├── Some((8, 0)): 40/66 ≈ 0.606
      ├── Some((8, 1)): 3/18 ≈ 0.167
      ├── Some((8, 2)): 23/45 ≈ 0.511
      ├── Some((8, 3)): 39/65 ≈ 0.600
      ├── Some((8, 4)): 26/49 ≈ 0.531
      ├── Some((8, 5)): 17/38 ≈ 0.447
      ├── Some((8, 6)): 32/57 ≈ 0.561
      ├── Some((8, 7)): 36/62 ≈ 0.581
      └── Some((8, 8)): 27/50 ≈ 0.540
  ├── Some((3, 2)): 1755/3284 ≈ 0.534
    ├── Some((2, 0)): 161/313 ≈ 0.514
      ├── Some((0, 0)): 19/36 ≈ 0.528
      ├── Some((0, 1)): 13/29 ≈ 0.448
      ├── Some((0, 2)): 25/43 ≈ 0.581
      ├── Some((0, 3)): 17/34 ≈ 0.500
      ├── Some((0, 4)): 24/42 ≈ 0.571
      ├── Some((0, 5)): 29/48 ≈ 0.604
      ├── Some((0, 6)): 12/28 ≈ 0.429
      ├── Some((0, 7)): 16/32 ≈ 0.500
      └── Some((0, 8)): 6/20 ≈ 0.300
    ├── Some((2, 1)): 194/364 ≈ 0.533
      ├── Some((1, 0)): 39/61 ≈ 0.639
      ├── Some((1, 1)): 17/35 ≈ 0.486
      ├── Some((1, 2)): 26/46 ≈ 0.565
      ├── Some((1, 3)): 25/45 ≈ 0.556
      ├── Some((1, 4)): 22/41 ≈ 0.537
      ├── Some((1, 5)): 15/33 ≈ 0.455
      ├── Some((1, 6)): 10/26 ≈ 0.385
      ├── Some((1, 7)): 17/35 ≈ 0.486
      └── Some((1, 8)): 22/41 ≈ 0.537
    ├── Some((2, 2)): 121/249 ≈ 0.486
      ├── Some((2, 0)): 21/38 ≈ 0.553
      ├── Some((2, 1)): 6/19 ≈ 0.316
      ├── Some((2, 3)): 19/36 ≈ 0.528
      ├── Some((2, 4)): 11/26 ≈ 0.423
      ├── Some((2, 5)): 21/38 ≈ 0.553
      ├── Some((2, 6)): 10/25 ≈ 0.400
      ├── Some((2, 7)): 16/32 ≈ 0.500
      └── Some((2, 8)): 17/34 ≈ 0.500
    ├── Some((2, 3)): 117/243 ≈ 0.481
      ├── Some((3, 0)): 14/30 ≈ 0.467
      ├── Some((3, 1)): 20/37 ≈ 0.541
      ├── Some((3, 3)): 5/18 ≈ 0.278
      ├── Some((3, 4)): 8/22 ≈ 0.364
      ├── Some((3, 5)): 13/28 ≈ 0.464
      ├── Some((3, 6)): 24/42 ≈ 0.571
      ├── Some((3, 7)): 16/32 ≈ 0.500
      └── Some((3, 8)): 17/33 ≈ 0.515
    ├── Some((2, 4)): 270/480 ≈ 0.562
      ├── Some((4, 0)): 36/63 ≈ 0.571
      ├── Some((4, 1)): 24/48 ≈ 0.500
      ├── Some((4, 2)): 34/60 ≈ 0.567
      ├── Some((4, 4)): 60/92 ≈ 0.652
      ├── Some((4, 5)): 30/56 ≈ 0.536
      ├── Some((4, 6)): 24/48 ≈ 0.500
      ├── Some((4, 7)): 32/58 ≈ 0.552
      └── Some((4, 8)): 29/54 ≈ 0.537
    ├── Some((2, 5)): 184/349 ≈ 0.527
      ├── Some((5, 0)): 34/55 ≈ 0.618
      ├── Some((5, 1)): 19/37 ≈ 0.514
      ├── Some((5, 2)): 14/31 ≈ 0.452
      ├── Some((5, 3)): 12/28 ≈ 0.429
      ├── Some((5, 4)): 25/44 ≈ 0.568
      ├── Some((5, 5)): 21/40 ≈ 0.525
      ├── Some((5, 6)): 23/42 ≈ 0.548
      ├── Some((5, 7)): 18/36 ≈ 0.500
      └── Some((5, 8)): 17/35 ≈ 0.486
    ├── Some((2, 6)): 213/393 ≈ 0.542
      ├── Some((6, 0)): 7/22 ≈ 0.318
      ├── Some((6, 1)): 22/42 ≈ 0.524
      ├── Some((6, 2)): 30/51 ≈ 0.588
      ├── Some((6, 3)): 13/31 ≈ 0.419
      ├── Some((6, 4)): 24/44 ≈ 0.545
      ├── Some((6, 5)): 35/57 ≈ 0.614
      ├── Some((6, 6)): 31/53 ≈ 0.585
      ├── Some((6, 7)): 33/55 ≈ 0.600
      └── Some((6, 8)): 18/37 ≈ 0.486
    ├── Some((2, 7)): 256/459 ≈ 0.558
      ├── Some((7, 0)): 23/44 ≈ 0.523
      ├── Some((7, 1)): 24/46 ≈ 0.522
      ├── Some((7, 2)): 57/85 ≈ 0.671
      ├── Some((7, 3)): 37/61 ≈ 0.607
      ├── Some((7, 4)): 22/43 ≈ 0.512
      ├── Some((7, 5)): 17/37 ≈ 0.459
      ├── Some((7, 6)): 20/41 ≈ 0.488
      ├── Some((7, 7)): 31/54 ≈ 0.574
      └── Some((7, 8)): 25/47 ≈ 0.532
    └── Some((2, 8)): 239/433 ≈ 0.552
      ├── Some((8, 0)): 27/49 ≈ 0.551
      ├── Some((8, 1)): 8/24 ≈ 0.333
      ├── Some((8, 2)): 27/49 ≈ 0.551
      ├── Some((8, 3)): 18/38 ≈ 0.474
      ├── Some((8, 4)): 53/79 ≈ 0.671
      ├── Some((8, 5)): 21/41 ≈ 0.512
      ├── Some((8, 6)): 33/56 ≈ 0.589
      ├── Some((8, 7)): 22/43 ≈ 0.512
      └── Some((8, 8)): 30/53 ≈ 0.566
  ├── Some((3, 3)): 2455/4490 ≈ 0.547
    ├── Some((3, 0)): 259/486 ≈ 0.533
      ├── Some((0, 0)): 34/61 ≈ 0.557
      ├── Some((0, 1)): 17/39 ≈ 0.436
      ├── Some((0, 2)): 14/35 ≈ 0.400
      ├── Some((0, 3)): 31/57 ≈ 0.544
      ├── Some((0, 4)): 45/74 ≈ 0.608
      ├── Some((0, 5)): 41/69 ≈ 0.594
      ├── Some((0, 6)): 29/55 ≈ 0.527
      ├── Some((0, 7)): 19/42 ≈ 0.452
      └── Some((0, 8)): 28/53 ≈ 0.528
    ├── Some((3, 1)): 333/602 ≈ 0.553
      ├── Some((1, 0)): 18/42 ≈ 0.429
      ├── Some((1, 1)): 20/45 ≈ 0.444
      ├── Some((1, 2)): 17/41 ≈ 0.415
      ├── Some((1, 3)): 47/80 ≈ 0.587
      ├── Some((1, 4)): 28/56 ≈ 0.500
      ├── Some((1, 5)): 42/74 ≈ 0.568
      ├── Some((1, 6)): 52/86 ≈ 0.605
      ├── Some((1, 7)): 51/85 ≈ 0.600
      └── Some((1, 8)): 57/92 ≈ 0.620
    ├── Some((3, 2)): 330/598 ≈ 0.552
      ├── Some((2, 0)): 27/54 ≈ 0.500
      ├── Some((2, 1)): 38/68 ≈ 0.559
      ├── Some((2, 2)): 28/56 ≈ 0.500
      ├── Some((2, 3)): 77/116 ≈ 0.664
      ├── Some((2, 4)): 27/54 ≈ 0.500
      ├── Some((2, 5)): 46/79 ≈ 0.582
      ├── Some((2, 6)): 22/48 ≈ 0.458
      ├── Some((2, 7)): 21/46 ≈ 0.457
      └── Some((2, 8)): 44/76 ≈ 0.579
    ├── Some((3, 4)): 325/590 ≈ 0.551
      ├── Some((4, 0)): 10/32 ≈ 0.312
      ├── Some((4, 1)): 58/97 ≈ 0.598
      ├── Some((4, 2)): 48/84 ≈ 0.571
      ├── Some((4, 4)): 41/75 ≈ 0.547
      ├── Some((4, 5)): 36/68 ≈ 0.529
      ├── Some((4, 6)): 42/76 ≈ 0.553
      ├── Some((4, 7)): 68/109 ≈ 0.624
      └── Some((4, 8)): 21/48 ≈ 0.438
    ├── Some((3, 5)): 332/601 ≈ 0.552
      ├── Some((5, 0)): 25/52 ≈ 0.481
      ├── Some((5, 1)): 23/49 ≈ 0.469
      ├── Some((5, 2)): 38/68 ≈ 0.559
      ├── Some((5, 3)): 45/77 ≈ 0.584
      ├── Some((5, 4)): 41/72 ≈ 0.569
      ├── Some((5, 5)): 31/59 ≈ 0.525
      ├── Some((5, 6)): 52/86 ≈ 0.605
      ├── Some((5, 7)): 51/85 ≈ 0.600
      └── Some((5, 8)): 25/52 ≈ 0.481
    ├── Some((3, 6)): 200/392 ≈ 0.510
      ├── Some((6, 0)): 29/52 ≈ 0.558
      ├── Some((6, 1)): 36/60 ≈ 0.600
      ├── Some((6, 2)): 23/45 ≈ 0.511
      ├── Some((6, 3)): 18/38 ≈ 0.474
      ├── Some((6, 4)): 11/29 ≈ 0.379
      ├── Some((6, 5)): 20/41 ≈ 0.488
      ├── Some((6, 6)): 19/40 ≈ 0.475
      ├── Some((6, 7)): 15/34 ≈ 0.441
      └── Some((6, 8)): 29/52 ≈ 0.558
    ├── Some((3, 7)): 373/664 ≈ 0.562
      ├── Some((7, 0)): 46/80 ≈ 0.575
      ├── Some((7, 1)): 32/62 ≈ 0.516
      ├── Some((7, 2)): 31/60 ≈ 0.517
      ├── Some((7, 3)): 32/62 ≈ 0.516
      ├── Some((7, 4)): 39/71 ≈ 0.549
      ├── Some((7, 5)): 33/63 ≈ 0.524
      ├── Some((7, 6)): 67/106 ≈ 0.632
      ├── Some((7, 7)): 44/77 ≈ 0.571
      └── Some((7, 8)): 48/82 ≈ 0.585
    └── Some((3, 8)): 303/556 ≈ 0.545
      ├── Some((8, 0)): 52/85 ≈ 0.612
      ├── Some((8, 1)): 37/66 ≈ 0.561
      ├── Some((8, 2)): 17/40 ≈ 0.425
      ├── Some((8, 3)): 30/57 ≈ 0.526
      ├── Some((8, 4)): 12/33 ≈ 0.364
      ├── Some((8, 5)): 41/71 ≈ 0.577
      ├── Some((8, 6)): 50/83 ≈ 0.602
      ├── Some((8, 7)): 35/64 ≈ 0.547
      └── Some((8, 8)): 29/56 ≈ 0.518
  ├── Some((3, 4)): 2537/4631 ≈ 0.548
    ├── Some((4, 0)): 388/691 ≈ 0.562
      ├── Some((0, 0)): 59/97 ≈ 0.608
      ├── Some((0, 1)): 28/58 ≈ 0.483
      ├── Some((0, 2)): 34/66 ≈ 0.515
      ├── Some((0, 3)): 17/42 ≈ 0.405
      ├── Some((0, 4)): 74/116 ≈ 0.638
      ├── Some((0, 5)): 33/64 ≈ 0.516
      ├── Some((0, 6)): 46/81 ≈ 0.568
      ├── Some((0, 7)): 59/97 ≈ 0.608
      └── Some((0, 8)): 37/69 ≈ 0.536
    ├── Some((4, 1)): 223/431 ≈ 0.517
      ├── Some((1, 0)): 10/29 ≈ 0.345
      ├── Some((1, 1)): 18/39 ≈ 0.462
      ├── Some((1, 2)): 30/55 ≈ 0.545
      ├── Some((1, 3)): 50/79 ≈ 0.633
      ├── Some((1, 4)): 33/58 ≈ 0.569
      ├── Some((1, 5)): 11/30 ≈ 0.367
      ├── Some((1, 6)): 20/42 ≈ 0.476
      ├── Some((1, 7)): 29/53 ≈ 0.547
      └── Some((1, 8)): 22/45 ≈ 0.489
    ├── Some((4, 2)): 248/471 ≈ 0.527
      ├── Some((2, 0)): 20/43 ≈ 0.465
      ├── Some((2, 1)): 17/39 ≈ 0.436
      ├── Some((2, 2)): 46/75 ≈ 0.613
      ├── Some((2, 3)): 32/58 ≈ 0.552
      ├── Some((2, 4)): 46/76 ≈ 0.605
      ├── Some((2, 5)): 30/56 ≈ 0.536
      ├── Some((2, 6)): 20/43 ≈ 0.465
      ├── Some((2, 7)): 18/40 ≈ 0.450
      └── Some((2, 8)): 18/40 ≈ 0.450
    ├── Some((4, 4)): 545/932 ≈ 0.585
      ├── Some((4, 0)): 126/196 ≈ 0.643
      ├── Some((4, 1)): 81/138 ≈ 0.587
      ├── Some((4, 2)): 67/119 ≈ 0.563
      ├── Some((4, 5)): 59/108 ≈ 0.546
      ├── Some((4, 6)): 30/68 ≈ 0.441
      ├── Some((4, 7)): 74/129 ≈ 0.574
      └── Some((4, 8)): 108/173 ≈ 0.624
    ├── Some((4, 5)): 350/631 ≈ 0.555
      ├── Some((5, 0)): 37/68 ≈ 0.544
      ├── Some((5, 1)): 32/61 ≈ 0.525
      ├── Some((5, 2)): 39/70 ≈ 0.557
      ├── Some((5, 3)): 26/54 ≈ 0.481
      ├── Some((5, 4)): 80/121 ≈ 0.661
      ├── Some((5, 5)): 41/73 ≈ 0.562
      ├── Some((5, 6)): 34/64 ≈ 0.531
      ├── Some((5, 7)): 31/60 ≈ 0.517
      └── Some((5, 8)): 30/59 ≈ 0.508
    ├── Some((4, 6)): 271/507 ≈ 0.535
      ├── Some((6, 0)): 20/43 ≈ 0.465
      ├── Some((6, 1)): 38/66 ≈ 0.576
      ├── Some((6, 2)): 40/69 ≈ 0.580
      ├── Some((6, 3)): 10/30 ≈ 0.333
      ├── Some((6, 4)): 27/53 ≈ 0.509
      ├── Some((6, 5)): 58/91 ≈ 0.637
      ├── Some((6, 6)): 25/50 ≈ 0.500
      ├── Some((6, 7)): 25/50 ≈ 0.500
      └── Some((6, 8)): 28/54 ≈ 0.519
    ├── Some((4, 7)): 254/480 ≈ 0.529
      ├── Some((7, 0)): 24/48 ≈ 0.500
      ├── Some((7, 1)): 43/72 ≈ 0.597
      ├── Some((7, 2)): 22/45 ≈ 0.489
      ├── Some((7, 3)): 28/53 ≈ 0.528
      ├── Some((7, 4)): 28/53 ≈ 0.528
      ├── Some((7, 5)): 19/42 ≈ 0.452
      ├── Some((7, 6)): 37/64 ≈ 0.578
      ├── Some((7, 7)): 36/63 ≈ 0.571
      └── Some((7, 8)): 17/39 ≈ 0.436
    └── Some((4, 8)): 258/487 ≈ 0.530
      ├── Some((8, 0)): 26/51 ≈ 0.510
      ├── Some((8, 1)): 19/42 ≈ 0.452
      ├── Some((8, 2)): 56/88 ≈ 0.636
      ├── Some((8, 3)): 37/65 ≈ 0.569
      ├── Some((8, 4)): 20/43 ≈ 0.465
      ├── Some((8, 5)): 21/44 ≈ 0.477
      ├── Some((8, 6)): 26/51 ≈ 0.510
      ├── Some((8, 7)): 24/48 ≈ 0.500
      └── Some((8, 8)): 28/54 ≈ 0.519
  ├── Some((3, 5)): 1473/2793 ≈ 0.527
    ├── Some((5, 0)): 117/238 ≈ 0.492
      ├── Some((0, 0)): 7/19 ≈ 0.368
      ├── Some((0, 1)): 14/28 ≈ 0.500
      ├── Some((0, 2)): 17/31 ≈ 0.548
      ├── Some((0, 3)): 12/25 ≈ 0.480
      ├── Some((0, 4)): 10/23 ≈ 0.435
      ├── Some((0, 5)): 12/25 ≈ 0.480
      ├── Some((0, 6)): 12/25 ≈ 0.480
      ├── Some((0, 7)): 15/29 ≈ 0.517
      └── Some((0, 8)): 18/32 ≈ 0.562
    ├── Some((5, 1)): 192/355 ≈ 0.541
      ├── Some((1, 0)): 2/14 ≈ 0.143
      ├── Some((1, 1)): 16/33 ≈ 0.485
      ├── Some((1, 2)): 35/56 ≈ 0.625
      ├── Some((1, 3)): 7/22 ≈ 0.318
      ├── Some((1, 4)): 25/44 ≈ 0.568
      ├── Some((1, 5)): 15/32 ≈ 0.469
      ├── Some((1, 6)): 35/56 ≈ 0.625
      ├── Some((1, 7)): 35/56 ≈ 0.625
      └── Some((1, 8)): 22/41 ≈ 0.537
    ├── Some((5, 2)): 143/279 ≈ 0.513
      ├── Some((2, 0)): 16/31 ≈ 0.516
      ├── Some((2, 1)): 24/40 ≈ 0.600
      ├── Some((2, 2)): 15/30 ≈ 0.500
      ├── Some((2, 3)): 8/21 ≈ 0.381
      ├── Some((2, 4)): 17/32 ≈ 0.531
      ├── Some((2, 5)): 19/35 ≈ 0.543
      ├── Some((2, 6)): 9/23 ≈ 0.391
      ├── Some((2, 7)): 21/37 ≈ 0.568
      └── Some((2, 8)): 14/29 ≈ 0.483
    ├── Some((5, 3)): 233/417 ≈ 0.559
      ├── Some((3, 0)): 35/59 ≈ 0.593
      ├── Some((3, 1)): 15/35 ≈ 0.429
      ├── Some((3, 2)): 40/65 ≈ 0.615
      ├── Some((3, 3)): 27/50 ≈ 0.540
      ├── Some((3, 4)): 33/57 ≈ 0.579
      ├── Some((3, 6)): 37/62 ≈ 0.597
      ├── Some((3, 7)): 30/53 ≈ 0.566
      └── Some((3, 8)): 15/35 ≈ 0.429
    ├── Some((5, 4)): 198/364 ≈ 0.544
      ├── Some((4, 0)): 20/40 ≈ 0.500
      ├── Some((4, 1)): 39/63 ≈ 0.619
      ├── Some((4, 2)): 24/45 ≈ 0.533
      ├── Some((4, 4)): 38/62 ≈ 0.613
      ├── Some((4, 5)): 10/27 ≈ 0.370
      ├── Some((4, 6)): 15/33 ≈ 0.455
      ├── Some((4, 7)): 29/51 ≈ 0.569
      └── Some((4, 8)): 22/42 ≈ 0.524
    ├── Some((5, 5)): 88/191 ≈ 0.461
      ├── Some((5, 0)): 14/27 ≈ 0.519
      ├── Some((5, 1)): 14/27 ≈ 0.519
      ├── Some((5, 2)): 8/20 ≈ 0.400
      ├── Some((5, 3)): 3/14 ≈ 0.214
      ├── Some((5, 4)): 14/27 ≈ 0.519
      ├── Some((5, 6)): 11/24 ≈ 0.458
      ├── Some((5, 7)): 10/23 ≈ 0.435
      └── Some((5, 8)): 14/28 ≈ 0.500
    ├── Some((5, 6)): 153/295 ≈ 0.519
      ├── Some((6, 0)): 14/29 ≈ 0.483
      ├── Some((6, 1)): 15/30 ≈ 0.500
      ├── Some((6, 2)): 12/27 ≈ 0.444
      ├── Some((6, 3)): 32/50 ≈ 0.640
      ├── Some((6, 4)): 19/35 ≈ 0.543
      ├── Some((6, 5)): 22/39 ≈ 0.564
      ├── Some((6, 6)): 13/28 ≈ 0.464
      ├── Some((6, 7)): 9/23 ≈ 0.391
      └── Some((6, 8)): 17/33 ≈ 0.515
    ├── Some((5, 7)): 133/263 ≈ 0.506
      ├── Some((7, 0)): 15/29 ≈ 0.517
      ├── Some((7, 1)): 22/38 ≈ 0.579
      ├── Some((7, 2)): 14/28 ≈ 0.500
      ├── Some((7, 3)): 17/32 ≈ 0.531
      ├── Some((7, 4)): 12/26 ≈ 0.462
      ├── Some((7, 5)): 16/31 ≈ 0.516
      ├── Some((7, 6)): 21/36 ≈ 0.583
      ├── Some((7, 7)): 4/16 ≈ 0.250
      └── Some((7, 8)): 12/26 ≈ 0.462
    └── Some((5, 8)): 215/390 ≈ 0.551
      ├── Some((8, 0)): 39/61 ≈ 0.639
      ├── Some((8, 1)): 25/45 ≈ 0.556
      ├── Some((8, 2)): 29/50 ≈ 0.580
      ├── Some((8, 3)): 12/29 ≈ 0.414
      ├── Some((8, 4)): 27/47 ≈ 0.574
      ├── Some((8, 5)): 32/53 ≈ 0.604
      ├── Some((8, 6)): 10/26 ≈ 0.385
      ├── Some((8, 7)): 28/48 ≈ 0.583
      └── Some((8, 8)): 13/30 ≈ 0.433
  ├── Some((3, 6)): 1621/3051 ≈ 0.531
    ├── Some((6, 0)): 161/310 ≈ 0.519
      ├── Some((0, 0)): 10/25 ≈ 0.400
      ├── Some((0, 1)): 15/31 ≈ 0.484
      ├── Some((0, 2)): 12/27 ≈ 0.444
      ├── Some((0, 3)): 12/28 ≈ 0.429
      ├── Some((0, 4)): 36/56 ≈ 0.643
      ├── Some((0, 5)): 25/43 ≈ 0.581
      ├── Some((0, 6)): 15/31 ≈ 0.484
      ├── Some((0, 7)): 19/36 ≈ 0.528
      └── Some((0, 8)): 16/32 ≈ 0.500
    ├── Some((6, 1)): 192/358 ≈ 0.536
      ├── Some((1, 0)): 16/34 ≈ 0.471
      ├── Some((1, 1)): 12/28 ≈ 0.429
      ├── Some((1, 2)): 19/37 ≈ 0.514
      ├── Some((1, 3)): 15/32 ≈ 0.469
      ├── Some((1, 4)): 26/46 ≈ 0.565
      ├── Some((1, 5)): 20/38 ≈ 0.526
      ├── Some((1, 6)): 34/55 ≈ 0.618
      ├── Some((1, 7)): 35/56 ≈ 0.625
      └── Some((1, 8)): 14/31 ≈ 0.452
    ├── Some((6, 2)): 234/422 ≈ 0.555
      ├── Some((2, 0)): 23/43 ≈ 0.535
      ├── Some((2, 1)): 20/40 ≈ 0.500
      ├── Some((2, 2)): 36/59 ≈ 0.610
      ├── Some((2, 3)): 29/51 ≈ 0.569
      ├── Some((2, 4)): 37/60 ≈ 0.617
      ├── Some((2, 5)): 10/27 ≈ 0.370
      ├── Some((2, 6)): 13/31 ≈ 0.419
      ├── Some((2, 7)): 23/44 ≈ 0.523
      └── Some((2, 8)): 42/66 ≈ 0.636
    ├── Some((6, 3)): 84/187 ≈ 0.449
      ├── Some((3, 0)): 11/24 ≈ 0.458
      ├── Some((3, 1)): 4/15 ≈ 0.267
      ├── Some((3, 2)): 17/31 ≈ 0.548
      ├── Some((3, 3)): 5/17 ≈ 0.294
      ├── Some((3, 4)): 13/27 ≈ 0.481
      ├── Some((3, 5)): 12/25 ≈ 0.480
      ├── Some((3, 7)): 11/24 ≈ 0.458
      └── Some((3, 8)): 10/23 ≈ 0.435
    ├── Some((6, 4)): 158/305 ≈ 0.518
      ├── Some((4, 0)): 22/41 ≈ 0.537
      ├── Some((4, 1)): 15/32 ≈ 0.469
      ├── Some((4, 2)): 19/37 ≈ 0.514
      ├── Some((4, 4)): 11/27 ≈ 0.407
      ├── Some((4, 5)): 15/32 ≈ 0.469
      ├── Some((4, 6)): 24/44 ≈ 0.545
      ├── Some((4, 7)): 30/51 ≈ 0.588
      └── Some((4, 8)): 21/40 ≈ 0.525
    ├── Some((6, 5)): 225/409 ≈ 0.550
      ├── Some((5, 0)): 22/42 ≈ 0.524
      ├── Some((5, 1)): 35/57 ≈ 0.614
      ├── Some((5, 2)): 21/41 ≈ 0.512
      ├── Some((5, 3)): 19/38 ≈ 0.500
      ├── Some((5, 4)): 21/41 ≈ 0.512
      ├── Some((5, 5)): 31/53 ≈ 0.585
      ├── Some((5, 6)): 28/49 ≈ 0.571
      ├── Some((5, 7)): 35/57 ≈ 0.614
      └── Some((5, 8)): 13/30 ≈ 0.433
    ├── Some((6, 6)): 160/309 ≈ 0.518
      ├── Some((6, 0)): 23/42 ≈ 0.548
      ├── Some((6, 1)): 10/26 ≈ 0.385
      ├── Some((6, 2)): 12/29 ≈ 0.414
      ├── Some((6, 3)): 29/50 ≈ 0.580
      ├── Some((6, 4)): 28/48 ≈ 0.583
      ├── Some((6, 5)): 19/38 ≈ 0.500
      ├── Some((6, 7)): 16/34 ≈ 0.471
      └── Some((6, 8)): 22/41 ≈ 0.537
    ├── Some((6, 7)): 239/430 ≈ 0.556
      ├── Some((7, 0)): 41/65 ≈ 0.631
      ├── Some((7, 1)): 30/52 ≈ 0.577
      ├── Some((7, 2)): 29/51 ≈ 0.569
      ├── Some((7, 3)): 15/33 ≈ 0.455
      ├── Some((7, 4)): 26/47 ≈ 0.553
      ├── Some((7, 5)): 21/41 ≈ 0.512
      ├── Some((7, 6)): 32/54 ≈ 0.593
      ├── Some((7, 7)): 26/47 ≈ 0.553
      └── Some((7, 8)): 19/39 ≈ 0.487
    └── Some((6, 8)): 167/320 ≈ 0.522
      ├── Some((8, 0)): 16/33 ≈ 0.485
      ├── Some((8, 1)): 19/36 ≈ 0.528
      ├── Some((8, 2)): 16/33 ≈ 0.485
      ├── Some((8, 3)): 26/45 ≈ 0.578
      ├── Some((8, 4)): 33/53 ≈ 0.623
      ├── Some((8, 5)): 4/17 ≈ 0.235
      ├── Some((8, 6)): 17/34 ≈ 0.500
      ├── Some((8, 7)): 20/37 ≈ 0.541
      └── Some((8, 8)): 15/31 ≈ 0.484
  ├── Some((3, 7)): 2405/4404 ≈ 0.546
    ├── Some((7, 0)): 312/559 ≈ 0.558
      ├── Some((0, 0)): 26/52 ≈ 0.500
      ├── Some((0, 1)): 36/64 ≈ 0.562
      ├── Some((0, 2)): 28/54 ≈ 0.519
      ├── Some((0, 3)): 28/54 ≈ 0.519
      ├── Some((0, 4)): 41/70 ≈ 0.586
      ├── Some((0, 5)): 10/30 ≈ 0.333
      ├── Some((0, 6)): 24/49 ≈ 0.490
      ├── Some((0, 7)): 43/73 ≈ 0.589
      └── Some((0, 8)): 76/112 ≈ 0.679
    ├── Some((7, 1)): 269/493 ≈ 0.546
      ├── Some((1, 0)): 35/61 ≈ 0.574
      ├── Some((1, 1)): 40/67 ≈ 0.597
      ├── Some((1, 2)): 41/69 ≈ 0.594
      ├── Some((1, 3)): 17/38 ≈ 0.447
      ├── Some((1, 4)): 39/66 ≈ 0.591
      ├── Some((1, 5)): 24/47 ≈ 0.511
      ├── Some((1, 6)): 29/54 ≈ 0.537
      ├── Some((1, 7)): 16/37 ≈ 0.432
      └── Some((1, 8)): 28/53 ≈ 0.528
    ├── Some((7, 2)): 217/412 ≈ 0.527
      ├── Some((2, 0)): 27/50 ≈ 0.540
      ├── Some((2, 1)): 12/30 ≈ 0.400
      ├── Some((2, 2)): 24/46 ≈ 0.522
      ├── Some((2, 3)): 41/66 ≈ 0.621
      ├── Some((2, 4)): 18/38 ≈ 0.474
      ├── Some((2, 5)): 28/51 ≈ 0.549
      ├── Some((2, 6)): 19/39 ≈ 0.487
      ├── Some((2, 7)): 27/50 ≈ 0.540
      └── Some((2, 8)): 20/41 ≈ 0.488
    ├── Some((7, 3)): 326/581 ≈ 0.561
      ├── Some((3, 0)): 49/83 ≈ 0.590
      ├── Some((3, 1)): 39/71 ≈ 0.549
      ├── Some((3, 2)): 49/84 ≈ 0.583
      ├── Some((3, 3)): 57/93 ≈ 0.613
      ├── Some((3, 4)): 50/85 ≈ 0.588
      ├── Some((3, 5)): 36/67 ≈ 0.537
      ├── Some((3, 6)): 31/60 ≈ 0.517
      └── Some((3, 8)): 14/37 ≈ 0.378
    ├── Some((7, 4)): 143/293 ≈ 0.488
      ├── Some((4, 0)): 38/62 ≈ 0.613
      ├── Some((4, 1)): 21/41 ≈ 0.512
      ├── Some((4, 2)): 27/48 ≈ 0.562
      ├── Some((4, 4)): 13/31 ≈ 0.419
      ├── Some((4, 5)): 14/32 ≈ 0.438
      ├── Some((4, 6)): 10/27 ≈ 0.370
      ├── Some((4, 7)): 12/29 ≈ 0.414
      └── Some((4, 8)): 7/22 ≈ 0.318
    ├── Some((7, 5)): 292/529 ≈ 0.552
      ├── Some((5, 0)): 28/53 ≈ 0.528
      ├── Some((5, 1)): 50/80 ≈ 0.625
      ├── Some((5, 2)): 52/83 ≈ 0.627
      ├── Some((5, 3)): 32/58 ≈ 0.552
      ├── Some((5, 4)): 29/55 ≈ 0.527
      ├── Some((5, 5)): 35/62 ≈ 0.565
      ├── Some((5, 6)): 12/32 ≈ 0.375
      ├── Some((5, 7)): 29/55 ≈ 0.527
      └── Some((5, 8)): 25/50 ≈ 0.500
    ├── Some((7, 6)): 254/470 ≈ 0.540
      ├── Some((6, 0)): 15/36 ≈ 0.417
      ├── Some((6, 1)): 11/30 ≈ 0.367
      ├── Some((6, 2)): 44/72 ≈ 0.611
      ├── Some((6, 3)): 33/59 ≈ 0.559
      ├── Some((6, 4)): 24/47 ≈ 0.511
      ├── Some((6, 5)): 23/46 ≈ 0.500
      ├── Some((6, 6)): 30/55 ≈ 0.545
      ├── Some((6, 7)): 58/88 ≈ 0.659
      └── Some((6, 8)): 15/36 ≈ 0.417
    ├── Some((7, 7)): 367/643 ≈ 0.571
      ├── Some((7, 0)): 45/80 ≈ 0.562
      ├── Some((7, 1)): 63/102 ≈ 0.618
      ├── Some((7, 2)): 41/74 ≈ 0.554
      ├── Some((7, 3)): 53/90 ≈ 0.589
      ├── Some((7, 4)): 38/70 ≈ 0.543
      ├── Some((7, 5)): 48/83 ≈ 0.578
      ├── Some((7, 6)): 50/86 ≈ 0.581
      └── Some((7, 8)): 28/57 ≈ 0.491
    └── Some((7, 8)): 224/423 ≈ 0.530
      ├── Some((8, 0)): 29/53 ≈ 0.547
      ├── Some((8, 1)): 43/69 ≈ 0.623
      ├── Some((8, 2)): 11/29 ≈ 0.379
      ├── Some((8, 3)): 8/25 ≈ 0.320
      ├── Some((8, 4)): 24/46 ≈ 0.522
      ├── Some((8, 5)): 24/46 ≈ 0.522
      ├── Some((8, 6)): 44/71 ≈ 0.620
      ├── Some((8, 7)): 24/46 ≈ 0.522
      └── Some((8, 8)): 17/37 ≈ 0.459
  └── Some((3, 8)): 1211/2334 ≈ 0.519
    ├── Some((8, 0)): 83/179 ≈ 0.464
      ├── Some((0, 0)): 6/16 ≈ 0.375
      ├── Some((0, 1)): 11/22 ≈ 0.500
      ├── Some((0, 2)): 2/11 ≈ 0.182
      ├── Some((0, 3)): 14/26 ≈ 0.538
      ├── Some((0, 4)): 15/27 ≈ 0.556
      ├── Some((0, 5)): 7/17 ≈ 0.412
      ├── Some((0, 6)): 10/21 ≈ 0.476
      ├── Some((0, 7)): 15/27 ≈ 0.556
      └── Some((0, 8)): 2/11 ≈ 0.182
    ├── Some((8, 1)): 149/282 ≈ 0.528
      ├── Some((1, 0)): 16/31 ≈ 0.516
      ├── Some((1, 1)): 17/32 ≈ 0.531
      ├── Some((1, 2)): 16/31 ≈ 0.516
      ├── Some((1, 3)): 20/36 ≈ 0.556
      ├── Some((1, 4)): 17/32 ≈ 0.531
      ├── Some((1, 5)): 7/20 ≈ 0.350
      ├── Some((1, 6)): 23/39 ≈ 0.590
      ├── Some((1, 7)): 27/43 ≈ 0.628
      └── Some((1, 8)): 5/17 ≈ 0.294
    ├── Some((8, 2)): 87/185 ≈ 0.470
      ├── Some((2, 0)): 21/33 ≈ 0.636
      ├── Some((2, 1)): 2/11 ≈ 0.182
      ├── Some((2, 2)): 9/20 ≈ 0.450
      ├── Some((2, 3)): 14/26 ≈ 0.538
      ├── Some((2, 4)): 12/23 ≈ 0.522
      ├── Some((2, 5)): 9/20 ≈ 0.450
      ├── Some((2, 6)): 6/16 ≈ 0.375
      ├── Some((2, 7)): 8/19 ≈ 0.421
      └── Some((2, 8)): 6/16 ≈ 0.375
    ├── Some((8, 3)): 88/187 ≈ 0.471
      ├── Some((3, 0)): 10/22 ≈ 0.455
      ├── Some((3, 1)): 18/31 ≈ 0.581
      ├── Some((3, 2)): 10/22 ≈ 0.455
      ├── Some((3, 3)): 7/19 ≈ 0.368
      ├── Some((3, 4)): 13/26 ≈ 0.500
      ├── Some((3, 5)): 6/17 ≈ 0.353
      ├── Some((3, 6)): 7/19 ≈ 0.368
      └── Some((3, 7)): 17/30 ≈ 0.567
    ├── Some((8, 4)): 159/297 ≈ 0.535
      ├── Some((4, 0)): 27/46 ≈ 0.587
      ├── Some((4, 1)): 14/30 ≈ 0.467
      ├── Some((4, 2)): 18/35 ≈ 0.514
      ├── Some((4, 4)): 19/36 ≈ 0.528
      ├── Some((4, 5)): 15/31 ≈ 0.484
      ├── Some((4, 6)): 36/56 ≈ 0.643
      ├── Some((4, 7)): 14/30 ≈ 0.467
      └── Some((4, 8)): 15/32 ≈ 0.469
    ├── Some((8, 5)): 155/291 ≈ 0.533
      ├── Some((5, 0)): 15/30 ≈ 0.500
      ├── Some((5, 1)): 4/16 ≈ 0.250
      ├── Some((5, 2)): 19/35 ≈ 0.543
      ├── Some((5, 3)): 20/36 ≈ 0.556
      ├── Some((5, 4)): 8/21 ≈ 0.381
      ├── Some((5, 5)): 25/41 ≈ 0.610
      ├── Some((5, 6)): 19/35 ≈ 0.543
      ├── Some((5, 7)): 21/37 ≈ 0.568
      └── Some((5, 8)): 23/39 ≈ 0.590
    ├── Some((8, 6)): 157/294 ≈ 0.534
      ├── Some((6, 0)): 32/49 ≈ 0.653
      ├── Some((6, 1)): 8/21 ≈ 0.381
      ├── Some((6, 2)): 13/28 ≈ 0.464
      ├── Some((6, 3)): 27/44 ≈ 0.614
      ├── Some((6, 4)): 9/23 ≈ 0.391
      ├── Some((6, 5)): 24/40 ≈ 0.600
      ├── Some((6, 6)): 15/30 ≈ 0.500
      ├── Some((6, 7)): 15/30 ≈ 0.500
      └── Some((6, 8)): 13/28 ≈ 0.464
    ├── Some((8, 7)): 177/325 ≈ 0.545
      ├── Some((7, 0)): 17/33 ≈ 0.515
      ├── Some((7, 1)): 22/39 ≈ 0.564
      ├── Some((7, 2)): 17/33 ≈ 0.515
      ├── Some((7, 3)): 18/34 ≈ 0.529
      ├── Some((7, 4)): 31/49 ≈ 0.633
      ├── Some((7, 5)): 24/42 ≈ 0.571
      ├── Some((7, 6)): 11/26 ≈ 0.423
      ├── Some((7, 7)): 23/40 ≈ 0.575
      └── Some((7, 8)): 13/28 ≈ 0.464
    └── Some((8, 8)): 156/293 ≈ 0.532
      ├── Some((8, 0)): 39/59 ≈ 0.661
      ├── Some((8, 1)): 16/33 ≈ 0.485
      ├── Some((8, 2)): 15/31 ≈ 0.484
      ├── Some((8, 3)): 19/36 ≈ 0.528
      ├── Some((8, 4)): 6/20 ≈ 0.300
      ├── Some((8, 5)): 12/28 ≈ 0.429
      ├── Some((8, 6)): 25/44 ≈ 0.568
      └── Some((8, 7)): 23/41 ≈ 0.561
├── Some((4, 4)): 7730925/8605307 ≈ 0.898
  ├── Some((4, 0)): 32245/57802 ≈ 0.558
    ├── Some((0, 0)): 2280/4201 ≈ 0.543
      ├── Some((0, 1)): 309/563 ≈ 0.549
      ├── Some((0, 2)): 271/504 ≈ 0.538
      ├── Some((0, 3)): 268/499 ≈ 0.537
      ├── Some((0, 4)): 316/574 ≈ 0.551
      ├── Some((0, 5)): 266/496 ≈ 0.536
      ├── Some((0, 6)): 332/599 ≈ 0.554
      ├── Some((0, 7)): 333/600 ≈ 0.555
      └── Some((0, 8)): 184/365 ≈ 0.504
    ├── Some((0, 1)): 4085/7279 ≈ 0.561
      ├── Some((1, 0)): 599/1037 ≈ 0.578
      ├── Some((1, 1)): 303/572 ≈ 0.530
      ├── Some((1, 2)): 396/720 ≈ 0.550
      ├── Some((1, 3)): 508/896 ≈ 0.567
      ├── Some((1, 4)): 816/1369 ≈ 0.596
      ├── Some((1, 5)): 256/496 ≈ 0.516
      ├── Some((1, 6)): 403/731 ≈ 0.551
      ├── Some((1, 7)): 337/627 ≈ 0.537
      └── Some((1, 8)): 466/830 ≈ 0.561
    ├── Some((0, 2)): 3217/5805 ≈ 0.554
      ├── Some((2, 0)): 427/754 ≈ 0.566
      ├── Some((2, 1)): 390/697 ≈ 0.560
      ├── Some((2, 2)): 212/415 ≈ 0.511
      ├── Some((2, 3)): 499/865 ≈ 0.577
      ├── Some((2, 4)): 287/535 ≈ 0.536
      ├── Some((2, 5)): 326/597 ≈ 0.546
      ├── Some((2, 6)): 324/594 ≈ 0.545
      ├── Some((2, 7)): 325/595 ≈ 0.546
      └── Some((2, 8)): 426/752 ≈ 0.566
    ├── Some((0, 3)): 2932/5319 ≈ 0.551
      ├── Some((3, 0)): 344/620 ≈ 0.555
      ├── Some((3, 1)): 355/637 ≈ 0.557
      ├── Some((3, 2)): 305/559 ≈ 0.546
      ├── Some((3, 3)): 303/556 ≈ 0.545
      ├── Some((3, 4)): 430/753 ≈ 0.571
      ├── Some((3, 5)): 245/464 ≈ 0.528
      ├── Some((3, 6)): 336/607 ≈ 0.554
      ├── Some((3, 7)): 334/604 ≈ 0.553
      └── Some((3, 8)): 279/518 ≈ 0.539
    ├── Some((0, 4)): 3603/6462 ≈ 0.558
      ├── Some((4, 1)): 239/482 ≈ 0.496
      ├── Some((4, 2)): 223/455 ≈ 0.490
      ├── Some((4, 3)): 648/1142 ≈ 0.567
      ├── Some((4, 5)): 893/1527 ≈ 0.585
      ├── Some((4, 6)): 167/360 ≈ 0.464
      ├── Some((4, 7)): 525/947 ≈ 0.554
      └── Some((4, 8)): 907/1548 ≈ 0.586
    ├── Some((0, 5)): 4795/8480 ≈ 0.565
      ├── Some((5, 0)): 398/733 ≈ 0.543
      ├── Some((5, 1)): 270/526 ≈ 0.513
      ├── Some((5, 2)): 566/998 ≈ 0.567
      ├── Some((5, 3)): 588/1033 ≈ 0.569
      ├── Some((5, 4)): 1212/1991 ≈ 0.609
      ├── Some((5, 5)): 417/763 ≈ 0.547
      ├── Some((5, 6)): 436/793 ≈ 0.550
      ├── Some((5, 7)): 363/677 ≈ 0.536
      └── Some((5, 8)): 545/965 ≈ 0.565
    ├── Some((0, 6)): 3401/6118 ≈ 0.556
      ├── Some((6, 0)): 427/757 ≈ 0.564
      ├── Some((6, 1)): 231/448 ≈ 0.516
      ├── Some((6, 2)): 309/573 ≈ 0.539
      ├── Some((6, 3)): 393/705 ≈ 0.557
      ├── Some((6, 4)): 598/1020 ≈ 0.586
      ├── Some((6, 5)): 331/608 ≈ 0.544
      ├── Some((6, 6)): 343/626 ≈ 0.548
      ├── Some((6, 7)): 460/809 ≈ 0.569
      └── Some((6, 8)): 308/571 ≈ 0.539
    ├── Some((0, 7)): 5248/9243 ≈ 0.568
      ├── Some((7, 0)): 352/662 ≈ 0.532
      ├── Some((7, 1)): 501/899 ≈ 0.557
      ├── Some((7, 2)): 517/925 ≈ 0.559
      ├── Some((7, 3)): 618/1083 ≈ 0.571
      ├── Some((7, 4)): 950/1597 ≈ 0.595
      ├── Some((7, 5)): 492/885 ≈ 0.556
      ├── Some((7, 6)): 575/1016 ≈ 0.566
      ├── Some((7, 7)): 594/1045 ≈ 0.568
      └── Some((7, 8)): 648/1130 ≈ 0.573
    └── Some((0, 8)): 2684/4894 ≈ 0.548
      ├── Some((8, 0)): 233/442 ≈ 0.527
      ├── Some((8, 1)): 181/359 ≈ 0.504
      ├── Some((8, 2)): 319/577 ≈ 0.553
      ├── Some((8, 3)): 444/769 ≈ 0.577
      ├── Some((8, 4)): 280/516 ≈ 0.543
      ├── Some((8, 5)): 272/504 ≈ 0.540
      ├── Some((8, 6)): 260/485 ≈ 0.536
      ├── Some((8, 7)): 342/613 ≈ 0.558
      └── Some((8, 8)): 352/628 ≈ 0.561
  ├── Some((4, 1)): 119791/210550 ≈ 0.569
    ├── Some((1, 0)): 13493/23710 ≈ 0.569
      ├── Some((0, 0)): 1535/2695 ≈ 0.570
      ├── Some((0, 1)): 1940/3351 ≈ 0.579
      ├── Some((0, 2)): 1101/1986 ≈ 0.554
      ├── Some((0, 3)): 2166/3715 ≈ 0.583
      ├── Some((0, 4)): 1950/3367 ≈ 0.579
      ├── Some((0, 5)): 1004/1826 ≈ 0.550
      ├── Some((0, 6)): 1122/2021 ≈ 0.555
      ├── Some((0, 7)): 1406/2486 ≈ 0.566
      └── Some((0, 8)): 1269/2262 ≈ 0.561
    ├── Some((1, 1)): 14090/24728 ≈ 0.570
      ├── Some((1, 0)): 1591/2814 ≈ 0.565
      ├── Some((1, 2)): 2031/3532 ≈ 0.575
      ├── Some((1, 3)): 1607/2840 ≈ 0.566
      ├── Some((1, 4)): 2083/3616 ≈ 0.576
      ├── Some((1, 5)): 2051/3565 ≈ 0.575
      ├── Some((1, 6)): 1974/3439 ≈ 0.574
      ├── Some((1, 7)): 1622/2865 ≈ 0.566
      └── Some((1, 8)): 1131/2056 ≈ 0.550
    ├── Some((1, 2)): 10183/18051 ≈ 0.564
      ├── Some((2, 0)): 1055/1883 ≈ 0.560
      ├── Some((2, 1)): 1567/2710 ≈ 0.578
      ├── Some((2, 2)): 1166/2063 ≈ 0.565
      ├── Some((2, 3)): 1062/1894 ≈ 0.561
      ├── Some((2, 4)): 907/1641 ≈ 0.553
      ├── Some((2, 5)): 1229/2165 ≈ 0.568
      ├── Some((2, 6)): 744/1373 ≈ 0.542
      ├── Some((2, 7)): 1149/2036 ≈ 0.564
      └── Some((2, 8)): 1303/2285 ≈ 0.570
    ├── Some((1, 3)): 14588/25577 ≈ 0.570
      ├── Some((3, 0)): 1714/2994 ≈ 0.572
      ├── Some((3, 1)): 1538/2708 ≈ 0.568
      ├── Some((3, 2)): 1793/3123 ≈ 0.574
      ├── Some((3, 3)): 1522/2682 ≈ 0.567
      ├── Some((3, 4)): 2040/3522 ≈ 0.579
      ├── Some((3, 5)): 1425/2524 ≈ 0.565
      ├── Some((3, 6)): 1146/2066 ≈ 0.555
      ├── Some((3, 7)): 1470/2597 ≈ 0.566
      └── Some((3, 8)): 1940/3360 ≈ 0.577
    ├── Some((1, 4)): 15488/27110 ≈ 0.571
      ├── Some((4, 0)): 866/1651 ≈ 0.525
      ├── Some((4, 2)): 770/1487 ≈ 0.518
      ├── Some((4, 3)): 2059/3656 ≈ 0.563
      ├── Some((4, 5)): 1688/3039 ≈ 0.555
      ├── Some((4, 6)): 943/1783 ≈ 0.529
      ├── Some((4, 7)): 7650/12750 ≈ 0.600
      └── Some((4, 8)): 1511/2743 ≈ 0.551
    ├── Some((1, 5)): 14519/25459 ≈ 0.570
      ├── Some((5, 0)): 2130/3667 ≈ 0.581
      ├── Some((5, 1)): 1746/3046 ≈ 0.573
      ├── Some((5, 2)): 1290/2303 ≈ 0.560
      ├── Some((5, 3)): 1635/2866 ≈ 0.570
      ├── Some((5, 4)): 2076/3580 ≈ 0.580
      ├── Some((5, 5)): 1559/2743 ≈ 0.568
      ├── Some((5, 6)): 1693/2960 ≈ 0.572
      ├── Some((5, 7)): 1076/1951 ≈ 0.552
      └── Some((5, 8)): 1314/2342 ≈ 0.561
    ├── Some((1, 6)): 10222/18118 ≈ 0.564
      ├── Some((6, 0)): 806/1476 ≈ 0.546
      ├── Some((6, 1)): 1105/1965 ≈ 0.562
      ├── Some((6, 2)): 1118/1987 ≈ 0.563
      ├── Some((6, 3)): 1472/2558 ≈ 0.575
      ├── Some((6, 4)): 1450/2523 ≈ 0.575
      ├── Some((6, 5)): 1045/1868 ≈ 0.559
      ├── Some((6, 6)): 671/1253 ≈ 0.536
      ├── Some((6, 7)): 1529/2650 ≈ 0.577
      └── Some((6, 8)): 1026/1837 ≈ 0.559
    ├── Some((1, 7)): 13372/23503 ≈ 0.569
      ├── Some((7, 0)): 1380/2442 ≈ 0.565
      ├── Some((7, 1)): 1780/3092 ≈ 0.576
      ├── Some((7, 2)): 1988/3427 ≈ 0.580
      ├── Some((7, 3)): 897/1649 ≈ 0.544
      ├── Some((7, 4)): 2229/3815 ≈ 0.584
      ├── Some((7, 5)): 1213/2169 ≈ 0.559
      ├── Some((7, 6)): 1450/2556 ≈ 0.567
      ├── Some((7, 7)): 1398/2472 ≈ 0.566
      └── Some((7, 8)): 1037/1880 ≈ 0.552
    └── Some((1, 8)): 13835/24293 ≈ 0.570
      ├── Some((8, 0)): 2126/3654 ≈ 0.582
      ├── Some((8, 1)): 1853/3214 ≈ 0.577
      ├── Some((8, 2)): 1174/2108 ≈ 0.557
      ├── Some((8, 3)): 1934/3344 ≈ 0.578
      ├── Some((8, 4)): 1321/2349 ≈ 0.562
      ├── Some((8, 5)): 1510/2657 ≈ 0.568
      ├── Some((8, 6)): 920/1689 ≈ 0.545
      ├── Some((8, 7)): 1387/2457 ≈ 0.565
      └── Some((8, 8)): 1610/2820 ≈ 0.571
  ├── Some((4, 2)): 42574/75914 ≈ 0.561
    ├── Some((2, 0)): 4335/7765 ≈ 0.558
      ├── Some((0, 0)): 268/522 ≈ 0.513
      ├── Some((0, 1)): 595/1042 ≈ 0.571
      ├── Some((0, 2)): 530/940 ≈ 0.564
      ├── Some((0, 3)): 430/782 ≈ 0.550
      ├── Some((0, 4)): 640/1112 ≈ 0.576
      ├── Some((0, 5)): 492/880 ≈ 0.559
      ├── Some((0, 6)): 496/886 ≈ 0.560
      ├── Some((0, 7)): 417/761 ≈ 0.548
      └── Some((0, 8)): 466/839 ≈ 0.555
    ├── Some((2, 1)): 5202/9239 ≈ 0.563
      ├── Some((1, 0)): 706/1229 ≈ 0.574
      ├── Some((1, 1)): 543/972 ≈ 0.559
      ├── Some((1, 2)): 810/1391 ≈ 0.582
      ├── Some((1, 3)): 499/902 ≈ 0.553
      ├── Some((1, 4)): 671/1174 ≈ 0.572
      ├── Some((1, 5)): 413/765 ≈ 0.540
      ├── Some((1, 6)): 492/891 ≈ 0.552
      ├── Some((1, 7)): 475/864 ≈ 0.550
      └── Some((1, 8)): 592/1050 ≈ 0.564
    ├── Some((2, 2)): 3585/6484 ≈ 0.553
      ├── Some((2, 0)): 526/934 ≈ 0.563
      ├── Some((2, 1)): 421/768 ≈ 0.548
      ├── Some((2, 3)): 489/875 ≈ 0.559
      ├── Some((2, 4)): 434/788 ≈ 0.551
      ├── Some((2, 5)): 434/788 ≈ 0.551
      ├── Some((2, 6)): 421/768 ≈ 0.548
      ├── Some((2, 7)): 479/860 ≈ 0.557
      └── Some((2, 8)): 380/702 ≈ 0.541
    ├── Some((2, 3)): 4105/7372 ≈ 0.557
      ├── Some((3, 0)): 466/836 ≈ 0.557
      ├── Some((3, 1)): 449/809 ≈ 0.555
      ├── Some((3, 2)): 571/1000 ≈ 0.571
      ├── Some((3, 3)): 424/769 ≈ 0.551
      ├── Some((3, 4)): 475/850 ≈ 0.559
      ├── Some((3, 5)): 521/922 ≈ 0.565
      ├── Some((3, 6)): 606/1054 ≈ 0.575
      ├── Some((3, 7)): 330/620 ≈ 0.532
      └── Some((3, 8)): 263/511 ≈ 0.515
    ├── Some((2, 4)): 3808/6865 ≈ 0.555
      ├── Some((4, 0)): 336/646 ≈ 0.520
      ├── Some((4, 1)): 487/891 ≈ 0.547
      ├── Some((4, 3)): 631/1121 ≈ 0.563
      ├── Some((4, 5)): 373/706 ≈ 0.528
      ├── Some((4, 6)): 696/1224 ≈ 0.569
      ├── Some((4, 7)): 710/1246 ≈ 0.570
      └── Some((4, 8)): 574/1030 ≈ 0.557
    ├── Some((2, 5)): 4426/7920 ≈ 0.559
      ├── Some((5, 0)): 416/761 ≈ 0.547
      ├── Some((5, 1)): 253/498 ≈ 0.508
      ├── Some((5, 2)): 490/879 ≈ 0.557
      ├── Some((5, 3)): 391/721 ≈ 0.542
      ├── Some((5, 4)): 738/1266 ≈ 0.583
      ├── Some((5, 5)): 605/1059 ≈ 0.571
      ├── Some((5, 6)): 470/847 ≈ 0.555
      ├── Some((5, 7)): 531/943 ≈ 0.563
      └── Some((5, 8)): 532/945 ≈ 0.563
    ├── Some((2, 6)): 5138/9130 ≈ 0.563
      ├── Some((6, 0)): 219/448 ≈ 0.489
      ├── Some((6, 1)): 616/1088 ≈ 0.566
      ├── Some((6, 2)): 739/1281 ≈ 0.577
      ├── Some((6, 3)): 521/938 ≈ 0.555
      ├── Some((6, 4)): 833/1427 ≈ 0.584
      ├── Some((6, 5)): 369/694 ≈ 0.532
      ├── Some((6, 6)): 648/1139 ≈ 0.569
      ├── Some((6, 7)): 676/1182 ≈ 0.572
      └── Some((6, 8)): 517/932 ≈ 0.555
    ├── Some((2, 7)): 5739/10149 ≈ 0.565
      ├── Some((7, 0)): 542/978 ≈ 0.554
      ├── Some((7, 1)): 512/930 ≈ 0.551
      ├── Some((7, 2)): 823/1421 ≈ 0.579
      ├── Some((7, 3)): 930/1588 ≈ 0.586
      ├── Some((7, 4)): 922/1576 ≈ 0.585
      ├── Some((7, 5)): 390/734 ≈ 0.531
      ├── Some((7, 6)): 680/1197 ≈ 0.568
      ├── Some((7, 7)): 465/855 ≈ 0.544
      └── Some((7, 8)): 474/869 ≈ 0.545
    └── Some((2, 8)): 6235/10989 ≈ 0.567
      ├── Some((8, 0)): 765/1336 ≈ 0.573
      ├── Some((8, 1)): 535/971 ≈ 0.551
      ├── Some((8, 2)): 694/1224 ≈ 0.567
      ├── Some((8, 3)): 709/1247 ≈ 0.569
      ├── Some((8, 4)): 694/1224 ≈ 0.567
      ├── Some((8, 5)): 955/1633 ≈ 0.585
      ├── Some((8, 6)): 545/987 ≈ 0.552
      ├── Some((8, 7)): 534/969 ≈ 0.551
      └── Some((8, 8)): 804/1397 ≈ 0.576
  ├── Some((4, 3)): 106582/187573 ≈ 0.568
    ├── Some((3, 0)): 12514/21992 ≈ 0.569
      ├── Some((0, 0)): 1212/2156 ≈ 0.562
      ├── Some((0, 1)): 1167/2082 ≈ 0.561
      ├── Some((0, 2)): 1047/1886 ≈ 0.555
      ├── Some((0, 3)): 1359/2395 ≈ 0.567
      ├── Some((0, 4)): 2193/3737 ≈ 0.587
      ├── Some((0, 5)): 1376/2422 ≈ 0.568
      ├── Some((0, 6)): 1806/3116 ≈ 0.580
      ├── Some((0, 7)): 1177/2098 ≈ 0.561
      └── Some((0, 8)): 1177/2099 ≈ 0.561
    ├── Some((3, 1)): 15380/26870 ≈ 0.572
      ├── Some((1, 0)): 2029/3507 ≈ 0.579
      ├── Some((1, 1)): 1372/2439 ≈ 0.563
      ├── Some((1, 2)): 1699/2972 ≈ 0.572
      ├── Some((1, 3)): 1897/3293 ≈ 0.576
      ├── Some((1, 4)): 1754/3062 ≈ 0.573
      ├── Some((1, 5)): 1088/1973 ≈ 0.551
      ├── Some((1, 6)): 1639/2875 ≈ 0.570
      ├── Some((1, 7)): 2648/4502 ≈ 0.588
      └── Some((1, 8)): 1254/2246 ≈ 0.558
    ├── Some((3, 2)): 14184/24836 ≈ 0.571
      ├── Some((2, 0)): 1356/2403 ≈ 0.564
      ├── Some((2, 1)): 1463/2577 ≈ 0.568
      ├── Some((2, 2)): 1420/2507 ≈ 0.566
      ├── Some((2, 3)): 2157/3698 ≈ 0.583
      ├── Some((2, 4)): 1825/3164 ≈ 0.577
      ├── Some((2, 5)): 1638/2861 ≈ 0.573
      ├── Some((2, 6)): 1287/2290 ≈ 0.562
      ├── Some((2, 7)): 1327/2356 ≈ 0.563
      └── Some((2, 8)): 1711/2979 ≈ 0.574
    ├── Some((3, 3)): 9280/16467 ≈ 0.564
      ├── Some((3, 0)): 880/1603 ≈ 0.549
      ├── Some((3, 1)): 1042/1869 ≈ 0.558
      ├── Some((3, 2)): 823/1509 ≈ 0.545
      ├── Some((3, 4)): 1786/3072 ≈ 0.581
      ├── Some((3, 5)): 1029/1848 ≈ 0.557
      ├── Some((3, 6)): 1431/2501 ≈ 0.572
      ├── Some((3, 7)): 1500/2612 ≈ 0.574
      └── Some((3, 8)): 788/1452 ≈ 0.543
    ├── Some((3, 4)): 13431/23554 ≈ 0.570
      ├── Some((4, 0)): 926/1736 ≈ 0.533
      ├── Some((4, 1)): 2108/3702 ≈ 0.569
      ├── Some((4, 2)): 1444/2605 ≈ 0.554
      ├── Some((4, 5)): 5886/9815 ≈ 0.600
      ├── Some((4, 6)): 931/1745 ≈ 0.534
      ├── Some((4, 7)): 1252/2285 ≈ 0.548
      └── Some((4, 8)): 884/1665 ≈ 0.531
    ├── Some((3, 5)): 8141/14515 ≈ 0.561
      ├── Some((5, 0)): 872/1563 ≈ 0.558
      ├── Some((5, 1)): 556/1045 ≈ 0.532
      ├── Some((5, 2)): 569/1067 ≈ 0.533
      ├── Some((5, 3)): 979/1736 ≈ 0.564
      ├── Some((5, 4)): 790/1429 ≈ 0.553
      ├── Some((5, 5)): 1221/2124 ≈ 0.575
      ├── Some((5, 6)): 1328/2295 ≈ 0.579
      ├── Some((5, 7)): 711/1301 ≈ 0.547
      └── Some((5, 8)): 1115/1954 ≈ 0.571
    ├── Some((3, 6)): 12066/21228 ≈ 0.568
      ├── Some((6, 0)): 1352/2378 ≈ 0.569
      ├── Some((6, 1)): 1757/3031 ≈ 0.580
      ├── Some((6, 2)): 1155/2058 ≈ 0.561
      ├── Some((6, 3)): 1309/2309 ≈ 0.567
      ├── Some((6, 4)): 1079/1934 ≈ 0.558
      ├── Some((6, 5)): 1304/2300 ≈ 0.567
      ├── Some((6, 6)): 1540/2682 ≈ 0.574
      ├── Some((6, 7)): 1503/2622 ≈ 0.573
      └── Some((6, 8)): 1066/1913 ≈ 0.557
    ├── Some((3, 7)): 11541/20333 ≈ 0.568
      ├── Some((7, 0)): 1498/2609 ≈ 0.574
      ├── Some((7, 1)): 1295/2281 ≈ 0.568
      ├── Some((7, 2)): 1149/2044 ≈ 0.562
      ├── Some((7, 3)): 1278/2253 ≈ 0.567
      ├── Some((7, 4)): 1811/3112 ≈ 0.582
      ├── Some((7, 5)): 974/1758 ≈ 0.554
      ├── Some((7, 6)): 1211/2145 ≈ 0.565
      ├── Some((7, 7)): 1020/1833 ≈ 0.556
      └── Some((7, 8)): 1305/2297 ≈ 0.568
    └── Some((3, 8)): 10045/17777 ≈ 0.565
      ├── Some((8, 0)): 944/1698 ≈ 0.556
      ├── Some((8, 1)): 1054/1877 ≈ 0.562
      ├── Some((8, 2)): 1104/1958 ≈ 0.564
      ├── Some((8, 3)): 1334/2330 ≈ 0.573
      ├── Some((8, 4)): 821/1497 ≈ 0.548
      ├── Some((8, 5)): 1918/3264 ≈ 0.588
      ├── Some((8, 6)): 893/1615 ≈ 0.553
      ├── Some((8, 7)): 1219/2144 ≈ 0.569
      └── Some((8, 8)): 758/1393 ≈ 0.544
  ├── Some((4, 5)): 139345/244540 ≈ 0.570
    ├── Some((5, 0)): 10573/18784 ≈ 0.563
      ├── Some((0, 0)): 1520/2647 ≈ 0.574
      ├── Some((0, 1)): 952/1724 ≈ 0.552
      ├── Some((0, 2)): 1614/2799 ≈ 0.577
      ├── Some((0, 3)): 1071/1919 ≈ 0.558
      ├── Some((0, 4)): 1042/1872 ≈ 0.557
      ├── Some((0, 5)): 1029/1850 ≈ 0.556
      ├── Some((0, 6)): 1001/1804 ≈ 0.555
      ├── Some((0, 7)): 1159/2063 ≈ 0.562
      └── Some((0, 8)): 1185/2105 ≈ 0.563
    ├── Some((5, 1)): 17893/31306 ≈ 0.572
      ├── Some((1, 0)): 1819/3206 ≈ 0.567
      ├── Some((1, 1)): 1685/2986 ≈ 0.564
      ├── Some((1, 2)): 1475/2640 ≈ 0.559
      ├── Some((1, 3)): 2196/3822 ≈ 0.575
      ├── Some((1, 4)): 3710/6270 ≈ 0.592
      ├── Some((1, 5)): 1529/2730 ≈ 0.560
      ├── Some((1, 6)): 2014/3525 ≈ 0.571
      ├── Some((1, 7)): 1849/3255 ≈ 0.568
      └── Some((1, 8)): 1615/2871 ≈ 0.563
    ├── Some((5, 2)): 10651/18918 ≈ 0.563
      ├── Some((2, 0)): 1221/2165 ≈ 0.564
      ├── Some((2, 1)): 951/1724 ≈ 0.552
      ├── Some((2, 2)): 1026/1847 ≈ 0.555
      ├── Some((2, 3)): 779/1440 ≈ 0.541
      ├── Some((2, 4)): 1420/2488 ≈ 0.571
      ├── Some((2, 5)): 1421/2490 ≈ 0.571
      ├── Some((2, 6)): 844/1548 ≈ 0.545
      ├── Some((2, 7)): 1287/2273 ≈ 0.566
      └── Some((2, 8)): 1701/2942 ≈ 0.578
    ├── Some((5, 3)): 12184/21549 ≈ 0.565
      ├── Some((3, 0)): 1422/2508 ≈ 0.567
      ├── Some((3, 1)): 1426/2514 ≈ 0.567
      ├── Some((3, 2)): 1489/2616 ≈ 0.569
      ├── Some((3, 3)): 1403/2477 ≈ 0.566
      ├── Some((3, 4)): 1774/3078 ≈ 0.576
      ├── Some((3, 5)): 1550/2715 ≈ 0.571
      ├── Some((3, 6)): 1024/1856 ≈ 0.552
      ├── Some((3, 7)): 760/1418 ≈ 0.536
      └── Some((3, 8)): 1335/2366 ≈ 0.564
    ├── Some((5, 4)): 29883/51685 ≈ 0.578
      ├── Some((4, 0)): 2628/4707 ≈ 0.558
      ├── Some((4, 1)): 3364/5941 ≈ 0.566
      ├── Some((4, 2)): 905/1765 ≈ 0.513
      ├── Some((4, 3)): 15173/25318 ≈ 0.599
      ├── Some((4, 6)): 2193/3973 ≈ 0.552
      ├── Some((4, 7)): 4357/7595 ≈ 0.574
      └── Some((4, 8)): 1262/2385 ≈ 0.529
    ├── Some((5, 5)): 11961/21166 ≈ 0.565
      ├── Some((5, 0)): 1208/2176 ≈ 0.555
      ├── Some((5, 1)): 1678/2947 ≈ 0.569
      ├── Some((5, 2)): 1441/2559 ≈ 0.563
      ├── Some((5, 3)): 874/1621 ≈ 0.539
      ├── Some((5, 4)): 1865/3251 ≈ 0.574
      ├── Some((5, 6)): 1826/3188 ≈ 0.573
      ├── Some((5, 7)): 1465/2599 ≈ 0.564
      └── Some((5, 8)): 1603/2824 ≈ 0.568
    ├── Some((5, 6)): 11226/19906 ≈ 0.564
      ├── Some((6, 0)): 1312/2318 ≈ 0.566
      ├── Some((6, 1)): 1633/2838 ≈ 0.575
      ├── Some((6, 2)): 1389/2444 ≈ 0.568
      ├── Some((6, 3)): 1078/1937 ≈ 0.557
      ├── Some((6, 4)): 1390/2445 ≈ 0.569
      ├── Some((6, 5)): 970/1759 ≈ 0.551
      ├── Some((6, 6)): 1438/2523 ≈ 0.570
      ├── Some((6, 7)): 1062/1910 ≈ 0.556
      └── Some((6, 8)): 953/1731 ≈ 0.551
    ├── Some((5, 7)): 18392/32156 ≈ 0.572
      ├── Some((7, 0)): 2094/3659 ≈ 0.572
      ├── Some((7, 1)): 2339/4058 ≈ 0.576
      ├── Some((7, 2)): 2866/4914 ≈ 0.583
      ├── Some((7, 3)): 2046/3580 ≈ 0.572
      ├── Some((7, 4)): 2884/4943 ≈ 0.583
      ├── Some((7, 5)): 1708/3026 ≈ 0.564
      ├── Some((7, 6)): 1441/2586 ≈ 0.557
      ├── Some((7, 7)): 1510/2700 ≈ 0.559
      └── Some((7, 8)): 1503/2689 ≈ 0.559
    └── Some((5, 8)): 16582/29069 ≈ 0.570
      ├── Some((8, 0)): 1337/2402 ≈ 0.557
      ├── Some((8, 1)): 1923/3363 ≈ 0.572
      ├── Some((8, 2)): 2139/3715 ≈ 0.576
      ├── Some((8, 3)): 2135/3709 ≈ 0.576
      ├── Some((8, 4)): 1664/2940 ≈ 0.566
      ├── Some((8, 5)): 2320/4009 ≈ 0.579
      ├── Some((8, 6)): 1283/2313 ≈ 0.555
      ├── Some((8, 7)): 2152/3736 ≈ 0.576
      └── Some((8, 8)): 1628/2881 ≈ 0.565
  ├── Some((4, 6)): 25414/45793 ≈ 0.555
    ├── Some((6, 0)): 3959/7009 ≈ 0.565
      ├── Some((0, 0)): 189/382 ≈ 0.495
      ├── Some((0, 1)): 516/899 ≈ 0.574
      ├── Some((0, 2)): 459/811 ≈ 0.566
      ├── Some((0, 3)): 538/933 ≈ 0.577
      ├── Some((0, 4)): 741/1242 ≈ 0.597
      ├── Some((0, 5)): 476/837 ≈ 0.569
      ├── Some((0, 6)): 308/574 ≈ 0.537
      ├── Some((0, 7)): 400/719 ≈ 0.556
      └── Some((0, 8)): 331/611 ≈ 0.542
    ├── Some((6, 1)): 2461/4474 ≈ 0.550
      ├── Some((1, 0)): 269/491 ≈ 0.548
      ├── Some((1, 1)): 257/472 ≈ 0.544
      ├── Some((1, 2)): 357/626 ≈ 0.570
      ├── Some((1, 3)): 192/371 ≈ 0.518
      ├── Some((1, 4)): 394/682 ≈ 0.578
      ├── Some((1, 5)): 266/486 ≈ 0.547
      ├── Some((1, 6)): 214/405 ≈ 0.528
      ├── Some((1, 7)): 284/514 ≈ 0.553
      └── Some((1, 8)): 227/426 ≈ 0.533
    ├── Some((6, 2)): 2335/4259 ≈ 0.548
      ├── Some((2, 0)): 288/517 ≈ 0.557
      ├── Some((2, 1)): 266/484 ≈ 0.550
      ├── Some((2, 2)): 230/428 ≈ 0.537
      ├── Some((2, 3)): 307/546 ≈ 0.562
      ├── Some((2, 4)): 297/531 ≈ 0.559
      ├── Some((2, 5)): 207/392 ≈ 0.528
      ├── Some((2, 6)): 212/400 ≈ 0.530
      ├── Some((2, 7)): 246/453 ≈ 0.543
      └── Some((2, 8)): 281/507 ≈ 0.554
    ├── Some((6, 3)): 3337/5960 ≈ 0.560
      ├── Some((3, 0)): 343/620 ≈ 0.553
      ├── Some((3, 1)): 510/877 ≈ 0.582
      ├── Some((3, 2)): 371/663 ≈ 0.560
      ├── Some((3, 3)): 342/618 ≈ 0.553
      ├── Some((3, 4)): 449/783 ≈ 0.573
      ├── Some((3, 5)): 306/562 ≈ 0.544
      ├── Some((3, 6)): 391/694 ≈ 0.563
      ├── Some((3, 7)): 344/621 ≈ 0.554
      └── Some((3, 8)): 280/521 ≈ 0.537
    ├── Some((6, 4)): 3462/6171 ≈ 0.561
      ├── Some((4, 0)): 200/410 ≈ 0.488
      ├── Some((4, 1)): 848/1437 ≈ 0.590
      ├── Some((4, 2)): 749/1284 ≈ 0.583
      ├── Some((4, 3)): 411/754 ≈ 0.545
      ├── Some((4, 5)): 572/1009 ≈ 0.567
      ├── Some((4, 7)): 192/397 ≈ 0.484
      └── Some((4, 8)): 490/879 ≈ 0.557
    ├── Some((6, 5)): 2551/4627 ≈ 0.551
      ├── Some((5, 0)): 272/497 ≈ 0.547
      ├── Some((5, 1)): 287/520 ≈ 0.552
      ├── Some((5, 2)): 260/479 ≈ 0.543
      ├── Some((5, 3)): 173/342 ≈ 0.506
      ├── Some((5, 4)): 353/622 ≈ 0.568
      ├── Some((5, 5)): 217/411 ≈ 0.528
      ├── Some((5, 6)): 353/622 ≈ 0.568
      ├── Some((5, 7)): 381/664 ≈ 0.574
      └── Some((5, 8)): 254/469 ≈ 0.542
    ├── Some((6, 6)): 2629/4760 ≈ 0.552
      ├── Some((6, 0)): 357/640 ≈ 0.558
      ├── Some((6, 1)): 203/397 ≈ 0.511
      ├── Some((6, 2)): 378/673 ≈ 0.562
      ├── Some((6, 3)): 347/625 ≈ 0.555
      ├── Some((6, 4)): 345/622 ≈ 0.555
      ├── Some((6, 5)): 204/399 ≈ 0.511
      ├── Some((6, 7)): 288/532 ≈ 0.541
      └── Some((6, 8)): 507/871 ≈ 0.582
    ├── Some((6, 7)): 2073/3811 ≈ 0.544
      ├── Some((7, 0)): 258/467 ≈ 0.552
      ├── Some((7, 1)): 235/431 ≈ 0.545
      ├── Some((7, 2)): 97/213 ≈ 0.455
      ├── Some((7, 3)): 263/474 ≈ 0.555
      ├── Some((7, 4)): 265/477 ≈ 0.556
      ├── Some((7, 5)): 255/462 ≈ 0.552
      ├── Some((7, 6)): 188/359 ≈ 0.524
      ├── Some((7, 7)): 230/424 ≈ 0.542
      └── Some((7, 8)): 282/503 ≈ 0.561
    └── Some((6, 8)): 2606/4721 ≈ 0.552
      ├── Some((8, 0)): 297/536 ≈ 0.554
      ├── Some((8, 1)): 286/519 ≈ 0.551
      ├── Some((8, 2)): 319/570 ≈ 0.560
      ├── Some((8, 3)): 257/474 ≈ 0.542
      ├── Some((8, 4)): 286/519 ≈ 0.551
      ├── Some((8, 5)): 320/572 ≈ 0.559
      ├── Some((8, 6)): 357/628 ≈ 0.568
      ├── Some((8, 7)): 241/449 ≈ 0.537
      └── Some((8, 8)): 243/453 ≈ 0.536
  ├── Some((4, 7)): 7228826/7718484 ≈ 0.937
    ├── Some((7, 0)): 15638/27492 ≈ 0.569
      ├── Some((0, 0)): 1532/2720 ≈ 0.563
      ├── Some((0, 1)): 2241/3876 ≈ 0.578
      ├── Some((0, 2)): 1434/2559 ≈ 0.560
      ├── Some((0, 3)): 1551/2751 ≈ 0.564
      ├── Some((0, 4)): 1348/2418 ≈ 0.557
      ├── Some((0, 5)): 2042/3553 ≈ 0.575
      ├── Some((0, 6)): 2315/3996 ≈ 0.579
      ├── Some((0, 7)): 1837/3219 ≈ 0.571
      └── Some((0, 8)): 1337/2399 ≈ 0.557
    ├── Some((7, 1)): 15765/27709 ≈ 0.569
      ├── Some((1, 0)): 2159/3745 ≈ 0.577
      ├── Some((1, 1)): 1973/3442 ≈ 0.573
      ├── Some((1, 2)): 1768/3108 ≈ 0.569
      ├── Some((1, 3)): 1297/2334 ≈ 0.556
      ├── Some((1, 4)): 2355/4063 ≈ 0.580
      ├── Some((1, 5)): 1658/2928 ≈ 0.566
      ├── Some((1, 6)): 1557/2762 ≈ 0.564
      ├── Some((1, 7)): 1030/1892 ≈ 0.544
      └── Some((1, 8)): 1968/3434 ≈ 0.573
    ├── Some((7, 2)): 15143/26646 ≈ 0.568
      ├── Some((2, 0)): 1596/2821 ≈ 0.566
      ├── Some((2, 1)): 1568/2775 ≈ 0.565
      ├── Some((2, 2)): 1244/2243 ≈ 0.555
      ├── Some((2, 3)): 2142/3710 ≈ 0.577
      ├── Some((2, 4)): 1488/2644 ≈ 0.563
      ├── Some((2, 5)): 1860/3252 ≈ 0.572
      ├── Some((2, 6)): 2427/4172 ≈ 0.582
      ├── Some((2, 7)): 1501/2665 ≈ 0.563
      └── Some((2, 8)): 1317/2363 ≈ 0.557
    ├── Some((7, 3)): 16168/28398 ≈ 0.569
      ├── Some((3, 0)): 1707/3014 ≈ 0.566
      ├── Some((3, 1)): 1760/3100 ≈ 0.568
      ├── Some((3, 2)): 2383/4115 ≈ 0.579
      ├── Some((3, 3)): 1261/2279 ≈ 0.553
      ├── Some((3, 4)): 3265/5539 ≈ 0.589
      ├── Some((3, 5)): 1568/2786 ≈ 0.563
      ├── Some((3, 6)): 1576/2799 ≈ 0.563
      ├── Some((3, 7)): 1269/2292 ≈ 0.554
      └── Some((3, 8)): 1378/2473 ≈ 0.557
    ├── Some((7, 4)): 7115049/7518014 ≈ 0.946
      ├── Some((4, 0)): 4858/8749 ≈ 0.555
      ├── Some((4, 1)): 7084945/7464038 ≈ 0.949
      ├── Some((4, 2)): 5006/9002 ≈ 0.556
      ├── Some((4, 3)): 9879/17269 ≈ 0.572
      ├── Some((4, 5)): 5792/10343 ≈ 0.560
      ├── Some((4, 6)): 2244/4236 ≈ 0.530
      └── Some((4, 8)): 2324/4376 ≈ 0.531
    ├── Some((7, 5)): 6988/12625 ≈ 0.554
      ├── Some((5, 0)): 769/1391 ≈ 0.553
      ├── Some((5, 1)): 995/1757 ≈ 0.566
      ├── Some((5, 2)): 647/1192 ≈ 0.543
      ├── Some((5, 3)): 826/1484 ≈ 0.557
      ├── Some((5, 4)): 807/1453 ≈ 0.555
      ├── Some((5, 5)): 720/1312 ≈ 0.549
      ├── Some((5, 6)): 959/1699 ≈ 0.564
      ├── Some((5, 7)): 731/1330 ≈ 0.550
      └── Some((5, 8)): 534/1006 ≈ 0.531
    ├── Some((7, 6)): 18902/33066 ≈ 0.572
      ├── Some((6, 0)): 1464/2629 ≈ 0.557
      ├── Some((6, 1)): 2337/4062 ≈ 0.575
      ├── Some((6, 2)): 1959/3444 ≈ 0.569
      ├── Some((6, 3)): 2377/4127 ≈ 0.576
      ├── Some((6, 4)): 2504/4334 ≈ 0.578
      ├── Some((6, 5)): 1833/3238 ≈ 0.566
      ├── Some((6, 6)): 1691/3004 ≈ 0.563
      ├── Some((6, 7)): 2436/4224 ≈ 0.577
      └── Some((6, 8)): 2301/4003 ≈ 0.575
    ├── Some((7, 7)): 12395/21939 ≈ 0.565
      ├── Some((7, 0)): 1132/2056 ≈ 0.551
      ├── Some((7, 1)): 1161/2104 ≈ 0.552
      ├── Some((7, 2)): 1797/3149 ≈ 0.571
      ├── Some((7, 3)): 1391/2484 ≈ 0.560
      ├── Some((7, 4)): 1394/2489 ≈ 0.560
      ├── Some((7, 5)): 2051/3563 ≈ 0.576
      ├── Some((7, 6)): 2014/3503 ≈ 0.575
      └── Some((7, 8)): 1455/2590 ≈ 0.562
    └── Some((7, 8)): 12777/22594 ≈ 0.566
      ├── Some((8, 0)): 935/1716 ≈ 0.545
      ├── Some((8, 1)): 1448/2559 ≈ 0.566
      ├── Some((8, 2)): 1499/2642 ≈ 0.567
      ├── Some((8, 3)): 1266/2261 ≈ 0.560
      ├── Some((8, 4)): 923/1696 ≈ 0.544
      ├── Some((8, 5)): 1466/2588 ≈ 0.566
      ├── Some((8, 6)): 2029/3501 ≈ 0.580
      ├── Some((8, 7)): 1555/2734 ≈ 0.569
      └── Some((8, 8)): 1655/2896 ≈ 0.571
  └── Some((4, 8)): 36147/64650 ≈ 0.559
    ├── Some((8, 0)): 3570/6425 ≈ 0.556
      ├── Some((0, 0)): 501/877 ≈ 0.571
      ├── Some((0, 1)): 317/589 ≈ 0.538
      ├── Some((0, 2)): 273/519 ≈ 0.526
      ├── Some((0, 3)): 386/698 ≈ 0.553
      ├── Some((0, 4)): 438/779 ≈ 0.562
      ├── Some((0, 5)): 388/701 ≈ 0.553
      ├── Some((0, 6)): 457/809 ≈ 0.565
      ├── Some((0, 7)): 537/933 ≈ 0.576
      └── Some((0, 8)): 273/519 ≈ 0.526
    ├── Some((8, 1)): 4454/7928 ≈ 0.562
      ├── Some((1, 0)): 456/821 ≈ 0.555
      ├── Some((1, 1)): 425/772 ≈ 0.551
      ├── Some((1, 2)): 315/596 ≈ 0.529
      ├── Some((1, 3)): 478/856 ≈ 0.558
      ├── Some((1, 4)): 546/962 ≈ 0.568
      ├── Some((1, 5)): 471/844 ≈ 0.558
      ├── Some((1, 6)): 438/792 ≈ 0.553
      ├── Some((1, 7)): 551/970 ≈ 0.568
      └── Some((1, 8)): 773/1314 ≈ 0.588
    ├── Some((8, 2)): 3879/6951 ≈ 0.558
      ├── Some((2, 0)): 462/822 ≈ 0.562
      ├── Some((2, 1)): 506/890 ≈ 0.569
      ├── Some((2, 2)): 447/798 ≈ 0.560
      ├── Some((2, 3)): 313/587 ≈ 0.533
      ├── Some((2, 4)): 583/1009 ≈ 0.578
      ├── Some((2, 5)): 458/815 ≈ 0.562
      ├── Some((2, 6)): 453/807 ≈ 0.561
      ├── Some((2, 7)): 343/634 ≈ 0.541
      └── Some((2, 8)): 314/588 ≈ 0.534
    ├── Some((8, 3)): 4699/8343 ≈ 0.563
      ├── Some((3, 0)): 340/639 ≈ 0.532
      ├── Some((3, 1)): 713/1226 ≈ 0.582
      ├── Some((3, 2)): 823/1396 ≈ 0.590
      ├── Some((3, 3)): 410/752 ≈ 0.545
      ├── Some((3, 4)): 422/771 ≈ 0.547
      ├── Some((3, 5)): 546/966 ≈ 0.565
      ├── Some((3, 6)): 581/1021 ≈ 0.569
      ├── Some((3, 7)): 524/932 ≈ 0.562
      └── Some((3, 8)): 340/639 ≈ 0.532
    ├── Some((8, 4)): 4177/7458 ≈ 0.560
      ├── Some((4, 0)): 1178/1981 ≈ 0.595
      ├── Some((4, 1)): 581/1044 ≈ 0.557
      ├── Some((4, 2)): 393/741 ≈ 0.530
      ├── Some((4, 3)): 719/1263 ≈ 0.569
      ├── Some((4, 5)): 423/789 ≈ 0.536
      ├── Some((4, 6)): 411/770 ≈ 0.534
      └── Some((4, 7)): 472/869 ≈ 0.543
    ├── Some((8, 5)): 3349/6048 ≈ 0.554
      ├── Some((5, 0)): 377/680 ≈ 0.554
      ├── Some((5, 1)): 493/860 ≈ 0.573
      ├── Some((5, 2)): 307/570 ≈ 0.539
      ├── Some((5, 3)): 435/771 ≈ 0.564
      ├── Some((5, 4)): 297/554 ≈ 0.536
      ├── Some((5, 5)): 356/647 ≈ 0.550
      ├── Some((5, 6)): 432/766 ≈ 0.564
      ├── Some((5, 7)): 328/603 ≈ 0.544
      └── Some((5, 8)): 323/596 ≈ 0.542
    ├── Some((8, 6)): 5032/8906 ≈ 0.565
      ├── Some((6, 0)): 467/845 ≈ 0.553
      ├── Some((6, 1)): 763/1308 ≈ 0.583
      ├── Some((6, 2)): 395/730 ≈ 0.541
      ├── Some((6, 3)): 565/1000 ≈ 0.565
      ├── Some((6, 4)): 521/931 ≈ 0.560
      ├── Some((6, 5)): 459/832 ≈ 0.552
      ├── Some((6, 6)): 650/1133 ≈ 0.574
      ├── Some((6, 7)): 596/1048 ≈ 0.569
      └── Some((6, 8)): 615/1078 ≈ 0.571
    ├── Some((8, 7)): 3691/6632 ≈ 0.557
      ├── Some((7, 0)): 306/573 ≈ 0.534
      ├── Some((7, 1)): 427/764 ≈ 0.559
      ├── Some((7, 2)): 372/678 ≈ 0.549
      ├── Some((7, 3)): 481/848 ≈ 0.567
      ├── Some((7, 4)): 634/1084 ≈ 0.585
      ├── Some((7, 5)): 357/654 ≈ 0.546
      ├── Some((7, 6)): 327/607 ≈ 0.539
      ├── Some((7, 7)): 336/621 ≈ 0.541
      └── Some((7, 8)): 451/802 ≈ 0.562
    └── Some((8, 8)): 3296/5958 ≈ 0.553
      ├── Some((8, 0)): 444/796 ≈ 0.558
      ├── Some((8, 1)): 349/646 ≈ 0.540
      ├── Some((8, 2)): 449/804 ≈ 0.558
      ├── Some((8, 3)): 340/631 ≈ 0.539
      ├── Some((8, 4)): 546/955 ≈ 0.572
      ├── Some((8, 5)): 408/739 ≈ 0.552
      ├── Some((8, 6)): 474/843 ≈ 0.562
      └── Some((8, 7)): 285/543 ≈ 0.525
├── Some((4, 5)): 22390/41226 ≈ 0.543
  ├── Some((5, 0)): 2751/5039 ≈ 0.546
    ├── Some((0, 0)): 282/523 ≈ 0.539
      ├── Some((0, 1)): 50/84 ≈ 0.595
      ├── Some((0, 2)): 42/74 ≈ 0.568
      ├── Some((0, 3)): 28/56 ≈ 0.500
      ├── Some((0, 4)): 27/55 ≈ 0.491
      ├── Some((0, 5)): 25/52 ≈ 0.481
      ├── Some((0, 6)): 29/58 ≈ 0.500
      ├── Some((0, 7)): 56/92 ≈ 0.609
      └── Some((0, 8)): 24/51 ≈ 0.471
    ├── Some((0, 1)): 226/435 ≈ 0.520
      ├── Some((1, 0)): 39/66 ≈ 0.591
      ├── Some((1, 1)): 38/65 ≈ 0.585
      ├── Some((1, 2)): 18/40 ≈ 0.450
      ├── Some((1, 3)): 20/42 ≈ 0.476
      ├── Some((1, 4)): 21/44 ≈ 0.477
      ├── Some((1, 5)): 50/80 ≈ 0.625
      ├── Some((1, 6)): 1/15 ≈ 0.067
      ├── Some((1, 7)): 22/45 ≈ 0.489
      └── Some((1, 8)): 16/37 ≈ 0.432
    ├── Some((0, 2)): 222/428 ≈ 0.519
      ├── Some((2, 0)): 10/28 ≈ 0.357
      ├── Some((2, 1)): 21/43 ≈ 0.488
      ├── Some((2, 2)): 19/40 ≈ 0.475
      ├── Some((2, 3)): 40/67 ≈ 0.597
      ├── Some((2, 4)): 17/38 ≈ 0.447
      ├── Some((2, 5)): 35/60 ≈ 0.583
      ├── Some((2, 6)): 35/61 ≈ 0.574
      ├── Some((2, 7)): 21/43 ≈ 0.488
      └── Some((2, 8)): 24/47 ≈ 0.511
    ├── Some((0, 3)): 354/636 ≈ 0.557
      ├── Some((3, 0)): 26/53 ≈ 0.491
      ├── Some((3, 1)): 43/75 ≈ 0.573
      ├── Some((3, 2)): 52/87 ≈ 0.598
      ├── Some((3, 3)): 50/84 ≈ 0.595
      ├── Some((3, 4)): 40/72 ≈ 0.556
      ├── Some((3, 5)): 36/67 ≈ 0.537
      ├── Some((3, 6)): 43/75 ≈ 0.573
      ├── Some((3, 7)): 26/53 ≈ 0.491
      └── Some((3, 8)): 38/69 ≈ 0.551
    ├── Some((0, 4)): 272/508 ≈ 0.535
      ├── Some((4, 0)): 47/81 ≈ 0.580
      ├── Some((4, 1)): 25/52 ≈ 0.481
      ├── Some((4, 2)): 53/88 ≈ 0.602
      ├── Some((4, 3)): 37/68 ≈ 0.544
      ├── Some((4, 4)): 49/83 ≈ 0.590
      ├── Some((4, 6)): 28/56 ≈ 0.500
      ├── Some((4, 7)): 19/44 ≈ 0.432
      └── Some((4, 8)): 13/35 ≈ 0.371
    ├── Some((0, 5)): 387/687 ≈ 0.563
      ├── Some((5, 1)): 55/95 ≈ 0.579
      ├── Some((5, 2)): 39/74 ≈ 0.527
      ├── Some((5, 3)): 28/59 ≈ 0.475
      ├── Some((5, 4)): 32/65 ≈ 0.492
      ├── Some((5, 5)): 85/132 ≈ 0.644
      ├── Some((5, 6)): 37/71 ≈ 0.521
      ├── Some((5, 7)): 68/111 ≈ 0.613
      └── Some((5, 8)): 43/79 ≈ 0.544
    ├── Some((0, 6)): 303/556 ≈ 0.545
      ├── Some((6, 0)): 59/93 ≈ 0.634
      ├── Some((6, 1)): 36/65 ≈ 0.554
      ├── Some((6, 2)): 50/82 ≈ 0.610
      ├── Some((6, 3)): 19/43 ≈ 0.442
      ├── Some((6, 4)): 25/51 ≈ 0.490
      ├── Some((6, 5)): 37/66 ≈ 0.561
      ├── Some((6, 6)): 28/55 ≈ 0.509
      ├── Some((6, 7)): 33/61 ≈ 0.541
      └── Some((6, 8)): 16/39 ≈ 0.410
    ├── Some((0, 7)): 292/539 ≈ 0.542
      ├── Some((7, 0)): 49/81 ≈ 0.605
      ├── Some((7, 1)): 39/68 ≈ 0.574
      ├── Some((7, 2)): 27/53 ≈ 0.509
      ├── Some((7, 3)): 28/54 ≈ 0.519
      ├── Some((7, 4)): 31/58 ≈ 0.534
      ├── Some((7, 5)): 24/49 ≈ 0.490
      ├── Some((7, 6)): 45/76 ≈ 0.592
      ├── Some((7, 7)): 25/51 ≈ 0.490
      └── Some((7, 8)): 23/48 ≈ 0.479
    └── Some((0, 8)): 412/726 ≈ 0.567
      ├── Some((8, 0)): 91/138 ≈ 0.659
      ├── Some((8, 1)): 60/99 ≈ 0.606
      ├── Some((8, 2)): 33/65 ≈ 0.508
      ├── Some((8, 3)): 33/65 ≈ 0.508
      ├── Some((8, 4)): 73/116 ≈ 0.629
      ├── Some((8, 5)): 32/63 ≈ 0.508
      ├── Some((8, 6)): 19/46 ≈ 0.413
      ├── Some((8, 7)): 52/89 ≈ 0.584
      └── Some((8, 8)): 18/44 ≈ 0.409
  ├── Some((5, 1)): 1651/3131 ≈ 0.527
    ├── Some((1, 0)): 194/365 ≈ 0.532
      ├── Some((0, 0)): 20/39 ≈ 0.513
      ├── Some((0, 1)): 34/56 ≈ 0.607
      ├── Some((0, 2)): 15/33 ≈ 0.455
      ├── Some((0, 3)): 25/45 ≈ 0.556
      ├── Some((0, 4)): 27/47 ≈ 0.574
      ├── Some((0, 5)): 25/45 ≈ 0.556
      ├── Some((0, 6)): 25/45 ≈ 0.556
      ├── Some((0, 7)): 5/19 ≈ 0.263
      └── Some((0, 8)): 17/35 ≈ 0.486
    ├── Some((1, 1)): 164/318 ≈ 0.516
      ├── Some((1, 0)): 33/55 ≈ 0.600
      ├── Some((1, 2)): 6/21 ≈ 0.286
      ├── Some((1, 3)): 34/57 ≈ 0.596
      ├── Some((1, 4)): 14/32 ≈ 0.438
      ├── Some((1, 5)): 30/52 ≈ 0.577
      ├── Some((1, 6)): 11/28 ≈ 0.393
      ├── Some((1, 7)): 23/43 ≈ 0.535
      └── Some((1, 8)): 12/29 ≈ 0.414
    ├── Some((1, 2)): 205/382 ≈ 0.537
      ├── Some((2, 0)): 24/44 ≈ 0.545
      ├── Some((2, 1)): 34/56 ≈ 0.607
      ├── Some((2, 2)): 15/33 ≈ 0.455
      ├── Some((2, 3)): 17/36 ≈ 0.472
      ├── Some((2, 4)): 37/60 ≈ 0.617
      ├── Some((2, 5)): 21/40 ≈ 0.525
      ├── Some((2, 6)): 13/30 ≈ 0.433
      ├── Some((2, 7)): 29/50 ≈ 0.580
      └── Some((2, 8)): 14/32 ≈ 0.438
    ├── Some((1, 3)): 191/360 ≈ 0.531
      ├── Some((3, 0)): 40/62 ≈ 0.645
      ├── Some((3, 1)): 22/41 ≈ 0.537
      ├── Some((3, 2)): 25/45 ≈ 0.556
      ├── Some((3, 3)): 13/30 ≈ 0.433
      ├── Some((3, 4)): 17/35 ≈ 0.486
      ├── Some((3, 5)): 18/36 ≈ 0.500
      ├── Some((3, 6)): 23/42 ≈ 0.548
      ├── Some((3, 7)): 8/23 ≈ 0.348
      └── Some((3, 8)): 25/45 ≈ 0.556
    ├── Some((1, 4)): 128/261 ≈ 0.490
      ├── Some((4, 0)): 24/43 ≈ 0.558
      ├── Some((4, 1)): 6/20 ≈ 0.300
      ├── Some((4, 2)): 21/40 ≈ 0.525
      ├── Some((4, 3)): 8/23 ≈ 0.348
      ├── Some((4, 4)): 1/12 ≈ 0.083
      ├── Some((4, 6)): 10/26 ≈ 0.385
      ├── Some((4, 7)): 37/58 ≈ 0.638
      └── Some((4, 8)): 20/38 ≈ 0.526
    ├── Some((1, 5)): 244/442 ≈ 0.552
      ├── Some((5, 0)): 20/42 ≈ 0.476
      ├── Some((5, 2)): 32/57 ≈ 0.561
      ├── Some((5, 3)): 25/48 ≈ 0.521
      ├── Some((5, 4)): 29/53 ≈ 0.547
      ├── Some((5, 5)): 33/58 ≈ 0.569
      ├── Some((5, 6)): 39/66 ≈ 0.591
      ├── Some((5, 7)): 30/55 ≈ 0.545
      └── Some((5, 8)): 36/62 ≈ 0.581
    ├── Some((1, 6)): 236/430 ≈ 0.549
      ├── Some((6, 0)): 31/54 ≈ 0.574
      ├── Some((6, 1)): 42/67 ≈ 0.627
      ├── Some((6, 2)): 30/52 ≈ 0.577
      ├── Some((6, 3)): 22/43 ≈ 0.512
      ├── Some((6, 4)): 16/35 ≈ 0.457
      ├── Some((6, 5)): 28/50 ≈ 0.560
      ├── Some((6, 6)): 26/48 ≈ 0.542
      ├── Some((6, 7)): 16/35 ≈ 0.457
      └── Some((6, 8)): 24/45 ≈ 0.533
    ├── Some((1, 7)): 142/283 ≈ 0.502
      ├── Some((7, 0)): 24/41 ≈ 0.585
      ├── Some((7, 1)): 6/19 ≈ 0.316
      ├── Some((7, 2)): 19/36 ≈ 0.528
      ├── Some((7, 3)): 8/22 ≈ 0.364
      ├── Some((7, 4)): 14/29 ≈ 0.483
      ├── Some((7, 5)): 20/37 ≈ 0.541
      ├── Some((7, 6)): 12/27 ≈ 0.444
      ├── Some((7, 7)): 17/33 ≈ 0.515
      └── Some((7, 8)): 21/38 ≈ 0.553
    └── Some((1, 8)): 146/289 ≈ 0.505
      ├── Some((8, 0)): 23/41 ≈ 0.561
      ├── Some((8, 1)): 9/23 ≈ 0.391
      ├── Some((8, 2)): 6/19 ≈ 0.316
      ├── Some((8, 3)): 35/54 ≈ 0.648
      ├── Some((8, 4)): 33/52 ≈ 0.635
      ├── Some((8, 5)): 11/26 ≈ 0.423
      ├── Some((8, 6)): 10/25 ≈ 0.400
      ├── Some((8, 7)): 14/30 ≈ 0.467
      └── Some((8, 8)): 5/18 ≈ 0.278
  ├── Some((5, 2)): 2802/5127 ≈ 0.547
    ├── Some((2, 0)): 244/464 ≈ 0.526
      ├── Some((0, 0)): 32/58 ≈ 0.552
      ├── Some((0, 1)): 16/37 ≈ 0.432
      ├── Some((0, 2)): 33/59 ≈ 0.559
      ├── Some((0, 3)): 37/64 ≈ 0.578
      ├── Some((0, 4)): 17/39 ≈ 0.436
      ├── Some((0, 5)): 17/39 ≈ 0.436
      ├── Some((0, 6)): 27/51 ≈ 0.529
      ├── Some((0, 7)): 30/55 ≈ 0.545
      └── Some((0, 8)): 35/61 ≈ 0.574
    ├── Some((2, 1)): 265/498 ≈ 0.532
      ├── Some((1, 0)): 51/82 ≈ 0.622
      ├── Some((1, 1)): 27/52 ≈ 0.519
      ├── Some((1, 2)): 14/35 ≈ 0.400
      ├── Some((1, 3)): 31/58 ≈ 0.534
      ├── Some((1, 4)): 32/59 ≈ 0.542
      ├── Some((1, 5)): 27/52 ≈ 0.519
      ├── Some((1, 6)): 19/42 ≈ 0.452
      ├── Some((1, 7)): 36/64 ≈ 0.562
      └── Some((1, 8)): 27/53 ≈ 0.509
    ├── Some((2, 2)): 413/728 ≈ 0.567
      ├── Some((2, 0)): 55/96 ≈ 0.573
      ├── Some((2, 1)): 27/58 ≈ 0.466
      ├── Some((2, 3)): 65/109 ≈ 0.596
      ├── Some((2, 4)): 63/106 ≈ 0.594
      ├── Some((2, 5)): 43/80 ≈ 0.538
      ├── Some((2, 6)): 44/81 ≈ 0.543
      ├── Some((2, 7)): 61/103 ≈ 0.592
      └── Some((2, 8)): 54/94 ≈ 0.574
    ├── Some((2, 3)): 460/801 ≈ 0.574
      ├── Some((3, 0)): 52/90 ≈ 0.578
      ├── Some((3, 1)): 48/85 ≈ 0.565
      ├── Some((3, 2)): 55/94 ≈ 0.585
      ├── Some((3, 3)): 48/85 ≈ 0.565
      ├── Some((3, 4)): 38/72 ≈ 0.528
      ├── Some((3, 5)): 33/65 ≈ 0.508
      ├── Some((3, 6)): 56/95 ≈ 0.589
      ├── Some((3, 7)): 69/112 ≈ 0.616
      └── Some((3, 8)): 61/102 ≈ 0.598
    ├── Some((2, 4)): 203/398 ≈ 0.510
      ├── Some((4, 0)): 41/70 ≈ 0.586
      ├── Some((4, 1)): 14/35 ≈ 0.400
      ├── Some((4, 2)): 36/63 ≈ 0.571
      ├── Some((4, 3)): 15/36 ≈ 0.417
      ├── Some((4, 4)): 20/43 ≈ 0.465
      ├── Some((4, 6)): 20/43 ≈ 0.465
      ├── Some((4, 7)): 36/63 ≈ 0.571
      └── Some((4, 8)): 21/44 ≈ 0.477
    ├── Some((2, 5)): 279/520 ≈ 0.537
      ├── Some((5, 0)): 44/77 ≈ 0.571
      ├── Some((5, 1)): 24/51 ≈ 0.471
      ├── Some((5, 3)): 27/55 ≈ 0.491
      ├── Some((5, 4)): 23/49 ≈ 0.469
      ├── Some((5, 5)): 57/93 ≈ 0.613
      ├── Some((5, 6)): 27/55 ≈ 0.491
      ├── Some((5, 7)): 28/56 ≈ 0.500
      └── Some((5, 8)): 49/83 ≈ 0.590
    ├── Some((2, 6)): 290/537 ≈ 0.540
      ├── Some((6, 0)): 30/57 ≈ 0.526
      ├── Some((6, 1)): 17/40 ≈ 0.425
      ├── Some((6, 2)): 38/67 ≈ 0.567
      ├── Some((6, 3)): 43/74 ≈ 0.581
      ├── Some((6, 4)): 47/78 ≈ 0.603
      ├── Some((6, 5)): 18/41 ≈ 0.439
      ├── Some((6, 6)): 45/76 ≈ 0.592
      ├── Some((6, 7)): 28/55 ≈ 0.509
      └── Some((6, 8)): 23/48 ≈ 0.479
    ├── Some((2, 7)): 315/576 ≈ 0.547
      ├── Some((7, 0)): 12/34 ≈ 0.353
      ├── Some((7, 1)): 35/65 ≈ 0.538
      ├── Some((7, 2)): 72/110 ≈ 0.655
      ├── Some((7, 3)): 40/71 ≈ 0.563
      ├── Some((7, 4)): 55/89 ≈ 0.618
      ├── Some((7, 5)): 30/58 ≈ 0.517
      ├── Some((7, 6)): 31/59 ≈ 0.525
      ├── Some((7, 7)): 12/34 ≈ 0.353
      └── Some((7, 8)): 28/55 ≈ 0.509
    └── Some((2, 8)): 333/604 ≈ 0.551
      ├── Some((8, 0)): 30/58 ≈ 0.517
      ├── Some((8, 1)): 41/72 ≈ 0.569
      ├── Some((8, 2)): 52/86 ≈ 0.605
      ├── Some((8, 3)): 45/78 ≈ 0.577
      ├── Some((8, 4)): 37/67 ≈ 0.552
      ├── Some((8, 5)): 43/75 ≈ 0.573
      ├── Some((8, 6)): 14/37 ≈ 0.378
      ├── Some((8, 7)): 36/66 ≈ 0.545
      └── Some((8, 8)): 34/64 ≈ 0.531
  ├── Some((5, 3)): 2884/5268 ≈ 0.547
    ├── Some((3, 0)): 492/852 ≈ 0.577
      ├── Some((0, 0)): 46/84 ≈ 0.548
      ├── Some((0, 1)): 60/102 ≈ 0.588
      ├── Some((0, 2)): 15/41 ≈ 0.366
      ├── Some((0, 3)): 55/95 ≈ 0.579
      ├── Some((0, 4)): 66/110 ≈ 0.600
      ├── Some((0, 5)): 59/101 ≈ 0.584
      ├── Some((0, 6)): 50/89 ≈ 0.562
      ├── Some((0, 7)): 97/148 ≈ 0.655
      └── Some((0, 8)): 44/81 ≈ 0.543
    ├── Some((3, 1)): 336/611 ≈ 0.550
      ├── Some((1, 0)): 25/52 ≈ 0.481
      ├── Some((1, 1)): 64/102 ≈ 0.627
      ├── Some((1, 2)): 44/77 ≈ 0.571
      ├── Some((1, 3)): 11/33 ≈ 0.333
      ├── Some((1, 4)): 57/93 ≈ 0.613
      ├── Some((1, 5)): 42/74 ≈ 0.568
      ├── Some((1, 6)): 34/64 ≈ 0.531
      ├── Some((1, 7)): 32/61 ≈ 0.525
      └── Some((1, 8)): 26/54 ≈ 0.481
    ├── Some((3, 2)): 216/420 ≈ 0.514
      ├── Some((2, 0)): 19/40 ≈ 0.475
      ├── Some((2, 1)): 16/37 ≈ 0.432
      ├── Some((2, 2)): 49/77 ≈ 0.636
      ├── Some((2, 3)): 24/47 ≈ 0.511
      ├── Some((2, 4)): 25/48 ≈ 0.521
      ├── Some((2, 5)): 29/53 ≈ 0.547
      ├── Some((2, 6)): 10/28 ≈ 0.357
      ├── Some((2, 7)): 25/48 ≈ 0.521
      └── Some((2, 8)): 19/41 ≈ 0.463
    ├── Some((3, 3)): 276/516 ≈ 0.535
      ├── Some((3, 0)): 45/79 ≈ 0.570
      ├── Some((3, 1)): 53/89 ≈ 0.596
      ├── Some((3, 2)): 39/71 ≈ 0.549
      ├── Some((3, 4)): 6/25 ≈ 0.240
      ├── Some((3, 5)): 31/60 ≈ 0.517
      ├── Some((3, 6)): 61/98 ≈ 0.622
      ├── Some((3, 7)): 18/43 ≈ 0.419
      └── Some((3, 8)): 23/50 ≈ 0.460
    ├── Some((3, 4)): 251/476 ≈ 0.527
      ├── Some((4, 0)): 31/60 ≈ 0.517
      ├── Some((4, 1)): 19/43 ≈ 0.442
      ├── Some((4, 2)): 66/103 ≈ 0.641
      ├── Some((4, 3)): 27/54 ≈ 0.500
      ├── Some((4, 4)): 15/38 ≈ 0.395
      ├── Some((4, 6)): 25/52 ≈ 0.481
      ├── Some((4, 7)): 24/50 ≈ 0.480
      └── Some((4, 8)): 43/75 ≈ 0.573
    ├── Some((3, 5)): 379/678 ≈ 0.559
      ├── Some((5, 0)): 64/106 ≈ 0.604
      ├── Some((5, 1)): 44/81 ≈ 0.543
      ├── Some((5, 2)): 37/71 ≈ 0.521
      ├── Some((5, 4)): 46/83 ≈ 0.554
      ├── Some((5, 5)): 65/108 ≈ 0.602
      ├── Some((5, 6)): 28/59 ≈ 0.475
      ├── Some((5, 7)): 47/84 ≈ 0.560
      └── Some((5, 8)): 47/85 ≈ 0.553
    ├── Some((3, 6)): 377/674 ≈ 0.559
      ├── Some((6, 0)): 68/108 ≈ 0.630
      ├── Some((6, 1)): 34/65 ≈ 0.523
      ├── Some((6, 2)): 39/71 ≈ 0.549
      ├── Some((6, 3)): 29/58 ≈ 0.500
      ├── Some((6, 4)): 36/68 ≈ 0.529
      ├── Some((6, 5)): 37/69 ≈ 0.536
      ├── Some((6, 6)): 33/64 ≈ 0.516
      ├── Some((6, 7)): 38/70 ≈ 0.543
      └── Some((6, 8)): 62/100 ≈ 0.620
    ├── Some((3, 7)): 279/521 ≈ 0.536
      ├── Some((7, 0)): 32/59 ≈ 0.542
      ├── Some((7, 1)): 30/57 ≈ 0.526
      ├── Some((7, 2)): 50/82 ≈ 0.610
      ├── Some((7, 3)): 31/58 ≈ 0.534
      ├── Some((7, 4)): 31/58 ≈ 0.534
      ├── Some((7, 5)): 33/61 ≈ 0.541
      ├── Some((7, 6)): 11/31 ≈ 0.355
      ├── Some((7, 7)): 19/43 ≈ 0.442
      └── Some((7, 8)): 41/71 ≈ 0.577
    └── Some((3, 8)): 278/519 ≈ 0.536
      ├── Some((8, 0)): 43/73 ≈ 0.589
      ├── Some((8, 1)): 51/83 ≈ 0.614
      ├── Some((8, 2)): 21/45 ≈ 0.467
      ├── Some((8, 3)): 11/31 ≈ 0.355
      ├── Some((8, 4)): 28/54 ≈ 0.519
      ├── Some((8, 5)): 32/59 ≈ 0.542
      ├── Some((8, 6)): 36/65 ≈ 0.554
      ├── Some((8, 7)): 25/50 ≈ 0.500
      └── Some((8, 8)): 31/58 ≈ 0.534
  ├── Some((5, 4)): 3694/6658 ≈ 0.555
    ├── Some((4, 0)): 417/763 ≈ 0.547
      ├── Some((0, 0)): 52/93 ≈ 0.559
      ├── Some((0, 1)): 33/67 ≈ 0.493
      ├── Some((0, 2)): 34/69 ≈ 0.493
      ├── Some((0, 3)): 53/94 ≈ 0.564
      ├── Some((0, 4)): 57/99 ≈ 0.576
      ├── Some((0, 5)): 60/103 ≈ 0.583
      ├── Some((0, 6)): 44/82 ≈ 0.537
      ├── Some((0, 7)): 18/46 ≈ 0.391
      └── Some((0, 8)): 65/109 ≈ 0.596
    ├── Some((4, 1)): 268/523 ≈ 0.512
      ├── Some((1, 0)): 29/58 ≈ 0.500
      ├── Some((1, 1)): 45/78 ≈ 0.577
      ├── Some((1, 2)): 19/44 ≈ 0.432
      ├── Some((1, 3)): 38/69 ≈ 0.551
      ├── Some((1, 4)): 32/61 ≈ 0.525
      ├── Some((1, 5)): 44/77 ≈ 0.571
      ├── Some((1, 6)): 12/34 ≈ 0.353
      ├── Some((1, 7)): 13/36 ≈ 0.361
      └── Some((1, 8)): 35/65 ≈ 0.538
    ├── Some((4, 2)): 404/743 ≈ 0.544
      ├── Some((2, 0)): 16/43 ≈ 0.372
      ├── Some((2, 1)): 38/74 ≈ 0.514
      ├── Some((2, 2)): 73/119 ≈ 0.613
      ├── Some((2, 3)): 49/88 ≈ 0.557
      ├── Some((2, 4)): 52/92 ≈ 0.565
      ├── Some((2, 5)): 54/95 ≈ 0.568
      ├── Some((2, 6)): 28/60 ≈ 0.467
      ├── Some((2, 7)): 64/108 ≈ 0.593
      └── Some((2, 8)): 30/63 ≈ 0.476
    ├── Some((4, 3)): 451/817 ≈ 0.552
      ├── Some((3, 0)): 43/82 ≈ 0.524
      ├── Some((3, 1)): 32/67 ≈ 0.478
      ├── Some((3, 2)): 63/108 ≈ 0.583
      ├── Some((3, 3)): 86/137 ≈ 0.628
      ├── Some((3, 4)): 45/84 ≈ 0.536
      ├── Some((3, 5)): 56/99 ≈ 0.566
      ├── Some((3, 6)): 45/84 ≈ 0.536
      ├── Some((3, 7)): 36/72 ≈ 0.500
      └── Some((3, 8)): 44/83 ≈ 0.530
    ├── Some((4, 4)): 868/1468 ≈ 0.591
      ├── Some((4, 0)): 108/188 ≈ 0.574
      ├── Some((4, 1)): 116/199 ≈ 0.583
      ├── Some((4, 2)): 154/251 ≈ 0.614
      ├── Some((4, 3)): 89/161 ≈ 0.553
      ├── Some((4, 6)): 131/219 ≈ 0.598
      ├── Some((4, 7)): 158/256 ≈ 0.617
      └── Some((4, 8)): 112/193 ≈ 0.580
    ├── Some((4, 6)): 376/698 ≈ 0.539
      ├── Some((6, 0)): 54/93 ≈ 0.581
      ├── Some((6, 1)): 37/71 ≈ 0.521
      ├── Some((6, 2)): 29/61 ≈ 0.475
      ├── Some((6, 3)): 48/86 ≈ 0.558
      ├── Some((6, 4)): 30/62 ≈ 0.484
      ├── Some((6, 5)): 54/93 ≈ 0.581
      ├── Some((6, 6)): 43/79 ≈ 0.544
      ├── Some((6, 7)): 40/75 ≈ 0.533
      └── Some((6, 8)): 41/77 ≈ 0.532
    ├── Some((4, 7)): 409/750 ≈ 0.545
      ├── Some((7, 0)): 64/108 ≈ 0.593
      ├── Some((7, 1)): 36/71 ≈ 0.507
      ├── Some((7, 2)): 66/110 ≈ 0.600
      ├── Some((7, 3)): 39/75 ≈ 0.520
      ├── Some((7, 4)): 26/57 ≈ 0.456
      ├── Some((7, 5)): 49/88 ≈ 0.557
      ├── Some((7, 6)): 47/86 ≈ 0.547
      ├── Some((7, 7)): 42/79 ≈ 0.532
      └── Some((7, 8)): 39/75 ≈ 0.520
    └── Some((4, 8)): 500/895 ≈ 0.559
      ├── Some((8, 0)): 47/88 ≈ 0.534
      ├── Some((8, 1)): 56/100 ≈ 0.560
      ├── Some((8, 2)): 46/87 ≈ 0.529
      ├── Some((8, 3)): 96/152 ≈ 0.632
      ├── Some((8, 4)): 27/61 ≈ 0.443
      ├── Some((8, 5)): 67/115 ≈ 0.583
      ├── Some((8, 6)): 44/84 ≈ 0.524
      ├── Some((8, 7)): 53/97 ≈ 0.546
      └── Some((8, 8)): 63/110 ≈ 0.573
  ├── Some((5, 5)): 1405/2699 ≈ 0.521
    ├── Some((5, 0)): 325/569 ≈ 0.571
      ├── Some((0, 0)): 29/54 ≈ 0.537
      ├── Some((0, 1)): 27/52 ≈ 0.519
      ├── Some((0, 2)): 41/69 ≈ 0.594
      ├── Some((0, 3)): 23/47 ≈ 0.489
      ├── Some((0, 4)): 43/72 ≈ 0.597
      ├── Some((0, 5)): 45/74 ≈ 0.608
      ├── Some((0, 6)): 32/58 ≈ 0.552
      ├── Some((0, 7)): 37/64 ≈ 0.578
      └── Some((0, 8)): 48/78 ≈ 0.615
    ├── Some((5, 1)): 204/383 ≈ 0.533
      ├── Some((1, 0)): 23/43 ≈ 0.535
      ├── Some((1, 1)): 28/49 ≈ 0.571
      ├── Some((1, 2)): 15/33 ≈ 0.455
      ├── Some((1, 3)): 15/33 ≈ 0.455
      ├── Some((1, 4)): 27/48 ≈ 0.562
      ├── Some((1, 5)): 35/58 ≈ 0.603
      ├── Some((1, 6)): 15/33 ≈ 0.455
      ├── Some((1, 7)): 28/49 ≈ 0.571
      └── Some((1, 8)): 17/36 ≈ 0.472
    ├── Some((5, 2)): 96/210 ≈ 0.457
      ├── Some((2, 0)): 17/31 ≈ 0.548
      ├── Some((2, 1)): 11/24 ≈ 0.458
      ├── Some((2, 2)): 7/19 ≈ 0.368
      ├── Some((2, 3)): 13/26 ≈ 0.500
      ├── Some((2, 4)): 14/27 ≈ 0.519
      ├── Some((2, 5)): 11/24 ≈ 0.458
      ├── Some((2, 6)): 4/15 ≈ 0.267
      ├── Some((2, 7)): 10/22 ≈ 0.455
      └── Some((2, 8)): 9/21 ≈ 0.429
    ├── Some((5, 3)): 144/288 ≈ 0.500
      ├── Some((3, 0)): 18/35 ≈ 0.514
      ├── Some((3, 1)): 13/28 ≈ 0.464
      ├── Some((3, 2)): 25/43 ≈ 0.581
      ├── Some((3, 3)): 14/30 ≈ 0.467
      ├── Some((3, 4)): 28/46 ≈ 0.609
      ├── Some((3, 5)): 12/27 ≈ 0.444
      ├── Some((3, 6)): 15/31 ≈ 0.484
      ├── Some((3, 7)): 13/29 ≈ 0.448
      └── Some((3, 8)): 5/18 ≈ 0.278
    ├── Some((5, 4)): 142/285 ≈ 0.498
      ├── Some((4, 0)): 17/35 ≈ 0.486
      ├── Some((4, 1)): 23/42 ≈ 0.548
      ├── Some((4, 2)): 24/44 ≈ 0.545
      ├── Some((4, 3)): 22/41 ≈ 0.537
      ├── Some((4, 4)): 23/43 ≈ 0.535
      ├── Some((4, 6)): 18/36 ≈ 0.500
      ├── Some((4, 7)): 8/23 ≈ 0.348
      └── Some((4, 8)): 6/20 ≈ 0.300
    ├── Some((5, 6)): 208/390 ≈ 0.533
      ├── Some((6, 0)): 33/55 ≈ 0.600
      ├── Some((6, 1)): 16/35 ≈ 0.457
      ├── Some((6, 2)): 21/41 ≈ 0.512
      ├── Some((6, 3)): 17/36 ≈ 0.472
      ├── Some((6, 4)): 25/46 ≈ 0.543
      ├── Some((6, 5)): 24/44 ≈ 0.545
      ├── Some((6, 6)): 19/38 ≈ 0.500
      ├── Some((6, 7)): 23/43 ≈ 0.535
      └── Some((6, 8)): 29/51 ≈ 0.569
    ├── Some((5, 7)): 167/325 ≈ 0.514
      ├── Some((7, 0)): 9/24 ≈ 0.375
      ├── Some((7, 1)): 11/27 ≈ 0.407
      ├── Some((7, 2)): 19/37 ≈ 0.514
      ├── Some((7, 3)): 7/21 ≈ 0.333
      ├── Some((7, 4)): 30/50 ≈ 0.600
      ├── Some((7, 5)): 17/34 ≈ 0.500
      ├── Some((7, 6)): 24/43 ≈ 0.558
      ├── Some((7, 7)): 24/43 ≈ 0.558
      └── Some((7, 8)): 26/45 ≈ 0.578
    └── Some((5, 8)): 119/248 ≈ 0.480
      ├── Some((8, 0)): 10/23 ≈ 0.435
      ├── Some((8, 1)): 12/26 ≈ 0.462
      ├── Some((8, 2)): 9/22 ≈ 0.409
      ├── Some((8, 3)): 22/38 ≈ 0.579
      ├── Some((8, 4)): 10/24 ≈ 0.417
      ├── Some((8, 5)): 23/39 ≈ 0.590
      ├── Some((8, 6)): 11/25 ≈ 0.440
      ├── Some((8, 7)): 10/24 ≈ 0.417
      └── Some((8, 8)): 12/26 ≈ 0.462
  ├── Some((5, 6)): 2382/4402 ≈ 0.541
    ├── Some((6, 0)): 196/381 ≈ 0.514
      ├── Some((0, 0)): 20/40 ≈ 0.500
      ├── Some((0, 1)): 13/31 ≈ 0.419
      ├── Some((0, 2)): 33/56 ≈ 0.589
      ├── Some((0, 3)): 17/36 ≈ 0.472
      ├── Some((0, 4)): 18/38 ≈ 0.474
      ├── Some((0, 5)): 35/58 ≈ 0.603
      ├── Some((0, 6)): 18/38 ≈ 0.474
      ├── Some((0, 7)): 28/50 ≈ 0.560
      └── Some((0, 8)): 14/33 ≈ 0.424
    ├── Some((6, 1)): 269/496 ≈ 0.542
      ├── Some((1, 0)): 14/35 ≈ 0.400
      ├── Some((1, 1)): 31/57 ≈ 0.544
      ├── Some((1, 2)): 18/40 ≈ 0.450
      ├── Some((1, 3)): 27/52 ≈ 0.519
      ├── Some((1, 4)): 52/82 ≈ 0.634
      ├── Some((1, 5)): 35/62 ≈ 0.565
      ├── Some((1, 6)): 43/71 ≈ 0.606
      ├── Some((1, 7)): 25/49 ≈ 0.510
      └── Some((1, 8)): 23/47 ≈ 0.489
    ├── Some((6, 2)): 260/482 ≈ 0.539
      ├── Some((2, 0)): 27/51 ≈ 0.529
      ├── Some((2, 1)): 40/67 ≈ 0.597
      ├── Some((2, 2)): 21/44 ≈ 0.477
      ├── Some((2, 3)): 34/60 ≈ 0.567
      ├── Some((2, 4)): 41/69 ≈ 0.594
      ├── Some((2, 5)): 15/36 ≈ 0.417
      ├── Some((2, 6)): 29/54 ≈ 0.537
      ├── Some((2, 7)): 32/58 ≈ 0.552
      └── Some((2, 8)): 20/42 ≈ 0.476
    ├── Some((6, 3)): 287/524 ≈ 0.548
      ├── Some((3, 0)): 26/51 ≈ 0.510
      ├── Some((3, 1)): 18/40 ≈ 0.450
      ├── Some((3, 2)): 51/82 ≈ 0.622
      ├── Some((3, 3)): 45/75 ≈ 0.600
      ├── Some((3, 4)): 21/44 ≈ 0.477
      ├── Some((3, 5)): 31/57 ≈ 0.544
      ├── Some((3, 6)): 31/57 ≈ 0.544
      ├── Some((3, 7)): 30/56 ≈ 0.536
      └── Some((3, 8)): 34/61 ≈ 0.557
    ├── Some((6, 4)): 254/473 ≈ 0.537
      ├── Some((4, 0)): 43/73 ≈ 0.589
      ├── Some((4, 1)): 18/41 ≈ 0.439
      ├── Some((4, 2)): 46/77 ≈ 0.597
      ├── Some((4, 3)): 30/57 ≈ 0.526
      ├── Some((4, 4)): 24/49 ≈ 0.490
      ├── Some((4, 6)): 32/60 ≈ 0.533
      ├── Some((4, 7)): 27/53 ≈ 0.509
      └── Some((4, 8)): 34/62 ≈ 0.548
    ├── Some((6, 5)): 191/373 ≈ 0.512
      ├── Some((5, 0)): 11/30 ≈ 0.367
      ├── Some((5, 1)): 21/43 ≈ 0.488
      ├── Some((5, 2)): 24/47 ≈ 0.511
      ├── Some((5, 3)): 15/35 ≈ 0.429
      ├── Some((5, 4)): 18/39 ≈ 0.462
      ├── Some((5, 5)): 49/78 ≈ 0.628
      ├── Some((5, 7)): 27/51 ≈ 0.529
      └── Some((5, 8)): 25/49 ≈ 0.510
    ├── Some((6, 6)): 344/613 ≈ 0.561
      ├── Some((6, 0)): 32/63 ≈ 0.508
      ├── Some((6, 1)): 31/61 ≈ 0.508
      ├── Some((6, 2)): 53/89 ≈ 0.596
      ├── Some((6, 3)): 25/53 ≈ 0.472
      ├── Some((6, 4)): 60/98 ≈ 0.612
      ├── Some((6, 5)): 46/81 ≈ 0.568
      ├── Some((6, 7)): 38/70 ≈ 0.543
      └── Some((6, 8)): 59/97 ≈ 0.608
    ├── Some((6, 7)): 280/514 ≈ 0.545
      ├── Some((7, 0)): 47/77 ≈ 0.610
      ├── Some((7, 1)): 22/46 ≈ 0.478
      ├── Some((7, 2)): 39/67 ≈ 0.582
      ├── Some((7, 3)): 46/75 ≈ 0.613
      ├── Some((7, 4)): 24/48 ≈ 0.500
      ├── Some((7, 5)): 24/48 ≈ 0.500
      ├── Some((7, 6)): 25/49 ≈ 0.510
      ├── Some((7, 7)): 24/48 ≈ 0.500
      └── Some((7, 8)): 29/55 ≈ 0.527
    └── Some((6, 8)): 300/545 ≈ 0.550
      ├── Some((8, 0)): 25/50 ≈ 0.500
      ├── Some((8, 1)): 30/57 ≈ 0.526
      ├── Some((8, 2)): 51/83 ≈ 0.614
      ├── Some((8, 3)): 12/33 ≈ 0.364
      ├── Some((8, 4)): 41/70 ≈ 0.586
      ├── Some((8, 5)): 57/90 ≈ 0.633
      ├── Some((8, 6)): 26/52 ≈ 0.500
      ├── Some((8, 7)): 20/44 ≈ 0.455
      └── Some((8, 8)): 37/65 ≈ 0.569
  ├── Some((5, 7)): 2099/3912 ≈ 0.537
    ├── Some((7, 0)): 143/292 ≈ 0.490
      ├── Some((0, 0)): 14/30 ≈ 0.467
      ├── Some((0, 1)): 10/25 ≈ 0.400
      ├── Some((0, 2)): 13/29 ≈ 0.448
      ├── Some((0, 3)): 16/33 ≈ 0.485
      ├── Some((0, 4)): 23/41 ≈ 0.561
      ├── Some((0, 5)): 17/34 ≈ 0.500
      ├── Some((0, 6)): 21/39 ≈ 0.538
      ├── Some((0, 7)): 14/30 ≈ 0.467
      └── Some((0, 8)): 14/30 ≈ 0.467
    ├── Some((7, 1)): 275/501 ≈ 0.549
      ├── Some((1, 0)): 22/45 ≈ 0.489
      ├── Some((1, 1)): 27/51 ≈ 0.529
      ├── Some((1, 2)): 27/52 ≈ 0.519
      ├── Some((1, 3)): 13/33 ≈ 0.394
      ├── Some((1, 4)): 39/66 ≈ 0.591
      ├── Some((1, 5)): 29/54 ≈ 0.537
      ├── Some((1, 6)): 41/69 ≈ 0.594
      ├── Some((1, 7)): 51/81 ≈ 0.630
      └── Some((1, 8)): 25/49 ≈ 0.510
    ├── Some((7, 2)): 154/310 ≈ 0.497
      ├── Some((2, 0)): 30/50 ≈ 0.600
      ├── Some((2, 1)): 14/30 ≈ 0.467
      ├── Some((2, 2)): 16/33 ≈ 0.485
      ├── Some((2, 3)): 15/32 ≈ 0.469
      ├── Some((2, 4)): 16/33 ≈ 0.485
      ├── Some((2, 5)): 11/27 ≈ 0.407
      ├── Some((2, 6)): 16/33 ≈ 0.485
      ├── Some((2, 7)): 19/37 ≈ 0.514
      └── Some((2, 8)): 17/34 ≈ 0.500
    ├── Some((7, 3)): 227/426 ≈ 0.533
      ├── Some((3, 0)): 37/62 ≈ 0.597
      ├── Some((3, 1)): 34/58 ≈ 0.586
      ├── Some((3, 2)): 20/41 ≈ 0.488
      ├── Some((3, 3)): 17/37 ≈ 0.459
      ├── Some((3, 4)): 12/30 ≈ 0.400
      ├── Some((3, 5)): 12/31 ≈ 0.387
      ├── Some((3, 6)): 46/73 ≈ 0.630
      ├── Some((3, 7)): 15/35 ≈ 0.429
      └── Some((3, 8)): 34/58 ≈ 0.586
    ├── Some((7, 4)): 302/543 ≈ 0.556
      ├── Some((4, 0)): 33/62 ≈ 0.532
      ├── Some((4, 1)): 34/63 ≈ 0.540
      ├── Some((4, 2)): 31/59 ≈ 0.525
      ├── Some((4, 3)): 58/93 ≈ 0.624
      ├── Some((4, 4)): 22/48 ≈ 0.458
      ├── Some((4, 6)): 45/77 ≈ 0.584
      ├── Some((4, 7)): 30/58 ≈ 0.517
      └── Some((4, 8)): 49/82 ≈ 0.598
    ├── Some((7, 5)): 336/595 ≈ 0.565
      ├── Some((5, 0)): 51/87 ≈ 0.586
      ├── Some((5, 1)): 24/51 ≈ 0.471
      ├── Some((5, 2)): 16/40 ≈ 0.400
      ├── Some((5, 3)): 69/109 ≈ 0.633
      ├── Some((5, 4)): 28/57 ≈ 0.491
      ├── Some((5, 5)): 36/67 ≈ 0.537
      ├── Some((5, 6)): 36/67 ≈ 0.537
      └── Some((5, 8)): 75/116 ≈ 0.647
    ├── Some((7, 6)): 186/361 ≈ 0.515
      ├── Some((6, 0)): 19/38 ≈ 0.500
      ├── Some((6, 1)): 14/32 ≈ 0.438
      ├── Some((6, 2)): 17/36 ≈ 0.472
      ├── Some((6, 3)): 20/39 ≈ 0.513
      ├── Some((6, 4)): 24/44 ≈ 0.545
      ├── Some((6, 5)): 21/41 ≈ 0.512
      ├── Some((6, 6)): 19/38 ≈ 0.500
      ├── Some((6, 7)): 28/49 ≈ 0.571
      └── Some((6, 8)): 23/43 ≈ 0.535
    ├── Some((7, 7)): 294/530 ≈ 0.555
      ├── Some((7, 0)): 34/63 ≈ 0.540
      ├── Some((7, 1)): 18/42 ≈ 0.429
      ├── Some((7, 2)): 42/73 ≈ 0.575
      ├── Some((7, 3)): 31/59 ≈ 0.525
      ├── Some((7, 4)): 57/92 ≈ 0.620
      ├── Some((7, 5)): 43/74 ≈ 0.581
      ├── Some((7, 6)): 31/59 ≈ 0.525
      └── Some((7, 8)): 37/67 ≈ 0.552
    └── Some((7, 8)): 181/353 ≈ 0.513
      ├── Some((8, 0)): 31/53 ≈ 0.585
      ├── Some((8, 1)): 23/43 ≈ 0.535
      ├── Some((8, 2)): 14/32 ≈ 0.438
      ├── Some((8, 3)): 26/47 ≈ 0.553
      ├── Some((8, 4)): 20/39 ≈ 0.513
      ├── Some((8, 5)): 10/26 ≈ 0.385
      ├── Some((8, 6)): 13/30 ≈ 0.433
      ├── Some((8, 7)): 32/54 ≈ 0.593
      └── Some((8, 8)): 11/28 ≈ 0.393
  └── Some((5, 8)): 2722/4989 ≈ 0.546
    ├── Some((8, 0)): 168/341 ≈ 0.493
      ├── Some((0, 0)): 16/35 ≈ 0.457
      ├── Some((0, 1)): 18/37 ≈ 0.486
      ├── Some((0, 2)): 21/41 ≈ 0.512
      ├── Some((0, 3)): 23/43 ≈ 0.535
      ├── Some((0, 4)): 16/35 ≈ 0.457
      ├── Some((0, 5)): 9/25 ≈ 0.360
      ├── Some((0, 6)): 31/53 ≈ 0.585
      ├── Some((0, 7)): 22/42 ≈ 0.524
      └── Some((0, 8)): 12/29 ≈ 0.414
    ├── Some((8, 1)): 370/661 ≈ 0.560
      ├── Some((1, 0)): 26/54 ≈ 0.481
      ├── Some((1, 1)): 14/38 ≈ 0.368
      ├── Some((1, 2)): 32/62 ≈ 0.516
      ├── Some((1, 3)): 50/86 ≈ 0.581
      ├── Some((1, 4)): 71/111 ≈ 0.640
      ├── Some((1, 5)): 25/53 ≈ 0.472
      ├── Some((1, 6)): 35/66 ≈ 0.530
      ├── Some((1, 7)): 58/95 ≈ 0.611
      └── Some((1, 8)): 58/95 ≈ 0.611
    ├── Some((8, 2)): 416/731 ≈ 0.569
      ├── Some((2, 0)): 74/116 ≈ 0.638
      ├── Some((2, 1)): 57/95 ≈ 0.600
      ├── Some((2, 2)): 44/79 ≈ 0.557
      ├── Some((2, 3)): 34/66 ≈ 0.515
      ├── Some((2, 4)): 26/55 ≈ 0.473
      ├── Some((2, 5)): 43/77 ≈ 0.558
      ├── Some((2, 6)): 37/69 ≈ 0.536
      ├── Some((2, 7)): 54/91 ≈ 0.593
      └── Some((2, 8)): 47/82 ≈ 0.573
    ├── Some((8, 3)): 285/528 ≈ 0.540
      ├── Some((3, 0)): 45/76 ≈ 0.592
      ├── Some((3, 1)): 28/54 ≈ 0.519
      ├── Some((3, 2)): 16/38 ≈ 0.421
      ├── Some((3, 3)): 25/50 ≈ 0.500
      ├── Some((3, 4)): 29/56 ≈ 0.518
      ├── Some((3, 5)): 32/59 ≈ 0.542
      ├── Some((3, 6)): 31/58 ≈ 0.534
      ├── Some((3, 7)): 38/67 ≈ 0.567
      └── Some((3, 8)): 40/69 ≈ 0.580
    ├── Some((8, 4)): 288/533 ≈ 0.540
      ├── Some((4, 0)): 27/55 ≈ 0.491
      ├── Some((4, 1)): 40/72 ≈ 0.556
      ├── Some((4, 2)): 33/63 ≈ 0.524
      ├── Some((4, 3)): 65/103 ≈ 0.631
      ├── Some((4, 4)): 25/52 ≈ 0.481
      ├── Some((4, 6)): 49/84 ≈ 0.583
      ├── Some((4, 7)): 30/59 ≈ 0.508
      └── Some((4, 8)): 19/44 ≈ 0.432
    ├── Some((8, 5)): 303/556 ≈ 0.545
      ├── Some((5, 0)): 61/99 ≈ 0.616
      ├── Some((5, 1)): 45/79 ≈ 0.570
      ├── Some((5, 2)): 51/87 ≈ 0.586
      ├── Some((5, 3)): 21/47 ≈ 0.447
      ├── Some((5, 4)): 28/57 ≈ 0.491
      ├── Some((5, 5)): 17/42 ≈ 0.405
      ├── Some((5, 6)): 35/66 ≈ 0.530
      └── Some((5, 7)): 44/78 ≈ 0.564
    ├── Some((8, 6)): 211/410 ≈ 0.515
      ├── Some((6, 0)): 34/59 ≈ 0.576
      ├── Some((6, 1)): 22/44 ≈ 0.500
      ├── Some((6, 2)): 28/52 ≈ 0.538
      ├── Some((6, 3)): 13/32 ≈ 0.406
      ├── Some((6, 4)): 9/27 ≈ 0.333
      ├── Some((6, 5)): 12/31 ≈ 0.387
      ├── Some((6, 6)): 16/36 ≈ 0.444
      ├── Some((6, 7)): 32/57 ≈ 0.561
      └── Some((6, 8)): 44/71 ≈ 0.620
    ├── Some((8, 7)): 399/705 ≈ 0.566
      ├── Some((7, 0)): 42/76 ≈ 0.553
      ├── Some((7, 1)): 34/65 ≈ 0.523
      ├── Some((7, 2)): 50/86 ≈ 0.581
      ├── Some((7, 3)): 33/64 ≈ 0.516
      ├── Some((7, 4)): 34/65 ≈ 0.523
      ├── Some((7, 5)): 31/61 ≈ 0.508
      ├── Some((7, 6)): 71/112 ≈ 0.634
      ├── Some((7, 7)): 40/73 ≈ 0.548
      └── Some((7, 8)): 63/102 ≈ 0.618
    └── Some((8, 8)): 282/523 ≈ 0.539
      ├── Some((8, 0)): 37/68 ≈ 0.544
      ├── Some((8, 1)): 18/43 ≈ 0.419
      ├── Some((8, 2)): 42/74 ≈ 0.568
      ├── Some((8, 3)): 20/45 ≈ 0.444
      ├── Some((8, 4)): 34/64 ≈ 0.531
      ├── Some((8, 5)): 57/93 ≈ 0.613
      ├── Some((8, 6)): 29/57 ≈ 0.509
      └── Some((8, 7)): 45/78 ≈ 0.577
├── Some((4, 6)): 38364/69798 ≈ 0.550
  ├── Some((6, 0)): 4359/7923 ≈ 0.550
    ├── Some((0, 0)): 569/1016 ≈ 0.560
      ├── Some((0, 1)): 39/82 ≈ 0.476
      ├── Some((0, 2)): 79/138 ≈ 0.572
      ├── Some((0, 3)): 103/170 ≈ 0.606
      ├── Some((0, 4)): 56/106 ≈ 0.528
      ├── Some((0, 5)): 78/136 ≈ 0.574
      ├── Some((0, 6)): 67/122 ≈ 0.549
      ├── Some((0, 7)): 73/130 ≈ 0.562
      └── Some((0, 8)): 74/131 ≈ 0.565
    ├── Some((0, 1)): 497/902 ≈ 0.551
      ├── Some((1, 0)): 49/92 ≈ 0.533
      ├── Some((1, 1)): 66/115 ≈ 0.574
      ├── Some((1, 2)): 94/152 ≈ 0.618
      ├── Some((1, 3)): 22/54 ≈ 0.407
      ├── Some((1, 4)): 62/110 ≈ 0.564
      ├── Some((1, 5)): 75/127 ≈ 0.591
      ├── Some((1, 6)): 40/80 ≈ 0.500
      ├── Some((1, 7)): 31/68 ≈ 0.456
      └── Some((1, 8)): 57/103 ≈ 0.553
    ├── Some((0, 2)): 611/1083 ≈ 0.564
      ├── Some((2, 0)): 35/75 ≈ 0.467
      ├── Some((2, 1)): 75/130 ≈ 0.577
      ├── Some((2, 2)): 94/155 ≈ 0.606
      ├── Some((2, 3)): 47/92 ≈ 0.511
      ├── Some((2, 4)): 73/127 ≈ 0.575
      ├── Some((2, 5)): 73/128 ≈ 0.570
      ├── Some((2, 6)): 87/146 ≈ 0.596
      ├── Some((2, 7)): 57/106 ≈ 0.538
      └── Some((2, 8)): 70/123 ≈ 0.569
    ├── Some((0, 3)): 388/726 ≈ 0.534
      ├── Some((3, 0)): 61/105 ≈ 0.581
      ├── Some((3, 1)): 61/105 ≈ 0.581
      ├── Some((3, 2)): 29/62 ≈ 0.468
      ├── Some((3, 3)): 53/94 ≈ 0.564
      ├── Some((3, 4)): 71/117 ≈ 0.607
      ├── Some((3, 5)): 45/84 ≈ 0.536
      ├── Some((3, 6)): 24/55 ≈ 0.436
      ├── Some((3, 7)): 23/54 ≈ 0.426
      └── Some((3, 8)): 20/49 ≈ 0.408
    ├── Some((0, 4)): 517/933 ≈ 0.554
      ├── Some((4, 0)): 35/76 ≈ 0.461
      ├── Some((4, 1)): 113/182 ≈ 0.621
      ├── Some((4, 2)): 58/108 ≈ 0.537
      ├── Some((4, 3)): 41/85 ≈ 0.482
      ├── Some((4, 4)): 40/83 ≈ 0.482
      ├── Some((4, 5)): 96/159 ≈ 0.604
      ├── Some((4, 7)): 86/146 ≈ 0.589
      └── Some((4, 8)): 47/93 ≈ 0.505
    ├── Some((0, 5)): 308/596 ≈ 0.517
      ├── Some((5, 0)): 37/70 ≈ 0.529
      ├── Some((5, 1)): 24/53 ≈ 0.453
      ├── Some((5, 2)): 47/83 ≈ 0.566
      ├── Some((5, 3)): 28/58 ≈ 0.483
      ├── Some((5, 4)): 13/37 ≈ 0.351
      ├── Some((5, 5)): 34/66 ≈ 0.515
      ├── Some((5, 6)): 34/66 ≈ 0.515
      ├── Some((5, 7)): 48/84 ≈ 0.571
      └── Some((5, 8)): 43/78 ≈ 0.551
    ├── Some((0, 6)): 427/789 ≈ 0.541
      ├── Some((6, 1)): 32/69 ≈ 0.464
      ├── Some((6, 2)): 52/97 ≈ 0.536
      ├── Some((6, 3)): 64/113 ≈ 0.566
      ├── Some((6, 4)): 62/111 ≈ 0.559
      ├── Some((6, 5)): 46/89 ≈ 0.517
      ├── Some((6, 6)): 44/86 ≈ 0.512
      ├── Some((6, 7)): 97/157 ≈ 0.618
      └── Some((6, 8)): 30/66 ≈ 0.455
    ├── Some((0, 7)): 439/809 ≈ 0.543
      ├── Some((7, 0)): 76/126 ≈ 0.603
      ├── Some((7, 1)): 22/53 ≈ 0.415
      ├── Some((7, 2)): 44/84 ≈ 0.524
      ├── Some((7, 3)): 86/139 ≈ 0.619
      ├── Some((7, 4)): 36/73 ≈ 0.493
      ├── Some((7, 5)): 42/81 ≈ 0.519
      ├── Some((7, 6)): 39/77 ≈ 0.506
      ├── Some((7, 7)): 45/85 ≈ 0.529
      └── Some((7, 8)): 48/90 ≈ 0.533
    └── Some((0, 8)): 602/1068 ≈ 0.564
      ├── Some((8, 0)): 38/79 ≈ 0.481
      ├── Some((8, 1)): 71/125 ≈ 0.568
      ├── Some((8, 2)): 53/100 ≈ 0.530
      ├── Some((8, 3)): 70/123 ≈ 0.569
      ├── Some((8, 4)): 86/145 ≈ 0.593
      ├── Some((8, 5)): 38/79 ≈ 0.481
      ├── Some((8, 6)): 82/139 ≈ 0.590
      ├── Some((8, 7)): 98/160 ≈ 0.613
      └── Some((8, 8)): 65/117 ≈ 0.556
  ├── Some((6, 1)): 4140/7544 ≈ 0.549
    ├── Some((1, 0)): 274/539 ≈ 0.508
      ├── Some((0, 0)): 41/74 ≈ 0.554
      ├── Some((0, 1)): 29/58 ≈ 0.500
      ├── Some((0, 2)): 27/56 ≈ 0.482
      ├── Some((0, 3)): 38/70 ≈ 0.543
      ├── Some((0, 4)): 42/75 ≈ 0.560
      ├── Some((0, 5)): 18/43 ≈ 0.419
      ├── Some((0, 6)): 21/48 ≈ 0.438
      ├── Some((0, 7)): 41/74 ≈ 0.554
      └── Some((0, 8)): 16/40 ≈ 0.400
    ├── Some((1, 1)): 724/1258 ≈ 0.576
      ├── Some((1, 0)): 103/175 ≈ 0.589
      ├── Some((1, 2)): 86/151 ≈ 0.570
      ├── Some((1, 3)): 83/147 ≈ 0.565
      ├── Some((1, 4)): 90/157 ≈ 0.573
      ├── Some((1, 5)): 97/166 ≈ 0.584
      ├── Some((1, 6)): 86/151 ≈ 0.570
      ├── Some((1, 7)): 53/106 ≈ 0.500
      └── Some((1, 8)): 125/204 ≈ 0.613
    ├── Some((1, 2)): 498/902 ≈ 0.552
      ├── Some((2, 0)): 106/167 ≈ 0.635
      ├── Some((2, 1)): 46/88 ≈ 0.523
      ├── Some((2, 2)): 73/124 ≈ 0.589
      ├── Some((2, 3)): 38/77 ≈ 0.494
      ├── Some((2, 4)): 49/92 ≈ 0.533
      ├── Some((2, 5)): 41/81 ≈ 0.506
      ├── Some((2, 6)): 51/95 ≈ 0.537
      ├── Some((2, 7)): 65/114 ≈ 0.570
      └── Some((2, 8)): 28/63 ≈ 0.444
    ├── Some((1, 3)): 653/1147 ≈ 0.569
      ├── Some((3, 0)): 130/203 ≈ 0.640
      ├── Some((3, 1)): 63/115 ≈ 0.548
      ├── Some((3, 2)): 34/75 ≈ 0.453
      ├── Some((3, 3)): 46/92 ≈ 0.500
      ├── Some((3, 4)): 44/89 ≈ 0.494
      ├── Some((3, 5)): 71/126 ≈ 0.563
      ├── Some((3, 6)): 99/163 ≈ 0.607
      ├── Some((3, 7)): 118/188 ≈ 0.628
      └── Some((3, 8)): 48/95 ≈ 0.505
    ├── Some((1, 4)): 266/526 ≈ 0.506
      ├── Some((4, 0)): 52/91 ≈ 0.571
      ├── Some((4, 1)): 29/60 ≈ 0.483
      ├── Some((4, 2)): 33/66 ≈ 0.500
      ├── Some((4, 3)): 32/65 ≈ 0.492
      ├── Some((4, 4)): 28/59 ≈ 0.475
      ├── Some((4, 5)): 15/40 ≈ 0.375
      ├── Some((4, 7)): 26/56 ≈ 0.464
      └── Some((4, 8)): 50/88 ≈ 0.568
    ├── Some((1, 5)): 322/618 ≈ 0.521
      ├── Some((5, 0)): 55/94 ≈ 0.585
      ├── Some((5, 1)): 42/77 ≈ 0.545
      ├── Some((5, 2)): 26/56 ≈ 0.464
      ├── Some((5, 3)): 22/50 ≈ 0.440
      ├── Some((5, 4)): 44/79 ≈ 0.557
      ├── Some((5, 5)): 29/60 ≈ 0.483
      ├── Some((5, 6)): 42/77 ≈ 0.545
      ├── Some((5, 7)): 28/58 ≈ 0.483
      └── Some((5, 8)): 34/66 ≈ 0.515
    ├── Some((1, 6)): 315/606 ≈ 0.520
      ├── Some((6, 0)): 23/53 ≈ 0.434
      ├── Some((6, 2)): 50/90 ≈ 0.556
      ├── Some((6, 3)): 40/77 ≈ 0.519
      ├── Some((6, 4)): 29/62 ≈ 0.468
      ├── Some((6, 5)): 52/93 ≈ 0.559
      ├── Some((6, 6)): 49/89 ≈ 0.551
      ├── Some((6, 7)): 26/58 ≈ 0.448
      └── Some((6, 8)): 45/83 ≈ 0.542
    ├── Some((1, 7)): 632/1114 ≈ 0.567
      ├── Some((7, 0)): 56/105 ≈ 0.533
      ├── Some((7, 1)): 90/150 ≈ 0.600
      ├── Some((7, 2)): 84/142 ≈ 0.592
      ├── Some((7, 3)): 89/149 ≈ 0.597
      ├── Some((7, 4)): 74/129 ≈ 0.574
      ├── Some((7, 5)): 57/106 ≈ 0.538
      ├── Some((7, 6)): 74/129 ≈ 0.574
      ├── Some((7, 7)): 42/86 ≈ 0.488
      └── Some((7, 8)): 65/117 ≈ 0.556
    └── Some((1, 8)): 455/833 ≈ 0.546
      ├── Some((8, 0)): 36/73 ≈ 0.493
      ├── Some((8, 1)): 55/99 ≈ 0.556
      ├── Some((8, 2)): 58/103 ≈ 0.563
      ├── Some((8, 3)): 86/139 ≈ 0.619
      ├── Some((8, 4)): 71/120 ≈ 0.592
      ├── Some((8, 5)): 41/80 ≈ 0.512
      ├── Some((8, 6)): 36/73 ≈ 0.493
      ├── Some((8, 7)): 42/82 ≈ 0.512
      └── Some((8, 8)): 29/63 ≈ 0.460
  ├── Some((6, 2)): 4836/8747 ≈ 0.553
    ├── Some((2, 0)): 542/980 ≈ 0.553
      ├── Some((0, 0)): 58/106 ≈ 0.547
      ├── Some((0, 1)): 89/148 ≈ 0.601
      ├── Some((0, 2)): 36/76 ≈ 0.474
      ├── Some((0, 3)): 69/121 ≈ 0.570
      ├── Some((0, 4)): 78/133 ≈ 0.586
      ├── Some((0, 5)): 22/56 ≈ 0.393
      ├── Some((0, 6)): 60/109 ≈ 0.550
      ├── Some((0, 7)): 48/93 ≈ 0.516
      └── Some((0, 8)): 81/137 ≈ 0.591
    ├── Some((2, 1)): 459/847 ≈ 0.542
      ├── Some((1, 0)): 31/67 ≈ 0.463
      ├── Some((1, 1)): 50/93 ≈ 0.538
      ├── Some((1, 2)): 40/80 ≈ 0.500
      ├── Some((1, 3)): 68/117 ≈ 0.581
      ├── Some((1, 4)): 62/109 ≈ 0.569
      ├── Some((1, 5)): 60/106 ≈ 0.566
      ├── Some((1, 6)): 45/86 ≈ 0.523
      ├── Some((1, 7)): 39/78 ≈ 0.500
      └── Some((1, 8)): 63/110 ≈ 0.573
    ├── Some((2, 2)): 635/1128 ≈ 0.563
      ├── Some((2, 0)): 50/100 ≈ 0.500
      ├── Some((2, 1)): 91/157 ≈ 0.580
      ├── Some((2, 3)): 111/184 ≈ 0.603
      ├── Some((2, 4)): 69/127 ≈ 0.543
      ├── Some((2, 5)): 99/168 ≈ 0.589
      ├── Some((2, 6)): 47/96 ≈ 0.490
      ├── Some((2, 7)): 79/141 ≈ 0.560
      └── Some((2, 8)): 89/154 ≈ 0.578
    ├── Some((2, 3)): 389/733 ≈ 0.531
      ├── Some((3, 0)): 56/99 ≈ 0.566
      ├── Some((3, 1)): 24/55 ≈ 0.436
      ├── Some((3, 2)): 29/62 ≈ 0.468
      ├── Some((3, 3)): 44/83 ≈ 0.530
      ├── Some((3, 4)): 37/73 ≈ 0.507
      ├── Some((3, 5)): 49/90 ≈ 0.544
      ├── Some((3, 6)): 30/64 ≈ 0.469
      ├── Some((3, 7)): 44/83 ≈ 0.530
      └── Some((3, 8)): 75/123 ≈ 0.610
    ├── Some((2, 4)): 385/727 ≈ 0.530
      ├── Some((4, 0)): 28/63 ≈ 0.444
      ├── Some((4, 1)): 45/87 ≈ 0.517
      ├── Some((4, 2)): 24/57 ≈ 0.421
      ├── Some((4, 3)): 78/131 ≈ 0.595
      ├── Some((4, 4)): 52/96 ≈ 0.542
      ├── Some((4, 5)): 49/92 ≈ 0.533
      ├── Some((4, 7)): 52/97 ≈ 0.536
      └── Some((4, 8)): 57/103 ≈ 0.553
    ├── Some((2, 5)): 548/990 ≈ 0.554
      ├── Some((5, 0)): 41/83 ≈ 0.494
      ├── Some((5, 1)): 90/149 ≈ 0.604
      ├── Some((5, 2)): 43/86 ≈ 0.500
      ├── Some((5, 3)): 71/124 ≈ 0.573
      ├── Some((5, 4)): 25/60 ≈ 0.417
      ├── Some((5, 5)): 94/155 ≈ 0.606
      ├── Some((5, 6)): 70/123 ≈ 0.569
      ├── Some((5, 7)): 49/94 ≈ 0.521
      └── Some((5, 8)): 64/115 ≈ 0.557
    ├── Some((2, 6)): 711/1248 ≈ 0.570
      ├── Some((6, 0)): 47/98 ≈ 0.480
      ├── Some((6, 1)): 217/327 ≈ 0.664
      ├── Some((6, 3)): 94/164 ≈ 0.573
      ├── Some((6, 4)): 59/115 ≈ 0.513
      ├── Some((6, 5)): 85/152 ≈ 0.559
      ├── Some((6, 6)): 61/118 ≈ 0.517
      ├── Some((6, 7)): 63/121 ≈ 0.521
      └── Some((6, 8)): 85/152 ≈ 0.559
    ├── Some((2, 7)): 595/1065 ≈ 0.559
      ├── Some((7, 0)): 87/146 ≈ 0.596
      ├── Some((7, 1)): 56/105 ≈ 0.533
      ├── Some((7, 2)): 72/127 ≈ 0.567
      ├── Some((7, 3)): 70/124 ≈ 0.565
      ├── Some((7, 4)): 49/95 ≈ 0.516
      ├── Some((7, 5)): 52/99 ≈ 0.525
      ├── Some((7, 6)): 57/106 ≈ 0.538
      ├── Some((7, 7)): 65/117 ≈ 0.556
      └── Some((7, 8)): 86/145 ≈ 0.593
    └── Some((2, 8)): 572/1028 ≈ 0.556
      ├── Some((8, 0)): 62/112 ≈ 0.554
      ├── Some((8, 1)): 50/96 ≈ 0.521
      ├── Some((8, 2)): 77/132 ≈ 0.583
      ├── Some((8, 3)): 53/100 ≈ 0.530
      ├── Some((8, 4)): 58/107 ≈ 0.542
      ├── Some((8, 5)): 92/152 ≈ 0.605
      ├── Some((8, 6)): 40/82 ≈ 0.488
      ├── Some((8, 7)): 74/128 ≈ 0.578
      └── Some((8, 8)): 66/118 ≈ 0.559
  ├── Some((6, 3)): 3562/6542 ≈ 0.544
    ├── Some((3, 0)): 453/819 ≈ 0.553
      ├── Some((0, 0)): 32/67 ≈ 0.478
      ├── Some((0, 1)): 48/88 ≈ 0.545
      ├── Some((0, 2)): 29/63 ≈ 0.460
      ├── Some((0, 3)): 67/113 ≈ 0.593
      ├── Some((0, 4)): 93/146 ≈ 0.637
      ├── Some((0, 5)): 79/129 ≈ 0.612
      ├── Some((0, 6)): 40/78 ≈ 0.513
      ├── Some((0, 7)): 16/44 ≈ 0.364
      └── Some((0, 8)): 49/90 ≈ 0.544
    ├── Some((3, 1)): 208/423 ≈ 0.492
      ├── Some((1, 0)): 26/51 ≈ 0.510
      ├── Some((1, 1)): 23/47 ≈ 0.489
      ├── Some((1, 2)): 30/56 ≈ 0.536
      ├── Some((1, 3)): 20/43 ≈ 0.465
      ├── Some((1, 4)): 23/47 ≈ 0.489
      ├── Some((1, 5)): 18/40 ≈ 0.450
      ├── Some((1, 6)): 25/50 ≈ 0.500
      ├── Some((1, 7)): 15/36 ≈ 0.417
      └── Some((1, 8)): 27/52 ≈ 0.519
    ├── Some((3, 2)): 386/712 ≈ 0.542
      ├── Some((2, 0)): 46/84 ≈ 0.548
      ├── Some((2, 1)): 28/59 ≈ 0.475
      ├── Some((2, 2)): 45/82 ≈ 0.549
      ├── Some((2, 3)): 67/111 ≈ 0.604
      ├── Some((2, 4)): 38/73 ≈ 0.521
      ├── Some((2, 5)): 18/45 ≈ 0.400
      ├── Some((2, 6)): 50/89 ≈ 0.562
      ├── Some((2, 7)): 39/74 ≈ 0.527
      └── Some((2, 8)): 54/94 ≈ 0.574
    ├── Some((3, 3)): 446/808 ≈ 0.552
      ├── Some((3, 0)): 56/102 ≈ 0.549
      ├── Some((3, 1)): 31/68 ≈ 0.456
      ├── Some((3, 2)): 66/115 ≈ 0.574
      ├── Some((3, 4)): 40/80 ≈ 0.500
      ├── Some((3, 5)): 46/88 ≈ 0.523
      ├── Some((3, 6)): 45/87 ≈ 0.517
      ├── Some((3, 7)): 45/87 ≈ 0.517
      └── Some((3, 8)): 116/180 ≈ 0.644
    ├── Some((3, 4)): 357/666 ≈ 0.536
      ├── Some((4, 0)): 46/86 ≈ 0.535
      ├── Some((4, 1)): 54/96 ≈ 0.562
      ├── Some((4, 2)): 39/76 ≈ 0.513
      ├── Some((4, 3)): 24/55 ≈ 0.436
      ├── Some((4, 4)): 66/112 ≈ 0.589
      ├── Some((4, 5)): 55/97 ≈ 0.567
      ├── Some((4, 7)): 49/89 ≈ 0.551
      └── Some((4, 8)): 23/54 ≈ 0.426
    ├── Some((3, 5)): 448/811 ≈ 0.552
      ├── Some((5, 0)): 36/72 ≈ 0.500
      ├── Some((5, 1)): 75/123 ≈ 0.610
      ├── Some((5, 2)): 35/70 ≈ 0.500
      ├── Some((5, 3)): 56/98 ≈ 0.571
      ├── Some((5, 4)): 49/89 ≈ 0.551
      ├── Some((5, 5)): 45/84 ≈ 0.536
      ├── Some((5, 6)): 48/88 ≈ 0.545
      ├── Some((5, 7)): 53/95 ≈ 0.558
      └── Some((5, 8)): 50/91 ≈ 0.549
    ├── Some((3, 6)): 466/839 ≈ 0.555
      ├── Some((6, 0)): 22/55 ≈ 0.400
      ├── Some((6, 1)): 97/157 ≈ 0.618
      ├── Some((6, 2)): 75/128 ≈ 0.586
      ├── Some((6, 4)): 12/39 ≈ 0.308
      ├── Some((6, 5)): 61/110 ≈ 0.555
      ├── Some((6, 6)): 72/124 ≈ 0.581
      ├── Some((6, 7)): 55/101 ≈ 0.545
      └── Some((6, 8)): 72/124 ≈ 0.581
    ├── Some((3, 7)): 358/667 ≈ 0.537
      ├── Some((7, 0)): 32/64 ≈ 0.500
      ├── Some((7, 1)): 42/77 ≈ 0.545
      ├── Some((7, 2)): 28/59 ≈ 0.475
      ├── Some((7, 3)): 59/99 ≈ 0.596
      ├── Some((7, 4)): 31/63 ≈ 0.492
      ├── Some((7, 5)): 16/42 ≈ 0.381
      ├── Some((7, 6)): 39/74 ≈ 0.527
      ├── Some((7, 7)): 63/104 ≈ 0.606
      └── Some((7, 8)): 47/84 ≈ 0.560
    └── Some((3, 8)): 439/796 ≈ 0.552
      ├── Some((8, 0)): 15/42 ≈ 0.357
      ├── Some((8, 1)): 37/73 ≈ 0.507
      ├── Some((8, 2)): 53/94 ≈ 0.564
      ├── Some((8, 3)): 76/124 ≈ 0.613
      ├── Some((8, 4)): 39/76 ≈ 0.513
      ├── Some((8, 5)): 55/97 ≈ 0.567
      ├── Some((8, 6)): 69/115 ≈ 0.600
      ├── Some((8, 7)): 58/101 ≈ 0.574
      └── Some((8, 8)): 37/73 ≈ 0.507
  ├── Some((6, 4)): 4058/7402 ≈ 0.548
    ├── Some((4, 0)): 431/803 ≈ 0.537
      ├── Some((0, 0)): 39/77 ≈ 0.506
      ├── Some((0, 1)): 32/68 ≈ 0.471
      ├── Some((0, 2)): 51/94 ≈ 0.543
      ├── Some((0, 3)): 79/130 ≈ 0.608
      ├── Some((0, 4)): 39/77 ≈ 0.506
      ├── Some((0, 5)): 30/65 ≈ 0.462
      ├── Some((0, 6)): 48/90 ≈ 0.533
      ├── Some((0, 7)): 41/80 ≈ 0.512
      └── Some((0, 8)): 72/121 ≈ 0.595
    ├── Some((4, 1)): 338/651 ≈ 0.519
      ├── Some((1, 0)): 48/86 ≈ 0.558
      ├── Some((1, 1)): 45/83 ≈ 0.542
      ├── Some((1, 2)): 59/101 ≈ 0.584
      ├── Some((1, 3)): 40/76 ≈ 0.526
      ├── Some((1, 4)): 38/73 ≈ 0.521
      ├── Some((1, 5)): 23/53 ≈ 0.434
      ├── Some((1, 6)): 22/51 ≈ 0.431
      ├── Some((1, 7)): 33/66 ≈ 0.500
      └── Some((1, 8)): 29/61 ≈ 0.475
    ├── Some((4, 2)): 673/1191 ≈ 0.565
      ├── Some((2, 0)): 86/148 ≈ 0.581
      ├── Some((2, 1)): 66/121 ≈ 0.545
      ├── Some((2, 2)): 52/101 ≈ 0.515
      ├── Some((2, 3)): 82/142 ≈ 0.577
      ├── Some((2, 4)): 52/101 ≈ 0.515
      ├── Some((2, 5)): 53/103 ≈ 0.515
      ├── Some((2, 6)): 86/148 ≈ 0.581
      ├── Some((2, 7)): 102/169 ≈ 0.604
      └── Some((2, 8)): 93/157 ≈ 0.592
    ├── Some((4, 3)): 557/1006 ≈ 0.554
      ├── Some((3, 0)): 70/123 ≈ 0.569
      ├── Some((3, 1)): 66/118 ≈ 0.559
      ├── Some((3, 2)): 95/156 ≈ 0.609
      ├── Some((3, 3)): 66/118 ≈ 0.559
      ├── Some((3, 4)): 81/137 ≈ 0.591
      ├── Some((3, 5)): 44/87 ≈ 0.506
      ├── Some((3, 6)): 45/89 ≈ 0.506
      ├── Some((3, 7)): 46/90 ≈ 0.511
      └── Some((3, 8)): 44/87 ≈ 0.506
    ├── Some((4, 4)): 691/1220 ≈ 0.566
      ├── Some((4, 0)): 97/172 ≈ 0.564
      ├── Some((4, 1)): 69/133 ≈ 0.519
      ├── Some((4, 2)): 67/130 ≈ 0.515
      ├── Some((4, 3)): 113/195 ≈ 0.579
      ├── Some((4, 5)): 87/158 ≈ 0.551
      ├── Some((4, 7)): 111/192 ≈ 0.578
      └── Some((4, 8)): 146/239 ≈ 0.611
    ├── Some((4, 5)): 360/687 ≈ 0.524
      ├── Some((5, 0)): 28/60 ≈ 0.467
      ├── Some((5, 1)): 52/92 ≈ 0.565
      ├── Some((5, 2)): 34/68 ≈ 0.500
      ├── Some((5, 3)): 44/82 ≈ 0.537
      ├── Some((5, 4)): 41/78 ≈ 0.526
      ├── Some((5, 5)): 46/85 ≈ 0.541
      ├── Some((5, 6)): 35/70 ≈ 0.500
      ├── Some((5, 7)): 42/79 ≈ 0.532
      └── Some((5, 8)): 37/72 ≈ 0.514
    ├── Some((4, 7)): 477/878 ≈ 0.543
      ├── Some((7, 0)): 35/73 ≈ 0.479
      ├── Some((7, 1)): 74/126 ≈ 0.587
      ├── Some((7, 2)): 81/135 ≈ 0.600
      ├── Some((7, 3)): 86/142 ≈ 0.606
      ├── Some((7, 4)): 37/76 ≈ 0.487
      ├── Some((7, 5)): 33/70 ≈ 0.471
      ├── Some((7, 6)): 36/75 ≈ 0.480
      ├── Some((7, 7)): 57/103 ≈ 0.553
      └── Some((7, 8)): 38/77 ≈ 0.494
    └── Some((4, 8)): 531/965 ≈ 0.550
      ├── Some((8, 0)): 74/127 ≈ 0.583
      ├── Some((8, 1)): 46/90 ≈ 0.511
      ├── Some((8, 2)): 40/81 ≈ 0.494
      ├── Some((8, 3)): 56/103 ≈ 0.544
      ├── Some((8, 4)): 59/107 ≈ 0.551
      ├── Some((8, 5)): 53/99 ≈ 0.535
      ├── Some((8, 6)): 54/101 ≈ 0.535
      ├── Some((8, 7)): 70/122 ≈ 0.574
      └── Some((8, 8)): 79/134 ≈ 0.590
  ├── Some((6, 5)): 5533/9948 ≈ 0.556
    ├── Some((5, 0)): 665/1186 ≈ 0.561
      ├── Some((0, 0)): 86/148 ≈ 0.581
      ├── Some((0, 1)): 62/116 ≈ 0.534
      ├── Some((0, 2)): 131/208 ≈ 0.630
      ├── Some((0, 3)): 67/123 ≈ 0.545
      ├── Some((0, 4)): 51/100 ≈ 0.510
      ├── Some((0, 5)): 58/110 ≈ 0.527
      ├── Some((0, 6)): 56/108 ≈ 0.519
      ├── Some((0, 7)): 81/142 ≈ 0.570
      └── Some((0, 8)): 72/130 ≈ 0.554
    ├── Some((5, 1)): 481/891 ≈ 0.540
      ├── Some((1, 0)): 38/78 ≈ 0.487
      ├── Some((1, 1)): 72/124 ≈ 0.581
      ├── Some((1, 2)): 44/87 ≈ 0.506
      ├── Some((1, 3)): 92/150 ≈ 0.613
      ├── Some((1, 4)): 49/93 ≈ 0.527
      ├── Some((1, 5)): 50/95 ≈ 0.526
      ├── Some((1, 6)): 63/112 ≈ 0.562
      ├── Some((1, 7)): 44/87 ≈ 0.506
      └── Some((1, 8)): 28/64 ≈ 0.438
    ├── Some((5, 2)): 628/1127 ≈ 0.557
      ├── Some((2, 0)): 106/174 ≈ 0.609
      ├── Some((2, 1)): 81/141 ≈ 0.574
      ├── Some((2, 2)): 40/84 ≈ 0.476
      ├── Some((2, 3)): 97/162 ≈ 0.599
      ├── Some((2, 4)): 50/99 ≈ 0.505
      ├── Some((2, 5)): 57/108 ≈ 0.528
      ├── Some((2, 6)): 91/155 ≈ 0.587
      ├── Some((2, 7)): 65/119 ≈ 0.546
      └── Some((2, 8)): 40/84 ≈ 0.476
    ├── Some((5, 3)): 819/1431 ≈ 0.572
      ├── Some((3, 0)): 77/140 ≈ 0.550
      ├── Some((3, 1)): 62/119 ≈ 0.521
      ├── Some((3, 2)): 102/174 ≈ 0.586
      ├── Some((3, 3)): 129/211 ≈ 0.611
      ├── Some((3, 4)): 68/128 ≈ 0.531
      ├── Some((3, 5)): 98/169 ≈ 0.580
      ├── Some((3, 6)): 67/126 ≈ 0.532
      ├── Some((3, 7)): 99/170 ≈ 0.582
      └── Some((3, 8)): 116/193 ≈ 0.601
    ├── Some((5, 4)): 531/972 ≈ 0.546
      ├── Some((4, 0)): 42/88 ≈ 0.477
      ├── Some((4, 1)): 53/103 ≈ 0.515
      ├── Some((4, 2)): 98/165 ≈ 0.594
      ├── Some((4, 3)): 82/143 ≈ 0.573
      ├── Some((4, 4)): 66/121 ≈ 0.545
      ├── Some((4, 5)): 76/135 ≈ 0.563
      ├── Some((4, 7)): 72/130 ≈ 0.554
      └── Some((4, 8)): 41/86 ≈ 0.477
    ├── Some((5, 5)): 576/1044 ≈ 0.552
      ├── Some((5, 0)): 86/150 ≈ 0.573
      ├── Some((5, 1)): 70/128 ≈ 0.547
      ├── Some((5, 2)): 77/138 ≈ 0.558
      ├── Some((5, 3)): 93/160 ≈ 0.581
      ├── Some((5, 4)): 63/118 ≈ 0.534
      ├── Some((5, 6)): 92/158 ≈ 0.582
      ├── Some((5, 7)): 59/113 ≈ 0.522
      └── Some((5, 8)): 35/78 ≈ 0.449
    ├── Some((5, 6)): 424/798 ≈ 0.531
      ├── Some((6, 0)): 45/89 ≈ 0.506
      ├── Some((6, 1)): 23/57 ≈ 0.404
      ├── Some((6, 2)): 71/124 ≈ 0.573
      ├── Some((6, 3)): 51/97 ≈ 0.526
      ├── Some((6, 4)): 61/111 ≈ 0.550
      ├── Some((6, 6)): 51/97 ≈ 0.526
      ├── Some((6, 7)): 63/114 ≈ 0.553
      └── Some((6, 8)): 59/108 ≈ 0.546
    ├── Some((5, 7)): 748/1319 ≈ 0.567
      ├── Some((7, 0)): 49/99 ≈ 0.495
      ├── Some((7, 1)): 68/126 ≈ 0.540
      ├── Some((7, 2)): 49/99 ≈ 0.495
      ├── Some((7, 3)): 119/195 ≈ 0.610
      ├── Some((7, 4)): 93/160 ≈ 0.581
      ├── Some((7, 5)): 89/155 ≈ 0.574
      ├── Some((7, 6)): 109/182 ≈ 0.599
      ├── Some((7, 7)): 70/129 ≈ 0.543
      └── Some((7, 8)): 102/173 ≈ 0.590
    └── Some((5, 8)): 660/1179 ≈ 0.560
      ├── Some((8, 0)): 63/117 ≈ 0.538
      ├── Some((8, 1)): 70/127 ≈ 0.551
      ├── Some((8, 2)): 54/104 ≈ 0.519
      ├── Some((8, 3)): 87/149 ≈ 0.584
      ├── Some((8, 4)): 77/136 ≈ 0.566
      ├── Some((8, 5)): 87/149 ≈ 0.584
      ├── Some((8, 6)): 68/124 ≈ 0.548
      ├── Some((8, 7)): 80/140 ≈ 0.571
      └── Some((8, 8)): 74/132 ≈ 0.561
  ├── Some((6, 6)): 3674/6737 ≈ 0.545
    ├── Some((6, 0)): 602/1072 ≈ 0.562
      ├── Some((0, 0)): 76/131 ≈ 0.580
      ├── Some((0, 1)): 54/102 ≈ 0.529
      ├── Some((0, 2)): 58/107 ≈ 0.542
      ├── Some((0, 3)): 63/114 ≈ 0.553
      ├── Some((0, 4)): 48/93 ≈ 0.516
      ├── Some((0, 5)): 61/111 ≈ 0.550
      ├── Some((0, 6)): 83/141 ≈ 0.589
      ├── Some((0, 7)): 76/131 ≈ 0.580
      └── Some((0, 8)): 83/141 ≈ 0.589
    ├── Some((6, 1)): 682/1199 ≈ 0.569
      ├── Some((1, 0)): 83/143 ≈ 0.580
      ├── Some((1, 1)): 82/142 ≈ 0.577
      ├── Some((1, 2)): 88/150 ≈ 0.587
      ├── Some((1, 3)): 67/122 ≈ 0.549
      ├── Some((1, 4)): 123/196 ≈ 0.628
      ├── Some((1, 5)): 72/128 ≈ 0.562
      ├── Some((1, 6)): 75/133 ≈ 0.564
      ├── Some((1, 7)): 31/71 ≈ 0.437
      └── Some((1, 8)): 61/113 ≈ 0.540
    ├── Some((6, 2)): 431/798 ≈ 0.540
      ├── Some((2, 0)): 69/116 ≈ 0.595
      ├── Some((2, 1)): 60/105 ≈ 0.571
      ├── Some((2, 2)): 41/80 ≈ 0.512
      ├── Some((2, 3)): 28/62 ≈ 0.452
      ├── Some((2, 4)): 35/71 ≈ 0.493
      ├── Some((2, 5)): 42/81 ≈ 0.519
      ├── Some((2, 6)): 62/107 ≈ 0.579
      ├── Some((2, 7)): 40/78 ≈ 0.513
      └── Some((2, 8)): 54/97 ≈ 0.557
    ├── Some((6, 3)): 219/450 ≈ 0.487
      ├── Some((3, 0)): 35/64 ≈ 0.547
      ├── Some((3, 1)): 32/60 ≈ 0.533
      ├── Some((3, 2)): 20/45 ≈ 0.444
      ├── Some((3, 3)): 20/45 ≈ 0.444
      ├── Some((3, 4)): 39/69 ≈ 0.565
      ├── Some((3, 5)): 28/55 ≈ 0.509
      ├── Some((3, 6)): 21/46 ≈ 0.457
      ├── Some((3, 7)): 13/35 ≈ 0.371
      └── Some((3, 8)): 10/30 ≈ 0.333
    ├── Some((6, 4)): 347/662 ≈ 0.524
      ├── Some((4, 0)): 55/100 ≈ 0.550
      ├── Some((4, 1)): 86/140 ≈ 0.614
      ├── Some((4, 2)): 20/51 ≈ 0.392
      ├── Some((4, 3)): 47/89 ≈ 0.528
      ├── Some((4, 4)): 24/56 ≈ 0.429
      ├── Some((4, 5)): 33/69 ≈ 0.478
      ├── Some((4, 7)): 67/115 ≈ 0.583
      └── Some((4, 8)): 14/41 ≈ 0.341
    ├── Some((6, 5)): 518/938 ≈ 0.552
      ├── Some((5, 0)): 74/126 ≈ 0.587
      ├── Some((5, 1)): 62/111 ≈ 0.559
      ├── Some((5, 2)): 51/96 ≈ 0.531
      ├── Some((5, 3)): 81/136 ≈ 0.596
      ├── Some((5, 4)): 43/85 ≈ 0.506
      ├── Some((5, 5)): 19/50 ≈ 0.380
      ├── Some((5, 6)): 79/133 ≈ 0.594
      ├── Some((5, 7)): 42/83 ≈ 0.506
      └── Some((5, 8)): 67/117 ≈ 0.573
    ├── Some((6, 7)): 360/683 ≈ 0.527
      ├── Some((7, 0)): 51/91 ≈ 0.560
      ├── Some((7, 1)): 53/93 ≈ 0.570
      ├── Some((7, 2)): 22/52 ≈ 0.423
      ├── Some((7, 3)): 19/47 ≈ 0.404
      ├── Some((7, 4)): 39/75 ≈ 0.520
      ├── Some((7, 5)): 57/99 ≈ 0.576
      ├── Some((7, 6)): 23/53 ≈ 0.434
      ├── Some((7, 7)): 61/104 ≈ 0.587
      └── Some((7, 8)): 34/68 ≈ 0.500
    └── Some((6, 8)): 515/934 ≈ 0.551
      ├── Some((8, 0)): 85/141 ≈ 0.603
      ├── Some((8, 1)): 99/159 ≈ 0.623
      ├── Some((8, 2)): 55/102 ≈ 0.539
      ├── Some((8, 3)): 60/108 ≈ 0.556
      ├── Some((8, 4)): 52/97 ≈ 0.536
      ├── Some((8, 5)): 19/51 ≈ 0.373
      ├── Some((8, 6)): 18/49 ≈ 0.367
      ├── Some((8, 7)): 61/110 ≈ 0.555
      └── Some((8, 8)): 66/116 ≈ 0.569
  ├── Some((6, 7)): 3944/7205 ≈ 0.547
    ├── Some((7, 0)): 489/883 ≈ 0.554
      ├── Some((0, 0)): 51/94 ≈ 0.543
      ├── Some((0, 1)): 38/77 ≈ 0.494
      ├── Some((0, 2)): 74/124 ≈ 0.597
      ├── Some((0, 3)): 46/87 ≈ 0.529
      ├── Some((0, 4)): 51/94 ≈ 0.543
      ├── Some((0, 5)): 79/131 ≈ 0.603
      ├── Some((0, 6)): 25/58 ≈ 0.431
      ├── Some((0, 7)): 82/135 ≈ 0.607
      └── Some((0, 8)): 42/82 ≈ 0.512
    ├── Some((7, 1)): 591/1044 ≈ 0.566
      ├── Some((1, 0)): 24/59 ≈ 0.407
      ├── Some((1, 1)): 65/116 ≈ 0.560
      ├── Some((1, 2)): 32/70 ≈ 0.457
      ├── Some((1, 3)): 81/137 ≈ 0.591
      ├── Some((1, 4)): 106/169 ≈ 0.627
      ├── Some((1, 5)): 71/124 ≈ 0.573
      ├── Some((1, 6)): 83/140 ≈ 0.593
      ├── Some((1, 7)): 55/102 ≈ 0.539
      └── Some((1, 8)): 73/126 ≈ 0.579
    ├── Some((7, 2)): 493/889 ≈ 0.555
      ├── Some((2, 0)): 53/97 ≈ 0.546
      ├── Some((2, 1)): 41/80 ≈ 0.512
      ├── Some((2, 2)): 80/132 ≈ 0.606
      ├── Some((2, 3)): 59/104 ≈ 0.567
      ├── Some((2, 4)): 31/67 ≈ 0.463
      ├── Some((2, 5)): 63/110 ≈ 0.573
      ├── Some((2, 6)): 57/102 ≈ 0.559
      ├── Some((2, 7)): 69/118 ≈ 0.585
      └── Some((2, 8)): 39/78 ≈ 0.500
    ├── Some((7, 3)): 329/626 ≈ 0.526
      ├── Some((3, 0)): 43/78 ≈ 0.551
      ├── Some((3, 1)): 55/94 ≈ 0.585
      ├── Some((3, 2)): 46/82 ≈ 0.561
      ├── Some((3, 3)): 32/64 ≈ 0.500
      ├── Some((3, 4)): 47/84 ≈ 0.560
      ├── Some((3, 5)): 13/37 ≈ 0.351
      ├── Some((3, 6)): 34/67 ≈ 0.507
      ├── Some((3, 7)): 40/75 ≈ 0.533
      └── Some((3, 8)): 18/44 ≈ 0.409
    ├── Some((7, 4)): 279/544 ≈ 0.513
      ├── Some((4, 0)): 43/79 ≈ 0.544
      ├── Some((4, 1)): 22/50 ≈ 0.440
      ├── Some((4, 2)): 17/43 ≈ 0.395
      ├── Some((4, 3)): 34/67 ≈ 0.507
      ├── Some((4, 4)): 40/75 ≈ 0.533
      ├── Some((4, 5)): 34/67 ≈ 0.507
      ├── Some((4, 7)): 44/80 ≈ 0.550
      └── Some((4, 8)): 45/82 ≈ 0.549
    ├── Some((7, 5)): 628/1103 ≈ 0.569
      ├── Some((5, 0)): 56/104 ≈ 0.538
      ├── Some((5, 1)): 51/97 ≈ 0.526
      ├── Some((5, 2)): 114/181 ≈ 0.630
      ├── Some((5, 3)): 45/89 ≈ 0.506
      ├── Some((5, 4)): 61/111 ≈ 0.550
      ├── Some((5, 5)): 74/128 ≈ 0.578
      ├── Some((5, 6)): 63/114 ≈ 0.553
      ├── Some((5, 7)): 88/147 ≈ 0.599
      └── Some((5, 8)): 76/131 ≈ 0.580
    ├── Some((7, 6)): 283/551 ≈ 0.514
      ├── Some((6, 0)): 17/43 ≈ 0.395
      ├── Some((6, 1)): 50/88 ≈ 0.568
      ├── Some((6, 2)): 46/83 ≈ 0.554
      ├── Some((6, 3)): 40/75 ≈ 0.533
      ├── Some((6, 4)): 32/64 ≈ 0.500
      ├── Some((6, 5)): 39/74 ≈ 0.527
      ├── Some((6, 6)): 32/65 ≈ 0.492
      └── Some((6, 8)): 27/58 ≈ 0.466
    ├── Some((7, 7)): 496/894 ≈ 0.555
      ├── Some((7, 0)): 65/116 ≈ 0.560
      ├── Some((7, 1)): 31/69 ≈ 0.449
      ├── Some((7, 2)): 101/164 ≈ 0.616
      ├── Some((7, 3)): 79/135 ≈ 0.585
      ├── Some((7, 4)): 52/99 ≈ 0.525
      ├── Some((7, 5)): 81/137 ≈ 0.591
      ├── Some((7, 6)): 53/100 ≈ 0.530
      └── Some((7, 8)): 34/73 ≈ 0.466
    └── Some((7, 8)): 356/670 ≈ 0.531
      ├── Some((8, 0)): 35/68 ≈ 0.515
      ├── Some((8, 1)): 31/63 ≈ 0.492
      ├── Some((8, 2)): 44/80 ≈ 0.550
      ├── Some((8, 3)): 30/62 ≈ 0.484
      ├── Some((8, 4)): 39/74 ≈ 0.527
      ├── Some((8, 5)): 47/84 ≈ 0.560
      ├── Some((8, 6)): 39/74 ≈ 0.527
      ├── Some((8, 7)): 51/89 ≈ 0.573
      └── Some((8, 8)): 40/75 ≈ 0.533
  └── Some((6, 8)): 4258/7749 ≈ 0.549
    ├── Some((8, 0)): 516/932 ≈ 0.554
      ├── Some((0, 0)): 88/144 ≈ 0.611
      ├── Some((0, 1)): 42/83 ≈ 0.506
      ├── Some((0, 2)): 80/134 ≈ 0.597
      ├── Some((0, 3)): 41/82 ≈ 0.500
      ├── Some((0, 4)): 27/62 ≈ 0.435
      ├── Some((0, 5)): 64/113 ≈ 0.566
      ├── Some((0, 6)): 78/131 ≈ 0.595
      ├── Some((0, 7)): 48/91 ≈ 0.527
      └── Some((0, 8)): 48/91 ≈ 0.527
    ├── Some((8, 1)): 454/833 ≈ 0.545
      ├── Some((1, 0)): 32/68 ≈ 0.471
      ├── Some((1, 1)): 27/61 ≈ 0.443
      ├── Some((1, 2)): 59/105 ≈ 0.562
      ├── Some((1, 3)): 34/71 ≈ 0.479
      ├── Some((1, 4)): 89/143 ≈ 0.622
      ├── Some((1, 5)): 62/108 ≈ 0.574
      ├── Some((1, 6)): 36/73 ≈ 0.493
      ├── Some((1, 7)): 76/127 ≈ 0.598
      └── Some((1, 8)): 38/76 ≈ 0.500
    ├── Some((8, 2)): 260/517 ≈ 0.503
      ├── Some((2, 0)): 26/54 ≈ 0.481
      ├── Some((2, 1)): 28/56 ≈ 0.500
      ├── Some((2, 2)): 32/62 ≈ 0.516
      ├── Some((2, 3)): 25/52 ≈ 0.481
      ├── Some((2, 4)): 41/73 ≈ 0.562
      ├── Some((2, 5)): 31/60 ≈ 0.517
      ├── Some((2, 6)): 34/64 ≈ 0.531
      ├── Some((2, 7)): 18/43 ≈ 0.419
      └── Some((2, 8)): 25/52 ≈ 0.481
    ├── Some((8, 3)): 412/765 ≈ 0.539
      ├── Some((3, 0)): 42/80 ≈ 0.525
      ├── Some((3, 1)): 68/114 ≈ 0.596
      ├── Some((3, 2)): 23/54 ≈ 0.426
      ├── Some((3, 3)): 45/84 ≈ 0.536
      ├── Some((3, 4)): 43/82 ≈ 0.524
      ├── Some((3, 5)): 40/78 ≈ 0.513
      ├── Some((3, 6)): 37/74 ≈ 0.500
      ├── Some((3, 7)): 77/126 ≈ 0.611
      └── Some((3, 8)): 36/72 ≈ 0.500
    ├── Some((8, 4)): 550/986 ≈ 0.558
      ├── Some((4, 0)): 89/151 ≈ 0.589
      ├── Some((4, 1)): 65/118 ≈ 0.551
      ├── Some((4, 2)): 61/113 ≈ 0.540
      ├── Some((4, 3)): 60/112 ≈ 0.536
      ├── Some((4, 4)): 49/96 ≈ 0.510
      ├── Some((4, 5)): 70/125 ≈ 0.560
      ├── Some((4, 7)): 68/122 ≈ 0.557
      └── Some((4, 8)): 87/148 ≈ 0.588
    ├── Some((8, 5)): 327/627 ≈ 0.522
      ├── Some((5, 0)): 47/84 ≈ 0.560
      ├── Some((5, 1)): 37/71 ≈ 0.521
      ├── Some((5, 2)): 52/91 ≈ 0.571
      ├── Some((5, 3)): 48/85 ≈ 0.565
      ├── Some((5, 4)): 50/88 ≈ 0.568
      ├── Some((5, 5)): 17/43 ≈ 0.395
      ├── Some((5, 6)): 15/40 ≈ 0.375
      ├── Some((5, 7)): 29/60 ≈ 0.483
      └── Some((5, 8)): 32/64 ≈ 0.500
    ├── Some((8, 6)): 805/1388 ≈ 0.580
      ├── Some((6, 0)): 110/187 ≈ 0.588
      ├── Some((6, 1)): 87/155 ≈ 0.561
      ├── Some((6, 2)): 111/188 ≈ 0.590
      ├── Some((6, 3)): 75/139 ≈ 0.540
      ├── Some((6, 4)): 142/229 ≈ 0.620
      ├── Some((6, 5)): 53/107 ≈ 0.495
      ├── Some((6, 6)): 95/166 ≈ 0.572
      └── Some((6, 7)): 132/216 ≈ 0.611
    ├── Some((8, 7)): 279/548 ≈ 0.509
      ├── Some((7, 0)): 57/95 ≈ 0.600
      ├── Some((7, 1)): 42/76 ≈ 0.553
      ├── Some((7, 2)): 19/45 ≈ 0.422
      ├── Some((7, 3)): 29/58 ≈ 0.500
      ├── Some((7, 4)): 25/53 ≈ 0.472
      ├── Some((7, 5)): 26/54 ≈ 0.481
      ├── Some((7, 6)): 31/61 ≈ 0.508
      ├── Some((7, 7)): 22/49 ≈ 0.449
      └── Some((7, 8)): 27/56 ≈ 0.482
    └── Some((8, 8)): 655/1152 ≈ 0.569
      ├── Some((8, 0)): 59/113 ≈ 0.522
      ├── Some((8, 1)): 73/132 ≈ 0.553
      ├── Some((8, 2)): 66/123 ≈ 0.537
      ├── Some((8, 3)): 71/130 ≈ 0.546
      ├── Some((8, 4)): 135/215 ≈ 0.628
      ├── Some((8, 5)): 92/158 ≈ 0.582
      ├── Some((8, 6)): 93/159 ≈ 0.585
      └── Some((8, 7)): 65/121 ≈ 0.537
├── Some((4, 7)): 14263/26601 ≈ 0.536
  ├── Some((7, 0)): 1838/3392 ≈ 0.542
    ├── Some((0, 0)): 177/335 ≈ 0.528
      ├── Some((0, 1)): 19/38 ≈ 0.500
      ├── Some((0, 2)): 25/46 ≈ 0.543
      ├── Some((0, 3)): 35/57 ≈ 0.614
      ├── Some((0, 4)): 17/36 ≈ 0.472
      ├── Some((0, 5)): 13/30 ≈ 0.433
      ├── Some((0, 6)): 31/53 ≈ 0.585
      ├── Some((0, 7)): 13/30 ≈ 0.433
      └── Some((0, 8)): 24/44 ≈ 0.545
    ├── Some((0, 1)): 267/473 ≈ 0.564
      ├── Some((1, 0)): 35/59 ≈ 0.593
      ├── Some((1, 1)): 27/49 ≈ 0.551
      ├── Some((1, 2)): 31/54 ≈ 0.574
      ├── Some((1, 3)): 19/40 ≈ 0.475
      ├── Some((1, 4)): 32/56 ≈ 0.571
      ├── Some((1, 5)): 39/64 ≈ 0.609
      ├── Some((1, 6)): 23/45 ≈ 0.511
      ├── Some((1, 7)): 14/33 ≈ 0.424
      └── Some((1, 8)): 46/72 ≈ 0.639
    ├── Some((0, 2)): 221/403 ≈ 0.548
      ├── Some((2, 0)): 34/56 ≈ 0.607
      ├── Some((2, 1)): 29/50 ≈ 0.580
      ├── Some((2, 2)): 18/37 ≈ 0.486
      ├── Some((2, 3)): 19/38 ≈ 0.500
      ├── Some((2, 4)): 11/28 ≈ 0.393
      ├── Some((2, 5)): 19/38 ≈ 0.500
      ├── Some((2, 6)): 35/57 ≈ 0.614
      ├── Some((2, 7)): 25/45 ≈ 0.556
      └── Some((2, 8)): 31/53 ≈ 0.585
    ├── Some((0, 3)): 187/351 ≈ 0.533
      ├── Some((3, 0)): 20/38 ≈ 0.526
      ├── Some((3, 1)): 9/25 ≈ 0.360
      ├── Some((3, 2)): 11/27 ≈ 0.407
      ├── Some((3, 3)): 11/27 ≈ 0.407
      ├── Some((3, 4)): 37/58 ≈ 0.638
      ├── Some((3, 5)): 27/47 ≈ 0.574
      ├── Some((3, 6)): 15/32 ≈ 0.469
      ├── Some((3, 7)): 16/34 ≈ 0.471
      └── Some((3, 8)): 40/62 ≈ 0.645
    ├── Some((0, 4)): 138/274 ≈ 0.504
      ├── Some((4, 0)): 10/25 ≈ 0.400
      ├── Some((4, 1)): 31/51 ≈ 0.608
      ├── Some((4, 2)): 15/32 ≈ 0.469
      ├── Some((4, 3)): 23/41 ≈ 0.561
      ├── Some((4, 4)): 21/39 ≈ 0.538
      ├── Some((4, 5)): 3/16 ≈ 0.188
      ├── Some((4, 6)): 19/37 ≈ 0.514
      └── Some((4, 8)): 15/32 ≈ 0.469
    ├── Some((0, 5)): 260/462 ≈ 0.563
      ├── Some((5, 0)): 37/61 ≈ 0.607
      ├── Some((5, 1)): 40/65 ≈ 0.615
      ├── Some((5, 2)): 36/60 ≈ 0.600
      ├── Some((5, 3)): 28/51 ≈ 0.549
      ├── Some((5, 4)): 15/34 ≈ 0.441
      ├── Some((5, 5)): 36/60 ≈ 0.600
      ├── Some((5, 6)): 15/34 ≈ 0.441
      ├── Some((5, 7)): 30/53 ≈ 0.566
      └── Some((5, 8)): 22/43 ≈ 0.512
    ├── Some((0, 6)): 188/353 ≈ 0.533
      ├── Some((6, 0)): 10/26 ≈ 0.385
      ├── Some((6, 1)): 19/37 ≈ 0.514
      ├── Some((6, 2)): 31/52 ≈ 0.596
      ├── Some((6, 3)): 12/28 ≈ 0.429
      ├── Some((6, 4)): 39/61 ≈ 0.639
      ├── Some((6, 5)): 31/52 ≈ 0.596
      ├── Some((6, 6)): 13/30 ≈ 0.433
      ├── Some((6, 7)): 20/38 ≈ 0.526
      └── Some((6, 8)): 12/28 ≈ 0.429
    ├── Some((0, 7)): 191/357 ≈ 0.535
      ├── Some((7, 1)): 34/57 ≈ 0.596
      ├── Some((7, 2)): 35/58 ≈ 0.603
      ├── Some((7, 3)): 13/31 ≈ 0.419
      ├── Some((7, 4)): 14/32 ≈ 0.438
      ├── Some((7, 5)): 28/50 ≈ 0.560
      ├── Some((7, 6)): 16/35 ≈ 0.457
      ├── Some((7, 7)): 28/50 ≈ 0.560
      └── Some((7, 8)): 22/43 ≈ 0.512
    └── Some((0, 8)): 208/383 ≈ 0.543
      ├── Some((8, 0)): 20/39 ≈ 0.513
      ├── Some((8, 1)): 31/52 ≈ 0.596
      ├── Some((8, 2)): 16/34 ≈ 0.471
      ├── Some((8, 3)): 38/60 ≈ 0.633
      ├── Some((8, 4)): 20/39 ≈ 0.513
      ├── Some((8, 5)): 34/56 ≈ 0.607
      ├── Some((8, 6)): 17/35 ≈ 0.486
      ├── Some((8, 7)): 12/29 ≈ 0.414
      └── Some((8, 8)): 19/38 ≈ 0.500
  ├── Some((7, 1)): 1683/3126 ≈ 0.538
    ├── Some((1, 0)): 130/259 ≈ 0.502
      ├── Some((0, 0)): 18/33 ≈ 0.545
      ├── Some((0, 1)): 22/38 ≈ 0.579
      ├── Some((0, 2)): 14/28 ≈ 0.500
      ├── Some((0, 3)): 9/22 ≈ 0.409
      ├── Some((0, 4)): 16/31 ≈ 0.516
      ├── Some((0, 5)): 14/28 ≈ 0.500
      ├── Some((0, 6)): 6/18 ≈ 0.333
      ├── Some((0, 7)): 8/21 ≈ 0.381
      └── Some((0, 8)): 23/39 ≈ 0.590
    ├── Some((1, 1)): 236/423 ≈ 0.558
      ├── Some((1, 0)): 26/49 ≈ 0.531
      ├── Some((1, 2)): 29/53 ≈ 0.547
      ├── Some((1, 3)): 26/49 ≈ 0.531
      ├── Some((1, 4)): 23/46 ≈ 0.500
      ├── Some((1, 5)): 49/77 ≈ 0.636
      ├── Some((1, 6)): 6/22 ≈ 0.273
      ├── Some((1, 7)): 10/28 ≈ 0.357
      └── Some((1, 8)): 67/98 ≈ 0.684
    ├── Some((1, 2)): 158/303 ≈ 0.521
      ├── Some((2, 0)): 31/50 ≈ 0.620
      ├── Some((2, 1)): 12/27 ≈ 0.444
      ├── Some((2, 2)): 19/36 ≈ 0.528
      ├── Some((2, 3)): 13/28 ≈ 0.464
      ├── Some((2, 4)): 17/33 ≈ 0.515
      ├── Some((2, 5)): 1/12 ≈ 0.083
      ├── Some((2, 6)): 26/44 ≈ 0.591
      ├── Some((2, 7)): 13/29 ≈ 0.448
      └── Some((2, 8)): 25/43 ≈ 0.581
    ├── Some((1, 3)): 214/389 ≈ 0.550
      ├── Some((3, 0)): 39/61 ≈ 0.639
      ├── Some((3, 1)): 10/26 ≈ 0.385
      ├── Some((3, 2)): 28/49 ≈ 0.571
      ├── Some((3, 3)): 21/40 ≈ 0.525
      ├── Some((3, 4)): 17/35 ≈ 0.486
      ├── Some((3, 5)): 16/34 ≈ 0.471
      ├── Some((3, 6)): 26/46 ≈ 0.565
      ├── Some((3, 7)): 23/43 ≈ 0.535
      └── Some((3, 8)): 33/54 ≈ 0.611
    ├── Some((1, 4)): 114/234 ≈ 0.487
      ├── Some((4, 0)): 10/24 ≈ 0.417
      ├── Some((4, 1)): 15/30 ≈ 0.500
      ├── Some((4, 2)): 12/27 ≈ 0.444
      ├── Some((4, 3)): 12/27 ≈ 0.444
      ├── Some((4, 4)): 3/15 ≈ 0.200
      ├── Some((4, 5)): 12/27 ≈ 0.444
      ├── Some((4, 6)): 29/47 ≈ 0.617
      └── Some((4, 8)): 20/36 ≈ 0.556
    ├── Some((1, 5)): 244/435 ≈ 0.561
      ├── Some((5, 0)): 30/52 ≈ 0.577
      ├── Some((5, 1)): 24/45 ≈ 0.533
      ├── Some((5, 2)): 10/27 ≈ 0.370
      ├── Some((5, 3)): 27/48 ≈ 0.562
      ├── Some((5, 4)): 35/58 ≈ 0.603
      ├── Some((5, 5)): 37/60 ≈ 0.617
      ├── Some((5, 6)): 21/41 ≈ 0.512
      ├── Some((5, 7)): 23/44 ≈ 0.523
      └── Some((5, 8)): 36/59 ≈ 0.610
    ├── Some((1, 6)): 149/289 ≈ 0.516
      ├── Some((6, 0)): 17/33 ≈ 0.515
      ├── Some((6, 1)): 25/42 ≈ 0.595
      ├── Some((6, 2)): 16/31 ≈ 0.516
      ├── Some((6, 3)): 16/32 ≈ 0.500
      ├── Some((6, 4)): 25/42 ≈ 0.595
      ├── Some((6, 5)): 10/24 ≈ 0.417
      ├── Some((6, 6)): 20/36 ≈ 0.556
      ├── Some((6, 7)): 6/19 ≈ 0.316
      └── Some((6, 8)): 14/29 ≈ 0.483
    ├── Some((1, 7)): 199/366 ≈ 0.544
      ├── Some((7, 0)): 22/43 ≈ 0.512
      ├── Some((7, 2)): 30/52 ≈ 0.577
      ├── Some((7, 3)): 26/47 ≈ 0.553
      ├── Some((7, 4)): 14/32 ≈ 0.438
      ├── Some((7, 5)): 8/24 ≈ 0.333
      ├── Some((7, 6)): 45/70 ≈ 0.643
      ├── Some((7, 7)): 37/61 ≈ 0.607
      └── Some((7, 8)): 17/36 ≈ 0.472
    └── Some((1, 8)): 239/427 ≈ 0.560
      ├── Some((8, 0)): 20/39 ≈ 0.513
      ├── Some((8, 1)): 21/41 ≈ 0.512
      ├── Some((8, 2)): 39/62 ≈ 0.629
      ├── Some((8, 3)): 21/41 ≈ 0.512
      ├── Some((8, 4)): 30/52 ≈ 0.577
      ├── Some((8, 5)): 26/47 ≈ 0.553
      ├── Some((8, 6)): 29/50 ≈ 0.580
      ├── Some((8, 7)): 32/54 ≈ 0.593
      └── Some((8, 8)): 20/40 ≈ 0.500
  ├── Some((7, 2)): 1773/3280 ≈ 0.541
    ├── Some((2, 0)): 230/415 ≈ 0.554
      ├── Some((0, 0)): 32/54 ≈ 0.593
      ├── Some((0, 1)): 21/41 ≈ 0.512
      ├── Some((0, 2)): 19/38 ≈ 0.500
      ├── Some((0, 3)): 12/29 ≈ 0.414
      ├── Some((0, 4)): 11/28 ≈ 0.393
      ├── Some((0, 5)): 43/67 ≈ 0.642
      ├── Some((0, 6)): 24/44 ≈ 0.545
      ├── Some((0, 7)): 29/51 ≈ 0.569
      └── Some((0, 8)): 39/62 ≈ 0.629
    ├── Some((2, 1)): 307/531 ≈ 0.578
      ├── Some((1, 0)): 18/39 ≈ 0.462
      ├── Some((1, 1)): 24/47 ≈ 0.511
      ├── Some((1, 2)): 59/89 ≈ 0.663
      ├── Some((1, 3)): 22/44 ≈ 0.500
      ├── Some((1, 4)): 25/48 ≈ 0.521
      ├── Some((1, 5)): 17/38 ≈ 0.447
      ├── Some((1, 6)): 46/74 ≈ 0.622
      ├── Some((1, 7)): 49/77 ≈ 0.636
      └── Some((1, 8)): 46/74 ≈ 0.622
    ├── Some((2, 2)): 135/269 ≈ 0.502
      ├── Some((2, 0)): 10/25 ≈ 0.400
      ├── Some((2, 1)): 18/35 ≈ 0.514
      ├── Some((2, 3)): 21/39 ≈ 0.538
      ├── Some((2, 4)): 19/37 ≈ 0.514
      ├── Some((2, 5)): 11/27 ≈ 0.407
      ├── Some((2, 6)): 5/18 ≈ 0.278
      ├── Some((2, 7)): 17/34 ≈ 0.500
      └── Some((2, 8)): 33/53 ≈ 0.623
    ├── Some((2, 3)): 194/361 ≈ 0.537
      ├── Some((3, 0)): 14/31 ≈ 0.452
      ├── Some((3, 1)): 26/45 ≈ 0.578
      ├── Some((3, 2)): 38/59 ≈ 0.644
      ├── Some((3, 3)): 21/40 ≈ 0.525
      ├── Some((3, 4)): 29/49 ≈ 0.592
      ├── Some((3, 5)): 15/32 ≈ 0.469
      ├── Some((3, 6)): 15/32 ≈ 0.469
      ├── Some((3, 7)): 15/32 ≈ 0.469
      └── Some((3, 8)): 21/40 ≈ 0.525
    ├── Some((2, 4)): 190/354 ≈ 0.537
      ├── Some((4, 0)): 26/47 ≈ 0.553
      ├── Some((4, 1)): 20/40 ≈ 0.500
      ├── Some((4, 2)): 22/42 ≈ 0.524
      ├── Some((4, 3)): 14/32 ≈ 0.438
      ├── Some((4, 4)): 31/53 ≈ 0.585
      ├── Some((4, 5)): 36/59 ≈ 0.610
      ├── Some((4, 6)): 28/50 ≈ 0.560
      └── Some((4, 8)): 12/30 ≈ 0.400
    ├── Some((2, 5)): 237/426 ≈ 0.556
      ├── Some((5, 0)): 22/42 ≈ 0.524
      ├── Some((5, 1)): 39/62 ≈ 0.629
      ├── Some((5, 2)): 12/30 ≈ 0.400
      ├── Some((5, 3)): 34/57 ≈ 0.596
      ├── Some((5, 4)): 36/59 ≈ 0.610
      ├── Some((5, 5)): 31/53 ≈ 0.585
      ├── Some((5, 6)): 29/51 ≈ 0.569
      ├── Some((5, 7)): 12/30 ≈ 0.400
      └── Some((5, 8)): 21/41 ≈ 0.512
    ├── Some((2, 6)): 165/316 ≈ 0.522
      ├── Some((6, 0)): 11/26 ≈ 0.423
      ├── Some((6, 1)): 8/22 ≈ 0.364
      ├── Some((6, 2)): 17/34 ≈ 0.500
      ├── Some((6, 3)): 10/25 ≈ 0.400
      ├── Some((6, 4)): 26/44 ≈ 0.591
      ├── Some((6, 5)): 27/46 ≈ 0.587
      ├── Some((6, 6)): 14/30 ≈ 0.467
      ├── Some((6, 7)): 29/48 ≈ 0.604
      └── Some((6, 8)): 22/40 ≈ 0.550
    ├── Some((2, 7)): 192/357 ≈ 0.538
      ├── Some((7, 0)): 34/57 ≈ 0.596
      ├── Some((7, 1)): 7/23 ≈ 0.304
      ├── Some((7, 3)): 24/45 ≈ 0.533
      ├── Some((7, 4)): 20/40 ≈ 0.500
      ├── Some((7, 5)): 49/74 ≈ 0.662
      ├── Some((7, 6)): 23/44 ≈ 0.523
      ├── Some((7, 7)): 12/30 ≈ 0.400
      └── Some((7, 8)): 22/43 ≈ 0.512
    └── Some((2, 8)): 123/250 ≈ 0.492
      ├── Some((8, 0)): 13/27 ≈ 0.481
      ├── Some((8, 1)): 17/32 ≈ 0.531
      ├── Some((8, 2)): 14/28 ≈ 0.500
      ├── Some((8, 3)): 5/17 ≈ 0.294
      ├── Some((8, 4)): 20/36 ≈ 0.556
      ├── Some((8, 5)): 18/33 ≈ 0.545
      ├── Some((8, 6)): 13/27 ≈ 0.481
      ├── Some((8, 7)): 9/22 ≈ 0.409
      └── Some((8, 8)): 13/27 ≈ 0.481
  ├── Some((7, 3)): 1258/2391 ≈ 0.526
    ├── Some((3, 0)): 212/376 ≈ 0.564
      ├── Some((0, 0)): 10/26 ≈ 0.385
      ├── Some((0, 1)): 15/32 ≈ 0.469
      ├── Some((0, 2)): 17/34 ≈ 0.500
      ├── Some((0, 3)): 22/40 ≈ 0.550
      ├── Some((0, 4)): 50/72 ≈ 0.694
      ├── Some((0, 5)): 20/38 ≈ 0.526
      ├── Some((0, 6)): 22/40 ≈ 0.550
      ├── Some((0, 7)): 21/39 ≈ 0.538
      └── Some((0, 8)): 34/54 ≈ 0.630
    ├── Some((3, 1)): 155/291 ≈ 0.533
      ├── Some((1, 0)): 22/38 ≈ 0.579
      ├── Some((1, 1)): 15/30 ≈ 0.500
      ├── Some((1, 2)): 13/27 ≈ 0.481
      ├── Some((1, 3)): 19/35 ≈ 0.543
      ├── Some((1, 4)): 7/20 ≈ 0.350
      ├── Some((1, 5)): 24/40 ≈ 0.600
      ├── Some((1, 6)): 13/27 ≈ 0.481
      ├── Some((1, 7)): 22/38 ≈ 0.579
      └── Some((1, 8)): 19/35 ≈ 0.543
    ├── Some((3, 2)): 214/379 ≈ 0.565
      ├── Some((2, 0)): 7/21 ≈ 0.333
      ├── Some((2, 1)): 17/34 ≈ 0.500
      ├── Some((2, 2)): 20/38 ≈ 0.526
      ├── Some((2, 3)): 26/45 ≈ 0.578
      ├── Some((2, 4)): 27/46 ≈ 0.587
      ├── Some((2, 5)): 21/39 ≈ 0.538
      ├── Some((2, 6)): 33/53 ≈ 0.623
      ├── Some((2, 7)): 36/56 ≈ 0.643
      └── Some((2, 8)): 27/46 ≈ 0.587
    ├── Some((3, 3)): 65/149 ≈ 0.436
      ├── Some((3, 0)): 7/17 ≈ 0.412
      ├── Some((3, 1)): 13/24 ≈ 0.542
      ├── Some((3, 2)): 7/17 ≈ 0.412
      ├── Some((3, 4)): 11/22 ≈ 0.500
      ├── Some((3, 5)): 6/16 ≈ 0.375
      ├── Some((3, 6)): 4/14 ≈ 0.286
      ├── Some((3, 7)): 11/22 ≈ 0.500
      └── Some((3, 8)): 6/16 ≈ 0.375
    ├── Some((3, 4)): 89/188 ≈ 0.473
      ├── Some((4, 0)): 6/17 ≈ 0.353
      ├── Some((4, 1)): 14/27 ≈ 0.519
      ├── Some((4, 2)): 12/25 ≈ 0.480
      ├── Some((4, 3)): 20/34 ≈ 0.588
      ├── Some((4, 4)): 14/27 ≈ 0.519
      ├── Some((4, 5)): 11/23 ≈ 0.478
      ├── Some((4, 6)): 10/22 ≈ 0.455
      └── Some((4, 8)): 2/12 ≈ 0.167
    ├── Some((3, 5)): 217/384 ≈ 0.565
      ├── Some((5, 0)): 23/41 ≈ 0.561
      ├── Some((5, 1)): 23/41 ≈ 0.561
      ├── Some((5, 2)): 12/28 ≈ 0.429
      ├── Some((5, 3)): 20/38 ≈ 0.526
      ├── Some((5, 4)): 29/48 ≈ 0.604
      ├── Some((5, 5)): 25/44 ≈ 0.568
      ├── Some((5, 6)): 27/46 ≈ 0.587
      ├── Some((5, 7)): 23/42 ≈ 0.548
      └── Some((5, 8)): 35/55 ≈ 0.636
    ├── Some((3, 6)): 88/187 ≈ 0.471
      ├── Some((6, 0)): 15/27 ≈ 0.556
      ├── Some((6, 1)): 10/21 ≈ 0.476
      ├── Some((6, 2)): 4/14 ≈ 0.286
      ├── Some((6, 3)): 13/24 ≈ 0.542
      ├── Some((6, 4)): 14/26 ≈ 0.538
      ├── Some((6, 5)): 8/19 ≈ 0.421
      ├── Some((6, 6)): 5/15 ≈ 0.333
      ├── Some((6, 7)): 8/19 ≈ 0.421
      └── Some((6, 8)): 10/21 ≈ 0.476
    ├── Some((3, 7)): 156/292 ≈ 0.534
      ├── Some((7, 0)): 12/28 ≈ 0.429
      ├── Some((7, 1)): 19/36 ≈ 0.528
      ├── Some((7, 2)): 16/32 ≈ 0.500
      ├── Some((7, 4)): 31/50 ≈ 0.620
      ├── Some((7, 5)): 11/26 ≈ 0.423
      ├── Some((7, 6)): 15/31 ≈ 0.484
      ├── Some((7, 7)): 23/41 ≈ 0.561
      └── Some((7, 8)): 28/47 ≈ 0.596
    └── Some((3, 8)): 62/144 ≈ 0.431
      ├── Some((8, 0)): 5/14 ≈ 0.357
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 0/7 ≈ 0.000
      ├── Some((8, 3)): 16/26 ≈ 0.615
      ├── Some((8, 4)): 2/10 ≈ 0.200
      ├── Some((8, 5)): 8/18 ≈ 0.444
      ├── Some((8, 6)): 12/22 ≈ 0.545
      ├── Some((8, 7)): 8/18 ≈ 0.444
      └── Some((8, 8)): 4/13 ≈ 0.308
  ├── Some((7, 4)): 1956/3594 ≈ 0.544
    ├── Some((4, 0)): 254/464 ≈ 0.547
      ├── Some((0, 0)): 28/52 ≈ 0.538
      ├── Some((0, 1)): 19/40 ≈ 0.475
      ├── Some((0, 2)): 27/50 ≈ 0.540
      ├── Some((0, 3)): 19/40 ≈ 0.475
      ├── Some((0, 4)): 24/47 ≈ 0.511
      ├── Some((0, 5)): 23/45 ≈ 0.511
      ├── Some((0, 6)): 48/75 ≈ 0.640
      ├── Some((0, 7)): 38/64 ≈ 0.594
      └── Some((0, 8)): 27/50 ≈ 0.540
    ├── Some((4, 1)): 280/504 ≈ 0.556
      ├── Some((1, 0)): 32/57 ≈ 0.561
      ├── Some((1, 1)): 30/55 ≈ 0.545
      ├── Some((1, 2)): 46/74 ≈ 0.622
      ├── Some((1, 3)): 29/53 ≈ 0.547
      ├── Some((1, 4)): 29/53 ≈ 0.547
      ├── Some((1, 5)): 28/52 ≈ 0.538
      ├── Some((1, 6)): 39/66 ≈ 0.591
      ├── Some((1, 7)): 20/42 ≈ 0.476
      └── Some((1, 8)): 27/51 ≈ 0.529
    ├── Some((4, 2)): 218/408 ≈ 0.534
      ├── Some((2, 0)): 23/44 ≈ 0.523
      ├── Some((2, 1)): 35/59 ≈ 0.593
      ├── Some((2, 2)): 13/31 ≈ 0.419
      ├── Some((2, 3)): 16/35 ≈ 0.457
      ├── Some((2, 4)): 37/61 ≈ 0.607
      ├── Some((2, 5)): 10/27 ≈ 0.370
      ├── Some((2, 6)): 30/53 ≈ 0.566
      ├── Some((2, 7)): 25/47 ≈ 0.532
      └── Some((2, 8)): 28/50 ≈ 0.560
    ├── Some((4, 3)): 211/397 ≈ 0.531
      ├── Some((3, 0)): 10/27 ≈ 0.370
      ├── Some((3, 1)): 17/36 ≈ 0.472
      ├── Some((3, 2)): 29/51 ≈ 0.569
      ├── Some((3, 3)): 29/51 ≈ 0.569
      ├── Some((3, 4)): 26/48 ≈ 0.542
      ├── Some((3, 5)): 35/58 ≈ 0.603
      ├── Some((3, 6)): 8/24 ≈ 0.333
      ├── Some((3, 7)): 34/57 ≈ 0.596
      └── Some((3, 8)): 23/44 ≈ 0.523
    ├── Some((4, 4)): 288/517 ≈ 0.557
      ├── Some((4, 0)): 51/86 ≈ 0.593
      ├── Some((4, 1)): 40/72 ≈ 0.556
      ├── Some((4, 2)): 43/76 ≈ 0.566
      ├── Some((4, 3)): 32/62 ≈ 0.516
      ├── Some((4, 5)): 47/81 ≈ 0.580
      ├── Some((4, 6)): 31/61 ≈ 0.508
      └── Some((4, 8)): 44/78 ≈ 0.564
    ├── Some((4, 5)): 281/506 ≈ 0.555
      ├── Some((5, 0)): 32/57 ≈ 0.561
      ├── Some((5, 1)): 39/66 ≈ 0.591
      ├── Some((5, 2)): 18/39 ≈ 0.462
      ├── Some((5, 3)): 24/47 ≈ 0.511
      ├── Some((5, 4)): 35/61 ≈ 0.574
      ├── Some((5, 5)): 25/49 ≈ 0.510
      ├── Some((5, 6)): 27/51 ≈ 0.529
      ├── Some((5, 7)): 36/62 ≈ 0.581
      └── Some((5, 8)): 45/73 ≈ 0.616
    ├── Some((4, 6)): 231/429 ≈ 0.538
      ├── Some((6, 0)): 20/41 ≈ 0.488
      ├── Some((6, 1)): 13/32 ≈ 0.406
      ├── Some((6, 2)): 25/47 ≈ 0.532
      ├── Some((6, 3)): 29/52 ≈ 0.558
      ├── Some((6, 4)): 24/46 ≈ 0.522
      ├── Some((6, 5)): 7/23 ≈ 0.304
      ├── Some((6, 6)): 40/65 ≈ 0.615
      ├── Some((6, 7)): 19/40 ≈ 0.475
      └── Some((6, 8)): 54/82 ≈ 0.659
    └── Some((4, 8)): 192/368 ≈ 0.522
      ├── Some((8, 0)): 22/42 ≈ 0.524
      ├── Some((8, 1)): 21/40 ≈ 0.525
      ├── Some((8, 2)): 29/50 ≈ 0.580
      ├── Some((8, 3)): 20/39 ≈ 0.513
      ├── Some((8, 4)): 24/44 ≈ 0.545
      ├── Some((8, 5)): 26/47 ≈ 0.553
      ├── Some((8, 6)): 23/43 ≈ 0.535
      ├── Some((8, 7)): 11/28 ≈ 0.393
      └── Some((8, 8)): 16/34 ≈ 0.471
  ├── Some((7, 5)): 1355/2560 ≈ 0.529
    ├── Some((5, 0)): 145/277 ≈ 0.523
      ├── Some((0, 0)): 20/35 ≈ 0.571
      ├── Some((0, 1)): 19/34 ≈ 0.559
      ├── Some((0, 2)): 15/30 ≈ 0.500
      ├── Some((0, 3)): 22/38 ≈ 0.579
      ├── Some((0, 4)): 18/33 ≈ 0.545
      ├── Some((0, 5)): 17/32 ≈ 0.531
      ├── Some((0, 6)): 9/22 ≈ 0.409
      ├── Some((0, 7)): 14/28 ≈ 0.500
      └── Some((0, 8)): 10/24 ≈ 0.417
    ├── Some((5, 1)): 213/379 ≈ 0.562
      ├── Some((1, 0)): 27/46 ≈ 0.587
      ├── Some((1, 1)): 22/40 ≈ 0.550
      ├── Some((1, 2)): 40/61 ≈ 0.656
      ├── Some((1, 3)): 11/27 ≈ 0.407
      ├── Some((1, 4)): 15/32 ≈ 0.469
      ├── Some((1, 5)): 16/33 ≈ 0.485
      ├── Some((1, 6)): 22/41 ≈ 0.537
      ├── Some((1, 7)): 25/44 ≈ 0.568
      └── Some((1, 8)): 34/54 ≈ 0.630
    ├── Some((5, 2)): 149/283 ≈ 0.527
      ├── Some((2, 0)): 26/43 ≈ 0.605
      ├── Some((2, 1)): 15/30 ≈ 0.500
      ├── Some((2, 2)): 18/33 ≈ 0.545
      ├── Some((2, 3)): 20/36 ≈ 0.556
      ├── Some((2, 4)): 13/27 ≈ 0.481
      ├── Some((2, 5)): 13/27 ≈ 0.481
      ├── Some((2, 6)): 12/26 ≈ 0.462
      ├── Some((2, 7)): 9/22 ≈ 0.409
      └── Some((2, 8)): 22/38 ≈ 0.579
    ├── Some((5, 3)): 164/306 ≈ 0.536
      ├── Some((3, 0)): 13/28 ≈ 0.464
      ├── Some((3, 1)): 28/45 ≈ 0.622
      ├── Some((3, 2)): 14/29 ≈ 0.483
      ├── Some((3, 3)): 17/33 ≈ 0.515
      ├── Some((3, 4)): 16/31 ≈ 0.516
      ├── Some((3, 5)): 27/44 ≈ 0.614
      ├── Some((3, 6)): 19/35 ≈ 0.543
      ├── Some((3, 7)): 13/28 ≈ 0.464
      └── Some((3, 8)): 16/32 ≈ 0.500
    ├── Some((5, 4)): 126/247 ≈ 0.510
      ├── Some((4, 0)): 20/36 ≈ 0.556
      ├── Some((4, 1)): 18/34 ≈ 0.529
      ├── Some((4, 2)): 10/24 ≈ 0.417
      ├── Some((4, 3)): 22/38 ≈ 0.579
      ├── Some((4, 4)): 8/21 ≈ 0.381
      ├── Some((4, 5)): 16/31 ≈ 0.516
      ├── Some((4, 6)): 17/32 ≈ 0.531
      └── Some((4, 8)): 15/30 ≈ 0.500
    ├── Some((5, 5)): 83/179 ≈ 0.464
      ├── Some((5, 0)): 16/29 ≈ 0.552
      ├── Some((5, 1)): 6/17 ≈ 0.353
      ├── Some((5, 2)): 4/14 ≈ 0.286
      ├── Some((5, 3)): 13/25 ≈ 0.520
      ├── Some((5, 4)): 8/20 ≈ 0.400
      ├── Some((5, 6)): 13/25 ≈ 0.520
      ├── Some((5, 7)): 10/22 ≈ 0.455
      └── Some((5, 8)): 13/26 ≈ 0.500
    ├── Some((5, 6)): 189/343 ≈ 0.551
      ├── Some((6, 0)): 19/36 ≈ 0.528
      ├── Some((6, 1)): 16/32 ≈ 0.500
      ├── Some((6, 2)): 11/26 ≈ 0.423
      ├── Some((6, 3)): 37/56 ≈ 0.661
      ├── Some((6, 4)): 14/30 ≈ 0.467
      ├── Some((6, 5)): 25/43 ≈ 0.581
      ├── Some((6, 6)): 27/45 ≈ 0.600
      ├── Some((6, 7)): 17/33 ≈ 0.515
      └── Some((6, 8)): 23/41 ≈ 0.561
    ├── Some((5, 7)): 158/296 ≈ 0.534
      ├── Some((7, 0)): 25/43 ≈ 0.581
      ├── Some((7, 1)): 16/33 ≈ 0.485
      ├── Some((7, 2)): 24/42 ≈ 0.571
      ├── Some((7, 3)): 23/41 ≈ 0.561
      ├── Some((7, 4)): 8/22 ≈ 0.364
      ├── Some((7, 6)): 15/31 ≈ 0.484
      ├── Some((7, 7)): 18/35 ≈ 0.514
      └── Some((7, 8)): 29/48 ≈ 0.604
    └── Some((5, 8)): 127/249 ≈ 0.510
      ├── Some((8, 0)): 10/23 ≈ 0.435
      ├── Some((8, 1)): 15/29 ≈ 0.517
      ├── Some((8, 2)): 14/28 ≈ 0.500
      ├── Some((8, 3)): 23/38 ≈ 0.605
      ├── Some((8, 4)): 10/23 ≈ 0.435
      ├── Some((8, 5)): 11/24 ≈ 0.458
      ├── Some((8, 6)): 13/26 ≈ 0.500
      ├── Some((8, 7)): 10/23 ≈ 0.435
      └── Some((8, 8)): 20/34 ≈ 0.588
  ├── Some((7, 6)): 1516/2838 ≈ 0.534
    ├── Some((6, 0)): 122/244 ≈ 0.500
      ├── Some((0, 0)): 24/39 ≈ 0.615
      ├── Some((0, 1)): 16/30 ≈ 0.533
      ├── Some((0, 2)): 8/20 ≈ 0.400
      ├── Some((0, 3)): 17/31 ≈ 0.548
      ├── Some((0, 4)): 13/27 ≈ 0.481
      ├── Some((0, 5)): 13/27 ≈ 0.481
      ├── Some((0, 6)): 15/29 ≈ 0.517
      ├── Some((0, 7)): 6/18 ≈ 0.333
      └── Some((0, 8)): 9/22 ≈ 0.409
    ├── Some((6, 1)): 211/380 ≈ 0.555
      ├── Some((1, 0)): 29/49 ≈ 0.592
      ├── Some((1, 1)): 17/35 ≈ 0.486
      ├── Some((1, 2)): 18/36 ≈ 0.500
      ├── Some((1, 3)): 25/44 ≈ 0.568
      ├── Some((1, 4)): 28/48 ≈ 0.583
      ├── Some((1, 5)): 15/32 ≈ 0.469
      ├── Some((1, 6)): 9/24 ≈ 0.375
      ├── Some((1, 7)): 36/57 ≈ 0.632
      └── Some((1, 8)): 33/54 ≈ 0.611
    ├── Some((6, 2)): 208/376 ≈ 0.553
      ├── Some((2, 0)): 18/36 ≈ 0.500
      ├── Some((2, 1)): 19/37 ≈ 0.514
      ├── Some((2, 2)): 25/44 ≈ 0.568
      ├── Some((2, 3)): 31/51 ≈ 0.608
      ├── Some((2, 4)): 19/37 ≈ 0.514
      ├── Some((2, 5)): 25/44 ≈ 0.568
      ├── Some((2, 6)): 31/51 ≈ 0.608
      ├── Some((2, 7)): 20/38 ≈ 0.526
      └── Some((2, 8)): 19/37 ≈ 0.514
    ├── Some((6, 3)): 114/231 ≈ 0.494
      ├── Some((3, 0)): 14/27 ≈ 0.519
      ├── Some((3, 1)): 8/20 ≈ 0.400
      ├── Some((3, 2)): 20/34 ≈ 0.588
      ├── Some((3, 3)): 8/20 ≈ 0.400
      ├── Some((3, 4)): 13/26 ≈ 0.500
      ├── Some((3, 5)): 8/20 ≈ 0.400
      ├── Some((3, 6)): 17/31 ≈ 0.548
      ├── Some((3, 7)): 9/22 ≈ 0.409
      └── Some((3, 8)): 16/30 ≈ 0.533
    ├── Some((6, 4)): 174/324 ≈ 0.537
      ├── Some((4, 0)): 13/30 ≈ 0.433
      ├── Some((4, 1)): 18/36 ≈ 0.500
      ├── Some((4, 2)): 37/59 ≈ 0.627
      ├── Some((4, 3)): 25/45 ≈ 0.556
      ├── Some((4, 4)): 20/38 ≈ 0.526
      ├── Some((4, 5)): 12/28 ≈ 0.429
      ├── Some((4, 6)): 22/41 ≈ 0.537
      └── Some((4, 8)): 26/46 ≈ 0.565
    ├── Some((6, 5)): 126/250 ≈ 0.504
      ├── Some((5, 0)): 23/38 ≈ 0.605
      ├── Some((5, 1)): 12/26 ≈ 0.462
      ├── Some((5, 2)): 16/30 ≈ 0.533
      ├── Some((5, 3)): 12/26 ≈ 0.462
      ├── Some((5, 4)): 4/15 ≈ 0.267
      ├── Some((5, 5)): 14/28 ≈ 0.500
      ├── Some((5, 6)): 16/30 ≈ 0.533
      ├── Some((5, 7)): 8/21 ≈ 0.381
      └── Some((5, 8)): 20/35 ≈ 0.571
    ├── Some((6, 6)): 196/358 ≈ 0.547
      ├── Some((6, 0)): 18/37 ≈ 0.486
      ├── Some((6, 1)): 23/43 ≈ 0.535
      ├── Some((6, 2)): 34/56 ≈ 0.607
      ├── Some((6, 3)): 20/39 ≈ 0.513
      ├── Some((6, 4)): 20/39 ≈ 0.513
      ├── Some((6, 5)): 27/47 ≈ 0.574
      ├── Some((6, 7)): 27/48 ≈ 0.562
      └── Some((6, 8)): 27/48 ≈ 0.562
    ├── Some((6, 7)): 184/340 ≈ 0.541
      ├── Some((7, 0)): 22/41 ≈ 0.537
      ├── Some((7, 1)): 18/37 ≈ 0.486
      ├── Some((7, 2)): 45/68 ≈ 0.662
      ├── Some((7, 3)): 25/45 ≈ 0.556
      ├── Some((7, 4)): 21/40 ≈ 0.525
      ├── Some((7, 5)): 15/33 ≈ 0.455
      ├── Some((7, 7)): 13/30 ≈ 0.433
      └── Some((7, 8)): 25/45 ≈ 0.556
    └── Some((6, 8)): 180/334 ≈ 0.539
      ├── Some((8, 0)): 13/29 ≈ 0.448
      ├── Some((8, 1)): 21/38 ≈ 0.553
      ├── Some((8, 2)): 30/49 ≈ 0.612
      ├── Some((8, 3)): 23/41 ≈ 0.561
      ├── Some((8, 4)): 10/25 ≈ 0.400
      ├── Some((8, 5)): 15/31 ≈ 0.484
      ├── Some((8, 6)): 26/44 ≈ 0.591
      ├── Some((8, 7)): 20/37 ≈ 0.541
      └── Some((8, 8)): 21/39 ≈ 0.538
  ├── Some((7, 7)): 1573/2936 ≈ 0.536
    ├── Some((7, 0)): 222/408 ≈ 0.544
      ├── Some((0, 0)): 18/37 ≈ 0.486
      ├── Some((0, 1)): 25/46 ≈ 0.543
      ├── Some((0, 2)): 23/43 ≈ 0.535
      ├── Some((0, 3)): 24/45 ≈ 0.533
      ├── Some((0, 4)): 21/41 ≈ 0.512
      ├── Some((0, 5)): 6/21 ≈ 0.286
      ├── Some((0, 6)): 30/52 ≈ 0.577
      ├── Some((0, 7)): 33/56 ≈ 0.589
      └── Some((0, 8)): 42/66 ≈ 0.636
    ├── Some((7, 1)): 73/170 ≈ 0.429
      ├── Some((1, 0)): 8/19 ≈ 0.421
      ├── Some((1, 1)): 7/18 ≈ 0.389
      ├── Some((1, 2)): 3/12 ≈ 0.250
      ├── Some((1, 3)): 12/23 ≈ 0.522
      ├── Some((1, 4)): 14/26 ≈ 0.538
      ├── Some((1, 5)): 10/21 ≈ 0.476
      ├── Some((1, 6)): 3/12 ≈ 0.250
      ├── Some((1, 7)): 7/18 ≈ 0.389
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((7, 2)): 141/282 ≈ 0.500
      ├── Some((2, 0)): 19/35 ≈ 0.543
      ├── Some((2, 1)): 17/33 ≈ 0.515
      ├── Some((2, 2)): 10/24 ≈ 0.417
      ├── Some((2, 3)): 21/38 ≈ 0.553
      ├── Some((2, 4)): 7/21 ≈ 0.333
      ├── Some((2, 5)): 11/26 ≈ 0.423
      ├── Some((2, 6)): 15/31 ≈ 0.484
      ├── Some((2, 7)): 17/33 ≈ 0.515
      └── Some((2, 8)): 23/40 ≈ 0.575
    ├── Some((7, 3)): 117/243 ≈ 0.481
      ├── Some((3, 0)): 27/44 ≈ 0.614
      ├── Some((3, 1)): 6/18 ≈ 0.333
      ├── Some((3, 2)): 23/39 ≈ 0.590
      ├── Some((3, 3)): 5/17 ≈ 0.294
      ├── Some((3, 4)): 4/16 ≈ 0.250
      ├── Some((3, 5)): 16/31 ≈ 0.516
      ├── Some((3, 6)): 19/34 ≈ 0.559
      ├── Some((3, 7)): 11/25 ≈ 0.440
      └── Some((3, 8)): 6/18 ≈ 0.333
    ├── Some((7, 4)): 269/480 ≈ 0.560
      ├── Some((4, 0)): 39/67 ≈ 0.582
      ├── Some((4, 1)): 52/82 ≈ 0.634
      ├── Some((4, 2)): 47/77 ≈ 0.610
      ├── Some((4, 3)): 25/49 ≈ 0.510
      ├── Some((4, 4)): 16/37 ≈ 0.432
      ├── Some((4, 5)): 35/62 ≈ 0.565
      ├── Some((4, 6)): 27/52 ≈ 0.519
      └── Some((4, 8)): 28/53 ≈ 0.528
    ├── Some((7, 5)): 300/527 ≈ 0.569
      ├── Some((5, 0)): 21/43 ≈ 0.488
      ├── Some((5, 1)): 35/61 ≈ 0.574
      ├── Some((5, 2)): 32/57 ≈ 0.561
      ├── Some((5, 3)): 44/71 ≈ 0.620
      ├── Some((5, 4)): 40/67 ≈ 0.597
      ├── Some((5, 5)): 22/44 ≈ 0.500
      ├── Some((5, 6)): 44/71 ≈ 0.620
      ├── Some((5, 7)): 31/56 ≈ 0.554
      └── Some((5, 8)): 31/56 ≈ 0.554
    ├── Some((7, 6)): 198/371 ≈ 0.534
      ├── Some((6, 0)): 31/52 ≈ 0.596
      ├── Some((6, 1)): 16/34 ≈ 0.471
      ├── Some((6, 2)): 21/40 ≈ 0.525
      ├── Some((6, 3)): 18/36 ≈ 0.500
      ├── Some((6, 4)): 40/62 ≈ 0.645
      ├── Some((6, 5)): 24/44 ≈ 0.545
      ├── Some((6, 6)): 12/29 ≈ 0.414
      ├── Some((6, 7)): 13/30 ≈ 0.433
      └── Some((6, 8)): 23/43 ≈ 0.535
    └── Some((7, 8)): 252/454 ≈ 0.555
      ├── Some((8, 0)): 35/59 ≈ 0.593
      ├── Some((8, 1)): 38/62 ≈ 0.613
      ├── Some((8, 2)): 33/57 ≈ 0.579
      ├── Some((8, 3)): 15/34 ≈ 0.441
      ├── Some((8, 4)): 38/62 ≈ 0.613
      ├── Some((8, 5)): 30/53 ≈ 0.566
      ├── Some((8, 6)): 20/41 ≈ 0.488
      ├── Some((8, 7)): 18/38 ≈ 0.474
      └── Some((8, 8)): 25/47 ≈ 0.532
  └── Some((7, 8)): 1311/2483 ≈ 0.528
    ├── Some((8, 0)): 137/263 ≈ 0.521
      ├── Some((0, 0)): 21/36 ≈ 0.583
      ├── Some((0, 1)): 7/19 ≈ 0.368
      ├── Some((0, 2)): 22/37 ≈ 0.595
      ├── Some((0, 3)): 17/32 ≈ 0.531
      ├── Some((0, 4)): 16/30 ≈ 0.533
      ├── Some((0, 5)): 19/34 ≈ 0.559
      ├── Some((0, 6)): 4/15 ≈ 0.267
      ├── Some((0, 7)): 18/33 ≈ 0.545
      └── Some((0, 8)): 12/26 ≈ 0.462
    ├── Some((8, 1)): 152/286 ≈ 0.531
      ├── Some((1, 0)): 19/34 ≈ 0.559
      ├── Some((1, 1)): 6/19 ≈ 0.316
      ├── Some((1, 2)): 11/25 ≈ 0.440
      ├── Some((1, 3)): 23/39 ≈ 0.590
      ├── Some((1, 4)): 11/25 ≈ 0.440
      ├── Some((1, 5)): 28/45 ≈ 0.622
      ├── Some((1, 6)): 17/32 ≈ 0.531
      ├── Some((1, 7)): 18/33 ≈ 0.545
      └── Some((1, 8)): 18/33 ≈ 0.545
    ├── Some((8, 2)): 86/184 ≈ 0.467
      ├── Some((2, 0)): 16/28 ≈ 0.571
      ├── Some((2, 1)): 6/16 ≈ 0.375
      ├── Some((2, 2)): 13/25 ≈ 0.520
      ├── Some((2, 3)): 16/28 ≈ 0.571
      ├── Some((2, 4)): 6/16 ≈ 0.375
      ├── Some((2, 5)): 6/17 ≈ 0.353
      ├── Some((2, 6)): 12/24 ≈ 0.500
      ├── Some((2, 7)): 0/8 ≈ 0.000
      └── Some((2, 8)): 10/21 ≈ 0.476
    ├── Some((8, 3)): 226/397 ≈ 0.569
      ├── Some((3, 0)): 12/28 ≈ 0.429
      ├── Some((3, 1)): 35/56 ≈ 0.625
      ├── Some((3, 2)): 17/35 ≈ 0.486
      ├── Some((3, 3)): 45/67 ≈ 0.672
      ├── Some((3, 4)): 19/37 ≈ 0.514
      ├── Some((3, 5)): 22/41 ≈ 0.537
      ├── Some((3, 6)): 15/32 ≈ 0.469
      ├── Some((3, 7)): 31/51 ≈ 0.608
      └── Some((3, 8)): 29/49 ≈ 0.592
    ├── Some((8, 4)): 112/225 ≈ 0.498
      ├── Some((4, 0)): 10/23 ≈ 0.435
      ├── Some((4, 1)): 9/22 ≈ 0.409
      ├── Some((4, 2)): 11/25 ≈ 0.440
      ├── Some((4, 3)): 10/24 ≈ 0.417
      ├── Some((4, 4)): 7/20 ≈ 0.350
      ├── Some((4, 5)): 25/41 ≈ 0.610
      ├── Some((4, 6)): 27/43 ≈ 0.628
      └── Some((4, 8)): 12/26 ≈ 0.462
    ├── Some((8, 5)): 110/221 ≈ 0.498
      ├── Some((5, 0)): 9/21 ≈ 0.429
      ├── Some((5, 1)): 19/32 ≈ 0.594
      ├── Some((5, 2)): 14/27 ≈ 0.519
      ├── Some((5, 3)): 3/13 ≈ 0.231
      ├── Some((5, 4)): 15/28 ≈ 0.536
      ├── Some((5, 5)): 6/17 ≈ 0.353
      ├── Some((5, 6)): 17/30 ≈ 0.567
      ├── Some((5, 7)): 13/26 ≈ 0.500
      └── Some((5, 8)): 13/26 ≈ 0.500
    ├── Some((8, 6)): 134/259 ≈ 0.517
      ├── Some((6, 0)): 23/38 ≈ 0.605
      ├── Some((6, 1)): 27/43 ≈ 0.628
      ├── Some((6, 2)): 26/42 ≈ 0.619
      ├── Some((6, 3)): 22/37 ≈ 0.595
      ├── Some((6, 4)): 9/22 ≈ 0.409
      ├── Some((6, 5)): 9/22 ≈ 0.409
      ├── Some((6, 6)): 6/18 ≈ 0.333
      ├── Some((6, 7)): 7/20 ≈ 0.350
      └── Some((6, 8)): 4/16 ≈ 0.250
    ├── Some((8, 7)): 141/269 ≈ 0.524
      ├── Some((7, 0)): 14/29 ≈ 0.483
      ├── Some((7, 1)): 14/30 ≈ 0.467
      ├── Some((7, 2)): 15/31 ≈ 0.484
      ├── Some((7, 3)): 37/56 ≈ 0.661
      ├── Some((7, 4)): 8/22 ≈ 0.364
      ├── Some((7, 5)): 17/33 ≈ 0.515
      ├── Some((7, 6)): 13/28 ≈ 0.464
      └── Some((7, 7)): 22/39 ≈ 0.564
    └── Some((8, 8)): 213/378 ≈ 0.563
      ├── Some((8, 0)): 34/56 ≈ 0.607
      ├── Some((8, 1)): 34/56 ≈ 0.607
      ├── Some((8, 2)): 21/41 ≈ 0.512
      ├── Some((8, 3)): 25/46 ≈ 0.543
      ├── Some((8, 4)): 30/51 ≈ 0.588
      ├── Some((8, 5)): 19/38 ≈ 0.500
      ├── Some((8, 6)): 15/33 ≈ 0.455
      └── Some((8, 7)): 34/56 ≈ 0.607
├── Some((4, 8)): 40614/73811 ≈ 0.550
  ├── Some((8, 0)): 4661/8463 ≈ 0.551
    ├── Some((0, 0)): 589/1056 ≈ 0.558
      ├── Some((0, 1)): 99/167 ≈ 0.593
      ├── Some((0, 2)): 75/134 ≈ 0.560
      ├── Some((0, 3)): 52/102 ≈ 0.510
      ├── Some((0, 4)): 78/139 ≈ 0.561
      ├── Some((0, 5)): 35/78 ≈ 0.449
      ├── Some((0, 6)): 117/191 ≈ 0.613
      ├── Some((0, 7)): 65/121 ≈ 0.537
      └── Some((0, 8)): 67/123 ≈ 0.545
    ├── Some((0, 1)): 431/802 ≈ 0.537
      ├── Some((1, 0)): 38/76 ≈ 0.500
      ├── Some((1, 1)): 55/99 ≈ 0.556
      ├── Some((1, 2)): 64/111 ≈ 0.577
      ├── Some((1, 3)): 50/92 ≈ 0.543
      ├── Some((1, 4)): 9/34 ≈ 0.265
      ├── Some((1, 5)): 52/95 ≈ 0.547
      ├── Some((1, 6)): 50/92 ≈ 0.543
      ├── Some((1, 7)): 66/114 ≈ 0.579
      └── Some((1, 8)): 47/88 ≈ 0.534
    ├── Some((0, 2)): 526/956 ≈ 0.550
      ├── Some((2, 0)): 93/152 ≈ 0.612
      ├── Some((2, 1)): 80/135 ≈ 0.593
      ├── Some((2, 2)): 47/91 ≈ 0.516
      ├── Some((2, 3)): 82/138 ≈ 0.594
      ├── Some((2, 4)): 40/81 ≈ 0.494
      ├── Some((2, 5)): 60/109 ≈ 0.550
      ├── Some((2, 6)): 43/86 ≈ 0.500
      ├── Some((2, 7)): 43/86 ≈ 0.500
      └── Some((2, 8)): 37/77 ≈ 0.481
    ├── Some((0, 3)): 874/1506 ≈ 0.580
      ├── Some((3, 0)): 98/169 ≈ 0.580
      ├── Some((3, 1)): 100/172 ≈ 0.581
      ├── Some((3, 2)): 129/210 ≈ 0.614
      ├── Some((3, 3)): 87/154 ≈ 0.565
      ├── Some((3, 4)): 125/205 ≈ 0.610
      ├── Some((3, 5)): 60/116 ≈ 0.517
      ├── Some((3, 6)): 137/221 ≈ 0.620
      ├── Some((3, 7)): 70/130 ≈ 0.538
      └── Some((3, 8)): 68/128 ≈ 0.531
    ├── Some((0, 4)): 277/550 ≈ 0.504
      ├── Some((4, 0)): 54/95 ≈ 0.568
      ├── Some((4, 1)): 29/61 ≈ 0.475
      ├── Some((4, 2)): 22/52 ≈ 0.423
      ├── Some((4, 3)): 49/88 ≈ 0.557
      ├── Some((4, 4)): 37/72 ≈ 0.514
      ├── Some((4, 5)): 28/60 ≈ 0.467
      ├── Some((4, 6)): 13/38 ≈ 0.342
      └── Some((4, 7)): 45/83 ≈ 0.542
    ├── Some((0, 5)): 601/1075 ≈ 0.559
      ├── Some((5, 0)): 103/168 ≈ 0.613
      ├── Some((5, 1)): 77/134 ≈ 0.575
      ├── Some((5, 2)): 36/77 ≈ 0.468
      ├── Some((5, 3)): 62/114 ≈ 0.544
      ├── Some((5, 4)): 107/173 ≈ 0.618
      ├── Some((5, 5)): 51/99 ≈ 0.515
      ├── Some((5, 6)): 81/139 ≈ 0.583
      ├── Some((5, 7)): 67/121 ≈ 0.554
      └── Some((5, 8)): 17/49 ≈ 0.347
    ├── Some((0, 6)): 360/687 ≈ 0.524
      ├── Some((6, 0)): 28/60 ≈ 0.467
      ├── Some((6, 1)): 53/94 ≈ 0.564
      ├── Some((6, 2)): 34/68 ≈ 0.500
      ├── Some((6, 3)): 54/95 ≈ 0.568
      ├── Some((6, 4)): 43/81 ≈ 0.531
      ├── Some((6, 5)): 26/57 ≈ 0.456
      ├── Some((6, 6)): 31/64 ≈ 0.484
      ├── Some((6, 7)): 51/91 ≈ 0.560
      └── Some((6, 8)): 40/76 ≈ 0.526
    ├── Some((0, 7)): 514/936 ≈ 0.549
      ├── Some((7, 0)): 45/88 ≈ 0.511
      ├── Some((7, 1)): 79/133 ≈ 0.594
      ├── Some((7, 2)): 34/73 ≈ 0.466
      ├── Some((7, 3)): 45/88 ≈ 0.511
      ├── Some((7, 4)): 37/77 ≈ 0.481
      ├── Some((7, 5)): 96/156 ≈ 0.615
      ├── Some((7, 6)): 48/92 ≈ 0.522
      ├── Some((7, 7)): 89/147 ≈ 0.605
      └── Some((7, 8)): 40/81 ≈ 0.494
    └── Some((0, 8)): 488/894 ≈ 0.546
      ├── Some((8, 1)): 64/116 ≈ 0.552
      ├── Some((8, 2)): 43/87 ≈ 0.494
      ├── Some((8, 3)): 65/117 ≈ 0.556
      ├── Some((8, 4)): 87/147 ≈ 0.592
      ├── Some((8, 5)): 39/81 ≈ 0.481
      ├── Some((8, 6)): 77/133 ≈ 0.579
      ├── Some((8, 7)): 47/93 ≈ 0.505
      └── Some((8, 8)): 66/119 ≈ 0.555
  ├── Some((8, 1)): 3543/6523 ≈ 0.543
    ├── Some((1, 0)): 448/813 ≈ 0.551
      ├── Some((0, 0)): 57/100 ≈ 0.570
      ├── Some((0, 1)): 56/99 ≈ 0.566
      ├── Some((0, 2)): 42/80 ≈ 0.525
      ├── Some((0, 3)): 58/101 ≈ 0.574
      ├── Some((0, 4)): 45/84 ≈ 0.536
      ├── Some((0, 5)): 61/105 ≈ 0.581
      ├── Some((0, 6)): 57/100 ≈ 0.570
      ├── Some((0, 7)): 33/68 ≈ 0.485
      └── Some((0, 8)): 38/75 ≈ 0.507
    ├── Some((1, 1)): 714/1230 ≈ 0.580
      ├── Some((1, 0)): 88/152 ≈ 0.579
      ├── Some((1, 2)): 95/162 ≈ 0.586
      ├── Some((1, 3)): 85/148 ≈ 0.574
      ├── Some((1, 4)): 76/136 ≈ 0.559
      ├── Some((1, 5)): 104/174 ≈ 0.598
      ├── Some((1, 6)): 63/118 ≈ 0.534
      ├── Some((1, 7)): 116/189 ≈ 0.614
      └── Some((1, 8)): 86/150 ≈ 0.573
    ├── Some((1, 2)): 357/668 ≈ 0.534
      ├── Some((2, 0)): 37/71 ≈ 0.521
      ├── Some((2, 1)): 27/57 ≈ 0.474
      ├── Some((2, 2)): 36/70 ≈ 0.514
      ├── Some((2, 3)): 39/73 ≈ 0.534
      ├── Some((2, 4)): 38/72 ≈ 0.528
      ├── Some((2, 5)): 36/70 ≈ 0.514
      ├── Some((2, 6)): 65/107 ≈ 0.607
      ├── Some((2, 7)): 25/55 ≈ 0.455
      └── Some((2, 8)): 53/92 ≈ 0.576
    ├── Some((1, 3)): 308/588 ≈ 0.524
      ├── Some((3, 0)): 15/39 ≈ 0.385
      ├── Some((3, 1)): 24/52 ≈ 0.462
      ├── Some((3, 2)): 29/59 ≈ 0.492
      ├── Some((3, 3)): 38/71 ≈ 0.535
      ├── Some((3, 4)): 14/38 ≈ 0.368
      ├── Some((3, 5)): 37/70 ≈ 0.529
      ├── Some((3, 6)): 40/73 ≈ 0.548
      ├── Some((3, 7)): 66/106 ≈ 0.623
      └── Some((3, 8)): 44/79 ≈ 0.557
    ├── Some((1, 4)): 412/756 ≈ 0.545
      ├── Some((4, 0)): 45/86 ≈ 0.523
      ├── Some((4, 1)): 68/116 ≈ 0.586
      ├── Some((4, 2)): 29/64 ≈ 0.453
      ├── Some((4, 3)): 68/117 ≈ 0.581
      ├── Some((4, 4)): 61/107 ≈ 0.570
      ├── Some((4, 5)): 37/75 ≈ 0.493
      ├── Some((4, 6)): 37/75 ≈ 0.493
      └── Some((4, 7)): 67/115 ≈ 0.583
    ├── Some((1, 5)): 292/562 ≈ 0.520
      ├── Some((5, 0)): 32/63 ≈ 0.508
      ├── Some((5, 1)): 55/92 ≈ 0.598
      ├── Some((5, 2)): 47/82 ≈ 0.573
      ├── Some((5, 3)): 41/74 ≈ 0.554
      ├── Some((5, 4)): 6/25 ≈ 0.240
      ├── Some((5, 5)): 29/59 ≈ 0.492
      ├── Some((5, 6)): 18/43 ≈ 0.419
      ├── Some((5, 7)): 28/57 ≈ 0.491
      └── Some((5, 8)): 35/66 ≈ 0.530
    ├── Some((1, 6)): 273/531 ≈ 0.514
      ├── Some((6, 0)): 57/93 ≈ 0.613
      ├── Some((6, 1)): 16/40 ≈ 0.400
      ├── Some((6, 2)): 44/77 ≈ 0.571
      ├── Some((6, 3)): 17/41 ≈ 0.415
      ├── Some((6, 4)): 28/56 ≈ 0.500
      ├── Some((6, 5)): 29/58 ≈ 0.500
      ├── Some((6, 6)): 26/54 ≈ 0.481
      ├── Some((6, 7)): 17/41 ≈ 0.415
      └── Some((6, 8)): 38/70 ≈ 0.543
    ├── Some((1, 7)): 321/609 ≈ 0.527
      ├── Some((7, 0)): 26/55 ≈ 0.473
      ├── Some((7, 1)): 23/51 ≈ 0.451
      ├── Some((7, 2)): 39/72 ≈ 0.542
      ├── Some((7, 3)): 57/95 ≈ 0.600
      ├── Some((7, 4)): 31/62 ≈ 0.500
      ├── Some((7, 5)): 46/81 ≈ 0.568
      ├── Some((7, 6)): 36/69 ≈ 0.522
      ├── Some((7, 7)): 47/83 ≈ 0.566
      └── Some((7, 8)): 15/40 ≈ 0.375
    └── Some((1, 8)): 418/765 ≈ 0.546
      ├── Some((8, 0)): 55/100 ≈ 0.550
      ├── Some((8, 2)): 41/81 ≈ 0.506
      ├── Some((8, 3)): 56/101 ≈ 0.554
      ├── Some((8, 4)): 58/103 ≈ 0.563
      ├── Some((8, 5)): 61/107 ≈ 0.570
      ├── Some((8, 6)): 46/87 ≈ 0.529
      ├── Some((8, 7)): 58/103 ≈ 0.563
      └── Some((8, 8)): 42/82 ≈ 0.512
  ├── Some((8, 2)): 5390/9723 ≈ 0.554
    ├── Some((2, 0)): 741/1308 ≈ 0.567
      ├── Some((0, 0)): 64/120 ≈ 0.533
      ├── Some((0, 1)): 94/161 ≈ 0.584
      ├── Some((0, 2)): 82/145 ≈ 0.566
      ├── Some((0, 3)): 86/151 ≈ 0.570
      ├── Some((0, 4)): 105/176 ≈ 0.597
      ├── Some((0, 5)): 88/153 ≈ 0.575
      ├── Some((0, 6)): 71/130 ≈ 0.546
      ├── Some((0, 7)): 79/141 ≈ 0.560
      └── Some((0, 8)): 71/130 ≈ 0.546
    ├── Some((2, 1)): 716/1268 ≈ 0.565
      ├── Some((1, 0)): 36/80 ≈ 0.450
      ├── Some((1, 1)): 89/154 ≈ 0.578
      ├── Some((1, 2)): 50/100 ≈ 0.500
      ├── Some((1, 3)): 81/143 ≈ 0.566
      ├── Some((1, 4)): 103/173 ≈ 0.595
      ├── Some((1, 5)): 103/173 ≈ 0.595
      ├── Some((1, 6)): 66/123 ≈ 0.537
      ├── Some((1, 7)): 87/152 ≈ 0.572
      └── Some((1, 8)): 100/169 ≈ 0.592
    ├── Some((2, 2)): 425/800 ≈ 0.531
      ├── Some((2, 0)): 78/134 ≈ 0.582
      ├── Some((2, 1)): 46/90 ≈ 0.511
      ├── Some((2, 3)): 65/117 ≈ 0.556
      ├── Some((2, 4)): 48/93 ≈ 0.516
      ├── Some((2, 5)): 51/97 ≈ 0.526
      ├── Some((2, 6)): 33/72 ≈ 0.458
      ├── Some((2, 7)): 35/75 ≈ 0.467
      └── Some((2, 8)): 68/121 ≈ 0.562
    ├── Some((2, 3)): 561/1020 ≈ 0.550
      ├── Some((3, 0)): 61/112 ≈ 0.545
      ├── Some((3, 1)): 42/85 ≈ 0.494
      ├── Some((3, 2)): 48/94 ≈ 0.511
      ├── Some((3, 3)): 77/133 ≈ 0.579
      ├── Some((3, 4)): 42/85 ≈ 0.494
      ├── Some((3, 5)): 80/137 ≈ 0.584
      ├── Some((3, 6)): 78/135 ≈ 0.578
      ├── Some((3, 7)): 65/117 ≈ 0.556
      └── Some((3, 8)): 68/121 ≈ 0.562
    ├── Some((2, 4)): 701/1245 ≈ 0.563
      ├── Some((4, 0)): 61/119 ≈ 0.513
      ├── Some((4, 1)): 65/124 ≈ 0.524
      ├── Some((4, 2)): 69/130 ≈ 0.531
      ├── Some((4, 3)): 93/163 ≈ 0.571
      ├── Some((4, 4)): 116/195 ≈ 0.595
      ├── Some((4, 5)): 123/204 ≈ 0.603
      ├── Some((4, 6)): 87/155 ≈ 0.561
      └── Some((4, 7)): 86/154 ≈ 0.558
    ├── Some((2, 5)): 441/826 ≈ 0.534
      ├── Some((5, 0)): 45/86 ≈ 0.523
      ├── Some((5, 1)): 54/99 ≈ 0.545
      ├── Some((5, 2)): 67/116 ≈ 0.578
      ├── Some((5, 3)): 27/61 ≈ 0.443
      ├── Some((5, 4)): 49/92 ≈ 0.533
      ├── Some((5, 5)): 60/107 ≈ 0.561
      ├── Some((5, 6)): 50/93 ≈ 0.538
      ├── Some((5, 7)): 55/100 ≈ 0.550
      └── Some((5, 8)): 34/71 ≈ 0.479
    ├── Some((2, 6)): 650/1163 ≈ 0.559
      ├── Some((6, 0)): 20/55 ≈ 0.364
      ├── Some((6, 1)): 93/158 ≈ 0.589
      ├── Some((6, 2)): 100/167 ≈ 0.599
      ├── Some((6, 3)): 93/158 ≈ 0.589
      ├── Some((6, 4)): 63/117 ≈ 0.538
      ├── Some((6, 5)): 69/125 ≈ 0.552
      ├── Some((6, 6)): 69/126 ≈ 0.548
      ├── Some((6, 7)): 54/105 ≈ 0.514
      └── Some((6, 8)): 88/151 ≈ 0.583
    ├── Some((2, 7)): 584/1057 ≈ 0.553
      ├── Some((7, 0)): 96/159 ≈ 0.604
      ├── Some((7, 1)): 51/99 ≈ 0.515
      ├── Some((7, 2)): 52/100 ≈ 0.520
      ├── Some((7, 3)): 87/147 ≈ 0.592
      ├── Some((7, 4)): 61/113 ≈ 0.540
      ├── Some((7, 5)): 87/147 ≈ 0.592
      ├── Some((7, 6)): 68/122 ≈ 0.557
      ├── Some((7, 7)): 47/93 ≈ 0.505
      └── Some((7, 8)): 35/76 ≈ 0.461
    └── Some((2, 8)): 570/1035 ≈ 0.551
      ├── Some((8, 0)): 82/144 ≈ 0.569
      ├── Some((8, 1)): 81/143 ≈ 0.566
      ├── Some((8, 3)): 45/93 ≈ 0.484
      ├── Some((8, 4)): 94/161 ≈ 0.584
      ├── Some((8, 5)): 73/132 ≈ 0.553
      ├── Some((8, 6)): 78/139 ≈ 0.561
      ├── Some((8, 7)): 68/125 ≈ 0.544
      └── Some((8, 8)): 48/97 ≈ 0.495
  ├── Some((8, 3)): 3093/5738 ≈ 0.539
    ├── Some((3, 0)): 410/743 ≈ 0.552
      ├── Some((0, 0)): 28/59 ≈ 0.475
      ├── Some((0, 1)): 17/44 ≈ 0.386
      ├── Some((0, 2)): 56/96 ≈ 0.583
      ├── Some((0, 3)): 60/101 ≈ 0.594
      ├── Some((0, 4)): 53/93 ≈ 0.570
      ├── Some((0, 5)): 37/72 ≈ 0.514
      ├── Some((0, 6)): 59/100 ≈ 0.590
      ├── Some((0, 7)): 42/78 ≈ 0.538
      └── Some((0, 8)): 58/99 ≈ 0.586
    ├── Some((3, 1)): 335/624 ≈ 0.537
      ├── Some((1, 0)): 51/87 ≈ 0.586
      ├── Some((1, 1)): 46/81 ≈ 0.568
      ├── Some((1, 2)): 25/53 ≈ 0.472
      ├── Some((1, 3)): 43/77 ≈ 0.558
      ├── Some((1, 4)): 43/77 ≈ 0.558
      ├── Some((1, 5)): 44/78 ≈ 0.564
      ├── Some((1, 6)): 33/64 ≈ 0.516
      ├── Some((1, 7)): 27/56 ≈ 0.482
      └── Some((1, 8)): 23/50 ≈ 0.460
    ├── Some((3, 2)): 319/599 ≈ 0.533
      ├── Some((2, 0)): 48/83 ≈ 0.578
      ├── Some((2, 1)): 16/41 ≈ 0.390
      ├── Some((2, 2)): 26/54 ≈ 0.481
      ├── Some((2, 3)): 45/79 ≈ 0.570
      ├── Some((2, 4)): 26/54 ≈ 0.481
      ├── Some((2, 5)): 39/71 ≈ 0.549
      ├── Some((2, 6)): 39/72 ≈ 0.542
      ├── Some((2, 7)): 32/62 ≈ 0.516
      └── Some((2, 8)): 47/82 ≈ 0.573
    ├── Some((3, 3)): 321/602 ≈ 0.533
      ├── Some((3, 0)): 48/86 ≈ 0.558
      ├── Some((3, 1)): 60/102 ≈ 0.588
      ├── Some((3, 2)): 40/75 ≈ 0.533
      ├── Some((3, 4)): 20/48 ≈ 0.417
      ├── Some((3, 5)): 25/55 ≈ 0.455
      ├── Some((3, 6)): 43/79 ≈ 0.544
      ├── Some((3, 7)): 63/105 ≈ 0.600
      └── Some((3, 8)): 22/51 ≈ 0.431
    ├── Some((3, 4)): 214/428 ≈ 0.500
      ├── Some((4, 0)): 37/67 ≈ 0.552
      ├── Some((4, 1)): 13/35 ≈ 0.371
      ├── Some((4, 2)): 29/57 ≈ 0.509
      ├── Some((4, 3)): 12/34 ≈ 0.353
      ├── Some((4, 4)): 17/41 ≈ 0.415
      ├── Some((4, 5)): 21/46 ≈ 0.457
      ├── Some((4, 6)): 55/90 ≈ 0.611
      └── Some((4, 7)): 29/57 ≈ 0.509
    ├── Some((3, 5)): 336/626 ≈ 0.537
      ├── Some((5, 0)): 29/59 ≈ 0.492
      ├── Some((5, 1)): 34/66 ≈ 0.515
      ├── Some((5, 2)): 43/77 ≈ 0.558
      ├── Some((5, 3)): 51/87 ≈ 0.586
      ├── Some((5, 4)): 34/66 ≈ 0.515
      ├── Some((5, 5)): 54/91 ≈ 0.593
      ├── Some((5, 6)): 41/75 ≈ 0.547
      ├── Some((5, 7)): 12/35 ≈ 0.343
      └── Some((5, 8)): 37/69 ≈ 0.536
    ├── Some((3, 6)): 376/690 ≈ 0.545
      ├── Some((6, 0)): 64/105 ≈ 0.610
      ├── Some((6, 1)): 57/97 ≈ 0.588
      ├── Some((6, 2)): 25/54 ≈ 0.463
      ├── Some((6, 3)): 49/86 ≈ 0.570
      ├── Some((6, 4)): 30/61 ≈ 0.492
      ├── Some((6, 5)): 40/75 ≈ 0.533
      ├── Some((6, 6)): 49/86 ≈ 0.570
      ├── Some((6, 7)): 35/68 ≈ 0.515
      └── Some((6, 8)): 27/57 ≈ 0.474
    ├── Some((3, 7)): 433/780 ≈ 0.555
      ├── Some((7, 0)): 45/83 ≈ 0.542
      ├── Some((7, 1)): 37/72 ≈ 0.514
      ├── Some((7, 2)): 45/83 ≈ 0.542
      ├── Some((7, 3)): 87/137 ≈ 0.635
      ├── Some((7, 4)): 53/93 ≈ 0.570
      ├── Some((7, 5)): 65/109 ≈ 0.596
      ├── Some((7, 6)): 42/79 ≈ 0.532
      ├── Some((7, 7)): 45/83 ≈ 0.542
      └── Some((7, 8)): 14/40 ≈ 0.350
    └── Some((3, 8)): 348/645 ≈ 0.540
      ├── Some((8, 0)): 26/57 ≈ 0.456
      ├── Some((8, 1)): 44/81 ≈ 0.543
      ├── Some((8, 2)): 44/81 ≈ 0.543
      ├── Some((8, 4)): 58/100 ≈ 0.580
      ├── Some((8, 5)): 42/79 ≈ 0.532
      ├── Some((8, 6)): 51/91 ≈ 0.560
      ├── Some((8, 7)): 45/83 ≈ 0.542
      └── Some((8, 8)): 37/72 ≈ 0.514
  ├── Some((8, 4)): 2874/5355 ≈ 0.537
    ├── Some((4, 0)): 387/716 ≈ 0.541
      ├── Some((0, 0)): 71/117 ≈ 0.607
      ├── Some((0, 1)): 34/68 ≈ 0.500
      ├── Some((0, 2)): 21/50 ≈ 0.420
      ├── Some((0, 3)): 16/43 ≈ 0.372
      ├── Some((0, 4)): 44/82 ≈ 0.537
      ├── Some((0, 5)): 37/72 ≈ 0.514
      ├── Some((0, 6)): 80/128 ≈ 0.625
      ├── Some((0, 7)): 23/53 ≈ 0.434
      └── Some((0, 8)): 60/102 ≈ 0.588
    ├── Some((4, 1)): 281/544 ≈ 0.517
      ├── Some((1, 0)): 56/93 ≈ 0.602
      ├── Some((1, 1)): 44/77 ≈ 0.571
      ├── Some((1, 2)): 10/31 ≈ 0.323
      ├── Some((1, 3)): 12/34 ≈ 0.353
      ├── Some((1, 4)): 37/68 ≈ 0.544
      ├── Some((1, 5)): 24/51 ≈ 0.471
      ├── Some((1, 6)): 29/58 ≈ 0.500
      ├── Some((1, 7)): 38/70 ≈ 0.543
      └── Some((1, 8)): 31/61 ≈ 0.508
    ├── Some((4, 2)): 408/749 ≈ 0.545
      ├── Some((2, 0)): 50/90 ≈ 0.556
      ├── Some((2, 1)): 35/70 ≈ 0.500
      ├── Some((2, 2)): 55/97 ≈ 0.567
      ├── Some((2, 3)): 39/75 ≈ 0.520
      ├── Some((2, 4)): 30/63 ≈ 0.476
      ├── Some((2, 5)): 39/75 ≈ 0.520
      ├── Some((2, 6)): 98/151 ≈ 0.649
      ├── Some((2, 7)): 31/64 ≈ 0.484
      └── Some((2, 8)): 30/63 ≈ 0.476
    ├── Some((4, 3)): 229/458 ≈ 0.500
      ├── Some((3, 0)): 28/54 ≈ 0.519
      ├── Some((3, 1)): 41/71 ≈ 0.577
      ├── Some((3, 2)): 14/36 ≈ 0.389
      ├── Some((3, 3)): 34/62 ≈ 0.548
      ├── Some((3, 4)): 17/40 ≈ 0.425
      ├── Some((3, 5)): 19/42 ≈ 0.452
      ├── Some((3, 6)): 34/62 ≈ 0.548
      ├── Some((3, 7)): 20/44 ≈ 0.455
      └── Some((3, 8)): 22/46 ≈ 0.478
    ├── Some((4, 4)): 495/888 ≈ 0.557
      ├── Some((4, 0)): 73/130 ≈ 0.562
      ├── Some((4, 1)): 65/119 ≈ 0.546
      ├── Some((4, 2)): 50/99 ≈ 0.505
      ├── Some((4, 3)): 43/89 ≈ 0.483
      ├── Some((4, 5)): 81/141 ≈ 0.574
      ├── Some((4, 6)): 74/132 ≈ 0.561
      └── Some((4, 7)): 108/177 ≈ 0.610
    ├── Some((4, 5)): 206/420 ≈ 0.490
      ├── Some((5, 0)): 22/46 ≈ 0.478
      ├── Some((5, 1)): 35/62 ≈ 0.565
      ├── Some((5, 2)): 11/31 ≈ 0.355
      ├── Some((5, 3)): 13/34 ≈ 0.382
      ├── Some((5, 4)): 44/74 ≈ 0.595
      ├── Some((5, 5)): 13/34 ≈ 0.382
      ├── Some((5, 6)): 20/43 ≈ 0.465
      ├── Some((5, 7)): 18/40 ≈ 0.450
      └── Some((5, 8)): 29/55 ≈ 0.527
    ├── Some((4, 6)): 356/666 ≈ 0.535
      ├── Some((6, 0)): 38/72 ≈ 0.528
      ├── Some((6, 1)): 41/76 ≈ 0.539
      ├── Some((6, 2)): 37/71 ≈ 0.521
      ├── Some((6, 3)): 54/93 ≈ 0.581
      ├── Some((6, 4)): 47/84 ≈ 0.560
      ├── Some((6, 5)): 33/65 ≈ 0.508
      ├── Some((6, 6)): 26/56 ≈ 0.464
      ├── Some((6, 7)): 46/83 ≈ 0.554
      └── Some((6, 8)): 33/65 ≈ 0.508
    └── Some((4, 7)): 511/913 ≈ 0.560
      ├── Some((7, 0)): 29/64 ≈ 0.453
      ├── Some((7, 1)): 39/78 ≈ 0.500
      ├── Some((7, 2)): 59/105 ≈ 0.562
      ├── Some((7, 3)): 54/98 ≈ 0.551
      ├── Some((7, 4)): 70/119 ≈ 0.588
      ├── Some((7, 5)): 43/83 ≈ 0.518
      ├── Some((7, 6)): 80/132 ≈ 0.606
      ├── Some((7, 7)): 70/119 ≈ 0.588
      └── Some((7, 8)): 66/114 ≈ 0.579
  ├── Some((8, 5)): 6281/11257 ≈ 0.558
    ├── Some((5, 0)): 826/1457 ≈ 0.567
      ├── Some((0, 0)): 96/168 ≈ 0.571
      ├── Some((0, 1)): 80/146 ≈ 0.548
      ├── Some((0, 2)): 68/129 ≈ 0.527
      ├── Some((0, 3)): 153/245 ≈ 0.624
      ├── Some((0, 4)): 105/181 ≈ 0.580
      ├── Some((0, 5)): 137/224 ≈ 0.612
      ├── Some((0, 6)): 51/105 ≈ 0.486
      ├── Some((0, 7)): 53/108 ≈ 0.491
      └── Some((0, 8)): 83/150 ≈ 0.553
    ├── Some((5, 1)): 676/1216 ≈ 0.556
      ├── Some((1, 0)): 62/117 ≈ 0.530
      ├── Some((1, 1)): 75/135 ≈ 0.556
      ├── Some((1, 2)): 75/135 ≈ 0.556
      ├── Some((1, 3)): 87/151 ≈ 0.576
      ├── Some((1, 4)): 57/110 ≈ 0.518
      ├── Some((1, 5)): 93/159 ≈ 0.585
      ├── Some((1, 6)): 88/153 ≈ 0.575
      ├── Some((1, 7)): 74/134 ≈ 0.552
      └── Some((1, 8)): 65/121 ≈ 0.537
    ├── Some((5, 2)): 869/1525 ≈ 0.570
      ├── Some((2, 0)): 135/222 ≈ 0.608
      ├── Some((2, 1)): 76/141 ≈ 0.539
      ├── Some((2, 2)): 96/169 ≈ 0.568
      ├── Some((2, 3)): 131/217 ≈ 0.604
      ├── Some((2, 4)): 71/134 ≈ 0.530
      ├── Some((2, 5)): 91/162 ≈ 0.562
      ├── Some((2, 6)): 101/176 ≈ 0.574
      ├── Some((2, 7)): 62/121 ≈ 0.512
      └── Some((2, 8)): 105/182 ≈ 0.577
    ├── Some((5, 3)): 546/1006 ≈ 0.543
      ├── Some((3, 0)): 56/106 ≈ 0.528
      ├── Some((3, 1)): 39/82 ≈ 0.476
      ├── Some((3, 2)): 34/75 ≈ 0.453
      ├── Some((3, 3)): 93/156 ≈ 0.596
      ├── Some((3, 4)): 102/168 ≈ 0.607
      ├── Some((3, 5)): 79/137 ≈ 0.577
      ├── Some((3, 6)): 59/110 ≈ 0.536
      ├── Some((3, 7)): 34/75 ≈ 0.453
      └── Some((3, 8)): 49/96 ≈ 0.510
    ├── Some((5, 4)): 748/1332 ≈ 0.562
      ├── Some((4, 0)): 90/162 ≈ 0.556
      ├── Some((4, 1)): 86/156 ≈ 0.551
      ├── Some((4, 2)): 85/155 ≈ 0.548
      ├── Some((4, 3)): 89/160 ≈ 0.556
      ├── Some((4, 4)): 73/138 ≈ 0.529
      ├── Some((4, 5)): 93/166 ≈ 0.560
      ├── Some((4, 6)): 83/152 ≈ 0.546
      └── Some((4, 7)): 149/242 ≈ 0.616
    ├── Some((5, 5)): 779/1382 ≈ 0.564
      ├── Some((5, 0)): 92/165 ≈ 0.558
      ├── Some((5, 1)): 146/240 ≈ 0.608
      ├── Some((5, 2)): 78/146 ≈ 0.534
      ├── Some((5, 3)): 106/185 ≈ 0.573
      ├── Some((5, 4)): 95/170 ≈ 0.559
      ├── Some((5, 6)): 93/167 ≈ 0.557
      ├── Some((5, 7)): 75/141 ≈ 0.532
      └── Some((5, 8)): 93/167 ≈ 0.557
    ├── Some((5, 6)): 526/974 ≈ 0.540
      ├── Some((6, 0)): 87/147 ≈ 0.592
      ├── Some((6, 1)): 41/85 ≈ 0.482
      ├── Some((6, 2)): 49/96 ≈ 0.510
      ├── Some((6, 3)): 19/52 ≈ 0.365
      ├── Some((6, 4)): 84/144 ≈ 0.583
      ├── Some((6, 5)): 60/111 ≈ 0.541
      ├── Some((6, 6)): 94/157 ≈ 0.599
      ├── Some((6, 7)): 61/112 ≈ 0.545
      └── Some((6, 8)): 30/69 ≈ 0.435
    ├── Some((5, 7)): 619/1124 ≈ 0.551
      ├── Some((7, 0)): 78/138 ≈ 0.565
      ├── Some((7, 1)): 98/164 ≈ 0.598
      ├── Some((7, 2)): 74/132 ≈ 0.561
      ├── Some((7, 3)): 64/119 ≈ 0.538
      ├── Some((7, 4)): 67/123 ≈ 0.545
      ├── Some((7, 5)): 46/93 ≈ 0.495
      ├── Some((7, 6)): 41/86 ≈ 0.477
      ├── Some((7, 7)): 79/139 ≈ 0.568
      └── Some((7, 8)): 72/129 ≈ 0.558
    └── Some((5, 8)): 691/1240 ≈ 0.557
      ├── Some((8, 0)): 43/94 ≈ 0.457
      ├── Some((8, 1)): 66/127 ≈ 0.520
      ├── Some((8, 2)): 94/166 ≈ 0.566
      ├── Some((8, 3)): 49/102 ≈ 0.480
      ├── Some((8, 4)): 68/130 ≈ 0.523
      ├── Some((8, 6)): 127/212 ≈ 0.599
      ├── Some((8, 7)): 170/269 ≈ 0.632
      └── Some((8, 8)): 74/139 ≈ 0.532
  ├── Some((8, 6)): 4484/8157 ≈ 0.550
    ├── Some((6, 0)): 493/900 ≈ 0.548
      ├── Some((0, 0)): 43/84 ≈ 0.512
      ├── Some((0, 1)): 57/103 ≈ 0.553
      ├── Some((0, 2)): 42/83 ≈ 0.506
      ├── Some((0, 3)): 76/128 ≈ 0.594
      ├── Some((0, 4)): 33/70 ≈ 0.471
      ├── Some((0, 5)): 53/98 ≈ 0.541
      ├── Some((0, 6)): 70/120 ≈ 0.583
      ├── Some((0, 7)): 60/107 ≈ 0.561
      └── Some((0, 8)): 59/106 ≈ 0.557
    ├── Some((6, 1)): 370/702 ≈ 0.527
      ├── Some((1, 0)): 54/95 ≈ 0.568
      ├── Some((1, 1)): 14/40 ≈ 0.350
      ├── Some((1, 2)): 46/85 ≈ 0.541
      ├── Some((1, 3)): 56/98 ≈ 0.571
      ├── Some((1, 4)): 33/67 ≈ 0.493
      ├── Some((1, 5)): 46/85 ≈ 0.541
      ├── Some((1, 6)): 48/87 ≈ 0.552
      ├── Some((1, 7)): 29/62 ≈ 0.468
      └── Some((1, 8)): 44/82 ≈ 0.537
    ├── Some((6, 2)): 725/1269 ≈ 0.571
      ├── Some((2, 0)): 76/135 ≈ 0.563
      ├── Some((2, 1)): 65/120 ≈ 0.542
      ├── Some((2, 2)): 60/113 ≈ 0.531
      ├── Some((2, 3)): 80/141 ≈ 0.567
      ├── Some((2, 4)): 45/92 ≈ 0.489
      ├── Some((2, 5)): 85/147 ≈ 0.578
      ├── Some((2, 6)): 114/186 ≈ 0.613
      ├── Some((2, 7)): 103/171 ≈ 0.602
      └── Some((2, 8)): 97/163 ≈ 0.595
    ├── Some((6, 3)): 262/523 ≈ 0.501
      ├── Some((3, 0)): 31/61 ≈ 0.508
      ├── Some((3, 1)): 33/63 ≈ 0.524
      ├── Some((3, 2)): 23/50 ≈ 0.460
      ├── Some((3, 3)): 30/59 ≈ 0.508
      ├── Some((3, 4)): 31/61 ≈ 0.508
      ├── Some((3, 5)): 10/31 ≈ 0.323
      ├── Some((3, 6)): 34/65 ≈ 0.523
      ├── Some((3, 7)): 41/74 ≈ 0.554
      └── Some((3, 8)): 29/58 ≈ 0.500
    ├── Some((6, 4)): 649/1149 ≈ 0.565
      ├── Some((4, 0)): 63/119 ≈ 0.529
      ├── Some((4, 1)): 65/122 ≈ 0.533
      ├── Some((4, 2)): 112/185 ≈ 0.605
      ├── Some((4, 3)): 58/112 ≈ 0.518
      ├── Some((4, 4)): 111/184 ≈ 0.603
      ├── Some((4, 5)): 71/130 ≈ 0.546
      ├── Some((4, 6)): 87/152 ≈ 0.572
      └── Some((4, 7)): 81/144 ≈ 0.562
    ├── Some((6, 5)): 287/565 ≈ 0.508
      ├── Some((5, 0)): 34/66 ≈ 0.515
      ├── Some((5, 1)): 39/72 ≈ 0.542
      ├── Some((5, 2)): 45/80 ≈ 0.562
      ├── Some((5, 3)): 29/59 ≈ 0.492
      ├── Some((5, 4)): 26/55 ≈ 0.473
      ├── Some((5, 5)): 15/40 ≈ 0.375
      ├── Some((5, 6)): 38/71 ≈ 0.535
      ├── Some((5, 7)): 38/71 ≈ 0.535
      └── Some((5, 8)): 22/50 ≈ 0.440
    ├── Some((6, 6)): 623/1108 ≈ 0.562
      ├── Some((6, 0)): 90/155 ≈ 0.581
      ├── Some((6, 1)): 56/108 ≈ 0.519
      ├── Some((6, 2)): 81/143 ≈ 0.566
      ├── Some((6, 3)): 94/161 ≈ 0.584
      ├── Some((6, 4)): 85/148 ≈ 0.574
      ├── Some((6, 5)): 61/115 ≈ 0.530
      ├── Some((6, 7)): 88/153 ≈ 0.575
      └── Some((6, 8)): 67/124 ≈ 0.540
    ├── Some((6, 7)): 435/807 ≈ 0.539
      ├── Some((7, 0)): 70/118 ≈ 0.593
      ├── Some((7, 1)): 65/112 ≈ 0.580
      ├── Some((7, 2)): 40/79 ≈ 0.506
      ├── Some((7, 3)): 40/79 ≈ 0.506
      ├── Some((7, 4)): 60/105 ≈ 0.571
      ├── Some((7, 5)): 39/77 ≈ 0.506
      ├── Some((7, 6)): 33/69 ≈ 0.478
      ├── Some((7, 7)): 57/102 ≈ 0.559
      └── Some((7, 8)): 30/65 ≈ 0.462
    └── Some((6, 8)): 639/1133 ≈ 0.564
      ├── Some((8, 0)): 68/126 ≈ 0.540
      ├── Some((8, 1)): 71/130 ≈ 0.546
      ├── Some((8, 2)): 95/162 ≈ 0.586
      ├── Some((8, 3)): 116/190 ≈ 0.611
      ├── Some((8, 4)): 100/169 ≈ 0.592
      ├── Some((8, 5)): 66/123 ≈ 0.537
      ├── Some((8, 7)): 58/112 ≈ 0.518
      └── Some((8, 8)): 64/120 ≈ 0.533
  ├── Some((8, 7)): 5720/10291 ≈ 0.556
    ├── Some((7, 0)): 766/1353 ≈ 0.566
      ├── Some((0, 0)): 98/168 ≈ 0.583
      ├── Some((0, 1)): 71/131 ≈ 0.542
      ├── Some((0, 2)): 125/205 ≈ 0.610
      ├── Some((0, 3)): 83/148 ≈ 0.561
      ├── Some((0, 4)): 87/153 ≈ 0.569
      ├── Some((0, 5)): 75/137 ≈ 0.547
      ├── Some((0, 6)): 45/94 ≈ 0.479
      ├── Some((0, 7)): 110/185 ≈ 0.595
      └── Some((0, 8)): 71/131 ≈ 0.542
    ├── Some((7, 1)): 576/1048 ≈ 0.550
      ├── Some((1, 0)): 39/82 ≈ 0.476
      ├── Some((1, 1)): 74/130 ≈ 0.569
      ├── Some((1, 2)): 46/92 ≈ 0.500
      ├── Some((1, 3)): 52/100 ≈ 0.520
      ├── Some((1, 4)): 69/124 ≈ 0.556
      ├── Some((1, 5)): 80/138 ≈ 0.580
      ├── Some((1, 6)): 73/129 ≈ 0.566
      ├── Some((1, 7)): 56/106 ≈ 0.528
      └── Some((1, 8)): 86/146 ≈ 0.589
    ├── Some((7, 2)): 688/1228 ≈ 0.560
      ├── Some((2, 0)): 82/145 ≈ 0.566
      ├── Some((2, 1)): 76/136 ≈ 0.559
      ├── Some((2, 2)): 50/100 ≈ 0.500
      ├── Some((2, 3)): 61/116 ≈ 0.526
      ├── Some((2, 4)): 79/140 ≈ 0.564
      ├── Some((2, 5)): 52/103 ≈ 0.505
      ├── Some((2, 6)): 130/208 ≈ 0.625
      ├── Some((2, 7)): 79/140 ≈ 0.564
      └── Some((2, 8)): 78/139 ≈ 0.561
    ├── Some((7, 3)): 776/1368 ≈ 0.567
      ├── Some((3, 0)): 48/99 ≈ 0.485
      ├── Some((3, 1)): 76/139 ≈ 0.547
      ├── Some((3, 2)): 117/194 ≈ 0.603
      ├── Some((3, 3)): 89/156 ≈ 0.571
      ├── Some((3, 4)): 72/133 ≈ 0.541
      ├── Some((3, 5)): 96/166 ≈ 0.578
      ├── Some((3, 6)): 161/252 ≈ 0.639
      ├── Some((3, 7)): 45/95 ≈ 0.474
      └── Some((3, 8)): 72/133 ≈ 0.541
    ├── Some((7, 4)): 712/1267 ≈ 0.562
      ├── Some((4, 0)): 96/169 ≈ 0.568
      ├── Some((4, 1)): 138/225 ≈ 0.613
      ├── Some((4, 2)): 72/135 ≈ 0.533
      ├── Some((4, 3)): 124/207 ≈ 0.599
      ├── Some((4, 4)): 74/138 ≈ 0.536
      ├── Some((4, 5)): 55/111 ≈ 0.495
      ├── Some((4, 6)): 82/149 ≈ 0.550
      └── Some((4, 7)): 70/132 ≈ 0.530
    ├── Some((7, 5)): 558/1019 ≈ 0.548
      ├── Some((5, 0)): 60/111 ≈ 0.541
      ├── Some((5, 1)): 58/108 ≈ 0.537
      ├── Some((5, 2)): 72/127 ≈ 0.567
      ├── Some((5, 3)): 50/97 ≈ 0.515
      ├── Some((5, 4)): 110/177 ≈ 0.621
      ├── Some((5, 5)): 56/105 ≈ 0.533
      ├── Some((5, 6)): 61/112 ≈ 0.545
      ├── Some((5, 7)): 46/92 ≈ 0.500
      └── Some((5, 8)): 44/89 ≈ 0.494
    ├── Some((7, 6)): 454/850 ≈ 0.534
      ├── Some((6, 0)): 41/82 ≈ 0.500
      ├── Some((6, 1)): 56/102 ≈ 0.549
      ├── Some((6, 2)): 54/99 ≈ 0.545
      ├── Some((6, 3)): 69/119 ≈ 0.580
      ├── Some((6, 4)): 44/86 ≈ 0.512
      ├── Some((6, 5)): 50/94 ≈ 0.532
      ├── Some((6, 6)): 47/90 ≈ 0.522
      ├── Some((6, 7)): 60/108 ≈ 0.556
      └── Some((6, 8)): 32/69 ≈ 0.464
    ├── Some((7, 7)): 606/1097 ≈ 0.552
      ├── Some((7, 0)): 59/114 ≈ 0.518
      ├── Some((7, 1)): 100/171 ≈ 0.585
      ├── Some((7, 2)): 34/78 ≈ 0.436
      ├── Some((7, 3)): 47/97 ≈ 0.485
      ├── Some((7, 4)): 134/217 ≈ 0.618
      ├── Some((7, 5)): 83/148 ≈ 0.561
      ├── Some((7, 6)): 79/142 ≈ 0.556
      └── Some((7, 8)): 69/129 ≈ 0.535
    └── Some((7, 8)): 583/1060 ≈ 0.550
      ├── Some((8, 0)): 68/126 ≈ 0.540
      ├── Some((8, 1)): 87/152 ≈ 0.572
      ├── Some((8, 2)): 59/113 ≈ 0.522
      ├── Some((8, 3)): 53/105 ≈ 0.505
      ├── Some((8, 4)): 103/174 ≈ 0.592
      ├── Some((8, 5)): 75/135 ≈ 0.556
      ├── Some((8, 6)): 48/98 ≈ 0.490
      └── Some((8, 8)): 90/156 ≈ 0.577
  └── Some((8, 8)): 4568/8303 ≈ 0.550
    ├── Some((8, 0)): 596/1080 ≈ 0.552
      ├── Some((0, 0)): 67/121 ≈ 0.554
      ├── Some((0, 1)): 54/103 ≈ 0.524
      ├── Some((0, 2)): 107/175 ≈ 0.611
      ├── Some((0, 3)): 73/130 ≈ 0.562
      ├── Some((0, 4)): 40/84 ≈ 0.476
      ├── Some((0, 5)): 76/134 ≈ 0.567
      ├── Some((0, 6)): 59/110 ≈ 0.536
      ├── Some((0, 7)): 50/98 ≈ 0.510
      └── Some((0, 8)): 69/124 ≈ 0.556
    ├── Some((8, 1)): 685/1223 ≈ 0.560
      ├── Some((1, 0)): 93/159 ≈ 0.585
      ├── Some((1, 1)): 73/132 ≈ 0.553
      ├── Some((1, 2)): 109/181 ≈ 0.602
      ├── Some((1, 3)): 56/109 ≈ 0.514
      ├── Some((1, 4)): 53/104 ≈ 0.510
      ├── Some((1, 5)): 68/125 ≈ 0.544
      ├── Some((1, 6)): 31/72 ≈ 0.431
      ├── Some((1, 7)): 98/166 ≈ 0.590
      └── Some((1, 8)): 104/174 ≈ 0.598
    ├── Some((8, 2)): 634/1141 ≈ 0.556
      ├── Some((2, 0)): 70/126 ≈ 0.556
      ├── Some((2, 1)): 67/122 ≈ 0.549
      ├── Some((2, 2)): 94/159 ≈ 0.591
      ├── Some((2, 3)): 101/168 ≈ 0.601
      ├── Some((2, 4)): 34/76 ≈ 0.447
      ├── Some((2, 5)): 61/114 ≈ 0.535
      ├── Some((2, 6)): 73/130 ≈ 0.562
      ├── Some((2, 7)): 73/131 ≈ 0.557
      └── Some((2, 8)): 61/114 ≈ 0.535
    ├── Some((8, 3)): 573/1043 ≈ 0.549
      ├── Some((3, 0)): 65/118 ≈ 0.551
      ├── Some((3, 1)): 54/103 ≈ 0.524
      ├── Some((3, 2)): 45/90 ≈ 0.500
      ├── Some((3, 3)): 88/149 ≈ 0.591
      ├── Some((3, 4)): 86/146 ≈ 0.589
      ├── Some((3, 5)): 41/85 ≈ 0.482
      ├── Some((3, 6)): 45/91 ≈ 0.495
      ├── Some((3, 7)): 57/107 ≈ 0.533
      └── Some((3, 8)): 91/153 ≈ 0.595
    ├── Some((8, 4)): 290/578 ≈ 0.502
      ├── Some((4, 0)): 36/72 ≈ 0.500
      ├── Some((4, 1)): 45/84 ≈ 0.536
      ├── Some((4, 2)): 40/77 ≈ 0.519
      ├── Some((4, 3)): 16/43 ≈ 0.372
      ├── Some((4, 4)): 35/71 ≈ 0.493
      ├── Some((4, 5)): 40/77 ≈ 0.519
      ├── Some((4, 6)): 38/75 ≈ 0.507
      └── Some((4, 7)): 40/78 ≈ 0.513
    ├── Some((8, 5)): 665/1190 ≈ 0.559
      ├── Some((5, 0)): 93/159 ≈ 0.585
      ├── Some((5, 1)): 93/159 ≈ 0.585
      ├── Some((5, 2)): 117/190 ≈ 0.616
      ├── Some((5, 3)): 44/91 ≈ 0.484
      ├── Some((5, 4)): 33/75 ≈ 0.440
      ├── Some((5, 5)): 75/134 ≈ 0.560
      ├── Some((5, 6)): 82/144 ≈ 0.569
      ├── Some((5, 7)): 90/155 ≈ 0.581
      └── Some((5, 8)): 38/82 ≈ 0.463
    ├── Some((8, 6)): 670/1198 ≈ 0.559
      ├── Some((6, 0)): 63/118 ≈ 0.534
      ├── Some((6, 1)): 77/137 ≈ 0.562
      ├── Some((6, 2)): 27/66 ≈ 0.409
      ├── Some((6, 3)): 73/131 ≈ 0.557
      ├── Some((6, 4)): 83/145 ≈ 0.572
      ├── Some((6, 5)): 89/153 ≈ 0.582
      ├── Some((6, 6)): 77/137 ≈ 0.562
      ├── Some((6, 7)): 73/132 ≈ 0.553
      └── Some((6, 8)): 108/178 ≈ 0.607
    └── Some((8, 7)): 454/849 ≈ 0.535
      ├── Some((7, 0)): 39/79 ≈ 0.494
      ├── Some((7, 1)): 49/93 ≈ 0.527
      ├── Some((7, 2)): 41/82 ≈ 0.500
      ├── Some((7, 3)): 24/58 ≈ 0.414
      ├── Some((7, 4)): 65/114 ≈ 0.570
      ├── Some((7, 5)): 22/55 ≈ 0.400
      ├── Some((7, 6)): 76/129 ≈ 0.589
      ├── Some((7, 7)): 59/106 ≈ 0.557
      └── Some((7, 8)): 78/132 ≈ 0.591
├── Some((5, 0)): 3384/6748 ≈ 0.501
  ├── Some((0, 0)): 237/510 ≈ 0.465
    ├── Some((0, 1)): 57/102 ≈ 0.559
      ├── Some((1, 0)): 7/12 ≈ 0.583
      ├── Some((1, 1)): 8/13 ≈ 0.615
      ├── Some((1, 2)): 8/13 ≈ 0.615
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 6/11 ≈ 0.545
      ├── Some((1, 6)): 7/12 ≈ 0.583
      ├── Some((1, 7)): 9/13 ≈ 0.692
      └── Some((1, 8)): 6/11 ≈ 0.545
    ├── Some((0, 2)): 15/43 ≈ 0.349
      ├── Some((2, 0)): 2/5 ≈ 0.400
      ├── Some((2, 1)): 1/4 ≈ 0.250
      ├── Some((2, 2)): 2/5 ≈ 0.400
      ├── Some((2, 3)): 1/4 ≈ 0.250
      ├── Some((2, 4)): 2/5 ≈ 0.400
      ├── Some((2, 5)): 1/4 ≈ 0.250
      ├── Some((2, 6)): 3/6 ≈ 0.500
      ├── Some((2, 7)): 2/5 ≈ 0.400
      └── Some((2, 8)): 1/4 ≈ 0.250
    ├── Some((0, 3)): 38/76 ≈ 0.500
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 2/6 ≈ 0.333
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 6/10 ≈ 0.600
      ├── Some((3, 4)): 9/13 ≈ 0.692
      ├── Some((3, 5)): 1/5 ≈ 0.200
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 4/8 ≈ 0.500
      └── Some((3, 8)): 4/8 ≈ 0.500
    ├── Some((0, 4)): 44/85 ≈ 0.518
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 5/9 ≈ 0.556
      ├── Some((4, 3)): 5/10 ≈ 0.500
      ├── Some((4, 4)): 4/9 ≈ 0.444
      ├── Some((4, 5)): 6/10 ≈ 0.600
      ├── Some((4, 6)): 8/12 ≈ 0.667
      ├── Some((4, 7)): 7/11 ≈ 0.636
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((0, 5)): 22/53 ≈ 0.415
      ├── Some((5, 1)): 4/8 ≈ 0.500
      ├── Some((5, 2)): 0/4 ≈ 0.000
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 2/6 ≈ 0.333
      ├── Some((5, 5)): 5/8 ≈ 0.625
      ├── Some((5, 6)): 6/9 ≈ 0.667
      ├── Some((5, 7)): 4/8 ≈ 0.500
      └── Some((5, 8)): 0/4 ≈ 0.000
    ├── Some((0, 6)): 36/74 ≈ 0.486
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 5/9 ≈ 0.556
      ├── Some((6, 2)): 6/10 ≈ 0.600
      ├── Some((6, 3)): 5/9 ≈ 0.556
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 4/8 ≈ 0.500
      ├── Some((6, 7)): 8/12 ≈ 0.667
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((0, 7)): 13/40 ≈ 0.325
      ├── Some((7, 0)): 1/4 ≈ 0.250
      ├── Some((7, 1)): 1/4 ≈ 0.250
      ├── Some((7, 2)): 2/5 ≈ 0.400
      ├── Some((7, 3)): 0/3 ≈ 0.000
      ├── Some((7, 4)): 3/5 ≈ 0.600
      ├── Some((7, 5)): 3/6 ≈ 0.500
      ├── Some((7, 6)): 3/6 ≈ 0.500
      ├── Some((7, 7)): 0/3 ≈ 0.000
      └── Some((7, 8)): 0/3 ≈ 0.000
    └── Some((0, 8)): 11/36 ≈ 0.306
      ├── Some((8, 0)): 2/4 ≈ 0.500
      ├── Some((8, 1)): 1/4 ≈ 0.250
      ├── Some((8, 2)): 1/4 ≈ 0.250
      ├── Some((8, 3)): 1/4 ≈ 0.250
      ├── Some((8, 4)): 1/4 ≈ 0.250
      ├── Some((8, 5)): 0/3 ≈ 0.000
      ├── Some((8, 6)): 2/4 ≈ 0.500
      ├── Some((8, 7)): 0/3 ≈ 0.000
      └── Some((8, 8)): 2/5 ≈ 0.400
  ├── Some((0, 1)): 368/738 ≈ 0.499
    ├── Some((1, 0)): 30/67 ≈ 0.448
      ├── Some((0, 0)): 9/13 ≈ 0.692
      ├── Some((0, 2)): 0/4 ≈ 0.000
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 1/5 ≈ 0.200
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((1, 1)): 43/85 ≈ 0.506
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 2)): 2/7 ≈ 0.286
      ├── Some((1, 3)): 7/12 ≈ 0.583
      ├── Some((1, 4)): 4/9 ≈ 0.444
      ├── Some((1, 5)): 4/9 ≈ 0.444
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 6/12 ≈ 0.500
      └── Some((1, 8)): 11/16 ≈ 0.688
    ├── Some((1, 2)): 20/52 ≈ 0.385
      ├── Some((2, 0)): 3/6 ≈ 0.500
      ├── Some((2, 1)): 4/7 ≈ 0.571
      ├── Some((2, 2)): 4/7 ≈ 0.571
      ├── Some((2, 3)): 0/4 ≈ 0.000
      ├── Some((2, 4)): 3/6 ≈ 0.500
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 1/5 ≈ 0.200
      ├── Some((2, 7)): 1/5 ≈ 0.200
      └── Some((2, 8)): 3/6 ≈ 0.500
    ├── Some((1, 3)): 31/68 ≈ 0.456
      ├── Some((3, 0)): 1/5 ≈ 0.200
      ├── Some((3, 1)): 3/7 ≈ 0.429
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 8/12 ≈ 0.667
      ├── Some((3, 4)): 2/6 ≈ 0.333
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 6/10 ≈ 0.600
      ├── Some((3, 7)): 1/5 ≈ 0.200
      └── Some((3, 8)): 6/10 ≈ 0.600
    ├── Some((1, 4)): 27/62 ≈ 0.435
      ├── Some((4, 0)): 3/7 ≈ 0.429
      ├── Some((4, 1)): 0/4 ≈ 0.000
      ├── Some((4, 2)): 2/6 ≈ 0.333
      ├── Some((4, 3)): 0/4 ≈ 0.000
      ├── Some((4, 4)): 6/9 ≈ 0.667
      ├── Some((4, 5)): 5/9 ≈ 0.556
      ├── Some((4, 6)): 3/7 ≈ 0.429
      ├── Some((4, 7)): 6/10 ≈ 0.600
      └── Some((4, 8)): 1/5 ≈ 0.200
    ├── Some((1, 5)): 58/106 ≈ 0.547
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 9/15 ≈ 0.600
      ├── Some((5, 3)): 12/17 ≈ 0.706
      ├── Some((5, 4)): 8/14 ≈ 0.571
      ├── Some((5, 5)): 9/15 ≈ 0.600
      ├── Some((5, 6)): 7/13 ≈ 0.538
      ├── Some((5, 7)): 2/8 ≈ 0.250
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((1, 6)): 51/96 ≈ 0.531
      ├── Some((6, 0)): 8/13 ≈ 0.615
      ├── Some((6, 1)): 9/14 ≈ 0.643
      ├── Some((6, 2)): 8/13 ≈ 0.615
      ├── Some((6, 3)): 6/11 ≈ 0.545
      ├── Some((6, 4)): 4/9 ≈ 0.444
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 6/11 ≈ 0.545
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 5/10 ≈ 0.500
    ├── Some((1, 7)): 58/106 ≈ 0.547
      ├── Some((7, 0)): 5/11 ≈ 0.455
      ├── Some((7, 1)): 11/16 ≈ 0.688
      ├── Some((7, 2)): 7/12 ≈ 0.583
      ├── Some((7, 3)): 8/13 ≈ 0.615
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 12/17 ≈ 0.706
      ├── Some((7, 7)): 1/6 ≈ 0.167
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((1, 8)): 50/95 ≈ 0.526
      ├── Some((8, 0)): 9/13 ≈ 0.692
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 7/12 ≈ 0.583
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 5/10 ≈ 0.500
      ├── Some((8, 6)): 8/13 ≈ 0.615
      ├── Some((8, 7)): 0/5 ≈ 0.000
      └── Some((8, 8)): 9/14 ≈ 0.643
  ├── Some((0, 2)): 545/1039 ≈ 0.525
    ├── Some((2, 0)): 52/104 ≈ 0.500
      ├── Some((0, 0)): 5/11 ≈ 0.455
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 3)): 10/16 ≈ 0.625
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 9/16 ≈ 0.562
      ├── Some((0, 6)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 1/7 ≈ 0.143
      └── Some((0, 8)): 10/17 ≈ 0.588
    ├── Some((2, 1)): 94/162 ≈ 0.580
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 15/22 ≈ 0.682
      ├── Some((1, 2)): 11/19 ≈ 0.579
      ├── Some((1, 3)): 16/23 ≈ 0.696
      ├── Some((1, 4)): 11/19 ≈ 0.579
      ├── Some((1, 5)): 11/19 ≈ 0.579
      ├── Some((1, 6)): 10/18 ≈ 0.556
      ├── Some((1, 7)): 12/20 ≈ 0.600
      └── Some((1, 8)): 1/8 ≈ 0.125
    ├── Some((2, 2)): 54/106 ≈ 0.509
      ├── Some((2, 0)): 11/18 ≈ 0.611
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 2/8 ≈ 0.250
      ├── Some((2, 4)): 6/13 ≈ 0.462
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 7/14 ≈ 0.500
      └── Some((2, 8)): 16/22 ≈ 0.727
    ├── Some((2, 3)): 78/140 ≈ 0.557
      ├── Some((3, 0)): 11/18 ≈ 0.611
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 9/16 ≈ 0.562
      ├── Some((3, 3)): 13/20 ≈ 0.650
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 14/20 ≈ 0.700
      ├── Some((3, 6)): 2/8 ≈ 0.250
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 9/16 ≈ 0.562
    ├── Some((2, 4)): 36/80 ≈ 0.450
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 10/14 ≈ 0.714
      ├── Some((4, 2)): 1/6 ≈ 0.167
      ├── Some((4, 3)): 2/7 ≈ 0.286
      ├── Some((4, 4)): 4/9 ≈ 0.444
      ├── Some((4, 5)): 9/13 ≈ 0.692
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((2, 5)): 66/123 ≈ 0.537
      ├── Some((5, 1)): 13/20 ≈ 0.650
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 7/14 ≈ 0.500
      ├── Some((5, 4)): 12/19 ≈ 0.632
      ├── Some((5, 5)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 13/20 ≈ 0.650
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((2, 6)): 33/76 ≈ 0.434
      ├── Some((6, 0)): 8/12 ≈ 0.667
      ├── Some((6, 1)): 0/4 ≈ 0.000
      ├── Some((6, 2)): 0/4 ≈ 0.000
      ├── Some((6, 3)): 1/6 ≈ 0.167
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 7/12 ≈ 0.583
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 7/12 ≈ 0.583
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((2, 7)): 52/104 ≈ 0.500
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 1/6 ≈ 0.167
      ├── Some((7, 2)): 10/16 ≈ 0.625
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 12/17 ≈ 0.706
      ├── Some((7, 5)): 9/15 ≈ 0.600
      ├── Some((7, 6)): 5/11 ≈ 0.455
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 3/9 ≈ 0.333
    └── Some((2, 8)): 80/143 ≈ 0.559
      ├── Some((8, 0)): 3/10 ≈ 0.300
      ├── Some((8, 1)): 7/14 ≈ 0.500
      ├── Some((8, 2)): 6/13 ≈ 0.462
      ├── Some((8, 3)): 14/21 ≈ 0.667
      ├── Some((8, 4)): 9/16 ≈ 0.562
      ├── Some((8, 5)): 6/13 ≈ 0.462
      ├── Some((8, 6)): 11/18 ≈ 0.611
      ├── Some((8, 7)): 15/21 ≈ 0.714
      └── Some((8, 8)): 9/16 ≈ 0.562
  ├── Some((0, 3)): 323/660 ≈ 0.489
    ├── Some((3, 0)): 45/86 ≈ 0.523
      ├── Some((0, 0)): 4/9 ≈ 0.444
      ├── Some((0, 1)): 7/12 ≈ 0.583
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 6/11 ≈ 0.545
      ├── Some((0, 5)): 7/12 ≈ 0.583
      ├── Some((0, 6)): 6/11 ≈ 0.545
      ├── Some((0, 7)): 6/11 ≈ 0.545
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((3, 1)): 51/94 ≈ 0.543
      ├── Some((1, 0)): 5/10 ≈ 0.500
      ├── Some((1, 1)): 7/12 ≈ 0.583
      ├── Some((1, 2)): 5/10 ≈ 0.500
      ├── Some((1, 3)): 6/11 ≈ 0.545
      ├── Some((1, 4)): 8/12 ≈ 0.667
      ├── Some((1, 5)): 6/11 ≈ 0.545
      ├── Some((1, 6)): 8/12 ≈ 0.667
      ├── Some((1, 7)): 1/6 ≈ 0.167
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((3, 2)): 46/88 ≈ 0.523
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 0/4 ≈ 0.000
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 4/9 ≈ 0.444
      ├── Some((2, 5)): 6/11 ≈ 0.545
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 14/18 ≈ 0.778
      └── Some((2, 8)): 8/12 ≈ 0.667
    ├── Some((3, 3)): 19/49 ≈ 0.388
      ├── Some((3, 0)): 3/6 ≈ 0.500
      ├── Some((3, 1)): 3/6 ≈ 0.500
      ├── Some((3, 2)): 1/5 ≈ 0.200
      ├── Some((3, 4)): 3/7 ≈ 0.429
      ├── Some((3, 5)): 2/6 ≈ 0.333
      ├── Some((3, 6)): 2/6 ≈ 0.333
      ├── Some((3, 7)): 1/5 ≈ 0.200
      └── Some((3, 8)): 3/7 ≈ 0.429
    ├── Some((3, 4)): 37/75 ≈ 0.493
      ├── Some((4, 0)): 0/4 ≈ 0.000
      ├── Some((4, 1)): 5/9 ≈ 0.556
      ├── Some((4, 2)): 4/8 ≈ 0.500
      ├── Some((4, 3)): 7/11 ≈ 0.636
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 4/8 ≈ 0.500
      ├── Some((4, 7)): 6/10 ≈ 0.600
      └── Some((4, 8)): 6/10 ≈ 0.600
    ├── Some((3, 5)): 30/65 ≈ 0.462
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 8/12 ≈ 0.667
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 2/7 ≈ 0.286
      ├── Some((5, 7)): 4/8 ≈ 0.500
      └── Some((5, 8)): 8/12 ≈ 0.667
    ├── Some((3, 6)): 40/79 ≈ 0.506
      ├── Some((6, 0)): 4/8 ≈ 0.500
      ├── Some((6, 1)): 4/8 ≈ 0.500
      ├── Some((6, 2)): 4/8 ≈ 0.500
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 5/9 ≈ 0.556
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 10/14 ≈ 0.714
    ├── Some((3, 7)): 20/51 ≈ 0.392
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 0/3 ≈ 0.000
      ├── Some((7, 2)): 0/3 ≈ 0.000
      ├── Some((7, 3)): 3/6 ≈ 0.500
      ├── Some((7, 4)): 2/6 ≈ 0.333
      ├── Some((7, 5)): 3/6 ≈ 0.500
      ├── Some((7, 6)): 5/8 ≈ 0.625
      ├── Some((7, 7)): 3/6 ≈ 0.500
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((3, 8)): 35/72 ≈ 0.486
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 2/6 ≈ 0.333
      ├── Some((8, 2)): 4/8 ≈ 0.500
      ├── Some((8, 3)): 5/9 ≈ 0.556
      ├── Some((8, 4)): 6/10 ≈ 0.600
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 1/5 ≈ 0.200
      ├── Some((8, 7)): 3/7 ≈ 0.429
      └── Some((8, 8)): 6/10 ≈ 0.600
  ├── Some((0, 4)): 501/965 ≈ 0.519
    ├── Some((4, 0)): 46/94 ≈ 0.489
      ├── Some((0, 0)): 6/12 ≈ 0.500
      ├── Some((0, 1)): 1/7 ≈ 0.143
      ├── Some((0, 2)): 6/12 ≈ 0.500
      ├── Some((0, 3)): 8/14 ≈ 0.571
      ├── Some((0, 5)): 15/20 ≈ 0.750
      ├── Some((0, 6)): 4/10 ≈ 0.400
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 1/7 ≈ 0.143
    ├── Some((4, 1)): 34/77 ≈ 0.442
      ├── Some((1, 0)): 3/8 ≈ 0.375
      ├── Some((1, 1)): 4/9 ≈ 0.444
      ├── Some((1, 2)): 5/10 ≈ 0.500
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 7/11 ≈ 0.636
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 1/6 ≈ 0.167
      └── Some((1, 8)): 7/11 ≈ 0.636
    ├── Some((4, 2)): 56/108 ≈ 0.519
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 6/12 ≈ 0.500
      ├── Some((2, 2)): 7/13 ≈ 0.538
      ├── Some((2, 3)): 8/13 ≈ 0.615
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 9/14 ≈ 0.643
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 8/13 ≈ 0.615
    ├── Some((4, 3)): 68/125 ≈ 0.544
      ├── Some((3, 0)): 10/16 ≈ 0.625
      ├── Some((3, 1)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 6/12 ≈ 0.500
      ├── Some((3, 3)): 10/16 ≈ 0.625
      ├── Some((3, 4)): 3/9 ≈ 0.333
      ├── Some((3, 5)): 14/20 ≈ 0.700
      ├── Some((3, 6)): 5/11 ≈ 0.455
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 8/15 ≈ 0.533
    ├── Some((4, 4)): 105/176 ≈ 0.597
      ├── Some((4, 0)): 13/22 ≈ 0.591
      ├── Some((4, 1)): 7/15 ≈ 0.467
      ├── Some((4, 2)): 13/22 ≈ 0.591
      ├── Some((4, 3)): 15/24 ≈ 0.625
      ├── Some((4, 5)): 19/28 ≈ 0.679
      ├── Some((4, 6)): 8/17 ≈ 0.471
      ├── Some((4, 7)): 10/19 ≈ 0.526
      └── Some((4, 8)): 19/28 ≈ 0.679
    ├── Some((4, 5)): 23/60 ≈ 0.383
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 0/4 ≈ 0.000
      ├── Some((5, 3)): 3/8 ≈ 0.375
      ├── Some((5, 4)): 4/8 ≈ 0.500
      ├── Some((5, 5)): 4/8 ≈ 0.500
      ├── Some((5, 6)): 2/6 ≈ 0.333
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((4, 6)): 78/139 ≈ 0.561
      ├── Some((6, 0)): 6/13 ≈ 0.462
      ├── Some((6, 1)): 8/15 ≈ 0.533
      ├── Some((6, 2)): 9/16 ≈ 0.562
      ├── Some((6, 3)): 11/17 ≈ 0.647
      ├── Some((6, 4)): 7/14 ≈ 0.500
      ├── Some((6, 5)): 10/16 ≈ 0.625
      ├── Some((6, 6)): 10/17 ≈ 0.588
      ├── Some((6, 7)): 9/16 ≈ 0.562
      └── Some((6, 8)): 7/14 ≈ 0.500
    ├── Some((4, 7)): 33/75 ≈ 0.440
      ├── Some((7, 0)): 5/10 ≈ 0.500
      ├── Some((7, 1)): 1/6 ≈ 0.167
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 3/8 ≈ 0.375
      ├── Some((7, 4)): 0/4 ≈ 0.000
      ├── Some((7, 5)): 4/9 ≈ 0.444
      ├── Some((7, 6)): 6/10 ≈ 0.600
      ├── Some((7, 7)): 4/9 ≈ 0.444
      └── Some((7, 8)): 6/10 ≈ 0.600
    └── Some((4, 8)): 57/110 ≈ 0.518
      ├── Some((8, 0)): 2/8 ≈ 0.250
      ├── Some((8, 1)): 8/14 ≈ 0.571
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 8/14 ≈ 0.571
      ├── Some((8, 4)): 9/14 ≈ 0.643
      ├── Some((8, 5)): 6/12 ≈ 0.500
      ├── Some((8, 6)): 7/13 ≈ 0.538
      ├── Some((8, 7)): 7/13 ≈ 0.538
      └── Some((8, 8)): 6/12 ≈ 0.500
  ├── Some((0, 5)): 489/944 ≈ 0.518
    ├── Some((5, 1)): 67/127 ≈ 0.528
      ├── Some((1, 0)): 3/9 ≈ 0.333
      ├── Some((1, 1)): 3/9 ≈ 0.333
      ├── Some((1, 2)): 11/18 ≈ 0.611
      ├── Some((1, 3)): 5/12 ≈ 0.417
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 11/18 ≈ 0.611
      ├── Some((1, 6)): 14/20 ≈ 0.700
      ├── Some((1, 7)): 6/13 ≈ 0.462
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((5, 2)): 44/93 ≈ 0.473
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 13/18 ≈ 0.722
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 7/13 ≈ 0.538
      ├── Some((2, 7)): 2/7 ≈ 0.286
      └── Some((2, 8)): 7/13 ≈ 0.538
    ├── Some((5, 3)): 62/119 ≈ 0.521
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 1/7 ≈ 0.143
      ├── Some((3, 2)): 15/21 ≈ 0.714
      ├── Some((3, 3)): 8/15 ≈ 0.533
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 2/8 ≈ 0.250
      ├── Some((3, 6)): 7/14 ≈ 0.500
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 16/22 ≈ 0.727
    ├── Some((5, 4)): 60/117 ≈ 0.513
      ├── Some((4, 0)): 8/14 ≈ 0.571
      ├── Some((4, 1)): 8/15 ≈ 0.533
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 9/15 ≈ 0.600
      ├── Some((4, 6)): 8/15 ≈ 0.533
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 9/15 ≈ 0.600
    ├── Some((5, 5)): 74/136 ≈ 0.544
      ├── Some((5, 1)): 19/28 ≈ 0.679
      ├── Some((5, 2)): 8/17 ≈ 0.471
      ├── Some((5, 3)): 6/14 ≈ 0.429
      ├── Some((5, 4)): 8/17 ≈ 0.471
      ├── Some((5, 6)): 10/19 ≈ 0.526
      ├── Some((5, 7)): 13/22 ≈ 0.591
      └── Some((5, 8)): 9/18 ≈ 0.500
    ├── Some((5, 6)): 70/131 ≈ 0.534
      ├── Some((6, 0)): 8/15 ≈ 0.533
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 8/15 ≈ 0.533
      ├── Some((6, 3)): 9/16 ≈ 0.562
      ├── Some((6, 4)): 10/16 ≈ 0.625
      ├── Some((6, 5)): 11/17 ≈ 0.647
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 7/14 ≈ 0.500
    ├── Some((5, 7)): 56/111 ≈ 0.505
      ├── Some((7, 0)): 8/14 ≈ 0.571
      ├── Some((7, 1)): 6/12 ≈ 0.500
      ├── Some((7, 2)): 1/7 ≈ 0.143
      ├── Some((7, 3)): 6/12 ≈ 0.500
      ├── Some((7, 4)): 3/9 ≈ 0.333
      ├── Some((7, 5)): 6/12 ≈ 0.500
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 15/21 ≈ 0.714
      └── Some((7, 8)): 7/13 ≈ 0.538
    └── Some((5, 8)): 55/109 ≈ 0.505
      ├── Some((8, 0)): 3/9 ≈ 0.333
      ├── Some((8, 1)): 12/17 ≈ 0.706
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 8/14 ≈ 0.571
      ├── Some((8, 6)): 12/18 ≈ 0.667
      ├── Some((8, 7)): 3/9 ≈ 0.333
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((0, 6)): 330/672 ≈ 0.491
    ├── Some((6, 0)): 33/70 ≈ 0.471
      ├── Some((0, 0)): 1/5 ≈ 0.200
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 4/9 ≈ 0.444
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 6/10 ≈ 0.600
      ├── Some((0, 5)): 5/9 ≈ 0.556
      ├── Some((0, 7)): 6/10 ≈ 0.600
      └── Some((0, 8)): 5/10 ≈ 0.500
    ├── Some((6, 1)): 32/68 ≈ 0.471
      ├── Some((1, 0)): 6/10 ≈ 0.600
      ├── Some((1, 1)): 7/11 ≈ 0.636
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 1/5 ≈ 0.200
      ├── Some((1, 4)): 9/12 ≈ 0.750
      ├── Some((1, 5)): 4/8 ≈ 0.500
      ├── Some((1, 6)): 1/5 ≈ 0.200
      ├── Some((1, 7)): 2/6 ≈ 0.333
      └── Some((1, 8)): 1/5 ≈ 0.200
    ├── Some((6, 2)): 7/30 ≈ 0.233
      ├── Some((2, 0)): 0/3 ≈ 0.000
      ├── Some((2, 1)): 2/4 ≈ 0.500
      ├── Some((2, 2)): 1/3 ≈ 0.333
      ├── Some((2, 3)): 0/3 ≈ 0.000
      ├── Some((2, 4)): 0/3 ≈ 0.000
      ├── Some((2, 5)): 0/3 ≈ 0.000
      ├── Some((2, 6)): 1/3 ≈ 0.333
      ├── Some((2, 7)): 1/3 ≈ 0.333
      └── Some((2, 8)): 1/4 ≈ 0.250
    ├── Some((6, 3)): 37/76 ≈ 0.487
      ├── Some((3, 0)): 5/9 ≈ 0.556
      ├── Some((3, 1)): 3/8 ≈ 0.375
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 10/14 ≈ 0.714
      ├── Some((3, 4)): 10/14 ≈ 0.714
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 4/8 ≈ 0.500
      ├── Some((3, 7)): 2/6 ≈ 0.333
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((6, 4)): 32/69 ≈ 0.464
      ├── Some((4, 0)): 5/9 ≈ 0.556
      ├── Some((4, 1)): 2/6 ≈ 0.333
      ├── Some((4, 2)): 4/8 ≈ 0.500
      ├── Some((4, 3)): 6/10 ≈ 0.600
      ├── Some((4, 4)): 0/4 ≈ 0.000
      ├── Some((4, 5)): 6/10 ≈ 0.600
      ├── Some((4, 6)): 4/8 ≈ 0.500
      ├── Some((4, 7)): 0/4 ≈ 0.000
      └── Some((4, 8)): 5/9 ≈ 0.556
    ├── Some((6, 5)): 55/100 ≈ 0.550
      ├── Some((5, 1)): 3/9 ≈ 0.333
      ├── Some((5, 2)): 7/13 ≈ 0.538
      ├── Some((5, 3)): 11/16 ≈ 0.688
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 6/12 ≈ 0.500
      ├── Some((5, 6)): 8/13 ≈ 0.615
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 9/14 ≈ 0.643
    ├── Some((6, 6)): 47/89 ≈ 0.528
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 9/14 ≈ 0.643
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 9/14 ≈ 0.643
      ├── Some((6, 7)): 9/14 ≈ 0.643
      └── Some((6, 8)): 8/13 ≈ 0.615
    ├── Some((6, 7)): 38/77 ≈ 0.494
      ├── Some((7, 0)): 1/5 ≈ 0.200
      ├── Some((7, 1)): 4/8 ≈ 0.500
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 3)): 1/5 ≈ 0.200
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 11/15 ≈ 0.733
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 5/9 ≈ 0.556
      └── Some((7, 8)): 6/10 ≈ 0.600
    └── Some((6, 8)): 49/92 ≈ 0.533
      ├── Some((8, 0)): 8/12 ≈ 0.667
      ├── Some((8, 1)): 2/7 ≈ 0.286
      ├── Some((8, 2)): 5/10 ≈ 0.500
      ├── Some((8, 3)): 6/11 ≈ 0.545
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 5/10 ≈ 0.500
      ├── Some((8, 6)): 7/11 ≈ 0.636
      ├── Some((8, 7)): 5/10 ≈ 0.500
      └── Some((8, 8)): 7/11 ≈ 0.636
  ├── Some((0, 7)): 410/810 ≈ 0.506
    ├── Some((7, 0)): 45/90 ≈ 0.500
      ├── Some((0, 0)): 4/10 ≈ 0.400
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 8/13 ≈ 0.615
      ├── Some((0, 4)): 10/15 ≈ 0.667
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 6/12 ≈ 0.500
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((7, 1)): 41/84 ≈ 0.488
      ├── Some((1, 0)): 0/4 ≈ 0.000
      ├── Some((1, 1)): 5/10 ≈ 0.500
      ├── Some((1, 2)): 7/11 ≈ 0.636
      ├── Some((1, 3)): 7/12 ≈ 0.583
      ├── Some((1, 4)): 5/10 ≈ 0.500
      ├── Some((1, 5)): 4/9 ≈ 0.444
      ├── Some((1, 6)): 4/9 ≈ 0.444
      ├── Some((1, 7)): 7/12 ≈ 0.583
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((7, 2)): 39/81 ≈ 0.481
      ├── Some((2, 0)): 5/9 ≈ 0.556
      ├── Some((2, 1)): 5/9 ≈ 0.556
      ├── Some((2, 2)): 7/11 ≈ 0.636
      ├── Some((2, 3)): 5/10 ≈ 0.500
      ├── Some((2, 4)): 1/6 ≈ 0.167
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 4/9 ≈ 0.444
      ├── Some((2, 7)): 2/7 ≈ 0.286
      └── Some((2, 8)): 7/11 ≈ 0.636
    ├── Some((7, 3)): 68/121 ≈ 0.562
      ├── Some((3, 0)): 6/12 ≈ 0.500
      ├── Some((3, 1)): 8/14 ≈ 0.571
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 12/17 ≈ 0.706
      ├── Some((3, 4)): 10/16 ≈ 0.625
      ├── Some((3, 5)): 7/13 ≈ 0.538
      ├── Some((3, 6)): 4/10 ≈ 0.400
      ├── Some((3, 7)): 7/13 ≈ 0.538
      └── Some((3, 8)): 9/15 ≈ 0.600
    ├── Some((7, 4)): 36/77 ≈ 0.468
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 10/14 ≈ 0.714
      ├── Some((4, 4)): 0/4 ≈ 0.000
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 6/10 ≈ 0.600
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((7, 5)): 31/69 ≈ 0.449
      ├── Some((5, 1)): 4/9 ≈ 0.444
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 3)): 2/7 ≈ 0.286
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 6/10 ≈ 0.600
      ├── Some((5, 7)): 4/9 ≈ 0.444
      └── Some((5, 8)): 7/11 ≈ 0.636
    ├── Some((7, 6)): 21/55 ≈ 0.382
      ├── Some((6, 0)): 3/7 ≈ 0.429
      ├── Some((6, 1)): 2/6 ≈ 0.333
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 1/5 ≈ 0.200
      ├── Some((6, 4)): 4/7 ≈ 0.571
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 5/8 ≈ 0.625
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 3/7 ≈ 0.429
    ├── Some((7, 7)): 66/118 ≈ 0.559
      ├── Some((7, 0)): 10/17 ≈ 0.588
      ├── Some((7, 1)): 11/17 ≈ 0.647
      ├── Some((7, 2)): 7/14 ≈ 0.500
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 14/20 ≈ 0.700
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 7/14 ≈ 0.500
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((7, 8)): 63/114 ≈ 0.553
      ├── Some((8, 0)): 8/13 ≈ 0.615
      ├── Some((8, 1)): 7/12 ≈ 0.583
      ├── Some((8, 2)): 7/13 ≈ 0.538
      ├── Some((8, 3)): 14/19 ≈ 0.737
      ├── Some((8, 4)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 5/11 ≈ 0.455
      └── Some((8, 8)): 7/13 ≈ 0.538
  └── Some((0, 8)): 181/409 ≈ 0.443
    ├── Some((8, 0)): 24/51 ≈ 0.471
      ├── Some((0, 0)): 3/6 ≈ 0.500
      ├── Some((0, 1)): 3/6 ≈ 0.500
      ├── Some((0, 2)): 3/6 ≈ 0.500
      ├── Some((0, 3)): 2/5 ≈ 0.400
      ├── Some((0, 4)): 2/6 ≈ 0.333
      ├── Some((0, 5)): 4/7 ≈ 0.571
      ├── Some((0, 6)): 2/6 ≈ 0.333
      └── Some((0, 7)): 5/8 ≈ 0.625
    ├── Some((8, 1)): 32/62 ≈ 0.516
      ├── Some((1, 0)): 2/5 ≈ 0.400
      ├── Some((1, 1)): 3/6 ≈ 0.500
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 7/10 ≈ 0.700
      ├── Some((1, 4)): 6/9 ≈ 0.667
      ├── Some((1, 5)): 4/7 ≈ 0.571
      ├── Some((1, 6)): 4/7 ≈ 0.571
      ├── Some((1, 7)): 1/5 ≈ 0.200
      └── Some((1, 8)): 2/6 ≈ 0.333
    ├── Some((8, 2)): 24/52 ≈ 0.462
      ├── Some((2, 0)): 1/4 ≈ 0.250
      ├── Some((2, 1)): 1/4 ≈ 0.250
      ├── Some((2, 2)): 2/5 ≈ 0.400
      ├── Some((2, 3)): 4/7 ≈ 0.571
      ├── Some((2, 4)): 3/6 ≈ 0.500
      ├── Some((2, 5)): 5/8 ≈ 0.625
      ├── Some((2, 6)): 2/5 ≈ 0.400
      ├── Some((2, 7)): 4/7 ≈ 0.571
      └── Some((2, 8)): 1/5 ≈ 0.200
    ├── Some((8, 3)): 11/33 ≈ 0.333
      ├── Some((3, 0)): 2/4 ≈ 0.500
      ├── Some((3, 1)): 0/3 ≈ 0.000
      ├── Some((3, 2)): 1/3 ≈ 0.333
      ├── Some((3, 3)): 3/5 ≈ 0.600
      ├── Some((3, 4)): 2/4 ≈ 0.500
      ├── Some((3, 5)): 1/3 ≈ 0.333
      ├── Some((3, 6)): 0/3 ≈ 0.000
      ├── Some((3, 7)): 1/3 ≈ 0.333
      └── Some((3, 8)): 1/4 ≈ 0.250
    ├── Some((8, 4)): 3/20 ≈ 0.150
      ├── Some((4, 0)): 0/2 ≈ 0.000
      ├── Some((4, 1)): 0/2 ≈ 0.000
      ├── Some((4, 2)): 0/2 ≈ 0.000
      ├── Some((4, 3)): 0/2 ≈ 0.000
      ├── Some((4, 4)): 1/2 ≈ 0.500
      ├── Some((4, 5)): 0/2 ≈ 0.000
      ├── Some((4, 6)): 1/2 ≈ 0.500
      ├── Some((4, 7)): 0/2 ≈ 0.000
      └── Some((4, 8)): 1/3 ≈ 0.333
    ├── Some((8, 5)): 26/54 ≈ 0.481
      ├── Some((5, 1)): 3/6 ≈ 0.500
      ├── Some((5, 2)): 7/10 ≈ 0.700
      ├── Some((5, 3)): 7/10 ≈ 0.700
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 2/5 ≈ 0.400
      ├── Some((5, 6)): 2/6 ≈ 0.333
      ├── Some((5, 7)): 2/6 ≈ 0.333
      └── Some((5, 8)): 1/5 ≈ 0.200
    ├── Some((8, 6)): 14/37 ≈ 0.378
      ├── Some((6, 0)): 0/3 ≈ 0.000
      ├── Some((6, 1)): 2/4 ≈ 0.500
      ├── Some((6, 2)): 1/4 ≈ 0.250
      ├── Some((6, 3)): 2/4 ≈ 0.500
      ├── Some((6, 4)): 2/4 ≈ 0.500
      ├── Some((6, 5)): 2/4 ≈ 0.500
      ├── Some((6, 6)): 2/5 ≈ 0.400
      ├── Some((6, 7)): 1/4 ≈ 0.250
      └── Some((6, 8)): 1/4 ≈ 0.250
    ├── Some((8, 7)): 32/62 ≈ 0.516
      ├── Some((7, 0)): 5/8 ≈ 0.625
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 11/13 ≈ 0.846
      ├── Some((7, 4)): 0/3 ≈ 0.000
      ├── Some((7, 5)): 0/4 ≈ 0.000
      ├── Some((7, 6)): 3/6 ≈ 0.500
      ├── Some((7, 7)): 3/6 ≈ 0.500
      └── Some((7, 8)): 7/10 ≈ 0.700
    └── Some((8, 8)): 14/37 ≈ 0.378
      ├── Some((8, 0)): 1/4 ≈ 0.250
      ├── Some((8, 1)): 1/4 ≈ 0.250
      ├── Some((8, 2)): 3/5 ≈ 0.600
      ├── Some((8, 3)): 0/3 ≈ 0.000
      ├── Some((8, 4)): 3/5 ≈ 0.600
      ├── Some((8, 5)): 2/5 ≈ 0.400
      ├── Some((8, 6)): 3/6 ≈ 0.500
      └── Some((8, 7)): 1/4 ≈ 0.250
├── Some((5, 1)): 5458/10586 ≈ 0.516
  ├── Some((1, 0)): 557/1092 ≈ 0.510
    ├── Some((0, 0)): 56/113 ≈ 0.496
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 3/10 ≈ 0.300
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 11/19 ≈ 0.579
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 3/10 ≈ 0.300
      ├── Some((0, 7)): 3/10 ≈ 0.300
      └── Some((0, 8)): 12/19 ≈ 0.632
    ├── Some((0, 1)): 75/141 ≈ 0.532
      ├── Some((1, 1)): 13/21 ≈ 0.619
      ├── Some((1, 2)): 6/14 ≈ 0.429
      ├── Some((1, 3)): 8/16 ≈ 0.500
      ├── Some((1, 4)): 8/16 ≈ 0.500
      ├── Some((1, 5)): 15/23 ≈ 0.652
      ├── Some((1, 6)): 5/13 ≈ 0.385
      ├── Some((1, 7)): 15/24 ≈ 0.625
      └── Some((1, 8)): 5/13 ≈ 0.385
    ├── Some((0, 2)): 53/109 ≈ 0.486
      ├── Some((2, 0)): 9/15 ≈ 0.600
      ├── Some((2, 1)): 10/16 ≈ 0.625
      ├── Some((2, 2)): 2/8 ≈ 0.250
      ├── Some((2, 3)): 9/16 ≈ 0.562
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 2/8 ≈ 0.250
      ├── Some((2, 6)): 5/11 ≈ 0.455
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 9/16 ≈ 0.562
    ├── Some((0, 3)): 52/107 ≈ 0.486
      ├── Some((3, 0)): 8/14 ≈ 0.571
      ├── Some((3, 1)): 8/14 ≈ 0.571
      ├── Some((3, 2)): 2/8 ≈ 0.250
      ├── Some((3, 3)): 8/14 ≈ 0.571
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 10/16 ≈ 0.625
      ├── Some((3, 6)): 4/10 ≈ 0.400
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 4/10 ≈ 0.400
    ├── Some((0, 4)): 60/119 ≈ 0.504
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 4/10 ≈ 0.400
      ├── Some((4, 3)): 12/18 ≈ 0.667
      ├── Some((4, 4)): 10/16 ≈ 0.625
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 6/13 ≈ 0.462
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((0, 5)): 76/142 ≈ 0.535
      ├── Some((5, 0)): 20/28 ≈ 0.714
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 3/11 ≈ 0.273
      ├── Some((5, 5)): 3/11 ≈ 0.273
      ├── Some((5, 6)): 14/23 ≈ 0.609
      ├── Some((5, 7)): 6/14 ≈ 0.429
      └── Some((5, 8)): 17/25 ≈ 0.680
    ├── Some((0, 6)): 36/83 ≈ 0.434
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 0/5 ≈ 0.000
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 7/12 ≈ 0.583
      ├── Some((6, 5)): 7/12 ≈ 0.583
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 8/13 ≈ 0.615
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((0, 7)): 87/157 ≈ 0.554
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 4/11 ≈ 0.364
      ├── Some((7, 2)): 9/17 ≈ 0.529
      ├── Some((7, 3)): 11/19 ≈ 0.579
      ├── Some((7, 4)): 14/22 ≈ 0.636
      ├── Some((7, 5)): 6/14 ≈ 0.429
      ├── Some((7, 6)): 8/16 ≈ 0.500
      ├── Some((7, 7)): 3/10 ≈ 0.300
      └── Some((7, 8)): 21/29 ≈ 0.724
    └── Some((0, 8)): 61/120 ≈ 0.508
      ├── Some((8, 0)): 8/15 ≈ 0.533
      ├── Some((8, 1)): 9/16 ≈ 0.562
      ├── Some((8, 2)): 9/16 ≈ 0.562
      ├── Some((8, 3)): 11/17 ≈ 0.647
      ├── Some((8, 4)): 6/12 ≈ 0.500
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 7/14 ≈ 0.500
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((1, 1)): 444/896 ≈ 0.496
    ├── Some((1, 0)): 60/119 ≈ 0.504
      ├── Some((0, 0)): 4/10 ≈ 0.400
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 12/18 ≈ 0.667
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 9/16 ≈ 0.562
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 7/14 ≈ 0.500
      └── Some((0, 8)): 8/15 ≈ 0.533
    ├── Some((1, 2)): 70/133 ≈ 0.526
      ├── Some((2, 0)): 4/11 ≈ 0.364
      ├── Some((2, 1)): 5/12 ≈ 0.417
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 15/22 ≈ 0.682
      ├── Some((2, 4)): 3/10 ≈ 0.300
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 19/26 ≈ 0.731
      ├── Some((2, 7)): 4/11 ≈ 0.364
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((1, 3)): 41/91 ≈ 0.451
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 3/8 ≈ 0.375
      ├── Some((3, 2)): 9/14 ≈ 0.643
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 5/11 ≈ 0.455
      ├── Some((3, 7)): 2/7 ≈ 0.286
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((1, 4)): 51/105 ≈ 0.486
      ├── Some((4, 0)): 10/15 ≈ 0.667
      ├── Some((4, 1)): 9/15 ≈ 0.600
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 5/11 ≈ 0.455
    ├── Some((1, 5)): 74/139 ≈ 0.532
      ├── Some((5, 0)): 10/18 ≈ 0.556
      ├── Some((5, 2)): 11/19 ≈ 0.579
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 13/21 ≈ 0.619
      ├── Some((5, 6)): 13/22 ≈ 0.591
      ├── Some((5, 7)): 6/14 ≈ 0.429
      └── Some((5, 8)): 8/16 ≈ 0.500
    ├── Some((1, 6)): 50/104 ≈ 0.481
      ├── Some((6, 0)): 9/15 ≈ 0.600
      ├── Some((6, 1)): 6/12 ≈ 0.500
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 9/15 ≈ 0.600
      ├── Some((6, 4)): 0/6 ≈ 0.000
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 2/8 ≈ 0.250
      └── Some((6, 8)): 8/14 ≈ 0.571
    ├── Some((1, 7)): 47/100 ≈ 0.470
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 6/12 ≈ 0.500
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 1/6 ≈ 0.167
      ├── Some((7, 4)): 6/12 ≈ 0.500
      ├── Some((7, 5)): 6/12 ≈ 0.500
      ├── Some((7, 6)): 6/12 ≈ 0.500
      ├── Some((7, 7)): 6/12 ≈ 0.500
      └── Some((7, 8)): 8/13 ≈ 0.615
    └── Some((1, 8)): 50/104 ≈ 0.481
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 9/15 ≈ 0.600
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 0/5 ≈ 0.000
      ├── Some((8, 6)): 8/14 ≈ 0.571
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 10/16 ≈ 0.625
  ├── Some((1, 2)): 730/1388 ≈ 0.526
    ├── Some((2, 0)): 57/119 ≈ 0.479
      ├── Some((0, 0)): 3/9 ≈ 0.333
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 2)): 9/16 ≈ 0.562
      ├── Some((0, 3)): 8/15 ≈ 0.533
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 4/11 ≈ 0.364
      ├── Some((0, 6)): 7/14 ≈ 0.500
      ├── Some((0, 7)): 8/15 ≈ 0.533
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((2, 1)): 85/160 ≈ 0.531
      ├── Some((1, 0)): 11/20 ≈ 0.550
      ├── Some((1, 1)): 8/17 ≈ 0.471
      ├── Some((1, 3)): 16/26 ≈ 0.615
      ├── Some((1, 4)): 4/13 ≈ 0.308
      ├── Some((1, 5)): 4/13 ≈ 0.308
      ├── Some((1, 6)): 16/26 ≈ 0.615
      ├── Some((1, 7)): 16/26 ≈ 0.615
      └── Some((1, 8)): 9/18 ≈ 0.500
    ├── Some((2, 2)): 97/178 ≈ 0.545
      ├── Some((2, 0)): 19/30 ≈ 0.633
      ├── Some((2, 1)): 8/18 ≈ 0.444
      ├── Some((2, 3)): 13/23 ≈ 0.565
      ├── Some((2, 4)): 4/13 ≈ 0.308
      ├── Some((2, 5)): 15/25 ≈ 0.600
      ├── Some((2, 6)): 15/26 ≈ 0.577
      ├── Some((2, 7)): 10/20 ≈ 0.500
      └── Some((2, 8)): 12/22 ≈ 0.545
    ├── Some((2, 3)): 78/150 ≈ 0.520
      ├── Some((3, 0)): 6/14 ≈ 0.429
      ├── Some((3, 1)): 7/15 ≈ 0.467
      ├── Some((3, 2)): 6/14 ≈ 0.429
      ├── Some((3, 3)): 10/18 ≈ 0.556
      ├── Some((3, 4)): 8/16 ≈ 0.500
      ├── Some((3, 5)): 7/15 ≈ 0.467
      ├── Some((3, 6)): 17/25 ≈ 0.680
      ├── Some((3, 7)): 2/9 ≈ 0.222
      └── Some((3, 8)): 14/23 ≈ 0.609
    ├── Some((2, 4)): 116/205 ≈ 0.566
      ├── Some((4, 0)): 6/15 ≈ 0.400
      ├── Some((4, 1)): 14/24 ≈ 0.583
      ├── Some((4, 2)): 13/23 ≈ 0.565
      ├── Some((4, 3)): 16/26 ≈ 0.615
      ├── Some((4, 4)): 7/17 ≈ 0.412
      ├── Some((4, 5)): 11/21 ≈ 0.524
      ├── Some((4, 6)): 13/23 ≈ 0.565
      ├── Some((4, 7)): 20/30 ≈ 0.667
      └── Some((4, 8)): 15/25 ≈ 0.600
    ├── Some((2, 5)): 80/153 ≈ 0.523
      ├── Some((5, 0)): 22/32 ≈ 0.688
      ├── Some((5, 2)): 14/24 ≈ 0.583
      ├── Some((5, 3)): 18/28 ≈ 0.643
      ├── Some((5, 4)): 4/12 ≈ 0.333
      ├── Some((5, 5)): 2/10 ≈ 0.200
      ├── Some((5, 6)): 9/18 ≈ 0.500
      ├── Some((5, 7)): 9/18 ≈ 0.500
      └── Some((5, 8)): 2/10 ≈ 0.200
    ├── Some((2, 6)): 74/144 ≈ 0.514
      ├── Some((6, 0)): 11/19 ≈ 0.579
      ├── Some((6, 1)): 10/18 ≈ 0.556
      ├── Some((6, 2)): 6/14 ≈ 0.429
      ├── Some((6, 3)): 7/15 ≈ 0.467
      ├── Some((6, 4)): 9/17 ≈ 0.529
      ├── Some((6, 5)): 3/10 ≈ 0.300
      ├── Some((6, 6)): 11/19 ≈ 0.579
      ├── Some((6, 7)): 12/20 ≈ 0.600
      └── Some((6, 8)): 4/11 ≈ 0.364
    ├── Some((2, 7)): 42/96 ≈ 0.438
      ├── Some((7, 0)): 4/10 ≈ 0.400
      ├── Some((7, 1)): 0/5 ≈ 0.000
      ├── Some((7, 2)): 0/6 ≈ 0.000
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 11/17 ≈ 0.647
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 9/15 ≈ 0.600
      ├── Some((7, 7)): 8/14 ≈ 0.571
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((2, 8)): 100/182 ≈ 0.549
      ├── Some((8, 0)): 3/11 ≈ 0.273
      ├── Some((8, 1)): 9/18 ≈ 0.500
      ├── Some((8, 2)): 12/21 ≈ 0.571
      ├── Some((8, 3)): 6/15 ≈ 0.400
      ├── Some((8, 4)): 23/33 ≈ 0.697
      ├── Some((8, 5)): 2/10 ≈ 0.200
      ├── Some((8, 6)): 13/22 ≈ 0.591
      ├── Some((8, 7)): 23/33 ≈ 0.697
      └── Some((8, 8)): 9/18 ≈ 0.500
  ├── Some((1, 3)): 719/1369 ≈ 0.525
    ├── Some((3, 0)): 57/119 ≈ 0.479
      ├── Some((0, 0)): 3/9 ≈ 0.333
      ├── Some((0, 1)): 3/10 ≈ 0.300
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 9/16 ≈ 0.562
      ├── Some((0, 4)): 13/20 ≈ 0.650
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 4/11 ≈ 0.364
      ├── Some((0, 7)): 7/14 ≈ 0.500
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((3, 1)): 86/161 ≈ 0.534
      ├── Some((1, 0)): 6/15 ≈ 0.400
      ├── Some((1, 1)): 7/16 ≈ 0.438
      ├── Some((1, 2)): 10/19 ≈ 0.526
      ├── Some((1, 4)): 19/29 ≈ 0.655
      ├── Some((1, 5)): 6/15 ≈ 0.400
      ├── Some((1, 6)): 10/20 ≈ 0.500
      ├── Some((1, 7)): 8/17 ≈ 0.471
      └── Some((1, 8)): 19/29 ≈ 0.655
    ├── Some((3, 2)): 96/176 ≈ 0.545
      ├── Some((2, 0)): 15/24 ≈ 0.625
      ├── Some((2, 1)): 11/20 ≈ 0.550
      ├── Some((2, 2)): 9/18 ≈ 0.500
      ├── Some((2, 3)): 1/8 ≈ 0.125
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 17/26 ≈ 0.654
      ├── Some((2, 6)): 13/22 ≈ 0.591
      ├── Some((2, 7)): 12/21 ≈ 0.571
      └── Some((2, 8)): 12/21 ≈ 0.571
    ├── Some((3, 3)): 69/136 ≈ 0.507
      ├── Some((3, 0)): 5/13 ≈ 0.385
      ├── Some((3, 1)): 2/9 ≈ 0.222
      ├── Some((3, 2)): 15/24 ≈ 0.625
      ├── Some((3, 4)): 7/15 ≈ 0.467
      ├── Some((3, 5)): 13/22 ≈ 0.591
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 11/19 ≈ 0.579
      └── Some((3, 8)): 11/20 ≈ 0.550
    ├── Some((3, 4)): 56/117 ≈ 0.479
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 6/13 ≈ 0.462
      ├── Some((4, 2)): 2/8 ≈ 0.250
      ├── Some((4, 3)): 8/15 ≈ 0.533
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 2/8 ≈ 0.250
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 12/19 ≈ 0.632
      └── Some((4, 8)): 8/15 ≈ 0.533
    ├── Some((3, 5)): 63/128 ≈ 0.492
      ├── Some((5, 0)): 10/18 ≈ 0.556
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 8/16 ≈ 0.500
      ├── Some((5, 4)): 7/15 ≈ 0.467
      ├── Some((5, 5)): 6/14 ≈ 0.429
      ├── Some((5, 6)): 2/9 ≈ 0.222
      ├── Some((5, 7)): 13/22 ≈ 0.591
      └── Some((5, 8)): 8/16 ≈ 0.500
    ├── Some((3, 6)): 90/167 ≈ 0.539
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 15/24 ≈ 0.625
      ├── Some((6, 2)): 7/15 ≈ 0.467
      ├── Some((6, 3)): 13/22 ≈ 0.591
      ├── Some((6, 4)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 13/22 ≈ 0.591
      ├── Some((6, 6)): 4/12 ≈ 0.333
      ├── Some((6, 7)): 13/22 ≈ 0.591
      └── Some((6, 8)): 7/15 ≈ 0.467
    ├── Some((3, 7)): 104/187 ≈ 0.556
      ├── Some((7, 0)): 10/19 ≈ 0.526
      ├── Some((7, 1)): 8/17 ≈ 0.471
      ├── Some((7, 2)): 10/19 ≈ 0.526
      ├── Some((7, 3)): 4/12 ≈ 0.333
      ├── Some((7, 4)): 7/16 ≈ 0.438
      ├── Some((7, 5)): 7/16 ≈ 0.438
      ├── Some((7, 6)): 21/31 ≈ 0.677
      ├── Some((7, 7)): 20/30 ≈ 0.667
      └── Some((7, 8)): 16/26 ≈ 0.615
    └── Some((3, 8)): 97/177 ≈ 0.548
      ├── Some((8, 0)): 6/15 ≈ 0.400
      ├── Some((8, 1)): 17/26 ≈ 0.654
      ├── Some((8, 2)): 11/20 ≈ 0.550
      ├── Some((8, 3)): 11/20 ≈ 0.550
      ├── Some((8, 4)): 13/22 ≈ 0.591
      ├── Some((8, 5)): 10/19 ≈ 0.526
      ├── Some((8, 6)): 14/23 ≈ 0.609
      ├── Some((8, 7)): 9/18 ≈ 0.500
      └── Some((8, 8)): 5/13 ≈ 0.385
  ├── Some((1, 4)): 663/1274 ≈ 0.520
    ├── Some((4, 0)): 95/173 ≈ 0.549
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 7/16 ≈ 0.438
      ├── Some((0, 2)): 6/14 ≈ 0.429
      ├── Some((0, 3)): 14/23 ≈ 0.609
      ├── Some((0, 4)): 14/23 ≈ 0.609
      ├── Some((0, 5)): 14/23 ≈ 0.609
      ├── Some((0, 6)): 6/14 ≈ 0.429
      ├── Some((0, 7)): 6/14 ≈ 0.429
      └── Some((0, 8)): 21/30 ≈ 0.700
    ├── Some((4, 1)): 91/167 ≈ 0.545
      ├── Some((1, 0)): 9/18 ≈ 0.500
      ├── Some((1, 1)): 18/28 ≈ 0.643
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 3)): 8/17 ≈ 0.471
      ├── Some((1, 5)): 10/19 ≈ 0.526
      ├── Some((1, 6)): 4/13 ≈ 0.308
      ├── Some((1, 7)): 23/33 ≈ 0.697
      └── Some((1, 8)): 10/20 ≈ 0.500
    ├── Some((4, 2)): 64/128 ≈ 0.500
      ├── Some((2, 0)): 10/18 ≈ 0.556
      ├── Some((2, 1)): 6/13 ≈ 0.462
      ├── Some((2, 2)): 4/11 ≈ 0.364
      ├── Some((2, 3)): 5/12 ≈ 0.417
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 15/22 ≈ 0.682
      ├── Some((2, 6)): 7/14 ≈ 0.500
      ├── Some((2, 7)): 8/15 ≈ 0.533
      └── Some((2, 8)): 3/10 ≈ 0.300
    ├── Some((4, 3)): 93/170 ≈ 0.547
      ├── Some((3, 0)): 10/18 ≈ 0.556
      ├── Some((3, 1)): 10/19 ≈ 0.526
      ├── Some((3, 2)): 7/15 ≈ 0.467
      ├── Some((3, 3)): 17/26 ≈ 0.654
      ├── Some((3, 4)): 14/23 ≈ 0.609
      ├── Some((3, 5)): 11/20 ≈ 0.550
      ├── Some((3, 6)): 8/16 ≈ 0.500
      ├── Some((3, 7)): 7/15 ≈ 0.467
      └── Some((3, 8)): 9/17 ≈ 0.529
    ├── Some((4, 4)): 109/192 ≈ 0.568
      ├── Some((4, 0)): 23/34 ≈ 0.676
      ├── Some((4, 1)): 10/20 ≈ 0.500
      ├── Some((4, 2)): 14/25 ≈ 0.560
      ├── Some((4, 3)): 22/33 ≈ 0.667
      ├── Some((4, 5)): 15/26 ≈ 0.577
      ├── Some((4, 6)): 16/27 ≈ 0.593
      ├── Some((4, 7)): 4/13 ≈ 0.308
      └── Some((4, 8)): 4/13 ≈ 0.308
    ├── Some((4, 5)): 51/109 ≈ 0.468
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 2)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 5/12 ≈ 0.417
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 8/15 ≈ 0.533
      ├── Some((5, 6)): 4/11 ≈ 0.364
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 2/9 ≈ 0.222
    ├── Some((4, 6)): 60/122 ≈ 0.492
      ├── Some((6, 0)): 11/18 ≈ 0.611
      ├── Some((6, 1)): 2/8 ≈ 0.250
      ├── Some((6, 2)): 9/16 ≈ 0.562
      ├── Some((6, 3)): 2/8 ≈ 0.250
      ├── Some((6, 4)): 9/16 ≈ 0.562
      ├── Some((6, 5)): 6/13 ≈ 0.462
      ├── Some((6, 6)): 4/11 ≈ 0.364
      ├── Some((6, 7)): 4/11 ≈ 0.364
      └── Some((6, 8)): 13/20 ≈ 0.650
    ├── Some((4, 7)): 27/71 ≈ 0.380
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 0/5 ≈ 0.000
      ├── Some((7, 2)): 4/9 ≈ 0.444
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 2/7 ≈ 0.286
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((4, 8)): 73/141 ≈ 0.518
      ├── Some((8, 0)): 3/10 ≈ 0.300
      ├── Some((8, 1)): 7/14 ≈ 0.500
      ├── Some((8, 2)): 15/23 ≈ 0.652
      ├── Some((8, 3)): 10/18 ≈ 0.556
      ├── Some((8, 4)): 3/10 ≈ 0.300
      ├── Some((8, 5)): 14/22 ≈ 0.636
      ├── Some((8, 6)): 6/13 ≈ 0.462
      ├── Some((8, 7)): 9/17 ≈ 0.529
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((1, 5)): 636/1228 ≈ 0.518
    ├── Some((5, 0)): 92/172 ≈ 0.535
      ├── Some((0, 0)): 16/25 ≈ 0.640
      ├── Some((0, 1)): 10/19 ≈ 0.526
      ├── Some((0, 2)): 9/18 ≈ 0.500
      ├── Some((0, 3)): 13/22 ≈ 0.591
      ├── Some((0, 4)): 15/24 ≈ 0.625
      ├── Some((0, 5)): 3/11 ≈ 0.273
      ├── Some((0, 6)): 8/17 ≈ 0.471
      ├── Some((0, 7)): 7/16 ≈ 0.438
      └── Some((0, 8)): 10/19 ≈ 0.526
    ├── Some((5, 2)): 88/166 ≈ 0.530
      ├── Some((2, 0)): 8/17 ≈ 0.471
      ├── Some((2, 1)): 7/16 ≈ 0.438
      ├── Some((2, 2)): 10/19 ≈ 0.526
      ├── Some((2, 3)): 7/16 ≈ 0.438
      ├── Some((2, 4)): 7/16 ≈ 0.438
      ├── Some((2, 5)): 30/38 ≈ 0.789
      ├── Some((2, 6)): 8/17 ≈ 0.471
      ├── Some((2, 7)): 6/14 ≈ 0.429
      └── Some((2, 8)): 4/12 ≈ 0.333
    ├── Some((5, 3)): 86/163 ≈ 0.528
      ├── Some((3, 0)): 7/15 ≈ 0.467
      ├── Some((3, 1)): 3/11 ≈ 0.273
      ├── Some((3, 2)): 14/23 ≈ 0.609
      ├── Some((3, 3)): 11/20 ≈ 0.550
      ├── Some((3, 4)): 19/28 ≈ 0.679
      ├── Some((3, 5)): 12/21 ≈ 0.571
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 9/18 ≈ 0.500
      └── Some((3, 8)): 5/13 ≈ 0.385
    ├── Some((5, 4)): 108/195 ≈ 0.554
      ├── Some((4, 0)): 15/25 ≈ 0.600
      ├── Some((4, 1)): 19/29 ≈ 0.655
      ├── Some((4, 2)): 13/23 ≈ 0.565
      ├── Some((4, 3)): 2/10 ≈ 0.200
      ├── Some((4, 4)): 7/17 ≈ 0.412
      ├── Some((4, 5)): 18/28 ≈ 0.643
      ├── Some((4, 6)): 8/18 ≈ 0.444
      ├── Some((4, 7)): 6/15 ≈ 0.400
      └── Some((4, 8)): 19/29 ≈ 0.655
    ├── Some((5, 5)): 28/75 ≈ 0.373
      ├── Some((5, 0)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 3/9 ≈ 0.333
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 2/8 ≈ 0.250
      ├── Some((5, 7)): 5/12 ≈ 0.417
      └── Some((5, 8)): 4/11 ≈ 0.364
    ├── Some((5, 6)): 72/143 ≈ 0.503
      ├── Some((6, 0)): 8/16 ≈ 0.500
      ├── Some((6, 1)): 8/16 ≈ 0.500
      ├── Some((6, 2)): 10/18 ≈ 0.556
      ├── Some((6, 3)): 3/10 ≈ 0.300
      ├── Some((6, 4)): 5/13 ≈ 0.385
      ├── Some((6, 5)): 19/27 ≈ 0.704
      ├── Some((6, 6)): 8/16 ≈ 0.500
      ├── Some((6, 7)): 5/13 ≈ 0.385
      └── Some((6, 8)): 5/13 ≈ 0.385
    ├── Some((5, 7)): 80/155 ≈ 0.516
      ├── Some((7, 0)): 6/14 ≈ 0.429
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 11/20 ≈ 0.550
      ├── Some((7, 3)): 2/9 ≈ 0.222
      ├── Some((7, 4)): 12/21 ≈ 0.571
      ├── Some((7, 5)): 9/18 ≈ 0.500
      ├── Some((7, 6)): 8/16 ≈ 0.500
      ├── Some((7, 7)): 2/9 ≈ 0.222
      └── Some((7, 8)): 23/32 ≈ 0.719
    └── Some((5, 8)): 82/158 ≈ 0.519
      ├── Some((8, 0)): 8/16 ≈ 0.500
      ├── Some((8, 1)): 12/21 ≈ 0.571
      ├── Some((8, 2)): 2/9 ≈ 0.222
      ├── Some((8, 3)): 10/19 ≈ 0.526
      ├── Some((8, 4)): 9/17 ≈ 0.529
      ├── Some((8, 5)): 9/18 ≈ 0.500
      ├── Some((8, 6)): 8/16 ≈ 0.500
      ├── Some((8, 7)): 12/21 ≈ 0.571
      └── Some((8, 8)): 11/20 ≈ 0.550
  ├── Some((1, 6)): 732/1392 ≈ 0.526
    ├── Some((6, 0)): 104/188 ≈ 0.553
      ├── Some((0, 0)): 10/19 ≈ 0.526
      ├── Some((0, 1)): 4/12 ≈ 0.333
      ├── Some((0, 2)): 13/22 ≈ 0.591
      ├── Some((0, 3)): 19/29 ≈ 0.655
      ├── Some((0, 4)): 10/19 ≈ 0.526
      ├── Some((0, 5)): 15/25 ≈ 0.600
      ├── Some((0, 6)): 12/21 ≈ 0.571
      ├── Some((0, 7)): 17/27 ≈ 0.630
      └── Some((0, 8)): 4/13 ≈ 0.308
    ├── Some((6, 1)): 59/122 ≈ 0.484
      ├── Some((1, 0)): 14/22 ≈ 0.636
      ├── Some((1, 1)): 7/15 ≈ 0.467
      ├── Some((1, 2)): 3/10 ≈ 0.300
      ├── Some((1, 3)): 8/16 ≈ 0.500
      ├── Some((1, 4)): 14/22 ≈ 0.636
      ├── Some((1, 5)): 9/17 ≈ 0.529
      ├── Some((1, 7)): 1/8 ≈ 0.125
      └── Some((1, 8)): 3/11 ≈ 0.273
    ├── Some((6, 2)): 54/115 ≈ 0.470
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 12/19 ≈ 0.632
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 5/12 ≈ 0.417
      ├── Some((2, 4)): 7/14 ≈ 0.500
      ├── Some((2, 5)): 7/14 ≈ 0.500
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 4/11 ≈ 0.364
      └── Some((2, 8)): 4/11 ≈ 0.364
    ├── Some((6, 3)): 97/178 ≈ 0.545
      ├── Some((3, 0)): 9/18 ≈ 0.500
      ├── Some((3, 1)): 18/27 ≈ 0.667
      ├── Some((3, 2)): 18/28 ≈ 0.643
      ├── Some((3, 3)): 6/15 ≈ 0.400
      ├── Some((3, 4)): 3/11 ≈ 0.273
      ├── Some((3, 5)): 3/11 ≈ 0.273
      ├── Some((3, 6)): 21/30 ≈ 0.700
      ├── Some((3, 7)): 12/21 ≈ 0.571
      └── Some((3, 8)): 7/16 ≈ 0.438
    ├── Some((6, 4)): 113/200 ≈ 0.565
      ├── Some((4, 0)): 17/27 ≈ 0.630
      ├── Some((4, 1)): 7/16 ≈ 0.438
      ├── Some((4, 2)): 10/20 ≈ 0.500
      ├── Some((4, 3)): 11/21 ≈ 0.524
      ├── Some((4, 4)): 7/16 ≈ 0.438
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 6)): 24/34 ≈ 0.706
      ├── Some((4, 7)): 17/27 ≈ 0.630
      └── Some((4, 8)): 11/21 ≈ 0.524
    ├── Some((6, 5)): 58/121 ≈ 0.479
      ├── Some((5, 0)): 11/19 ≈ 0.579
      ├── Some((5, 2)): 2/9 ≈ 0.222
      ├── Some((5, 3)): 3/10 ≈ 0.300
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 12/20 ≈ 0.600
      ├── Some((5, 6)): 10/18 ≈ 0.556
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((6, 6)): 99/180 ≈ 0.550
      ├── Some((6, 0)): 11/21 ≈ 0.524
      ├── Some((6, 1)): 10/20 ≈ 0.500
      ├── Some((6, 2)): 6/15 ≈ 0.400
      ├── Some((6, 3)): 12/22 ≈ 0.545
      ├── Some((6, 4)): 10/20 ≈ 0.500
      ├── Some((6, 5)): 11/21 ≈ 0.524
      ├── Some((6, 7)): 33/44 ≈ 0.750
      └── Some((6, 8)): 6/16 ≈ 0.375
    ├── Some((6, 7)): 73/143 ≈ 0.510
      ├── Some((7, 0)): 5/13 ≈ 0.385
      ├── Some((7, 1)): 1/8 ≈ 0.125
      ├── Some((7, 2)): 10/18 ≈ 0.556
      ├── Some((7, 3)): 16/24 ≈ 0.667
      ├── Some((7, 4)): 2/9 ≈ 0.222
      ├── Some((7, 5)): 15/23 ≈ 0.652
      ├── Some((7, 6)): 12/20 ≈ 0.600
      ├── Some((7, 7)): 2/9 ≈ 0.222
      └── Some((7, 8)): 10/18 ≈ 0.556
    └── Some((6, 8)): 74/144 ≈ 0.514
      ├── Some((8, 0)): 7/15 ≈ 0.467
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 9/17 ≈ 0.529
      ├── Some((8, 3)): 13/21 ≈ 0.619
      ├── Some((8, 4)): 7/15 ≈ 0.467
      ├── Some((8, 5)): 15/23 ≈ 0.652
      ├── Some((8, 6)): 3/10 ≈ 0.300
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 8/16 ≈ 0.500
  ├── Some((1, 7)): 451/908 ≈ 0.497
    ├── Some((7, 0)): 41/88 ≈ 0.466
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 10/15 ≈ 0.667
      ├── Some((0, 2)): 7/12 ≈ 0.583
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((7, 1)): 55/108 ≈ 0.509
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 1)): 4/10 ≈ 0.400
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 12/19 ≈ 0.632
      ├── Some((1, 4)): 14/20 ≈ 0.700
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 5/12 ≈ 0.417
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((7, 2)): 79/142 ≈ 0.556
      ├── Some((2, 0)): 11/18 ≈ 0.611
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 2)): 10/17 ≈ 0.588
      ├── Some((2, 3)): 12/19 ≈ 0.632
      ├── Some((2, 4)): 4/11 ≈ 0.364
      ├── Some((2, 5)): 10/17 ≈ 0.588
      ├── Some((2, 6)): 7/14 ≈ 0.500
      ├── Some((2, 7)): 13/20 ≈ 0.650
      └── Some((2, 8)): 8/15 ≈ 0.533
    ├── Some((7, 3)): 49/99 ≈ 0.495
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 11/16 ≈ 0.688
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 6/11 ≈ 0.545
      ├── Some((3, 6)): 8/13 ≈ 0.615
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 6/12 ≈ 0.500
    ├── Some((7, 4)): 48/98 ≈ 0.490
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 6/12 ≈ 0.500
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 8/13 ≈ 0.615
      ├── Some((4, 6)): 7/13 ≈ 0.538
      ├── Some((4, 7)): 8/13 ≈ 0.615
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((7, 5)): 71/131 ≈ 0.542
      ├── Some((5, 0)): 12/20 ≈ 0.600
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 13/21 ≈ 0.619
      ├── Some((5, 4)): 6/13 ≈ 0.462
      ├── Some((5, 5)): 3/10 ≈ 0.300
      ├── Some((5, 6)): 13/21 ≈ 0.619
      ├── Some((5, 7)): 18/26 ≈ 0.692
      └── Some((5, 8)): 1/8 ≈ 0.125
    ├── Some((7, 6)): 35/79 ≈ 0.443
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 4)): 9/13 ≈ 0.692
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 6/11 ≈ 0.545
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 6/11 ≈ 0.545
    ├── Some((7, 7)): 31/73 ≈ 0.425
      ├── Some((7, 0)): 10/15 ≈ 0.667
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 1/6 ≈ 0.167
      ├── Some((7, 5)): 0/5 ≈ 0.000
      ├── Some((7, 6)): 4/9 ≈ 0.444
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((7, 8)): 42/89 ≈ 0.472
      ├── Some((8, 0)): 5/10 ≈ 0.500
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 5/11 ≈ 0.455
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 6/11 ≈ 0.545
      ├── Some((8, 6)): 6/11 ≈ 0.545
      ├── Some((8, 7)): 3/8 ≈ 0.375
      └── Some((8, 8)): 6/11 ≈ 0.545
  └── Some((1, 8)): 526/1038 ≈ 0.507
    ├── Some((8, 0)): 38/85 ≈ 0.447
      ├── Some((0, 0)): 1/6 ≈ 0.167
      ├── Some((0, 1)): 7/12 ≈ 0.583
      ├── Some((0, 2)): 9/14 ≈ 0.643
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 0/5 ≈ 0.000
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 4/10 ≈ 0.400
      └── Some((0, 8)): 9/14 ≈ 0.643
    ├── Some((8, 1)): 52/106 ≈ 0.491
      ├── Some((1, 0)): 3/9 ≈ 0.333
      ├── Some((1, 1)): 10/17 ≈ 0.588
      ├── Some((1, 2)): 5/12 ≈ 0.417
      ├── Some((1, 3)): 7/14 ≈ 0.500
      ├── Some((1, 4)): 8/15 ≈ 0.533
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 15/22 ≈ 0.682
      └── Some((1, 7)): 2/8 ≈ 0.250
    ├── Some((8, 2)): 42/91 ≈ 0.462
      ├── Some((2, 0)): 8/13 ≈ 0.615
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 2)): 1/6 ≈ 0.167
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 9/14 ≈ 0.643
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 0/5 ≈ 0.000
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 7/13 ≈ 0.538
    ├── Some((8, 3)): 55/110 ≈ 0.500
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 8/15 ≈ 0.533
      ├── Some((3, 2)): 6/12 ≈ 0.500
      ├── Some((3, 3)): 11/17 ≈ 0.647
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 12/18 ≈ 0.667
      ├── Some((3, 7)): 0/6 ≈ 0.000
      └── Some((3, 8)): 6/12 ≈ 0.500
    ├── Some((8, 4)): 81/148 ≈ 0.547
      ├── Some((4, 0)): 1/8 ≈ 0.125
      ├── Some((4, 1)): 8/16 ≈ 0.500
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 12/20 ≈ 0.600
      ├── Some((4, 4)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 12/20 ≈ 0.600
      ├── Some((4, 7)): 16/23 ≈ 0.696
      └── Some((4, 8)): 14/22 ≈ 0.636
    ├── Some((8, 5)): 68/129 ≈ 0.527
      ├── Some((5, 0)): 13/21 ≈ 0.619
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 13/21 ≈ 0.619
      ├── Some((5, 4)): 14/22 ≈ 0.636
      ├── Some((5, 5)): 4/11 ≈ 0.364
      ├── Some((5, 6)): 8/16 ≈ 0.500
      ├── Some((5, 7)): 3/10 ≈ 0.300
      └── Some((5, 8)): 4/11 ≈ 0.364
    ├── Some((8, 6)): 53/108 ≈ 0.491
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 11/17 ≈ 0.647
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 11/17 ≈ 0.647
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 1/7 ≈ 0.143
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 9/16 ≈ 0.562
    ├── Some((8, 7)): 55/111 ≈ 0.495
      ├── Some((7, 0)): 12/18 ≈ 0.667
      ├── Some((7, 1)): 2/8 ≈ 0.250
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 6/13 ≈ 0.462
      ├── Some((7, 4)): 5/11 ≈ 0.455
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 5/11 ≈ 0.455
      ├── Some((7, 7)): 10/17 ≈ 0.588
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((8, 8)): 82/149 ≈ 0.550
      ├── Some((8, 0)): 9/17 ≈ 0.529
      ├── Some((8, 1)): 12/20 ≈ 0.600
      ├── Some((8, 2)): 6/14 ≈ 0.429
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 12/20 ≈ 0.600
      ├── Some((8, 5)): 13/22 ≈ 0.591
      ├── Some((8, 6)): 7/15 ≈ 0.467
      └── Some((8, 7)): 16/25 ≈ 0.640
├── Some((5, 2)): 4451/8728 ≈ 0.510
  ├── Some((2, 0)): 438/873 ≈ 0.502
    ├── Some((0, 0)): 55/106 ≈ 0.519
      ├── Some((0, 1)): 10/16 ≈ 0.625
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 9/16 ≈ 0.562
      ├── Some((0, 4)): 11/17 ≈ 0.647
      ├── Some((0, 5)): 10/16 ≈ 0.625
      ├── Some((0, 6)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 4/10 ≈ 0.400
      └── Some((0, 8)): 2/8 ≈ 0.250
    ├── Some((0, 1)): 49/98 ≈ 0.500
      ├── Some((1, 0)): 7/12 ≈ 0.583
      ├── Some((1, 1)): 5/11 ≈ 0.455
      ├── Some((1, 2)): 9/14 ≈ 0.643
      ├── Some((1, 3)): 6/12 ≈ 0.500
      ├── Some((1, 4)): 7/13 ≈ 0.538
      ├── Some((1, 5)): 10/15 ≈ 0.667
      ├── Some((1, 6)): 0/5 ≈ 0.000
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((0, 2)): 81/142 ≈ 0.570
      ├── Some((2, 1)): 5/12 ≈ 0.417
      ├── Some((2, 2)): 13/21 ≈ 0.619
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 9/17 ≈ 0.529
      ├── Some((2, 5)): 9/17 ≈ 0.529
      ├── Some((2, 6)): 15/23 ≈ 0.652
      ├── Some((2, 7)): 17/25 ≈ 0.680
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((0, 3)): 43/89 ≈ 0.483
      ├── Some((3, 0)): 7/12 ≈ 0.583
      ├── Some((3, 1)): 0/5 ≈ 0.000
      ├── Some((3, 2)): 0/5 ≈ 0.000
      ├── Some((3, 3)): 10/15 ≈ 0.667
      ├── Some((3, 4)): 7/12 ≈ 0.583
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 6/11 ≈ 0.545
    ├── Some((0, 4)): 31/72 ≈ 0.431
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 6/10 ≈ 0.600
      ├── Some((4, 2)): 3/8 ≈ 0.375
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 4/9 ≈ 0.444
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 7/11 ≈ 0.636
      └── Some((4, 8)): 1/5 ≈ 0.200
    ├── Some((0, 5)): 32/73 ≈ 0.438
      ├── Some((5, 0)): 6/11 ≈ 0.545
      ├── Some((5, 1)): 1/6 ≈ 0.167
      ├── Some((5, 3)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 5/10 ≈ 0.500
      ├── Some((5, 6)): 2/7 ≈ 0.286
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 7/12 ≈ 0.583
    ├── Some((0, 6)): 72/130 ≈ 0.554
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 11/17 ≈ 0.647
      ├── Some((6, 3)): 10/17 ≈ 0.588
      ├── Some((6, 4)): 7/14 ≈ 0.500
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 11/17 ≈ 0.647
      ├── Some((6, 7)): 15/21 ≈ 0.714
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((0, 7)): 45/92 ≈ 0.489
      ├── Some((7, 0)): 0/5 ≈ 0.000
      ├── Some((7, 1)): 4/9 ≈ 0.444
      ├── Some((7, 2)): 1/6 ≈ 0.167
      ├── Some((7, 3)): 6/11 ≈ 0.545
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 10/15 ≈ 0.667
      ├── Some((7, 6)): 8/13 ≈ 0.615
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 7/12 ≈ 0.583
    └── Some((0, 8)): 30/70 ≈ 0.429
      ├── Some((8, 0)): 8/12 ≈ 0.667
      ├── Some((8, 1)): 3/7 ≈ 0.429
      ├── Some((8, 2)): 2/6 ≈ 0.333
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((2, 1)): 667/1265 ≈ 0.527
    ├── Some((1, 0)): 48/103 ≈ 0.466
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 3/9 ≈ 0.333
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 1/7 ≈ 0.143
      ├── Some((0, 4)): 9/15 ≈ 0.600
      ├── Some((0, 5)): 7/13 ≈ 0.538
      ├── Some((0, 6)): 7/13 ≈ 0.538
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 4/10 ≈ 0.400
    ├── Some((1, 1)): 58/118 ≈ 0.492
      ├── Some((1, 0)): 8/15 ≈ 0.533
      ├── Some((1, 2)): 3/10 ≈ 0.300
      ├── Some((1, 3)): 8/16 ≈ 0.500
      ├── Some((1, 4)): 15/23 ≈ 0.652
      ├── Some((1, 5)): 11/19 ≈ 0.579
      ├── Some((1, 6)): 3/10 ≈ 0.300
      ├── Some((1, 7)): 6/13 ≈ 0.462
      └── Some((1, 8)): 4/11 ≈ 0.364
    ├── Some((1, 2)): 117/202 ≈ 0.579
      ├── Some((2, 0)): 30/41 ≈ 0.732
      ├── Some((2, 2)): 13/24 ≈ 0.542
      ├── Some((2, 3)): 21/32 ≈ 0.656
      ├── Some((2, 4)): 6/16 ≈ 0.375
      ├── Some((2, 5)): 11/21 ≈ 0.524
      ├── Some((2, 6)): 9/19 ≈ 0.474
      ├── Some((2, 7)): 19/30 ≈ 0.633
      └── Some((2, 8)): 8/18 ≈ 0.444
    ├── Some((1, 3)): 99/176 ≈ 0.562
      ├── Some((3, 0)): 7/15 ≈ 0.467
      ├── Some((3, 1)): 9/17 ≈ 0.529
      ├── Some((3, 2)): 10/19 ≈ 0.526
      ├── Some((3, 3)): 5/13 ≈ 0.385
      ├── Some((3, 4)): 13/22 ≈ 0.591
      ├── Some((3, 5)): 20/29 ≈ 0.690
      ├── Some((3, 6)): 15/24 ≈ 0.625
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 14/23 ≈ 0.609
    ├── Some((1, 4)): 52/109 ≈ 0.477
      ├── Some((4, 0)): 7/13 ≈ 0.538
      ├── Some((4, 1)): 12/18 ≈ 0.667
      ├── Some((4, 2)): 1/7 ≈ 0.143
      ├── Some((4, 3)): 4/10 ≈ 0.400
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((1, 5)): 108/189 ≈ 0.571
      ├── Some((5, 0)): 19/30 ≈ 0.633
      ├── Some((5, 1)): 16/26 ≈ 0.615
      ├── Some((5, 3)): 9/19 ≈ 0.474
      ├── Some((5, 4)): 10/20 ≈ 0.500
      ├── Some((5, 5)): 17/27 ≈ 0.630
      ├── Some((5, 6)): 10/20 ≈ 0.500
      ├── Some((5, 7)): 11/21 ≈ 0.524
      └── Some((5, 8)): 15/25 ≈ 0.600
    ├── Some((1, 6)): 42/94 ≈ 0.447
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 6/12 ≈ 0.500
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 0/5 ≈ 0.000
      ├── Some((6, 7)): 8/14 ≈ 0.571
      └── Some((6, 8)): 9/15 ≈ 0.600
    ├── Some((1, 7)): 57/116 ≈ 0.491
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 5/11 ≈ 0.455
      ├── Some((7, 2)): 9/16 ≈ 0.562
      ├── Some((7, 3)): 10/17 ≈ 0.588
      ├── Some((7, 4)): 11/17 ≈ 0.647
      ├── Some((7, 5)): 0/6 ≈ 0.000
      ├── Some((7, 6)): 1/7 ≈ 0.143
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 9/16 ≈ 0.562
    └── Some((1, 8)): 85/157 ≈ 0.541
      ├── Some((8, 0)): 15/23 ≈ 0.652
      ├── Some((8, 1)): 11/19 ≈ 0.579
      ├── Some((8, 2)): 11/19 ≈ 0.579
      ├── Some((8, 3)): 8/16 ≈ 0.500
      ├── Some((8, 4)): 7/15 ≈ 0.467
      ├── Some((8, 5)): 13/21 ≈ 0.619
      ├── Some((8, 6)): 4/12 ≈ 0.333
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 9/17 ≈ 0.529
  ├── Some((2, 2)): 448/891 ≈ 0.503
    ├── Some((2, 0)): 79/144 ≈ 0.549
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 12/20 ≈ 0.600
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 13/20 ≈ 0.650
      ├── Some((0, 4)): 7/14 ≈ 0.500
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 7/14 ≈ 0.500
      ├── Some((0, 7)): 16/23 ≈ 0.696
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((2, 1)): 58/115 ≈ 0.504
      ├── Some((1, 0)): 1/7 ≈ 0.143
      ├── Some((1, 1)): 9/16 ≈ 0.562
      ├── Some((1, 2)): 10/16 ≈ 0.625
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 1/7 ≈ 0.143
      ├── Some((1, 6)): 13/19 ≈ 0.684
      ├── Some((1, 7)): 10/17 ≈ 0.588
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((2, 3)): 35/80 ≈ 0.438
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 0/4 ≈ 0.000
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 6/11 ≈ 0.545
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 1/6 ≈ 0.167
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 5/10 ≈ 0.500
    ├── Some((2, 4)): 57/113 ≈ 0.504
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 2/8 ≈ 0.250
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 7/13 ≈ 0.538
      ├── Some((4, 4)): 8/15 ≈ 0.533
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 19/25 ≈ 0.760
      └── Some((4, 8)): 2/8 ≈ 0.250
    ├── Some((2, 5)): 60/117 ≈ 0.513
      ├── Some((5, 0)): 1/7 ≈ 0.143
      ├── Some((5, 1)): 2/9 ≈ 0.222
      ├── Some((5, 3)): 9/17 ≈ 0.529
      ├── Some((5, 4)): 16/23 ≈ 0.696
      ├── Some((5, 5)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 13/21 ≈ 0.619
      └── Some((5, 8)): 5/12 ≈ 0.417
    ├── Some((2, 6)): 36/82 ≈ 0.439
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 5/10 ≈ 0.500
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 3/8 ≈ 0.375
      ├── Some((6, 7)): 0/5 ≈ 0.000
      └── Some((6, 8)): 8/13 ≈ 0.615
    ├── Some((2, 7)): 77/142 ≈ 0.542
      ├── Some((7, 0)): 3/10 ≈ 0.300
      ├── Some((7, 1)): 14/21 ≈ 0.667
      ├── Some((7, 2)): 11/18 ≈ 0.611
      ├── Some((7, 3)): 4/11 ≈ 0.364
      ├── Some((7, 4)): 6/13 ≈ 0.462
      ├── Some((7, 5)): 1/8 ≈ 0.125
      ├── Some((7, 6)): 12/19 ≈ 0.632
      ├── Some((7, 7)): 11/19 ≈ 0.579
      └── Some((7, 8)): 15/22 ≈ 0.682
    └── Some((2, 8)): 46/97 ≈ 0.474
      ├── Some((8, 0)): 8/14 ≈ 0.571
      ├── Some((8, 1)): 7/13 ≈ 0.538
      ├── Some((8, 2)): 9/14 ≈ 0.643
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 8/14 ≈ 0.571
      ├── Some((8, 7)): 2/7 ≈ 0.286
      └── Some((8, 8)): 3/9 ≈ 0.333
  ├── Some((2, 3)): 633/1207 ≈ 0.524
    ├── Some((3, 0)): 73/139 ≈ 0.525
      ├── Some((0, 0)): 2/9 ≈ 0.222
      ├── Some((0, 1)): 4/11 ≈ 0.364
      ├── Some((0, 2)): 19/26 ≈ 0.731
      ├── Some((0, 3)): 8/15 ≈ 0.533
      ├── Some((0, 4)): 7/14 ≈ 0.500
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 13/21 ≈ 0.619
      ├── Some((0, 7)): 6/13 ≈ 0.462
      └── Some((0, 8)): 9/17 ≈ 0.529
    ├── Some((3, 1)): 26/68 ≈ 0.382
      ├── Some((1, 0)): 5/9 ≈ 0.556
      ├── Some((1, 1)): 4/9 ≈ 0.444
      ├── Some((1, 2)): 5/10 ≈ 0.500
      ├── Some((1, 3)): 1/5 ≈ 0.200
      ├── Some((1, 4)): 4/9 ≈ 0.444
      ├── Some((1, 5)): 1/5 ≈ 0.200
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((3, 2)): 104/182 ≈ 0.571
      ├── Some((2, 0)): 13/23 ≈ 0.565
      ├── Some((2, 1)): 15/25 ≈ 0.600
      ├── Some((2, 2)): 9/18 ≈ 0.500
      ├── Some((2, 4)): 16/26 ≈ 0.615
      ├── Some((2, 5)): 21/31 ≈ 0.677
      ├── Some((2, 6)): 10/19 ≈ 0.526
      ├── Some((2, 7)): 8/17 ≈ 0.471
      └── Some((2, 8)): 12/22 ≈ 0.545
    ├── Some((3, 3)): 94/168 ≈ 0.560
      ├── Some((3, 0)): 11/20 ≈ 0.550
      ├── Some((3, 1)): 12/21 ≈ 0.571
      ├── Some((3, 2)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 11/20 ≈ 0.550
      ├── Some((3, 5)): 5/14 ≈ 0.357
      ├── Some((3, 6)): 19/29 ≈ 0.655
      ├── Some((3, 7)): 12/21 ≈ 0.571
      └── Some((3, 8)): 15/25 ≈ 0.600
    ├── Some((3, 4)): 60/120 ≈ 0.500
      ├── Some((4, 0)): 11/18 ≈ 0.611
      ├── Some((4, 1)): 6/13 ≈ 0.462
      ├── Some((4, 2)): 2/8 ≈ 0.250
      ├── Some((4, 3)): 12/19 ≈ 0.632
      ├── Some((4, 4)): 1/7 ≈ 0.143
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 12/19 ≈ 0.632
      ├── Some((4, 7)): 10/17 ≈ 0.588
      └── Some((4, 8)): 2/8 ≈ 0.250
    ├── Some((3, 5)): 61/121 ≈ 0.504
      ├── Some((5, 0)): 3/10 ≈ 0.300
      ├── Some((5, 1)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 10/18 ≈ 0.556
      ├── Some((5, 6)): 12/20 ≈ 0.600
      ├── Some((5, 7)): 3/10 ≈ 0.300
      └── Some((5, 8)): 11/19 ≈ 0.579
    ├── Some((3, 6)): 103/181 ≈ 0.569
      ├── Some((6, 0)): 14/23 ≈ 0.609
      ├── Some((6, 1)): 5/13 ≈ 0.385
      ├── Some((6, 2)): 4/12 ≈ 0.333
      ├── Some((6, 3)): 14/23 ≈ 0.609
      ├── Some((6, 4)): 27/35 ≈ 0.771
      ├── Some((6, 5)): 11/20 ≈ 0.550
      ├── Some((6, 6)): 10/19 ≈ 0.526
      ├── Some((6, 7)): 8/17 ≈ 0.471
      └── Some((6, 8)): 9/18 ≈ 0.500
    ├── Some((3, 7)): 55/112 ≈ 0.491
      ├── Some((7, 0)): 19/25 ≈ 0.760
      ├── Some((7, 1)): 8/15 ≈ 0.533
      ├── Some((7, 2)): 10/17 ≈ 0.588
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 4)): 2/8 ≈ 0.250
      ├── Some((7, 5)): 1/7 ≈ 0.143
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 2/8 ≈ 0.250
    └── Some((3, 8)): 57/115 ≈ 0.496
      ├── Some((8, 0)): 6/12 ≈ 0.500
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 1/7 ≈ 0.143
      ├── Some((8, 3)): 11/17 ≈ 0.647
      ├── Some((8, 4)): 9/16 ≈ 0.562
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 8/15 ≈ 0.533
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 7/14 ≈ 0.500
  ├── Some((2, 4)): 443/882 ≈ 0.502
    ├── Some((4, 0)): 55/106 ≈ 0.519
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 10/15 ≈ 0.667
      ├── Some((0, 2)): 6/12 ≈ 0.500
      ├── Some((0, 3)): 6/12 ≈ 0.500
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 16/21 ≈ 0.762
      └── Some((0, 8)): 2/8 ≈ 0.250
    ├── Some((4, 1)): 30/70 ≈ 0.429
      ├── Some((1, 0)): 4/8 ≈ 0.500
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 4/8 ≈ 0.500
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 1/5 ≈ 0.200
      ├── Some((1, 5)): 5/9 ≈ 0.556
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 4/8 ≈ 0.500
    ├── Some((4, 2)): 48/96 ≈ 0.500
      ├── Some((2, 0)): 2/8 ≈ 0.250
      ├── Some((2, 1)): 10/16 ≈ 0.625
      ├── Some((2, 2)): 11/17 ≈ 0.647
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 10/16 ≈ 0.625
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 2/8 ≈ 0.250
    ├── Some((4, 3)): 35/77 ≈ 0.455
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 1)): 5/10 ≈ 0.500
      ├── Some((3, 2)): 0/4 ≈ 0.000
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 8/12 ≈ 0.667
      ├── Some((3, 5)): 11/15 ≈ 0.733
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((4, 4)): 48/96 ≈ 0.500
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 7/13 ≈ 0.538
      ├── Some((4, 2)): 8/14 ≈ 0.571
      ├── Some((4, 3)): 7/13 ≈ 0.538
      ├── Some((4, 5)): 1/7 ≈ 0.143
      ├── Some((4, 6)): 8/14 ≈ 0.571
      ├── Some((4, 7)): 8/14 ≈ 0.571
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((4, 5)): 58/111 ≈ 0.523
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 14/20 ≈ 0.700
      ├── Some((5, 3)): 3/9 ≈ 0.333
      ├── Some((5, 4)): 13/20 ≈ 0.650
      ├── Some((5, 5)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 7/14 ≈ 0.500
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 5/12 ≈ 0.417
    ├── Some((4, 6)): 47/95 ≈ 0.495
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 8/13 ≈ 0.615
      ├── Some((6, 3)): 9/14 ≈ 0.643
      ├── Some((6, 4)): 8/13 ≈ 0.615
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 0/5 ≈ 0.000
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((4, 7)): 51/101 ≈ 0.505
      ├── Some((7, 0)): 6/12 ≈ 0.500
      ├── Some((7, 1)): 7/13 ≈ 0.538
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 3)): 2/7 ≈ 0.286
      ├── Some((7, 4)): 8/14 ≈ 0.571
      ├── Some((7, 5)): 8/14 ≈ 0.571
      ├── Some((7, 6)): 7/13 ≈ 0.538
      ├── Some((7, 7)): 9/14 ≈ 0.643
      └── Some((7, 8)): 1/6 ≈ 0.167
    └── Some((4, 8)): 71/129 ≈ 0.550
      ├── Some((8, 0)): 6/13 ≈ 0.462
      ├── Some((8, 1)): 11/17 ≈ 0.647
      ├── Some((8, 2)): 11/17 ≈ 0.647
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 13/19 ≈ 0.684
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 11/18 ≈ 0.611
      └── Some((8, 8)): 5/12 ≈ 0.417
  ├── Some((2, 5)): 441/878 ≈ 0.502
    ├── Some((5, 0)): 49/101 ≈ 0.485
      ├── Some((0, 0)): 10/15 ≈ 0.667
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 8/14 ≈ 0.571
      ├── Some((0, 3)): 2/8 ≈ 0.250
      ├── Some((0, 4)): 7/13 ≈ 0.538
      ├── Some((0, 5)): 10/15 ≈ 0.667
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 2/8 ≈ 0.250
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((5, 1)): 57/112 ≈ 0.509
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 9/15 ≈ 0.600
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 3/9 ≈ 0.333
      ├── Some((1, 4)): 7/13 ≈ 0.538
      ├── Some((1, 5)): 3/9 ≈ 0.333
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 10/16 ≈ 0.625
    ├── Some((5, 3)): 65/124 ≈ 0.524
      ├── Some((3, 0)): 10/17 ≈ 0.588
      ├── Some((3, 1)): 3/9 ≈ 0.333
      ├── Some((3, 2)): 10/17 ≈ 0.588
      ├── Some((3, 3)): 9/16 ≈ 0.562
      ├── Some((3, 4)): 1/7 ≈ 0.143
      ├── Some((3, 5)): 2/8 ≈ 0.250
      ├── Some((3, 6)): 12/18 ≈ 0.667
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 10/17 ≈ 0.588
    ├── Some((5, 4)): 47/98 ≈ 0.480
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 5/11 ≈ 0.455
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 2/7 ≈ 0.286
      ├── Some((4, 4)): 6/12 ≈ 0.500
      ├── Some((4, 5)): 3/9 ≈ 0.333
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 12/17 ≈ 0.706
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((5, 5)): 44/94 ≈ 0.468
      ├── Some((5, 0)): 3/10 ≈ 0.300
      ├── Some((5, 1)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 8/15 ≈ 0.533
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 5/12 ≈ 0.417
      ├── Some((5, 7)): 5/12 ≈ 0.417
      └── Some((5, 8)): 5/12 ≈ 0.417
    ├── Some((5, 6)): 77/141 ≈ 0.546
      ├── Some((6, 0)): 12/19 ≈ 0.632
      ├── Some((6, 1)): 8/15 ≈ 0.533
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 3)): 6/13 ≈ 0.462
      ├── Some((6, 4)): 2/9 ≈ 0.222
      ├── Some((6, 5)): 16/23 ≈ 0.696
      ├── Some((6, 6)): 9/16 ≈ 0.562
      ├── Some((6, 7)): 9/16 ≈ 0.562
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((5, 7)): 52/105 ≈ 0.495
      ├── Some((7, 0)): 8/14 ≈ 0.571
      ├── Some((7, 1)): 9/15 ≈ 0.600
      ├── Some((7, 2)): 3/9 ≈ 0.333
      ├── Some((7, 3)): 10/15 ≈ 0.667
      ├── Some((7, 4)): 3/9 ≈ 0.333
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 0/5 ≈ 0.000
      ├── Some((7, 7)): 10/16 ≈ 0.625
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((5, 8)): 50/102 ≈ 0.490
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 8/13 ≈ 0.615
      ├── Some((8, 2)): 8/14 ≈ 0.571
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 6/12 ≈ 0.500
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 8/14 ≈ 0.571
      └── Some((8, 8)): 3/9 ≈ 0.333
  ├── Some((2, 6)): 558/1079 ≈ 0.517
    ├── Some((6, 0)): 53/107 ≈ 0.495
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 1/7 ≈ 0.143
      ├── Some((0, 3)): 8/14 ≈ 0.571
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 8/14 ≈ 0.571
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 11/17 ≈ 0.647
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((6, 1)): 44/94 ≈ 0.468
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 1/6 ≈ 0.167
      ├── Some((1, 2)): 8/13 ≈ 0.615
      ├── Some((1, 3)): 3/9 ≈ 0.333
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 10/15 ≈ 0.667
      ├── Some((1, 6)): 1/6 ≈ 0.167
      ├── Some((1, 7)): 6/12 ≈ 0.500
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((6, 2)): 65/124 ≈ 0.524
      ├── Some((2, 0)): 12/20 ≈ 0.600
      ├── Some((2, 1)): 6/13 ≈ 0.462
      ├── Some((2, 2)): 12/20 ≈ 0.600
      ├── Some((2, 3)): 2/9 ≈ 0.222
      ├── Some((2, 4)): 15/22 ≈ 0.682
      ├── Some((2, 5)): 6/13 ≈ 0.462
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((6, 3)): 70/132 ≈ 0.530
      ├── Some((3, 0)): 8/15 ≈ 0.533
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 16/23 ≈ 0.696
      ├── Some((3, 3)): 1/7 ≈ 0.143
      ├── Some((3, 4)): 8/15 ≈ 0.533
      ├── Some((3, 5)): 3/10 ≈ 0.300
      ├── Some((3, 6)): 12/19 ≈ 0.632
      ├── Some((3, 7)): 10/17 ≈ 0.588
      └── Some((3, 8)): 4/11 ≈ 0.364
    ├── Some((6, 4)): 60/117 ≈ 0.513
      ├── Some((4, 0)): 13/19 ≈ 0.684
      ├── Some((4, 1)): 6/12 ≈ 0.500
      ├── Some((4, 2)): 4/10 ≈ 0.400
      ├── Some((4, 3)): 11/17 ≈ 0.647
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 2/8 ≈ 0.250
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((6, 5)): 88/157 ≈ 0.561
      ├── Some((5, 0)): 9/18 ≈ 0.500
      ├── Some((5, 1)): 9/18 ≈ 0.500
      ├── Some((5, 3)): 13/22 ≈ 0.591
      ├── Some((5, 4)): 10/19 ≈ 0.526
      ├── Some((5, 5)): 20/29 ≈ 0.690
      ├── Some((5, 6)): 2/9 ≈ 0.222
      ├── Some((5, 7)): 16/25 ≈ 0.640
      └── Some((5, 8)): 8/16 ≈ 0.500
    ├── Some((6, 6)): 49/101 ≈ 0.485
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 3/9 ≈ 0.333
      ├── Some((6, 3)): 10/16 ≈ 0.625
      ├── Some((6, 4)): 1/7 ≈ 0.143
      ├── Some((6, 5)): 10/17 ≈ 0.588
      ├── Some((6, 7)): 10/17 ≈ 0.588
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((6, 7)): 84/151 ≈ 0.556
      ├── Some((7, 0)): 5/12 ≈ 0.417
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 14/22 ≈ 0.636
      ├── Some((7, 3)): 4/11 ≈ 0.364
      ├── Some((7, 4)): 17/24 ≈ 0.708
      ├── Some((7, 5)): 7/14 ≈ 0.500
      ├── Some((7, 6)): 3/10 ≈ 0.300
      ├── Some((7, 7)): 12/20 ≈ 0.600
      └── Some((7, 8)): 13/21 ≈ 0.619
    └── Some((6, 8)): 45/95 ≈ 0.474
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 7/13 ≈ 0.538
      ├── Some((8, 2)): 5/11 ≈ 0.455
      ├── Some((8, 3)): 8/13 ≈ 0.615
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 9/14 ≈ 0.643
  ├── Some((2, 7)): 381/774 ≈ 0.492
    ├── Some((7, 0)): 42/86 ≈ 0.488
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 8/12 ≈ 0.667
      ├── Some((0, 2)): 4/9 ≈ 0.444
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 9/13 ≈ 0.692
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((7, 1)): 54/103 ≈ 0.524
      ├── Some((1, 0)): 7/12 ≈ 0.583
      ├── Some((1, 1)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 1/6 ≈ 0.167
      ├── Some((1, 4)): 9/14 ≈ 0.643
      ├── Some((1, 5)): 5/11 ≈ 0.455
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 13/18 ≈ 0.722
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((7, 2)): 25/61 ≈ 0.410
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 0/4 ≈ 0.000
      ├── Some((2, 2)): 5/9 ≈ 0.556
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 5/9 ≈ 0.556
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 2/7 ≈ 0.286
      └── Some((2, 8)): 5/10 ≈ 0.500
    ├── Some((7, 3)): 52/100 ≈ 0.520
      ├── Some((3, 0)): 12/17 ≈ 0.706
      ├── Some((3, 1)): 9/14 ≈ 0.643
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 4/10 ≈ 0.400
      ├── Some((3, 6)): 6/11 ≈ 0.545
      ├── Some((3, 7)): 9/14 ≈ 0.643
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((7, 4)): 40/83 ≈ 0.482
      ├── Some((4, 0)): 7/11 ≈ 0.636
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 5/9 ≈ 0.556
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 4)): 4/9 ≈ 0.444
      ├── Some((4, 5)): 6/10 ≈ 0.600
      ├── Some((4, 6)): 4/9 ≈ 0.444
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 4/9 ≈ 0.444
    ├── Some((7, 5)): 53/101 ≈ 0.525
      ├── Some((5, 0)): 6/12 ≈ 0.500
      ├── Some((5, 1)): 7/13 ≈ 0.538
      ├── Some((5, 3)): 6/12 ≈ 0.500
      ├── Some((5, 4)): 10/15 ≈ 0.667
      ├── Some((5, 5)): 3/9 ≈ 0.333
      ├── Some((5, 6)): 7/13 ≈ 0.538
      ├── Some((5, 7)): 7/13 ≈ 0.538
      └── Some((5, 8)): 7/13 ≈ 0.538
    ├── Some((7, 6)): 26/62 ≈ 0.419
      ├── Some((6, 0)): 4/7 ≈ 0.571
      ├── Some((6, 1)): 3/7 ≈ 0.429
      ├── Some((6, 2)): 3/7 ≈ 0.429
      ├── Some((6, 3)): 4/8 ≈ 0.500
      ├── Some((6, 4)): 3/7 ≈ 0.429
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 4/8 ≈ 0.500
      ├── Some((6, 7)): 2/6 ≈ 0.333
      └── Some((6, 8)): 1/5 ≈ 0.200
    ├── Some((7, 7)): 39/81 ≈ 0.481
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 6/11 ≈ 0.545
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 6/11 ≈ 0.545
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 4/9 ≈ 0.444
      └── Some((7, 8)): 6/12 ≈ 0.500
    └── Some((7, 8)): 49/96 ≈ 0.510
      ├── Some((8, 0)): 4/9 ≈ 0.444
      ├── Some((8, 1)): 7/12 ≈ 0.583
      ├── Some((8, 2)): 11/16 ≈ 0.688
      ├── Some((8, 3)): 6/11 ≈ 0.545
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 7/12 ≈ 0.583
      └── Some((8, 8)): 3/8 ≈ 0.375
  └── Some((2, 8)): 441/878 ≈ 0.502
    ├── Some((8, 0)): 61/115 ≈ 0.530
      ├── Some((0, 0)): 5/11 ≈ 0.455
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 10/16 ≈ 0.625
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 7/13 ≈ 0.538
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 13/19 ≈ 0.684
      ├── Some((0, 7)): 6/12 ≈ 0.500
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((8, 1)): 35/77 ≈ 0.455
      ├── Some((1, 0)): 4/8 ≈ 0.500
      ├── Some((1, 1)): 5/9 ≈ 0.556
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 5/9 ≈ 0.556
      ├── Some((1, 4)): 4/9 ≈ 0.444
      ├── Some((1, 5)): 4/9 ≈ 0.444
      ├── Some((1, 6)): 2/7 ≈ 0.286
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((8, 2)): 68/124 ≈ 0.548
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 8/15 ≈ 0.533
      ├── Some((2, 2)): 18/25 ≈ 0.720
      ├── Some((2, 3)): 12/19 ≈ 0.632
      ├── Some((2, 4)): 1/7 ≈ 0.143
      ├── Some((2, 5)): 3/10 ≈ 0.300
      ├── Some((2, 6)): 9/16 ≈ 0.562
      └── Some((2, 7)): 11/18 ≈ 0.611
    ├── Some((8, 3)): 35/78 ≈ 0.449
      ├── Some((3, 0)): 8/13 ≈ 0.615
      ├── Some((3, 1)): 5/10 ≈ 0.500
      ├── Some((3, 2)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 0/4 ≈ 0.000
      ├── Some((3, 7)): 9/13 ≈ 0.692
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((8, 4)): 39/83 ≈ 0.470
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 4/9 ≈ 0.444
      ├── Some((4, 3)): 5/10 ≈ 0.500
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 6/10 ≈ 0.600
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((8, 5)): 59/112 ≈ 0.527
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 14/20 ≈ 0.700
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 1/7 ≈ 0.143
      ├── Some((5, 5)): 10/17 ≈ 0.588
      ├── Some((5, 6)): 7/14 ≈ 0.500
      ├── Some((5, 7)): 8/15 ≈ 0.533
      └── Some((5, 8)): 10/17 ≈ 0.588
    ├── Some((8, 6)): 26/64 ≈ 0.406
      ├── Some((6, 0)): 0/4 ≈ 0.000
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 4/8 ≈ 0.500
      ├── Some((6, 4)): 0/4 ≈ 0.000
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 6/10 ≈ 0.600
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 4/8 ≈ 0.500
    ├── Some((8, 7)): 51/101 ≈ 0.505
      ├── Some((7, 0)): 3/8 ≈ 0.375
      ├── Some((7, 1)): 11/16 ≈ 0.688
      ├── Some((7, 2)): 8/13 ≈ 0.615
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 4)): 6/11 ≈ 0.545
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 6/11 ≈ 0.545
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((8, 8)): 67/123 ≈ 0.545
      ├── Some((8, 0)): 11/18 ≈ 0.611
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 5/12 ≈ 0.417
      ├── Some((8, 3)): 7/14 ≈ 0.500
      ├── Some((8, 4)): 14/21 ≈ 0.667
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 9/16 ≈ 0.562
      └── Some((8, 7)): 7/14 ≈ 0.500
├── Some((5, 3)): 3671/7282 ≈ 0.504
  ├── Some((3, 0)): 442/868 ≈ 0.509
    ├── Some((0, 0)): 67/122 ≈ 0.549
      ├── Some((0, 1)): 10/17 ≈ 0.588
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 4/10 ≈ 0.400
      ├── Some((0, 7)): 17/23 ≈ 0.739
      └── Some((0, 8)): 10/17 ≈ 0.588
    ├── Some((0, 1)): 39/82 ≈ 0.476
      ├── Some((1, 0)): 7/12 ≈ 0.583
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 0/4 ≈ 0.000
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 11/15 ≈ 0.733
      ├── Some((1, 6)): 2/7 ≈ 0.286
      ├── Some((1, 7)): 5/10 ≈ 0.500
      └── Some((1, 8)): 5/10 ≈ 0.500
    ├── Some((0, 2)): 63/116 ≈ 0.543
      ├── Some((2, 0)): 3/9 ≈ 0.333
      ├── Some((2, 1)): 15/20 ≈ 0.750
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 9/15 ≈ 0.600
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 5/11 ≈ 0.455
      ├── Some((2, 7)): 9/15 ≈ 0.600
      └── Some((2, 8)): 7/13 ≈ 0.538
    ├── Some((0, 3)): 31/71 ≈ 0.437
      ├── Some((3, 1)): 6/10 ≈ 0.600
      ├── Some((3, 2)): 1/6 ≈ 0.167
      ├── Some((3, 3)): 5/10 ≈ 0.500
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 5/10 ≈ 0.500
      ├── Some((3, 6)): 3/8 ≈ 0.375
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 6/11 ≈ 0.545
    ├── Some((0, 4)): 37/79 ≈ 0.468
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 1/5 ≈ 0.200
      ├── Some((4, 2)): 4/9 ≈ 0.444
      ├── Some((4, 3)): 8/12 ≈ 0.667
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 7/11 ≈ 0.636
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 6/10 ≈ 0.600
    ├── Some((0, 5)): 46/92 ≈ 0.500
      ├── Some((5, 0)): 10/15 ≈ 0.667
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 0/5 ≈ 0.000
      ├── Some((5, 4)): 14/19 ≈ 0.737
      ├── Some((5, 5)): 3/9 ≈ 0.333
      ├── Some((5, 6)): 2/8 ≈ 0.250
      ├── Some((5, 7)): 8/14 ≈ 0.571
      └── Some((5, 8)): 4/10 ≈ 0.400
    ├── Some((0, 6)): 48/95 ≈ 0.505
      ├── Some((6, 0)): 4/9 ≈ 0.444
      ├── Some((6, 1)): 8/13 ≈ 0.615
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 6/11 ≈ 0.545
      ├── Some((6, 4)): 9/14 ≈ 0.643
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 0/5 ≈ 0.000
      ├── Some((6, 7)): 9/14 ≈ 0.643
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((0, 7)): 42/87 ≈ 0.483
      ├── Some((7, 0)): 8/13 ≈ 0.615
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 4/9 ≈ 0.444
      ├── Some((7, 3)): 1/6 ≈ 0.167
      ├── Some((7, 4)): 8/13 ≈ 0.615
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 0/5 ≈ 0.000
      ├── Some((7, 7)): 9/13 ≈ 0.692
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((0, 8)): 68/123 ≈ 0.553
      ├── Some((8, 0)): 12/18 ≈ 0.667
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 15/21 ≈ 0.714
      ├── Some((8, 4)): 8/14 ≈ 0.571
      ├── Some((8, 5)): 8/14 ≈ 0.571
      ├── Some((8, 6)): 2/8 ≈ 0.250
      ├── Some((8, 7)): 10/16 ≈ 0.625
      └── Some((8, 8)): 3/9 ≈ 0.333
  ├── Some((3, 1)): 417/825 ≈ 0.505
    ├── Some((1, 0)): 84/143 ≈ 0.587
      ├── Some((0, 0)): 7/14 ≈ 0.500
      ├── Some((0, 1)): 11/18 ≈ 0.611
      ├── Some((0, 2)): 12/18 ≈ 0.667
      ├── Some((0, 3)): 13/19 ≈ 0.684
      ├── Some((0, 4)): 12/18 ≈ 0.667
      ├── Some((0, 5)): 12/18 ≈ 0.667
      ├── Some((0, 6)): 10/17 ≈ 0.588
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((1, 1)): 40/83 ≈ 0.482
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 2/7 ≈ 0.286
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 9/14 ≈ 0.643
      ├── Some((1, 7)): 10/15 ≈ 0.667
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((1, 2)): 46/92 ≈ 0.500
      ├── Some((2, 0)): 6/12 ≈ 0.500
      ├── Some((2, 1)): 9/14 ≈ 0.643
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 0/5 ≈ 0.000
      ├── Some((2, 4)): 10/15 ≈ 0.667
      ├── Some((2, 5)): 0/5 ≈ 0.000
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 7/12 ≈ 0.583
      └── Some((2, 8)): 8/13 ≈ 0.615
    ├── Some((1, 3)): 30/68 ≈ 0.441
      ├── Some((3, 0)): 6/11 ≈ 0.545
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 0/4 ≈ 0.000
      ├── Some((3, 5)): 5/10 ≈ 0.500
      ├── Some((3, 6)): 7/11 ≈ 0.636
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 3/8 ≈ 0.375
    ├── Some((1, 4)): 42/86 ≈ 0.488
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 8/13 ≈ 0.615
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 4)): 1/6 ≈ 0.167
      ├── Some((4, 5)): 1/6 ≈ 0.167
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 9/13 ≈ 0.692
      └── Some((4, 8)): 9/14 ≈ 0.643
    ├── Some((1, 5)): 45/90 ≈ 0.500
      ├── Some((5, 0)): 6/11 ≈ 0.545
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 4/10 ≈ 0.400
      ├── Some((5, 5)): 7/12 ≈ 0.583
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 7/12 ≈ 0.583
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((1, 6)): 41/84 ≈ 0.488
      ├── Some((6, 0)): 7/11 ≈ 0.636
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 5/10 ≈ 0.500
      ├── Some((6, 3)): 6/10 ≈ 0.600
      ├── Some((6, 4)): 4/9 ≈ 0.444
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 6/10 ≈ 0.600
    ├── Some((1, 7)): 65/118 ≈ 0.551
      ├── Some((7, 0)): 6/12 ≈ 0.500
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 8/14 ≈ 0.571
      ├── Some((7, 3)): 6/12 ≈ 0.500
      ├── Some((7, 4)): 9/15 ≈ 0.600
      ├── Some((7, 5)): 8/14 ≈ 0.571
      ├── Some((7, 6)): 5/11 ≈ 0.455
      ├── Some((7, 7)): 6/12 ≈ 0.500
      └── Some((7, 8)): 12/17 ≈ 0.706
    └── Some((1, 8)): 24/60 ≈ 0.400
      ├── Some((8, 0)): 0/4 ≈ 0.000
      ├── Some((8, 1)): 2/6 ≈ 0.333
      ├── Some((8, 2)): 0/4 ≈ 0.000
      ├── Some((8, 3)): 7/10 ≈ 0.700
      ├── Some((8, 4)): 3/7 ≈ 0.429
      ├── Some((8, 5)): 3/7 ≈ 0.429
      ├── Some((8, 6)): 1/5 ≈ 0.200
      ├── Some((8, 7)): 2/6 ≈ 0.333
      └── Some((8, 8)): 6/10 ≈ 0.600
  ├── Some((3, 2)): 513/989 ≈ 0.519
    ├── Some((2, 0)): 67/124 ≈ 0.540
      ├── Some((0, 0)): 13/19 ≈ 0.684
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 2)): 10/16 ≈ 0.625
      ├── Some((0, 3)): 2/8 ≈ 0.250
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 1/7 ≈ 0.143
      ├── Some((0, 6)): 7/14 ≈ 0.500
      ├── Some((0, 7)): 12/18 ≈ 0.667
      └── Some((0, 8)): 11/17 ≈ 0.647
    ├── Some((2, 1)): 71/130 ≈ 0.546
      ├── Some((1, 0)): 10/16 ≈ 0.625
      ├── Some((1, 1)): 7/14 ≈ 0.500
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 11/17 ≈ 0.647
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 10/17 ≈ 0.588
      ├── Some((1, 6)): 9/16 ≈ 0.562
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 9/16 ≈ 0.562
    ├── Some((2, 2)): 37/81 ≈ 0.457
      ├── Some((2, 0)): 7/13 ≈ 0.538
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 3/8 ≈ 0.375
      ├── Some((2, 4)): 11/16 ≈ 0.688
      ├── Some((2, 5)): 6/12 ≈ 0.500
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 1/6 ≈ 0.167
    ├── Some((2, 3)): 39/84 ≈ 0.464
      ├── Some((3, 0)): 8/13 ≈ 0.615
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 3)): 8/14 ≈ 0.571
      ├── Some((3, 4)): 6/12 ≈ 0.500
      ├── Some((3, 5)): 4/10 ≈ 0.400
      ├── Some((3, 6)): 7/13 ≈ 0.538
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((2, 4)): 59/113 ≈ 0.522
      ├── Some((4, 0)): 7/13 ≈ 0.538
      ├── Some((4, 1)): 6/12 ≈ 0.500
      ├── Some((4, 2)): 8/14 ≈ 0.571
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 10/15 ≈ 0.667
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 7/13 ≈ 0.538
      └── Some((4, 8)): 5/11 ≈ 0.455
    ├── Some((2, 5)): 45/93 ≈ 0.484
      ├── Some((5, 0)): 7/13 ≈ 0.538
      ├── Some((5, 1)): 3/9 ≈ 0.333
      ├── Some((5, 2)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 14/20 ≈ 0.700
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 3/9 ≈ 0.333
      └── Some((5, 8)): 1/7 ≈ 0.143
    ├── Some((2, 6)): 80/142 ≈ 0.563
      ├── Some((6, 0)): 6/13 ≈ 0.462
      ├── Some((6, 1)): 15/21 ≈ 0.714
      ├── Some((6, 2)): 13/20 ≈ 0.650
      ├── Some((6, 3)): 11/18 ≈ 0.611
      ├── Some((6, 4)): 10/17 ≈ 0.588
      ├── Some((6, 5)): 3/10 ≈ 0.300
      ├── Some((6, 6)): 6/13 ≈ 0.462
      ├── Some((6, 7)): 12/19 ≈ 0.632
      └── Some((6, 8)): 3/10 ≈ 0.300
    ├── Some((2, 7)): 59/113 ≈ 0.522
      ├── Some((7, 0)): 2/8 ≈ 0.250
      ├── Some((7, 1)): 8/14 ≈ 0.571
      ├── Some((7, 2)): 1/7 ≈ 0.143
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 9/15 ≈ 0.600
      ├── Some((7, 5)): 10/16 ≈ 0.625
      ├── Some((7, 6)): 9/15 ≈ 0.600
      ├── Some((7, 7)): 9/15 ≈ 0.600
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((2, 8)): 55/108 ≈ 0.509
      ├── Some((8, 0)): 6/12 ≈ 0.500
      ├── Some((8, 1)): 6/12 ≈ 0.500
      ├── Some((8, 2)): 7/13 ≈ 0.538
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 8/14 ≈ 0.571
      ├── Some((8, 5)): 9/14 ≈ 0.643
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 7/13 ≈ 0.538
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((3, 3)): 337/687 ≈ 0.491
    ├── Some((3, 0)): 75/132 ≈ 0.568
      ├── Some((0, 0)): 8/15 ≈ 0.533
      ├── Some((0, 1)): 10/16 ≈ 0.625
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 12/18 ≈ 0.667
      ├── Some((0, 4)): 12/18 ≈ 0.667
      ├── Some((0, 5)): 11/17 ≈ 0.647
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 7/14 ≈ 0.500
      └── Some((0, 8)): 2/8 ≈ 0.250
    ├── Some((3, 1)): 14/44 ≈ 0.318
      ├── Some((1, 0)): 2/6 ≈ 0.333
      ├── Some((1, 1)): 3/6 ≈ 0.500
      ├── Some((1, 2)): 0/3 ≈ 0.000
      ├── Some((1, 3)): 0/3 ≈ 0.000
      ├── Some((1, 4)): 3/6 ≈ 0.500
      ├── Some((1, 5)): 0/3 ≈ 0.000
      ├── Some((1, 6)): 0/3 ≈ 0.000
      ├── Some((1, 7)): 3/6 ≈ 0.500
      └── Some((1, 8)): 3/7 ≈ 0.429
    ├── Some((3, 2)): 31/70 ≈ 0.443
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 0/4 ≈ 0.000
      ├── Some((2, 2)): 4/8 ≈ 0.500
      ├── Some((2, 3)): 5/9 ≈ 0.556
      ├── Some((2, 4)): 0/4 ≈ 0.000
      ├── Some((2, 5)): 11/15 ≈ 0.733
      ├── Some((2, 6)): 5/9 ≈ 0.556
      ├── Some((2, 7)): 0/4 ≈ 0.000
      └── Some((2, 8)): 4/9 ≈ 0.444
    ├── Some((3, 4)): 38/80 ≈ 0.475
      ├── Some((4, 0)): 0/4 ≈ 0.000
      ├── Some((4, 1)): 5/10 ≈ 0.500
      ├── Some((4, 2)): 7/11 ≈ 0.636
      ├── Some((4, 3)): 6/11 ≈ 0.545
      ├── Some((4, 4)): 4/9 ≈ 0.444
      ├── Some((4, 5)): 0/4 ≈ 0.000
      ├── Some((4, 6)): 5/10 ≈ 0.500
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((3, 5)): 41/85 ≈ 0.482
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 10/15 ≈ 0.667
      ├── Some((5, 4)): 4/9 ≈ 0.444
      ├── Some((5, 5)): 6/12 ≈ 0.500
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 3/8 ≈ 0.375
    ├── Some((3, 6)): 60/112 ≈ 0.536
      ├── Some((6, 0)): 9/15 ≈ 0.600
      ├── Some((6, 1)): 1/6 ≈ 0.167
      ├── Some((6, 2)): 16/21 ≈ 0.762
      ├── Some((6, 3)): 3/9 ≈ 0.333
      ├── Some((6, 4)): 1/7 ≈ 0.143
      ├── Some((6, 5)): 7/13 ≈ 0.538
      ├── Some((6, 6)): 8/14 ≈ 0.571
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 12/17 ≈ 0.706
    ├── Some((3, 7)): 53/102 ≈ 0.520
      ├── Some((7, 0)): 1/6 ≈ 0.167
      ├── Some((7, 1)): 11/16 ≈ 0.688
      ├── Some((7, 2)): 6/12 ≈ 0.500
      ├── Some((7, 3)): 3/9 ≈ 0.333
      ├── Some((7, 4)): 8/14 ≈ 0.571
      ├── Some((7, 5)): 13/18 ≈ 0.722
      ├── Some((7, 6)): 1/6 ≈ 0.167
      ├── Some((7, 7)): 0/5 ≈ 0.000
      └── Some((7, 8)): 9/15 ≈ 0.600
    └── Some((3, 8)): 25/61 ≈ 0.410
      ├── Some((8, 0)): 1/5 ≈ 0.200
      ├── Some((8, 1)): 7/10 ≈ 0.700
      ├── Some((8, 2)): 5/9 ≈ 0.556
      ├── Some((8, 3)): 0/4 ≈ 0.000
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 3/7 ≈ 0.429
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 1/5 ≈ 0.200
  ├── Some((3, 4)): 514/991 ≈ 0.519
    ├── Some((4, 0)): 51/102 ≈ 0.500
      ├── Some((0, 0)): 3/9 ≈ 0.333
      ├── Some((0, 1)): 6/12 ≈ 0.500
      ├── Some((0, 2)): 13/18 ≈ 0.722
      ├── Some((0, 3)): 9/14 ≈ 0.643
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 4/10 ≈ 0.400
      ├── Some((0, 6)): 9/15 ≈ 0.600
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((4, 1)): 88/154 ≈ 0.571
      ├── Some((1, 0)): 12/20 ≈ 0.600
      ├── Some((1, 1)): 4/11 ≈ 0.364
      ├── Some((1, 2)): 10/18 ≈ 0.556
      ├── Some((1, 3)): 17/24 ≈ 0.708
      ├── Some((1, 4)): 8/15 ≈ 0.533
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 14/21 ≈ 0.667
      ├── Some((1, 7)): 6/13 ≈ 0.462
      └── Some((1, 8)): 10/18 ≈ 0.556
    ├── Some((4, 2)): 76/137 ≈ 0.555
      ├── Some((2, 0)): 16/22 ≈ 0.727
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 2)): 12/19 ≈ 0.632
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 12/19 ≈ 0.632
      ├── Some((2, 5)): 3/10 ≈ 0.300
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 3/10 ≈ 0.300
      └── Some((2, 8)): 15/21 ≈ 0.714
    ├── Some((4, 3)): 19/54 ≈ 0.352
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 4/9 ≈ 0.444
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 1/5 ≈ 0.200
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 0/4 ≈ 0.000
      ├── Some((3, 7)): 1/5 ≈ 0.200
      └── Some((3, 8)): 5/9 ≈ 0.556
    ├── Some((4, 4)): 45/93 ≈ 0.484
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 7/13 ≈ 0.538
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 8/14 ≈ 0.571
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 9/15 ≈ 0.600
    ├── Some((4, 5)): 88/154 ≈ 0.571
      ├── Some((5, 0)): 17/26 ≈ 0.654
      ├── Some((5, 1)): 9/17 ≈ 0.529
      ├── Some((5, 2)): 18/27 ≈ 0.667
      ├── Some((5, 4)): 2/9 ≈ 0.222
      ├── Some((5, 5)): 19/28 ≈ 0.679
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((4, 6)): 38/83 ≈ 0.458
      ├── Some((6, 0)): 8/13 ≈ 0.615
      ├── Some((6, 1)): 6/11 ≈ 0.545
      ├── Some((6, 2)): 2/7 ≈ 0.286
      ├── Some((6, 3)): 0/5 ≈ 0.000
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 7/12 ≈ 0.583
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 9/13 ≈ 0.692
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((4, 7)): 64/120 ≈ 0.533
      ├── Some((7, 0)): 5/11 ≈ 0.455
      ├── Some((7, 1)): 7/14 ≈ 0.500
      ├── Some((7, 2)): 4/10 ≈ 0.400
      ├── Some((7, 3)): 3/9 ≈ 0.333
      ├── Some((7, 4)): 12/18 ≈ 0.667
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 8/15 ≈ 0.533
      ├── Some((7, 7)): 11/17 ≈ 0.647
      └── Some((7, 8)): 9/15 ≈ 0.600
    └── Some((4, 8)): 45/93 ≈ 0.484
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 6/11 ≈ 0.545
      ├── Some((8, 2)): 1/6 ≈ 0.167
      ├── Some((8, 3)): 7/12 ≈ 0.583
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 6/11 ≈ 0.545
      └── Some((8, 8)): 9/14 ≈ 0.643
  ├── Some((3, 5)): 333/680 ≈ 0.490
    ├── Some((5, 0)): 63/115 ≈ 0.548
      ├── Some((0, 0)): 13/18 ≈ 0.722
      ├── Some((0, 1)): 14/19 ≈ 0.737
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 1/7 ≈ 0.143
      ├── Some((0, 4)): 8/14 ≈ 0.571
      ├── Some((0, 5)): 1/7 ≈ 0.143
      ├── Some((0, 6)): 13/19 ≈ 0.684
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 2/8 ≈ 0.250
    ├── Some((5, 1)): 39/82 ≈ 0.476
      ├── Some((1, 0)): 7/11 ≈ 0.636
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 7/12 ≈ 0.583
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 14/18 ≈ 0.778
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((5, 2)): 26/62 ≈ 0.419
      ├── Some((2, 0)): 2/6 ≈ 0.333
      ├── Some((2, 1)): 6/10 ≈ 0.600
      ├── Some((2, 2)): 5/9 ≈ 0.556
      ├── Some((2, 3)): 4/8 ≈ 0.500
      ├── Some((2, 4)): 5/9 ≈ 0.556
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 0/4 ≈ 0.000
      ├── Some((2, 7)): 1/5 ≈ 0.200
      └── Some((2, 8)): 1/5 ≈ 0.200
    ├── Some((5, 4)): 45/90 ≈ 0.500
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 0/5 ≈ 0.000
      ├── Some((4, 2)): 7/12 ≈ 0.583
      ├── Some((4, 3)): 8/12 ≈ 0.667
      ├── Some((4, 4)): 5/10 ≈ 0.500
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 7/12 ≈ 0.583
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 7/12 ≈ 0.583
    ├── Some((5, 5)): 43/87 ≈ 0.494
      ├── Some((5, 0)): 10/17 ≈ 0.588
      ├── Some((5, 1)): 1/7 ≈ 0.143
      ├── Some((5, 2)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 1/7 ≈ 0.143
      ├── Some((5, 6)): 14/20 ≈ 0.700
      ├── Some((5, 7)): 11/17 ≈ 0.647
      └── Some((5, 8)): 1/7 ≈ 0.143
    ├── Some((5, 6)): 47/93 ≈ 0.505
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 9/14 ≈ 0.643
      ├── Some((6, 2)): 9/14 ≈ 0.643
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 5/10 ≈ 0.500
      ├── Some((6, 7)): 7/12 ≈ 0.583
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((5, 7)): 34/74 ≈ 0.459
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 7/11 ≈ 0.636
      ├── Some((7, 3)): 4/8 ≈ 0.500
      ├── Some((7, 4)): 8/12 ≈ 0.667
      ├── Some((7, 5)): 1/5 ≈ 0.200
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 4/8 ≈ 0.500
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((5, 8)): 35/76 ≈ 0.461
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 4/9 ≈ 0.444
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 9/13 ≈ 0.692
      ├── Some((8, 7)): 5/9 ≈ 0.556
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((3, 6)): 399/794 ≈ 0.503
    ├── Some((6, 0)): 33/72 ≈ 0.458
      ├── Some((0, 0)): 2/6 ≈ 0.333
      ├── Some((0, 1)): 7/11 ≈ 0.636
      ├── Some((0, 2)): 5/9 ≈ 0.556
      ├── Some((0, 3)): 4/8 ≈ 0.500
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 4/8 ≈ 0.500
      ├── Some((0, 6)): 2/7 ≈ 0.286
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((6, 1)): 39/81 ≈ 0.481
      ├── Some((1, 0)): 6/10 ≈ 0.600
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 0/4 ≈ 0.000
      ├── Some((1, 3)): 6/10 ≈ 0.600
      ├── Some((1, 4)): 4/9 ≈ 0.444
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 6/11 ≈ 0.545
      ├── Some((1, 7)): 6/11 ≈ 0.545
      └── Some((1, 8)): 2/7 ≈ 0.286
    ├── Some((6, 2)): 74/129 ≈ 0.574
      ├── Some((2, 0)): 14/20 ≈ 0.700
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 11/17 ≈ 0.647
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 14/20 ≈ 0.700
      ├── Some((2, 6)): 6/12 ≈ 0.500
      ├── Some((2, 7)): 8/14 ≈ 0.571
      └── Some((2, 8)): 4/10 ≈ 0.400
    ├── Some((6, 3)): 32/71 ≈ 0.451
      ├── Some((3, 0)): 7/12 ≈ 0.583
      ├── Some((3, 1)): 3/8 ≈ 0.375
      ├── Some((3, 2)): 4/9 ≈ 0.444
      ├── Some((3, 3)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 0/4 ≈ 0.000
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 7)): 9/14 ≈ 0.643
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((6, 4)): 50/97 ≈ 0.515
      ├── Some((4, 0)): 9/14 ≈ 0.643
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 2/7 ≈ 0.286
      ├── Some((4, 3)): 2/7 ≈ 0.286
      ├── Some((4, 4)): 11/16 ≈ 0.688
      ├── Some((4, 5)): 7/12 ≈ 0.583
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 7/12 ≈ 0.583
    ├── Some((6, 5)): 19/52 ≈ 0.365
      ├── Some((5, 0)): 4/8 ≈ 0.500
      ├── Some((5, 1)): 0/4 ≈ 0.000
      ├── Some((5, 2)): 5/9 ≈ 0.556
      ├── Some((5, 4)): 0/4 ≈ 0.000
      ├── Some((5, 5)): 5/9 ≈ 0.556
      ├── Some((5, 6)): 1/5 ≈ 0.200
      ├── Some((5, 7)): 1/5 ≈ 0.200
      └── Some((5, 8)): 3/7 ≈ 0.429
    ├── Some((6, 6)): 51/98 ≈ 0.520
      ├── Some((6, 0)): 9/15 ≈ 0.600
      ├── Some((6, 1)): 0/5 ≈ 0.000
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 12/17 ≈ 0.706
      ├── Some((6, 5)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 5/11 ≈ 0.455
      └── Some((6, 8)): 10/16 ≈ 0.625
    ├── Some((6, 7)): 31/70 ≈ 0.443
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 4/8 ≈ 0.500
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 5/9 ≈ 0.556
      ├── Some((7, 6)): 2/7 ≈ 0.286
      ├── Some((7, 7)): 5/9 ≈ 0.556
      └── Some((7, 8)): 5/9 ≈ 0.556
    └── Some((6, 8)): 69/123 ≈ 0.561
      ├── Some((8, 0)): 6/12 ≈ 0.500
      ├── Some((8, 1)): 11/17 ≈ 0.647
      ├── Some((8, 2)): 12/17 ≈ 0.706
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 8/14 ≈ 0.571
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 12/18 ≈ 0.667
      ├── Some((8, 7)): 9/15 ≈ 0.600
      └── Some((8, 8)): 4/10 ≈ 0.400
  ├── Some((3, 7)): 360/727 ≈ 0.495
    ├── Some((7, 0)): 36/75 ≈ 0.480
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 3/8 ≈ 0.375
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 4/8 ≈ 0.500
      ├── Some((0, 5)): 9/13 ≈ 0.692
      ├── Some((0, 6)): 1/5 ≈ 0.200
      ├── Some((0, 7)): 5/9 ≈ 0.556
      └── Some((0, 8)): 4/8 ≈ 0.500
    ├── Some((7, 1)): 47/91 ≈ 0.516
      ├── Some((1, 0)): 9/13 ≈ 0.692
      ├── Some((1, 1)): 6/11 ≈ 0.545
      ├── Some((1, 2)): 4/9 ≈ 0.444
      ├── Some((1, 3)): 5/10 ≈ 0.500
      ├── Some((1, 4)): 6/11 ≈ 0.545
      ├── Some((1, 5)): 6/11 ≈ 0.545
      ├── Some((1, 6)): 7/11 ≈ 0.636
      ├── Some((1, 7)): 1/6 ≈ 0.167
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((7, 2)): 49/94 ≈ 0.521
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 13/18 ≈ 0.722
      ├── Some((2, 2)): 0/5 ≈ 0.000
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 7/12 ≈ 0.583
      ├── Some((2, 5)): 0/5 ≈ 0.000
      ├── Some((2, 6)): 10/15 ≈ 0.667
      ├── Some((2, 7)): 8/13 ≈ 0.615
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((7, 3)): 24/58 ≈ 0.414
      ├── Some((3, 0)): 1/5 ≈ 0.200
      ├── Some((3, 1)): 2/6 ≈ 0.333
      ├── Some((3, 2)): 3/7 ≈ 0.429
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 4/8 ≈ 0.500
      ├── Some((3, 5)): 2/6 ≈ 0.333
      ├── Some((3, 6)): 5/9 ≈ 0.556
      └── Some((3, 8)): 4/8 ≈ 0.500
    ├── Some((7, 4)): 21/54 ≈ 0.389
      ├── Some((4, 0)): 2/6 ≈ 0.333
      ├── Some((4, 1)): 2/6 ≈ 0.333
      ├── Some((4, 2)): 6/9 ≈ 0.667
      ├── Some((4, 3)): 2/6 ≈ 0.333
      ├── Some((4, 4)): 1/5 ≈ 0.200
      ├── Some((4, 5)): 2/6 ≈ 0.333
      ├── Some((4, 6)): 0/3 ≈ 0.000
      ├── Some((4, 7)): 1/5 ≈ 0.200
      └── Some((4, 8)): 4/7 ≈ 0.571
    ├── Some((7, 5)): 56/103 ≈ 0.544
      ├── Some((5, 0)): 12/17 ≈ 0.706
      ├── Some((5, 1)): 8/14 ≈ 0.571
      ├── Some((5, 2)): 1/6 ≈ 0.167
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 3/9 ≈ 0.333
      ├── Some((5, 6)): 8/14 ≈ 0.571
      ├── Some((5, 7)): 10/16 ≈ 0.625
      └── Some((5, 8)): 8/14 ≈ 0.571
    ├── Some((7, 6)): 57/105 ≈ 0.543
      ├── Some((6, 0)): 6/12 ≈ 0.500
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 8/14 ≈ 0.571
      ├── Some((6, 3)): 1/6 ≈ 0.167
      ├── Some((6, 4)): 14/19 ≈ 0.737
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 6)): 10/15 ≈ 0.667
      ├── Some((6, 7)): 2/8 ≈ 0.250
      └── Some((6, 8)): 12/17 ≈ 0.706
    ├── Some((7, 7)): 42/84 ≈ 0.500
      ├── Some((7, 0)): 6/11 ≈ 0.545
      ├── Some((7, 1)): 5/11 ≈ 0.455
      ├── Some((7, 2)): 7/12 ≈ 0.583
      ├── Some((7, 3)): 6/11 ≈ 0.545
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 7/12 ≈ 0.583
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((7, 8)): 27/62 ≈ 0.435
      ├── Some((8, 0)): 9/12 ≈ 0.750
      ├── Some((8, 1)): 1/5 ≈ 0.200
      ├── Some((8, 2)): 2/6 ≈ 0.333
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 4/7 ≈ 0.571
      ├── Some((8, 6)): 3/7 ≈ 0.429
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 2/6 ≈ 0.333
  └── Some((3, 8)): 356/720 ≈ 0.494
    ├── Some((8, 0)): 34/73 ≈ 0.466
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 0/4 ≈ 0.000
      ├── Some((0, 2)): 0/4 ≈ 0.000
      ├── Some((0, 3)): 4/8 ≈ 0.500
      ├── Some((0, 4)): 4/8 ≈ 0.500
      ├── Some((0, 5)): 3/8 ≈ 0.375
      ├── Some((0, 6)): 5/9 ≈ 0.556
      ├── Some((0, 7)): 7/11 ≈ 0.636
      └── Some((0, 8)): 9/13 ≈ 0.692
    ├── Some((8, 1)): 57/105 ≈ 0.543
      ├── Some((1, 0)): 7/12 ≈ 0.583
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 15/20 ≈ 0.750
      ├── Some((1, 3)): 6/11 ≈ 0.545
      ├── Some((1, 4)): 6/12 ≈ 0.500
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 2/7 ≈ 0.286
      ├── Some((1, 7)): 9/14 ≈ 0.643
      └── Some((1, 8)): 6/12 ≈ 0.500
    ├── Some((8, 2)): 51/96 ≈ 0.531
      ├── Some((2, 0)): 7/12 ≈ 0.583
      ├── Some((2, 1)): 10/15 ≈ 0.667
      ├── Some((2, 2)): 5/10 ≈ 0.500
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 4/9 ≈ 0.444
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 8/13 ≈ 0.615
      ├── Some((2, 7)): 4/9 ≈ 0.444
      └── Some((2, 8)): 6/11 ≈ 0.545
    ├── Some((8, 3)): 69/121 ≈ 0.570
      ├── Some((3, 0)): 8/15 ≈ 0.533
      ├── Some((3, 1)): 12/18 ≈ 0.667
      ├── Some((3, 2)): 10/16 ≈ 0.625
      ├── Some((3, 3)): 8/15 ≈ 0.533
      ├── Some((3, 4)): 9/15 ≈ 0.600
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 9/15 ≈ 0.600
      └── Some((3, 7)): 7/14 ≈ 0.500
    ├── Some((8, 4)): 21/54 ≈ 0.389
      ├── Some((4, 0)): 1/5 ≈ 0.200
      ├── Some((4, 1)): 3/6 ≈ 0.500
      ├── Some((4, 2)): 1/5 ≈ 0.200
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 3/7 ≈ 0.429
      ├── Some((4, 5)): 3/7 ≈ 0.429
      ├── Some((4, 6)): 0/4 ≈ 0.000
      ├── Some((4, 7)): 4/7 ≈ 0.571
      └── Some((4, 8)): 4/7 ≈ 0.571
    ├── Some((8, 5)): 33/71 ≈ 0.465
      ├── Some((5, 0)): 0/4 ≈ 0.000
      ├── Some((5, 1)): 7/12 ≈ 0.583
      ├── Some((5, 2)): 10/14 ≈ 0.714
      ├── Some((5, 4)): 0/4 ≈ 0.000
      ├── Some((5, 5)): 7/12 ≈ 0.583
      ├── Some((5, 6)): 1/6 ≈ 0.167
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 5/10 ≈ 0.500
    ├── Some((8, 6)): 40/81 ≈ 0.494
      ├── Some((6, 0)): 0/4 ≈ 0.000
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 4/9 ≈ 0.444
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 11/15 ≈ 0.733
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 10/14 ≈ 0.714
    ├── Some((8, 7)): 31/68 ≈ 0.456
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 5/9 ≈ 0.556
      ├── Some((7, 2)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 7/11 ≈ 0.636
      ├── Some((7, 6)): 2/6 ≈ 0.333
      ├── Some((7, 7)): 4/8 ≈ 0.500
      └── Some((7, 8)): 6/10 ≈ 0.600
    └── Some((8, 8)): 19/50 ≈ 0.380
      ├── Some((8, 0)): 3/7 ≈ 0.429
      ├── Some((8, 1)): 4/7 ≈ 0.571
      ├── Some((8, 2)): 3/7 ≈ 0.429
      ├── Some((8, 3)): 3/7 ≈ 0.429
      ├── Some((8, 4)): 0/4 ≈ 0.000
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 2/6 ≈ 0.333
      └── Some((8, 7)): 2/6 ≈ 0.333
├── Some((5, 4)): 3652/7247 ≈ 0.504
  ├── Some((4, 0)): 298/619 ≈ 0.481
    ├── Some((0, 0)): 35/72 ≈ 0.486
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 8/12 ≈ 0.667
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 9/13 ≈ 0.692
      ├── Some((0, 6)): 6/10 ≈ 0.600
      ├── Some((0, 7)): 5/10 ≈ 0.500
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((0, 1)): 48/89 ≈ 0.539
      ├── Some((1, 0)): 3/8 ≈ 0.375
      ├── Some((1, 1)): 7/11 ≈ 0.636
      ├── Some((1, 2)): 4/9 ≈ 0.444
      ├── Some((1, 3)): 0/4 ≈ 0.000
      ├── Some((1, 4)): 5/9 ≈ 0.556
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 11/15 ≈ 0.733
      ├── Some((1, 7)): 8/12 ≈ 0.667
      └── Some((1, 8)): 5/10 ≈ 0.500
    ├── Some((0, 2)): 17/46 ≈ 0.370
      ├── Some((2, 0)): 1/5 ≈ 0.200
      ├── Some((2, 1)): 0/3 ≈ 0.000
      ├── Some((2, 2)): 0/3 ≈ 0.000
      ├── Some((2, 3)): 5/8 ≈ 0.625
      ├── Some((2, 4)): 2/5 ≈ 0.400
      ├── Some((2, 5)): 2/5 ≈ 0.400
      ├── Some((2, 6)): 2/5 ≈ 0.400
      ├── Some((2, 7)): 3/6 ≈ 0.500
      └── Some((2, 8)): 2/5 ≈ 0.400
    ├── Some((0, 3)): 31/66 ≈ 0.470
      ├── Some((3, 0)): 1/5 ≈ 0.200
      ├── Some((3, 1)): 0/4 ≈ 0.000
      ├── Some((3, 2)): 6/9 ≈ 0.667
      ├── Some((3, 3)): 11/14 ≈ 0.786
      ├── Some((3, 4)): 3/7 ≈ 0.429
      ├── Some((3, 5)): 5/9 ≈ 0.556
      ├── Some((3, 6)): 3/7 ≈ 0.429
      ├── Some((3, 7)): 1/5 ≈ 0.200
      └── Some((3, 8)): 1/5 ≈ 0.200
    ├── Some((0, 4)): 46/87 ≈ 0.529
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 4/9 ≈ 0.444
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 13/18 ≈ 0.722
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 6/11 ≈ 0.545
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 6/11 ≈ 0.545
    ├── Some((0, 5)): 35/72 ≈ 0.486
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 5/10 ≈ 0.500
      ├── Some((5, 2)): 0/4 ≈ 0.000
      ├── Some((5, 3)): 7/11 ≈ 0.636
      ├── Some((5, 5)): 7/11 ≈ 0.636
      ├── Some((5, 6)): 6/10 ≈ 0.600
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((0, 6)): 24/56 ≈ 0.429
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 5/8 ≈ 0.625
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 3/6 ≈ 0.500
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 6/9 ≈ 0.667
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 3/6 ≈ 0.500
    ├── Some((0, 7)): 20/50 ≈ 0.400
      ├── Some((7, 0)): 0/3 ≈ 0.000
      ├── Some((7, 1)): 0/3 ≈ 0.000
      ├── Some((7, 2)): 3/6 ≈ 0.500
      ├── Some((7, 3)): 1/5 ≈ 0.200
      ├── Some((7, 4)): 1/5 ≈ 0.200
      ├── Some((7, 5)): 2/5 ≈ 0.400
      ├── Some((7, 6)): 5/8 ≈ 0.625
      ├── Some((7, 7)): 2/5 ≈ 0.400
      └── Some((7, 8)): 6/9 ≈ 0.667
    └── Some((0, 8)): 41/80 ≈ 0.512
      ├── Some((8, 0)): 7/12 ≈ 0.583
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 8/12 ≈ 0.667
      ├── Some((8, 4)): 0/4 ≈ 0.000
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 10/14 ≈ 0.714
      ├── Some((8, 7)): 9/13 ≈ 0.692
      └── Some((8, 8)): 4/9 ≈ 0.444
  ├── Some((4, 1)): 568/1082 ≈ 0.525
    ├── Some((1, 0)): 60/116 ≈ 0.517
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 1/7 ≈ 0.143
      ├── Some((0, 2)): 14/20 ≈ 0.700
      ├── Some((0, 3)): 11/17 ≈ 0.647
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 2/8 ≈ 0.250
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 15/21 ≈ 0.714
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((1, 1)): 49/100 ≈ 0.490
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 6/13 ≈ 0.462
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 4/10 ≈ 0.400
      ├── Some((1, 5)): 12/18 ≈ 0.667
      ├── Some((1, 6)): 10/17 ≈ 0.588
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 5/11 ≈ 0.455
    ├── Some((1, 2)): 99/170 ≈ 0.582
      ├── Some((2, 0)): 23/30 ≈ 0.767
      ├── Some((2, 1)): 9/17 ≈ 0.529
      ├── Some((2, 2)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 17/25 ≈ 0.680
      ├── Some((2, 4)): 4/12 ≈ 0.333
      ├── Some((2, 5)): 11/19 ≈ 0.579
      ├── Some((2, 6)): 3/10 ≈ 0.300
      ├── Some((2, 7)): 4/12 ≈ 0.333
      └── Some((2, 8)): 21/29 ≈ 0.724
    ├── Some((1, 3)): 49/100 ≈ 0.490
      ├── Some((3, 0)): 0/5 ≈ 0.000
      ├── Some((3, 1)): 11/16 ≈ 0.688
      ├── Some((3, 2)): 7/13 ≈ 0.538
      ├── Some((3, 3)): 10/15 ≈ 0.667
      ├── Some((3, 4)): 3/9 ≈ 0.333
      ├── Some((3, 5)): 10/16 ≈ 0.625
      ├── Some((3, 6)): 1/6 ≈ 0.167
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 3/9 ≈ 0.333
    ├── Some((1, 4)): 63/120 ≈ 0.525
      ├── Some((4, 0)): 11/19 ≈ 0.579
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 13/20 ≈ 0.650
      ├── Some((4, 4)): 1/7 ≈ 0.143
      ├── Some((4, 5)): 18/25 ≈ 0.720
      ├── Some((4, 6)): 9/16 ≈ 0.562
      ├── Some((4, 7)): 3/10 ≈ 0.300
      └── Some((4, 8)): 4/11 ≈ 0.364
    ├── Some((1, 5)): 72/133 ≈ 0.541
      ├── Some((5, 0)): 5/12 ≈ 0.417
      ├── Some((5, 1)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 11/19 ≈ 0.579
      ├── Some((5, 3)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 8/16 ≈ 0.500
      ├── Some((5, 7)): 7/15 ≈ 0.467
      └── Some((5, 8)): 19/26 ≈ 0.731
    ├── Some((1, 6)): 47/98 ≈ 0.480
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 8/14 ≈ 0.571
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 12/17 ≈ 0.706
      ├── Some((6, 6)): 6/12 ≈ 0.500
      ├── Some((6, 7)): 8/14 ≈ 0.571
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((1, 7)): 56/111 ≈ 0.505
      ├── Some((7, 0)): 6/12 ≈ 0.500
      ├── Some((7, 1)): 8/14 ≈ 0.571
      ├── Some((7, 2)): 1/7 ≈ 0.143
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 8/15 ≈ 0.533
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 9/15 ≈ 0.600
      └── Some((7, 8)): 10/16 ≈ 0.625
    └── Some((1, 8)): 72/133 ≈ 0.541
      ├── Some((8, 0)): 10/16 ≈ 0.625
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 6/13 ≈ 0.462
      ├── Some((8, 3)): 7/14 ≈ 0.500
      ├── Some((8, 4)): 11/17 ≈ 0.647
      ├── Some((8, 5)): 9/16 ≈ 0.562
      ├── Some((8, 6)): 6/13 ≈ 0.462
      ├── Some((8, 7)): 9/16 ≈ 0.562
      └── Some((8, 8)): 5/12 ≈ 0.417
  ├── Some((4, 2)): 367/739 ≈ 0.497
    ├── Some((2, 0)): 16/46 ≈ 0.348
      ├── Some((0, 0)): 1/5 ≈ 0.200
      ├── Some((0, 1)): 2/5 ≈ 0.400
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 4/7 ≈ 0.571
      ├── Some((0, 4)): 0/3 ≈ 0.000
      ├── Some((0, 5)): 0/3 ≈ 0.000
      ├── Some((0, 6)): 3/6 ≈ 0.500
      ├── Some((0, 7)): 2/5 ≈ 0.400
      └── Some((0, 8)): 2/6 ≈ 0.333
    ├── Some((2, 1)): 62/112 ≈ 0.554
      ├── Some((1, 0)): 12/17 ≈ 0.706
      ├── Some((1, 1)): 4/10 ≈ 0.400
      ├── Some((1, 2)): 10/15 ≈ 0.667
      ├── Some((1, 3)): 6/12 ≈ 0.500
      ├── Some((1, 4)): 7/13 ≈ 0.538
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 8/13 ≈ 0.615
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 7/13 ≈ 0.538
    ├── Some((2, 2)): 23/57 ≈ 0.404
      ├── Some((2, 0)): 3/7 ≈ 0.429
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 0/4 ≈ 0.000
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 9/13 ≈ 0.692
      ├── Some((2, 7)): 4/8 ≈ 0.500
      └── Some((2, 8)): 2/6 ≈ 0.333
    ├── Some((2, 3)): 36/76 ≈ 0.474
      ├── Some((3, 0)): 4/8 ≈ 0.500
      ├── Some((3, 1)): 4/8 ≈ 0.500
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 6/10 ≈ 0.600
      ├── Some((3, 5)): 4/8 ≈ 0.500
      ├── Some((3, 6)): 4/8 ≈ 0.500
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((2, 4)): 66/118 ≈ 0.559
      ├── Some((4, 0)): 10/16 ≈ 0.625
      ├── Some((4, 1)): 9/15 ≈ 0.600
      ├── Some((4, 3)): 13/19 ≈ 0.684
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 8/15 ≈ 0.533
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((2, 5)): 41/83 ≈ 0.494
      ├── Some((5, 0)): 9/14 ≈ 0.643
      ├── Some((5, 1)): 7/12 ≈ 0.583
      ├── Some((5, 2)): 6/12 ≈ 0.500
      ├── Some((5, 3)): 2/7 ≈ 0.286
      ├── Some((5, 5)): 7/12 ≈ 0.583
      ├── Some((5, 6)): 7/12 ≈ 0.583
      ├── Some((5, 7)): 0/5 ≈ 0.000
      └── Some((5, 8)): 3/8 ≈ 0.375
    ├── Some((2, 6)): 64/115 ≈ 0.557
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 10/15 ≈ 0.667
      ├── Some((6, 4)): 8/14 ≈ 0.571
      ├── Some((6, 5)): 9/14 ≈ 0.643
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 7/13 ≈ 0.538
      └── Some((6, 8)): 9/15 ≈ 0.600
    ├── Some((2, 7)): 34/73 ≈ 0.466
      ├── Some((7, 0)): 4/8 ≈ 0.500
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 7/11 ≈ 0.636
      ├── Some((7, 3)): 4/8 ≈ 0.500
      ├── Some((7, 4)): 0/4 ≈ 0.000
      ├── Some((7, 5)): 1/5 ≈ 0.200
      ├── Some((7, 6)): 5/9 ≈ 0.556
      ├── Some((7, 7)): 4/9 ≈ 0.444
      └── Some((7, 8)): 7/11 ≈ 0.636
    └── Some((2, 8)): 24/58 ≈ 0.414
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 3/7 ≈ 0.429
      ├── Some((8, 2)): 0/4 ≈ 0.000
      ├── Some((8, 3)): 5/8 ≈ 0.625
      ├── Some((8, 4)): 4/7 ≈ 0.571
      ├── Some((8, 5)): 3/7 ≈ 0.429
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 0/4 ≈ 0.000
      └── Some((8, 8)): 5/8 ≈ 0.625
  ├── Some((4, 3)): 472/919 ≈ 0.514
    ├── Some((3, 0)): 81/142 ≈ 0.570
      ├── Some((0, 0)): 11/18 ≈ 0.611
      ├── Some((0, 1)): 12/19 ≈ 0.632
      ├── Some((0, 2)): 5/12 ≈ 0.417
      ├── Some((0, 3)): 15/21 ≈ 0.714
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 11/18 ≈ 0.611
      ├── Some((0, 6)): 6/13 ≈ 0.462
      ├── Some((0, 7)): 11/18 ≈ 0.611
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((3, 1)): 57/109 ≈ 0.523
      ├── Some((1, 0)): 7/13 ≈ 0.538
      ├── Some((1, 1)): 8/14 ≈ 0.571
      ├── Some((1, 2)): 2/8 ≈ 0.250
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 14/19 ≈ 0.737
      ├── Some((1, 5)): 9/14 ≈ 0.643
      ├── Some((1, 6)): 1/6 ≈ 0.167
      ├── Some((1, 7)): 7/13 ≈ 0.538
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((3, 2)): 55/106 ≈ 0.519
      ├── Some((2, 0)): 4/10 ≈ 0.400
      ├── Some((2, 1)): 11/16 ≈ 0.688
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 6/12 ≈ 0.500
      ├── Some((2, 6)): 5/11 ≈ 0.455
      ├── Some((2, 7)): 7/12 ≈ 0.583
      └── Some((2, 8)): 9/14 ≈ 0.643
    ├── Some((3, 3)): 73/131 ≈ 0.557
      ├── Some((3, 0)): 5/12 ≈ 0.417
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 8/15 ≈ 0.533
      ├── Some((3, 4)): 12/19 ≈ 0.632
      ├── Some((3, 5)): 12/19 ≈ 0.632
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 10/17 ≈ 0.588
      └── Some((3, 8)): 11/19 ≈ 0.579
    ├── Some((3, 4)): 47/95 ≈ 0.495
      ├── Some((4, 0)): 13/18 ≈ 0.722
      ├── Some((4, 1)): 8/14 ≈ 0.571
      ├── Some((4, 2)): 7/13 ≈ 0.538
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 2/8 ≈ 0.250
      └── Some((4, 8)): 3/9 ≈ 0.333
    ├── Some((3, 5)): 39/83 ≈ 0.470
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 7/12 ≈ 0.583
      ├── Some((5, 6)): 4/9 ≈ 0.444
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 7/12 ≈ 0.583
    ├── Some((3, 6)): 60/113 ≈ 0.531
      ├── Some((6, 0)): 9/15 ≈ 0.600
      ├── Some((6, 1)): 6/12 ≈ 0.500
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 12/17 ≈ 0.706
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 4/10 ≈ 0.400
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 8/14 ≈ 0.571
    ├── Some((3, 7)): 39/83 ≈ 0.470
      ├── Some((7, 0)): 6/10 ≈ 0.600
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 6/11 ≈ 0.545
      ├── Some((7, 3)): 3/8 ≈ 0.375
      ├── Some((7, 4)): 8/12 ≈ 0.667
      ├── Some((7, 5)): 3/8 ≈ 0.375
      ├── Some((7, 6)): 4/9 ≈ 0.444
      ├── Some((7, 7)): 2/7 ≈ 0.286
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((3, 8)): 21/56 ≈ 0.375
      ├── Some((8, 0)): 0/4 ≈ 0.000
      ├── Some((8, 1)): 3/7 ≈ 0.429
      ├── Some((8, 2)): 2/6 ≈ 0.333
      ├── Some((8, 3)): 5/8 ≈ 0.625
      ├── Some((8, 4)): 0/4 ≈ 0.000
      ├── Some((8, 5)): 4/8 ≈ 0.500
      ├── Some((8, 6)): 1/5 ≈ 0.200
      ├── Some((8, 7)): 5/8 ≈ 0.625
      └── Some((8, 8)): 1/5 ≈ 0.200
  ├── Some((4, 4)): 343/698 ≈ 0.491
    ├── Some((4, 0)): 30/69 ≈ 0.435
      ├── Some((0, 0)): 6/10 ≈ 0.600
      ├── Some((0, 1)): 2/6 ≈ 0.333
      ├── Some((0, 2)): 6/10 ≈ 0.600
      ├── Some((0, 3)): 7/11 ≈ 0.636
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 1/5 ≈ 0.200
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 1/5 ≈ 0.200
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((4, 1)): 55/105 ≈ 0.524
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 11/16 ≈ 0.688
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 8/13 ≈ 0.615
      ├── Some((1, 5)): 7/13 ≈ 0.538
      ├── Some((1, 6)): 1/6 ≈ 0.167
      ├── Some((1, 7)): 8/13 ≈ 0.615
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((4, 2)): 42/86 ≈ 0.488
      ├── Some((2, 0)): 7/11 ≈ 0.636
      ├── Some((2, 1)): 7/12 ≈ 0.583
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 4/9 ≈ 0.444
      ├── Some((2, 5)): 5/10 ≈ 0.500
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 7/12 ≈ 0.583
      └── Some((2, 8)): 7/12 ≈ 0.583
    ├── Some((4, 3)): 46/92 ≈ 0.500
      ├── Some((3, 0)): 9/14 ≈ 0.643
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 7/12 ≈ 0.583
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 7/12 ≈ 0.583
      ├── Some((3, 7)): 6/11 ≈ 0.545
      └── Some((3, 8)): 5/10 ≈ 0.500
    ├── Some((4, 5)): 49/96 ≈ 0.510
      ├── Some((5, 0)): 2/8 ≈ 0.250
      ├── Some((5, 1)): 1/6 ≈ 0.167
      ├── Some((5, 2)): 1/7 ≈ 0.143
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 5)): 10/16 ≈ 0.625
      ├── Some((5, 6)): 9/15 ≈ 0.600
      ├── Some((5, 7)): 13/19 ≈ 0.684
      └── Some((5, 8)): 8/14 ≈ 0.571
    ├── Some((4, 6)): 62/115 ≈ 0.539
      ├── Some((6, 0)): 11/16 ≈ 0.688
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 8/14 ≈ 0.571
      ├── Some((6, 3)): 8/14 ≈ 0.571
      ├── Some((6, 4)): 5/11 ≈ 0.455
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 6/12 ≈ 0.500
    ├── Some((4, 7)): 13/42 ≈ 0.310
      ├── Some((7, 0)): 1/4 ≈ 0.250
      ├── Some((7, 1)): 2/5 ≈ 0.400
      ├── Some((7, 2)): 0/3 ≈ 0.000
      ├── Some((7, 3)): 1/5 ≈ 0.200
      ├── Some((7, 4)): 3/6 ≈ 0.500
      ├── Some((7, 5)): 0/3 ≈ 0.000
      ├── Some((7, 6)): 2/5 ≈ 0.400
      ├── Some((7, 7)): 2/5 ≈ 0.400
      └── Some((7, 8)): 2/5 ≈ 0.400
    └── Some((4, 8)): 46/92 ≈ 0.500
      ├── Some((8, 0)): 9/14 ≈ 0.643
      ├── Some((8, 1)): 7/12 ≈ 0.583
      ├── Some((8, 2)): 3/8 ≈ 0.375
      ├── Some((8, 3)): 4/9 ≈ 0.444
      ├── Some((8, 4)): 0/5 ≈ 0.000
      ├── Some((8, 5)): 8/13 ≈ 0.615
      ├── Some((8, 6)): 4/9 ≈ 0.444
      ├── Some((8, 7)): 7/12 ≈ 0.583
      └── Some((8, 8)): 4/9 ≈ 0.444
  ├── Some((4, 5)): 388/776 ≈ 0.500
    ├── Some((5, 0)): 48/96 ≈ 0.500
      ├── Some((0, 0)): 6/11 ≈ 0.545
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 6/12 ≈ 0.500
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 7/12 ≈ 0.583
      ├── Some((0, 7)): 14/19 ≈ 0.737
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((5, 1)): 72/130 ≈ 0.554
      ├── Some((1, 0)): 10/16 ≈ 0.625
      ├── Some((1, 1)): 3/9 ≈ 0.333
      ├── Some((1, 2)): 1/7 ≈ 0.143
      ├── Some((1, 3)): 6/13 ≈ 0.462
      ├── Some((1, 4)): 8/15 ≈ 0.533
      ├── Some((1, 5)): 10/16 ≈ 0.625
      ├── Some((1, 6)): 13/19 ≈ 0.684
      ├── Some((1, 7)): 10/17 ≈ 0.588
      └── Some((1, 8)): 10/17 ≈ 0.588
    ├── Some((5, 2)): 50/99 ≈ 0.505
      ├── Some((2, 0)): 6/11 ≈ 0.545
      ├── Some((2, 1)): 1/6 ≈ 0.167
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 7/12 ≈ 0.583
      ├── Some((2, 5)): 6/12 ≈ 0.500
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 14/19 ≈ 0.737
      └── Some((2, 8)): 5/11 ≈ 0.455
    ├── Some((5, 3)): 41/86 ≈ 0.477
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 5/10 ≈ 0.500
      ├── Some((3, 2)): 4/9 ≈ 0.444
      ├── Some((3, 3)): 4/9 ≈ 0.444
      ├── Some((3, 4)): 5/10 ≈ 0.500
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 9/14 ≈ 0.643
      ├── Some((3, 7)): 0/5 ≈ 0.000
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((5, 5)): 41/86 ≈ 0.477
      ├── Some((5, 0)): 7/14 ≈ 0.500
      ├── Some((5, 1)): 11/18 ≈ 0.611
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 8/15 ≈ 0.533
      └── Some((5, 8)): 1/7 ≈ 0.143
    ├── Some((5, 6)): 36/79 ≈ 0.456
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 6/10 ≈ 0.600
      ├── Some((6, 3)): 6/10 ≈ 0.600
      ├── Some((6, 4)): 4/9 ≈ 0.444
      ├── Some((6, 5)): 0/4 ≈ 0.000
      ├── Some((6, 6)): 5/10 ≈ 0.500
      ├── Some((6, 7)): 5/10 ≈ 0.500
      └── Some((6, 8)): 5/10 ≈ 0.500
    ├── Some((5, 7)): 53/104 ≈ 0.510
      ├── Some((7, 0)): 9/14 ≈ 0.643
      ├── Some((7, 1)): 9/14 ≈ 0.643
      ├── Some((7, 2)): 7/13 ≈ 0.538
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 1/6 ≈ 0.167
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 8/14 ≈ 0.571
    └── Some((5, 8)): 47/95 ≈ 0.495
      ├── Some((8, 0)): 6/11 ≈ 0.545
      ├── Some((8, 1)): 6/11 ≈ 0.545
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 10/15 ≈ 0.667
      ├── Some((8, 4)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 6/12 ≈ 0.500
      ├── Some((8, 7)): 8/13 ≈ 0.615
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((4, 6)): 306/633 ≈ 0.483
    ├── Some((6, 0)): 13/40 ≈ 0.325
      ├── Some((0, 0)): 2/5 ≈ 0.400
      ├── Some((0, 1)): 1/4 ≈ 0.250
      ├── Some((0, 2)): 2/5 ≈ 0.400
      ├── Some((0, 3)): 2/5 ≈ 0.400
      ├── Some((0, 4)): 1/4 ≈ 0.250
      ├── Some((0, 5)): 1/4 ≈ 0.250
      ├── Some((0, 6)): 1/4 ≈ 0.250
      ├── Some((0, 7)): 3/5 ≈ 0.600
      └── Some((0, 8)): 0/3 ≈ 0.000
    ├── Some((6, 1)): 50/93 ≈ 0.538
      ├── Some((1, 0)): 6/10 ≈ 0.600
      ├── Some((1, 1)): 5/10 ≈ 0.500
      ├── Some((1, 2)): 6/10 ≈ 0.600
      ├── Some((1, 3)): 5/10 ≈ 0.500
      ├── Some((1, 4)): 6/10 ≈ 0.600
      ├── Some((1, 5)): 6/11 ≈ 0.545
      ├── Some((1, 6)): 5/10 ≈ 0.500
      ├── Some((1, 7)): 6/11 ≈ 0.545
      └── Some((1, 8)): 5/10 ≈ 0.500
    ├── Some((6, 2)): 15/43 ≈ 0.349
      ├── Some((2, 0)): 2/5 ≈ 0.400
      ├── Some((2, 1)): 0/3 ≈ 0.000
      ├── Some((2, 2)): 0/3 ≈ 0.000
      ├── Some((2, 3)): 3/6 ≈ 0.500
      ├── Some((2, 4)): 2/6 ≈ 0.333
      ├── Some((2, 5)): 4/7 ≈ 0.571
      ├── Some((2, 6)): 0/3 ≈ 0.000
      ├── Some((2, 7)): 3/6 ≈ 0.500
      └── Some((2, 8)): 0/3 ≈ 0.000
    ├── Some((6, 3)): 58/104 ≈ 0.558
      ├── Some((3, 0)): 9/14 ≈ 0.643
      ├── Some((3, 1)): 5/10 ≈ 0.500
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 9/14 ≈ 0.643
      ├── Some((3, 4)): 14/19 ≈ 0.737
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 6/11 ≈ 0.545
      ├── Some((3, 7)): 6/11 ≈ 0.545
      └── Some((3, 8)): 4/9 ≈ 0.444
    ├── Some((6, 4)): 48/90 ≈ 0.533
      ├── Some((4, 0)): 7/12 ≈ 0.583
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 7/13 ≈ 0.538
      └── Some((4, 8)): 14/19 ≈ 0.737
    ├── Some((6, 5)): 23/55 ≈ 0.418
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 6/10 ≈ 0.600
      ├── Some((5, 2)): 1/5 ≈ 0.200
      ├── Some((5, 3)): 4/8 ≈ 0.500
      ├── Some((5, 5)): 0/4 ≈ 0.000
      ├── Some((5, 6)): 2/6 ≈ 0.333
      ├── Some((5, 7)): 2/6 ≈ 0.333
      └── Some((5, 8)): 6/10 ≈ 0.600
    ├── Some((6, 6)): 43/83 ≈ 0.518
      ├── Some((6, 0)): 4/9 ≈ 0.444
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 6/11 ≈ 0.545
      ├── Some((6, 4)): 6/11 ≈ 0.545
      ├── Some((6, 5)): 9/14 ≈ 0.643
      ├── Some((6, 7)): 5/10 ≈ 0.500
      └── Some((6, 8)): 6/11 ≈ 0.545
    ├── Some((6, 7)): 28/62 ≈ 0.452
      ├── Some((7, 0)): 3/7 ≈ 0.429
      ├── Some((7, 1)): 5/8 ≈ 0.625
      ├── Some((7, 2)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 6/9 ≈ 0.667
      ├── Some((7, 4)): 2/6 ≈ 0.333
      ├── Some((7, 5)): 5/9 ≈ 0.556
      ├── Some((7, 6)): 2/6 ≈ 0.333
      ├── Some((7, 7)): 3/7 ≈ 0.429
      └── Some((7, 8)): 0/4 ≈ 0.000
    └── Some((6, 8)): 28/62 ≈ 0.452
      ├── Some((8, 0)): 4/7 ≈ 0.571
      ├── Some((8, 1)): 4/7 ≈ 0.571
      ├── Some((8, 2)): 3/7 ≈ 0.429
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 4/8 ≈ 0.500
      ├── Some((8, 6)): 4/8 ≈ 0.500
      ├── Some((8, 7)): 0/4 ≈ 0.000
      └── Some((8, 8)): 6/9 ≈ 0.667
  ├── Some((4, 7)): 476/926 ≈ 0.514
    ├── Some((7, 0)): 47/95 ≈ 0.495
      ├── Some((0, 0)): 1/6 ≈ 0.167
      ├── Some((0, 1)): 6/12 ≈ 0.500
      ├── Some((0, 2)): 2/7 ≈ 0.286
      ├── Some((0, 3)): 10/15 ≈ 0.667
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 11/16 ≈ 0.688
      ├── Some((0, 7)): 9/15 ≈ 0.600
      └── Some((0, 8)): 0/5 ≈ 0.000
    ├── Some((7, 1)): 69/126 ≈ 0.548
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 12/18 ≈ 0.667
      ├── Some((1, 2)): 9/15 ≈ 0.600
      ├── Some((1, 3)): 7/14 ≈ 0.500
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 9/16 ≈ 0.562
      ├── Some((1, 6)): 10/16 ≈ 0.625
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 5/11 ≈ 0.455
    ├── Some((7, 2)): 30/70 ≈ 0.429
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 0/4 ≈ 0.000
      ├── Some((2, 4)): 5/9 ≈ 0.556
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 1/5 ≈ 0.200
      ├── Some((2, 7)): 8/12 ≈ 0.667
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((7, 3)): 46/94 ≈ 0.489
      ├── Some((3, 0)): 7/13 ≈ 0.538
      ├── Some((3, 1)): 6/12 ≈ 0.500
      ├── Some((3, 2)): 9/14 ≈ 0.643
      ├── Some((3, 3)): 0/5 ≈ 0.000
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 7/13 ≈ 0.538
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 9/14 ≈ 0.643
    ├── Some((7, 4)): 62/116 ≈ 0.534
      ├── Some((4, 0)): 9/16 ≈ 0.562
      ├── Some((4, 1)): 2/8 ≈ 0.250
      ├── Some((4, 2)): 10/17 ≈ 0.588
      ├── Some((4, 3)): 1/7 ≈ 0.143
      ├── Some((4, 4)): 14/21 ≈ 0.667
      ├── Some((4, 5)): 15/21 ≈ 0.714
      ├── Some((4, 6)): 7/14 ≈ 0.500
      └── Some((4, 8)): 4/11 ≈ 0.364
    ├── Some((7, 5)): 23/60 ≈ 0.383
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 9/13 ≈ 0.692
      ├── Some((5, 3)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 1/6 ≈ 0.167
      ├── Some((5, 7)): 5/10 ≈ 0.500
      └── Some((5, 8)): 2/7 ≈ 0.286
    ├── Some((7, 6)): 91/156 ≈ 0.583
      ├── Some((6, 0)): 8/15 ≈ 0.533
      ├── Some((6, 1)): 13/21 ≈ 0.619
      ├── Some((6, 2)): 6/13 ≈ 0.462
      ├── Some((6, 3)): 14/21 ≈ 0.667
      ├── Some((6, 4)): 7/14 ≈ 0.500
      ├── Some((6, 5)): 16/23 ≈ 0.696
      ├── Some((6, 6)): 5/12 ≈ 0.417
      ├── Some((6, 7)): 8/15 ≈ 0.533
      └── Some((6, 8)): 13/21 ≈ 0.619
    ├── Some((7, 7)): 47/95 ≈ 0.495
      ├── Some((7, 0)): 10/16 ≈ 0.625
      ├── Some((7, 1)): 2/8 ≈ 0.250
      ├── Some((7, 2)): 1/7 ≈ 0.143
      ├── Some((7, 3)): 1/7 ≈ 0.143
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 13/19 ≈ 0.684
      ├── Some((7, 6)): 8/14 ≈ 0.571
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((7, 8)): 60/113 ≈ 0.531
      ├── Some((8, 0)): 11/16 ≈ 0.688
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 7/13 ≈ 0.538
      ├── Some((8, 3)): 8/14 ≈ 0.571
      ├── Some((8, 4)): 9/15 ≈ 0.600
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 11/17 ≈ 0.647
      └── Some((8, 8)): 1/6 ≈ 0.167
  └── Some((4, 8)): 434/854 ≈ 0.508
    ├── Some((8, 0)): 61/113 ≈ 0.540
      ├── Some((0, 0)): 5/11 ≈ 0.455
      ├── Some((0, 1)): 7/13 ≈ 0.538
      ├── Some((0, 2)): 12/17 ≈ 0.706
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 8/13 ≈ 0.615
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 7/13 ≈ 0.538
      └── Some((0, 8)): 6/12 ≈ 0.500
    ├── Some((8, 1)): 39/82 ≈ 0.476
      ├── Some((1, 0)): 4/9 ≈ 0.444
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 4/9 ≈ 0.444
      ├── Some((1, 3)): 5/9 ≈ 0.556
      ├── Some((1, 4)): 5/9 ≈ 0.556
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 4/9 ≈ 0.444
      ├── Some((1, 7)): 6/10 ≈ 0.600
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((8, 2)): 39/82 ≈ 0.476
      ├── Some((2, 0)): 5/9 ≈ 0.556
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 5/9 ≈ 0.556
      ├── Some((2, 3)): 5/10 ≈ 0.500
      ├── Some((2, 4)): 7/11 ≈ 0.636
      ├── Some((2, 5)): 5/10 ≈ 0.500
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 1/6 ≈ 0.167
      └── Some((2, 8)): 5/10 ≈ 0.500
    ├── Some((8, 3)): 66/120 ≈ 0.550
      ├── Some((3, 0)): 12/17 ≈ 0.706
      ├── Some((3, 1)): 10/16 ≈ 0.625
      ├── Some((3, 2)): 9/15 ≈ 0.600
      ├── Some((3, 3)): 9/15 ≈ 0.600
      ├── Some((3, 4)): 3/9 ≈ 0.333
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 10/16 ≈ 0.625
      ├── Some((3, 7)): 1/7 ≈ 0.143
      └── Some((3, 8)): 7/13 ≈ 0.538
    ├── Some((8, 4)): 41/85 ≈ 0.482
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 7/12 ≈ 0.583
      ├── Some((4, 2)): 7/13 ≈ 0.538
      ├── Some((4, 3)): 8/13 ≈ 0.615
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 3/8 ≈ 0.375
      └── Some((4, 7)): 4/10 ≈ 0.400
    ├── Some((8, 5)): 65/118 ≈ 0.551
      ├── Some((5, 0)): 9/16 ≈ 0.562
      ├── Some((5, 1)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 2/8 ≈ 0.250
      ├── Some((5, 3)): 10/17 ≈ 0.588
      ├── Some((5, 5)): 10/17 ≈ 0.588
      ├── Some((5, 6)): 5/11 ≈ 0.455
      ├── Some((5, 7)): 15/21 ≈ 0.714
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((8, 6)): 59/110 ≈ 0.536
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 10/15 ≈ 0.667
      ├── Some((6, 3)): 7/13 ≈ 0.538
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 7/13 ≈ 0.538
      ├── Some((6, 6)): 1/6 ≈ 0.167
      ├── Some((6, 7)): 8/13 ≈ 0.615
      └── Some((6, 8)): 9/14 ≈ 0.643
    ├── Some((8, 7)): 25/61 ≈ 0.410
      ├── Some((7, 0)): 5/9 ≈ 0.556
      ├── Some((7, 1)): 3/7 ≈ 0.429
      ├── Some((7, 2)): 2/6 ≈ 0.333
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 4/8 ≈ 0.500
      ├── Some((7, 5)): 2/6 ≈ 0.333
      ├── Some((7, 6)): 0/4 ≈ 0.000
      ├── Some((7, 7)): 2/6 ≈ 0.333
      └── Some((7, 8)): 4/8 ≈ 0.500
    └── Some((8, 8)): 39/82 ≈ 0.476
      ├── Some((8, 0)): 7/12 ≈ 0.583
      ├── Some((8, 1)): 7/12 ≈ 0.583
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 1/6 ≈ 0.167
      ├── Some((8, 4)): 7/12 ≈ 0.583
      ├── Some((8, 5)): 7/13 ≈ 0.538
      ├── Some((8, 6)): 3/8 ≈ 0.375
      └── Some((8, 7)): 3/8 ≈ 0.375
├── Some((5, 5)): 5424/10523 ≈ 0.515
  ├── Some((5, 0)): 711/1376 ≈ 0.517
    ├── Some((0, 0)): 75/147 ≈ 0.510
      ├── Some((0, 1)): 4/12 ≈ 0.333
      ├── Some((0, 2)): 14/23 ≈ 0.609
      ├── Some((0, 3)): 3/11 ≈ 0.273
      ├── Some((0, 4)): 13/22 ≈ 0.591
      ├── Some((0, 5)): 2/10 ≈ 0.200
      ├── Some((0, 6)): 14/24 ≈ 0.583
      ├── Some((0, 7)): 6/15 ≈ 0.400
      └── Some((0, 8)): 19/29 ≈ 0.655
    ├── Some((0, 1)): 51/111 ≈ 0.459
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 4/10 ≈ 0.400
      ├── Some((1, 2)): 8/15 ≈ 0.533
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 2/8 ≈ 0.250
      ├── Some((1, 5)): 4/10 ≈ 0.400
      ├── Some((1, 6)): 10/17 ≈ 0.588
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((0, 2)): 95/177 ≈ 0.537
      ├── Some((2, 0)): 10/19 ≈ 0.526
      ├── Some((2, 1)): 13/22 ≈ 0.591
      ├── Some((2, 2)): 7/16 ≈ 0.438
      ├── Some((2, 3)): 5/14 ≈ 0.357
      ├── Some((2, 4)): 4/12 ≈ 0.333
      ├── Some((2, 5)): 24/34 ≈ 0.706
      ├── Some((2, 6)): 6/15 ≈ 0.400
      ├── Some((2, 7)): 6/15 ≈ 0.400
      └── Some((2, 8)): 19/29 ≈ 0.655
    ├── Some((0, 3)): 88/166 ≈ 0.530
      ├── Some((3, 0)): 8/16 ≈ 0.500
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 2)): 11/20 ≈ 0.550
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 8/17 ≈ 0.471
      ├── Some((3, 5)): 9/18 ≈ 0.500
      ├── Some((3, 6)): 15/24 ≈ 0.625
      ├── Some((3, 7)): 19/28 ≈ 0.679
      └── Some((3, 8)): 6/14 ≈ 0.429
    ├── Some((0, 4)): 62/128 ≈ 0.484
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 11/19 ≈ 0.579
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 3/10 ≈ 0.300
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 8/15 ≈ 0.533
      └── Some((4, 8)): 13/21 ≈ 0.619
    ├── Some((0, 5)): 84/161 ≈ 0.522
      ├── Some((5, 1)): 8/18 ≈ 0.444
      ├── Some((5, 2)): 17/29 ≈ 0.586
      ├── Some((5, 3)): 15/26 ≈ 0.577
      ├── Some((5, 4)): 10/21 ≈ 0.476
      ├── Some((5, 6)): 12/23 ≈ 0.522
      ├── Some((5, 7)): 16/28 ≈ 0.571
      └── Some((5, 8)): 5/15 ≈ 0.333
    ├── Some((0, 6)): 59/123 ≈ 0.480
      ├── Some((6, 0)): 10/18 ≈ 0.556
      ├── Some((6, 1)): 9/16 ≈ 0.562
      ├── Some((6, 2)): 6/13 ≈ 0.462
      ├── Some((6, 3)): 3/10 ≈ 0.300
      ├── Some((6, 4)): 3/10 ≈ 0.300
      ├── Some((6, 5)): 7/14 ≈ 0.500
      ├── Some((6, 6)): 4/11 ≈ 0.364
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 9/16 ≈ 0.562
    ├── Some((0, 7)): 131/228 ≈ 0.575
      ├── Some((7, 0)): 20/31 ≈ 0.645
      ├── Some((7, 1)): 30/41 ≈ 0.732
      ├── Some((7, 2)): 19/30 ≈ 0.633
      ├── Some((7, 3)): 14/25 ≈ 0.560
      ├── Some((7, 4)): 13/24 ≈ 0.542
      ├── Some((7, 5)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 5/15 ≈ 0.333
      ├── Some((7, 7)): 14/25 ≈ 0.560
      └── Some((7, 8)): 5/15 ≈ 0.333
    └── Some((0, 8)): 66/134 ≈ 0.493
      ├── Some((8, 0)): 8/16 ≈ 0.500
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 4/11 ≈ 0.364
      ├── Some((8, 3)): 4/11 ≈ 0.364
      ├── Some((8, 4)): 6/13 ≈ 0.462
      ├── Some((8, 5)): 13/21 ≈ 0.619
      ├── Some((8, 6)): 14/22 ≈ 0.636
      ├── Some((8, 7)): 3/10 ≈ 0.300
      └── Some((8, 8)): 8/16 ≈ 0.500
  ├── Some((5, 1)): 326/699 ≈ 0.466
    ├── Some((1, 0)): 30/69 ≈ 0.435
      ├── Some((0, 0)): 6/10 ≈ 0.600
      ├── Some((0, 1)): 4/8 ≈ 0.500
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 0/4 ≈ 0.000
      ├── Some((0, 4)): 5/9 ≈ 0.556
      ├── Some((0, 5)): 0/4 ≈ 0.000
      ├── Some((0, 6)): 2/7 ≈ 0.286
      ├── Some((0, 7)): 5/9 ≈ 0.556
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((1, 1)): 49/96 ≈ 0.510
      ├── Some((1, 0)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 9/15 ≈ 0.600
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 4/10 ≈ 0.400
      ├── Some((1, 5)): 9/15 ≈ 0.600
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 0/5 ≈ 0.000
      └── Some((1, 8)): 10/15 ≈ 0.667
    ├── Some((1, 2)): 44/89 ≈ 0.494
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 6/11 ≈ 0.545
      ├── Some((2, 2)): 0/5 ≈ 0.000
      ├── Some((2, 3)): 9/14 ≈ 0.643
      ├── Some((2, 4)): 2/7 ≈ 0.286
      ├── Some((2, 5)): 7/12 ≈ 0.583
      ├── Some((2, 6)): 5/10 ≈ 0.500
      ├── Some((2, 7)): 5/10 ≈ 0.500
      └── Some((2, 8)): 6/11 ≈ 0.545
    ├── Some((1, 3)): 22/57 ≈ 0.386
      ├── Some((3, 0)): 3/6 ≈ 0.500
      ├── Some((3, 1)): 7/10 ≈ 0.700
      ├── Some((3, 2)): 2/6 ≈ 0.333
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 4)): 3/7 ≈ 0.429
      ├── Some((3, 5)): 2/6 ≈ 0.333
      ├── Some((3, 6)): 1/5 ≈ 0.200
      ├── Some((3, 7)): 1/5 ≈ 0.200
      └── Some((3, 8)): 3/7 ≈ 0.429
    ├── Some((1, 4)): 28/66 ≈ 0.424
      ├── Some((4, 0)): 4/8 ≈ 0.500
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 1/5 ≈ 0.200
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 0/4 ≈ 0.000
      ├── Some((4, 5)): 1/5 ≈ 0.200
      ├── Some((4, 6)): 7/11 ≈ 0.636
      ├── Some((4, 7)): 4/8 ≈ 0.500
      └── Some((4, 8)): 4/8 ≈ 0.500
    ├── Some((1, 5)): 34/75 ≈ 0.453
      ├── Some((5, 0)): 9/15 ≈ 0.600
      ├── Some((5, 2)): 7/13 ≈ 0.538
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 6)): 2/7 ≈ 0.286
      ├── Some((5, 7)): 3/9 ≈ 0.333
      └── Some((5, 8)): 8/14 ≈ 0.571
    ├── Some((1, 6)): 29/67 ≈ 0.433
      ├── Some((6, 0)): 8/12 ≈ 0.667
      ├── Some((6, 1)): 3/7 ≈ 0.429
      ├── Some((6, 2)): 3/7 ≈ 0.429
      ├── Some((6, 3)): 0/4 ≈ 0.000
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 6/10 ≈ 0.600
      ├── Some((6, 6)): 0/4 ≈ 0.000
      ├── Some((6, 7)): 2/6 ≈ 0.333
      └── Some((6, 8)): 4/8 ≈ 0.500
    ├── Some((1, 7)): 58/109 ≈ 0.532
      ├── Some((7, 0)): 10/15 ≈ 0.667
      ├── Some((7, 1)): 5/11 ≈ 0.455
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 4)): 10/15 ≈ 0.667
      ├── Some((7, 5)): 6/12 ≈ 0.500
      ├── Some((7, 6)): 15/20 ≈ 0.750
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 2/8 ≈ 0.250
    └── Some((1, 8)): 31/70 ≈ 0.443
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 5/9 ≈ 0.556
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 4/8 ≈ 0.500
      ├── Some((8, 6)): 5/9 ≈ 0.556
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((5, 2)): 635/1245 ≈ 0.510
    ├── Some((2, 0)): 85/159 ≈ 0.535
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 16/25 ≈ 0.640
      ├── Some((0, 2)): 11/19 ≈ 0.579
      ├── Some((0, 3)): 9/17 ≈ 0.529
      ├── Some((0, 4)): 2/9 ≈ 0.222
      ├── Some((0, 5)): 10/18 ≈ 0.556
      ├── Some((0, 6)): 9/17 ≈ 0.529
      ├── Some((0, 7)): 13/22 ≈ 0.591
      └── Some((0, 8)): 8/16 ≈ 0.500
    ├── Some((2, 1)): 52/111 ≈ 0.468
      ├── Some((1, 0)): 8/15 ≈ 0.533
      ├── Some((1, 1)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 9/16 ≈ 0.562
      ├── Some((1, 3)): 9/16 ≈ 0.562
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 6/12 ≈ 0.500
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 1/7 ≈ 0.143
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((2, 2)): 44/99 ≈ 0.444
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 4/11 ≈ 0.364
      ├── Some((2, 4)): 3/10 ≈ 0.300
      ├── Some((2, 5)): 6/13 ≈ 0.462
      ├── Some((2, 6)): 8/15 ≈ 0.533
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 3/10 ≈ 0.300
    ├── Some((2, 3)): 62/126 ≈ 0.492
      ├── Some((3, 0)): 0/6 ≈ 0.000
      ├── Some((3, 1)): 2/9 ≈ 0.222
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 6/13 ≈ 0.462
      ├── Some((3, 4)): 11/19 ≈ 0.579
      ├── Some((3, 5)): 5/12 ≈ 0.417
      ├── Some((3, 6)): 19/26 ≈ 0.731
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 3/10 ≈ 0.300
    ├── Some((2, 4)): 67/133 ≈ 0.504
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 9/17 ≈ 0.529
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 15/23 ≈ 0.652
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 5/12 ≈ 0.417
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((2, 5)): 97/177 ≈ 0.548
      ├── Some((5, 0)): 26/38 ≈ 0.684
      ├── Some((5, 1)): 13/25 ≈ 0.520
      ├── Some((5, 3)): 18/30 ≈ 0.600
      ├── Some((5, 4)): 9/20 ≈ 0.450
      ├── Some((5, 6)): 14/26 ≈ 0.538
      ├── Some((5, 7)): 5/15 ≈ 0.333
      └── Some((5, 8)): 11/22 ≈ 0.500
    ├── Some((2, 6)): 68/135 ≈ 0.504
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 9/17 ≈ 0.529
      ├── Some((6, 2)): 11/19 ≈ 0.579
      ├── Some((6, 3)): 3/10 ≈ 0.300
      ├── Some((6, 4)): 2/9 ≈ 0.222
      ├── Some((6, 5)): 9/17 ≈ 0.529
      ├── Some((6, 6)): 8/15 ≈ 0.533
      ├── Some((6, 7)): 6/13 ≈ 0.462
      └── Some((6, 8)): 13/20 ≈ 0.650
    ├── Some((2, 7)): 95/174 ≈ 0.546
      ├── Some((7, 0)): 17/26 ≈ 0.654
      ├── Some((7, 1)): 11/20 ≈ 0.550
      ├── Some((7, 2)): 13/22 ≈ 0.591
      ├── Some((7, 3)): 16/25 ≈ 0.640
      ├── Some((7, 4)): 8/17 ≈ 0.471
      ├── Some((7, 5)): 9/18 ≈ 0.500
      ├── Some((7, 6)): 10/19 ≈ 0.526
      ├── Some((7, 7)): 0/7 ≈ 0.000
      └── Some((7, 8)): 10/19 ≈ 0.526
    └── Some((2, 8)): 65/130 ≈ 0.500
      ├── Some((8, 0)): 2/9 ≈ 0.222
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 8/15 ≈ 0.533
      ├── Some((8, 3)): 12/20 ≈ 0.600
      ├── Some((8, 4)): 8/15 ≈ 0.533
      ├── Some((8, 5)): 14/22 ≈ 0.636
      ├── Some((8, 6)): 1/8 ≈ 0.125
      ├── Some((8, 7)): 7/14 ≈ 0.500
      └── Some((8, 8)): 7/14 ≈ 0.500
  ├── Some((5, 3)): 445/911 ≈ 0.488
    ├── Some((3, 0)): 89/158 ≈ 0.563
      ├── Some((0, 0)): 6/14 ≈ 0.429
      ├── Some((0, 1)): 3/10 ≈ 0.300
      ├── Some((0, 2)): 13/21 ≈ 0.619
      ├── Some((0, 3)): 7/15 ≈ 0.467
      ├── Some((0, 4)): 21/28 ≈ 0.750
      ├── Some((0, 5)): 15/23 ≈ 0.652
      ├── Some((0, 6)): 3/10 ≈ 0.300
      ├── Some((0, 7)): 12/20 ≈ 0.600
      └── Some((0, 8)): 8/16 ≈ 0.500
    ├── Some((3, 1)): 43/92 ≈ 0.467
      ├── Some((1, 0)): 2/7 ≈ 0.286
      ├── Some((1, 1)): 5/11 ≈ 0.455
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 11/16 ≈ 0.688
      ├── Some((1, 4)): 7/13 ≈ 0.538
      ├── Some((1, 5)): 4/10 ≈ 0.400
      ├── Some((1, 6)): 8/13 ≈ 0.615
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 0/5 ≈ 0.000
    ├── Some((3, 2)): 45/95 ≈ 0.474
      ├── Some((2, 0)): 1/6 ≈ 0.167
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 9/15 ≈ 0.600
      ├── Some((2, 5)): 9/15 ≈ 0.600
      ├── Some((2, 6)): 6/12 ≈ 0.500
      ├── Some((2, 7)): 2/7 ≈ 0.286
      └── Some((2, 8)): 11/16 ≈ 0.688
    ├── Some((3, 3)): 48/100 ≈ 0.480
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 8/15 ≈ 0.533
      ├── Some((3, 2)): 11/18 ≈ 0.611
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 4/10 ≈ 0.400
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 4/10 ≈ 0.400
    ├── Some((3, 4)): 34/79 ≈ 0.430
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 3/8 ≈ 0.375
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 6/11 ≈ 0.545
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 0/4 ≈ 0.000
      ├── Some((4, 7)): 6/11 ≈ 0.545
      └── Some((4, 8)): 7/12 ≈ 0.583
    ├── Some((3, 5)): 31/74 ≈ 0.419
      ├── Some((5, 0)): 3/9 ≈ 0.333
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 4)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 9/15 ≈ 0.600
      ├── Some((5, 7)): 3/9 ≈ 0.333
      └── Some((5, 8)): 2/8 ≈ 0.250
    ├── Some((3, 6)): 28/70 ≈ 0.400
      ├── Some((6, 0)): 6/10 ≈ 0.600
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 0/4 ≈ 0.000
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 2/7 ≈ 0.286
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((3, 7)): 82/148 ≈ 0.554
      ├── Some((7, 0)): 9/16 ≈ 0.562
      ├── Some((7, 1)): 14/21 ≈ 0.667
      ├── Some((7, 2)): 6/13 ≈ 0.462
      ├── Some((7, 3)): 10/18 ≈ 0.556
      ├── Some((7, 4)): 8/15 ≈ 0.533
      ├── Some((7, 5)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 11/19 ≈ 0.579
      ├── Some((7, 7)): 12/19 ≈ 0.632
      └── Some((7, 8)): 7/14 ≈ 0.500
    └── Some((3, 8)): 44/94 ≈ 0.468
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 0/5 ≈ 0.000
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 7/13 ≈ 0.538
      ├── Some((8, 4)): 6/12 ≈ 0.500
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 6/12 ≈ 0.500
      └── Some((8, 8)): 8/13 ≈ 0.615
  ├── Some((5, 4)): 921/1737 ≈ 0.530
    ├── Some((4, 0)): 122/223 ≈ 0.547
      ├── Some((0, 0)): 26/38 ≈ 0.684
      ├── Some((0, 1)): 12/23 ≈ 0.522
      ├── Some((0, 2)): 8/19 ≈ 0.421
      ├── Some((0, 3)): 15/27 ≈ 0.556
      ├── Some((0, 4)): 11/22 ≈ 0.500
      ├── Some((0, 5)): 20/32 ≈ 0.625
      ├── Some((0, 6)): 12/23 ≈ 0.522
      ├── Some((0, 7)): 10/21 ≈ 0.476
      └── Some((0, 8)): 7/17 ≈ 0.412
    ├── Some((4, 1)): 103/195 ≈ 0.528
      ├── Some((1, 0)): 14/24 ≈ 0.583
      ├── Some((1, 1)): 2/11 ≈ 0.182
      ├── Some((1, 2)): 14/25 ≈ 0.560
      ├── Some((1, 3)): 16/27 ≈ 0.593
      ├── Some((1, 4)): 13/23 ≈ 0.565
      ├── Some((1, 5)): 8/18 ≈ 0.444
      ├── Some((1, 6)): 17/28 ≈ 0.607
      ├── Some((1, 7)): 9/19 ≈ 0.474
      └── Some((1, 8)): 9/19 ≈ 0.474
    ├── Some((4, 2)): 110/205 ≈ 0.537
      ├── Some((2, 0)): 23/34 ≈ 0.676
      ├── Some((2, 1)): 13/24 ≈ 0.542
      ├── Some((2, 2)): 16/27 ≈ 0.593
      ├── Some((2, 3)): 10/20 ≈ 0.500
      ├── Some((2, 4)): 10/20 ≈ 0.500
      ├── Some((2, 5)): 12/23 ≈ 0.522
      ├── Some((2, 6)): 9/19 ≈ 0.474
      ├── Some((2, 7)): 6/16 ≈ 0.375
      └── Some((2, 8)): 10/21 ≈ 0.476
    ├── Some((4, 3)): 86/169 ≈ 0.509
      ├── Some((3, 0)): 17/27 ≈ 0.630
      ├── Some((3, 1)): 11/20 ≈ 0.550
      ├── Some((3, 2)): 14/23 ≈ 0.609
      ├── Some((3, 3)): 6/15 ≈ 0.400
      ├── Some((3, 4)): 6/15 ≈ 0.400
      ├── Some((3, 5)): 6/15 ≈ 0.400
      ├── Some((3, 6)): 6/15 ≈ 0.400
      ├── Some((3, 7)): 11/20 ≈ 0.550
      └── Some((3, 8)): 9/18 ≈ 0.500
    ├── Some((4, 4)): 184/311 ≈ 0.592
      ├── Some((4, 0)): 21/37 ≈ 0.568
      ├── Some((4, 1)): 30/47 ≈ 0.638
      ├── Some((4, 2)): 15/30 ≈ 0.500
      ├── Some((4, 3)): 8/21 ≈ 0.381
      ├── Some((4, 5)): 25/41 ≈ 0.610
      ├── Some((4, 6)): 24/40 ≈ 0.600
      ├── Some((4, 7)): 37/55 ≈ 0.673
      └── Some((4, 8)): 23/39 ≈ 0.590
    ├── Some((4, 5)): 68/142 ≈ 0.479
      ├── Some((5, 0)): 7/17 ≈ 0.412
      ├── Some((5, 1)): 10/21 ≈ 0.476
      ├── Some((5, 2)): 8/18 ≈ 0.444
      ├── Some((5, 3)): 16/28 ≈ 0.571
      ├── Some((5, 6)): 7/17 ≈ 0.412
      ├── Some((5, 7)): 5/15 ≈ 0.333
      └── Some((5, 8)): 14/25 ≈ 0.560
    ├── Some((4, 6)): 98/187 ≈ 0.524
      ├── Some((6, 0)): 9/19 ≈ 0.474
      ├── Some((6, 1)): 4/13 ≈ 0.308
      ├── Some((6, 2)): 17/28 ≈ 0.607
      ├── Some((6, 3)): 16/26 ≈ 0.615
      ├── Some((6, 4)): 10/20 ≈ 0.500
      ├── Some((6, 5)): 2/10 ≈ 0.200
      ├── Some((6, 6)): 8/18 ≈ 0.444
      ├── Some((6, 7)): 8/18 ≈ 0.444
      └── Some((6, 8)): 23/34 ≈ 0.676
    ├── Some((4, 7)): 67/141 ≈ 0.475
      ├── Some((7, 0)): 11/19 ≈ 0.579
      ├── Some((7, 1)): 5/13 ≈ 0.385
      ├── Some((7, 2)): 7/15 ≈ 0.467
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 7/15 ≈ 0.467
      ├── Some((7, 5)): 3/11 ≈ 0.273
      ├── Some((7, 6)): 6/14 ≈ 0.429
      ├── Some((7, 7)): 12/21 ≈ 0.571
      └── Some((7, 8)): 7/15 ≈ 0.467
    └── Some((4, 8)): 82/163 ≈ 0.503
      ├── Some((8, 0)): 4/12 ≈ 0.333
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 7/16 ≈ 0.438
      ├── Some((8, 3)): 11/20 ≈ 0.550
      ├── Some((8, 4)): 14/23 ≈ 0.609
      ├── Some((8, 5)): 12/21 ≈ 0.571
      ├── Some((8, 6)): 5/14 ≈ 0.357
      ├── Some((8, 7)): 12/21 ≈ 0.571
      └── Some((8, 8)): 11/20 ≈ 0.550
  ├── Some((5, 6)): 1041/1942 ≈ 0.536
    ├── Some((6, 0)): 145/259 ≈ 0.560
      ├── Some((0, 0)): 21/34 ≈ 0.618
      ├── Some((0, 1)): 29/43 ≈ 0.674
      ├── Some((0, 2)): 22/35 ≈ 0.629
      ├── Some((0, 3)): 6/17 ≈ 0.353
      ├── Some((0, 4)): 17/30 ≈ 0.567
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 13/26 ≈ 0.500
      ├── Some((0, 7)): 5/16 ≈ 0.312
      └── Some((0, 8)): 20/33 ≈ 0.606
    ├── Some((6, 1)): 118/219 ≈ 0.539
      ├── Some((1, 0)): 8/19 ≈ 0.421
      ├── Some((1, 1)): 15/26 ≈ 0.577
      ├── Some((1, 2)): 5/15 ≈ 0.333
      ├── Some((1, 3)): 17/29 ≈ 0.586
      ├── Some((1, 4)): 10/21 ≈ 0.476
      ├── Some((1, 5)): 12/23 ≈ 0.522
      ├── Some((1, 6)): 15/26 ≈ 0.577
      ├── Some((1, 7)): 15/27 ≈ 0.556
      └── Some((1, 8)): 20/32 ≈ 0.625
    ├── Some((6, 2)): 131/238 ≈ 0.550
      ├── Some((2, 0)): 21/34 ≈ 0.618
      ├── Some((2, 1)): 16/28 ≈ 0.571
      ├── Some((2, 2)): 17/29 ≈ 0.586
      ├── Some((2, 3)): 13/25 ≈ 0.520
      ├── Some((2, 4)): 10/21 ≈ 0.476
      ├── Some((2, 5)): 18/30 ≈ 0.600
      ├── Some((2, 6)): 13/25 ≈ 0.520
      ├── Some((2, 7)): 12/24 ≈ 0.500
      └── Some((2, 8)): 10/21 ≈ 0.476
    ├── Some((6, 3)): 94/184 ≈ 0.511
      ├── Some((3, 0)): 3/12 ≈ 0.250
      ├── Some((3, 1)): 27/38 ≈ 0.711
      ├── Some((3, 2)): 19/30 ≈ 0.633
      ├── Some((3, 3)): 2/11 ≈ 0.182
      ├── Some((3, 4)): 6/16 ≈ 0.375
      ├── Some((3, 5)): 24/35 ≈ 0.686
      ├── Some((3, 6)): 6/16 ≈ 0.375
      ├── Some((3, 7)): 3/12 ≈ 0.250
      └── Some((3, 8)): 4/13 ≈ 0.308
    ├── Some((6, 4)): 115/215 ≈ 0.535
      ├── Some((4, 0)): 15/27 ≈ 0.556
      ├── Some((4, 1)): 4/14 ≈ 0.286
      ├── Some((4, 2)): 19/31 ≈ 0.613
      ├── Some((4, 3)): 8/19 ≈ 0.421
      ├── Some((4, 4)): 22/34 ≈ 0.647
      ├── Some((4, 5)): 18/30 ≈ 0.600
      ├── Some((4, 6)): 3/12 ≈ 0.250
      ├── Some((4, 7)): 12/23 ≈ 0.522
      └── Some((4, 8)): 13/24 ≈ 0.542
    ├── Some((6, 5)): 134/243 ≈ 0.551
      ├── Some((5, 0)): 17/33 ≈ 0.515
      ├── Some((5, 1)): 42/61 ≈ 0.689
      ├── Some((5, 2)): 3/15 ≈ 0.200
      ├── Some((5, 3)): 22/38 ≈ 0.579
      ├── Some((5, 4)): 15/30 ≈ 0.500
      ├── Some((5, 7)): 14/29 ≈ 0.483
      └── Some((5, 8)): 20/36 ≈ 0.556
    ├── Some((6, 6)): 80/163 ≈ 0.491
      ├── Some((6, 0)): 13/24 ≈ 0.542
      ├── Some((6, 1)): 4/13 ≈ 0.308
      ├── Some((6, 2)): 11/22 ≈ 0.500
      ├── Some((6, 3)): 4/13 ≈ 0.308
      ├── Some((6, 4)): 23/34 ≈ 0.676
      ├── Some((6, 5)): 5/15 ≈ 0.333
      ├── Some((6, 7)): 12/23 ≈ 0.522
      └── Some((6, 8)): 8/18 ≈ 0.444
    ├── Some((6, 7)): 115/215 ≈ 0.535
      ├── Some((7, 0)): 23/35 ≈ 0.657
      ├── Some((7, 1)): 5/15 ≈ 0.333
      ├── Some((7, 2)): 7/17 ≈ 0.412
      ├── Some((7, 3)): 17/29 ≈ 0.586
      ├── Some((7, 4)): 9/20 ≈ 0.450
      ├── Some((7, 5)): 7/18 ≈ 0.389
      ├── Some((7, 6)): 12/23 ≈ 0.522
      ├── Some((7, 7)): 12/23 ≈ 0.522
      └── Some((7, 8)): 22/34 ≈ 0.647
    └── Some((6, 8)): 108/205 ≈ 0.527
      ├── Some((8, 0)): 11/22 ≈ 0.500
      ├── Some((8, 1)): 25/36 ≈ 0.694
      ├── Some((8, 2)): 9/19 ≈ 0.474
      ├── Some((8, 3)): 11/22 ≈ 0.500
      ├── Some((8, 4)): 11/22 ≈ 0.500
      ├── Some((8, 5)): 9/19 ≈ 0.474
      ├── Some((8, 6)): 6/16 ≈ 0.375
      ├── Some((8, 7)): 15/26 ≈ 0.577
      └── Some((8, 8)): 11/22 ≈ 0.500
  ├── Some((5, 7)): 883/1672 ≈ 0.528
    ├── Some((7, 0)): 113/208 ≈ 0.543
      ├── Some((0, 0)): 13/24 ≈ 0.542
      ├── Some((0, 1)): 10/20 ≈ 0.500
      ├── Some((0, 2)): 3/12 ≈ 0.250
      ├── Some((0, 3)): 17/28 ≈ 0.607
      ├── Some((0, 4)): 14/25 ≈ 0.560
      ├── Some((0, 5)): 12/23 ≈ 0.522
      ├── Some((0, 6)): 16/27 ≈ 0.593
      ├── Some((0, 7)): 17/28 ≈ 0.607
      └── Some((0, 8)): 10/20 ≈ 0.500
    ├── Some((7, 1)): 86/168 ≈ 0.512
      ├── Some((1, 0)): 9/18 ≈ 0.500
      ├── Some((1, 1)): 5/14 ≈ 0.357
      ├── Some((1, 2)): 13/22 ≈ 0.591
      ├── Some((1, 3)): 2/10 ≈ 0.200
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 7/16 ≈ 0.438
      ├── Some((1, 7)): 12/21 ≈ 0.571
      └── Some((1, 8)): 16/26 ≈ 0.615
    ├── Some((7, 2)): 57/124 ≈ 0.460
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 4/11 ≈ 0.364
      ├── Some((2, 2)): 2/9 ≈ 0.222
      ├── Some((2, 3)): 10/18 ≈ 0.556
      ├── Some((2, 4)): 8/16 ≈ 0.500
      ├── Some((2, 5)): 10/18 ≈ 0.556
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 7/15 ≈ 0.467
      └── Some((2, 8)): 3/10 ≈ 0.300
    ├── Some((7, 3)): 121/220 ≈ 0.550
      ├── Some((3, 0)): 5/15 ≈ 0.333
      ├── Some((3, 1)): 11/22 ≈ 0.500
      ├── Some((3, 2)): 10/21 ≈ 0.476
      ├── Some((3, 3)): 13/24 ≈ 0.542
      ├── Some((3, 4)): 12/23 ≈ 0.522
      ├── Some((3, 5)): 13/24 ≈ 0.542
      ├── Some((3, 6)): 9/19 ≈ 0.474
      ├── Some((3, 7)): 22/34 ≈ 0.647
      └── Some((3, 8)): 25/37 ≈ 0.676
    ├── Some((7, 4)): 84/166 ≈ 0.506
      ├── Some((4, 0)): 15/25 ≈ 0.600
      ├── Some((4, 1)): 2/10 ≈ 0.200
      ├── Some((4, 2)): 8/17 ≈ 0.471
      ├── Some((4, 3)): 11/20 ≈ 0.550
      ├── Some((4, 4)): 12/21 ≈ 0.571
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 6)): 4/12 ≈ 0.333
      ├── Some((4, 7)): 8/17 ≈ 0.471
      └── Some((4, 8)): 16/26 ≈ 0.615
    ├── Some((7, 5)): 180/304 ≈ 0.592
      ├── Some((5, 0)): 34/53 ≈ 0.642
      ├── Some((5, 1)): 17/33 ≈ 0.515
      ├── Some((5, 2)): 40/60 ≈ 0.667
      ├── Some((5, 3)): 23/40 ≈ 0.575
      ├── Some((5, 4)): 17/33 ≈ 0.515
      ├── Some((5, 6)): 22/39 ≈ 0.564
      └── Some((5, 8)): 27/45 ≈ 0.600
    ├── Some((7, 6)): 73/149 ≈ 0.490
      ├── Some((6, 0)): 11/20 ≈ 0.550
      ├── Some((6, 1)): 5/13 ≈ 0.385
      ├── Some((6, 2)): 7/15 ≈ 0.467
      ├── Some((6, 3)): 6/14 ≈ 0.429
      ├── Some((6, 4)): 14/23 ≈ 0.609
      ├── Some((6, 5)): 8/16 ≈ 0.500
      ├── Some((6, 6)): 3/11 ≈ 0.273
      ├── Some((6, 7)): 9/17 ≈ 0.529
      └── Some((6, 8)): 10/19 ≈ 0.526
    ├── Some((7, 7)): 86/168 ≈ 0.512
      ├── Some((7, 0)): 4/13 ≈ 0.308
      ├── Some((7, 1)): 8/18 ≈ 0.444
      ├── Some((7, 2)): 15/26 ≈ 0.577
      ├── Some((7, 3)): 11/21 ≈ 0.524
      ├── Some((7, 4)): 6/16 ≈ 0.375
      ├── Some((7, 5)): 19/30 ≈ 0.633
      ├── Some((7, 6)): 14/25 ≈ 0.560
      └── Some((7, 8)): 8/18 ≈ 0.444
    └── Some((7, 8)): 83/164 ≈ 0.506
      ├── Some((8, 0)): 4/12 ≈ 0.333
      ├── Some((8, 1)): 9/18 ≈ 0.500
      ├── Some((8, 2)): 18/28 ≈ 0.643
      ├── Some((8, 3)): 12/21 ≈ 0.571
      ├── Some((8, 4)): 4/12 ≈ 0.333
      ├── Some((8, 5)): 7/16 ≈ 0.438
      ├── Some((8, 6)): 9/18 ≈ 0.500
      ├── Some((8, 7)): 15/24 ≈ 0.625
      └── Some((8, 8)): 5/14 ≈ 0.357
  └── Some((5, 8)): 461/940 ≈ 0.490
    ├── Some((8, 0)): 45/96 ≈ 0.469
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 8/14 ≈ 0.571
      ├── Some((0, 2)): 9/14 ≈ 0.643
      ├── Some((0, 3)): 7/13 ≈ 0.538
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 2/7 ≈ 0.286
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((8, 1)): 27/68 ≈ 0.397
      ├── Some((1, 0)): 1/5 ≈ 0.200
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 8/12 ≈ 0.667
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 1/5 ≈ 0.200
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 0/4 ≈ 0.000
      ├── Some((1, 7)): 5/10 ≈ 0.500
      └── Some((1, 8)): 6/10 ≈ 0.600
    ├── Some((8, 2)): 62/120 ≈ 0.517
      ├── Some((2, 0)): 2/8 ≈ 0.250
      ├── Some((2, 1)): 11/17 ≈ 0.647
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 3/9 ≈ 0.333
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 10/17 ≈ 0.588
      ├── Some((2, 6)): 11/18 ≈ 0.611
      ├── Some((2, 7)): 12/18 ≈ 0.667
      └── Some((2, 8)): 3/9 ≈ 0.333
    ├── Some((8, 3)): 39/87 ≈ 0.448
      ├── Some((3, 0)): 7/13 ≈ 0.538
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 8/13 ≈ 0.615
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 7/13 ≈ 0.538
      ├── Some((3, 5)): 0/5 ≈ 0.000
      ├── Some((3, 6)): 8/13 ≈ 0.615
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((8, 4)): 51/105 ≈ 0.486
      ├── Some((4, 0)): 8/14 ≈ 0.571
      ├── Some((4, 1)): 8/14 ≈ 0.571
      ├── Some((4, 2)): 9/15 ≈ 0.600
      ├── Some((4, 3)): 3/9 ≈ 0.333
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 6/12 ≈ 0.500
    ├── Some((8, 5)): 46/97 ≈ 0.474
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 1)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 13/21 ≈ 0.619
      ├── Some((5, 3)): 3/10 ≈ 0.300
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 5/12 ≈ 0.417
      └── Some((5, 7)): 6/13 ≈ 0.462
    ├── Some((8, 6)): 44/94 ≈ 0.468
      ├── Some((6, 0)): 5/11 ≈ 0.455
      ├── Some((6, 1)): 8/13 ≈ 0.615
      ├── Some((6, 2)): 2/7 ≈ 0.286
      ├── Some((6, 3)): 7/13 ≈ 0.538
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 7/13 ≈ 0.538
    ├── Some((8, 7)): 94/166 ≈ 0.566
      ├── Some((7, 0)): 9/17 ≈ 0.529
      ├── Some((7, 1)): 6/14 ≈ 0.429
      ├── Some((7, 2)): 17/25 ≈ 0.680
      ├── Some((7, 3)): 18/26 ≈ 0.692
      ├── Some((7, 4)): 17/25 ≈ 0.680
      ├── Some((7, 5)): 6/14 ≈ 0.429
      ├── Some((7, 6)): 11/19 ≈ 0.579
      ├── Some((7, 7)): 7/15 ≈ 0.467
      └── Some((7, 8)): 3/10 ≈ 0.300
    └── Some((8, 8)): 52/106 ≈ 0.491
      ├── Some((8, 0)): 10/17 ≈ 0.588
      ├── Some((8, 1)): 9/16 ≈ 0.562
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 11/18 ≈ 0.611
      ├── Some((8, 4)): 1/7 ≈ 0.143
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 2/8 ≈ 0.250
      └── Some((8, 7)): 7/14 ≈ 0.500
├── Some((5, 6)): 4046/7978 ≈ 0.507
  ├── Some((6, 0)): 372/753 ≈ 0.494
    ├── Some((0, 0)): 48/93 ≈ 0.516
      ├── Some((0, 1)): 6/12 ≈ 0.500
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 7/13 ≈ 0.538
      ├── Some((0, 4)): 4/10 ≈ 0.400
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 9/14 ≈ 0.643
      ├── Some((0, 7)): 8/13 ≈ 0.615
      └── Some((0, 8)): 0/5 ≈ 0.000
    ├── Some((0, 1)): 42/85 ≈ 0.494
      ├── Some((1, 0)): 7/11 ≈ 0.636
      ├── Some((1, 1)): 0/4 ≈ 0.000
      ├── Some((1, 2)): 7/12 ≈ 0.583
      ├── Some((1, 3)): 7/12 ≈ 0.583
      ├── Some((1, 4)): 6/11 ≈ 0.545
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 5/10 ≈ 0.500
      └── Some((1, 8)): 5/10 ≈ 0.500
    ├── Some((0, 2)): 43/86 ≈ 0.500
      ├── Some((2, 0)): 6/11 ≈ 0.545
      ├── Some((2, 1)): 11/15 ≈ 0.733
      ├── Some((2, 2)): 1/6 ≈ 0.167
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 4/9 ≈ 0.444
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 0/5 ≈ 0.000
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 8/12 ≈ 0.667
    ├── Some((0, 3)): 45/89 ≈ 0.506
      ├── Some((3, 0)): 5/10 ≈ 0.500
      ├── Some((3, 1)): 3/8 ≈ 0.375
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 5/10 ≈ 0.500
      ├── Some((3, 5)): 7/11 ≈ 0.636
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 7/12 ≈ 0.583
      └── Some((3, 8)): 7/12 ≈ 0.583
    ├── Some((0, 4)): 26/62 ≈ 0.419
      ├── Some((4, 0)): 2/6 ≈ 0.333
      ├── Some((4, 1)): 2/6 ≈ 0.333
      ├── Some((4, 2)): 4/8 ≈ 0.500
      ├── Some((4, 3)): 3/7 ≈ 0.429
      ├── Some((4, 4)): 2/6 ≈ 0.333
      ├── Some((4, 5)): 5/8 ≈ 0.625
      ├── Some((4, 6)): 2/6 ≈ 0.333
      ├── Some((4, 7)): 1/5 ≈ 0.200
      └── Some((4, 8)): 5/9 ≈ 0.556
    ├── Some((0, 5)): 30/68 ≈ 0.441
      ├── Some((5, 0)): 6/10 ≈ 0.600
      ├── Some((5, 1)): 6/10 ≈ 0.600
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 3)): 0/4 ≈ 0.000
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 7)): 4/9 ≈ 0.444
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((0, 6)): 48/93 ≈ 0.516
      ├── Some((6, 1)): 9/15 ≈ 0.600
      ├── Some((6, 2)): 10/15 ≈ 0.667
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 10/15 ≈ 0.667
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 6)): 6/12 ≈ 0.500
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 0/5 ≈ 0.000
    ├── Some((0, 7)): 30/68 ≈ 0.441
      ├── Some((7, 0)): 3/7 ≈ 0.429
      ├── Some((7, 1)): 3/7 ≈ 0.429
      ├── Some((7, 2)): 4/8 ≈ 0.500
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 1/5 ≈ 0.200
      ├── Some((7, 5)): 7/11 ≈ 0.636
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 5/9 ≈ 0.556
      └── Some((7, 8)): 4/8 ≈ 0.500
    └── Some((0, 8)): 59/108 ≈ 0.546
      ├── Some((8, 0)): 9/14 ≈ 0.643
      ├── Some((8, 1)): 9/14 ≈ 0.643
      ├── Some((8, 2)): 9/14 ≈ 0.643
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 1/6 ≈ 0.167
      ├── Some((8, 5)): 10/15 ≈ 0.667
      ├── Some((8, 6)): 2/8 ≈ 0.250
      ├── Some((8, 7)): 8/14 ≈ 0.571
      └── Some((8, 8)): 5/11 ≈ 0.455
  ├── Some((6, 1)): 552/1062 ≈ 0.520
    ├── Some((1, 0)): 41/89 ≈ 0.461
      ├── Some((0, 0)): 3/8 ≈ 0.375
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 6/12 ≈ 0.500
      ├── Some((0, 3)): 7/12 ≈ 0.583
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 10/15 ≈ 0.667
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 4/10 ≈ 0.400
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((1, 1)): 73/135 ≈ 0.541
      ├── Some((1, 0)): 11/19 ≈ 0.579
      ├── Some((1, 2)): 11/19 ≈ 0.579
      ├── Some((1, 3)): 11/19 ≈ 0.579
      ├── Some((1, 4)): 12/20 ≈ 0.600
      ├── Some((1, 5)): 9/16 ≈ 0.562
      ├── Some((1, 6)): 10/18 ≈ 0.556
      ├── Some((1, 7)): 5/12 ≈ 0.417
      └── Some((1, 8)): 4/11 ≈ 0.364
    ├── Some((1, 2)): 71/132 ≈ 0.538
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 1)): 6/13 ≈ 0.462
      ├── Some((2, 2)): 13/19 ≈ 0.684
      ├── Some((2, 3)): 7/14 ≈ 0.500
      ├── Some((2, 4)): 7/14 ≈ 0.500
      ├── Some((2, 5)): 2/8 ≈ 0.250
      ├── Some((2, 6)): 9/16 ≈ 0.562
      ├── Some((2, 7)): 12/19 ≈ 0.632
      └── Some((2, 8)): 9/16 ≈ 0.562
    ├── Some((1, 3)): 44/94 ≈ 0.468
      ├── Some((3, 0)): 6/12 ≈ 0.500
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 6/12 ≈ 0.500
      ├── Some((3, 5)): 4/10 ≈ 0.400
      ├── Some((3, 6)): 8/13 ≈ 0.615
      ├── Some((3, 7)): 6/12 ≈ 0.500
      └── Some((3, 8)): 7/12 ≈ 0.583
    ├── Some((1, 4)): 107/182 ≈ 0.588
      ├── Some((4, 0)): 10/18 ≈ 0.556
      ├── Some((4, 1)): 10/18 ≈ 0.556
      ├── Some((4, 2)): 10/18 ≈ 0.556
      ├── Some((4, 3)): 13/22 ≈ 0.591
      ├── Some((4, 4)): 9/17 ≈ 0.529
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 16/24 ≈ 0.667
      ├── Some((4, 7)): 13/22 ≈ 0.591
      └── Some((4, 8)): 18/26 ≈ 0.692
    ├── Some((1, 5)): 78/142 ≈ 0.549
      ├── Some((5, 0)): 5/13 ≈ 0.385
      ├── Some((5, 1)): 6/14 ≈ 0.429
      ├── Some((5, 2)): 11/19 ≈ 0.579
      ├── Some((5, 3)): 17/25 ≈ 0.680
      ├── Some((5, 4)): 7/15 ≈ 0.467
      ├── Some((5, 5)): 10/18 ≈ 0.556
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 13/21 ≈ 0.619
    ├── Some((1, 6)): 28/69 ≈ 0.406
      ├── Some((6, 0)): 5/10 ≈ 0.500
      ├── Some((6, 2)): 0/5 ≈ 0.000
      ├── Some((6, 3)): 8/13 ≈ 0.615
      ├── Some((6, 4)): 4/9 ≈ 0.444
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 2/7 ≈ 0.286
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((1, 7)): 44/94 ≈ 0.468
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 8/13 ≈ 0.615
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 8/14 ≈ 0.571
      ├── Some((7, 6)): 8/14 ≈ 0.571
      ├── Some((7, 7)): 1/6 ≈ 0.167
      └── Some((7, 8)): 6/12 ≈ 0.500
    └── Some((1, 8)): 65/124 ≈ 0.524
      ├── Some((8, 0)): 8/15 ≈ 0.533
      ├── Some((8, 1)): 9/15 ≈ 0.600
      ├── Some((8, 2)): 9/16 ≈ 0.562
      ├── Some((8, 3)): 3/9 ≈ 0.333
      ├── Some((8, 4)): 3/9 ≈ 0.333
      ├── Some((8, 5)): 10/16 ≈ 0.625
      ├── Some((8, 6)): 8/15 ≈ 0.533
      ├── Some((8, 7)): 6/13 ≈ 0.462
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((6, 2)): 423/841 ≈ 0.503
    ├── Some((2, 0)): 46/92 ≈ 0.500
      ├── Some((0, 0)): 4/9 ≈ 0.444
      ├── Some((0, 1)): 5/10 ≈ 0.500
      ├── Some((0, 2)): 4/9 ≈ 0.444
      ├── Some((0, 3)): 12/17 ≈ 0.706
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 9/14 ≈ 0.643
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((2, 1)): 61/113 ≈ 0.540
      ├── Some((1, 0)): 7/13 ≈ 0.538
      ├── Some((1, 1)): 11/17 ≈ 0.647
      ├── Some((1, 2)): 10/16 ≈ 0.625
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 3/9 ≈ 0.333
      ├── Some((1, 6)): 12/17 ≈ 0.706
      ├── Some((1, 7)): 8/14 ≈ 0.571
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((2, 2)): 44/90 ≈ 0.489
      ├── Some((2, 0)): 11/16 ≈ 0.688
      ├── Some((2, 1)): 7/13 ≈ 0.538
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 2/8 ≈ 0.250
      ├── Some((2, 5)): 0/5 ≈ 0.000
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 9/15 ≈ 0.600
      └── Some((2, 8)): 6/12 ≈ 0.500
    ├── Some((2, 3)): 42/87 ≈ 0.483
      ├── Some((3, 0)): 3/8 ≈ 0.375
      ├── Some((3, 1)): 6/11 ≈ 0.545
      ├── Some((3, 2)): 6/11 ≈ 0.545
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 7/12 ≈ 0.583
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 6/11 ≈ 0.545
      ├── Some((3, 7)): 7/12 ≈ 0.583
      └── Some((3, 8)): 1/6 ≈ 0.167
    ├── Some((2, 4)): 75/132 ≈ 0.568
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 14/20 ≈ 0.700
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 3/9 ≈ 0.333
      ├── Some((4, 4)): 14/20 ≈ 0.700
      ├── Some((4, 5)): 11/17 ≈ 0.647
      ├── Some((4, 6)): 10/17 ≈ 0.588
      ├── Some((4, 7)): 3/9 ≈ 0.333
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((2, 5)): 39/82 ≈ 0.476
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 0/5 ≈ 0.000
      ├── Some((5, 2)): 7/12 ≈ 0.583
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 11/16 ≈ 0.688
      ├── Some((5, 7)): 6/12 ≈ 0.500
      └── Some((5, 8)): 6/12 ≈ 0.500
    ├── Some((2, 6)): 40/84 ≈ 0.476
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 7/13 ≈ 0.538
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 18/23 ≈ 0.783
    ├── Some((2, 7)): 30/69 ≈ 0.435
      ├── Some((7, 0)): 4/8 ≈ 0.500
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 6/10 ≈ 0.600
      ├── Some((7, 3)): 3/8 ≈ 0.375
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 2/6 ≈ 0.333
      ├── Some((7, 6)): 4/8 ≈ 0.500
      ├── Some((7, 7)): 1/5 ≈ 0.200
      └── Some((7, 8)): 6/10 ≈ 0.600
    └── Some((2, 8)): 45/91 ≈ 0.495
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 7/12 ≈ 0.583
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 6/11 ≈ 0.545
      ├── Some((8, 4)): 0/5 ≈ 0.000
      ├── Some((8, 5)): 7/12 ≈ 0.583
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 8/13 ≈ 0.615
      └── Some((8, 8)): 9/14 ≈ 0.643
  ├── Some((6, 3)): 384/774 ≈ 0.496
    ├── Some((3, 0)): 36/77 ≈ 0.468
      ├── Some((0, 0)): 3/8 ≈ 0.375
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 7/11 ≈ 0.636
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 5/9 ≈ 0.556
      ├── Some((0, 6)): 5/9 ≈ 0.556
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((3, 1)): 34/74 ≈ 0.459
      ├── Some((1, 0)): 5/9 ≈ 0.556
      ├── Some((1, 1)): 0/4 ≈ 0.000
      ├── Some((1, 2)): 5/9 ≈ 0.556
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 7/11 ≈ 0.636
      ├── Some((1, 6)): 2/7 ≈ 0.286
      ├── Some((1, 7)): 4/8 ≈ 0.500
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((3, 2)): 41/84 ≈ 0.488
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 7/12 ≈ 0.583
      ├── Some((2, 2)): 5/10 ≈ 0.500
      ├── Some((2, 3)): 0/4 ≈ 0.000
      ├── Some((2, 4)): 5/10 ≈ 0.500
      ├── Some((2, 5)): 5/10 ≈ 0.500
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 9/13 ≈ 0.692
    ├── Some((3, 3)): 53/101 ≈ 0.525
      ├── Some((3, 0)): 9/15 ≈ 0.600
      ├── Some((3, 1)): 0/5 ≈ 0.000
      ├── Some((3, 2)): 6/12 ≈ 0.500
      ├── Some((3, 4)): 8/14 ≈ 0.571
      ├── Some((3, 5)): 11/17 ≈ 0.647
      ├── Some((3, 6)): 2/8 ≈ 0.250
      ├── Some((3, 7)): 12/18 ≈ 0.667
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((3, 4)): 37/78 ≈ 0.474
      ├── Some((4, 0)): 1/5 ≈ 0.200
      ├── Some((4, 1)): 13/16 ≈ 0.812
      ├── Some((4, 2)): 1/5 ≈ 0.200
      ├── Some((4, 3)): 5/10 ≈ 0.500
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 4/9 ≈ 0.444
      ├── Some((4, 6)): 6/10 ≈ 0.600
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((3, 5)): 26/62 ≈ 0.419
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 2/6 ≈ 0.333
      ├── Some((5, 2)): 4/9 ≈ 0.444
      ├── Some((5, 3)): 2/6 ≈ 0.333
      ├── Some((5, 4)): 0/4 ≈ 0.000
      ├── Some((5, 5)): 4/9 ≈ 0.444
      ├── Some((5, 7)): 10/14 ≈ 0.714
      └── Some((5, 8)): 3/8 ≈ 0.375
    ├── Some((3, 6)): 52/99 ≈ 0.525
      ├── Some((6, 0)): 10/15 ≈ 0.667
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 9/15 ≈ 0.600
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 8/14 ≈ 0.571
    ├── Some((3, 7)): 72/126 ≈ 0.571
      ├── Some((7, 0)): 10/16 ≈ 0.625
      ├── Some((7, 1)): 13/18 ≈ 0.722
      ├── Some((7, 2)): 12/18 ≈ 0.667
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 2/8 ≈ 0.250
      ├── Some((7, 5)): 10/16 ≈ 0.625
      ├── Some((7, 6)): 5/11 ≈ 0.455
      ├── Some((7, 7)): 7/13 ≈ 0.538
      └── Some((7, 8)): 11/17 ≈ 0.647
    └── Some((3, 8)): 33/72 ≈ 0.458
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 4/8 ≈ 0.500
      ├── Some((8, 2)): 6/10 ≈ 0.600
      ├── Some((8, 3)): 4/8 ≈ 0.500
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 6/10 ≈ 0.600
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((6, 4)): 362/736 ≈ 0.492
    ├── Some((4, 0)): 40/82 ≈ 0.488
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 4/9 ≈ 0.444
      ├── Some((0, 3)): 5/9 ≈ 0.556
      ├── Some((0, 4)): 4/9 ≈ 0.444
      ├── Some((0, 5)): 5/9 ≈ 0.556
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 8/12 ≈ 0.667
      └── Some((0, 8)): 7/11 ≈ 0.636
    ├── Some((4, 1)): 65/116 ≈ 0.560
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 8/14 ≈ 0.571
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 12/17 ≈ 0.706
      ├── Some((1, 4)): 9/14 ≈ 0.643
      ├── Some((1, 5)): 4/10 ≈ 0.400
      ├── Some((1, 6)): 10/15 ≈ 0.667
      ├── Some((1, 7)): 9/14 ≈ 0.643
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((4, 2)): 38/79 ≈ 0.481
      ├── Some((2, 0)): 10/14 ≈ 0.714
      ├── Some((2, 1)): 5/9 ≈ 0.556
      ├── Some((2, 2)): 5/9 ≈ 0.556
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 1/6 ≈ 0.167
      ├── Some((2, 5)): 5/9 ≈ 0.556
      ├── Some((2, 6)): 5/10 ≈ 0.500
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 1/6 ≈ 0.167
    ├── Some((4, 3)): 36/76 ≈ 0.474
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 5/9 ≈ 0.556
      ├── Some((3, 2)): 0/4 ≈ 0.000
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 6/10 ≈ 0.600
      ├── Some((3, 5)): 5/9 ≈ 0.556
      ├── Some((3, 6)): 8/12 ≈ 0.667
      ├── Some((3, 7)): 4/8 ≈ 0.500
      └── Some((3, 8)): 3/8 ≈ 0.375
    ├── Some((4, 4)): 37/77 ≈ 0.481
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 7/11 ≈ 0.636
      ├── Some((4, 2)): 5/10 ≈ 0.500
      ├── Some((4, 3)): 5/10 ≈ 0.500
      ├── Some((4, 5)): 1/6 ≈ 0.167
      ├── Some((4, 6)): 5/10 ≈ 0.500
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 6/11 ≈ 0.545
    ├── Some((4, 5)): 46/90 ≈ 0.511
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 8/13 ≈ 0.615
      ├── Some((5, 3)): 7/12 ≈ 0.583
      ├── Some((5, 4)): 7/12 ≈ 0.583
      ├── Some((5, 5)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 4/10 ≈ 0.400
    ├── Some((4, 6)): 34/73 ≈ 0.466
      ├── Some((6, 0)): 6/11 ≈ 0.545
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 0/4 ≈ 0.000
      ├── Some((6, 5)): 7/12 ≈ 0.583
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 8/13 ≈ 0.615
    ├── Some((4, 7)): 31/69 ≈ 0.449
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 6/10 ≈ 0.600
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 6/10 ≈ 0.600
      ├── Some((7, 5)): 3/8 ≈ 0.375
      ├── Some((7, 6)): 4/8 ≈ 0.500
      ├── Some((7, 7)): 4/8 ≈ 0.500
      └── Some((7, 8)): 2/6 ≈ 0.333
    └── Some((4, 8)): 34/73 ≈ 0.466
      ├── Some((8, 0)): 4/9 ≈ 0.444
      ├── Some((8, 1)): 6/10 ≈ 0.600
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 5/9 ≈ 0.556
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 5/9 ≈ 0.556
      ├── Some((8, 7)): 5/9 ≈ 0.556
      └── Some((8, 8)): 5/10 ≈ 0.500
  ├── Some((6, 5)): 435/862 ≈ 0.505
    ├── Some((5, 0)): 49/100 ≈ 0.490
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 1/6 ≈ 0.167
      ├── Some((0, 4)): 7/13 ≈ 0.538
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 8/13 ≈ 0.615
      ├── Some((0, 7)): 8/14 ≈ 0.571
      └── Some((0, 8)): 0/5 ≈ 0.000
    ├── Some((5, 1)): 95/165 ≈ 0.576
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 8/16 ≈ 0.500
      ├── Some((1, 2)): 6/14 ≈ 0.429
      ├── Some((1, 3)): 12/20 ≈ 0.600
      ├── Some((1, 4)): 13/21 ≈ 0.619
      ├── Some((1, 5)): 16/24 ≈ 0.667
      ├── Some((1, 6)): 7/15 ≈ 0.467
      ├── Some((1, 7)): 9/17 ≈ 0.529
      └── Some((1, 8)): 17/24 ≈ 0.708
    ├── Some((5, 2)): 44/93 ≈ 0.473
      ├── Some((2, 0)): 15/20 ≈ 0.750
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 6/11 ≈ 0.545
      ├── Some((2, 6)): 5/11 ≈ 0.455
      ├── Some((2, 7)): 1/6 ≈ 0.167
      └── Some((2, 8)): 5/11 ≈ 0.455
    ├── Some((5, 3)): 46/96 ≈ 0.479
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 10/15 ≈ 0.667
      ├── Some((3, 3)): 4/10 ≈ 0.400
      ├── Some((3, 4)): 11/16 ≈ 0.688
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 1/6 ≈ 0.167
      ├── Some((3, 7)): 7/13 ≈ 0.538
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((5, 4)): 36/81 ≈ 0.444
      ├── Some((4, 0)): 5/10 ≈ 0.500
      ├── Some((4, 1)): 7/12 ≈ 0.583
      ├── Some((4, 2)): 5/10 ≈ 0.500
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 4)): 8/13 ≈ 0.615
      ├── Some((4, 5)): 0/4 ≈ 0.000
      ├── Some((4, 6)): 2/7 ≈ 0.286
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((5, 5)): 62/119 ≈ 0.521
      ├── Some((5, 0)): 14/23 ≈ 0.609
      ├── Some((5, 1)): 5/13 ≈ 0.385
      ├── Some((5, 2)): 6/14 ≈ 0.429
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 7)): 13/21 ≈ 0.619
      └── Some((5, 8)): 9/17 ≈ 0.529
    ├── Some((5, 7)): 46/96 ≈ 0.479
      ├── Some((7, 0)): 7/13 ≈ 0.538
      ├── Some((7, 1)): 8/13 ≈ 0.615
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 2/7 ≈ 0.286
      ├── Some((7, 4)): 10/15 ≈ 0.667
      ├── Some((7, 5)): 7/13 ≈ 0.538
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 0/5 ≈ 0.000
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((5, 8)): 56/111 ≈ 0.505
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 8/14 ≈ 0.571
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 3/9 ≈ 0.333
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 8/15 ≈ 0.533
      ├── Some((8, 7)): 2/8 ≈ 0.250
      └── Some((8, 8)): 13/19 ≈ 0.684
  ├── Some((6, 6)): 500/973 ≈ 0.514
    ├── Some((6, 0)): 78/144 ≈ 0.542
      ├── Some((0, 0)): 13/20 ≈ 0.650
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 9/16 ≈ 0.562
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 8/15 ≈ 0.533
      ├── Some((0, 7)): 10/18 ≈ 0.556
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((6, 1)): 36/83 ≈ 0.434
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 6/11 ≈ 0.545
      ├── Some((1, 2)): 2/7 ≈ 0.286
      ├── Some((1, 3)): 1/6 ≈ 0.167
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 7/12 ≈ 0.583
      ├── Some((1, 7)): 6/11 ≈ 0.545
      └── Some((1, 8)): 0/5 ≈ 0.000
    ├── Some((6, 2)): 45/97 ≈ 0.464
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 1/6 ≈ 0.167
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 9/15 ≈ 0.600
      ├── Some((2, 7)): 13/18 ≈ 0.722
      └── Some((2, 8)): 4/10 ≈ 0.400
    ├── Some((6, 3)): 58/116 ≈ 0.500
      ├── Some((3, 0)): 14/20 ≈ 0.700
      ├── Some((3, 1)): 2/8 ≈ 0.250
      ├── Some((3, 2)): 4/11 ≈ 0.364
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 1/7 ≈ 0.143
      ├── Some((3, 5)): 12/19 ≈ 0.632
      ├── Some((3, 6)): 2/8 ≈ 0.250
      ├── Some((3, 7)): 13/20 ≈ 0.650
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((6, 4)): 51/105 ≈ 0.486
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 9/15 ≈ 0.600
      ├── Some((4, 2)): 4/10 ≈ 0.400
      ├── Some((4, 3)): 1/7 ≈ 0.143
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 10/16 ≈ 0.625
      └── Some((4, 8)): 7/13 ≈ 0.538
    ├── Some((6, 5)): 72/136 ≈ 0.529
      ├── Some((5, 0)): 9/17 ≈ 0.529
      ├── Some((5, 1)): 5/13 ≈ 0.385
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 10/18 ≈ 0.556
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 7)): 5/13 ≈ 0.385
      └── Some((5, 8)): 22/30 ≈ 0.733
    ├── Some((6, 7)): 45/97 ≈ 0.464
      ├── Some((7, 0)): 2/7 ≈ 0.286
      ├── Some((7, 1)): 6/12 ≈ 0.500
      ├── Some((7, 2)): 7/13 ≈ 0.538
      ├── Some((7, 3)): 2/7 ≈ 0.286
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 8/14 ≈ 0.571
      ├── Some((7, 7)): 2/7 ≈ 0.286
      └── Some((7, 8)): 6/12 ≈ 0.500
    └── Some((6, 8)): 114/194 ≈ 0.588
      ├── Some((8, 0)): 18/28 ≈ 0.643
      ├── Some((8, 1)): 3/11 ≈ 0.273
      ├── Some((8, 2)): 7/16 ≈ 0.438
      ├── Some((8, 3)): 3/11 ≈ 0.273
      ├── Some((8, 4)): 10/19 ≈ 0.526
      ├── Some((8, 5)): 22/31 ≈ 0.710
      ├── Some((8, 6)): 15/24 ≈ 0.625
      ├── Some((8, 7)): 24/33 ≈ 0.727
      └── Some((8, 8)): 11/20 ≈ 0.550
  ├── Some((6, 7)): 540/1041 ≈ 0.519
    ├── Some((7, 0)): 83/148 ≈ 0.561
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 5/12 ≈ 0.417
      ├── Some((0, 3)): 8/15 ≈ 0.533
      ├── Some((0, 4)): 4/11 ≈ 0.364
      ├── Some((0, 5)): 15/22 ≈ 0.682
      ├── Some((0, 6)): 13/21 ≈ 0.619
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 20/27 ≈ 0.741
    ├── Some((7, 1)): 50/102 ≈ 0.490
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 7/13 ≈ 0.538
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 6/12 ≈ 0.500
      ├── Some((1, 5)): 7/13 ≈ 0.538
      ├── Some((1, 6)): 1/6 ≈ 0.167
      ├── Some((1, 7)): 7/13 ≈ 0.538
      └── Some((1, 8)): 8/13 ≈ 0.615
    ├── Some((7, 2)): 37/83 ≈ 0.446
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 1/6 ≈ 0.167
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 6/11 ≈ 0.545
      ├── Some((2, 5)): 9/14 ≈ 0.643
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 8/13 ≈ 0.615
      └── Some((2, 8)): 0/5 ≈ 0.000
    ├── Some((7, 3)): 78/141 ≈ 0.553
      ├── Some((3, 0)): 8/15 ≈ 0.533
      ├── Some((3, 1)): 3/9 ≈ 0.333
      ├── Some((3, 2)): 14/21 ≈ 0.667
      ├── Some((3, 3)): 5/12 ≈ 0.417
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 13/20 ≈ 0.650
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 10/17 ≈ 0.588
    ├── Some((7, 4)): 43/91 ≈ 0.473
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 10/15 ≈ 0.667
      ├── Some((4, 2)): 4/10 ≈ 0.400
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 7/12 ≈ 0.583
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((7, 5)): 50/102 ≈ 0.490
      ├── Some((5, 0)): 3/9 ≈ 0.333
      ├── Some((5, 1)): 10/17 ≈ 0.588
      ├── Some((5, 2)): 10/17 ≈ 0.588
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 9/16 ≈ 0.562
      ├── Some((5, 5)): 2/8 ≈ 0.250
      ├── Some((5, 7)): 1/7 ≈ 0.143
      └── Some((5, 8)): 9/16 ≈ 0.562
    ├── Some((7, 6)): 92/161 ≈ 0.571
      ├── Some((6, 0)): 5/13 ≈ 0.385
      ├── Some((6, 1)): 19/28 ≈ 0.679
      ├── Some((6, 2)): 6/15 ≈ 0.400
      ├── Some((6, 3)): 14/23 ≈ 0.609
      ├── Some((6, 4)): 9/18 ≈ 0.500
      ├── Some((6, 5)): 14/23 ≈ 0.609
      ├── Some((6, 6)): 1/8 ≈ 0.125
      └── Some((6, 8)): 23/32 ≈ 0.719
    ├── Some((7, 7)): 56/110 ≈ 0.509
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 8/15 ≈ 0.533
      ├── Some((7, 2)): 6/13 ≈ 0.462
      ├── Some((7, 3)): 3/9 ≈ 0.333
      ├── Some((7, 4)): 11/18 ≈ 0.611
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 12/18 ≈ 0.667
      └── Some((7, 8)): 5/12 ≈ 0.417
    └── Some((7, 8)): 50/102 ≈ 0.490
      ├── Some((8, 0)): 10/15 ≈ 0.667
      ├── Some((8, 1)): 1/6 ≈ 0.167
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 6/12 ≈ 0.500
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 9/14 ≈ 0.643
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 5/11 ≈ 0.455
  └── Some((6, 8)): 478/935 ≈ 0.511
    ├── Some((8, 0)): 56/108 ≈ 0.519
      ├── Some((0, 0)): 1/6 ≈ 0.167
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 9/15 ≈ 0.600
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 10/15 ≈ 0.667
      ├── Some((0, 6)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 9/15 ≈ 0.600
      └── Some((0, 8)): 10/15 ≈ 0.667
    ├── Some((8, 1)): 44/91 ≈ 0.484
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 9/14 ≈ 0.643
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 6/12 ≈ 0.500
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 8/13 ≈ 0.615
      ├── Some((1, 7)): 9/14 ≈ 0.643
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((8, 2)): 58/111 ≈ 0.523
      ├── Some((2, 0)): 9/14 ≈ 0.643
      ├── Some((2, 1)): 6/12 ≈ 0.500
      ├── Some((2, 2)): 7/13 ≈ 0.538
      ├── Some((2, 3)): 11/16 ≈ 0.688
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 2/8 ≈ 0.250
      ├── Some((2, 6)): 6/12 ≈ 0.500
      ├── Some((2, 7)): 9/15 ≈ 0.600
      └── Some((2, 8)): 5/11 ≈ 0.455
    ├── Some((8, 3)): 35/78 ≈ 0.449
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 4/9 ≈ 0.444
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 1/5 ≈ 0.200
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 5/9 ≈ 0.556
      ├── Some((3, 7)): 10/14 ≈ 0.714
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((8, 4)): 39/84 ≈ 0.464
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 5/10 ≈ 0.500
      ├── Some((4, 2)): 2/7 ≈ 0.286
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 7/12 ≈ 0.583
      ├── Some((4, 6)): 4/9 ≈ 0.444
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 8/12 ≈ 0.667
    ├── Some((8, 5)): 58/111 ≈ 0.523
      ├── Some((5, 0)): 2/8 ≈ 0.250
      ├── Some((5, 1)): 12/19 ≈ 0.632
      ├── Some((5, 2)): 1/7 ≈ 0.143
      ├── Some((5, 3)): 0/6 ≈ 0.000
      ├── Some((5, 4)): 10/17 ≈ 0.588
      ├── Some((5, 5)): 11/18 ≈ 0.611
      ├── Some((5, 7)): 9/16 ≈ 0.562
      └── Some((5, 8)): 12/19 ≈ 0.632
    ├── Some((8, 6)): 35/78 ≈ 0.449
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 7/12 ≈ 0.583
      ├── Some((6, 2)): 0/5 ≈ 0.000
      ├── Some((6, 3)): 7/12 ≈ 0.583
      ├── Some((6, 4)): 4/10 ≈ 0.400
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 5/11 ≈ 0.455
      └── Some((6, 7)): 6/12 ≈ 0.500
    ├── Some((8, 7)): 91/157 ≈ 0.580
      ├── Some((7, 0)): 7/14 ≈ 0.500
      ├── Some((7, 1)): 13/20 ≈ 0.650
      ├── Some((7, 2)): 15/22 ≈ 0.682
      ├── Some((7, 3)): 8/15 ≈ 0.533
      ├── Some((7, 4)): 14/21 ≈ 0.667
      ├── Some((7, 5)): 9/17 ≈ 0.529
      ├── Some((7, 6)): 3/10 ≈ 0.300
      ├── Some((7, 7)): 10/18 ≈ 0.556
      └── Some((7, 8)): 11/19 ≈ 0.579
    └── Some((8, 8)): 61/116 ≈ 0.526
      ├── Some((8, 0)): 10/17 ≈ 0.588
      ├── Some((8, 1)): 7/14 ≈ 0.500
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 11/18 ≈ 0.611
      ├── Some((8, 4)): 10/17 ≈ 0.588
      ├── Some((8, 5)): 10/17 ≈ 0.588
      ├── Some((8, 6)): 7/14 ≈ 0.500
      └── Some((8, 7)): 2/8 ≈ 0.250
├── Some((5, 7)): 4066/8015 ≈ 0.507
  ├── Some((7, 0)): 377/764 ≈ 0.493
    ├── Some((0, 0)): 46/91 ≈ 0.505
      ├── Some((0, 1)): 8/14 ≈ 0.571
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 10/15 ≈ 0.667
      ├── Some((0, 4)): 10/16 ≈ 0.625
      ├── Some((0, 5)): 0/5 ≈ 0.000
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 11/16 ≈ 0.688
      └── Some((0, 8)): 1/6 ≈ 0.167
    ├── Some((0, 1)): 26/62 ≈ 0.419
      ├── Some((1, 0)): 0/4 ≈ 0.000
      ├── Some((1, 1)): 5/9 ≈ 0.556
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 6/10 ≈ 0.600
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 1/5 ≈ 0.200
      ├── Some((1, 6)): 4/8 ≈ 0.500
      ├── Some((1, 7)): 0/4 ≈ 0.000
      └── Some((1, 8)): 3/7 ≈ 0.429
    ├── Some((0, 2)): 69/123 ≈ 0.561
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 7/13 ≈ 0.538
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 9/15 ≈ 0.600
      ├── Some((2, 4)): 9/15 ≈ 0.600
      ├── Some((2, 5)): 12/17 ≈ 0.706
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 12/18 ≈ 0.667
      └── Some((2, 8)): 6/12 ≈ 0.500
    ├── Some((0, 3)): 43/87 ≈ 0.494
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 6/11 ≈ 0.545
      ├── Some((3, 2)): 1/6 ≈ 0.167
      ├── Some((3, 3)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 6/11 ≈ 0.545
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 9/13 ≈ 0.692
      └── Some((3, 8)): 1/6 ≈ 0.167
    ├── Some((0, 4)): 35/75 ≈ 0.467
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 6/10 ≈ 0.600
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 6/10 ≈ 0.600
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 2/6 ≈ 0.333
      └── Some((4, 8)): 2/6 ≈ 0.333
    ├── Some((0, 5)): 34/74 ≈ 0.459
      ├── Some((5, 0)): 6/11 ≈ 0.545
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 3/8 ≈ 0.375
      ├── Some((5, 3)): 4/9 ≈ 0.444
      ├── Some((5, 4)): 5/10 ≈ 0.500
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 3/8 ≈ 0.375
      └── Some((5, 8)): 8/13 ≈ 0.615
    ├── Some((0, 6)): 22/56 ≈ 0.393
      ├── Some((6, 0)): 3/6 ≈ 0.500
      ├── Some((6, 1)): 5/8 ≈ 0.625
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 5/8 ≈ 0.625
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 2/6 ≈ 0.333
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 3/7 ≈ 0.429
    ├── Some((0, 7)): 66/119 ≈ 0.555
      ├── Some((7, 1)): 14/20 ≈ 0.700
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 11/17 ≈ 0.647
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 4/10 ≈ 0.400
      ├── Some((7, 6)): 5/12 ≈ 0.417
      ├── Some((7, 7)): 10/17 ≈ 0.588
      └── Some((7, 8)): 6/13 ≈ 0.462
    └── Some((0, 8)): 35/76 ≈ 0.461
      ├── Some((8, 0)): 4/9 ≈ 0.444
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 5/10 ≈ 0.500
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 6/10 ≈ 0.600
      ├── Some((8, 7)): 6/10 ≈ 0.600
      └── Some((8, 8)): 6/10 ≈ 0.600
  ├── Some((7, 1)): 449/889 ≈ 0.505
    ├── Some((1, 0)): 30/70 ≈ 0.429
      ├── Some((0, 0)): 3/8 ≈ 0.375
      ├── Some((0, 1)): 2/6 ≈ 0.333
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 5/9 ≈ 0.556
      ├── Some((0, 6)): 0/4 ≈ 0.000
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 8/12 ≈ 0.667
    ├── Some((1, 1)): 80/142 ≈ 0.563
      ├── Some((1, 0)): 15/23 ≈ 0.652
      ├── Some((1, 2)): 11/19 ≈ 0.579
      ├── Some((1, 3)): 9/17 ≈ 0.529
      ├── Some((1, 4)): 7/15 ≈ 0.467
      ├── Some((1, 5)): 15/23 ≈ 0.652
      ├── Some((1, 6)): 1/8 ≈ 0.125
      ├── Some((1, 7)): 6/13 ≈ 0.462
      └── Some((1, 8)): 15/23 ≈ 0.652
    ├── Some((1, 2)): 30/71 ≈ 0.423
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 8/12 ≈ 0.667
      ├── Some((2, 2)): 5/10 ≈ 0.500
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 1/6 ≈ 0.167
      ├── Some((2, 5)): 0/4 ≈ 0.000
      ├── Some((2, 6)): 0/4 ≈ 0.000
      ├── Some((2, 7)): 7/11 ≈ 0.636
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((1, 3)): 62/117 ≈ 0.530
      ├── Some((3, 0)): 10/16 ≈ 0.625
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 11/17 ≈ 0.647
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 9/15 ≈ 0.600
      ├── Some((3, 6)): 7/14 ≈ 0.500
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 8/14 ≈ 0.571
    ├── Some((1, 4)): 12/42 ≈ 0.286
      ├── Some((4, 0)): 0/3 ≈ 0.000
      ├── Some((4, 1)): 1/4 ≈ 0.250
      ├── Some((4, 2)): 2/5 ≈ 0.400
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 2/5 ≈ 0.400
      ├── Some((4, 5)): 2/5 ≈ 0.400
      ├── Some((4, 6)): 0/3 ≈ 0.000
      ├── Some((4, 7)): 1/5 ≈ 0.200
      └── Some((4, 8)): 3/6 ≈ 0.500
    ├── Some((1, 5)): 59/113 ≈ 0.522
      ├── Some((5, 0)): 4/11 ≈ 0.364
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 10/17 ≈ 0.588
      ├── Some((5, 3)): 8/15 ≈ 0.533
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 18/24 ≈ 0.750
      └── Some((5, 8)): 3/9 ≈ 0.333
    ├── Some((1, 6)): 29/69 ≈ 0.420
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 9/13 ≈ 0.692
      ├── Some((6, 2)): 4/8 ≈ 0.500
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 3/8 ≈ 0.375
      ├── Some((6, 7)): 5/9 ≈ 0.556
      └── Some((6, 8)): 0/4 ≈ 0.000
    ├── Some((1, 7)): 83/146 ≈ 0.568
      ├── Some((7, 0)): 14/22 ≈ 0.636
      ├── Some((7, 2)): 4/11 ≈ 0.364
      ├── Some((7, 3)): 13/21 ≈ 0.619
      ├── Some((7, 4)): 11/19 ≈ 0.579
      ├── Some((7, 5)): 15/23 ≈ 0.652
      ├── Some((7, 6)): 6/14 ≈ 0.429
      ├── Some((7, 7)): 10/18 ≈ 0.556
      └── Some((7, 8)): 9/17 ≈ 0.529
    └── Some((1, 8)): 63/118 ≈ 0.534
      ├── Some((8, 0)): 3/9 ≈ 0.333
      ├── Some((8, 1)): 9/15 ≈ 0.600
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 9/15 ≈ 0.600
      ├── Some((8, 5)): 6/12 ≈ 0.500
      ├── Some((8, 6)): 11/17 ≈ 0.647
      ├── Some((8, 7)): 8/14 ≈ 0.571
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((7, 2)): 362/738 ≈ 0.491
    ├── Some((2, 0)): 16/46 ≈ 0.348
      ├── Some((0, 0)): 3/6 ≈ 0.500
      ├── Some((0, 1)): 3/6 ≈ 0.500
      ├── Some((0, 2)): 0/3 ≈ 0.000
      ├── Some((0, 3)): 1/5 ≈ 0.200
      ├── Some((0, 4)): 0/3 ≈ 0.000
      ├── Some((0, 5)): 3/6 ≈ 0.500
      ├── Some((0, 6)): 3/7 ≈ 0.429
      ├── Some((0, 7)): 0/3 ≈ 0.000
      └── Some((0, 8)): 2/6 ≈ 0.333
    ├── Some((2, 1)): 35/75 ≈ 0.467
      ├── Some((1, 0)): 5/9 ≈ 0.556
      ├── Some((1, 1)): 6/10 ≈ 0.600
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 0/4 ≈ 0.000
      ├── Some((1, 5)): 7/11 ≈ 0.636
      ├── Some((1, 6)): 5/9 ≈ 0.556
      ├── Some((1, 7)): 4/9 ≈ 0.444
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((2, 2)): 66/118 ≈ 0.559
      ├── Some((2, 0)): 9/16 ≈ 0.562
      ├── Some((2, 1)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 4/10 ≈ 0.400
      ├── Some((2, 4)): 10/16 ≈ 0.625
      ├── Some((2, 5)): 1/7 ≈ 0.143
      ├── Some((2, 6)): 11/17 ≈ 0.647
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 15/21 ≈ 0.714
    ├── Some((2, 3)): 32/71 ≈ 0.451
      ├── Some((3, 0)): 8/12 ≈ 0.667
      ├── Some((3, 1)): 3/8 ≈ 0.375
      ├── Some((3, 2)): 2/6 ≈ 0.333
      ├── Some((3, 3)): 4/8 ≈ 0.500
      ├── Some((3, 4)): 5/9 ≈ 0.556
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 4/8 ≈ 0.500
      ├── Some((3, 7)): 4/8 ≈ 0.500
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((2, 4)): 42/85 ≈ 0.494
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 7/11 ≈ 0.636
      ├── Some((4, 2)): 6/11 ≈ 0.545
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 4)): 6/11 ≈ 0.545
      ├── Some((4, 5)): 4/9 ≈ 0.444
      ├── Some((4, 6)): 2/7 ≈ 0.286
      ├── Some((4, 7)): 7/11 ≈ 0.636
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((2, 5)): 25/60 ≈ 0.417
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 4/8 ≈ 0.500
      ├── Some((5, 3)): 4/8 ≈ 0.500
      ├── Some((5, 4)): 2/6 ≈ 0.333
      ├── Some((5, 5)): 6/10 ≈ 0.600
      ├── Some((5, 6)): 4/9 ≈ 0.444
      └── Some((5, 8)): 1/5 ≈ 0.200
    ├── Some((2, 6)): 59/108 ≈ 0.546
      ├── Some((6, 0)): 6/11 ≈ 0.545
      ├── Some((6, 1)): 6/11 ≈ 0.545
      ├── Some((6, 2)): 8/13 ≈ 0.615
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 13/18 ≈ 0.722
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 6/12 ≈ 0.500
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((2, 7)): 54/102 ≈ 0.529
      ├── Some((7, 0)): 6/12 ≈ 0.500
      ├── Some((7, 1)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 10/16 ≈ 0.625
      ├── Some((7, 6)): 6/12 ≈ 0.500
      ├── Some((7, 7)): 7/13 ≈ 0.538
      └── Some((7, 8)): 14/19 ≈ 0.737
    └── Some((2, 8)): 33/72 ≈ 0.458
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 8/12 ≈ 0.667
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 0/4 ≈ 0.000
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 4/8 ≈ 0.500
      ├── Some((8, 7)): 7/11 ≈ 0.636
      └── Some((8, 8)): 4/8 ≈ 0.500
  ├── Some((7, 3)): 439/872 ≈ 0.503
    ├── Some((3, 0)): 70/127 ≈ 0.551
      ├── Some((0, 0)): 16/22 ≈ 0.727
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 3/9 ≈ 0.333
      ├── Some((0, 4)): 12/18 ≈ 0.667
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 10/17 ≈ 0.588
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((3, 1)): 37/80 ≈ 0.463
      ├── Some((1, 0)): 7/12 ≈ 0.583
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 1/6 ≈ 0.167
      ├── Some((1, 3)): 1/6 ≈ 0.167
      ├── Some((1, 4)): 7/12 ≈ 0.583
      ├── Some((1, 5)): 7/12 ≈ 0.583
      ├── Some((1, 6)): 8/12 ≈ 0.667
      ├── Some((1, 7)): 0/4 ≈ 0.000
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((3, 2)): 31/72 ≈ 0.431
      ├── Some((2, 0)): 0/4 ≈ 0.000
      ├── Some((2, 1)): 2/7 ≈ 0.286
      ├── Some((2, 2)): 7/11 ≈ 0.636
      ├── Some((2, 3)): 1/5 ≈ 0.200
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 12/16 ≈ 0.750
    ├── Some((3, 3)): 35/77 ≈ 0.455
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 1)): 4/9 ≈ 0.444
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 5/10 ≈ 0.500
      ├── Some((3, 7)): 8/13 ≈ 0.615
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((3, 4)): 38/82 ≈ 0.463
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 4/9 ≈ 0.444
      ├── Some((4, 3)): 5/10 ≈ 0.500
      ├── Some((4, 4)): 6/11 ≈ 0.545
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 0/4 ≈ 0.000
      ├── Some((4, 7)): 11/15 ≈ 0.733
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((3, 5)): 33/74 ≈ 0.446
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 6/11 ≈ 0.545
      ├── Some((5, 3)): 0/5 ≈ 0.000
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 11/16 ≈ 0.688
      ├── Some((5, 6)): 3/8 ≈ 0.375
      └── Some((5, 8)): 1/6 ≈ 0.167
    ├── Some((3, 6)): 57/109 ≈ 0.523
      ├── Some((6, 0)): 6/12 ≈ 0.500
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 9/14 ≈ 0.643
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 12/17 ≈ 0.706
      └── Some((6, 8)): 2/8 ≈ 0.250
    ├── Some((3, 7)): 70/127 ≈ 0.551
      ├── Some((7, 0)): 12/19 ≈ 0.632
      ├── Some((7, 1)): 8/15 ≈ 0.533
      ├── Some((7, 2)): 4/11 ≈ 0.364
      ├── Some((7, 4)): 11/18 ≈ 0.611
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 16/23 ≈ 0.696
      ├── Some((7, 7)): 10/17 ≈ 0.588
      └── Some((7, 8)): 3/10 ≈ 0.300
    └── Some((3, 8)): 67/123 ≈ 0.545
      ├── Some((8, 0)): 14/20 ≈ 0.700
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 9/15 ≈ 0.600
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 11/17 ≈ 0.647
      ├── Some((8, 5)): 10/16 ≈ 0.625
      ├── Some((8, 6)): 4/10 ≈ 0.400
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 5/11 ≈ 0.455
  ├── Some((7, 4)): 670/1265 ≈ 0.530
    ├── Some((4, 0)): 55/113 ≈ 0.487
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 5/12 ≈ 0.417
      ├── Some((0, 2)): 12/18 ≈ 0.667
      ├── Some((0, 3)): 12/18 ≈ 0.667
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 4/10 ≈ 0.400
      ├── Some((0, 6)): 1/7 ≈ 0.143
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 11/18 ≈ 0.611
    ├── Some((4, 1)): 103/181 ≈ 0.569
      ├── Some((1, 0)): 8/16 ≈ 0.500
      ├── Some((1, 1)): 14/23 ≈ 0.609
      ├── Some((1, 2)): 10/18 ≈ 0.556
      ├── Some((1, 3)): 17/26 ≈ 0.654
      ├── Some((1, 4)): 14/23 ≈ 0.609
      ├── Some((1, 5)): 18/27 ≈ 0.667
      ├── Some((1, 6)): 11/20 ≈ 0.550
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 5/13 ≈ 0.385
    ├── Some((4, 2)): 79/147 ≈ 0.537
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 9/17 ≈ 0.529
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 8/16 ≈ 0.500
      ├── Some((2, 4)): 4/11 ≈ 0.364
      ├── Some((2, 5)): 16/23 ≈ 0.696
      ├── Some((2, 6)): 9/17 ≈ 0.529
      ├── Some((2, 7)): 10/18 ≈ 0.556
      └── Some((2, 8)): 9/17 ≈ 0.529
    ├── Some((4, 3)): 63/124 ≈ 0.508
      ├── Some((3, 0)): 8/15 ≈ 0.533
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 11/17 ≈ 0.647
      ├── Some((3, 3)): 10/17 ≈ 0.588
      ├── Some((3, 4)): 9/16 ≈ 0.562
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 5/12 ≈ 0.417
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((4, 4)): 63/124 ≈ 0.508
      ├── Some((4, 0)): 6/13 ≈ 0.462
      ├── Some((4, 1)): 10/18 ≈ 0.556
      ├── Some((4, 2)): 6/13 ≈ 0.462
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 14/22 ≈ 0.636
      ├── Some((4, 6)): 8/16 ≈ 0.500
      ├── Some((4, 7)): 4/11 ≈ 0.364
      └── Some((4, 8)): 8/16 ≈ 0.500
    ├── Some((4, 5)): 83/153 ≈ 0.542
      ├── Some((5, 0)): 20/29 ≈ 0.690
      ├── Some((5, 1)): 7/15 ≈ 0.467
      ├── Some((5, 2)): 19/28 ≈ 0.679
      ├── Some((5, 3)): 12/21 ≈ 0.571
      ├── Some((5, 4)): 3/11 ≈ 0.273
      ├── Some((5, 5)): 7/16 ≈ 0.438
      ├── Some((5, 6)): 7/16 ≈ 0.438
      └── Some((5, 8)): 7/16 ≈ 0.438
    ├── Some((4, 6)): 54/111 ≈ 0.486
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 2/8 ≈ 0.250
      ├── Some((6, 3)): 9/15 ≈ 0.600
      ├── Some((6, 4)): 9/15 ≈ 0.600
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 9/16 ≈ 0.562
    ├── Some((4, 7)): 74/140 ≈ 0.529
      ├── Some((7, 0)): 7/15 ≈ 0.467
      ├── Some((7, 1)): 15/24 ≈ 0.625
      ├── Some((7, 2)): 12/20 ≈ 0.600
      ├── Some((7, 3)): 6/14 ≈ 0.429
      ├── Some((7, 5)): 5/13 ≈ 0.385
      ├── Some((7, 6)): 7/15 ≈ 0.467
      ├── Some((7, 7)): 9/17 ≈ 0.529
      └── Some((7, 8)): 12/21 ≈ 0.571
    └── Some((4, 8)): 96/171 ≈ 0.561
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 1)): 2/9 ≈ 0.222
      ├── Some((8, 2)): 6/14 ≈ 0.429
      ├── Some((8, 3)): 14/23 ≈ 0.609
      ├── Some((8, 4)): 15/24 ≈ 0.625
      ├── Some((8, 5)): 12/21 ≈ 0.571
      ├── Some((8, 6)): 22/30 ≈ 0.733
      ├── Some((8, 7)): 5/13 ≈ 0.385
      └── Some((8, 8)): 9/17 ≈ 0.529
  ├── Some((7, 5)): 192/436 ≈ 0.440
    ├── Some((5, 0)): 8/31 ≈ 0.258
      ├── Some((0, 0)): 1/3 ≈ 0.333
      ├── Some((0, 1)): 0/3 ≈ 0.000
      ├── Some((0, 2)): 0/3 ≈ 0.000
      ├── Some((0, 3)): 1/3 ≈ 0.333
      ├── Some((0, 4)): 0/3 ≈ 0.000
      ├── Some((0, 5)): 1/3 ≈ 0.333
      ├── Some((0, 6)): 1/4 ≈ 0.250
      ├── Some((0, 7)): 2/4 ≈ 0.500
      └── Some((0, 8)): 2/4 ≈ 0.500
    ├── Some((5, 1)): 15/42 ≈ 0.357
      ├── Some((1, 0)): 1/4 ≈ 0.250
      ├── Some((1, 1)): 2/4 ≈ 0.500
      ├── Some((1, 2)): 2/5 ≈ 0.400
      ├── Some((1, 3)): 2/5 ≈ 0.400
      ├── Some((1, 4)): 2/5 ≈ 0.400
      ├── Some((1, 5)): 2/5 ≈ 0.400
      ├── Some((1, 6)): 0/3 ≈ 0.000
      ├── Some((1, 7)): 2/5 ≈ 0.400
      └── Some((1, 8)): 2/5 ≈ 0.400
    ├── Some((5, 2)): 12/37 ≈ 0.324
      ├── Some((2, 0)): 1/4 ≈ 0.250
      ├── Some((2, 1)): 2/4 ≈ 0.500
      ├── Some((2, 2)): 2/4 ≈ 0.500
      ├── Some((2, 3)): 1/4 ≈ 0.250
      ├── Some((2, 4)): 0/3 ≈ 0.000
      ├── Some((2, 5)): 1/4 ≈ 0.250
      ├── Some((2, 6)): 1/4 ≈ 0.250
      ├── Some((2, 7)): 1/4 ≈ 0.250
      └── Some((2, 8)): 2/5 ≈ 0.400
    ├── Some((5, 3)): 25/57 ≈ 0.439
      ├── Some((3, 0)): 0/4 ≈ 0.000
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 3/6 ≈ 0.500
      ├── Some((3, 3)): 3/6 ≈ 0.500
      ├── Some((3, 4)): 3/7 ≈ 0.429
      ├── Some((3, 5)): 4/7 ≈ 0.571
      ├── Some((3, 6)): 1/5 ≈ 0.200
      ├── Some((3, 7)): 2/6 ≈ 0.333
      └── Some((3, 8)): 7/10 ≈ 0.700
    ├── Some((5, 4)): 36/72 ≈ 0.500
      ├── Some((4, 0)): 2/6 ≈ 0.333
      ├── Some((4, 1)): 1/5 ≈ 0.200
      ├── Some((4, 2)): 1/5 ≈ 0.200
      ├── Some((4, 3)): 7/11 ≈ 0.636
      ├── Some((4, 4)): 5/9 ≈ 0.556
      ├── Some((4, 5)): 6/10 ≈ 0.600
      ├── Some((4, 6)): 7/11 ≈ 0.636
      ├── Some((4, 7)): 4/8 ≈ 0.500
      └── Some((4, 8)): 2/6 ≈ 0.333
    ├── Some((5, 5)): 54/96 ≈ 0.562
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 11/17 ≈ 0.647
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 8/14 ≈ 0.571
      ├── Some((5, 6)): 8/14 ≈ 0.571
      └── Some((5, 8)): 10/16 ≈ 0.625
    ├── Some((5, 6)): 26/58 ≈ 0.448
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 0/4 ≈ 0.000
      ├── Some((6, 2)): 6/9 ≈ 0.667
      ├── Some((6, 3)): 0/4 ≈ 0.000
      ├── Some((6, 4)): 3/6 ≈ 0.500
      ├── Some((6, 5)): 4/7 ≈ 0.571
      ├── Some((6, 6)): 5/8 ≈ 0.625
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 6/9 ≈ 0.667
    └── Some((5, 8)): 15/42 ≈ 0.357
      ├── Some((8, 0)): 1/4 ≈ 0.250
      ├── Some((8, 1)): 3/5 ≈ 0.600
      ├── Some((8, 2)): 3/6 ≈ 0.500
      ├── Some((8, 3)): 0/3 ≈ 0.000
      ├── Some((8, 4)): 0/3 ≈ 0.000
      ├── Some((8, 5)): 2/5 ≈ 0.400
      ├── Some((8, 6)): 2/5 ≈ 0.400
      ├── Some((8, 7)): 1/4 ≈ 0.250
      └── Some((8, 8)): 3/6 ≈ 0.500
  ├── Some((7, 6)): 284/601 ≈ 0.473
    ├── Some((6, 0)): 30/65 ≈ 0.462
      ├── Some((0, 0)): 2/6 ≈ 0.333
      ├── Some((0, 1)): 0/4 ≈ 0.000
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 3/7 ≈ 0.429
      ├── Some((0, 4)): 3/7 ≈ 0.429
      ├── Some((0, 5)): 2/6 ≈ 0.333
      ├── Some((0, 6)): 2/6 ≈ 0.333
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 10/12 ≈ 0.833
    ├── Some((6, 1)): 45/86 ≈ 0.523
      ├── Some((1, 0)): 5/10 ≈ 0.500
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 6/10 ≈ 0.600
      ├── Some((1, 3)): 8/12 ≈ 0.667
      ├── Some((1, 4)): 6/11 ≈ 0.545
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 7/11 ≈ 0.636
      ├── Some((1, 7)): 0/4 ≈ 0.000
      └── Some((1, 8)): 7/11 ≈ 0.636
    ├── Some((6, 2)): 30/65 ≈ 0.462
      ├── Some((2, 0)): 2/6 ≈ 0.333
      ├── Some((2, 1)): 2/6 ≈ 0.333
      ├── Some((2, 2)): 4/8 ≈ 0.500
      ├── Some((2, 3)): 2/6 ≈ 0.333
      ├── Some((2, 4)): 2/6 ≈ 0.333
      ├── Some((2, 5)): 5/9 ≈ 0.556
      ├── Some((2, 6)): 9/12 ≈ 0.750
      ├── Some((2, 7)): 1/5 ≈ 0.200
      └── Some((2, 8)): 2/6 ≈ 0.333
    ├── Some((6, 3)): 45/86 ≈ 0.523
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 6/10 ≈ 0.600
      ├── Some((3, 2)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 5/10 ≈ 0.500
      ├── Some((3, 4)): 0/4 ≈ 0.000
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 4/9 ≈ 0.444
      ├── Some((3, 7)): 6/10 ≈ 0.600
      └── Some((3, 8)): 10/14 ≈ 0.714
    ├── Some((6, 4)): 20/50 ≈ 0.400
      ├── Some((4, 0)): 1/4 ≈ 0.250
      ├── Some((4, 1)): 1/5 ≈ 0.200
      ├── Some((4, 2)): 2/5 ≈ 0.400
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 3/6 ≈ 0.500
      ├── Some((4, 5)): 1/5 ≈ 0.200
      ├── Some((4, 6)): 2/5 ≈ 0.400
      ├── Some((4, 7)): 6/9 ≈ 0.667
      └── Some((4, 8)): 2/5 ≈ 0.400
    ├── Some((6, 5)): 28/62 ≈ 0.452
      ├── Some((5, 0)): 2/6 ≈ 0.333
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 5/9 ≈ 0.556
      ├── Some((5, 4)): 4/9 ≈ 0.444
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 6/10 ≈ 0.600
      └── Some((5, 8)): 6/10 ≈ 0.600
    ├── Some((6, 6)): 37/75 ≈ 0.493
      ├── Some((6, 0)): 6/11 ≈ 0.545
      ├── Some((6, 1)): 7/11 ≈ 0.636
      ├── Some((6, 2)): 6/11 ≈ 0.545
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 4)): 7/11 ≈ 0.636
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 4/9 ≈ 0.444
    ├── Some((6, 7)): 4/25 ≈ 0.160
      ├── Some((7, 0)): 0/2 ≈ 0.000
      ├── Some((7, 1)): 2/4 ≈ 0.500
      ├── Some((7, 2)): 0/2 ≈ 0.000
      ├── Some((7, 3)): 0/3 ≈ 0.000
      ├── Some((7, 4)): 0/3 ≈ 0.000
      ├── Some((7, 5)): 0/3 ≈ 0.000
      ├── Some((7, 7)): 0/3 ≈ 0.000
      └── Some((7, 8)): 2/4 ≈ 0.500
    └── Some((6, 8)): 45/86 ≈ 0.523
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 10/14 ≈ 0.714
      ├── Some((8, 2)): 5/10 ≈ 0.500
      ├── Some((8, 3)): 6/10 ≈ 0.600
      ├── Some((8, 4)): 3/8 ≈ 0.375
      ├── Some((8, 5)): 1/6 ≈ 0.167
      ├── Some((8, 6)): 9/13 ≈ 0.692
      ├── Some((8, 7)): 8/12 ≈ 0.667
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((7, 7)): 635/1206 ≈ 0.527
    ├── Some((7, 0)): 118/206 ≈ 0.573
      ├── Some((0, 0)): 12/22 ≈ 0.545
      ├── Some((0, 1)): 16/26 ≈ 0.615
      ├── Some((0, 2)): 9/18 ≈ 0.500
      ├── Some((0, 3)): 6/15 ≈ 0.400
      ├── Some((0, 4)): 10/20 ≈ 0.500
      ├── Some((0, 5)): 8/17 ≈ 0.471
      ├── Some((0, 6)): 27/37 ≈ 0.730
      ├── Some((0, 7)): 11/21 ≈ 0.524
      └── Some((0, 8)): 19/29 ≈ 0.655
    ├── Some((7, 1)): 66/131 ≈ 0.504
      ├── Some((1, 0)): 1/8 ≈ 0.125
      ├── Some((1, 1)): 4/11 ≈ 0.364
      ├── Some((1, 2)): 8/15 ≈ 0.533
      ├── Some((1, 3)): 17/24 ≈ 0.708
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 5/12 ≈ 0.417
      ├── Some((1, 6)): 9/16 ≈ 0.562
      ├── Some((1, 7)): 12/20 ≈ 0.600
      └── Some((1, 8)): 4/11 ≈ 0.364
    ├── Some((7, 2)): 76/146 ≈ 0.521
      ├── Some((2, 0)): 11/19 ≈ 0.579
      ├── Some((2, 1)): 5/13 ≈ 0.385
      ├── Some((2, 2)): 16/24 ≈ 0.667
      ├── Some((2, 3)): 2/9 ≈ 0.222
      ├── Some((2, 4)): 14/22 ≈ 0.636
      ├── Some((2, 5)): 7/15 ≈ 0.467
      ├── Some((2, 6)): 9/17 ≈ 0.529
      ├── Some((2, 7)): 3/10 ≈ 0.300
      └── Some((2, 8)): 8/16 ≈ 0.500
    ├── Some((7, 3)): 78/149 ≈ 0.523
      ├── Some((3, 0)): 3/10 ≈ 0.300
      ├── Some((3, 1)): 7/15 ≈ 0.467
      ├── Some((3, 2)): 15/23 ≈ 0.652
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 14/22 ≈ 0.636
      ├── Some((3, 5)): 9/17 ≈ 0.529
      ├── Some((3, 6)): 4/12 ≈ 0.333
      ├── Some((3, 7)): 13/21 ≈ 0.619
      └── Some((3, 8)): 5/13 ≈ 0.385
    ├── Some((7, 4)): 91/168 ≈ 0.542
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 1/8 ≈ 0.125
      ├── Some((4, 2)): 5/13 ≈ 0.385
      ├── Some((4, 3)): 9/17 ≈ 0.529
      ├── Some((4, 4)): 13/22 ≈ 0.591
      ├── Some((4, 5)): 9/18 ≈ 0.500
      ├── Some((4, 6)): 21/30 ≈ 0.700
      ├── Some((4, 7)): 17/26 ≈ 0.654
      └── Some((4, 8)): 9/18 ≈ 0.500
    ├── Some((7, 5)): 67/133 ≈ 0.504
      ├── Some((5, 0)): 2/9 ≈ 0.222
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 10/19 ≈ 0.526
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 5)): 17/26 ≈ 0.654
      ├── Some((5, 6)): 4/12 ≈ 0.333
      └── Some((5, 8)): 10/19 ≈ 0.526
    ├── Some((7, 6)): 48/104 ≈ 0.462
      ├── Some((6, 0)): 1/7 ≈ 0.143
      ├── Some((6, 1)): 8/15 ≈ 0.533
      ├── Some((6, 2)): 0/6 ≈ 0.000
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 10/16 ≈ 0.625
      └── Some((6, 8)): 6/12 ≈ 0.500
    └── Some((7, 8)): 91/168 ≈ 0.542
      ├── Some((8, 0)): 14/23 ≈ 0.609
      ├── Some((8, 1)): 13/22 ≈ 0.591
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 13/22 ≈ 0.591
      ├── Some((8, 4)): 7/15 ≈ 0.467
      ├── Some((8, 5)): 4/12 ≈ 0.333
      ├── Some((8, 6)): 10/19 ≈ 0.526
      ├── Some((8, 7)): 19/28 ≈ 0.679
      └── Some((8, 8)): 1/8 ≈ 0.125
  └── Some((7, 8)): 657/1243 ≈ 0.529
    ├── Some((8, 0)): 67/130 ≈ 0.515
      ├── Some((0, 0)): 11/18 ≈ 0.611
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 3/10 ≈ 0.300
      ├── Some((0, 4)): 6/13 ≈ 0.462
      ├── Some((0, 5)): 11/18 ≈ 0.611
      ├── Some((0, 6)): 10/17 ≈ 0.588
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((8, 1)): 68/131 ≈ 0.519
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 12/19 ≈ 0.632
      ├── Some((1, 2)): 10/17 ≈ 0.588
      ├── Some((1, 3)): 7/14 ≈ 0.500
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((8, 2)): 89/161 ≈ 0.553
      ├── Some((2, 0)): 7/15 ≈ 0.467
      ├── Some((2, 1)): 6/14 ≈ 0.429
      ├── Some((2, 2)): 8/16 ≈ 0.500
      ├── Some((2, 3)): 10/18 ≈ 0.556
      ├── Some((2, 4)): 6/14 ≈ 0.429
      ├── Some((2, 5)): 8/16 ≈ 0.500
      ├── Some((2, 6)): 15/23 ≈ 0.652
      ├── Some((2, 7)): 12/20 ≈ 0.600
      └── Some((2, 8)): 16/24 ≈ 0.667
    ├── Some((8, 3)): 78/146 ≈ 0.534
      ├── Some((3, 0)): 14/22 ≈ 0.636
      ├── Some((3, 1)): 12/20 ≈ 0.600
      ├── Some((3, 2)): 6/13 ≈ 0.462
      ├── Some((3, 3)): 12/20 ≈ 0.600
      ├── Some((3, 4)): 9/17 ≈ 0.529
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 5/12 ≈ 0.417
      ├── Some((3, 7)): 5/12 ≈ 0.417
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((8, 4)): 63/124 ≈ 0.508
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 11/17 ≈ 0.647
      ├── Some((4, 2)): 8/15 ≈ 0.533
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 5/12 ≈ 0.417
      ├── Some((4, 6)): 4/10 ≈ 0.400
      ├── Some((4, 7)): 11/18 ≈ 0.611
      └── Some((4, 8)): 3/9 ≈ 0.333
    ├── Some((8, 5)): 68/131 ≈ 0.519
      ├── Some((5, 0)): 0/6 ≈ 0.000
      ├── Some((5, 1)): 15/23 ≈ 0.652
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 12/20 ≈ 0.600
      ├── Some((5, 4)): 8/16 ≈ 0.500
      ├── Some((5, 5)): 11/19 ≈ 0.579
      ├── Some((5, 6)): 11/19 ≈ 0.579
      └── Some((5, 8)): 4/12 ≈ 0.333
    ├── Some((8, 6)): 64/126 ≈ 0.508
      ├── Some((6, 0)): 4/11 ≈ 0.364
      ├── Some((6, 1)): 8/15 ≈ 0.533
      ├── Some((6, 2)): 3/10 ≈ 0.300
      ├── Some((6, 3)): 11/18 ≈ 0.611
      ├── Some((6, 4)): 9/16 ≈ 0.562
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 6)): 5/12 ≈ 0.417
      ├── Some((6, 7)): 12/19 ≈ 0.632
      └── Some((6, 8)): 9/16 ≈ 0.562
    ├── Some((8, 7)): 117/200 ≈ 0.585
      ├── Some((7, 0)): 23/34 ≈ 0.676
      ├── Some((7, 1)): 15/26 ≈ 0.577
      ├── Some((7, 2)): 19/30 ≈ 0.633
      ├── Some((7, 3)): 14/24 ≈ 0.583
      ├── Some((7, 4)): 12/22 ≈ 0.545
      ├── Some((7, 5)): 5/14 ≈ 0.357
      ├── Some((7, 6)): 7/17 ≈ 0.412
      └── Some((7, 7)): 21/32 ≈ 0.656
    └── Some((8, 8)): 42/93 ≈ 0.452
      ├── Some((8, 0)): 1/7 ≈ 0.143
      ├── Some((8, 1)): 3/9 ≈ 0.333
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 3/9 ≈ 0.333
      ├── Some((8, 6)): 12/18 ≈ 0.667
      └── Some((8, 7)): 7/14 ≈ 0.500
├── Some((5, 8)): 3654/7250 ≈ 0.504
  ├── Some((8, 0)): 430/848 ≈ 0.507
    ├── Some((0, 0)): 45/91 ≈ 0.495
      ├── Some((0, 1)): 1/6 ≈ 0.167
      ├── Some((0, 2)): 5/11 ≈ 0.455
      ├── Some((0, 3)): 7/13 ≈ 0.538
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 8/13 ≈ 0.615
      ├── Some((0, 7)): 11/16 ≈ 0.688
      └── Some((0, 8)): 4/10 ≈ 0.400
    ├── Some((0, 1)): 65/118 ≈ 0.551
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 6/12 ≈ 0.500
      ├── Some((1, 2)): 12/17 ≈ 0.706
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 10/15 ≈ 0.667
      ├── Some((1, 5)): 9/15 ≈ 0.600
      ├── Some((1, 6)): 7/13 ≈ 0.538
      ├── Some((1, 7)): 7/13 ≈ 0.538
      └── Some((1, 8)): 5/11 ≈ 0.455
    ├── Some((0, 2)): 37/79 ≈ 0.468
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 6/11 ≈ 0.545
      ├── Some((2, 2)): 7/11 ≈ 0.636
      ├── Some((2, 3)): 3/8 ≈ 0.375
      ├── Some((2, 4)): 5/10 ≈ 0.500
      ├── Some((2, 5)): 0/4 ≈ 0.000
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 10/14 ≈ 0.714
      └── Some((2, 8)): 0/4 ≈ 0.000
    ├── Some((0, 3)): 29/67 ≈ 0.433
      ├── Some((3, 0)): 4/8 ≈ 0.500
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 8/12 ≈ 0.667
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 4)): 1/5 ≈ 0.200
      ├── Some((3, 5)): 5/9 ≈ 0.556
      ├── Some((3, 6)): 5/9 ≈ 0.556
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((0, 4)): 44/89 ≈ 0.494
      ├── Some((4, 0)): 2/7 ≈ 0.286
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 8/13 ≈ 0.615
      ├── Some((4, 3)): 11/15 ≈ 0.733
      ├── Some((4, 4)): 0/5 ≈ 0.000
      ├── Some((4, 5)): 4/9 ≈ 0.444
      ├── Some((4, 6)): 8/13 ≈ 0.615
      ├── Some((4, 7)): 6/11 ≈ 0.545
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((0, 5)): 62/114 ≈ 0.544
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 9/16 ≈ 0.562
      ├── Some((5, 2)): 10/16 ≈ 0.625
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 9/16 ≈ 0.562
      ├── Some((5, 6)): 12/18 ≈ 0.667
      └── Some((5, 7)): 8/15 ≈ 0.533
    ├── Some((0, 6)): 38/81 ≈ 0.469
      ├── Some((6, 0)): 5/10 ≈ 0.500
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 2/7 ≈ 0.286
      ├── Some((6, 3)): 6/10 ≈ 0.600
      ├── Some((6, 4)): 5/10 ≈ 0.500
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 6/11 ≈ 0.545
      ├── Some((6, 7)): 7/11 ≈ 0.636
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((0, 7)): 53/102 ≈ 0.520
      ├── Some((7, 0)): 2/7 ≈ 0.286
      ├── Some((7, 1)): 8/14 ≈ 0.571
      ├── Some((7, 2)): 9/14 ≈ 0.643
      ├── Some((7, 3)): 9/14 ≈ 0.643
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 1/6 ≈ 0.167
      ├── Some((7, 6)): 9/14 ≈ 0.643
      ├── Some((7, 7)): 2/7 ≈ 0.286
      └── Some((7, 8)): 9/15 ≈ 0.600
    └── Some((0, 8)): 56/106 ≈ 0.528
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 10/16 ≈ 0.625
      ├── Some((8, 4)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 10/16 ≈ 0.625
      ├── Some((8, 6)): 10/16 ≈ 0.625
      ├── Some((8, 7)): 3/9 ≈ 0.333
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((8, 1)): 446/875 ≈ 0.510
    ├── Some((1, 0)): 38/81 ≈ 0.469
      ├── Some((0, 0)): 4/9 ≈ 0.444
      ├── Some((0, 1)): 6/10 ≈ 0.600
      ├── Some((0, 2)): 9/13 ≈ 0.692
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 4/9 ≈ 0.444
      ├── Some((0, 5)): 4/9 ≈ 0.444
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 1/6 ≈ 0.167
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((1, 1)): 51/100 ≈ 0.510
      ├── Some((1, 0)): 9/15 ≈ 0.600
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 4/10 ≈ 0.400
      ├── Some((1, 4)): 6/12 ≈ 0.500
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 13/19 ≈ 0.684
      └── Some((1, 8)): 7/13 ≈ 0.538
    ├── Some((1, 2)): 28/66 ≈ 0.424
      ├── Some((2, 0)): 4/8 ≈ 0.500
      ├── Some((2, 1)): 2/6 ≈ 0.333
      ├── Some((2, 2)): 1/5 ≈ 0.200
      ├── Some((2, 3)): 4/8 ≈ 0.500
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 6/10 ≈ 0.600
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 8/12 ≈ 0.667
      └── Some((2, 8)): 0/4 ≈ 0.000
    ├── Some((1, 3)): 63/116 ≈ 0.543
      ├── Some((3, 0)): 7/13 ≈ 0.538
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 9/15 ≈ 0.600
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 10/16 ≈ 0.625
      ├── Some((3, 5)): 10/16 ≈ 0.625
      ├── Some((3, 6)): 5/11 ≈ 0.455
      ├── Some((3, 7)): 9/15 ≈ 0.600
      └── Some((3, 8)): 8/14 ≈ 0.571
    ├── Some((1, 4)): 50/98 ≈ 0.510
      ├── Some((4, 0)): 10/15 ≈ 0.667
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 9/14 ≈ 0.643
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 7/12 ≈ 0.583
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((1, 5)): 50/98 ≈ 0.510
      ├── Some((5, 0)): 6/12 ≈ 0.500
      ├── Some((5, 1)): 3/9 ≈ 0.333
      ├── Some((5, 2)): 3/9 ≈ 0.333
      ├── Some((5, 3)): 9/15 ≈ 0.600
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 10/16 ≈ 0.625
      ├── Some((5, 6)): 2/8 ≈ 0.250
      └── Some((5, 7)): 11/16 ≈ 0.688
    ├── Some((1, 6)): 32/72 ≈ 0.444
      ├── Some((6, 0)): 0/4 ≈ 0.000
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 11/15 ≈ 0.733
      ├── Some((6, 7)): 6/10 ≈ 0.600
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((1, 7)): 75/133 ≈ 0.564
      ├── Some((7, 0)): 15/21 ≈ 0.714
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 3/9 ≈ 0.333
      ├── Some((7, 4)): 9/16 ≈ 0.562
      ├── Some((7, 5)): 9/16 ≈ 0.562
      ├── Some((7, 6)): 12/18 ≈ 0.667
      ├── Some((7, 7)): 17/23 ≈ 0.739
      └── Some((7, 8)): 2/8 ≈ 0.250
    └── Some((1, 8)): 58/110 ≈ 0.527
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 16/22 ≈ 0.727
      ├── Some((8, 4)): 15/21 ≈ 0.714
      ├── Some((8, 5)): 2/8 ≈ 0.250
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 3/9 ≈ 0.333
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((8, 2)): 470/916 ≈ 0.513
    ├── Some((2, 0)): 43/89 ≈ 0.483
      ├── Some((0, 0)): 8/13 ≈ 0.615
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 5/10 ≈ 0.500
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 6/11 ≈ 0.545
      ├── Some((0, 5)): 4/9 ≈ 0.444
      ├── Some((0, 6)): 7/12 ≈ 0.583
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 5/10 ≈ 0.500
    ├── Some((2, 1)): 37/80 ≈ 0.463
      ├── Some((1, 0)): 3/8 ≈ 0.375
      ├── Some((1, 1)): 0/4 ≈ 0.000
      ├── Some((1, 2)): 7/11 ≈ 0.636
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 5/10 ≈ 0.500
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 5/10 ≈ 0.500
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 5/10 ≈ 0.500
    ├── Some((2, 2)): 69/126 ≈ 0.548
      ├── Some((2, 0)): 11/19 ≈ 0.579
      ├── Some((2, 1)): 13/20 ≈ 0.650
      ├── Some((2, 3)): 9/16 ≈ 0.562
      ├── Some((2, 4)): 6/13 ≈ 0.462
      ├── Some((2, 5)): 3/10 ≈ 0.300
      ├── Some((2, 6)): 8/15 ≈ 0.533
      ├── Some((2, 7)): 8/15 ≈ 0.533
      └── Some((2, 8)): 10/17 ≈ 0.588
    ├── Some((2, 3)): 42/88 ≈ 0.477
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 1)): 6/11 ≈ 0.545
      ├── Some((3, 2)): 6/12 ≈ 0.500
      ├── Some((3, 3)): 7/12 ≈ 0.583
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 4/9 ≈ 0.444
      ├── Some((3, 7)): 13/18 ≈ 0.722
      └── Some((3, 8)): 0/5 ≈ 0.000
    ├── Some((2, 4)): 43/89 ≈ 0.483
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 0/5 ≈ 0.000
      ├── Some((4, 2)): 5/10 ≈ 0.500
      ├── Some((4, 3)): 5/10 ≈ 0.500
      ├── Some((4, 4)): 6/11 ≈ 0.545
      ├── Some((4, 5)): 5/10 ≈ 0.500
      ├── Some((4, 6)): 6/11 ≈ 0.545
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 10/15 ≈ 0.667
    ├── Some((2, 5)): 51/100 ≈ 0.510
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 8/14 ≈ 0.571
      ├── Some((5, 2)): 7/13 ≈ 0.538
      ├── Some((5, 3)): 8/14 ≈ 0.571
      ├── Some((5, 4)): 9/15 ≈ 0.600
      ├── Some((5, 5)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 4/10 ≈ 0.400
      └── Some((5, 7)): 4/10 ≈ 0.400
    ├── Some((2, 6)): 44/90 ≈ 0.489
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 9/14 ≈ 0.643
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 8/13 ≈ 0.615
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 7/12 ≈ 0.583
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((2, 7)): 63/117 ≈ 0.538
      ├── Some((7, 0)): 9/15 ≈ 0.600
      ├── Some((7, 1)): 5/11 ≈ 0.455
      ├── Some((7, 2)): 6/12 ≈ 0.500
      ├── Some((7, 3)): 5/11 ≈ 0.455
      ├── Some((7, 4)): 9/15 ≈ 0.600
      ├── Some((7, 5)): 7/13 ≈ 0.538
      ├── Some((7, 6)): 3/9 ≈ 0.333
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 14/20 ≈ 0.700
    └── Some((2, 8)): 77/136 ≈ 0.566
      ├── Some((8, 0)): 9/17 ≈ 0.529
      ├── Some((8, 1)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 7/14 ≈ 0.500
      ├── Some((8, 4)): 10/18 ≈ 0.556
      ├── Some((8, 5)): 16/23 ≈ 0.696
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 14/22 ≈ 0.636
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((8, 3)): 361/729 ≈ 0.495
    ├── Some((3, 0)): 50/95 ≈ 0.526
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 6/11 ≈ 0.545
      ├── Some((0, 2)): 6/11 ≈ 0.545
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 6/11 ≈ 0.545
      ├── Some((0, 5)): 7/12 ≈ 0.583
      ├── Some((0, 6)): 7/12 ≈ 0.583
      ├── Some((0, 7)): 6/11 ≈ 0.545
      └── Some((0, 8)): 8/12 ≈ 0.667
    ├── Some((3, 1)): 33/71 ≈ 0.465
      ├── Some((1, 0)): 4/8 ≈ 0.500
      ├── Some((1, 1)): 8/12 ≈ 0.667
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 4/8 ≈ 0.500
      ├── Some((1, 6)): 4/8 ≈ 0.500
      ├── Some((1, 7)): 0/4 ≈ 0.000
      └── Some((1, 8)): 5/9 ≈ 0.556
    ├── Some((3, 2)): 51/97 ≈ 0.526
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 10/15 ≈ 0.667
      ├── Some((2, 3)): 8/13 ≈ 0.615
      ├── Some((2, 4)): 1/6 ≈ 0.167
      ├── Some((2, 5)): 8/13 ≈ 0.615
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 10/15 ≈ 0.667
    ├── Some((3, 3)): 29/66 ≈ 0.439
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 5/9 ≈ 0.556
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 7/11 ≈ 0.636
      ├── Some((3, 6)): 3/8 ≈ 0.375
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 3/8 ≈ 0.375
    ├── Some((3, 4)): 44/87 ≈ 0.506
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 13/17 ≈ 0.765
      ├── Some((4, 2)): 5/10 ≈ 0.500
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 6/10 ≈ 0.600
      ├── Some((4, 5)): 3/8 ≈ 0.375
      ├── Some((4, 6)): 2/7 ≈ 0.286
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 6/10 ≈ 0.600
    ├── Some((3, 5)): 17/47 ≈ 0.362
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 1/5 ≈ 0.200
      ├── Some((5, 3)): 0/3 ≈ 0.000
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 8/11 ≈ 0.727
      ├── Some((5, 6)): 2/6 ≈ 0.333
      └── Some((5, 7)): 2/6 ≈ 0.333
    ├── Some((3, 6)): 60/109 ≈ 0.550
      ├── Some((6, 0)): 6/12 ≈ 0.500
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 0/5 ≈ 0.000
      ├── Some((6, 4)): 11/16 ≈ 0.688
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 3/8 ≈ 0.375
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 17/21 ≈ 0.810
    ├── Some((3, 7)): 38/78 ≈ 0.487
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 5/9 ≈ 0.556
      ├── Some((7, 2)): 5/9 ≈ 0.556
      ├── Some((7, 3)): 5/9 ≈ 0.556
      ├── Some((7, 4)): 5/10 ≈ 0.500
      ├── Some((7, 5)): 6/10 ≈ 0.600
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 4/9 ≈ 0.444
      └── Some((7, 8)): 0/4 ≈ 0.000
    └── Some((3, 8)): 38/78 ≈ 0.487
      ├── Some((8, 0)): 2/7 ≈ 0.286
      ├── Some((8, 1)): 7/12 ≈ 0.583
      ├── Some((8, 2)): 5/10 ≈ 0.500
      ├── Some((8, 4)): 6/11 ≈ 0.545
      ├── Some((8, 5)): 12/16 ≈ 0.750
      ├── Some((8, 6)): 1/6 ≈ 0.167
      ├── Some((8, 7)): 3/8 ≈ 0.375
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((8, 4)): 333/680 ≈ 0.490
    ├── Some((4, 0)): 48/91 ≈ 0.527
      ├── Some((0, 0)): 5/10 ≈ 0.500
      ├── Some((0, 1)): 7/11 ≈ 0.636
      ├── Some((0, 2)): 12/16 ≈ 0.750
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 2/7 ≈ 0.286
      ├── Some((0, 5)): 6/11 ≈ 0.545
      ├── Some((0, 6)): 5/10 ≈ 0.500
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((4, 1)): 31/68 ≈ 0.456
      ├── Some((1, 0)): 3/7 ≈ 0.429
      ├── Some((1, 1)): 4/8 ≈ 0.500
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 5/9 ≈ 0.556
      ├── Some((1, 4)): 3/7 ≈ 0.429
      ├── Some((1, 5)): 5/9 ≈ 0.556
      ├── Some((1, 6)): 5/9 ≈ 0.556
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 1/5 ≈ 0.200
    ├── Some((4, 2)): 45/87 ≈ 0.517
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 5/9 ≈ 0.556
      ├── Some((2, 2)): 6/10 ≈ 0.600
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 5/9 ≈ 0.556
      ├── Some((2, 5)): 12/16 ≈ 0.750
      ├── Some((2, 6)): 4/9 ≈ 0.444
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((4, 3)): 51/95 ≈ 0.537
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 9/14 ≈ 0.643
      ├── Some((3, 2)): 6/11 ≈ 0.545
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 15/19 ≈ 0.789
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 6/11 ≈ 0.545
      └── Some((3, 8)): 0/5 ≈ 0.000
    ├── Some((4, 4)): 38/78 ≈ 0.487
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 6/11 ≈ 0.545
      ├── Some((4, 2)): 8/12 ≈ 0.667
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 5)): 4/9 ≈ 0.444
      ├── Some((4, 6)): 7/12 ≈ 0.583
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((4, 5)): 22/54 ≈ 0.407
      ├── Some((5, 0)): 2/6 ≈ 0.333
      ├── Some((5, 1)): 7/11 ≈ 0.636
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 5/9 ≈ 0.556
      └── Some((5, 7)): 2/6 ≈ 0.333
    ├── Some((4, 6)): 8/32 ≈ 0.250
      ├── Some((6, 0)): 2/4 ≈ 0.500
      ├── Some((6, 1)): 1/3 ≈ 0.333
      ├── Some((6, 2)): 1/3 ≈ 0.333
      ├── Some((6, 3)): 1/3 ≈ 0.333
      ├── Some((6, 4)): 1/4 ≈ 0.250
      ├── Some((6, 5)): 1/4 ≈ 0.250
      ├── Some((6, 6)): 0/3 ≈ 0.000
      ├── Some((6, 7)): 1/4 ≈ 0.250
      └── Some((6, 8)): 0/3 ≈ 0.000
    ├── Some((4, 7)): 40/80 ≈ 0.500
      ├── Some((7, 0)): 4/8 ≈ 0.500
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 6/10 ≈ 0.600
      ├── Some((7, 4)): 12/15 ≈ 0.800
      ├── Some((7, 5)): 4/8 ≈ 0.500
      ├── Some((7, 6)): 2/7 ≈ 0.286
      ├── Some((7, 7)): 5/9 ≈ 0.556
      └── Some((7, 8)): 2/7 ≈ 0.286
    └── Some((4, 8)): 50/94 ≈ 0.532
      ├── Some((8, 0)): 7/13 ≈ 0.538
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 5)): 12/17 ≈ 0.706
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 9/14 ≈ 0.643
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((8, 5)): 325/666 ≈ 0.488
    ├── Some((5, 0)): 40/83 ≈ 0.482
      ├── Some((0, 0)): 5/9 ≈ 0.556
      ├── Some((0, 1)): 5/9 ≈ 0.556
      ├── Some((0, 2)): 5/9 ≈ 0.556
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 5/10 ≈ 0.500
      ├── Some((0, 7)): 5/10 ≈ 0.500
      └── Some((0, 8)): 5/10 ≈ 0.500
    ├── Some((5, 1)): 44/89 ≈ 0.494
      ├── Some((1, 0)): 4/9 ≈ 0.444
      ├── Some((1, 1)): 10/14 ≈ 0.714
      ├── Some((1, 2)): 6/11 ≈ 0.545
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 6/11 ≈ 0.545
      ├── Some((1, 6)): 4/9 ≈ 0.444
      ├── Some((1, 7)): 5/10 ≈ 0.500
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((5, 2)): 25/61 ≈ 0.410
      ├── Some((2, 0)): 5/8 ≈ 0.625
      ├── Some((2, 1)): 4/8 ≈ 0.500
      ├── Some((2, 2)): 2/6 ≈ 0.333
      ├── Some((2, 3)): 1/5 ≈ 0.200
      ├── Some((2, 4)): 3/7 ≈ 0.429
      ├── Some((2, 5)): 0/4 ≈ 0.000
      ├── Some((2, 6)): 5/9 ≈ 0.556
      ├── Some((2, 7)): 3/7 ≈ 0.429
      └── Some((2, 8)): 2/6 ≈ 0.333
    ├── Some((5, 3)): 34/74 ≈ 0.459
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 0/4 ≈ 0.000
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 5/9 ≈ 0.556
      ├── Some((3, 5)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 5/9 ≈ 0.556
      ├── Some((3, 7)): 12/16 ≈ 0.750
      └── Some((3, 8)): 1/5 ≈ 0.200
    ├── Some((5, 4)): 17/48 ≈ 0.354
      ├── Some((4, 0)): 0/3 ≈ 0.000
      ├── Some((4, 1)): 3/6 ≈ 0.500
      ├── Some((4, 2)): 1/5 ≈ 0.200
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 2/5 ≈ 0.400
      ├── Some((4, 5)): 1/5 ≈ 0.200
      ├── Some((4, 6)): 3/6 ≈ 0.500
      ├── Some((4, 7)): 4/7 ≈ 0.571
      └── Some((4, 8)): 2/5 ≈ 0.400
    ├── Some((5, 5)): 58/108 ≈ 0.537
      ├── Some((5, 0)): 3/10 ≈ 0.300
      ├── Some((5, 1)): 14/21 ≈ 0.667
      ├── Some((5, 2)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 2/9 ≈ 0.222
      ├── Some((5, 4)): 16/23 ≈ 0.696
      ├── Some((5, 6)): 5/12 ≈ 0.417
      └── Some((5, 7)): 7/14 ≈ 0.500
    ├── Some((5, 6)): 64/116 ≈ 0.552
      ├── Some((6, 0)): 21/25 ≈ 0.840
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 8/14 ≈ 0.571
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 1/7 ≈ 0.143
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 9/15 ≈ 0.600
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 2/8 ≈ 0.250
    └── Some((5, 7)): 42/86 ≈ 0.488
      ├── Some((7, 0)): 1/6 ≈ 0.167
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 2)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 7/12 ≈ 0.583
      ├── Some((7, 5)): 5/10 ≈ 0.500
      ├── Some((7, 6)): 0/5 ≈ 0.000
      ├── Some((7, 7)): 10/14 ≈ 0.714
      └── Some((7, 8)): 4/9 ≈ 0.444
  ├── Some((8, 6)): 491/952 ≈ 0.516
    ├── Some((6, 0)): 44/91 ≈ 0.484
      ├── Some((0, 0)): 10/15 ≈ 0.667
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 6/11 ≈ 0.545
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 4/9 ≈ 0.444
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 6/11 ≈ 0.545
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((6, 1)): 54/105 ≈ 0.514
      ├── Some((1, 0)): 2/7 ≈ 0.286
      ├── Some((1, 1)): 8/14 ≈ 0.571
      ├── Some((1, 2)): 3/9 ≈ 0.333
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 9/15 ≈ 0.600
      ├── Some((1, 5)): 7/13 ≈ 0.538
      ├── Some((1, 6)): 0/5 ≈ 0.000
      ├── Some((1, 7)): 10/15 ≈ 0.667
      └── Some((1, 8)): 10/15 ≈ 0.667
    ├── Some((6, 2)): 55/107 ≈ 0.514
      ├── Some((2, 0)): 13/18 ≈ 0.722
      ├── Some((2, 1)): 1/6 ≈ 0.167
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 13/18 ≈ 0.722
      ├── Some((2, 4)): 1/7 ≈ 0.143
      ├── Some((2, 5)): 1/7 ≈ 0.143
      ├── Some((2, 6)): 7/13 ≈ 0.538
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 9/15 ≈ 0.600
    ├── Some((6, 3)): 31/72 ≈ 0.431
      ├── Some((3, 0)): 0/4 ≈ 0.000
      ├── Some((3, 1)): 6/10 ≈ 0.600
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 4/8 ≈ 0.500
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 6/10 ≈ 0.600
      └── Some((3, 8)): 5/9 ≈ 0.556
    ├── Some((6, 4)): 46/94 ≈ 0.489
      ├── Some((4, 0)): 9/14 ≈ 0.643
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 6/11 ≈ 0.545
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 4)): 4/9 ≈ 0.444
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 10/15 ≈ 0.667
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((6, 5)): 80/141 ≈ 0.567
      ├── Some((5, 0)): 9/17 ≈ 0.529
      ├── Some((5, 1)): 13/20 ≈ 0.650
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 3)): 13/21 ≈ 0.619
      ├── Some((5, 4)): 13/21 ≈ 0.619
      ├── Some((5, 5)): 10/18 ≈ 0.556
      ├── Some((5, 6)): 10/18 ≈ 0.556
      └── Some((5, 7)): 5/12 ≈ 0.417
    ├── Some((6, 6)): 66/122 ≈ 0.541
      ├── Some((6, 0)): 5/12 ≈ 0.417
      ├── Some((6, 1)): 4/11 ≈ 0.364
      ├── Some((6, 2)): 10/17 ≈ 0.588
      ├── Some((6, 3)): 9/16 ≈ 0.562
      ├── Some((6, 4)): 8/15 ≈ 0.533
      ├── Some((6, 5)): 8/15 ≈ 0.533
      ├── Some((6, 7)): 14/21 ≈ 0.667
      └── Some((6, 8)): 7/14 ≈ 0.500
    ├── Some((6, 7)): 68/125 ≈ 0.544
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 7/14 ≈ 0.500
      ├── Some((7, 2)): 10/16 ≈ 0.625
      ├── Some((7, 3)): 9/15 ≈ 0.600
      ├── Some((7, 4)): 9/15 ≈ 0.600
      ├── Some((7, 5)): 7/14 ≈ 0.500
      ├── Some((7, 6)): 9/15 ≈ 0.600
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((6, 8)): 46/94 ≈ 0.489
      ├── Some((8, 0)): 0/6 ≈ 0.000
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 7/13 ≈ 0.538
      ├── Some((8, 4)): 9/15 ≈ 0.600
      ├── Some((8, 5)): 12/18 ≈ 0.667
      ├── Some((8, 7)): 4/10 ≈ 0.400
      └── Some((8, 8)): 5/11 ≈ 0.455
  ├── Some((8, 7)): 286/598 ≈ 0.478
    ├── Some((7, 0)): 28/62 ≈ 0.452
      ├── Some((0, 0)): 1/5 ≈ 0.200
      ├── Some((0, 1)): 3/7 ≈ 0.429
      ├── Some((0, 2)): 3/7 ≈ 0.429
      ├── Some((0, 3)): 3/7 ≈ 0.429
      ├── Some((0, 4)): 6/9 ≈ 0.667
      ├── Some((0, 5)): 4/7 ≈ 0.571
      ├── Some((0, 6)): 5/8 ≈ 0.625
      ├── Some((0, 7)): 3/7 ≈ 0.429
      └── Some((0, 8)): 0/4 ≈ 0.000
    ├── Some((7, 1)): 21/51 ≈ 0.412
      ├── Some((1, 0)): 0/3 ≈ 0.000
      ├── Some((1, 1)): 4/7 ≈ 0.571
      ├── Some((1, 2)): 5/8 ≈ 0.625
      ├── Some((1, 3)): 3/6 ≈ 0.500
      ├── Some((1, 4)): 3/6 ≈ 0.500
      ├── Some((1, 5)): 0/4 ≈ 0.000
      ├── Some((1, 6)): 3/6 ≈ 0.500
      ├── Some((1, 7)): 3/6 ≈ 0.500
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((7, 2)): 15/42 ≈ 0.357
      ├── Some((2, 0)): 2/5 ≈ 0.400
      ├── Some((2, 1)): 0/3 ≈ 0.000
      ├── Some((2, 2)): 3/6 ≈ 0.500
      ├── Some((2, 3)): 4/6 ≈ 0.667
      ├── Some((2, 4)): 0/3 ≈ 0.000
      ├── Some((2, 5)): 1/4 ≈ 0.250
      ├── Some((2, 6)): 2/5 ≈ 0.400
      ├── Some((2, 7)): 0/3 ≈ 0.000
      └── Some((2, 8)): 3/6 ≈ 0.500
    ├── Some((7, 3)): 42/81 ≈ 0.519
      ├── Some((3, 0)): 8/12 ≈ 0.667
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 0/4 ≈ 0.000
      ├── Some((3, 3)): 7/11 ≈ 0.636
      ├── Some((3, 4)): 5/10 ≈ 0.500
      ├── Some((3, 5)): 6/10 ≈ 0.600
      ├── Some((3, 6)): 7/11 ≈ 0.636
      ├── Some((3, 7)): 6/11 ≈ 0.545
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((7, 4)): 21/51 ≈ 0.412
      ├── Some((4, 0)): 2/5 ≈ 0.400
      ├── Some((4, 1)): 4/7 ≈ 0.571
      ├── Some((4, 2)): 2/5 ≈ 0.400
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 1/5 ≈ 0.200
      ├── Some((4, 5)): 2/5 ≈ 0.400
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 2/5 ≈ 0.400
      └── Some((4, 8)): 5/8 ≈ 0.625
    ├── Some((7, 5)): 21/52 ≈ 0.404
      ├── Some((5, 0)): 2/6 ≈ 0.333
      ├── Some((5, 1)): 0/4 ≈ 0.000
      ├── Some((5, 2)): 5/9 ≈ 0.556
      ├── Some((5, 3)): 2/6 ≈ 0.333
      ├── Some((5, 4)): 6/9 ≈ 0.667
      ├── Some((5, 5)): 2/6 ≈ 0.333
      ├── Some((5, 6)): 1/5 ≈ 0.200
      └── Some((5, 7)): 2/6 ≈ 0.333
    ├── Some((7, 6)): 42/81 ≈ 0.519
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 5/9 ≈ 0.556
      ├── Some((6, 2)): 6/10 ≈ 0.600
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 0/4 ≈ 0.000
      ├── Some((6, 5)): 4/9 ≈ 0.444
      ├── Some((6, 6)): 13/16 ≈ 0.812
      ├── Some((6, 7)): 6/10 ≈ 0.600
      └── Some((6, 8)): 5/9 ≈ 0.556
    ├── Some((7, 7)): 35/72 ≈ 0.486
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 9/13 ≈ 0.692
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 5/9 ≈ 0.556
      ├── Some((7, 6)): 5/9 ≈ 0.556
      └── Some((7, 8)): 4/9 ≈ 0.444
    └── Some((7, 8)): 60/105 ≈ 0.571
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 11/16 ≈ 0.688
      ├── Some((8, 2)): 8/13 ≈ 0.615
      ├── Some((8, 3)): 8/14 ≈ 0.571
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 9/14 ≈ 0.643
      └── Some((8, 8)): 6/12 ≈ 0.500
  └── Some((8, 8)): 511/985 ≈ 0.519
    ├── Some((8, 0)): 85/153 ≈ 0.556
      ├── Some((0, 0)): 10/18 ≈ 0.556
      ├── Some((0, 1)): 14/22 ≈ 0.636
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 12/20 ≈ 0.600
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 5/12 ≈ 0.417
      ├── Some((0, 7)): 10/18 ≈ 0.556
      └── Some((0, 8)): 15/23 ≈ 0.652
    ├── Some((8, 1)): 54/109 ≈ 0.495
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 10/16 ≈ 0.625
      ├── Some((1, 2)): 5/11 ≈ 0.455
      ├── Some((1, 3)): 7/13 ≈ 0.538
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 4/10 ≈ 0.400
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((8, 2)): 67/128 ≈ 0.523
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 1)): 8/15 ≈ 0.533
      ├── Some((2, 2)): 12/18 ≈ 0.667
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 8/15 ≈ 0.533
      ├── Some((2, 5)): 1/7 ≈ 0.143
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 13/19 ≈ 0.684
      └── Some((2, 8)): 9/16 ≈ 0.562
    ├── Some((8, 3)): 63/122 ≈ 0.516
      ├── Some((3, 0)): 11/17 ≈ 0.647
      ├── Some((3, 1)): 10/17 ≈ 0.588
      ├── Some((3, 2)): 6/13 ≈ 0.462
      ├── Some((3, 3)): 6/13 ≈ 0.462
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 2/8 ≈ 0.250
      ├── Some((3, 6)): 13/19 ≈ 0.684
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((8, 4)): 67/128 ≈ 0.523
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 9/16 ≈ 0.562
      ├── Some((4, 3)): 11/18 ≈ 0.611
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 9/16 ≈ 0.562
      ├── Some((4, 6)): 0/6 ≈ 0.000
      ├── Some((4, 7)): 12/19 ≈ 0.632
      └── Some((4, 8)): 13/20 ≈ 0.650
    ├── Some((8, 5)): 76/141 ≈ 0.539
      ├── Some((5, 0)): 9/17 ≈ 0.529
      ├── Some((5, 1)): 9/17 ≈ 0.529
      ├── Some((5, 2)): 16/25 ≈ 0.640
      ├── Some((5, 3)): 9/17 ≈ 0.529
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 5)): 6/14 ≈ 0.429
      ├── Some((5, 6)): 11/19 ≈ 0.579
      └── Some((5, 7)): 6/14 ≈ 0.429
    ├── Some((8, 6)): 71/133 ≈ 0.534
      ├── Some((6, 0)): 13/20 ≈ 0.650
      ├── Some((6, 1)): 12/19 ≈ 0.632
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 3)): 3/9 ≈ 0.333
      ├── Some((6, 4)): 13/20 ≈ 0.650
      ├── Some((6, 5)): 0/6 ≈ 0.000
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 8/15 ≈ 0.533
      └── Some((6, 8)): 8/15 ≈ 0.533
    └── Some((8, 7)): 28/70 ≈ 0.400
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 2)): 4/9 ≈ 0.444
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 5/9 ≈ 0.556
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 5/9 ≈ 0.556
      ├── Some((7, 7)): 5/10 ≈ 0.500
      └── Some((7, 8)): 2/7 ≈ 0.286
├── Some((6, 0)): 7085/13570 ≈ 0.522
  ├── Some((0, 0)): 677/1320 ≈ 0.513
    ├── Some((0, 1)): 92/176 ≈ 0.523
      ├── Some((1, 0)): 11/21 ≈ 0.524
      ├── Some((1, 1)): 18/28 ≈ 0.643
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 3)): 14/24 ≈ 0.583
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 10/19 ≈ 0.526
      ├── Some((1, 6)): 0/7 ≈ 0.000
      ├── Some((1, 7)): 11/21 ≈ 0.524
      └── Some((1, 8)): 10/19 ≈ 0.526
    ├── Some((0, 2)): 72/146 ≈ 0.493
      ├── Some((2, 0)): 9/17 ≈ 0.529
      ├── Some((2, 1)): 11/19 ≈ 0.579
      ├── Some((2, 2)): 3/11 ≈ 0.273
      ├── Some((2, 3)): 13/22 ≈ 0.591
      ├── Some((2, 4)): 4/12 ≈ 0.333
      ├── Some((2, 5)): 11/19 ≈ 0.579
      ├── Some((2, 6)): 10/18 ≈ 0.556
      ├── Some((2, 7)): 11/20 ≈ 0.550
      └── Some((2, 8)): 0/7 ≈ 0.000
    ├── Some((0, 3)): 84/164 ≈ 0.512
      ├── Some((3, 0)): 10/19 ≈ 0.526
      ├── Some((3, 1)): 4/12 ≈ 0.333
      ├── Some((3, 2)): 12/21 ≈ 0.571
      ├── Some((3, 3)): 17/27 ≈ 0.630
      ├── Some((3, 4)): 10/19 ≈ 0.526
      ├── Some((3, 5)): 11/20 ≈ 0.550
      ├── Some((3, 6)): 10/19 ≈ 0.526
      ├── Some((3, 7)): 4/12 ≈ 0.333
      └── Some((3, 8)): 5/14 ≈ 0.357
    ├── Some((0, 4)): 68/140 ≈ 0.486
      ├── Some((4, 0)): 4/11 ≈ 0.364
      ├── Some((4, 1)): 4/12 ≈ 0.333
      ├── Some((4, 2)): 14/22 ≈ 0.636
      ├── Some((4, 3)): 8/16 ≈ 0.500
      ├── Some((4, 4)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 4/12 ≈ 0.333
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 16/24 ≈ 0.667
    ├── Some((0, 5)): 86/167 ≈ 0.515
      ├── Some((5, 0)): 19/28 ≈ 0.679
      ├── Some((5, 1)): 6/15 ≈ 0.400
      ├── Some((5, 2)): 4/12 ≈ 0.333
      ├── Some((5, 3)): 8/17 ≈ 0.471
      ├── Some((5, 4)): 8/17 ≈ 0.471
      ├── Some((5, 5)): 14/23 ≈ 0.609
      ├── Some((5, 6)): 8/17 ≈ 0.471
      ├── Some((5, 7)): 12/21 ≈ 0.571
      └── Some((5, 8)): 7/16 ≈ 0.438
    ├── Some((0, 6)): 102/191 ≈ 0.534
      ├── Some((6, 1)): 7/17 ≈ 0.412
      ├── Some((6, 2)): 11/22 ≈ 0.500
      ├── Some((6, 3)): 12/23 ≈ 0.522
      ├── Some((6, 4)): 9/20 ≈ 0.450
      ├── Some((6, 5)): 11/22 ≈ 0.500
      ├── Some((6, 6)): 13/24 ≈ 0.542
      ├── Some((6, 7)): 15/26 ≈ 0.577
      └── Some((6, 8)): 24/36 ≈ 0.667
    ├── Some((0, 7)): 65/135 ≈ 0.481
      ├── Some((7, 0)): 3/10 ≈ 0.300
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 14/22 ≈ 0.636
      ├── Some((7, 3)): 5/13 ≈ 0.385
      ├── Some((7, 4)): 10/18 ≈ 0.556
      ├── Some((7, 5)): 4/12 ≈ 0.333
      ├── Some((7, 6)): 10/18 ≈ 0.556
      ├── Some((7, 7)): 6/14 ≈ 0.429
      └── Some((7, 8)): 9/17 ≈ 0.529
    └── Some((0, 8)): 108/200 ≈ 0.540
      ├── Some((8, 0)): 4/13 ≈ 0.308
      ├── Some((8, 1)): 10/20 ≈ 0.500
      ├── Some((8, 2)): 22/33 ≈ 0.667
      ├── Some((8, 3)): 6/16 ≈ 0.375
      ├── Some((8, 4)): 13/24 ≈ 0.542
      ├── Some((8, 5)): 10/20 ≈ 0.500
      ├── Some((8, 6)): 18/29 ≈ 0.621
      ├── Some((8, 7)): 20/31 ≈ 0.645
      └── Some((8, 8)): 4/13 ≈ 0.308
  ├── Some((0, 1)): 827/1579 ≈ 0.524
    ├── Some((1, 0)): 33/85 ≈ 0.388
      ├── Some((0, 0)): 1/7 ≈ 0.143
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 8/15 ≈ 0.533
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 5/12 ≈ 0.417
      ├── Some((0, 7)): 4/10 ≈ 0.400
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((1, 1)): 114/209 ≈ 0.545
      ├── Some((1, 0)): 21/34 ≈ 0.618
      ├── Some((1, 2)): 14/26 ≈ 0.538
      ├── Some((1, 3)): 9/20 ≈ 0.450
      ├── Some((1, 4)): 18/30 ≈ 0.600
      ├── Some((1, 5)): 14/26 ≈ 0.538
      ├── Some((1, 6)): 13/25 ≈ 0.520
      ├── Some((1, 7)): 15/27 ≈ 0.556
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((1, 2)): 100/188 ≈ 0.532
      ├── Some((2, 0)): 11/21 ≈ 0.524
      ├── Some((2, 1)): 9/18 ≈ 0.500
      ├── Some((2, 2)): 11/21 ≈ 0.524
      ├── Some((2, 3)): 12/22 ≈ 0.545
      ├── Some((2, 4)): 15/25 ≈ 0.600
      ├── Some((2, 5)): 15/25 ≈ 0.600
      ├── Some((2, 6)): 4/13 ≈ 0.308
      ├── Some((2, 7)): 10/20 ≈ 0.500
      └── Some((2, 8)): 12/22 ≈ 0.545
    ├── Some((1, 3)): 125/225 ≈ 0.556
      ├── Some((3, 0)): 20/32 ≈ 0.625
      ├── Some((3, 1)): 13/24 ≈ 0.542
      ├── Some((3, 2)): 18/29 ≈ 0.621
      ├── Some((3, 3)): 12/23 ≈ 0.522
      ├── Some((3, 4)): 11/22 ≈ 0.500
      ├── Some((3, 5)): 12/23 ≈ 0.522
      ├── Some((3, 6)): 11/22 ≈ 0.500
      ├── Some((3, 7)): 15/26 ≈ 0.577
      └── Some((3, 8)): 12/23 ≈ 0.522
    ├── Some((1, 4)): 106/197 ≈ 0.538
      ├── Some((4, 0)): 7/17 ≈ 0.412
      ├── Some((4, 1)): 11/21 ≈ 0.524
      ├── Some((4, 2)): 2/10 ≈ 0.200
      ├── Some((4, 3)): 20/31 ≈ 0.645
      ├── Some((4, 4)): 10/20 ≈ 0.500
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 18/29 ≈ 0.621
      ├── Some((4, 7)): 10/20 ≈ 0.500
      └── Some((4, 8)): 18/29 ≈ 0.621
    ├── Some((1, 5)): 54/119 ≈ 0.454
      ├── Some((5, 0)): 5/12 ≈ 0.417
      ├── Some((5, 1)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 2/9 ≈ 0.222
      ├── Some((5, 3)): 7/14 ≈ 0.500
      ├── Some((5, 4)): 2/9 ≈ 0.222
      ├── Some((5, 5)): 17/25 ≈ 0.680
      ├── Some((5, 6)): 2/9 ≈ 0.222
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 5/12 ≈ 0.417
    ├── Some((1, 6)): 109/201 ≈ 0.542
      ├── Some((6, 1)): 16/28 ≈ 0.571
      ├── Some((6, 2)): 20/32 ≈ 0.625
      ├── Some((6, 3)): 22/34 ≈ 0.647
      ├── Some((6, 4)): 7/18 ≈ 0.389
      ├── Some((6, 5)): 9/20 ≈ 0.450
      ├── Some((6, 6)): 15/27 ≈ 0.556
      ├── Some((6, 7)): 10/21 ≈ 0.476
      └── Some((6, 8)): 9/20 ≈ 0.450
    ├── Some((1, 7)): 90/173 ≈ 0.520
      ├── Some((7, 0)): 17/27 ≈ 0.630
      ├── Some((7, 1)): 6/15 ≈ 0.400
      ├── Some((7, 2)): 19/29 ≈ 0.655
      ├── Some((7, 3)): 2/10 ≈ 0.200
      ├── Some((7, 4)): 10/19 ≈ 0.526
      ├── Some((7, 5)): 12/21 ≈ 0.571
      ├── Some((7, 6)): 8/17 ≈ 0.471
      ├── Some((7, 7)): 11/20 ≈ 0.550
      └── Some((7, 8)): 5/14 ≈ 0.357
    └── Some((1, 8)): 95/181 ≈ 0.525
      ├── Some((8, 0)): 10/20 ≈ 0.500
      ├── Some((8, 1)): 11/21 ≈ 0.524
      ├── Some((8, 2)): 7/16 ≈ 0.438
      ├── Some((8, 3)): 6/15 ≈ 0.400
      ├── Some((8, 4)): 11/21 ≈ 0.524
      ├── Some((8, 5)): 9/19 ≈ 0.474
      ├── Some((8, 6)): 7/16 ≈ 0.438
      ├── Some((8, 7)): 28/38 ≈ 0.737
      └── Some((8, 8)): 5/14 ≈ 0.357
  ├── Some((0, 2)): 925/1747 ≈ 0.529
    ├── Some((2, 0)): 68/143 ≈ 0.476
      ├── Some((0, 0)): 15/25 ≈ 0.600
      ├── Some((0, 1)): 4/13 ≈ 0.308
      ├── Some((0, 3)): 5/14 ≈ 0.357
      ├── Some((0, 4)): 9/18 ≈ 0.500
      ├── Some((0, 5)): 9/19 ≈ 0.474
      ├── Some((0, 6)): 13/23 ≈ 0.565
      ├── Some((0, 7)): 7/16 ≈ 0.438
      └── Some((0, 8)): 5/14 ≈ 0.357
    ├── Some((2, 1)): 95/183 ≈ 0.519
      ├── Some((1, 0)): 12/22 ≈ 0.545
      ├── Some((1, 1)): 15/25 ≈ 0.600
      ├── Some((1, 2)): 10/20 ≈ 0.500
      ├── Some((1, 3)): 13/23 ≈ 0.565
      ├── Some((1, 4)): 3/12 ≈ 0.250
      ├── Some((1, 5)): 7/16 ≈ 0.438
      ├── Some((1, 6)): 8/18 ≈ 0.444
      ├── Some((1, 7)): 8/18 ≈ 0.444
      └── Some((1, 8)): 18/28 ≈ 0.643
    ├── Some((2, 2)): 142/252 ≈ 0.563
      ├── Some((2, 0)): 8/20 ≈ 0.400
      ├── Some((2, 1)): 16/30 ≈ 0.533
      ├── Some((2, 3)): 25/39 ≈ 0.641
      ├── Some((2, 4)): 21/35 ≈ 0.600
      ├── Some((2, 5)): 18/32 ≈ 0.562
      ├── Some((2, 6)): 13/26 ≈ 0.500
      ├── Some((2, 7)): 28/43 ≈ 0.651
      └── Some((2, 8)): 13/26 ≈ 0.500
    ├── Some((2, 3)): 152/266 ≈ 0.571
      ├── Some((3, 0)): 29/43 ≈ 0.674
      ├── Some((3, 1)): 11/23 ≈ 0.478
      ├── Some((3, 2)): 18/31 ≈ 0.581
      ├── Some((3, 3)): 24/37 ≈ 0.649
      ├── Some((3, 4)): 19/32 ≈ 0.594
      ├── Some((3, 5)): 7/18 ≈ 0.389
      ├── Some((3, 6)): 17/30 ≈ 0.567
      ├── Some((3, 7)): 18/31 ≈ 0.581
      └── Some((3, 8)): 8/20 ≈ 0.400
    ├── Some((2, 4)): 97/186 ≈ 0.522
      ├── Some((4, 0)): 8/18 ≈ 0.444
      ├── Some((4, 1)): 16/26 ≈ 0.615
      ├── Some((4, 2)): 3/12 ≈ 0.250
      ├── Some((4, 3)): 9/19 ≈ 0.474
      ├── Some((4, 4)): 15/25 ≈ 0.600
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 10/20 ≈ 0.500
      ├── Some((4, 7)): 14/24 ≈ 0.583
      └── Some((4, 8)): 12/22 ≈ 0.545
    ├── Some((2, 5)): 101/192 ≈ 0.526
      ├── Some((5, 0)): 9/19 ≈ 0.474
      ├── Some((5, 1)): 5/15 ≈ 0.333
      ├── Some((5, 2)): 6/16 ≈ 0.375
      ├── Some((5, 3)): 28/39 ≈ 0.718
      ├── Some((5, 4)): 12/23 ≈ 0.522
      ├── Some((5, 5)): 22/33 ≈ 0.667
      ├── Some((5, 6)): 14/25 ≈ 0.560
      ├── Some((5, 7)): 3/12 ≈ 0.250
      └── Some((5, 8)): 1/9 ≈ 0.111
    ├── Some((2, 6)): 112/208 ≈ 0.538
      ├── Some((6, 1)): 8/19 ≈ 0.421
      ├── Some((6, 2)): 14/26 ≈ 0.538
      ├── Some((6, 3)): 19/32 ≈ 0.594
      ├── Some((6, 4)): 24/37 ≈ 0.649
      ├── Some((6, 5)): 13/25 ≈ 0.520
      ├── Some((6, 6)): 6/17 ≈ 0.353
      ├── Some((6, 7)): 16/28 ≈ 0.571
      └── Some((6, 8)): 11/23 ≈ 0.478
    ├── Some((2, 7)): 62/133 ≈ 0.466
      ├── Some((7, 0)): 12/20 ≈ 0.600
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 2/9 ≈ 0.222
      ├── Some((7, 3)): 5/13 ≈ 0.385
      ├── Some((7, 4)): 8/16 ≈ 0.500
      ├── Some((7, 5)): 10/18 ≈ 0.556
      ├── Some((7, 6)): 7/15 ≈ 0.467
      ├── Some((7, 7)): 1/8 ≈ 0.125
      └── Some((7, 8)): 9/17 ≈ 0.529
    └── Some((2, 8)): 95/183 ≈ 0.519
      ├── Some((8, 0)): 5/14 ≈ 0.357
      ├── Some((8, 1)): 10/20 ≈ 0.500
      ├── Some((8, 2)): 12/22 ≈ 0.545
      ├── Some((8, 3)): 12/22 ≈ 0.545
      ├── Some((8, 4)): 15/25 ≈ 0.600
      ├── Some((8, 5)): 7/16 ≈ 0.438
      ├── Some((8, 6)): 11/21 ≈ 0.524
      ├── Some((8, 7)): 12/22 ≈ 0.545
      └── Some((8, 8)): 10/20 ≈ 0.500
  ├── Some((0, 3)): 592/1173 ≈ 0.505
    ├── Some((3, 0)): 37/88 ≈ 0.420
      ├── Some((0, 0)): 4/10 ≈ 0.400
      ├── Some((0, 1)): 4/10 ≈ 0.400
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 7/14 ≈ 0.500
      ├── Some((0, 7)): 3/9 ≈ 0.333
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((3, 1)): 73/142 ≈ 0.514
      ├── Some((1, 0)): 5/12 ≈ 0.417
      ├── Some((1, 1)): 10/18 ≈ 0.556
      ├── Some((1, 2)): 2/9 ≈ 0.222
      ├── Some((1, 3)): 4/11 ≈ 0.364
      ├── Some((1, 4)): 15/23 ≈ 0.652
      ├── Some((1, 5)): 9/17 ≈ 0.529
      ├── Some((1, 6)): 2/9 ≈ 0.222
      ├── Some((1, 7)): 11/19 ≈ 0.579
      └── Some((1, 8)): 15/23 ≈ 0.652
    ├── Some((3, 2)): 131/224 ≈ 0.585
      ├── Some((2, 0)): 12/22 ≈ 0.545
      ├── Some((2, 1)): 29/40 ≈ 0.725
      ├── Some((2, 2)): 11/21 ≈ 0.524
      ├── Some((2, 3)): 13/23 ≈ 0.565
      ├── Some((2, 4)): 26/37 ≈ 0.703
      ├── Some((2, 5)): 15/26 ≈ 0.577
      ├── Some((2, 6)): 11/21 ≈ 0.524
      ├── Some((2, 7)): 5/14 ≈ 0.357
      └── Some((2, 8)): 9/19 ≈ 0.474
    ├── Some((3, 3)): 34/83 ≈ 0.410
      ├── Some((3, 0)): 4/10 ≈ 0.400
      ├── Some((3, 1)): 6/13 ≈ 0.462
      ├── Some((3, 2)): 12/19 ≈ 0.632
      ├── Some((3, 4)): 0/5 ≈ 0.000
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 2/8 ≈ 0.250
      ├── Some((3, 7)): 5/11 ≈ 0.455
      └── Some((3, 8)): 1/7 ≈ 0.143
    ├── Some((3, 4)): 96/175 ≈ 0.549
      ├── Some((4, 0)): 11/20 ≈ 0.550
      ├── Some((4, 1)): 12/21 ≈ 0.571
      ├── Some((4, 2)): 1/8 ≈ 0.125
      ├── Some((4, 3)): 18/27 ≈ 0.667
      ├── Some((4, 4)): 11/20 ≈ 0.550
      ├── Some((4, 5)): 11/20 ≈ 0.550
      ├── Some((4, 6)): 16/25 ≈ 0.640
      ├── Some((4, 7)): 6/15 ≈ 0.400
      └── Some((4, 8)): 9/18 ≈ 0.500
    ├── Some((3, 5)): 63/127 ≈ 0.496
      ├── Some((5, 0)): 10/17 ≈ 0.588
      ├── Some((5, 1)): 14/21 ≈ 0.667
      ├── Some((5, 2)): 1/8 ≈ 0.125
      ├── Some((5, 3)): 10/18 ≈ 0.556
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((3, 6)): 25/68 ≈ 0.368
      ├── Some((6, 1)): 1/6 ≈ 0.167
      ├── Some((6, 2)): 2/7 ≈ 0.286
      ├── Some((6, 3)): 8/14 ≈ 0.571
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 3/8 ≈ 0.375
      ├── Some((6, 7)): 0/5 ≈ 0.000
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((3, 7)): 61/124 ≈ 0.492
      ├── Some((7, 0)): 4/11 ≈ 0.364
      ├── Some((7, 1)): 7/14 ≈ 0.500
      ├── Some((7, 2)): 11/19 ≈ 0.579
      ├── Some((7, 3)): 7/14 ≈ 0.500
      ├── Some((7, 4)): 6/13 ≈ 0.462
      ├── Some((7, 5)): 8/15 ≈ 0.533
      ├── Some((7, 6)): 0/6 ≈ 0.000
      ├── Some((7, 7)): 8/15 ≈ 0.533
      └── Some((7, 8)): 9/16 ≈ 0.562
    └── Some((3, 8)): 72/141 ≈ 0.511
      ├── Some((8, 0)): 12/20 ≈ 0.600
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 8/16 ≈ 0.500
      ├── Some((8, 4)): 9/17 ≈ 0.529
      ├── Some((8, 5)): 6/14 ≈ 0.429
      ├── Some((8, 6)): 0/6 ≈ 0.000
      ├── Some((8, 7)): 7/15 ≈ 0.467
      └── Some((8, 8)): 16/24 ≈ 0.667
  ├── Some((0, 4)): 993/1863 ≈ 0.533
    ├── Some((4, 0)): 136/246 ≈ 0.553
      ├── Some((0, 0)): 19/33 ≈ 0.576
      ├── Some((0, 1)): 9/22 ≈ 0.409
      ├── Some((0, 2)): 14/28 ≈ 0.500
      ├── Some((0, 3)): 31/46 ≈ 0.674
      ├── Some((0, 5)): 17/31 ≈ 0.548
      ├── Some((0, 6)): 5/16 ≈ 0.312
      ├── Some((0, 7)): 12/25 ≈ 0.480
      └── Some((0, 8)): 29/44 ≈ 0.659
    ├── Some((4, 1)): 94/183 ≈ 0.514
      ├── Some((1, 0)): 7/16 ≈ 0.438
      ├── Some((1, 1)): 11/21 ≈ 0.524
      ├── Some((1, 2)): 7/17 ≈ 0.412
      ├── Some((1, 3)): 7/17 ≈ 0.412
      ├── Some((1, 4)): 8/18 ≈ 0.444
      ├── Some((1, 5)): 9/19 ≈ 0.474
      ├── Some((1, 6)): 19/29 ≈ 0.655
      ├── Some((1, 7)): 15/25 ≈ 0.600
      └── Some((1, 8)): 10/20 ≈ 0.500
    ├── Some((4, 2)): 117/218 ≈ 0.537
      ├── Some((2, 0)): 3/13 ≈ 0.231
      ├── Some((2, 1)): 21/33 ≈ 0.636
      ├── Some((2, 2)): 5/15 ≈ 0.333
      ├── Some((2, 3)): 12/23 ≈ 0.522
      ├── Some((2, 4)): 12/23 ≈ 0.522
      ├── Some((2, 5)): 16/28 ≈ 0.571
      ├── Some((2, 6)): 20/32 ≈ 0.625
      ├── Some((2, 7)): 10/21 ≈ 0.476
      └── Some((2, 8)): 17/29 ≈ 0.586
    ├── Some((4, 3)): 140/251 ≈ 0.558
      ├── Some((3, 0)): 9/21 ≈ 0.429
      ├── Some((3, 1)): 6/17 ≈ 0.353
      ├── Some((3, 2)): 12/24 ≈ 0.500
      ├── Some((3, 3)): 14/26 ≈ 0.538
      ├── Some((3, 4)): 16/28 ≈ 0.571
      ├── Some((3, 5)): 25/38 ≈ 0.658
      ├── Some((3, 6)): 16/28 ≈ 0.571
      ├── Some((3, 7)): 19/32 ≈ 0.594
      └── Some((3, 8)): 23/36 ≈ 0.639
    ├── Some((4, 4)): 72/150 ≈ 0.480
      ├── Some((4, 0)): 6/15 ≈ 0.400
      ├── Some((4, 1)): 13/23 ≈ 0.565
      ├── Some((4, 2)): 2/10 ≈ 0.200
      ├── Some((4, 3)): 8/18 ≈ 0.444
      ├── Some((4, 5)): 13/23 ≈ 0.565
      ├── Some((4, 6)): 10/20 ≈ 0.500
      ├── Some((4, 7)): 11/21 ≈ 0.524
      └── Some((4, 8)): 9/19 ≈ 0.474
    ├── Some((4, 5)): 123/226 ≈ 0.544
      ├── Some((5, 0)): 15/27 ≈ 0.556
      ├── Some((5, 1)): 30/42 ≈ 0.714
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 16/28 ≈ 0.571
      ├── Some((5, 4)): 11/22 ≈ 0.500
      ├── Some((5, 5)): 12/23 ≈ 0.522
      ├── Some((5, 6)): 8/19 ≈ 0.421
      ├── Some((5, 7)): 13/24 ≈ 0.542
      └── Some((5, 8)): 7/18 ≈ 0.389
    ├── Some((4, 6)): 71/148 ≈ 0.480
      ├── Some((6, 1)): 3/11 ≈ 0.273
      ├── Some((6, 2)): 14/24 ≈ 0.583
      ├── Some((6, 3)): 11/21 ≈ 0.524
      ├── Some((6, 4)): 9/19 ≈ 0.474
      ├── Some((6, 5)): 5/14 ≈ 0.357
      ├── Some((6, 6)): 12/22 ≈ 0.545
      ├── Some((6, 7)): 8/18 ≈ 0.444
      └── Some((6, 8)): 8/18 ≈ 0.444
    ├── Some((4, 7)): 66/141 ≈ 0.468
      ├── Some((7, 0)): 9/18 ≈ 0.500
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 8/16 ≈ 0.500
      ├── Some((7, 4)): 11/20 ≈ 0.550
      ├── Some((7, 5)): 12/21 ≈ 0.571
      ├── Some((7, 6)): 4/12 ≈ 0.333
      ├── Some((7, 7)): 4/12 ≈ 0.333
      └── Some((7, 8)): 2/9 ≈ 0.222
    └── Some((4, 8)): 173/299 ≈ 0.579
      ├── Some((8, 0)): 23/38 ≈ 0.605
      ├── Some((8, 1)): 18/32 ≈ 0.562
      ├── Some((8, 2)): 14/27 ≈ 0.519
      ├── Some((8, 3)): 13/26 ≈ 0.500
      ├── Some((8, 4)): 17/31 ≈ 0.548
      ├── Some((8, 5)): 25/40 ≈ 0.625
      ├── Some((8, 6)): 11/24 ≈ 0.458
      ├── Some((8, 7)): 16/30 ≈ 0.533
      └── Some((8, 8)): 35/50 ≈ 0.700
  ├── Some((0, 5)): 1013/1897 ≈ 0.534
    ├── Some((5, 0)): 130/237 ≈ 0.549
      ├── Some((0, 0)): 10/22 ≈ 0.455
      ├── Some((0, 1)): 25/40 ≈ 0.625
      ├── Some((0, 2)): 9/21 ≈ 0.429
      ├── Some((0, 3)): 8/20 ≈ 0.400
      ├── Some((0, 4)): 22/36 ≈ 0.611
      ├── Some((0, 6)): 18/32 ≈ 0.562
      ├── Some((0, 7)): 18/32 ≈ 0.562
      └── Some((0, 8)): 19/33 ≈ 0.576
    ├── Some((5, 1)): 119/220 ≈ 0.541
      ├── Some((1, 0)): 20/32 ≈ 0.625
      ├── Some((1, 1)): 9/20 ≈ 0.450
      ├── Some((1, 2)): 1/10 ≈ 0.100
      ├── Some((1, 3)): 13/24 ≈ 0.542
      ├── Some((1, 4)): 18/30 ≈ 0.600
      ├── Some((1, 5)): 19/31 ≈ 0.613
      ├── Some((1, 6)): 13/24 ≈ 0.542
      ├── Some((1, 7)): 12/23 ≈ 0.522
      └── Some((1, 8)): 14/25 ≈ 0.560
    ├── Some((5, 2)): 84/168 ≈ 0.500
      ├── Some((2, 0)): 10/20 ≈ 0.500
      ├── Some((2, 1)): 3/11 ≈ 0.273
      ├── Some((2, 2)): 5/14 ≈ 0.357
      ├── Some((2, 3)): 6/15 ≈ 0.400
      ├── Some((2, 4)): 12/22 ≈ 0.545
      ├── Some((2, 5)): 4/13 ≈ 0.308
      ├── Some((2, 6)): 18/28 ≈ 0.643
      ├── Some((2, 7)): 18/28 ≈ 0.643
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((5, 3)): 107/203 ≈ 0.527
      ├── Some((3, 0)): 6/16 ≈ 0.375
      ├── Some((3, 1)): 2/11 ≈ 0.182
      ├── Some((3, 2)): 12/23 ≈ 0.522
      ├── Some((3, 3)): 25/36 ≈ 0.694
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 17/28 ≈ 0.607
      ├── Some((3, 6)): 11/22 ≈ 0.500
      ├── Some((3, 7)): 11/22 ≈ 0.500
      └── Some((3, 8)): 15/26 ≈ 0.577
    ├── Some((5, 4)): 83/167 ≈ 0.497
      ├── Some((4, 0)): 6/15 ≈ 0.400
      ├── Some((4, 1)): 7/16 ≈ 0.438
      ├── Some((4, 2)): 11/21 ≈ 0.524
      ├── Some((4, 3)): 19/29 ≈ 0.655
      ├── Some((4, 4)): 9/19 ≈ 0.474
      ├── Some((4, 5)): 6/15 ≈ 0.400
      ├── Some((4, 6)): 3/11 ≈ 0.273
      ├── Some((4, 7)): 15/25 ≈ 0.600
      └── Some((4, 8)): 6/15 ≈ 0.400
    ├── Some((5, 5)): 168/292 ≈ 0.575
      ├── Some((5, 0)): 24/40 ≈ 0.600
      ├── Some((5, 1)): 32/49 ≈ 0.653
      ├── Some((5, 2)): 15/30 ≈ 0.500
      ├── Some((5, 3)): 22/38 ≈ 0.579
      ├── Some((5, 4)): 19/34 ≈ 0.559
      ├── Some((5, 6)): 32/49 ≈ 0.653
      ├── Some((5, 7)): 9/22 ≈ 0.409
      └── Some((5, 8)): 14/29 ≈ 0.483
    ├── Some((5, 6)): 93/182 ≈ 0.511
      ├── Some((6, 1)): 10/21 ≈ 0.476
      ├── Some((6, 2)): 19/31 ≈ 0.613
      ├── Some((6, 3)): 4/14 ≈ 0.286
      ├── Some((6, 4)): 13/25 ≈ 0.520
      ├── Some((6, 5)): 23/35 ≈ 0.657
      ├── Some((6, 6)): 9/20 ≈ 0.450
      ├── Some((6, 7)): 8/19 ≈ 0.421
      └── Some((6, 8)): 6/16 ≈ 0.375
    ├── Some((5, 7)): 146/260 ≈ 0.562
      ├── Some((7, 0)): 25/38 ≈ 0.658
      ├── Some((7, 1)): 14/27 ≈ 0.519
      ├── Some((7, 2)): 11/23 ≈ 0.478
      ├── Some((7, 3)): 15/28 ≈ 0.536
      ├── Some((7, 4)): 18/31 ≈ 0.581
      ├── Some((7, 5)): 10/22 ≈ 0.455
      ├── Some((7, 6)): 16/29 ≈ 0.552
      ├── Some((7, 7)): 23/36 ≈ 0.639
      └── Some((7, 8)): 13/25 ≈ 0.520
    └── Some((5, 8)): 83/167 ≈ 0.497
      ├── Some((8, 0)): 6/15 ≈ 0.400
      ├── Some((8, 1)): 3/11 ≈ 0.273
      ├── Some((8, 2)): 8/17 ≈ 0.471
      ├── Some((8, 3)): 17/27 ≈ 0.630
      ├── Some((8, 4)): 8/17 ≈ 0.471
      ├── Some((8, 5)): 11/21 ≈ 0.524
      ├── Some((8, 6)): 11/21 ≈ 0.524
      ├── Some((8, 7)): 11/21 ≈ 0.524
      └── Some((8, 8)): 7/16 ≈ 0.438
  ├── Some((0, 6)): 941/1775 ≈ 0.530
    ├── Some((6, 1)): 112/214 ≈ 0.523
      ├── Some((1, 0)): 5/15 ≈ 0.333
      ├── Some((1, 1)): 9/20 ≈ 0.450
      ├── Some((1, 2)): 12/23 ≈ 0.522
      ├── Some((1, 3)): 9/20 ≈ 0.450
      ├── Some((1, 4)): 26/38 ≈ 0.684
      ├── Some((1, 5)): 8/19 ≈ 0.421
      ├── Some((1, 6)): 10/21 ≈ 0.476
      ├── Some((1, 7)): 26/39 ≈ 0.667
      └── Some((1, 8)): 7/18 ≈ 0.389
    ├── Some((6, 2)): 170/300 ≈ 0.567
      ├── Some((2, 0)): 18/32 ≈ 0.562
      ├── Some((2, 1)): 12/26 ≈ 0.462
      ├── Some((2, 2)): 15/29 ≈ 0.517
      ├── Some((2, 3)): 21/36 ≈ 0.583
      ├── Some((2, 4)): 14/28 ≈ 0.500
      ├── Some((2, 5)): 13/27 ≈ 0.481
      ├── Some((2, 6)): 20/35 ≈ 0.571
      ├── Some((2, 7)): 38/54 ≈ 0.704
      └── Some((2, 8)): 18/32 ≈ 0.562
    ├── Some((6, 3)): 136/250 ≈ 0.544
      ├── Some((3, 0)): 19/32 ≈ 0.594
      ├── Some((3, 1)): 7/19 ≈ 0.368
      ├── Some((3, 2)): 17/30 ≈ 0.567
      ├── Some((3, 3)): 5/16 ≈ 0.312
      ├── Some((3, 4)): 33/47 ≈ 0.702
      ├── Some((3, 5)): 10/22 ≈ 0.455
      ├── Some((3, 6)): 15/28 ≈ 0.536
      ├── Some((3, 7)): 5/16 ≈ 0.312
      └── Some((3, 8)): 25/39 ≈ 0.641
    ├── Some((6, 4)): 53/123 ≈ 0.431
      ├── Some((4, 0)): 5/13 ≈ 0.385
      ├── Some((4, 1)): 10/18 ≈ 0.556
      ├── Some((4, 2)): 9/17 ≈ 0.529
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 8/16 ≈ 0.500
      ├── Some((4, 5)): 2/9 ≈ 0.222
      ├── Some((4, 6)): 6/14 ≈ 0.429
      ├── Some((4, 7)): 4/11 ≈ 0.364
      └── Some((4, 8)): 6/14 ≈ 0.429
    ├── Some((6, 5)): 59/132 ≈ 0.447
      ├── Some((5, 0)): 7/15 ≈ 0.467
      ├── Some((5, 1)): 5/13 ≈ 0.385
      ├── Some((5, 2)): 3/11 ≈ 0.273
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 3/11 ≈ 0.273
      ├── Some((5, 5)): 6/14 ≈ 0.429
      ├── Some((5, 6)): 11/20 ≈ 0.550
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 10/18 ≈ 0.556
    ├── Some((6, 6)): 139/255 ≈ 0.545
      ├── Some((6, 1)): 18/34 ≈ 0.529
      ├── Some((6, 2)): 25/42 ≈ 0.595
      ├── Some((6, 3)): 22/39 ≈ 0.564
      ├── Some((6, 4)): 33/52 ≈ 0.635
      ├── Some((6, 5)): 15/31 ≈ 0.484
      ├── Some((6, 7)): 6/19 ≈ 0.316
      └── Some((6, 8)): 20/37 ≈ 0.541
    ├── Some((6, 7)): 140/256 ≈ 0.547
      ├── Some((7, 0)): 22/36 ≈ 0.611
      ├── Some((7, 1)): 30/44 ≈ 0.682
      ├── Some((7, 2)): 15/28 ≈ 0.536
      ├── Some((7, 3)): 9/21 ≈ 0.429
      ├── Some((7, 4)): 16/29 ≈ 0.552
      ├── Some((7, 5)): 12/24 ≈ 0.500
      ├── Some((7, 6)): 13/26 ≈ 0.500
      ├── Some((7, 7)): 14/27 ≈ 0.519
      └── Some((7, 8)): 8/20 ≈ 0.400
    └── Some((6, 8)): 132/244 ≈ 0.541
      ├── Some((8, 0)): 2/12 ≈ 0.167
      ├── Some((8, 1)): 11/23 ≈ 0.478
      ├── Some((8, 2)): 16/29 ≈ 0.552
      ├── Some((8, 3)): 26/40 ≈ 0.650
      ├── Some((8, 4)): 27/41 ≈ 0.659
      ├── Some((8, 5)): 15/28 ≈ 0.536
      ├── Some((8, 6)): 13/25 ≈ 0.520
      ├── Some((8, 7)): 9/21 ≈ 0.429
      └── Some((8, 8)): 12/24 ≈ 0.500
  ├── Some((0, 7)): 802/1536 ≈ 0.522
    ├── Some((7, 0)): 70/142 ≈ 0.493
      ├── Some((0, 0)): 10/19 ≈ 0.526
      ├── Some((0, 1)): 15/25 ≈ 0.600
      ├── Some((0, 2)): 20/30 ≈ 0.667
      ├── Some((0, 3)): 2/10 ≈ 0.200
      ├── Some((0, 4)): 4/12 ≈ 0.333
      ├── Some((0, 5)): 7/16 ≈ 0.438
      ├── Some((0, 6)): 4/12 ≈ 0.333
      └── Some((0, 8)): 8/17 ≈ 0.471
    ├── Some((7, 1)): 100/187 ≈ 0.535
      ├── Some((1, 0)): 12/22 ≈ 0.545
      ├── Some((1, 1)): 7/16 ≈ 0.438
      ├── Some((1, 2)): 7/17 ≈ 0.412
      ├── Some((1, 3)): 17/27 ≈ 0.630
      ├── Some((1, 4)): 7/17 ≈ 0.412
      ├── Some((1, 5)): 2/10 ≈ 0.200
      ├── Some((1, 6)): 20/30 ≈ 0.667
      ├── Some((1, 7)): 20/30 ≈ 0.667
      └── Some((1, 8)): 7/17 ≈ 0.412
    ├── Some((7, 2)): 60/127 ≈ 0.472
      ├── Some((2, 0)): 10/18 ≈ 0.556
      ├── Some((2, 1)): 14/22 ≈ 0.636
      ├── Some((2, 2)): 2/9 ≈ 0.222
      ├── Some((2, 3)): 10/18 ≈ 0.556
      ├── Some((2, 4)): 3/10 ≈ 0.300
      ├── Some((2, 5)): 6/13 ≈ 0.462
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 3/10 ≈ 0.300
      └── Some((2, 8)): 6/14 ≈ 0.429
    ├── Some((7, 3)): 98/184 ≈ 0.533
      ├── Some((3, 0)): 5/14 ≈ 0.357
      ├── Some((3, 1)): 9/18 ≈ 0.500
      ├── Some((3, 2)): 16/26 ≈ 0.615
      ├── Some((3, 3)): 7/16 ≈ 0.438
      ├── Some((3, 4)): 12/22 ≈ 0.545
      ├── Some((3, 5)): 10/20 ≈ 0.500
      ├── Some((3, 6)): 9/18 ≈ 0.500
      ├── Some((3, 7)): 12/22 ≈ 0.545
      └── Some((3, 8)): 17/27 ≈ 0.630
    ├── Some((7, 4)): 111/203 ≈ 0.547
      ├── Some((4, 0)): 10/20 ≈ 0.500
      ├── Some((4, 1)): 7/17 ≈ 0.412
      ├── Some((4, 2)): 11/21 ≈ 0.524
      ├── Some((4, 3)): 6/16 ≈ 0.375
      ├── Some((4, 4)): 19/30 ≈ 0.633
      ├── Some((4, 5)): 19/30 ≈ 0.633
      ├── Some((4, 6)): 5/14 ≈ 0.357
      ├── Some((4, 7)): 9/19 ≈ 0.474
      └── Some((4, 8)): 24/35 ≈ 0.686
    ├── Some((7, 5)): 107/197 ≈ 0.543
      ├── Some((5, 0)): 6/15 ≈ 0.400
      ├── Some((5, 1)): 18/29 ≈ 0.621
      ├── Some((5, 2)): 15/25 ≈ 0.600
      ├── Some((5, 3)): 10/20 ≈ 0.500
      ├── Some((5, 4)): 21/32 ≈ 0.656
      ├── Some((5, 5)): 8/18 ≈ 0.444
      ├── Some((5, 6)): 13/23 ≈ 0.565
      ├── Some((5, 7)): 4/13 ≈ 0.308
      └── Some((5, 8)): 11/21 ≈ 0.524
    ├── Some((7, 6)): 75/150 ≈ 0.500
      ├── Some((6, 1)): 8/17 ≈ 0.471
      ├── Some((6, 2)): 11/21 ≈ 0.524
      ├── Some((6, 3)): 13/23 ≈ 0.565
      ├── Some((6, 4)): 13/23 ≈ 0.565
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 10/19 ≈ 0.526
      ├── Some((6, 7)): 6/15 ≈ 0.400
      └── Some((6, 8)): 4/13 ≈ 0.308
    ├── Some((7, 7)): 91/173 ≈ 0.526
      ├── Some((7, 0)): 10/20 ≈ 0.500
      ├── Some((7, 1)): 4/13 ≈ 0.308
      ├── Some((7, 2)): 10/20 ≈ 0.500
      ├── Some((7, 3)): 5/14 ≈ 0.357
      ├── Some((7, 4)): 8/18 ≈ 0.444
      ├── Some((7, 5)): 16/27 ≈ 0.593
      ├── Some((7, 6)): 23/34 ≈ 0.676
      └── Some((7, 8)): 15/26 ≈ 0.577
    └── Some((7, 8)): 90/172 ≈ 0.523
      ├── Some((8, 0)): 25/35 ≈ 0.714
      ├── Some((8, 1)): 12/22 ≈ 0.545
      ├── Some((8, 2)): 5/14 ≈ 0.357
      ├── Some((8, 3)): 8/17 ≈ 0.471
      ├── Some((8, 4)): 7/16 ≈ 0.438
      ├── Some((8, 5)): 3/11 ≈ 0.273
      ├── Some((8, 6)): 1/9 ≈ 0.111
      ├── Some((8, 7)): 10/19 ≈ 0.526
      └── Some((8, 8)): 18/28 ≈ 0.643
  └── Some((0, 8)): 314/679 ≈ 0.462
    ├── Some((8, 0)): 30/68 ≈ 0.441
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 0/4 ≈ 0.000
      ├── Some((0, 2)): 0/5 ≈ 0.000
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 10/14 ≈ 0.714
      ├── Some((0, 6)): 5/10 ≈ 0.500
      └── Some((0, 7)): 6/11 ≈ 0.545
    ├── Some((8, 1)): 35/76 ≈ 0.461
      ├── Some((1, 0)): 4/9 ≈ 0.444
      ├── Some((1, 1)): 6/10 ≈ 0.600
      ├── Some((1, 2)): 4/9 ≈ 0.444
      ├── Some((1, 3)): 5/9 ≈ 0.556
      ├── Some((1, 4)): 1/5 ≈ 0.200
      ├── Some((1, 5)): 7/11 ≈ 0.636
      ├── Some((1, 6)): 4/9 ≈ 0.444
      ├── Some((1, 7)): 1/5 ≈ 0.200
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((8, 2)): 38/80 ≈ 0.475
      ├── Some((2, 0)): 6/10 ≈ 0.600
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 3/8 ≈ 0.375
      ├── Some((2, 4)): 7/11 ≈ 0.636
      ├── Some((2, 5)): 5/10 ≈ 0.500
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 6/10 ≈ 0.600
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((8, 3)): 50/97 ≈ 0.515
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 6/11 ≈ 0.545
      ├── Some((3, 2)): 7/12 ≈ 0.583
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 5/10 ≈ 0.500
      ├── Some((3, 5)): 6/11 ≈ 0.545
      ├── Some((3, 6)): 6/11 ≈ 0.545
      ├── Some((3, 7)): 8/13 ≈ 0.615
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((8, 4)): 42/86 ≈ 0.488
      ├── Some((4, 0)): 14/18 ≈ 0.778
      ├── Some((4, 1)): 5/10 ≈ 0.500
      ├── Some((4, 2)): 5/10 ≈ 0.500
      ├── Some((4, 3)): 2/7 ≈ 0.286
      ├── Some((4, 4)): 4/9 ≈ 0.444
      ├── Some((4, 5)): 5/10 ≈ 0.500
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 1/6 ≈ 0.167
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((8, 5)): 31/70 ≈ 0.443
      ├── Some((5, 0)): 6/10 ≈ 0.600
      ├── Some((5, 1)): 0/4 ≈ 0.000
      ├── Some((5, 2)): 7/11 ≈ 0.636
      ├── Some((5, 3)): 2/6 ≈ 0.333
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 7/11 ≈ 0.636
      ├── Some((5, 7)): 0/4 ≈ 0.000
      └── Some((5, 8)): 4/8 ≈ 0.500
    ├── Some((8, 6)): 42/86 ≈ 0.488
      ├── Some((6, 1)): 3/8 ≈ 0.375
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 7/12 ≈ 0.583
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 4/10 ≈ 0.400
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 10/15 ≈ 0.667
    ├── Some((8, 7)): 24/59 ≈ 0.407
      ├── Some((7, 0)): 3/7 ≈ 0.429
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 3/7 ≈ 0.429
      ├── Some((7, 3)): 3/7 ≈ 0.429
      ├── Some((7, 4)): 1/5 ≈ 0.200
      ├── Some((7, 5)): 4/7 ≈ 0.571
      ├── Some((7, 6)): 1/5 ≈ 0.200
      ├── Some((7, 7)): 2/6 ≈ 0.333
      └── Some((7, 8)): 4/8 ≈ 0.500
    └── Some((8, 8)): 22/56 ≈ 0.393
      ├── Some((8, 0)): 5/9 ≈ 0.556
      ├── Some((8, 1)): 5/9 ≈ 0.556
      ├── Some((8, 2)): 4/9 ≈ 0.444
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 0/4 ≈ 0.000
      └── Some((8, 7)): 2/7 ≈ 0.286
├── Some((6, 1)): 12600/23595 ≈ 0.534
  ├── Some((1, 0)): 1712/3162 ≈ 0.541
    ├── Some((0, 0)): 102/214 ≈ 0.477
      ├── Some((0, 1)): 10/23 ≈ 0.435
      ├── Some((0, 2)): 9/22 ≈ 0.409
      ├── Some((0, 3)): 18/33 ≈ 0.545
      ├── Some((0, 4)): 10/24 ≈ 0.417
      ├── Some((0, 5)): 18/33 ≈ 0.545
      ├── Some((0, 6)): 9/22 ≈ 0.409
      ├── Some((0, 7)): 8/21 ≈ 0.381
      └── Some((0, 8)): 20/35 ≈ 0.571
    ├── Some((0, 1)): 244/434 ≈ 0.562
      ├── Some((1, 1)): 33/57 ≈ 0.579
      ├── Some((1, 2)): 23/45 ≈ 0.511
      ├── Some((1, 3)): 31/55 ≈ 0.564
      ├── Some((1, 4)): 39/64 ≈ 0.609
      ├── Some((1, 5)): 41/67 ≈ 0.612
      ├── Some((1, 6)): 23/45 ≈ 0.511
      ├── Some((1, 7)): 36/61 ≈ 0.590
      └── Some((1, 8)): 18/39 ≈ 0.462
    ├── Some((0, 2)): 198/364 ≈ 0.544
      ├── Some((2, 0)): 24/43 ≈ 0.558
      ├── Some((2, 1)): 34/55 ≈ 0.618
      ├── Some((2, 2)): 22/41 ≈ 0.537
      ├── Some((2, 3)): 7/22 ≈ 0.318
      ├── Some((2, 4)): 16/33 ≈ 0.485
      ├── Some((2, 5)): 24/43 ≈ 0.558
      ├── Some((2, 6)): 20/38 ≈ 0.526
      ├── Some((2, 7)): 21/39 ≈ 0.538
      └── Some((2, 8)): 29/49 ≈ 0.592
    ├── Some((0, 3)): 187/347 ≈ 0.539
      ├── Some((3, 0)): 13/29 ≈ 0.448
      ├── Some((3, 1)): 18/35 ≈ 0.514
      ├── Some((3, 2)): 37/58 ≈ 0.638
      ├── Some((3, 3)): 17/34 ≈ 0.500
      ├── Some((3, 4)): 13/29 ≈ 0.448
      ├── Some((3, 5)): 23/41 ≈ 0.561
      ├── Some((3, 6)): 18/35 ≈ 0.514
      ├── Some((3, 7)): 14/31 ≈ 0.452
      └── Some((3, 8)): 34/54 ≈ 0.630
    ├── Some((0, 4)): 288/499 ≈ 0.577
      ├── Some((4, 0)): 18/38 ≈ 0.474
      ├── Some((4, 1)): 29/52 ≈ 0.558
      ├── Some((4, 2)): 46/72 ≈ 0.639
      ├── Some((4, 3)): 36/60 ≈ 0.600
      ├── Some((4, 4)): 56/84 ≈ 0.667
      ├── Some((4, 5)): 26/48 ≈ 0.542
      ├── Some((4, 6)): 24/46 ≈ 0.522
      ├── Some((4, 7)): 30/53 ≈ 0.566
      └── Some((4, 8)): 23/45 ≈ 0.511
    ├── Some((0, 5)): 171/323 ≈ 0.529
      ├── Some((5, 0)): 33/52 ≈ 0.635
      ├── Some((5, 1)): 12/28 ≈ 0.429
      ├── Some((5, 2)): 34/53 ≈ 0.642
      ├── Some((5, 3)): 11/26 ≈ 0.423
      ├── Some((5, 4)): 7/21 ≈ 0.333
      ├── Some((5, 5)): 18/35 ≈ 0.514
      ├── Some((5, 6)): 9/24 ≈ 0.375
      ├── Some((5, 7)): 20/37 ≈ 0.541
      └── Some((5, 8)): 27/46 ≈ 0.587
    ├── Some((0, 6)): 207/378 ≈ 0.548
      ├── Some((6, 0)): 37/61 ≈ 0.607
      ├── Some((6, 2)): 23/44 ≈ 0.523
      ├── Some((6, 3)): 20/40 ≈ 0.500
      ├── Some((6, 4)): 16/35 ≈ 0.457
      ├── Some((6, 5)): 45/70 ≈ 0.643
      ├── Some((6, 6)): 21/42 ≈ 0.500
      ├── Some((6, 7)): 19/39 ≈ 0.487
      └── Some((6, 8)): 25/46 ≈ 0.543
    ├── Some((0, 7)): 154/296 ≈ 0.520
      ├── Some((7, 0)): 24/41 ≈ 0.585
      ├── Some((7, 1)): 18/34 ≈ 0.529
      ├── Some((7, 2)): 8/22 ≈ 0.364
      ├── Some((7, 3)): 18/34 ≈ 0.529
      ├── Some((7, 4)): 11/25 ≈ 0.440
      ├── Some((7, 5)): 20/36 ≈ 0.556
      ├── Some((7, 6)): 13/28 ≈ 0.464
      ├── Some((7, 7)): 13/28 ≈ 0.464
      └── Some((7, 8)): 29/47 ≈ 0.617
    └── Some((0, 8)): 160/306 ≈ 0.523
      ├── Some((8, 0)): 13/28 ≈ 0.464
      ├── Some((8, 1)): 16/32 ≈ 0.500
      ├── Some((8, 2)): 17/33 ≈ 0.515
      ├── Some((8, 3)): 13/29 ≈ 0.448
      ├── Some((8, 4)): 20/37 ≈ 0.541
      ├── Some((8, 5)): 29/47 ≈ 0.617
      ├── Some((8, 6)): 12/27 ≈ 0.444
      ├── Some((8, 7)): 27/45 ≈ 0.600
      └── Some((8, 8)): 12/27 ≈ 0.444
  ├── Some((1, 1)): 991/1916 ≈ 0.517
    ├── Some((1, 0)): 119/233 ≈ 0.511
      ├── Some((0, 0)): 10/22 ≈ 0.455
      ├── Some((0, 1)): 23/37 ≈ 0.622
      ├── Some((0, 2)): 20/34 ≈ 0.588
      ├── Some((0, 3)): 16/29 ≈ 0.552
      ├── Some((0, 4)): 6/17 ≈ 0.353
      ├── Some((0, 5)): 4/15 ≈ 0.267
      ├── Some((0, 6)): 11/24 ≈ 0.458
      ├── Some((0, 7)): 14/27 ≈ 0.519
      └── Some((0, 8)): 14/27 ≈ 0.519
    ├── Some((1, 2)): 105/211 ≈ 0.498
      ├── Some((2, 0)): 13/25 ≈ 0.520
      ├── Some((2, 1)): 15/27 ≈ 0.556
      ├── Some((2, 2)): 13/25 ≈ 0.520
      ├── Some((2, 3)): 9/20 ≈ 0.450
      ├── Some((2, 4)): 8/19 ≈ 0.421
      ├── Some((2, 5)): 20/33 ≈ 0.606
      ├── Some((2, 6)): 15/27 ≈ 0.556
      ├── Some((2, 7)): 9/21 ≈ 0.429
      └── Some((2, 8)): 3/13 ≈ 0.231
    ├── Some((1, 3)): 78/169 ≈ 0.462
      ├── Some((3, 0)): 9/19 ≈ 0.474
      ├── Some((3, 1)): 13/24 ≈ 0.542
      ├── Some((3, 2)): 7/17 ≈ 0.412
      ├── Some((3, 3)): 11/21 ≈ 0.524
      ├── Some((3, 4)): 6/16 ≈ 0.375
      ├── Some((3, 5)): 10/20 ≈ 0.500
      ├── Some((3, 6)): 5/14 ≈ 0.357
      ├── Some((3, 7)): 7/17 ≈ 0.412
      └── Some((3, 8)): 10/20 ≈ 0.500
    ├── Some((1, 4)): 67/151 ≈ 0.444
      ├── Some((4, 0)): 5/14 ≈ 0.357
      ├── Some((4, 1)): 5/14 ≈ 0.357
      ├── Some((4, 2)): 9/18 ≈ 0.500
      ├── Some((4, 3)): 9/18 ≈ 0.500
      ├── Some((4, 4)): 2/10 ≈ 0.200
      ├── Some((4, 5)): 6/15 ≈ 0.400
      ├── Some((4, 6)): 9/19 ≈ 0.474
      ├── Some((4, 7)): 12/22 ≈ 0.545
      └── Some((4, 8)): 10/20 ≈ 0.500
    ├── Some((1, 5)): 129/248 ≈ 0.520
      ├── Some((5, 0)): 20/34 ≈ 0.588
      ├── Some((5, 1)): 13/26 ≈ 0.500
      ├── Some((5, 2)): 5/16 ≈ 0.312
      ├── Some((5, 3)): 12/25 ≈ 0.480
      ├── Some((5, 4)): 11/24 ≈ 0.458
      ├── Some((5, 5)): 22/36 ≈ 0.611
      ├── Some((5, 6)): 10/23 ≈ 0.435
      ├── Some((5, 7)): 24/38 ≈ 0.632
      └── Some((5, 8)): 12/25 ≈ 0.480
    ├── Some((1, 6)): 97/199 ≈ 0.487
      ├── Some((6, 0)): 20/34 ≈ 0.588
      ├── Some((6, 2)): 8/20 ≈ 0.400
      ├── Some((6, 3)): 13/26 ≈ 0.500
      ├── Some((6, 4)): 7/19 ≈ 0.368
      ├── Some((6, 5)): 13/26 ≈ 0.500
      ├── Some((6, 6)): 5/16 ≈ 0.312
      ├── Some((6, 7)): 8/20 ≈ 0.400
      └── Some((6, 8)): 22/37 ≈ 0.595
    ├── Some((1, 7)): 196/349 ≈ 0.562
      ├── Some((7, 0)): 20/37 ≈ 0.541
      ├── Some((7, 1)): 17/33 ≈ 0.515
      ├── Some((7, 2)): 24/41 ≈ 0.585
      ├── Some((7, 3)): 36/55 ≈ 0.655
      ├── Some((7, 4)): 15/31 ≈ 0.484
      ├── Some((7, 5)): 18/34 ≈ 0.529
      ├── Some((7, 6)): 11/26 ≈ 0.423
      ├── Some((7, 7)): 23/40 ≈ 0.575
      └── Some((7, 8)): 32/51 ≈ 0.627
    └── Some((1, 8)): 200/355 ≈ 0.563
      ├── Some((8, 0)): 28/46 ≈ 0.609
      ├── Some((8, 1)): 12/27 ≈ 0.444
      ├── Some((8, 2)): 18/35 ≈ 0.514
      ├── Some((8, 3)): 27/45 ≈ 0.600
      ├── Some((8, 4)): 39/59 ≈ 0.661
      ├── Some((8, 5)): 30/49 ≈ 0.612
      ├── Some((8, 6)): 26/44 ≈ 0.591
      ├── Some((8, 7)): 12/27 ≈ 0.444
      └── Some((8, 8)): 8/22 ≈ 0.364
  ├── Some((1, 2)): 1134/2165 ≈ 0.524
    ├── Some((2, 0)): 46/115 ≈ 0.400
      ├── Some((0, 0)): 3/10 ≈ 0.300
      ├── Some((0, 1)): 1/8 ≈ 0.125
      ├── Some((0, 2)): 8/16 ≈ 0.500
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 7/15 ≈ 0.467
      ├── Some((0, 5)): 6/14 ≈ 0.429
      ├── Some((0, 6)): 3/10 ≈ 0.300
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 4/12 ≈ 0.333
    ├── Some((2, 1)): 90/186 ≈ 0.484
      ├── Some((1, 0)): 8/20 ≈ 0.400
      ├── Some((1, 1)): 12/24 ≈ 0.500
      ├── Some((1, 3)): 15/28 ≈ 0.536
      ├── Some((1, 4)): 7/18 ≈ 0.389
      ├── Some((1, 5)): 0/9 ≈ 0.000
      ├── Some((1, 6)): 7/18 ≈ 0.389
      ├── Some((1, 7)): 22/36 ≈ 0.611
      └── Some((1, 8)): 19/32 ≈ 0.594
    ├── Some((2, 2)): 157/289 ≈ 0.543
      ├── Some((2, 0)): 18/34 ≈ 0.529
      ├── Some((2, 1)): 22/39 ≈ 0.564
      ├── Some((2, 3)): 23/40 ≈ 0.575
      ├── Some((2, 4)): 14/29 ≈ 0.483
      ├── Some((2, 5)): 19/36 ≈ 0.528
      ├── Some((2, 6)): 28/46 ≈ 0.609
      ├── Some((2, 7)): 10/24 ≈ 0.417
      └── Some((2, 8)): 23/40 ≈ 0.575
    ├── Some((2, 3)): 156/288 ≈ 0.542
      ├── Some((3, 0)): 20/35 ≈ 0.571
      ├── Some((3, 1)): 6/18 ≈ 0.333
      ├── Some((3, 2)): 27/43 ≈ 0.628
      ├── Some((3, 3)): 14/28 ≈ 0.500
      ├── Some((3, 4)): 16/30 ≈ 0.533
      ├── Some((3, 5)): 19/34 ≈ 0.559
      ├── Some((3, 6)): 25/41 ≈ 0.610
      ├── Some((3, 7)): 11/25 ≈ 0.440
      └── Some((3, 8)): 18/33 ≈ 0.545
    ├── Some((2, 4)): 78/168 ≈ 0.464
      ├── Some((4, 0)): 9/19 ≈ 0.474
      ├── Some((4, 1)): 5/14 ≈ 0.357
      ├── Some((4, 2)): 13/24 ≈ 0.542
      ├── Some((4, 3)): 10/20 ≈ 0.500
      ├── Some((4, 4)): 5/15 ≈ 0.333
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 10/20 ≈ 0.500
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 8/18 ≈ 0.444
    ├── Some((2, 5)): 155/286 ≈ 0.542
      ├── Some((5, 0)): 12/26 ≈ 0.462
      ├── Some((5, 1)): 20/35 ≈ 0.571
      ├── Some((5, 2)): 22/37 ≈ 0.595
      ├── Some((5, 3)): 6/18 ≈ 0.333
      ├── Some((5, 4)): 26/42 ≈ 0.619
      ├── Some((5, 5)): 17/32 ≈ 0.531
      ├── Some((5, 6)): 24/40 ≈ 0.600
      ├── Some((5, 7)): 18/33 ≈ 0.545
      └── Some((5, 8)): 9/22 ≈ 0.409
    ├── Some((2, 6)): 131/250 ≈ 0.524
      ├── Some((6, 0)): 17/32 ≈ 0.531
      ├── Some((6, 2)): 12/26 ≈ 0.462
      ├── Some((6, 3)): 14/29 ≈ 0.483
      ├── Some((6, 4)): 16/31 ≈ 0.516
      ├── Some((6, 5)): 6/18 ≈ 0.333
      ├── Some((6, 6)): 31/48 ≈ 0.646
      ├── Some((6, 7)): 20/36 ≈ 0.556
      └── Some((6, 8)): 14/29 ≈ 0.483
    ├── Some((2, 7)): 255/434 ≈ 0.588
      ├── Some((7, 0)): 21/40 ≈ 0.525
      ├── Some((7, 1)): 46/68 ≈ 0.676
      ├── Some((7, 2)): 18/36 ≈ 0.500
      ├── Some((7, 3)): 18/36 ≈ 0.500
      ├── Some((7, 4)): 49/72 ≈ 0.681
      ├── Some((7, 5)): 33/54 ≈ 0.611
      ├── Some((7, 6)): 21/40 ≈ 0.525
      ├── Some((7, 7)): 31/52 ≈ 0.596
      └── Some((7, 8)): 17/35 ≈ 0.486
    └── Some((2, 8)): 66/148 ≈ 0.446
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 1)): 1/9 ≈ 0.111
      ├── Some((8, 2)): 15/25 ≈ 0.600
      ├── Some((8, 3)): 11/21 ≈ 0.524
      ├── Some((8, 4)): 10/19 ≈ 0.526
      ├── Some((8, 5)): 2/10 ≈ 0.200
      ├── Some((8, 6)): 4/13 ≈ 0.308
      ├── Some((8, 7)): 6/15 ≈ 0.400
      └── Some((8, 8)): 7/16 ≈ 0.438
  ├── Some((1, 3)): 1176/2238 ≈ 0.525
    ├── Some((3, 0)): 122/236 ≈ 0.517
      ├── Some((0, 0)): 12/25 ≈ 0.480
      ├── Some((0, 1)): 5/16 ≈ 0.312
      ├── Some((0, 2)): 20/34 ≈ 0.588
      ├── Some((0, 3)): 13/26 ≈ 0.500
      ├── Some((0, 4)): 9/21 ≈ 0.429
      ├── Some((0, 5)): 24/38 ≈ 0.632
      ├── Some((0, 6)): 7/18 ≈ 0.389
      ├── Some((0, 7)): 16/29 ≈ 0.552
      └── Some((0, 8)): 15/28 ≈ 0.536
    ├── Some((3, 1)): 135/256 ≈ 0.527
      ├── Some((1, 0)): 14/29 ≈ 0.483
      ├── Some((1, 1)): 27/44 ≈ 0.614
      ├── Some((1, 2)): 11/25 ≈ 0.440
      ├── Some((1, 4)): 19/35 ≈ 0.543
      ├── Some((1, 5)): 21/37 ≈ 0.568
      ├── Some((1, 6)): 3/14 ≈ 0.214
      ├── Some((1, 7)): 24/41 ≈ 0.585
      └── Some((1, 8)): 15/30 ≈ 0.500
    ├── Some((3, 2)): 94/193 ≈ 0.487
      ├── Some((2, 0)): 5/15 ≈ 0.333
      ├── Some((2, 1)): 7/18 ≈ 0.389
      ├── Some((2, 2)): 4/14 ≈ 0.286
      ├── Some((2, 3)): 10/21 ≈ 0.476
      ├── Some((2, 4)): 20/32 ≈ 0.625
      ├── Some((2, 5)): 12/23 ≈ 0.522
      ├── Some((2, 6)): 6/16 ≈ 0.375
      ├── Some((2, 7)): 17/29 ≈ 0.586
      └── Some((2, 8)): 12/24 ≈ 0.500
    ├── Some((3, 3)): 156/288 ≈ 0.542
      ├── Some((3, 0)): 20/37 ≈ 0.541
      ├── Some((3, 1)): 14/30 ≈ 0.467
      ├── Some((3, 2)): 15/31 ≈ 0.484
      ├── Some((3, 4)): 27/45 ≈ 0.600
      ├── Some((3, 5)): 36/55 ≈ 0.655
      ├── Some((3, 6)): 21/38 ≈ 0.553
      ├── Some((3, 7)): 16/32 ≈ 0.500
      └── Some((3, 8)): 6/19 ≈ 0.316
    ├── Some((3, 4)): 81/172 ≈ 0.471
      ├── Some((4, 0)): 5/14 ≈ 0.357
      ├── Some((4, 1)): 11/21 ≈ 0.524
      ├── Some((4, 2)): 8/18 ≈ 0.444
      ├── Some((4, 3)): 7/17 ≈ 0.412
      ├── Some((4, 4)): 11/21 ≈ 0.524
      ├── Some((4, 5)): 7/17 ≈ 0.412
      ├── Some((4, 6)): 13/24 ≈ 0.542
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 11/21 ≈ 0.524
    ├── Some((3, 5)): 176/317 ≈ 0.555
      ├── Some((5, 0)): 4/16 ≈ 0.250
      ├── Some((5, 1)): 16/31 ≈ 0.516
      ├── Some((5, 2)): 14/29 ≈ 0.483
      ├── Some((5, 3)): 25/42 ≈ 0.595
      ├── Some((5, 4)): 7/20 ≈ 0.350
      ├── Some((5, 5)): 25/42 ≈ 0.595
      ├── Some((5, 6)): 21/37 ≈ 0.568
      ├── Some((5, 7)): 32/50 ≈ 0.640
      └── Some((5, 8)): 31/49 ≈ 0.633
    ├── Some((3, 6)): 184/329 ≈ 0.559
      ├── Some((6, 0)): 23/41 ≈ 0.561
      ├── Some((6, 2)): 15/32 ≈ 0.469
      ├── Some((6, 3)): 25/44 ≈ 0.568
      ├── Some((6, 4)): 16/33 ≈ 0.485
      ├── Some((6, 5)): 23/41 ≈ 0.561
      ├── Some((6, 6)): 11/27 ≈ 0.407
      ├── Some((6, 7)): 27/46 ≈ 0.587
      └── Some((6, 8)): 43/64 ≈ 0.672
    ├── Some((3, 7)): 78/168 ≈ 0.464
      ├── Some((7, 0)): 16/27 ≈ 0.593
      ├── Some((7, 1)): 4/13 ≈ 0.308
      ├── Some((7, 2)): 4/13 ≈ 0.308
      ├── Some((7, 3)): 11/21 ≈ 0.524
      ├── Some((7, 4)): 11/22 ≈ 0.500
      ├── Some((7, 5)): 7/17 ≈ 0.412
      ├── Some((7, 6)): 10/20 ≈ 0.500
      ├── Some((7, 7)): 11/22 ≈ 0.500
      └── Some((7, 8)): 3/12 ≈ 0.250
    └── Some((3, 8)): 150/278 ≈ 0.540
      ├── Some((8, 0)): 21/36 ≈ 0.583
      ├── Some((8, 1)): 5/17 ≈ 0.294
      ├── Some((8, 2)): 11/25 ≈ 0.440
      ├── Some((8, 3)): 31/47 ≈ 0.660
      ├── Some((8, 4)): 12/26 ≈ 0.462
      ├── Some((8, 5)): 16/30 ≈ 0.533
      ├── Some((8, 6)): 16/31 ≈ 0.516
      ├── Some((8, 7)): 6/18 ≈ 0.333
      └── Some((8, 8)): 31/47 ≈ 0.660
  ├── Some((1, 4)): 1471/2749 ≈ 0.535
    ├── Some((4, 0)): 132/258 ≈ 0.512
      ├── Some((0, 0)): 11/24 ≈ 0.458
      ├── Some((0, 1)): 16/30 ≈ 0.533
      ├── Some((0, 2)): 14/28 ≈ 0.500
      ├── Some((0, 3)): 19/33 ≈ 0.576
      ├── Some((0, 4)): 13/27 ≈ 0.481
      ├── Some((0, 5)): 19/34 ≈ 0.559
      ├── Some((0, 6)): 21/36 ≈ 0.583
      ├── Some((0, 7)): 5/17 ≈ 0.294
      └── Some((0, 8)): 14/28 ≈ 0.500
    ├── Some((4, 1)): 186/340 ≈ 0.547
      ├── Some((1, 0)): 20/39 ≈ 0.513
      ├── Some((1, 1)): 13/30 ≈ 0.433
      ├── Some((1, 2)): 27/47 ≈ 0.574
      ├── Some((1, 3)): 29/49 ≈ 0.592
      ├── Some((1, 5)): 21/40 ≈ 0.525
      ├── Some((1, 6)): 24/43 ≈ 0.558
      ├── Some((1, 7)): 34/55 ≈ 0.618
      └── Some((1, 8)): 18/36 ≈ 0.500
    ├── Some((4, 2)): 155/293 ≈ 0.529
      ├── Some((2, 0)): 26/43 ≈ 0.605
      ├── Some((2, 1)): 22/38 ≈ 0.579
      ├── Some((2, 2)): 26/43 ≈ 0.605
      ├── Some((2, 3)): 9/23 ≈ 0.391
      ├── Some((2, 4)): 10/24 ≈ 0.417
      ├── Some((2, 5)): 24/40 ≈ 0.600
      ├── Some((2, 6)): 12/26 ≈ 0.462
      ├── Some((2, 7)): 7/20 ≈ 0.350
      └── Some((2, 8)): 19/35 ≈ 0.543
    ├── Some((4, 3)): 151/287 ≈ 0.526
      ├── Some((3, 0)): 23/39 ≈ 0.590
      ├── Some((3, 1)): 17/32 ≈ 0.531
      ├── Some((3, 2)): 14/29 ≈ 0.483
      ├── Some((3, 3)): 28/45 ≈ 0.622
      ├── Some((3, 4)): 18/34 ≈ 0.529
      ├── Some((3, 5)): 5/17 ≈ 0.294
      ├── Some((3, 6)): 26/43 ≈ 0.605
      ├── Some((3, 7)): 12/26 ≈ 0.462
      └── Some((3, 8)): 8/21 ≈ 0.381
    ├── Some((4, 4)): 240/421 ≈ 0.570
      ├── Some((4, 0)): 31/54 ≈ 0.574
      ├── Some((4, 1)): 18/38 ≈ 0.474
      ├── Some((4, 2)): 37/61 ≈ 0.607
      ├── Some((4, 3)): 32/55 ≈ 0.582
      ├── Some((4, 5)): 18/38 ≈ 0.474
      ├── Some((4, 6)): 23/44 ≈ 0.523
      ├── Some((4, 7)): 33/57 ≈ 0.579
      └── Some((4, 8)): 47/73 ≈ 0.644
    ├── Some((4, 5)): 88/188 ≈ 0.468
      ├── Some((5, 0)): 11/22 ≈ 0.500
      ├── Some((5, 1)): 9/20 ≈ 0.450
      ├── Some((5, 2)): 12/23 ≈ 0.522
      ├── Some((5, 3)): 3/13 ≈ 0.231
      ├── Some((5, 4)): 8/19 ≈ 0.421
      ├── Some((5, 5)): 12/23 ≈ 0.522
      ├── Some((5, 6)): 10/21 ≈ 0.476
      ├── Some((5, 7)): 15/27 ≈ 0.556
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((4, 6)): 194/353 ≈ 0.550
      ├── Some((6, 0)): 32/53 ≈ 0.604
      ├── Some((6, 2)): 20/39 ≈ 0.513
      ├── Some((6, 3)): 14/32 ≈ 0.438
      ├── Some((6, 4)): 27/48 ≈ 0.562
      ├── Some((6, 5)): 21/40 ≈ 0.525
      ├── Some((6, 6)): 16/34 ≈ 0.471
      ├── Some((6, 7)): 35/57 ≈ 0.614
      └── Some((6, 8)): 28/49 ≈ 0.571
    ├── Some((4, 7)): 172/319 ≈ 0.539
      ├── Some((7, 0)): 22/39 ≈ 0.564
      ├── Some((7, 1)): 18/34 ≈ 0.529
      ├── Some((7, 2)): 13/28 ≈ 0.464
      ├── Some((7, 3)): 22/39 ≈ 0.564
      ├── Some((7, 4)): 32/51 ≈ 0.627
      ├── Some((7, 5)): 17/33 ≈ 0.515
      ├── Some((7, 6)): 12/27 ≈ 0.444
      ├── Some((7, 7)): 18/34 ≈ 0.529
      └── Some((7, 8)): 17/33 ≈ 0.515
    └── Some((4, 8)): 152/289 ≈ 0.526
      ├── Some((8, 0)): 12/26 ≈ 0.462
      ├── Some((8, 1)): 25/42 ≈ 0.595
      ├── Some((8, 2)): 26/43 ≈ 0.605
      ├── Some((8, 3)): 20/36 ≈ 0.556
      ├── Some((8, 4)): 12/26 ≈ 0.462
      ├── Some((8, 5)): 12/26 ≈ 0.462
      ├── Some((8, 6)): 11/25 ≈ 0.440
      ├── Some((8, 7)): 13/28 ≈ 0.464
      └── Some((8, 8)): 20/36 ≈ 0.556
  ├── Some((1, 5)): 1130/2159 ≈ 0.523
    ├── Some((5, 0)): 47/117 ≈ 0.402
      ├── Some((0, 0)): 12/20 ≈ 0.600
      ├── Some((0, 1)): 5/13 ≈ 0.385
      ├── Some((0, 2)): 8/16 ≈ 0.500
      ├── Some((0, 3)): 9/17 ≈ 0.529
      ├── Some((0, 4)): 1/8 ≈ 0.125
      ├── Some((0, 5)): 1/8 ≈ 0.125
      ├── Some((0, 6)): 7/15 ≈ 0.467
      ├── Some((0, 7)): 1/8 ≈ 0.125
      └── Some((0, 8)): 3/11 ≈ 0.273
    ├── Some((5, 1)): 95/194 ≈ 0.490
      ├── Some((1, 0)): 10/22 ≈ 0.455
      ├── Some((1, 1)): 12/25 ≈ 0.480
      ├── Some((1, 2)): 13/26 ≈ 0.500
      ├── Some((1, 3)): 7/18 ≈ 0.389
      ├── Some((1, 4)): 16/29 ≈ 0.552
      ├── Some((1, 6)): 9/21 ≈ 0.429
      ├── Some((1, 7)): 19/32 ≈ 0.594
      └── Some((1, 8)): 8/20 ≈ 0.400
    ├── Some((5, 2)): 54/128 ≈ 0.422
      ├── Some((2, 0)): 12/21 ≈ 0.571
      ├── Some((2, 1)): 5/13 ≈ 0.385
      ├── Some((2, 2)): 8/17 ≈ 0.471
      ├── Some((2, 3)): 6/14 ≈ 0.429
      ├── Some((2, 4)): 3/11 ≈ 0.273
      ├── Some((2, 5)): 3/11 ≈ 0.273
      ├── Some((2, 6)): 3/11 ≈ 0.273
      ├── Some((2, 7)): 6/14 ≈ 0.429
      └── Some((2, 8)): 7/15 ≈ 0.467
    ├── Some((5, 3)): 80/171 ≈ 0.468
      ├── Some((3, 0)): 10/20 ≈ 0.500
      ├── Some((3, 1)): 8/18 ≈ 0.444
      ├── Some((3, 2)): 20/31 ≈ 0.645
      ├── Some((3, 3)): 8/18 ≈ 0.444
      ├── Some((3, 4)): 4/13 ≈ 0.308
      ├── Some((3, 5)): 6/16 ≈ 0.375
      ├── Some((3, 6)): 12/23 ≈ 0.522
      ├── Some((3, 7)): 5/14 ≈ 0.357
      └── Some((3, 8)): 7/17 ≈ 0.412
    ├── Some((5, 4)): 159/292 ≈ 0.545
      ├── Some((4, 0)): 17/32 ≈ 0.531
      ├── Some((4, 1)): 7/20 ≈ 0.350
      ├── Some((4, 2)): 16/31 ≈ 0.516
      ├── Some((4, 3)): 14/28 ≈ 0.500
      ├── Some((4, 4)): 28/44 ≈ 0.636
      ├── Some((4, 5)): 18/33 ≈ 0.545
      ├── Some((4, 6)): 23/39 ≈ 0.590
      ├── Some((4, 7)): 25/41 ≈ 0.610
      └── Some((4, 8)): 10/23 ≈ 0.435
    ├── Some((5, 5)): 176/317 ≈ 0.555
      ├── Some((5, 0)): 32/51 ≈ 0.627
      ├── Some((5, 1)): 25/43 ≈ 0.581
      ├── Some((5, 2)): 30/49 ≈ 0.612
      ├── Some((5, 3)): 11/26 ≈ 0.423
      ├── Some((5, 4)): 13/29 ≈ 0.448
      ├── Some((5, 6)): 17/34 ≈ 0.500
      ├── Some((5, 7)): 26/44 ≈ 0.591
      └── Some((5, 8)): 22/40 ≈ 0.550
    ├── Some((5, 6)): 183/328 ≈ 0.558
      ├── Some((6, 0)): 29/48 ≈ 0.604
      ├── Some((6, 2)): 16/33 ≈ 0.485
      ├── Some((6, 3)): 11/27 ≈ 0.407
      ├── Some((6, 4)): 31/51 ≈ 0.608
      ├── Some((6, 5)): 19/36 ≈ 0.528
      ├── Some((6, 6)): 21/39 ≈ 0.538
      ├── Some((6, 7)): 19/36 ≈ 0.528
      └── Some((6, 8)): 37/57 ≈ 0.649
    ├── Some((5, 7)): 177/319 ≈ 0.555
      ├── Some((7, 0)): 19/34 ≈ 0.559
      ├── Some((7, 1)): 15/30 ≈ 0.500
      ├── Some((7, 2)): 15/30 ≈ 0.500
      ├── Some((7, 3)): 27/44 ≈ 0.614
      ├── Some((7, 4)): 21/37 ≈ 0.568
      ├── Some((7, 5)): 20/36 ≈ 0.556
      ├── Some((7, 6)): 21/37 ≈ 0.568
      ├── Some((7, 7)): 15/30 ≈ 0.500
      └── Some((7, 8)): 24/40 ≈ 0.600
    └── Some((5, 8)): 159/292 ≈ 0.545
      ├── Some((8, 0)): 16/31 ≈ 0.516
      ├── Some((8, 1)): 17/32 ≈ 0.531
      ├── Some((8, 2)): 14/28 ≈ 0.500
      ├── Some((8, 3)): 22/38 ≈ 0.579
      ├── Some((8, 4)): 20/35 ≈ 0.571
      ├── Some((8, 5)): 10/23 ≈ 0.435
      ├── Some((8, 6)): 15/29 ≈ 0.517
      ├── Some((8, 7)): 30/46 ≈ 0.652
      └── Some((8, 8)): 15/29 ≈ 0.517
  ├── Some((1, 6)): 1478/2761 ≈ 0.535
    ├── Some((6, 0)): 224/405 ≈ 0.553
      ├── Some((0, 0)): 25/45 ≈ 0.556
      ├── Some((0, 1)): 32/54 ≈ 0.593
      ├── Some((0, 2)): 17/36 ≈ 0.472
      ├── Some((0, 3)): 31/53 ≈ 0.585
      ├── Some((0, 4)): 28/49 ≈ 0.571
      ├── Some((0, 5)): 10/26 ≈ 0.385
      ├── Some((0, 6)): 40/63 ≈ 0.635
      ├── Some((0, 7)): 28/49 ≈ 0.571
      └── Some((0, 8)): 12/29 ≈ 0.414
    ├── Some((6, 2)): 128/257 ≈ 0.498
      ├── Some((2, 0)): 11/25 ≈ 0.440
      ├── Some((2, 1)): 25/41 ≈ 0.610
      ├── Some((2, 2)): 11/25 ≈ 0.440
      ├── Some((2, 3)): 7/20 ≈ 0.350
      ├── Some((2, 4)): 20/35 ≈ 0.571
      ├── Some((2, 5)): 18/33 ≈ 0.545
      ├── Some((2, 6)): 8/21 ≈ 0.381
      ├── Some((2, 7)): 15/29 ≈ 0.517
      └── Some((2, 8)): 13/27 ≈ 0.481
    ├── Some((6, 3)): 206/378 ≈ 0.545
      ├── Some((3, 0)): 14/32 ≈ 0.438
      ├── Some((3, 1)): 10/26 ≈ 0.385
      ├── Some((3, 2)): 22/41 ≈ 0.537
      ├── Some((3, 3)): 30/51 ≈ 0.588
      ├── Some((3, 4)): 23/43 ≈ 0.535
      ├── Some((3, 5)): 49/73 ≈ 0.671
      ├── Some((3, 6)): 5/19 ≈ 0.263
      ├── Some((3, 7)): 30/51 ≈ 0.588
      └── Some((3, 8)): 22/41 ≈ 0.537
    ├── Some((6, 4)): 218/396 ≈ 0.551
      ├── Some((4, 0)): 22/41 ≈ 0.537
      ├── Some((4, 1)): 27/47 ≈ 0.574
      ├── Some((4, 2)): 16/34 ≈ 0.471
      ├── Some((4, 3)): 33/54 ≈ 0.611
      ├── Some((4, 4)): 22/41 ≈ 0.537
      ├── Some((4, 5)): 31/52 ≈ 0.596
      ├── Some((4, 6)): 19/38 ≈ 0.500
      ├── Some((4, 7)): 20/39 ≈ 0.513
      └── Some((4, 8)): 28/49 ≈ 0.571
    ├── Some((6, 5)): 148/288 ≈ 0.514
      ├── Some((5, 0)): 12/27 ≈ 0.444
      ├── Some((5, 1)): 21/38 ≈ 0.553
      ├── Some((5, 2)): 3/15 ≈ 0.200
      ├── Some((5, 3)): 14/29 ≈ 0.483
      ├── Some((5, 4)): 14/29 ≈ 0.483
      ├── Some((5, 5)): 34/53 ≈ 0.642
      ├── Some((5, 6)): 21/38 ≈ 0.553
      ├── Some((5, 7)): 10/24 ≈ 0.417
      └── Some((5, 8)): 18/34 ≈ 0.529
    ├── Some((6, 6)): 205/377 ≈ 0.544
      ├── Some((6, 0)): 32/57 ≈ 0.561
      ├── Some((6, 2)): 37/64 ≈ 0.578
      ├── Some((6, 3)): 35/61 ≈ 0.574
      ├── Some((6, 4)): 20/42 ≈ 0.476
      ├── Some((6, 5)): 31/56 ≈ 0.554
      ├── Some((6, 7)): 18/39 ≈ 0.462
      └── Some((6, 8)): 32/57 ≈ 0.561
    ├── Some((6, 7)): 143/281 ≈ 0.509
      ├── Some((7, 0)): 15/30 ≈ 0.500
      ├── Some((7, 1)): 6/19 ≈ 0.316
      ├── Some((7, 2)): 9/23 ≈ 0.391
      ├── Some((7, 3)): 16/31 ≈ 0.516
      ├── Some((7, 4)): 30/48 ≈ 0.625
      ├── Some((7, 5)): 9/23 ≈ 0.391
      ├── Some((7, 6)): 16/31 ≈ 0.516
      ├── Some((7, 7)): 25/42 ≈ 0.595
      └── Some((7, 8)): 17/33 ≈ 0.515
    └── Some((6, 8)): 206/378 ≈ 0.545
      ├── Some((8, 0)): 15/33 ≈ 0.455
      ├── Some((8, 1)): 43/66 ≈ 0.652
      ├── Some((8, 2)): 11/27 ≈ 0.407
      ├── Some((8, 3)): 18/36 ≈ 0.500
      ├── Some((8, 4)): 15/33 ≈ 0.455
      ├── Some((8, 5)): 32/53 ≈ 0.604
      ├── Some((8, 6)): 18/36 ≈ 0.500
      ├── Some((8, 7)): 31/52 ≈ 0.596
      └── Some((8, 8)): 22/41 ≈ 0.537
  ├── Some((1, 7)): 2560/4605 ≈ 0.556
    ├── Some((7, 0)): 283/511 ≈ 0.554
      ├── Some((0, 0)): 17/39 ≈ 0.436
      ├── Some((0, 1)): 26/50 ≈ 0.520
      ├── Some((0, 2)): 29/54 ≈ 0.537
      ├── Some((0, 3)): 58/89 ≈ 0.652
      ├── Some((0, 4)): 35/61 ≈ 0.574
      ├── Some((0, 5)): 27/51 ≈ 0.529
      ├── Some((0, 6)): 52/82 ≈ 0.634
      ├── Some((0, 7)): 18/40 ≈ 0.450
      └── Some((0, 8)): 21/44 ≈ 0.477
    ├── Some((7, 1)): 307/547 ≈ 0.561
      ├── Some((1, 0)): 56/91 ≈ 0.615
      ├── Some((1, 1)): 35/64 ≈ 0.547
      ├── Some((1, 2)): 26/53 ≈ 0.491
      ├── Some((1, 3)): 67/104 ≈ 0.644
      ├── Some((1, 4)): 27/54 ≈ 0.500
      ├── Some((1, 5)): 31/59 ≈ 0.525
      ├── Some((1, 6)): 33/62 ≈ 0.532
      └── Some((1, 8)): 31/59 ≈ 0.525
    ├── Some((7, 2)): 128/267 ≈ 0.479
      ├── Some((2, 0)): 21/38 ≈ 0.553
      ├── Some((2, 1)): 2/13 ≈ 0.154
      ├── Some((2, 2)): 12/27 ≈ 0.444
      ├── Some((2, 3)): 15/31 ≈ 0.484
      ├── Some((2, 4)): 8/22 ≈ 0.364
      ├── Some((2, 5)): 19/36 ≈ 0.528
      ├── Some((2, 6)): 19/36 ≈ 0.528
      ├── Some((2, 7)): 15/31 ≈ 0.484
      └── Some((2, 8)): 16/32 ≈ 0.500
    ├── Some((7, 3)): 316/561 ≈ 0.563
      ├── Some((3, 0)): 54/86 ≈ 0.628
      ├── Some((3, 1)): 47/77 ≈ 0.610
      ├── Some((3, 2)): 44/74 ≈ 0.595
      ├── Some((3, 3)): 22/46 ≈ 0.478
      ├── Some((3, 4)): 25/50 ≈ 0.500
      ├── Some((3, 5)): 43/72 ≈ 0.597
      ├── Some((3, 6)): 19/42 ≈ 0.452
      ├── Some((3, 7)): 16/38 ≈ 0.421
      └── Some((3, 8)): 45/75 ≈ 0.600
    ├── Some((7, 4)): 201/383 ≈ 0.525
      ├── Some((4, 0)): 20/40 ≈ 0.500
      ├── Some((4, 1)): 4/18 ≈ 0.222
      ├── Some((4, 2)): 35/58 ≈ 0.603
      ├── Some((4, 3)): 25/46 ≈ 0.543
      ├── Some((4, 4)): 24/45 ≈ 0.533
      ├── Some((4, 5)): 32/55 ≈ 0.582
      ├── Some((4, 6)): 26/48 ≈ 0.542
      ├── Some((4, 7)): 21/41 ≈ 0.512
      └── Some((4, 8)): 13/31 ≈ 0.419
    ├── Some((7, 5)): 315/559 ≈ 0.564
      ├── Some((5, 0)): 27/52 ≈ 0.519
      ├── Some((5, 1)): 25/50 ≈ 0.500
      ├── Some((5, 2)): 16/38 ≈ 0.421
      ├── Some((5, 3)): 43/72 ≈ 0.597
      ├── Some((5, 4)): 43/72 ≈ 0.597
      ├── Some((5, 5)): 38/66 ≈ 0.576
      ├── Some((5, 6)): 31/57 ≈ 0.544
      ├── Some((5, 7)): 40/69 ≈ 0.580
      └── Some((5, 8)): 51/82 ≈ 0.622
    ├── Some((7, 6)): 363/632 ≈ 0.574
      ├── Some((6, 0)): 47/81 ≈ 0.580
      ├── Some((6, 2)): 65/104 ≈ 0.625
      ├── Some((6, 3)): 51/86 ≈ 0.593
      ├── Some((6, 4)): 28/57 ≈ 0.491
      ├── Some((6, 5)): 37/69 ≈ 0.536
      ├── Some((6, 6)): 42/75 ≈ 0.560
      ├── Some((6, 7)): 56/92 ≈ 0.609
      └── Some((6, 8)): 36/67 ≈ 0.537
    ├── Some((7, 7)): 298/534 ≈ 0.558
      ├── Some((7, 0)): 63/99 ≈ 0.636
      ├── Some((7, 1)): 40/70 ≈ 0.571
      ├── Some((7, 2)): 23/49 ≈ 0.469
      ├── Some((7, 3)): 35/64 ≈ 0.547
      ├── Some((7, 4)): 21/46 ≈ 0.457
      ├── Some((7, 5)): 23/49 ≈ 0.469
      ├── Some((7, 6)): 44/76 ≈ 0.579
      └── Some((7, 8)): 48/80 ≈ 0.600
    └── Some((7, 8)): 348/610 ≈ 0.570
      ├── Some((8, 0)): 35/64 ≈ 0.547
      ├── Some((8, 1)): 26/52 ≈ 0.500
      ├── Some((8, 2)): 55/88 ≈ 0.625
      ├── Some((8, 3)): 31/59 ≈ 0.525
      ├── Some((8, 4)): 69/105 ≈ 0.657
      ├── Some((8, 5)): 47/78 ≈ 0.603
      ├── Some((8, 6)): 42/72 ≈ 0.583
      ├── Some((8, 7)): 20/44 ≈ 0.455
      └── Some((8, 8)): 22/47 ≈ 0.468
  └── Some((1, 8)): 947/1839 ≈ 0.515
    ├── Some((8, 0)): 117/222 ≈ 0.527
      ├── Some((0, 0)): 15/27 ≈ 0.556
      ├── Some((0, 1)): 6/16 ≈ 0.375
      ├── Some((0, 2)): 11/22 ≈ 0.500
      ├── Some((0, 3)): 18/30 ≈ 0.600
      ├── Some((0, 4)): 9/20 ≈ 0.450
      ├── Some((0, 5)): 14/26 ≈ 0.538
      ├── Some((0, 6)): 12/24 ≈ 0.500
      ├── Some((0, 7)): 15/27 ≈ 0.556
      └── Some((0, 8)): 17/29 ≈ 0.586
    ├── Some((8, 1)): 49/117 ≈ 0.419
      ├── Some((1, 0)): 1/8 ≈ 0.125
      ├── Some((1, 1)): 4/12 ≈ 0.333
      ├── Some((1, 2)): 8/17 ≈ 0.471
      ├── Some((1, 3)): 1/8 ≈ 0.125
      ├── Some((1, 4)): 4/12 ≈ 0.333
      ├── Some((1, 5)): 5/14 ≈ 0.357
      ├── Some((1, 6)): 18/28 ≈ 0.643
      └── Some((1, 7)): 8/17 ≈ 0.471
    ├── Some((8, 2)): 122/230 ≈ 0.530
      ├── Some((2, 0)): 10/22 ≈ 0.455
      ├── Some((2, 1)): 20/33 ≈ 0.606
      ├── Some((2, 2)): 18/30 ≈ 0.600
      ├── Some((2, 3)): 8/19 ≈ 0.421
      ├── Some((2, 4)): 20/33 ≈ 0.606
      ├── Some((2, 5)): 18/31 ≈ 0.581
      ├── Some((2, 6)): 4/14 ≈ 0.286
      ├── Some((2, 7)): 11/23 ≈ 0.478
      └── Some((2, 8)): 12/24 ≈ 0.500
    ├── Some((8, 3)): 86/175 ≈ 0.491
      ├── Some((3, 0)): 2/10 ≈ 0.200
      ├── Some((3, 1)): 12/22 ≈ 0.545
      ├── Some((3, 2)): 18/29 ≈ 0.621
      ├── Some((3, 3)): 14/25 ≈ 0.560
      ├── Some((3, 4)): 10/20 ≈ 0.500
      ├── Some((3, 5)): 9/19 ≈ 0.474
      ├── Some((3, 6)): 11/21 ≈ 0.524
      ├── Some((3, 7)): 8/18 ≈ 0.444
      └── Some((3, 8)): 2/10 ≈ 0.200
    ├── Some((8, 4)): 134/248 ≈ 0.540
      ├── Some((4, 0)): 19/32 ≈ 0.594
      ├── Some((4, 1)): 15/28 ≈ 0.536
      ├── Some((4, 2)): 23/36 ≈ 0.639
      ├── Some((4, 3)): 11/23 ≈ 0.478
      ├── Some((4, 4)): 10/22 ≈ 0.455
      ├── Some((4, 5)): 18/31 ≈ 0.581
      ├── Some((4, 6)): 17/30 ≈ 0.567
      ├── Some((4, 7)): 17/30 ≈ 0.567
      └── Some((4, 8)): 4/15 ≈ 0.267
    ├── Some((8, 5)): 99/195 ≈ 0.508
      ├── Some((5, 0)): 10/21 ≈ 0.476
      ├── Some((5, 1)): 18/29 ≈ 0.621
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 7/17 ≈ 0.412
      ├── Some((5, 4)): 8/18 ≈ 0.444
      ├── Some((5, 5)): 9/20 ≈ 0.450
      ├── Some((5, 6)): 11/22 ≈ 0.500
      ├── Some((5, 7)): 16/27 ≈ 0.593
      └── Some((5, 8)): 8/18 ≈ 0.444
    ├── Some((8, 6)): 101/198 ≈ 0.510
      ├── Some((6, 0)): 15/28 ≈ 0.536
      ├── Some((6, 2)): 7/18 ≈ 0.389
      ├── Some((6, 3)): 7/18 ≈ 0.389
      ├── Some((6, 4)): 16/29 ≈ 0.552
      ├── Some((6, 5)): 20/33 ≈ 0.606
      ├── Some((6, 6)): 4/14 ≈ 0.286
      ├── Some((6, 7)): 13/25 ≈ 0.520
      └── Some((6, 8)): 19/32 ≈ 0.594
    ├── Some((8, 7)): 119/226 ≈ 0.527
      ├── Some((7, 0)): 14/26 ≈ 0.538
      ├── Some((7, 1)): 2/12 ≈ 0.167
      ├── Some((7, 2)): 10/22 ≈ 0.455
      ├── Some((7, 3)): 9/20 ≈ 0.450
      ├── Some((7, 4)): 9/20 ≈ 0.450
      ├── Some((7, 5)): 20/33 ≈ 0.606
      ├── Some((7, 6)): 15/27 ≈ 0.556
      ├── Some((7, 7)): 19/32 ≈ 0.594
      └── Some((7, 8)): 20/33 ≈ 0.606
    └── Some((8, 8)): 120/227 ≈ 0.529
      ├── Some((8, 0)): 21/35 ≈ 0.600
      ├── Some((8, 1)): 12/25 ≈ 0.480
      ├── Some((8, 2)): 9/21 ≈ 0.429
      ├── Some((8, 3)): 20/34 ≈ 0.588
      ├── Some((8, 4)): 15/29 ≈ 0.517
      ├── Some((8, 5)): 30/45 ≈ 0.667
      ├── Some((8, 6)): 9/22 ≈ 0.409
      └── Some((8, 7)): 4/15 ≈ 0.267
├── Some((6, 2)): 13293/24848 ≈ 0.535
  ├── Some((2, 0)): 1130/2161 ≈ 0.523
    ├── Some((0, 0)): 85/178 ≈ 0.478
      ├── Some((0, 1)): 20/33 ≈ 0.606
      ├── Some((0, 2)): 3/13 ≈ 0.231
      ├── Some((0, 3)): 7/18 ≈ 0.389
      ├── Some((0, 4)): 21/34 ≈ 0.618
      ├── Some((0, 5)): 7/18 ≈ 0.389
      ├── Some((0, 6)): 20/33 ≈ 0.606
      ├── Some((0, 7)): 5/16 ≈ 0.312
      └── Some((0, 8)): 2/12 ≈ 0.167
    ├── Some((0, 1)): 204/358 ≈ 0.570
      ├── Some((1, 0)): 28/46 ≈ 0.609
      ├── Some((1, 1)): 24/41 ≈ 0.585
      ├── Some((1, 2)): 28/46 ≈ 0.609
      ├── Some((1, 3)): 24/41 ≈ 0.585
      ├── Some((1, 4)): 24/41 ≈ 0.585
      ├── Some((1, 5)): 19/36 ≈ 0.528
      ├── Some((1, 6)): 27/45 ≈ 0.600
      ├── Some((1, 7)): 21/38 ≈ 0.553
      └── Some((1, 8)): 9/23 ≈ 0.391
    ├── Some((0, 2)): 120/232 ≈ 0.517
      ├── Some((2, 1)): 25/41 ≈ 0.610
      ├── Some((2, 2)): 13/27 ≈ 0.481
      ├── Some((2, 3)): 19/34 ≈ 0.559
      ├── Some((2, 4)): 7/19 ≈ 0.368
      ├── Some((2, 5)): 6/18 ≈ 0.333
      ├── Some((2, 6)): 17/32 ≈ 0.531
      ├── Some((2, 7)): 22/37 ≈ 0.595
      └── Some((2, 8)): 10/23 ≈ 0.435
    ├── Some((0, 3)): 82/173 ≈ 0.474
      ├── Some((3, 0)): 5/14 ≈ 0.357
      ├── Some((3, 1)): 12/23 ≈ 0.522
      ├── Some((3, 2)): 6/16 ≈ 0.375
      ├── Some((3, 3)): 11/22 ≈ 0.500
      ├── Some((3, 4)): 7/17 ≈ 0.412
      ├── Some((3, 5)): 3/12 ≈ 0.250
      ├── Some((3, 6)): 7/17 ≈ 0.412
      ├── Some((3, 7)): 9/19 ≈ 0.474
      └── Some((3, 8)): 21/32 ≈ 0.656
    ├── Some((0, 4)): 98/199 ≈ 0.492
      ├── Some((4, 0)): 10/21 ≈ 0.476
      ├── Some((4, 1)): 9/20 ≈ 0.450
      ├── Some((4, 2)): 10/21 ≈ 0.476
      ├── Some((4, 3)): 13/24 ≈ 0.542
      ├── Some((4, 4)): 12/23 ≈ 0.522
      ├── Some((4, 5)): 11/22 ≈ 0.500
      ├── Some((4, 6)): 14/26 ≈ 0.538
      ├── Some((4, 7)): 6/16 ≈ 0.375
      └── Some((4, 8)): 13/25 ≈ 0.520
    ├── Some((0, 5)): 131/249 ≈ 0.526
      ├── Some((5, 0)): 8/20 ≈ 0.400
      ├── Some((5, 1)): 20/34 ≈ 0.588
      ├── Some((5, 2)): 12/25 ≈ 0.480
      ├── Some((5, 3)): 18/32 ≈ 0.562
      ├── Some((5, 4)): 7/19 ≈ 0.368
      ├── Some((5, 5)): 4/15 ≈ 0.267
      ├── Some((5, 6)): 22/36 ≈ 0.611
      ├── Some((5, 7)): 14/27 ≈ 0.519
      └── Some((5, 8)): 25/40 ≈ 0.625
    ├── Some((0, 6)): 104/208 ≈ 0.500
      ├── Some((6, 0)): 12/25 ≈ 0.480
      ├── Some((6, 1)): 14/27 ≈ 0.519
      ├── Some((6, 3)): 14/27 ≈ 0.519
      ├── Some((6, 4)): 15/29 ≈ 0.517
      ├── Some((6, 5)): 5/16 ≈ 0.312
      ├── Some((6, 6)): 19/33 ≈ 0.576
      ├── Some((6, 7)): 18/32 ≈ 0.562
      └── Some((6, 8)): 6/18 ≈ 0.333
    ├── Some((0, 7)): 107/212 ≈ 0.505
      ├── Some((7, 0)): 15/27 ≈ 0.556
      ├── Some((7, 1)): 4/14 ≈ 0.286
      ├── Some((7, 2)): 13/25 ≈ 0.520
      ├── Some((7, 3)): 7/18 ≈ 0.389
      ├── Some((7, 4)): 22/35 ≈ 0.629
      ├── Some((7, 5)): 11/23 ≈ 0.478
      ├── Some((7, 6)): 12/24 ≈ 0.500
      ├── Some((7, 7)): 3/13 ≈ 0.231
      └── Some((7, 8)): 19/32 ≈ 0.594
    └── Some((0, 8)): 199/351 ≈ 0.567
      ├── Some((8, 0)): 21/38 ≈ 0.553
      ├── Some((8, 1)): 6/19 ≈ 0.316
      ├── Some((8, 2)): 29/47 ≈ 0.617
      ├── Some((8, 3)): 16/32 ≈ 0.500
      ├── Some((8, 4)): 21/38 ≈ 0.553
      ├── Some((8, 5)): 40/59 ≈ 0.678
      ├── Some((8, 6)): 18/35 ≈ 0.514
      ├── Some((8, 7)): 28/46 ≈ 0.609
      └── Some((8, 8)): 19/36 ≈ 0.528
  ├── Some((2, 1)): 1551/2889 ≈ 0.537
    ├── Some((1, 0)): 126/251 ≈ 0.502
      ├── Some((0, 0)): 11/25 ≈ 0.440
      ├── Some((0, 1)): 10/23 ≈ 0.435
      ├── Some((0, 2)): 14/28 ≈ 0.500
      ├── Some((0, 3)): 15/29 ≈ 0.517
      ├── Some((0, 4)): 26/42 ≈ 0.619
      ├── Some((0, 5)): 22/38 ≈ 0.579
      ├── Some((0, 6)): 9/22 ≈ 0.409
      ├── Some((0, 7)): 17/32 ≈ 0.531
      └── Some((0, 8)): 1/11 ≈ 0.091
    ├── Some((1, 1)): 246/433 ≈ 0.568
      ├── Some((1, 0)): 34/58 ≈ 0.586
      ├── Some((1, 2)): 31/55 ≈ 0.564
      ├── Some((1, 3)): 41/66 ≈ 0.621
      ├── Some((1, 4)): 33/57 ≈ 0.579
      ├── Some((1, 5)): 17/37 ≈ 0.459
      ├── Some((1, 6)): 31/55 ≈ 0.564
      ├── Some((1, 7)): 32/56 ≈ 0.571
      └── Some((1, 8)): 26/48 ≈ 0.542
    ├── Some((1, 2)): 82/180 ≈ 0.456
      ├── Some((2, 0)): 8/20 ≈ 0.400
      ├── Some((2, 2)): 5/16 ≈ 0.312
      ├── Some((2, 3)): 12/25 ≈ 0.480
      ├── Some((2, 4)): 10/22 ≈ 0.455
      ├── Some((2, 5)): 18/32 ≈ 0.562
      ├── Some((2, 6)): 18/32 ≈ 0.562
      ├── Some((2, 7)): 7/19 ≈ 0.368
      └── Some((2, 8)): 3/13 ≈ 0.231
    ├── Some((1, 3)): 142/275 ≈ 0.516
      ├── Some((3, 0)): 19/34 ≈ 0.559
      ├── Some((3, 1)): 14/29 ≈ 0.483
      ├── Some((3, 2)): 20/36 ≈ 0.556
      ├── Some((3, 3)): 25/41 ≈ 0.610
      ├── Some((3, 4)): 9/22 ≈ 0.409
      ├── Some((3, 5)): 21/37 ≈ 0.568
      ├── Some((3, 6)): 17/32 ≈ 0.531
      ├── Some((3, 7)): 5/17 ≈ 0.294
      └── Some((3, 8)): 12/26 ≈ 0.462
    ├── Some((1, 4)): 222/397 ≈ 0.559
      ├── Some((4, 0)): 1/13 ≈ 0.077
      ├── Some((4, 1)): 26/46 ≈ 0.565
      ├── Some((4, 2)): 29/50 ≈ 0.580
      ├── Some((4, 3)): 14/31 ≈ 0.452
      ├── Some((4, 4)): 24/44 ≈ 0.545
      ├── Some((4, 5)): 37/59 ≈ 0.627
      ├── Some((4, 6)): 25/45 ≈ 0.556
      ├── Some((4, 7)): 35/57 ≈ 0.614
      └── Some((4, 8)): 30/51 ≈ 0.588
    ├── Some((1, 5)): 145/280 ≈ 0.518
      ├── Some((5, 0)): 22/38 ≈ 0.579
      ├── Some((5, 1)): 4/16 ≈ 0.250
      ├── Some((5, 2)): 8/21 ≈ 0.381
      ├── Some((5, 3)): 16/31 ≈ 0.516
      ├── Some((5, 4)): 22/38 ≈ 0.579
      ├── Some((5, 5)): 24/41 ≈ 0.585
      ├── Some((5, 6)): 26/43 ≈ 0.605
      ├── Some((5, 7)): 9/23 ≈ 0.391
      └── Some((5, 8)): 13/28 ≈ 0.464
    ├── Some((1, 6)): 183/338 ≈ 0.541
      ├── Some((6, 0)): 6/21 ≈ 0.286
      ├── Some((6, 1)): 39/61 ≈ 0.639
      ├── Some((6, 3)): 26/46 ≈ 0.565
      ├── Some((6, 4)): 16/34 ≈ 0.471
      ├── Some((6, 5)): 29/50 ≈ 0.580
      ├── Some((6, 6)): 18/36 ≈ 0.500
      ├── Some((6, 7)): 28/49 ≈ 0.571
      └── Some((6, 8)): 21/40 ≈ 0.525
    ├── Some((1, 7)): 216/388 ≈ 0.557
      ├── Some((7, 0)): 19/37 ≈ 0.514
      ├── Some((7, 1)): 21/40 ≈ 0.525
      ├── Some((7, 2)): 26/46 ≈ 0.565
      ├── Some((7, 3)): 16/33 ≈ 0.485
      ├── Some((7, 4)): 31/51 ≈ 0.608
      ├── Some((7, 5)): 13/30 ≈ 0.433
      ├── Some((7, 6)): 30/50 ≈ 0.600
      ├── Some((7, 7)): 37/58 ≈ 0.638
      └── Some((7, 8)): 23/42 ≈ 0.548
    └── Some((1, 8)): 188/346 ≈ 0.543
      ├── Some((8, 0)): 24/42 ≈ 0.571
      ├── Some((8, 1)): 20/38 ≈ 0.526
      ├── Some((8, 2)): 11/26 ≈ 0.423
      ├── Some((8, 3)): 19/36 ≈ 0.528
      ├── Some((8, 4)): 26/45 ≈ 0.578
      ├── Some((8, 5)): 18/35 ≈ 0.514
      ├── Some((8, 6)): 16/33 ≈ 0.485
      ├── Some((8, 7)): 23/41 ≈ 0.561
      └── Some((8, 8)): 30/49 ≈ 0.612
  ├── Some((2, 2)): 1869/3434 ≈ 0.544
    ├── Some((2, 0)): 255/463 ≈ 0.551
      ├── Some((0, 0)): 13/32 ≈ 0.406
      ├── Some((0, 1)): 17/38 ≈ 0.447
      ├── Some((0, 2)): 54/83 ≈ 0.651
      ├── Some((0, 3)): 26/49 ≈ 0.531
      ├── Some((0, 4)): 19/40 ≈ 0.475
      ├── Some((0, 5)): 23/45 ≈ 0.511
      ├── Some((0, 6)): 50/78 ≈ 0.641
      ├── Some((0, 7)): 36/61 ≈ 0.590
      └── Some((0, 8)): 16/36 ≈ 0.444
    ├── Some((2, 1)): 213/398 ≈ 0.535
      ├── Some((1, 0)): 17/36 ≈ 0.472
      ├── Some((1, 1)): 52/78 ≈ 0.667
      ├── Some((1, 2)): 16/35 ≈ 0.457
      ├── Some((1, 3)): 28/50 ≈ 0.560
      ├── Some((1, 4)): 32/55 ≈ 0.582
      ├── Some((1, 5)): 20/40 ≈ 0.500
      ├── Some((1, 6)): 12/30 ≈ 0.400
      ├── Some((1, 7)): 18/37 ≈ 0.486
      └── Some((1, 8)): 17/36 ≈ 0.472
    ├── Some((2, 3)): 392/671 ≈ 0.584
      ├── Some((3, 0)): 44/76 ≈ 0.579
      ├── Some((3, 1)): 26/53 ≈ 0.491
      ├── Some((3, 2)): 64/100 ≈ 0.640
      ├── Some((3, 3)): 28/55 ≈ 0.509
      ├── Some((3, 4)): 89/130 ≈ 0.685
      ├── Some((3, 5)): 28/55 ≈ 0.509
      ├── Some((3, 6)): 45/77 ≈ 0.584
      ├── Some((3, 7)): 19/43 ≈ 0.442
      └── Some((3, 8)): 48/81 ≈ 0.593
    ├── Some((2, 4)): 216/403 ≈ 0.536
      ├── Some((4, 0)): 18/38 ≈ 0.474
      ├── Some((4, 1)): 21/41 ≈ 0.512
      ├── Some((4, 2)): 25/46 ≈ 0.543
      ├── Some((4, 3)): 13/31 ≈ 0.419
      ├── Some((4, 4)): 16/35 ≈ 0.457
      ├── Some((4, 5)): 21/41 ≈ 0.512
      ├── Some((4, 6)): 17/36 ≈ 0.472
      ├── Some((4, 7)): 36/59 ≈ 0.610
      └── Some((4, 8)): 49/75 ≈ 0.653
    ├── Some((2, 5)): 190/362 ≈ 0.525
      ├── Some((5, 0)): 13/30 ≈ 0.433
      ├── Some((5, 1)): 17/36 ≈ 0.472
      ├── Some((5, 2)): 30/51 ≈ 0.588
      ├── Some((5, 3)): 14/32 ≈ 0.438
      ├── Some((5, 4)): 18/37 ≈ 0.486
      ├── Some((5, 5)): 10/26 ≈ 0.385
      ├── Some((5, 6)): 42/65 ≈ 0.646
      ├── Some((5, 7)): 16/34 ≈ 0.471
      └── Some((5, 8)): 29/50 ≈ 0.580
    ├── Some((2, 6)): 231/426 ≈ 0.542
      ├── Some((6, 0)): 47/77 ≈ 0.610
      ├── Some((6, 1)): 40/68 ≈ 0.588
      ├── Some((6, 3)): 30/56 ≈ 0.536
      ├── Some((6, 4)): 32/58 ≈ 0.552
      ├── Some((6, 5)): 3/18 ≈ 0.167
      ├── Some((6, 6)): 45/74 ≈ 0.608
      ├── Some((6, 7)): 4/20 ≈ 0.200
      └── Some((6, 8)): 29/54 ≈ 0.537
    ├── Some((2, 7)): 174/337 ≈ 0.516
      ├── Some((7, 0)): 11/27 ≈ 0.407
      ├── Some((7, 1)): 17/35 ≈ 0.486
      ├── Some((7, 2)): 27/47 ≈ 0.574
      ├── Some((7, 3)): 8/23 ≈ 0.348
      ├── Some((7, 4)): 26/45 ≈ 0.578
      ├── Some((7, 5)): 12/28 ≈ 0.429
      ├── Some((7, 6)): 27/47 ≈ 0.574
      ├── Some((7, 7)): 22/41 ≈ 0.537
      └── Some((7, 8)): 24/43 ≈ 0.558
    └── Some((2, 8)): 197/373 ≈ 0.528
      ├── Some((8, 0)): 32/54 ≈ 0.593
      ├── Some((8, 1)): 25/45 ≈ 0.556
      ├── Some((8, 2)): 39/62 ≈ 0.629
      ├── Some((8, 3)): 29/50 ≈ 0.580
      ├── Some((8, 4)): 6/21 ≈ 0.286
      ├── Some((8, 5)): 18/37 ≈ 0.486
      ├── Some((8, 6)): 11/28 ≈ 0.393
      ├── Some((8, 7)): 19/38 ≈ 0.500
      └── Some((8, 8)): 18/37 ≈ 0.486
  ├── Some((2, 3)): 1339/2524 ≈ 0.531
    ├── Some((3, 0)): 176/322 ≈ 0.547
      ├── Some((0, 0)): 32/50 ≈ 0.640
      ├── Some((0, 1)): 19/35 ≈ 0.543
      ├── Some((0, 2)): 15/31 ≈ 0.484
      ├── Some((0, 3)): 18/34 ≈ 0.529
      ├── Some((0, 4)): 19/35 ≈ 0.543
      ├── Some((0, 5)): 14/29 ≈ 0.483
      ├── Some((0, 6)): 19/35 ≈ 0.543
      ├── Some((0, 7)): 17/33 ≈ 0.515
      └── Some((0, 8)): 22/39 ≈ 0.564
    ├── Some((3, 1)): 121/238 ≈ 0.508
      ├── Some((1, 0)): 13/26 ≈ 0.500
      ├── Some((1, 1)): 14/27 ≈ 0.519
      ├── Some((1, 2)): 19/33 ≈ 0.576
      ├── Some((1, 3)): 13/26 ≈ 0.500
      ├── Some((1, 4)): 9/21 ≈ 0.429
      ├── Some((1, 5)): 16/30 ≈ 0.533
      ├── Some((1, 6)): 25/40 ≈ 0.625
      ├── Some((1, 7)): 2/12 ≈ 0.167
      └── Some((1, 8)): 9/22 ≈ 0.409
    ├── Some((3, 2)): 145/275 ≈ 0.527
      ├── Some((2, 0)): 25/43 ≈ 0.581
      ├── Some((2, 1)): 16/32 ≈ 0.500
      ├── Some((2, 2)): 24/41 ≈ 0.585
      ├── Some((2, 4)): 23/40 ≈ 0.575
      ├── Some((2, 5)): 19/36 ≈ 0.528
      ├── Some((2, 6)): 19/36 ≈ 0.528
      ├── Some((2, 7)): 6/19 ≈ 0.316
      └── Some((2, 8)): 12/27 ≈ 0.444
    ├── Some((3, 3)): 157/293 ≈ 0.536
      ├── Some((3, 0)): 26/44 ≈ 0.591
      ├── Some((3, 1)): 21/39 ≈ 0.538
      ├── Some((3, 2)): 12/28 ≈ 0.429
      ├── Some((3, 4)): 10/25 ≈ 0.400
      ├── Some((3, 5)): 10/25 ≈ 0.400
      ├── Some((3, 6)): 8/22 ≈ 0.364
      ├── Some((3, 7)): 26/45 ≈ 0.578
      └── Some((3, 8)): 43/64 ≈ 0.672
    ├── Some((3, 4)): 92/193 ≈ 0.477
      ├── Some((4, 0)): 3/13 ≈ 0.231
      ├── Some((4, 1)): 7/18 ≈ 0.389
      ├── Some((4, 2)): 6/17 ≈ 0.353
      ├── Some((4, 3)): 10/21 ≈ 0.476
      ├── Some((4, 4)): 5/15 ≈ 0.333
      ├── Some((4, 5)): 20/32 ≈ 0.625
      ├── Some((4, 6)): 18/30 ≈ 0.600
      ├── Some((4, 7)): 8/19 ≈ 0.421
      └── Some((4, 8)): 15/27 ≈ 0.556
    ├── Some((3, 5)): 155/290 ≈ 0.534
      ├── Some((5, 0)): 26/42 ≈ 0.619
      ├── Some((5, 1)): 13/27 ≈ 0.481
      ├── Some((5, 2)): 18/33 ≈ 0.545
      ├── Some((5, 3)): 12/26 ≈ 0.462
      ├── Some((5, 4)): 19/35 ≈ 0.543
      ├── Some((5, 5)): 21/37 ≈ 0.568
      ├── Some((5, 6)): 9/22 ≈ 0.409
      ├── Some((5, 7)): 9/23 ≈ 0.391
      └── Some((5, 8)): 27/44 ≈ 0.614
    ├── Some((3, 6)): 145/275 ≈ 0.527
      ├── Some((6, 0)): 13/28 ≈ 0.464
      ├── Some((6, 1)): 16/32 ≈ 0.500
      ├── Some((6, 3)): 12/27 ≈ 0.444
      ├── Some((6, 4)): 26/44 ≈ 0.591
      ├── Some((6, 5)): 9/23 ≈ 0.391
      ├── Some((6, 6)): 15/31 ≈ 0.484
      ├── Some((6, 7)): 28/46 ≈ 0.609
      └── Some((6, 8)): 25/43 ≈ 0.581
    ├── Some((3, 7)): 199/357 ≈ 0.557
      ├── Some((7, 0)): 21/38 ≈ 0.553
      ├── Some((7, 1)): 27/45 ≈ 0.600
      ├── Some((7, 2)): 16/33 ≈ 0.485
      ├── Some((7, 3)): 17/34 ≈ 0.500
      ├── Some((7, 4)): 18/35 ≈ 0.514
      ├── Some((7, 5)): 20/37 ≈ 0.541
      ├── Some((7, 6)): 37/57 ≈ 0.649
      ├── Some((7, 7)): 25/43 ≈ 0.581
      └── Some((7, 8)): 17/34 ≈ 0.500
    └── Some((3, 8)): 148/280 ≈ 0.529
      ├── Some((8, 0)): 21/36 ≈ 0.583
      ├── Some((8, 1)): 9/22 ≈ 0.409
      ├── Some((8, 2)): 7/20 ≈ 0.350
      ├── Some((8, 3)): 21/36 ≈ 0.583
      ├── Some((8, 4)): 11/25 ≈ 0.440
      ├── Some((8, 5)): 18/33 ≈ 0.545
      ├── Some((8, 6)): 15/29 ≈ 0.517
      ├── Some((8, 7)): 31/48 ≈ 0.646
      └── Some((8, 8)): 15/30 ≈ 0.500
  ├── Some((2, 4)): 1583/2944 ≈ 0.538
    ├── Some((4, 0)): 251/441 ≈ 0.569
      ├── Some((0, 0)): 30/52 ≈ 0.577
      ├── Some((0, 1)): 19/38 ≈ 0.500
      ├── Some((0, 2)): 19/38 ≈ 0.500
      ├── Some((0, 3)): 29/51 ≈ 0.569
      ├── Some((0, 4)): 22/42 ≈ 0.524
      ├── Some((0, 5)): 27/48 ≈ 0.562
      ├── Some((0, 6)): 47/72 ≈ 0.653
      ├── Some((0, 7)): 44/68 ≈ 0.647
      └── Some((0, 8)): 13/31 ≈ 0.419
    ├── Some((4, 1)): 147/284 ≈ 0.518
      ├── Some((1, 0)): 9/23 ≈ 0.391
      ├── Some((1, 1)): 27/44 ≈ 0.614
      ├── Some((1, 2)): 10/24 ≈ 0.417
      ├── Some((1, 3)): 8/22 ≈ 0.364
      ├── Some((1, 4)): 7/20 ≈ 0.350
      ├── Some((1, 5)): 25/42 ≈ 0.595
      ├── Some((1, 6)): 20/36 ≈ 0.556
      ├── Some((1, 7)): 30/48 ≈ 0.625
      └── Some((1, 8)): 10/24 ≈ 0.417
    ├── Some((4, 2)): 145/281 ≈ 0.516
      ├── Some((2, 0)): 13/29 ≈ 0.448
      ├── Some((2, 1)): 16/33 ≈ 0.485
      ├── Some((2, 2)): 23/41 ≈ 0.561
      ├── Some((2, 3)): 23/41 ≈ 0.561
      ├── Some((2, 5)): 20/38 ≈ 0.526
      ├── Some((2, 6)): 3/16 ≈ 0.188
      ├── Some((2, 7)): 18/35 ≈ 0.514
      └── Some((2, 8)): 28/47 ≈ 0.596
    ├── Some((4, 3)): 241/427 ≈ 0.564
      ├── Some((3, 0)): 29/51 ≈ 0.569
      ├── Some((3, 1)): 22/42 ≈ 0.524
      ├── Some((3, 2)): 17/36 ≈ 0.472
      ├── Some((3, 3)): 32/54 ≈ 0.593
      ├── Some((3, 4)): 24/44 ≈ 0.545
      ├── Some((3, 5)): 12/29 ≈ 0.414
      ├── Some((3, 6)): 51/76 ≈ 0.671
      ├── Some((3, 7)): 15/33 ≈ 0.455
      └── Some((3, 8)): 38/61 ≈ 0.623
    ├── Some((4, 4)): 226/404 ≈ 0.559
      ├── Some((4, 0)): 22/43 ≈ 0.512
      ├── Some((4, 1)): 25/47 ≈ 0.532
      ├── Some((4, 2)): 24/46 ≈ 0.522
      ├── Some((4, 3)): 30/53 ≈ 0.566
      ├── Some((4, 5)): 12/30 ≈ 0.400
      ├── Some((4, 6)): 43/68 ≈ 0.632
      ├── Some((4, 7)): 38/62 ≈ 0.613
      └── Some((4, 8)): 31/54 ≈ 0.574
    ├── Some((4, 5)): 88/190 ≈ 0.463
      ├── Some((5, 0)): 17/30 ≈ 0.567
      ├── Some((5, 1)): 7/18 ≈ 0.389
      ├── Some((5, 2)): 2/11 ≈ 0.182
      ├── Some((5, 3)): 7/18 ≈ 0.389
      ├── Some((5, 4)): 15/27 ≈ 0.556
      ├── Some((5, 5)): 10/22 ≈ 0.455
      ├── Some((5, 6)): 7/18 ≈ 0.389
      ├── Some((5, 7)): 4/14 ≈ 0.286
      └── Some((5, 8)): 18/31 ≈ 0.581
    ├── Some((4, 6)): 125/249 ≈ 0.502
      ├── Some((6, 0)): 6/19 ≈ 0.316
      ├── Some((6, 1)): 22/39 ≈ 0.564
      ├── Some((6, 3)): 5/18 ≈ 0.278
      ├── Some((6, 4)): 15/31 ≈ 0.484
      ├── Some((6, 5)): 19/35 ≈ 0.543
      ├── Some((6, 6)): 21/38 ≈ 0.553
      ├── Some((6, 7)): 22/39 ≈ 0.564
      └── Some((6, 8)): 14/29 ≈ 0.483
    ├── Some((4, 7)): 156/298 ≈ 0.523
      ├── Some((7, 0)): 15/30 ≈ 0.500
      ├── Some((7, 1)): 11/26 ≈ 0.423
      ├── Some((7, 2)): 20/36 ≈ 0.556
      ├── Some((7, 3)): 12/27 ≈ 0.444
      ├── Some((7, 4)): 23/40 ≈ 0.575
      ├── Some((7, 5)): 14/29 ≈ 0.483
      ├── Some((7, 6)): 19/35 ≈ 0.543
      ├── Some((7, 7)): 21/38 ≈ 0.553
      └── Some((7, 8)): 20/36 ≈ 0.556
    └── Some((4, 8)): 203/369 ≈ 0.550
      ├── Some((8, 0)): 18/36 ≈ 0.500
      ├── Some((8, 1)): 16/33 ≈ 0.485
      ├── Some((8, 2)): 16/33 ≈ 0.485
      ├── Some((8, 3)): 9/24 ≈ 0.375
      ├── Some((8, 4)): 14/31 ≈ 0.452
      ├── Some((8, 5)): 35/56 ≈ 0.625
      ├── Some((8, 6)): 32/52 ≈ 0.615
      ├── Some((8, 7)): 32/53 ≈ 0.604
      └── Some((8, 8)): 30/50 ≈ 0.600
  ├── Some((2, 5)): 1490/2784 ≈ 0.535
    ├── Some((5, 0)): 122/243 ≈ 0.502
      ├── Some((0, 0)): 24/39 ≈ 0.615
      ├── Some((0, 1)): 15/29 ≈ 0.517
      ├── Some((0, 2)): 27/42 ≈ 0.643
      ├── Some((0, 3)): 6/18 ≈ 0.333
      ├── Some((0, 4)): 14/28 ≈ 0.500
      ├── Some((0, 5)): 15/29 ≈ 0.517
      ├── Some((0, 6)): 5/17 ≈ 0.294
      ├── Some((0, 7)): 8/20 ≈ 0.400
      └── Some((0, 8)): 8/20 ≈ 0.400
    ├── Some((5, 1)): 231/409 ≈ 0.565
      ├── Some((1, 0)): 24/44 ≈ 0.545
      ├── Some((1, 1)): 35/57 ≈ 0.614
      ├── Some((1, 2)): 38/60 ≈ 0.633
      ├── Some((1, 3)): 33/55 ≈ 0.600
      ├── Some((1, 4)): 22/41 ≈ 0.537
      ├── Some((1, 5)): 15/33 ≈ 0.455
      ├── Some((1, 6)): 22/41 ≈ 0.537
      ├── Some((1, 7)): 5/19 ≈ 0.263
      └── Some((1, 8)): 36/58 ≈ 0.621
    ├── Some((5, 2)): 203/367 ≈ 0.553
      ├── Some((2, 0)): 34/56 ≈ 0.607
      ├── Some((2, 1)): 26/47 ≈ 0.553
      ├── Some((2, 2)): 24/44 ≈ 0.545
      ├── Some((2, 3)): 28/49 ≈ 0.571
      ├── Some((2, 4)): 16/34 ≈ 0.471
      ├── Some((2, 6)): 24/44 ≈ 0.545
      ├── Some((2, 7)): 24/44 ≈ 0.545
      └── Some((2, 8)): 27/48 ≈ 0.562
    ├── Some((5, 3)): 128/253 ≈ 0.506
      ├── Some((3, 0)): 15/29 ≈ 0.517
      ├── Some((3, 1)): 10/23 ≈ 0.435
      ├── Some((3, 2)): 14/28 ≈ 0.500
      ├── Some((3, 3)): 12/26 ≈ 0.462
      ├── Some((3, 4)): 11/24 ≈ 0.458
      ├── Some((3, 5)): 11/24 ≈ 0.458
      ├── Some((3, 6)): 20/35 ≈ 0.571
      ├── Some((3, 7)): 21/36 ≈ 0.583
      └── Some((3, 8)): 13/27 ≈ 0.481
    ├── Some((5, 4)): 105/216 ≈ 0.486
      ├── Some((4, 0)): 7/19 ≈ 0.368
      ├── Some((4, 1)): 5/16 ≈ 0.312
      ├── Some((4, 2)): 16/29 ≈ 0.552
      ├── Some((4, 3)): 5/16 ≈ 0.312
      ├── Some((4, 4)): 12/25 ≈ 0.480
      ├── Some((4, 5)): 18/31 ≈ 0.581
      ├── Some((4, 6)): 22/36 ≈ 0.611
      ├── Some((4, 7)): 10/22 ≈ 0.455
      └── Some((4, 8)): 9/21 ≈ 0.429
    ├── Some((5, 5)): 262/455 ≈ 0.576
      ├── Some((5, 0)): 14/33 ≈ 0.424
      ├── Some((5, 1)): 28/51 ≈ 0.549
      ├── Some((5, 2)): 38/64 ≈ 0.594
      ├── Some((5, 3)): 23/45 ≈ 0.511
      ├── Some((5, 4)): 40/66 ≈ 0.606
      ├── Some((5, 6)): 30/54 ≈ 0.556
      ├── Some((5, 7)): 41/67 ≈ 0.612
      └── Some((5, 8)): 47/74 ≈ 0.635
    ├── Some((5, 6)): 175/325 ≈ 0.538
      ├── Some((6, 0)): 18/36 ≈ 0.500
      ├── Some((6, 1)): 32/53 ≈ 0.604
      ├── Some((6, 3)): 30/51 ≈ 0.588
      ├── Some((6, 4)): 24/43 ≈ 0.558
      ├── Some((6, 5)): 23/42 ≈ 0.548
      ├── Some((6, 6)): 16/34 ≈ 0.471
      ├── Some((6, 7)): 28/48 ≈ 0.583
      └── Some((6, 8)): 4/17 ≈ 0.235
    ├── Some((5, 7)): 90/192 ≈ 0.469
      ├── Some((7, 0)): 17/29 ≈ 0.586
      ├── Some((7, 1)): 8/19 ≈ 0.421
      ├── Some((7, 2)): 8/19 ≈ 0.421
      ├── Some((7, 3)): 7/18 ≈ 0.389
      ├── Some((7, 4)): 12/24 ≈ 0.500
      ├── Some((7, 5)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 8/19 ≈ 0.421
      ├── Some((7, 7)): 10/22 ≈ 0.455
      └── Some((7, 8)): 9/20 ≈ 0.450
    └── Some((5, 8)): 174/323 ≈ 0.539
      ├── Some((8, 0)): 10/25 ≈ 0.400
      ├── Some((8, 1)): 33/52 ≈ 0.635
      ├── Some((8, 2)): 16/32 ≈ 0.500
      ├── Some((8, 3)): 21/38 ≈ 0.553
      ├── Some((8, 4)): 12/27 ≈ 0.444
      ├── Some((8, 5)): 19/36 ≈ 0.528
      ├── Some((8, 6)): 30/48 ≈ 0.625
      ├── Some((8, 7)): 25/43 ≈ 0.581
      └── Some((8, 8)): 7/21 ≈ 0.333
  ├── Some((2, 6)): 1429/2679 ≈ 0.533
    ├── Some((6, 0)): 153/296 ≈ 0.517
      ├── Some((0, 0)): 10/25 ≈ 0.400
      ├── Some((0, 1)): 4/16 ≈ 0.250
      ├── Some((0, 2)): 20/37 ≈ 0.541
      ├── Some((0, 3)): 18/34 ≈ 0.529
      ├── Some((0, 4)): 16/32 ≈ 0.500
      ├── Some((0, 5)): 23/40 ≈ 0.575
      ├── Some((0, 6)): 27/45 ≈ 0.600
      ├── Some((0, 7)): 23/40 ≈ 0.575
      └── Some((0, 8)): 11/26 ≈ 0.423
    ├── Some((6, 1)): 251/446 ≈ 0.563
      ├── Some((1, 0)): 21/41 ≈ 0.512
      ├── Some((1, 1)): 24/45 ≈ 0.533
      ├── Some((1, 2)): 33/56 ≈ 0.589
      ├── Some((1, 3)): 25/46 ≈ 0.543
      ├── Some((1, 4)): 22/43 ≈ 0.512
      ├── Some((1, 5)): 16/35 ≈ 0.457
      ├── Some((1, 6)): 60/87 ≈ 0.690
      ├── Some((1, 7)): 21/42 ≈ 0.500
      └── Some((1, 8)): 28/50 ≈ 0.560
    ├── Some((6, 3)): 83/184 ≈ 0.451
      ├── Some((3, 0)): 12/24 ≈ 0.500
      ├── Some((3, 1)): 15/27 ≈ 0.556
      ├── Some((3, 2)): 13/25 ≈ 0.520
      ├── Some((3, 3)): 15/27 ≈ 0.556
      ├── Some((3, 4)): 2/11 ≈ 0.182
      ├── Some((3, 5)): 5/16 ≈ 0.312
      ├── Some((3, 6)): 2/11 ≈ 0.182
      ├── Some((3, 7)): 9/20 ≈ 0.450
      └── Some((3, 8)): 10/22 ≈ 0.455
    ├── Some((6, 4)): 155/299 ≈ 0.518
      ├── Some((4, 0)): 17/33 ≈ 0.515
      ├── Some((4, 1)): 16/32 ≈ 0.500
      ├── Some((4, 2)): 15/31 ≈ 0.484
      ├── Some((4, 3)): 20/37 ≈ 0.541
      ├── Some((4, 4)): 4/17 ≈ 0.235
      ├── Some((4, 5)): 9/23 ≈ 0.391
      ├── Some((4, 6)): 36/55 ≈ 0.655
      ├── Some((4, 7)): 24/42 ≈ 0.571
      └── Some((4, 8)): 13/28 ≈ 0.464
    ├── Some((6, 5)): 246/439 ≈ 0.560
      ├── Some((5, 0)): 26/47 ≈ 0.553
      ├── Some((5, 1)): 19/39 ≈ 0.487
      ├── Some((5, 2)): 20/40 ≈ 0.500
      ├── Some((5, 3)): 49/74 ≈ 0.662
      ├── Some((5, 4)): 37/60 ≈ 0.617
      ├── Some((5, 5)): 31/53 ≈ 0.585
      ├── Some((5, 6)): 22/43 ≈ 0.512
      ├── Some((5, 7)): 14/32 ≈ 0.438
      └── Some((5, 8)): 28/50 ≈ 0.560
    ├── Some((6, 6)): 223/404 ≈ 0.552
      ├── Some((6, 0)): 29/55 ≈ 0.527
      ├── Some((6, 1)): 23/47 ≈ 0.489
      ├── Some((6, 3)): 16/37 ≈ 0.432
      ├── Some((6, 4)): 31/57 ≈ 0.544
      ├── Some((6, 5)): 61/93 ≈ 0.656
      ├── Some((6, 7)): 25/49 ≈ 0.510
      └── Some((6, 8)): 37/65 ≈ 0.569
    ├── Some((6, 7)): 170/323 ≈ 0.526
      ├── Some((7, 0)): 17/34 ≈ 0.500
      ├── Some((7, 1)): 35/55 ≈ 0.636
      ├── Some((7, 2)): 16/32 ≈ 0.500
      ├── Some((7, 3)): 8/22 ≈ 0.364
      ├── Some((7, 4)): 23/41 ≈ 0.561
      ├── Some((7, 5)): 11/26 ≈ 0.423
      ├── Some((7, 6)): 23/41 ≈ 0.561
      ├── Some((7, 7)): 14/30 ≈ 0.467
      └── Some((7, 8)): 23/41 ≈ 0.561
    └── Some((6, 8)): 147/287 ≈ 0.512
      ├── Some((8, 0)): 15/30 ≈ 0.500
      ├── Some((8, 1)): 31/49 ≈ 0.633
      ├── Some((8, 2)): 18/34 ≈ 0.529
      ├── Some((8, 3)): 1/12 ≈ 0.083
      ├── Some((8, 4)): 17/33 ≈ 0.515
      ├── Some((8, 5)): 23/40 ≈ 0.575
      ├── Some((8, 6)): 13/28 ≈ 0.464
      ├── Some((8, 7)): 15/31 ≈ 0.484
      └── Some((8, 8)): 14/29 ≈ 0.483
  ├── Some((2, 7)): 1414/2653 ≈ 0.533
    ├── Some((7, 0)): 119/236 ≈ 0.504
      ├── Some((0, 0)): 15/28 ≈ 0.536
      ├── Some((0, 1)): 17/30 ≈ 0.567
      ├── Some((0, 2)): 18/32 ≈ 0.562
      ├── Some((0, 3)): 8/20 ≈ 0.400
      ├── Some((0, 4)): 20/34 ≈ 0.588
      ├── Some((0, 5)): 9/21 ≈ 0.429
      ├── Some((0, 6)): 11/24 ≈ 0.458
      ├── Some((0, 7)): 11/24 ≈ 0.458
      └── Some((0, 8)): 10/22 ≈ 0.455
    ├── Some((7, 1)): 202/363 ≈ 0.556
      ├── Some((1, 0)): 31/50 ≈ 0.620
      ├── Some((1, 1)): 23/41 ≈ 0.561
      ├── Some((1, 2)): 17/34 ≈ 0.500
      ├── Some((1, 3)): 25/43 ≈ 0.581
      ├── Some((1, 4)): 25/43 ≈ 0.581
      ├── Some((1, 5)): 23/41 ≈ 0.561
      ├── Some((1, 6)): 21/39 ≈ 0.538
      ├── Some((1, 7)): 11/26 ≈ 0.423
      └── Some((1, 8)): 26/45 ≈ 0.578
    ├── Some((7, 2)): 156/293 ≈ 0.532
      ├── Some((2, 0)): 14/30 ≈ 0.467
      ├── Some((2, 1)): 8/22 ≈ 0.364
      ├── Some((2, 2)): 35/55 ≈ 0.636
      ├── Some((2, 3)): 19/36 ≈ 0.528
      ├── Some((2, 4)): 11/26 ≈ 0.423
      ├── Some((2, 5)): 23/41 ≈ 0.561
      ├── Some((2, 6)): 25/43 ≈ 0.581
      └── Some((2, 8)): 21/39 ≈ 0.538
    ├── Some((7, 3)): 132/257 ≈ 0.514
      ├── Some((3, 0)): 16/30 ≈ 0.533
      ├── Some((3, 1)): 11/24 ≈ 0.458
      ├── Some((3, 2)): 15/29 ≈ 0.517
      ├── Some((3, 3)): 15/29 ≈ 0.517
      ├── Some((3, 4)): 14/28 ≈ 0.500
      ├── Some((3, 5)): 11/24 ≈ 0.458
      ├── Some((3, 6)): 14/28 ≈ 0.500
      ├── Some((3, 7)): 24/40 ≈ 0.600
      └── Some((3, 8)): 11/24 ≈ 0.458
    ├── Some((7, 4)): 115/230 ≈ 0.500
      ├── Some((4, 0)): 7/19 ≈ 0.368
      ├── Some((4, 1)): 8/20 ≈ 0.400
      ├── Some((4, 2)): 14/27 ≈ 0.519
      ├── Some((4, 3)): 6/17 ≈ 0.353
      ├── Some((4, 4)): 18/32 ≈ 0.562
      ├── Some((4, 5)): 10/22 ≈ 0.455
      ├── Some((4, 6)): 27/42 ≈ 0.643
      ├── Some((4, 7)): 19/33 ≈ 0.576
      └── Some((4, 8)): 6/17 ≈ 0.353
    ├── Some((7, 5)): 173/319 ≈ 0.542
      ├── Some((5, 0)): 29/47 ≈ 0.617
      ├── Some((5, 1)): 15/30 ≈ 0.500
      ├── Some((5, 2)): 23/40 ≈ 0.575
      ├── Some((5, 3)): 15/31 ≈ 0.484
      ├── Some((5, 4)): 13/28 ≈ 0.464
      ├── Some((5, 5)): 25/42 ≈ 0.595
      ├── Some((5, 6)): 17/33 ≈ 0.515
      ├── Some((5, 7)): 15/31 ≈ 0.484
      └── Some((5, 8)): 20/36 ≈ 0.556
    ├── Some((7, 6)): 141/271 ≈ 0.520
      ├── Some((6, 0)): 9/23 ≈ 0.391
      ├── Some((6, 1)): 17/33 ≈ 0.515
      ├── Some((6, 3)): 21/38 ≈ 0.553
      ├── Some((6, 4)): 14/30 ≈ 0.467
      ├── Some((6, 5)): 15/31 ≈ 0.484
      ├── Some((6, 6)): 15/31 ≈ 0.484
      ├── Some((6, 7)): 25/43 ≈ 0.581
      └── Some((6, 8)): 24/41 ≈ 0.585
    ├── Some((7, 7)): 224/396 ≈ 0.566
      ├── Some((7, 0)): 12/30 ≈ 0.400
      ├── Some((7, 1)): 13/31 ≈ 0.419
      ├── Some((7, 2)): 32/55 ≈ 0.582
      ├── Some((7, 3)): 26/47 ≈ 0.553
      ├── Some((7, 4)): 39/63 ≈ 0.619
      ├── Some((7, 5)): 21/41 ≈ 0.512
      ├── Some((7, 6)): 38/62 ≈ 0.613
      └── Some((7, 8)): 42/66 ≈ 0.636
    └── Some((7, 8)): 152/287 ≈ 0.530
      ├── Some((8, 0)): 15/30 ≈ 0.500
      ├── Some((8, 1)): 14/29 ≈ 0.483
      ├── Some((8, 2)): 14/29 ≈ 0.483
      ├── Some((8, 3)): 30/47 ≈ 0.638
      ├── Some((8, 4)): 18/33 ≈ 0.545
      ├── Some((8, 5)): 25/41 ≈ 0.610
      ├── Some((8, 6)): 7/20 ≈ 0.350
      ├── Some((8, 7)): 21/37 ≈ 0.568
      └── Some((8, 8)): 7/20 ≈ 0.350
  └── Some((2, 8)): 1487/2779 ≈ 0.535
    ├── Some((8, 0)): 183/337 ≈ 0.543
      ├── Some((0, 0)): 35/55 ≈ 0.636
      ├── Some((0, 1)): 35/55 ≈ 0.636
      ├── Some((0, 2)): 10/25 ≈ 0.400
      ├── Some((0, 3)): 15/31 ≈ 0.484
      ├── Some((0, 4)): 28/47 ≈ 0.596
      ├── Some((0, 5)): 6/20 ≈ 0.300
      ├── Some((0, 6)): 27/45 ≈ 0.600
      ├── Some((0, 7)): 4/17 ≈ 0.235
      └── Some((0, 8)): 23/41 ≈ 0.561
    ├── Some((8, 1)): 164/308 ≈ 0.532
      ├── Some((1, 0)): 15/31 ≈ 0.484
      ├── Some((1, 1)): 13/28 ≈ 0.464
      ├── Some((1, 2)): 24/41 ≈ 0.585
      ├── Some((1, 3)): 14/29 ≈ 0.483
      ├── Some((1, 4)): 27/44 ≈ 0.614
      ├── Some((1, 5)): 26/43 ≈ 0.605
      ├── Some((1, 6)): 11/26 ≈ 0.423
      ├── Some((1, 7)): 10/24 ≈ 0.417
      └── Some((1, 8)): 24/41 ≈ 0.585
    ├── Some((8, 2)): 202/365 ≈ 0.553
      ├── Some((2, 0)): 20/39 ≈ 0.513
      ├── Some((2, 1)): 32/54 ≈ 0.593
      ├── Some((2, 2)): 26/47 ≈ 0.553
      ├── Some((2, 3)): 22/42 ≈ 0.524
      ├── Some((2, 4)): 29/50 ≈ 0.580
      ├── Some((2, 5)): 13/31 ≈ 0.419
      ├── Some((2, 6)): 40/63 ≈ 0.635
      └── Some((2, 7)): 19/38 ≈ 0.500
    ├── Some((8, 3)): 184/338 ≈ 0.544
      ├── Some((3, 0)): 15/31 ≈ 0.484
      ├── Some((3, 1)): 5/18 ≈ 0.278
      ├── Some((3, 2)): 32/51 ≈ 0.627
      ├── Some((3, 3)): 30/49 ≈ 0.612
      ├── Some((3, 4)): 20/37 ≈ 0.541
      ├── Some((3, 5)): 15/31 ≈ 0.484
      ├── Some((3, 6)): 27/46 ≈ 0.587
      ├── Some((3, 7)): 29/48 ≈ 0.604
      └── Some((3, 8)): 11/26 ≈ 0.423
    ├── Some((8, 4)): 106/218 ≈ 0.486
      ├── Some((4, 0)): 21/35 ≈ 0.600
      ├── Some((4, 1)): 10/22 ≈ 0.455
      ├── Some((4, 2)): 15/28 ≈ 0.536
      ├── Some((4, 3)): 18/32 ≈ 0.562
      ├── Some((4, 4)): 14/27 ≈ 0.519
      ├── Some((4, 5)): 6/17 ≈ 0.353
      ├── Some((4, 6)): 6/18 ≈ 0.333
      ├── Some((4, 7)): 5/16 ≈ 0.312
      └── Some((4, 8)): 10/22 ≈ 0.455
    ├── Some((8, 5)): 235/415 ≈ 0.566
      ├── Some((5, 0)): 34/55 ≈ 0.618
      ├── Some((5, 1)): 20/39 ≈ 0.513
      ├── Some((5, 2)): 41/63 ≈ 0.651
      ├── Some((5, 3)): 23/43 ≈ 0.535
      ├── Some((5, 4)): 34/55 ≈ 0.618
      ├── Some((5, 5)): 20/39 ≈ 0.513
      ├── Some((5, 6)): 27/47 ≈ 0.574
      ├── Some((5, 7)): 20/39 ≈ 0.513
      └── Some((5, 8)): 16/34 ≈ 0.471
    ├── Some((8, 6)): 67/155 ≈ 0.432
      ├── Some((6, 0)): 4/14 ≈ 0.286
      ├── Some((6, 1)): 16/28 ≈ 0.571
      ├── Some((6, 3)): 5/15 ≈ 0.333
      ├── Some((6, 4)): 6/17 ≈ 0.353
      ├── Some((6, 5)): 15/27 ≈ 0.556
      ├── Some((6, 6)): 3/13 ≈ 0.231
      ├── Some((6, 7)): 11/23 ≈ 0.478
      └── Some((6, 8)): 6/17 ≈ 0.353
    ├── Some((8, 7)): 158/298 ≈ 0.530
      ├── Some((7, 0)): 19/35 ≈ 0.543
      ├── Some((7, 1)): 14/29 ≈ 0.483
      ├── Some((7, 2)): 25/42 ≈ 0.595
      ├── Some((7, 3)): 22/38 ≈ 0.579
      ├── Some((7, 4)): 15/30 ≈ 0.500
      ├── Some((7, 5)): 13/28 ≈ 0.464
      ├── Some((7, 6)): 18/34 ≈ 0.529
      ├── Some((7, 7)): 24/41 ≈ 0.585
      └── Some((7, 8)): 7/20 ≈ 0.350
    └── Some((8, 8)): 188/344 ≈ 0.547
      ├── Some((8, 0)): 13/30 ≈ 0.433
      ├── Some((8, 1)): 21/40 ≈ 0.525
      ├── Some((8, 2)): 15/33 ≈ 0.455
      ├── Some((8, 3)): 51/75 ≈ 0.680
      ├── Some((8, 4)): 17/35 ≈ 0.486
      ├── Some((8, 5)): 25/45 ≈ 0.556
      ├── Some((8, 6)): 28/49 ≈ 0.571
      └── Some((8, 7)): 18/36 ≈ 0.500
├── Some((6, 3)): 7664/14628 ≈ 0.524
  ├── Some((3, 0)): 1047/1963 ≈ 0.533
    ├── Some((0, 0)): 129/237 ≈ 0.544
      ├── Some((0, 1)): 14/27 ≈ 0.519
      ├── Some((0, 2)): 14/27 ≈ 0.519
      ├── Some((0, 3)): 13/26 ≈ 0.500
      ├── Some((0, 4)): 18/32 ≈ 0.562
      ├── Some((0, 5)): 20/34 ≈ 0.588
      ├── Some((0, 6)): 22/36 ≈ 0.611
      ├── Some((0, 7)): 21/35 ≈ 0.600
      └── Some((0, 8)): 7/19 ≈ 0.368
    ├── Some((0, 1)): 109/207 ≈ 0.527
      ├── Some((1, 0)): 4/13 ≈ 0.308
      ├── Some((1, 1)): 15/26 ≈ 0.577
      ├── Some((1, 2)): 24/36 ≈ 0.667
      ├── Some((1, 3)): 10/21 ≈ 0.476
      ├── Some((1, 4)): 14/25 ≈ 0.560
      ├── Some((1, 5)): 10/21 ≈ 0.476
      ├── Some((1, 6)): 14/25 ≈ 0.560
      ├── Some((1, 7)): 7/17 ≈ 0.412
      └── Some((1, 8)): 11/22 ≈ 0.500
    ├── Some((0, 2)): 114/215 ≈ 0.530
      ├── Some((2, 0)): 17/29 ≈ 0.586
      ├── Some((2, 1)): 3/13 ≈ 0.231
      ├── Some((2, 2)): 16/28 ≈ 0.571
      ├── Some((2, 3)): 6/16 ≈ 0.375
      ├── Some((2, 4)): 19/31 ≈ 0.613
      ├── Some((2, 5)): 11/22 ≈ 0.500
      ├── Some((2, 6)): 8/19 ≈ 0.421
      ├── Some((2, 7)): 25/37 ≈ 0.676
      └── Some((2, 8)): 8/19 ≈ 0.421
    ├── Some((0, 3)): 103/198 ≈ 0.520
      ├── Some((3, 1)): 14/26 ≈ 0.538
      ├── Some((3, 2)): 14/26 ≈ 0.538
      ├── Some((3, 3)): 12/24 ≈ 0.500
      ├── Some((3, 4)): 9/20 ≈ 0.450
      ├── Some((3, 5)): 13/25 ≈ 0.520
      ├── Some((3, 6)): 10/21 ≈ 0.476
      ├── Some((3, 7)): 7/18 ≈ 0.389
      └── Some((3, 8)): 24/37 ≈ 0.649
    ├── Some((0, 4)): 128/236 ≈ 0.542
      ├── Some((4, 0)): 7/18 ≈ 0.389
      ├── Some((4, 1)): 11/23 ≈ 0.478
      ├── Some((4, 2)): 17/29 ≈ 0.586
      ├── Some((4, 3)): 14/26 ≈ 0.538
      ├── Some((4, 4)): 17/29 ≈ 0.586
      ├── Some((4, 5)): 19/32 ≈ 0.594
      ├── Some((4, 6)): 10/22 ≈ 0.455
      ├── Some((4, 7)): 14/26 ≈ 0.538
      └── Some((4, 8)): 18/30 ≈ 0.600
    ├── Some((0, 5)): 143/258 ≈ 0.554
      ├── Some((5, 0)): 16/29 ≈ 0.552
      ├── Some((5, 1)): 19/32 ≈ 0.594
      ├── Some((5, 2)): 15/28 ≈ 0.536
      ├── Some((5, 3)): 38/53 ≈ 0.717
      ├── Some((5, 4)): 8/20 ≈ 0.400
      ├── Some((5, 5)): 16/29 ≈ 0.552
      ├── Some((5, 6)): 12/25 ≈ 0.480
      ├── Some((5, 7)): 15/28 ≈ 0.536
      └── Some((5, 8)): 3/13 ≈ 0.231
    ├── Some((0, 6)): 115/216 ≈ 0.532
      ├── Some((6, 0)): 31/45 ≈ 0.689
      ├── Some((6, 1)): 8/20 ≈ 0.400
      ├── Some((6, 2)): 9/21 ≈ 0.429
      ├── Some((6, 4)): 13/26 ≈ 0.500
      ├── Some((6, 5)): 7/19 ≈ 0.368
      ├── Some((6, 6)): 25/39 ≈ 0.641
      ├── Some((6, 7)): 15/28 ≈ 0.536
      └── Some((6, 8)): 6/17 ≈ 0.353
    ├── Some((0, 7)): 106/203 ≈ 0.522
      ├── Some((7, 0)): 20/32 ≈ 0.625
      ├── Some((7, 1)): 13/24 ≈ 0.542
      ├── Some((7, 2)): 9/20 ≈ 0.450
      ├── Some((7, 3)): 13/24 ≈ 0.542
      ├── Some((7, 4)): 8/18 ≈ 0.444
      ├── Some((7, 5)): 13/24 ≈ 0.542
      ├── Some((7, 6)): 15/26 ≈ 0.577
      ├── Some((7, 7)): 7/17 ≈ 0.412
      └── Some((7, 8)): 7/17 ≈ 0.412
    └── Some((0, 8)): 99/192 ≈ 0.516
      ├── Some((8, 0)): 8/18 ≈ 0.444
      ├── Some((8, 1)): 7/17 ≈ 0.412
      ├── Some((8, 2)): 15/26 ≈ 0.577
      ├── Some((8, 3)): 10/21 ≈ 0.476
      ├── Some((8, 4)): 1/9 ≈ 0.111
      ├── Some((8, 5)): 9/19 ≈ 0.474
      ├── Some((8, 6)): 7/17 ≈ 0.412
      ├── Some((8, 7)): 26/38 ≈ 0.684
      └── Some((8, 8)): 15/26 ≈ 0.577
  ├── Some((3, 1)): 505/1025 ≈ 0.493
    ├── Some((1, 0)): 51/107 ≈ 0.477
      ├── Some((0, 0)): 5/11 ≈ 0.455
      ├── Some((0, 1)): 7/13 ≈ 0.538
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 2/8 ≈ 0.250
      ├── Some((0, 4)): 1/7 ≈ 0.143
      ├── Some((0, 5)): 4/10 ≈ 0.400
      ├── Some((0, 6)): 7/13 ≈ 0.538
      ├── Some((0, 7)): 7/14 ≈ 0.500
      └── Some((0, 8)): 11/17 ≈ 0.647
    ├── Some((1, 1)): 38/87 ≈ 0.437
      ├── Some((1, 0)): 1/7 ≈ 0.143
      ├── Some((1, 2)): 3/9 ≈ 0.333
      ├── Some((1, 3)): 9/15 ≈ 0.600
      ├── Some((1, 4)): 9/16 ≈ 0.562
      ├── Some((1, 5)): 6/12 ≈ 0.500
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 1/7 ≈ 0.143
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((1, 2)): 61/121 ≈ 0.504
      ├── Some((2, 0)): 11/17 ≈ 0.647
      ├── Some((2, 1)): 7/14 ≈ 0.500
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 7/14 ≈ 0.500
      ├── Some((2, 4)): 11/18 ≈ 0.611
      ├── Some((2, 5)): 10/17 ≈ 0.588
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 3/9 ≈ 0.333
    ├── Some((1, 3)): 48/102 ≈ 0.471
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 16/23 ≈ 0.696
      ├── Some((3, 5)): 3/10 ≈ 0.300
      ├── Some((3, 6)): 5/12 ≈ 0.417
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 7/14 ≈ 0.500
    ├── Some((1, 4)): 59/118 ≈ 0.500
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 11/18 ≈ 0.611
      ├── Some((4, 3)): 1/7 ≈ 0.143
      ├── Some((4, 4)): 9/16 ≈ 0.562
      ├── Some((4, 5)): 2/8 ≈ 0.250
      ├── Some((4, 6)): 4/10 ≈ 0.400
      ├── Some((4, 7)): 11/18 ≈ 0.611
      └── Some((4, 8)): 8/15 ≈ 0.533
    ├── Some((1, 5)): 66/128 ≈ 0.516
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 1)): 2/8 ≈ 0.250
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 5/12 ≈ 0.417
      ├── Some((5, 4)): 11/18 ≈ 0.611
      ├── Some((5, 5)): 17/24 ≈ 0.708
      ├── Some((5, 6)): 3/10 ≈ 0.300
      ├── Some((5, 7)): 9/16 ≈ 0.562
      └── Some((5, 8)): 8/15 ≈ 0.533
    ├── Some((1, 6)): 49/104 ≈ 0.471
      ├── Some((6, 0)): 1/7 ≈ 0.143
      ├── Some((6, 1)): 15/22 ≈ 0.682
      ├── Some((6, 2)): 11/19 ≈ 0.579
      ├── Some((6, 4)): 1/7 ≈ 0.143
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 6/13 ≈ 0.462
      ├── Some((6, 7)): 5/12 ≈ 0.417
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((1, 7)): 85/156 ≈ 0.545
      ├── Some((7, 0)): 4/11 ≈ 0.364
      ├── Some((7, 1)): 13/21 ≈ 0.619
      ├── Some((7, 2)): 16/24 ≈ 0.667
      ├── Some((7, 3)): 12/20 ≈ 0.600
      ├── Some((7, 4)): 3/10 ≈ 0.300
      ├── Some((7, 5)): 9/17 ≈ 0.529
      ├── Some((7, 6)): 14/22 ≈ 0.636
      ├── Some((7, 7)): 8/16 ≈ 0.500
      └── Some((7, 8)): 6/14 ≈ 0.429
    └── Some((1, 8)): 47/101 ≈ 0.465
      ├── Some((8, 0)): 2/8 ≈ 0.250
      ├── Some((8, 1)): 7/13 ≈ 0.538
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 6/12 ≈ 0.500
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 1/7 ≈ 0.143
      ├── Some((8, 7)): 10/16 ≈ 0.625
      └── Some((8, 8)): 6/12 ≈ 0.500
  ├── Some((3, 2)): 1030/1934 ≈ 0.533
    ├── Some((2, 0)): 104/200 ≈ 0.520
      ├── Some((0, 0)): 3/12 ≈ 0.250
      ├── Some((0, 1)): 16/27 ≈ 0.593
      ├── Some((0, 2)): 18/29 ≈ 0.621
      ├── Some((0, 3)): 11/22 ≈ 0.500
      ├── Some((0, 4)): 12/23 ≈ 0.522
      ├── Some((0, 5)): 3/12 ≈ 0.250
      ├── Some((0, 6)): 11/22 ≈ 0.500
      ├── Some((0, 7)): 16/27 ≈ 0.593
      └── Some((0, 8)): 14/25 ≈ 0.560
    ├── Some((2, 1)): 72/151 ≈ 0.477
      ├── Some((1, 0)): 1/9 ≈ 0.111
      ├── Some((1, 1)): 9/18 ≈ 0.500
      ├── Some((1, 2)): 15/24 ≈ 0.625
      ├── Some((1, 3)): 8/17 ≈ 0.471
      ├── Some((1, 4)): 5/14 ≈ 0.357
      ├── Some((1, 5)): 4/12 ≈ 0.333
      ├── Some((1, 6)): 10/19 ≈ 0.526
      ├── Some((1, 7)): 9/18 ≈ 0.500
      └── Some((1, 8)): 10/19 ≈ 0.526
    ├── Some((2, 2)): 128/236 ≈ 0.542
      ├── Some((2, 0)): 9/21 ≈ 0.429
      ├── Some((2, 1)): 12/25 ≈ 0.480
      ├── Some((2, 3)): 16/29 ≈ 0.552
      ├── Some((2, 4)): 18/32 ≈ 0.562
      ├── Some((2, 5)): 26/41 ≈ 0.634
      ├── Some((2, 6)): 21/35 ≈ 0.600
      ├── Some((2, 7)): 18/32 ≈ 0.562
      └── Some((2, 8)): 8/20 ≈ 0.400
    ├── Some((2, 3)): 92/182 ≈ 0.505
      ├── Some((3, 0)): 9/20 ≈ 0.450
      ├── Some((3, 1)): 4/14 ≈ 0.286
      ├── Some((3, 3)): 7/18 ≈ 0.389
      ├── Some((3, 4)): 19/31 ≈ 0.613
      ├── Some((3, 5)): 5/15 ≈ 0.333
      ├── Some((3, 6)): 17/29 ≈ 0.586
      ├── Some((3, 7)): 10/21 ≈ 0.476
      └── Some((3, 8)): 20/33 ≈ 0.606
    ├── Some((2, 4)): 187/321 ≈ 0.583
      ├── Some((4, 0)): 32/48 ≈ 0.667
      ├── Some((4, 1)): 28/44 ≈ 0.636
      ├── Some((4, 2)): 9/22 ≈ 0.409
      ├── Some((4, 3)): 22/37 ≈ 0.595
      ├── Some((4, 4)): 11/25 ≈ 0.440
      ├── Some((4, 5)): 27/43 ≈ 0.628
      ├── Some((4, 6)): 22/37 ≈ 0.595
      ├── Some((4, 7)): 22/37 ≈ 0.595
      └── Some((4, 8)): 13/27 ≈ 0.481
    ├── Some((2, 5)): 170/297 ≈ 0.572
      ├── Some((5, 0)): 13/26 ≈ 0.500
      ├── Some((5, 1)): 21/35 ≈ 0.600
      ├── Some((5, 2)): 14/28 ≈ 0.500
      ├── Some((5, 3)): 18/32 ≈ 0.562
      ├── Some((5, 4)): 24/39 ≈ 0.615
      ├── Some((5, 5)): 26/41 ≈ 0.634
      ├── Some((5, 6)): 18/32 ≈ 0.562
      ├── Some((5, 7)): 14/28 ≈ 0.500
      └── Some((5, 8)): 21/35 ≈ 0.600
    ├── Some((2, 6)): 121/226 ≈ 0.535
      ├── Some((6, 0)): 8/20 ≈ 0.400
      ├── Some((6, 1)): 24/39 ≈ 0.615
      ├── Some((6, 2)): 22/36 ≈ 0.611
      ├── Some((6, 4)): 25/40 ≈ 0.625
      ├── Some((6, 5)): 17/31 ≈ 0.548
      ├── Some((6, 6)): 4/15 ≈ 0.267
      ├── Some((6, 7)): 5/16 ≈ 0.312
      └── Some((6, 8)): 15/28 ≈ 0.536
    ├── Some((2, 7)): 51/118 ≈ 0.432
      ├── Some((7, 0)): 4/11 ≈ 0.364
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 9/17 ≈ 0.529
      ├── Some((7, 3)): 12/20 ≈ 0.600
      ├── Some((7, 4)): 5/12 ≈ 0.417
      ├── Some((7, 5)): 3/10 ≈ 0.300
      ├── Some((7, 6)): 6/14 ≈ 0.429
      ├── Some((7, 7)): 2/9 ≈ 0.222
      └── Some((7, 8)): 4/11 ≈ 0.364
    └── Some((2, 8)): 105/202 ≈ 0.520
      ├── Some((8, 0)): 4/14 ≈ 0.286
      ├── Some((8, 1)): 14/25 ≈ 0.560
      ├── Some((8, 2)): 13/24 ≈ 0.542
      ├── Some((8, 3)): 8/18 ≈ 0.444
      ├── Some((8, 4)): 8/18 ≈ 0.444
      ├── Some((8, 5)): 18/29 ≈ 0.621
      ├── Some((8, 6)): 10/21 ≈ 0.476
      ├── Some((8, 7)): 16/27 ≈ 0.593
      └── Some((8, 8)): 14/25 ≈ 0.560
  ├── Some((3, 3)): 593/1179 ≈ 0.503
    ├── Some((3, 0)): 64/132 ≈ 0.485
      ├── Some((0, 0)): 7/15 ≈ 0.467
      ├── Some((0, 1)): 10/18 ≈ 0.556
      ├── Some((0, 2)): 7/15 ≈ 0.467
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 9/17 ≈ 0.529
      ├── Some((0, 5)): 4/11 ≈ 0.364
      ├── Some((0, 6)): 12/20 ≈ 0.600
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((3, 1)): 96/180 ≈ 0.533
      ├── Some((1, 0)): 8/17 ≈ 0.471
      ├── Some((1, 1)): 3/11 ≈ 0.273
      ├── Some((1, 2)): 15/25 ≈ 0.600
      ├── Some((1, 3)): 24/34 ≈ 0.706
      ├── Some((1, 4)): 7/16 ≈ 0.438
      ├── Some((1, 5)): 3/11 ≈ 0.273
      ├── Some((1, 6)): 10/19 ≈ 0.526
      ├── Some((1, 7)): 12/22 ≈ 0.545
      └── Some((1, 8)): 14/24 ≈ 0.583
    ├── Some((3, 2)): 78/153 ≈ 0.510
      ├── Some((2, 0)): 5/13 ≈ 0.385
      ├── Some((2, 1)): 8/16 ≈ 0.500
      ├── Some((2, 2)): 7/15 ≈ 0.467
      ├── Some((2, 3)): 9/17 ≈ 0.529
      ├── Some((2, 4)): 8/16 ≈ 0.500
      ├── Some((2, 5)): 13/22 ≈ 0.591
      ├── Some((2, 6)): 12/21 ≈ 0.571
      ├── Some((2, 7)): 11/19 ≈ 0.579
      └── Some((2, 8)): 5/13 ≈ 0.385
    ├── Some((3, 4)): 72/145 ≈ 0.497
      ├── Some((4, 0)): 5/13 ≈ 0.385
      ├── Some((4, 1)): 5/13 ≈ 0.385
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 11/19 ≈ 0.579
      ├── Some((4, 4)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 12/21 ≈ 0.571
      ├── Some((4, 6)): 9/17 ≈ 0.529
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 3/11 ≈ 0.273
    ├── Some((3, 5)): 70/141 ≈ 0.496
      ├── Some((5, 0)): 13/21 ≈ 0.619
      ├── Some((5, 1)): 10/18 ≈ 0.556
      ├── Some((5, 2)): 4/12 ≈ 0.333
      ├── Some((5, 3)): 8/16 ≈ 0.500
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 14/22 ≈ 0.636
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 6/14 ≈ 0.429
      └── Some((5, 8)): 2/9 ≈ 0.222
    ├── Some((3, 6)): 70/142 ≈ 0.493
      ├── Some((6, 0)): 15/25 ≈ 0.600
      ├── Some((6, 1)): 2/10 ≈ 0.200
      ├── Some((6, 2)): 11/20 ≈ 0.550
      ├── Some((6, 4)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 8/17 ≈ 0.471
      ├── Some((6, 7)): 9/18 ≈ 0.500
      └── Some((6, 8)): 5/14 ≈ 0.357
    ├── Some((3, 7)): 97/182 ≈ 0.533
      ├── Some((7, 0)): 9/18 ≈ 0.500
      ├── Some((7, 1)): 1/9 ≈ 0.111
      ├── Some((7, 2)): 14/24 ≈ 0.583
      ├── Some((7, 3)): 12/21 ≈ 0.571
      ├── Some((7, 4)): 6/15 ≈ 0.400
      ├── Some((7, 5)): 12/22 ≈ 0.545
      ├── Some((7, 6)): 7/16 ≈ 0.438
      ├── Some((7, 7)): 22/32 ≈ 0.688
      └── Some((7, 8)): 14/24 ≈ 0.583
    └── Some((3, 8)): 45/103 ≈ 0.437
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 7/14 ≈ 0.500
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 8/15 ≈ 0.533
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 3/9 ≈ 0.333
      ├── Some((8, 7)): 6/13 ≈ 0.462
      └── Some((8, 8)): 4/10 ≈ 0.400
  ├── Some((3, 4)): 1280/2359 ≈ 0.543
    ├── Some((4, 0)): 153/278 ≈ 0.550
      ├── Some((0, 0)): 15/29 ≈ 0.517
      ├── Some((0, 1)): 7/19 ≈ 0.368
      ├── Some((0, 2)): 19/33 ≈ 0.576
      ├── Some((0, 3)): 23/38 ≈ 0.605
      ├── Some((0, 4)): 18/32 ≈ 0.562
      ├── Some((0, 5)): 12/25 ≈ 0.480
      ├── Some((0, 6)): 8/21 ≈ 0.381
      ├── Some((0, 7)): 25/40 ≈ 0.625
      └── Some((0, 8)): 25/40 ≈ 0.625
    ├── Some((4, 1)): 183/323 ≈ 0.567
      ├── Some((1, 0)): 13/28 ≈ 0.464
      ├── Some((1, 1)): 31/48 ≈ 0.646
      ├── Some((1, 2)): 12/26 ≈ 0.462
      ├── Some((1, 3)): 25/41 ≈ 0.610
      ├── Some((1, 4)): 43/61 ≈ 0.705
      ├── Some((1, 5)): 20/36 ≈ 0.556
      ├── Some((1, 6)): 17/32 ≈ 0.531
      ├── Some((1, 7)): 15/30 ≈ 0.500
      └── Some((1, 8)): 7/20 ≈ 0.350
    ├── Some((4, 2)): 128/241 ≈ 0.531
      ├── Some((2, 0)): 6/17 ≈ 0.353
      ├── Some((2, 1)): 20/33 ≈ 0.606
      ├── Some((2, 2)): 8/20 ≈ 0.400
      ├── Some((2, 3)): 14/27 ≈ 0.519
      ├── Some((2, 4)): 22/36 ≈ 0.611
      ├── Some((2, 5)): 23/37 ≈ 0.622
      ├── Some((2, 6)): 6/17 ≈ 0.353
      ├── Some((2, 7)): 21/35 ≈ 0.600
      └── Some((2, 8)): 7/18 ≈ 0.389
    ├── Some((4, 3)): 88/180 ≈ 0.489
      ├── Some((3, 0)): 13/25 ≈ 0.520
      ├── Some((3, 1)): 5/15 ≈ 0.333
      ├── Some((3, 2)): 11/23 ≈ 0.478
      ├── Some((3, 3)): 19/32 ≈ 0.594
      ├── Some((3, 5)): 19/32 ≈ 0.594
      ├── Some((3, 6)): 4/14 ≈ 0.286
      ├── Some((3, 7)): 8/19 ≈ 0.421
      └── Some((3, 8)): 8/19 ≈ 0.421
    ├── Some((4, 4)): 153/279 ≈ 0.548
      ├── Some((4, 0)): 8/22 ≈ 0.364
      ├── Some((4, 1)): 18/34 ≈ 0.529
      ├── Some((4, 2)): 22/39 ≈ 0.564
      ├── Some((4, 3)): 24/41 ≈ 0.585
      ├── Some((4, 5)): 7/20 ≈ 0.350
      ├── Some((4, 6)): 37/55 ≈ 0.673
      ├── Some((4, 7)): 20/36 ≈ 0.556
      └── Some((4, 8)): 16/31 ≈ 0.516
    ├── Some((4, 5)): 128/241 ≈ 0.531
      ├── Some((5, 0)): 24/38 ≈ 0.632
      ├── Some((5, 1)): 8/20 ≈ 0.400
      ├── Some((5, 2)): 15/28 ≈ 0.536
      ├── Some((5, 3)): 18/31 ≈ 0.581
      ├── Some((5, 4)): 8/20 ≈ 0.400
      ├── Some((5, 5)): 18/31 ≈ 0.581
      ├── Some((5, 6)): 20/33 ≈ 0.606
      ├── Some((5, 7)): 5/16 ≈ 0.312
      └── Some((5, 8)): 11/23 ≈ 0.478
    ├── Some((4, 6)): 185/326 ≈ 0.567
      ├── Some((6, 0)): 8/22 ≈ 0.364
      ├── Some((6, 1)): 19/36 ≈ 0.528
      ├── Some((6, 2)): 26/44 ≈ 0.591
      ├── Some((6, 4)): 46/67 ≈ 0.687
      ├── Some((6, 5)): 12/28 ≈ 0.429
      ├── Some((6, 6)): 21/38 ≈ 0.553
      ├── Some((6, 7)): 28/47 ≈ 0.596
      └── Some((6, 8)): 25/43 ≈ 0.581
    ├── Some((4, 7)): 153/279 ≈ 0.548
      ├── Some((7, 0)): 17/31 ≈ 0.548
      ├── Some((7, 1)): 10/23 ≈ 0.435
      ├── Some((7, 2)): 20/35 ≈ 0.571
      ├── Some((7, 3)): 18/32 ≈ 0.562
      ├── Some((7, 4)): 18/32 ≈ 0.562
      ├── Some((7, 5)): 13/26 ≈ 0.500
      ├── Some((7, 6)): 11/24 ≈ 0.458
      ├── Some((7, 7)): 13/26 ≈ 0.500
      └── Some((7, 8)): 33/49 ≈ 0.673
    └── Some((4, 8)): 108/211 ≈ 0.512
      ├── Some((8, 0)): 15/27 ≈ 0.556
      ├── Some((8, 1)): 19/31 ≈ 0.613
      ├── Some((8, 2)): 8/19 ≈ 0.421
      ├── Some((8, 3)): 11/22 ≈ 0.500
      ├── Some((8, 4)): 9/20 ≈ 0.450
      ├── Some((8, 5)): 11/23 ≈ 0.478
      ├── Some((8, 6)): 2/11 ≈ 0.182
      ├── Some((8, 7)): 9/20 ≈ 0.450
      └── Some((8, 8)): 24/37 ≈ 0.649
  ├── Some((3, 5)): 714/1391 ≈ 0.513
    ├── Some((5, 0)): 55/118 ≈ 0.466
      ├── Some((0, 0)): 1/7 ≈ 0.143
      ├── Some((0, 1)): 12/20 ≈ 0.600
      ├── Some((0, 2)): 10/17 ≈ 0.588
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 7/14 ≈ 0.500
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 2/9 ≈ 0.222
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 5/12 ≈ 0.417
    ├── Some((5, 1)): 95/178 ≈ 0.534
      ├── Some((1, 0)): 13/22 ≈ 0.591
      ├── Some((1, 1)): 10/19 ≈ 0.526
      ├── Some((1, 2)): 12/21 ≈ 0.571
      ├── Some((1, 3)): 6/15 ≈ 0.400
      ├── Some((1, 4)): 12/21 ≈ 0.571
      ├── Some((1, 5)): 9/18 ≈ 0.500
      ├── Some((1, 6)): 17/27 ≈ 0.630
      ├── Some((1, 7)): 13/23 ≈ 0.565
      └── Some((1, 8)): 3/11 ≈ 0.273
    ├── Some((5, 2)): 97/181 ≈ 0.536
      ├── Some((2, 0)): 6/15 ≈ 0.400
      ├── Some((2, 1)): 9/18 ≈ 0.500
      ├── Some((2, 2)): 6/15 ≈ 0.400
      ├── Some((2, 3)): 12/22 ≈ 0.545
      ├── Some((2, 4)): 8/17 ≈ 0.471
      ├── Some((2, 5)): 10/19 ≈ 0.526
      ├── Some((2, 6)): 5/14 ≈ 0.357
      ├── Some((2, 7)): 20/30 ≈ 0.667
      └── Some((2, 8)): 20/30 ≈ 0.667
    ├── Some((5, 3)): 62/129 ≈ 0.481
      ├── Some((3, 0)): 21/30 ≈ 0.700
      ├── Some((3, 1)): 4/12 ≈ 0.333
      ├── Some((3, 2)): 6/14 ≈ 0.429
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 6/14 ≈ 0.429
      ├── Some((3, 6)): 9/18 ≈ 0.500
      ├── Some((3, 7)): 2/10 ≈ 0.200
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((5, 4)): 69/139 ≈ 0.496
      ├── Some((4, 0)): 11/19 ≈ 0.579
      ├── Some((4, 1)): 13/21 ≈ 0.619
      ├── Some((4, 2)): 3/10 ≈ 0.300
      ├── Some((4, 3)): 10/18 ≈ 0.556
      ├── Some((4, 4)): 8/16 ≈ 0.500
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 3/10 ≈ 0.300
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 3/11 ≈ 0.273
    ├── Some((5, 5)): 82/159 ≈ 0.516
      ├── Some((5, 0)): 14/24 ≈ 0.583
      ├── Some((5, 1)): 11/21 ≈ 0.524
      ├── Some((5, 2)): 6/15 ≈ 0.400
      ├── Some((5, 3)): 10/19 ≈ 0.526
      ├── Some((5, 4)): 9/18 ≈ 0.500
      ├── Some((5, 6)): 13/23 ≈ 0.565
      ├── Some((5, 7)): 10/20 ≈ 0.500
      └── Some((5, 8)): 9/18 ≈ 0.500
    ├── Some((5, 6)): 86/164 ≈ 0.524
      ├── Some((6, 0)): 15/25 ≈ 0.600
      ├── Some((6, 1)): 10/20 ≈ 0.500
      ├── Some((6, 2)): 11/21 ≈ 0.524
      ├── Some((6, 4)): 14/24 ≈ 0.583
      ├── Some((6, 5)): 15/25 ≈ 0.600
      ├── Some((6, 6)): 9/18 ≈ 0.500
      ├── Some((6, 7)): 8/17 ≈ 0.471
      └── Some((6, 8)): 4/13 ≈ 0.308
    ├── Some((5, 7)): 69/139 ≈ 0.496
      ├── Some((7, 0)): 5/13 ≈ 0.385
      ├── Some((7, 1)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 7/15 ≈ 0.467
      ├── Some((7, 3)): 17/25 ≈ 0.680
      ├── Some((7, 4)): 7/15 ≈ 0.467
      ├── Some((7, 5)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 2/9 ≈ 0.222
      ├── Some((7, 7)): 11/19 ≈ 0.579
      └── Some((7, 8)): 9/17 ≈ 0.529
    └── Some((5, 8)): 99/183 ≈ 0.541
      ├── Some((8, 0)): 10/20 ≈ 0.500
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 9/18 ≈ 0.500
      ├── Some((8, 4)): 7/16 ≈ 0.438
      ├── Some((8, 5)): 19/29 ≈ 0.655
      ├── Some((8, 6)): 19/29 ≈ 0.655
      ├── Some((8, 7)): 3/11 ≈ 0.273
      └── Some((8, 8)): 16/26 ≈ 0.615
  ├── Some((3, 6)): 657/1291 ≈ 0.509
    ├── Some((6, 0)): 73/148 ≈ 0.493
      ├── Some((0, 0)): 8/16 ≈ 0.500
      ├── Some((0, 1)): 10/18 ≈ 0.556
      ├── Some((0, 2)): 7/15 ≈ 0.467
      ├── Some((0, 3)): 4/12 ≈ 0.333
      ├── Some((0, 4)): 6/14 ≈ 0.429
      ├── Some((0, 5)): 11/20 ≈ 0.550
      ├── Some((0, 6)): 10/19 ≈ 0.526
      ├── Some((0, 7)): 5/13 ≈ 0.385
      └── Some((0, 8)): 11/20 ≈ 0.550
    ├── Some((6, 1)): 81/160 ≈ 0.506
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 1)): 5/14 ≈ 0.357
      ├── Some((1, 2)): 6/15 ≈ 0.400
      ├── Some((1, 3)): 8/17 ≈ 0.471
      ├── Some((1, 4)): 8/17 ≈ 0.471
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 11/20 ≈ 0.550
      ├── Some((1, 7)): 18/27 ≈ 0.667
      └── Some((1, 8)): 1/8 ≈ 0.125
    ├── Some((6, 2)): 64/134 ≈ 0.478
      ├── Some((2, 0)): 3/10 ≈ 0.300
      ├── Some((2, 1)): 6/14 ≈ 0.429
      ├── Some((2, 2)): 8/16 ≈ 0.500
      ├── Some((2, 3)): 4/12 ≈ 0.333
      ├── Some((2, 4)): 9/17 ≈ 0.529
      ├── Some((2, 5)): 13/21 ≈ 0.619
      ├── Some((2, 6)): 2/9 ≈ 0.222
      ├── Some((2, 7)): 8/16 ≈ 0.500
      └── Some((2, 8)): 10/18 ≈ 0.556
    ├── Some((6, 4)): 101/190 ≈ 0.532
      ├── Some((4, 0)): 19/29 ≈ 0.655
      ├── Some((4, 1)): 13/23 ≈ 0.565
      ├── Some((4, 2)): 12/22 ≈ 0.545
      ├── Some((4, 3)): 9/19 ≈ 0.474
      ├── Some((4, 4)): 12/22 ≈ 0.545
      ├── Some((4, 5)): 6/15 ≈ 0.400
      ├── Some((4, 6)): 7/16 ≈ 0.438
      ├── Some((4, 7)): 9/19 ≈ 0.474
      └── Some((4, 8)): 14/24 ≈ 0.583
    ├── Some((6, 5)): 80/159 ≈ 0.503
      ├── Some((5, 0)): 11/20 ≈ 0.550
      ├── Some((5, 1)): 15/24 ≈ 0.625
      ├── Some((5, 2)): 9/18 ≈ 0.500
      ├── Some((5, 3)): 6/14 ≈ 0.429
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 7/16 ≈ 0.438
      ├── Some((5, 6)): 7/16 ≈ 0.438
      ├── Some((5, 7)): 11/20 ≈ 0.550
      └── Some((5, 8)): 8/17 ≈ 0.471
    ├── Some((6, 6)): 119/216 ≈ 0.551
      ├── Some((6, 0)): 10/23 ≈ 0.435
      ├── Some((6, 1)): 26/41 ≈ 0.634
      ├── Some((6, 2)): 34/50 ≈ 0.680
      ├── Some((6, 4)): 15/29 ≈ 0.517
      ├── Some((6, 5)): 5/16 ≈ 0.312
      ├── Some((6, 7)): 11/24 ≈ 0.458
      └── Some((6, 8)): 18/32 ≈ 0.562
    ├── Some((6, 7)): 57/123 ≈ 0.463
      ├── Some((7, 0)): 7/15 ≈ 0.467
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 4/11 ≈ 0.364
      ├── Some((7, 4)): 5/12 ≈ 0.417
      ├── Some((7, 5)): 1/8 ≈ 0.125
      ├── Some((7, 6)): 16/24 ≈ 0.667
      ├── Some((7, 7)): 11/19 ≈ 0.579
      └── Some((7, 8)): 6/13 ≈ 0.462
    └── Some((6, 8)): 81/160 ≈ 0.506
      ├── Some((8, 0)): 9/18 ≈ 0.500
      ├── Some((8, 1)): 5/13 ≈ 0.385
      ├── Some((8, 2)): 8/17 ≈ 0.471
      ├── Some((8, 3)): 10/19 ≈ 0.526
      ├── Some((8, 4)): 6/14 ≈ 0.429
      ├── Some((8, 5)): 8/17 ≈ 0.471
      ├── Some((8, 6)): 16/25 ≈ 0.640
      ├── Some((8, 7)): 11/20 ≈ 0.550
      └── Some((8, 8)): 7/16 ≈ 0.438
  ├── Some((3, 7)): 770/1488 ≈ 0.517
    ├── Some((7, 0)): 75/150 ≈ 0.500
      ├── Some((0, 0)): 10/18 ≈ 0.556
      ├── Some((0, 1)): 5/13 ≈ 0.385
      ├── Some((0, 2)): 4/12 ≈ 0.333
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 10/19 ≈ 0.526
      ├── Some((0, 6)): 17/26 ≈ 0.654
      ├── Some((0, 7)): 7/15 ≈ 0.467
      └── Some((0, 8)): 7/15 ≈ 0.467
    ├── Some((7, 1)): 107/197 ≈ 0.543
      ├── Some((1, 0)): 11/21 ≈ 0.524
      ├── Some((1, 1)): 23/34 ≈ 0.676
      ├── Some((1, 2)): 15/25 ≈ 0.600
      ├── Some((1, 3)): 12/22 ≈ 0.545
      ├── Some((1, 4)): 2/10 ≈ 0.200
      ├── Some((1, 5)): 17/28 ≈ 0.607
      ├── Some((1, 6)): 6/16 ≈ 0.375
      ├── Some((1, 7)): 10/20 ≈ 0.500
      └── Some((1, 8)): 10/20 ≈ 0.500
    ├── Some((7, 2)): 97/183 ≈ 0.530
      ├── Some((2, 0)): 10/20 ≈ 0.500
      ├── Some((2, 1)): 5/14 ≈ 0.357
      ├── Some((2, 2)): 12/22 ≈ 0.545
      ├── Some((2, 3)): 15/25 ≈ 0.600
      ├── Some((2, 4)): 9/18 ≈ 0.500
      ├── Some((2, 5)): 17/27 ≈ 0.630
      ├── Some((2, 6)): 14/24 ≈ 0.583
      ├── Some((2, 7)): 9/18 ≈ 0.500
      └── Some((2, 8)): 5/14 ≈ 0.357
    ├── Some((7, 3)): 53/116 ≈ 0.457
      ├── Some((3, 0)): 2/9 ≈ 0.222
      ├── Some((3, 1)): 8/16 ≈ 0.500
      ├── Some((3, 2)): 6/14 ≈ 0.429
      ├── Some((3, 3)): 10/18 ≈ 0.556
      ├── Some((3, 4)): 3/10 ≈ 0.300
      ├── Some((3, 5)): 5/13 ≈ 0.385
      ├── Some((3, 6)): 12/20 ≈ 0.600
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((7, 4)): 60/127 ≈ 0.472
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 7/14 ≈ 0.500
      ├── Some((4, 2)): 8/16 ≈ 0.500
      ├── Some((4, 3)): 5/12 ≈ 0.417
      ├── Some((4, 4)): 2/9 ≈ 0.222
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 8/16 ≈ 0.500
      ├── Some((4, 7)): 12/20 ≈ 0.600
      └── Some((4, 8)): 4/11 ≈ 0.364
    ├── Some((7, 5)): 133/234 ≈ 0.568
      ├── Some((5, 0)): 22/34 ≈ 0.647
      ├── Some((5, 1)): 21/33 ≈ 0.636
      ├── Some((5, 2)): 0/8 ≈ 0.000
      ├── Some((5, 3)): 5/15 ≈ 0.333
      ├── Some((5, 4)): 15/27 ≈ 0.556
      ├── Some((5, 5)): 19/31 ≈ 0.613
      ├── Some((5, 6)): 20/32 ≈ 0.625
      ├── Some((5, 7)): 21/33 ≈ 0.636
      └── Some((5, 8)): 9/20 ≈ 0.450
    ├── Some((7, 6)): 89/171 ≈ 0.520
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 10/20 ≈ 0.500
      ├── Some((6, 2)): 10/20 ≈ 0.500
      ├── Some((6, 4)): 13/23 ≈ 0.565
      ├── Some((6, 5)): 8/18 ≈ 0.444
      ├── Some((6, 6)): 13/24 ≈ 0.542
      ├── Some((6, 7)): 19/30 ≈ 0.633
      └── Some((6, 8)): 8/18 ≈ 0.444
    ├── Some((7, 7)): 71/144 ≈ 0.493
      ├── Some((7, 0)): 7/16 ≈ 0.438
      ├── Some((7, 1)): 5/14 ≈ 0.357
      ├── Some((7, 2)): 12/22 ≈ 0.545
      ├── Some((7, 3)): 9/18 ≈ 0.500
      ├── Some((7, 4)): 8/17 ≈ 0.471
      ├── Some((7, 5)): 16/26 ≈ 0.615
      ├── Some((7, 6)): 4/12 ≈ 0.333
      └── Some((7, 8)): 9/18 ≈ 0.500
    └── Some((7, 8)): 85/165 ≈ 0.515
      ├── Some((8, 0)): 8/17 ≈ 0.471
      ├── Some((8, 1)): 1/9 ≈ 0.111
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 12/21 ≈ 0.571
      ├── Some((8, 4)): 23/32 ≈ 0.719
      ├── Some((8, 5)): 8/17 ≈ 0.471
      ├── Some((8, 6)): 11/20 ≈ 0.550
      ├── Some((8, 7)): 6/15 ≈ 0.400
      └── Some((8, 8)): 6/15 ≈ 0.400
  └── Some((3, 8)): 1067/1997 ≈ 0.534
    ├── Some((8, 0)): 86/173 ≈ 0.497
      ├── Some((0, 0)): 14/24 ≈ 0.583
      ├── Some((0, 1)): 10/20 ≈ 0.500
      ├── Some((0, 2)): 1/9 ≈ 0.111
      ├── Some((0, 3)): 2/10 ≈ 0.200
      ├── Some((0, 4)): 15/26 ≈ 0.577
      ├── Some((0, 5)): 17/28 ≈ 0.607
      ├── Some((0, 6)): 2/10 ≈ 0.200
      ├── Some((0, 7)): 15/26 ≈ 0.577
      └── Some((0, 8)): 9/19 ≈ 0.474
    ├── Some((8, 1)): 100/194 ≈ 0.515
      ├── Some((1, 0)): 16/27 ≈ 0.593
      ├── Some((1, 1)): 4/13 ≈ 0.308
      ├── Some((1, 2)): 7/17 ≈ 0.412
      ├── Some((1, 3)): 18/29 ≈ 0.621
      ├── Some((1, 4)): 2/11 ≈ 0.182
      ├── Some((1, 5)): 9/20 ≈ 0.450
      ├── Some((1, 6)): 21/33 ≈ 0.636
      ├── Some((1, 7)): 16/27 ≈ 0.593
      └── Some((1, 8)): 6/16 ≈ 0.375
    ├── Some((8, 2)): 135/247 ≈ 0.547
      ├── Some((2, 0)): 7/18 ≈ 0.389
      ├── Some((2, 1)): 13/25 ≈ 0.520
      ├── Some((2, 2)): 21/34 ≈ 0.618
      ├── Some((2, 3)): 21/34 ≈ 0.618
      ├── Some((2, 4)): 29/42 ≈ 0.690
      ├── Some((2, 5)): 10/22 ≈ 0.455
      ├── Some((2, 6)): 16/29 ≈ 0.552
      ├── Some((2, 7)): 9/21 ≈ 0.429
      └── Some((2, 8)): 9/21 ≈ 0.429
    ├── Some((8, 3)): 150/268 ≈ 0.560
      ├── Some((3, 0)): 17/31 ≈ 0.548
      ├── Some((3, 1)): 22/37 ≈ 0.595
      ├── Some((3, 2)): 19/34 ≈ 0.559
      ├── Some((3, 3)): 27/43 ≈ 0.628
      ├── Some((3, 4)): 20/35 ≈ 0.571
      ├── Some((3, 5)): 18/33 ≈ 0.545
      ├── Some((3, 6)): 22/37 ≈ 0.595
      └── Some((3, 7)): 5/17 ≈ 0.294
    ├── Some((8, 4)): 133/244 ≈ 0.545
      ├── Some((4, 0)): 12/24 ≈ 0.500
      ├── Some((4, 1)): 27/41 ≈ 0.659
      ├── Some((4, 2)): 16/29 ≈ 0.552
      ├── Some((4, 3)): 20/33 ≈ 0.606
      ├── Some((4, 4)): 14/26 ≈ 0.538
      ├── Some((4, 5)): 12/24 ≈ 0.500
      ├── Some((4, 6)): 20/33 ≈ 0.606
      ├── Some((4, 7)): 2/12 ≈ 0.167
      └── Some((4, 8)): 9/21 ≈ 0.429
    ├── Some((8, 5)): 156/277 ≈ 0.563
      ├── Some((5, 0)): 13/26 ≈ 0.500
      ├── Some((5, 1)): 19/33 ≈ 0.576
      ├── Some((5, 2)): 12/25 ≈ 0.480
      ├── Some((5, 3)): 9/21 ≈ 0.429
      ├── Some((5, 4)): 25/39 ≈ 0.641
      ├── Some((5, 5)): 14/27 ≈ 0.519
      ├── Some((5, 6)): 27/41 ≈ 0.659
      ├── Some((5, 7)): 17/30 ≈ 0.567
      └── Some((5, 8)): 20/34 ≈ 0.588
    ├── Some((8, 6)): 83/169 ≈ 0.491
      ├── Some((6, 0)): 13/24 ≈ 0.542
      ├── Some((6, 1)): 14/26 ≈ 0.538
      ├── Some((6, 2)): 4/14 ≈ 0.286
      ├── Some((6, 4)): 5/15 ≈ 0.333
      ├── Some((6, 5)): 28/40 ≈ 0.700
      ├── Some((6, 6)): 3/12 ≈ 0.250
      ├── Some((6, 7)): 4/14 ≈ 0.286
      └── Some((6, 8)): 12/23 ≈ 0.522
    ├── Some((8, 7)): 83/169 ≈ 0.491
      ├── Some((7, 0)): 6/15 ≈ 0.400
      ├── Some((7, 1)): 17/27 ≈ 0.630
      ├── Some((7, 2)): 9/19 ≈ 0.474
      ├── Some((7, 3)): 8/17 ≈ 0.471
      ├── Some((7, 4)): 8/17 ≈ 0.471
      ├── Some((7, 5)): 5/14 ≈ 0.357
      ├── Some((7, 6)): 6/15 ≈ 0.400
      ├── Some((7, 7)): 14/24 ≈ 0.583
      └── Some((7, 8)): 10/20 ≈ 0.500
    └── Some((8, 8)): 141/255 ≈ 0.553
      ├── Some((8, 0)): 21/36 ≈ 0.583
      ├── Some((8, 1)): 3/14 ≈ 0.214
      ├── Some((8, 2)): 16/30 ≈ 0.533
      ├── Some((8, 3)): 22/37 ≈ 0.595
      ├── Some((8, 4)): 19/34 ≈ 0.559
      ├── Some((8, 5)): 17/31 ≈ 0.548
      ├── Some((8, 6)): 18/33 ≈ 0.545
      └── Some((8, 7)): 24/39 ≈ 0.615
├── Some((6, 4)): 9894/18689 ≈ 0.529
  ├── Some((4, 0)): 1464/2705 ≈ 0.541
    ├── Some((0, 0)): 145/275 ≈ 0.527
      ├── Some((0, 1)): 15/31 ≈ 0.484
      ├── Some((0, 2)): 8/22 ≈ 0.364
      ├── Some((0, 3)): 20/37 ≈ 0.541
      ├── Some((0, 4)): 17/33 ≈ 0.515
      ├── Some((0, 5)): 29/47 ≈ 0.617
      ├── Some((0, 6)): 9/23 ≈ 0.391
      ├── Some((0, 7)): 14/29 ≈ 0.483
      └── Some((0, 8)): 33/52 ≈ 0.635
    ├── Some((0, 1)): 88/186 ≈ 0.473
      ├── Some((1, 0)): 2/11 ≈ 0.182
      ├── Some((1, 1)): 9/20 ≈ 0.450
      ├── Some((1, 2)): 16/28 ≈ 0.571
      ├── Some((1, 3)): 18/30 ≈ 0.600
      ├── Some((1, 4)): 9/20 ≈ 0.450
      ├── Some((1, 5)): 12/24 ≈ 0.500
      ├── Some((1, 6)): 5/15 ≈ 0.333
      ├── Some((1, 7)): 2/11 ≈ 0.182
      └── Some((1, 8)): 14/26 ≈ 0.538
    ├── Some((0, 2)): 182/330 ≈ 0.552
      ├── Some((2, 0)): 10/24 ≈ 0.417
      ├── Some((2, 1)): 35/54 ≈ 0.648
      ├── Some((2, 2)): 17/33 ≈ 0.515
      ├── Some((2, 3)): 32/50 ≈ 0.640
      ├── Some((2, 4)): 13/28 ≈ 0.464
      ├── Some((2, 5)): 17/33 ≈ 0.515
      ├── Some((2, 6)): 17/33 ≈ 0.515
      ├── Some((2, 7)): 17/33 ≈ 0.515
      └── Some((2, 8)): 24/41 ≈ 0.585
    ├── Some((0, 3)): 199/356 ≈ 0.559
      ├── Some((3, 0)): 27/45 ≈ 0.600
      ├── Some((3, 1)): 20/37 ≈ 0.541
      ├── Some((3, 2)): 24/42 ≈ 0.571
      ├── Some((3, 3)): 31/50 ≈ 0.620
      ├── Some((3, 4)): 15/31 ≈ 0.484
      ├── Some((3, 5)): 19/36 ≈ 0.528
      ├── Some((3, 6)): 32/51 ≈ 0.627
      ├── Some((3, 7)): 12/27 ≈ 0.444
      └── Some((3, 8)): 19/36 ≈ 0.528
    ├── Some((0, 4)): 234/408 ≈ 0.574
      ├── Some((4, 1)): 46/71 ≈ 0.648
      ├── Some((4, 2)): 32/55 ≈ 0.582
      ├── Some((4, 3)): 14/32 ≈ 0.438
      ├── Some((4, 4)): 18/37 ≈ 0.486
      ├── Some((4, 5)): 24/45 ≈ 0.533
      ├── Some((4, 6)): 33/56 ≈ 0.589
      ├── Some((4, 7)): 31/53 ≈ 0.585
      └── Some((4, 8)): 35/58 ≈ 0.603
    ├── Some((0, 5)): 122/239 ≈ 0.510
      ├── Some((5, 0)): 9/21 ≈ 0.429
      ├── Some((5, 1)): 17/30 ≈ 0.567
      ├── Some((5, 2)): 10/22 ≈ 0.455
      ├── Some((5, 3)): 18/32 ≈ 0.562
      ├── Some((5, 4)): 22/36 ≈ 0.611
      ├── Some((5, 5)): 8/20 ≈ 0.400
      ├── Some((5, 6)): 16/29 ≈ 0.552
      ├── Some((5, 7)): 11/24 ≈ 0.458
      └── Some((5, 8)): 11/24 ≈ 0.458
    ├── Some((0, 6)): 222/390 ≈ 0.569
      ├── Some((6, 0)): 29/51 ≈ 0.569
      ├── Some((6, 1)): 19/38 ≈ 0.500
      ├── Some((6, 2)): 16/35 ≈ 0.457
      ├── Some((6, 3)): 9/25 ≈ 0.360
      ├── Some((6, 5)): 22/42 ≈ 0.524
      ├── Some((6, 6)): 50/75 ≈ 0.667
      ├── Some((6, 7)): 51/76 ≈ 0.671
      └── Some((6, 8)): 26/47 ≈ 0.553
    ├── Some((0, 7)): 98/202 ≈ 0.485
      ├── Some((7, 0)): 20/33 ≈ 0.606
      ├── Some((7, 1)): 14/26 ≈ 0.538
      ├── Some((7, 2)): 13/25 ≈ 0.520
      ├── Some((7, 3)): 1/10 ≈ 0.100
      ├── Some((7, 4)): 10/22 ≈ 0.455
      ├── Some((7, 5)): 4/14 ≈ 0.286
      ├── Some((7, 6)): 7/18 ≈ 0.389
      ├── Some((7, 7)): 8/19 ≈ 0.421
      └── Some((7, 8)): 21/34 ≈ 0.618
    └── Some((0, 8)): 174/318 ≈ 0.547
      ├── Some((8, 0)): 28/46 ≈ 0.609
      ├── Some((8, 1)): 27/45 ≈ 0.600
      ├── Some((8, 2)): 4/16 ≈ 0.250
      ├── Some((8, 3)): 24/41 ≈ 0.585
      ├── Some((8, 4)): 18/34 ≈ 0.529
      ├── Some((8, 5)): 4/16 ≈ 0.250
      ├── Some((8, 6)): 24/41 ≈ 0.585
      ├── Some((8, 7)): 21/38 ≈ 0.553
      └── Some((8, 8)): 23/40 ≈ 0.575
  ├── Some((4, 1)): 1353/2516 ≈ 0.538
    ├── Some((1, 0)): 124/240 ≈ 0.517
      ├── Some((0, 0)): 16/29 ≈ 0.552
      ├── Some((0, 1)): 3/13 ≈ 0.231
      ├── Some((0, 2)): 7/19 ≈ 0.368
      ├── Some((0, 3)): 14/27 ≈ 0.519
      ├── Some((0, 4)): 12/25 ≈ 0.480
      ├── Some((0, 5)): 16/29 ≈ 0.552
      ├── Some((0, 6)): 11/24 ≈ 0.458
      ├── Some((0, 7)): 29/44 ≈ 0.659
      └── Some((0, 8)): 16/29 ≈ 0.552
    ├── Some((1, 1)): 153/284 ≈ 0.539
      ├── Some((1, 0)): 4/17 ≈ 0.235
      ├── Some((1, 2)): 28/46 ≈ 0.609
      ├── Some((1, 3)): 7/21 ≈ 0.333
      ├── Some((1, 4)): 19/36 ≈ 0.528
      ├── Some((1, 5)): 30/48 ≈ 0.625
      ├── Some((1, 6)): 11/26 ≈ 0.423
      ├── Some((1, 7)): 27/45 ≈ 0.600
      └── Some((1, 8)): 26/44 ≈ 0.591
    ├── Some((1, 2)): 145/272 ≈ 0.533
      ├── Some((2, 0)): 22/37 ≈ 0.595
      ├── Some((2, 1)): 18/33 ≈ 0.545
      ├── Some((2, 2)): 15/29 ≈ 0.517
      ├── Some((2, 3)): 15/29 ≈ 0.517
      ├── Some((2, 4)): 15/29 ≈ 0.517
      ├── Some((2, 5)): 22/37 ≈ 0.595
      ├── Some((2, 6)): 9/22 ≈ 0.409
      ├── Some((2, 7)): 16/30 ≈ 0.533
      └── Some((2, 8)): 12/25 ≈ 0.480
    ├── Some((1, 3)): 181/326 ≈ 0.555
      ├── Some((3, 0)): 18/34 ≈ 0.529
      ├── Some((3, 1)): 22/38 ≈ 0.579
      ├── Some((3, 2)): 9/23 ≈ 0.391
      ├── Some((3, 3)): 13/28 ≈ 0.464
      ├── Some((3, 4)): 29/46 ≈ 0.630
      ├── Some((3, 5)): 15/30 ≈ 0.500
      ├── Some((3, 6)): 25/42 ≈ 0.595
      ├── Some((3, 7)): 23/40 ≈ 0.575
      └── Some((3, 8)): 27/44 ≈ 0.614
    ├── Some((1, 4)): 106/212 ≈ 0.500
      ├── Some((4, 0)): 22/37 ≈ 0.595
      ├── Some((4, 2)): 8/20 ≈ 0.400
      ├── Some((4, 3)): 22/37 ≈ 0.595
      ├── Some((4, 4)): 6/18 ≈ 0.333
      ├── Some((4, 5)): 8/20 ≈ 0.400
      ├── Some((4, 6)): 16/30 ≈ 0.533
      ├── Some((4, 7)): 12/25 ≈ 0.480
      └── Some((4, 8)): 11/24 ≈ 0.458
    ├── Some((1, 5)): 219/382 ≈ 0.573
      ├── Some((5, 0)): 27/46 ≈ 0.587
      ├── Some((5, 1)): 20/38 ≈ 0.526
      ├── Some((5, 2)): 17/34 ≈ 0.500
      ├── Some((5, 3)): 50/71 ≈ 0.704
      ├── Some((5, 4)): 29/48 ≈ 0.604
      ├── Some((5, 5)): 16/33 ≈ 0.485
      ├── Some((5, 6)): 26/45 ≈ 0.578
      ├── Some((5, 7)): 23/41 ≈ 0.561
      └── Some((5, 8)): 10/25 ≈ 0.400
    ├── Some((1, 6)): 155/287 ≈ 0.540
      ├── Some((6, 0)): 27/45 ≈ 0.600
      ├── Some((6, 1)): 14/29 ≈ 0.483
      ├── Some((6, 2)): 18/34 ≈ 0.529
      ├── Some((6, 3)): 16/32 ≈ 0.500
      ├── Some((6, 5)): 20/37 ≈ 0.541
      ├── Some((6, 6)): 18/34 ≈ 0.529
      ├── Some((6, 7)): 25/43 ≈ 0.581
      └── Some((6, 8)): 16/32 ≈ 0.500
    ├── Some((1, 7)): 184/331 ≈ 0.556
      ├── Some((7, 0)): 17/33 ≈ 0.515
      ├── Some((7, 1)): 18/34 ≈ 0.529
      ├── Some((7, 2)): 11/26 ≈ 0.423
      ├── Some((7, 3)): 19/35 ≈ 0.543
      ├── Some((7, 4)): 14/29 ≈ 0.483
      ├── Some((7, 5)): 21/38 ≈ 0.553
      ├── Some((7, 6)): 28/45 ≈ 0.622
      ├── Some((7, 7)): 37/55 ≈ 0.673
      └── Some((7, 8)): 19/35 ≈ 0.543
    └── Some((1, 8)): 86/181 ≈ 0.475
      ├── Some((8, 0)): 6/16 ≈ 0.375
      ├── Some((8, 1)): 14/25 ≈ 0.560
      ├── Some((8, 2)): 6/16 ≈ 0.375
      ├── Some((8, 3)): 15/26 ≈ 0.577
      ├── Some((8, 4)): 17/29 ≈ 0.586
      ├── Some((8, 5)): 6/16 ≈ 0.375
      ├── Some((8, 6)): 7/17 ≈ 0.412
      ├── Some((8, 7)): 8/18 ≈ 0.444
      └── Some((8, 8)): 7/17 ≈ 0.412
  ├── Some((4, 2)): 966/1850 ≈ 0.522
    ├── Some((2, 0)): 175/306 ≈ 0.572
      ├── Some((0, 0)): 25/40 ≈ 0.625
      ├── Some((0, 1)): 24/39 ≈ 0.615
      ├── Some((0, 2)): 25/40 ≈ 0.625
      ├── Some((0, 3)): 25/40 ≈ 0.625
      ├── Some((0, 4)): 14/28 ≈ 0.500
      ├── Some((0, 5)): 12/26 ≈ 0.462
      ├── Some((0, 6)): 13/27 ≈ 0.481
      ├── Some((0, 7)): 21/36 ≈ 0.583
      └── Some((0, 8)): 15/29 ≈ 0.517
    ├── Some((2, 1)): 128/237 ≈ 0.540
      ├── Some((1, 0)): 23/36 ≈ 0.639
      ├── Some((1, 1)): 10/21 ≈ 0.476
      ├── Some((1, 2)): 13/25 ≈ 0.520
      ├── Some((1, 3)): 15/27 ≈ 0.556
      ├── Some((1, 4)): 21/34 ≈ 0.618
      ├── Some((1, 5)): 10/22 ≈ 0.455
      ├── Some((1, 6)): 8/19 ≈ 0.421
      ├── Some((1, 7)): 13/25 ≈ 0.520
      └── Some((1, 8)): 15/27 ≈ 0.556
    ├── Some((2, 2)): 83/169 ≈ 0.491
      ├── Some((2, 0)): 6/16 ≈ 0.375
      ├── Some((2, 1)): 9/20 ≈ 0.450
      ├── Some((2, 3)): 15/26 ≈ 0.577
      ├── Some((2, 4)): 4/14 ≈ 0.286
      ├── Some((2, 5)): 19/31 ≈ 0.613
      ├── Some((2, 6)): 10/21 ≈ 0.476
      ├── Some((2, 7)): 18/30 ≈ 0.600
      └── Some((2, 8)): 1/10 ≈ 0.100
    ├── Some((2, 3)): 156/278 ≈ 0.561
      ├── Some((3, 0)): 23/37 ≈ 0.622
      ├── Some((3, 1)): 12/25 ≈ 0.480
      ├── Some((3, 2)): 8/20 ≈ 0.400
      ├── Some((3, 3)): 25/40 ≈ 0.625
      ├── Some((3, 4)): 20/34 ≈ 0.588
      ├── Some((3, 5)): 35/50 ≈ 0.700
      ├── Some((3, 6)): 8/20 ≈ 0.400
      ├── Some((3, 7)): 17/31 ≈ 0.548
      └── Some((3, 8)): 8/20 ≈ 0.400
    ├── Some((2, 4)): 67/144 ≈ 0.465
      ├── Some((4, 0)): 14/24 ≈ 0.583
      ├── Some((4, 1)): 5/14 ≈ 0.357
      ├── Some((4, 3)): 9/19 ≈ 0.474
      ├── Some((4, 4)): 11/21 ≈ 0.524
      ├── Some((4, 5)): 7/16 ≈ 0.438
      ├── Some((4, 6)): 4/13 ≈ 0.308
      ├── Some((4, 7)): 8/17 ≈ 0.471
      └── Some((4, 8)): 9/19 ≈ 0.474
    ├── Some((2, 5)): 88/177 ≈ 0.497
      ├── Some((5, 0)): 5/14 ≈ 0.357
      ├── Some((5, 1)): 8/18 ≈ 0.444
      ├── Some((5, 2)): 14/24 ≈ 0.583
      ├── Some((5, 3)): 8/18 ≈ 0.444
      ├── Some((5, 4)): 22/33 ≈ 0.667
      ├── Some((5, 5)): 10/20 ≈ 0.500
      ├── Some((5, 6)): 8/18 ≈ 0.444
      ├── Some((5, 7)): 7/16 ≈ 0.438
      └── Some((5, 8)): 6/15 ≈ 0.400
    ├── Some((2, 6)): 82/168 ≈ 0.488
      ├── Some((6, 0)): 8/18 ≈ 0.444
      ├── Some((6, 1)): 20/32 ≈ 0.625
      ├── Some((6, 2)): 4/14 ≈ 0.286
      ├── Some((6, 3)): 13/24 ≈ 0.542
      ├── Some((6, 5)): 16/28 ≈ 0.571
      ├── Some((6, 6)): 6/16 ≈ 0.375
      ├── Some((6, 7)): 10/21 ≈ 0.476
      └── Some((6, 8)): 4/14 ≈ 0.286
    ├── Some((2, 7)): 105/202 ≈ 0.520
      ├── Some((7, 0)): 6/16 ≈ 0.375
      ├── Some((7, 1)): 13/24 ≈ 0.542
      ├── Some((7, 2)): 7/17 ≈ 0.412
      ├── Some((7, 3)): 15/26 ≈ 0.577
      ├── Some((7, 4)): 13/24 ≈ 0.542
      ├── Some((7, 5)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 16/27 ≈ 0.593
      ├── Some((7, 7)): 9/20 ≈ 0.450
      └── Some((7, 8)): 15/26 ≈ 0.577
    └── Some((2, 8)): 82/168 ≈ 0.488
      ├── Some((8, 0)): 9/18 ≈ 0.500
      ├── Some((8, 1)): 8/17 ≈ 0.471
      ├── Some((8, 2)): 9/19 ≈ 0.474
      ├── Some((8, 3)): 9/19 ≈ 0.474
      ├── Some((8, 4)): 13/23 ≈ 0.565
      ├── Some((8, 5)): 13/23 ≈ 0.565
      ├── Some((8, 6)): 11/21 ≈ 0.524
      ├── Some((8, 7)): 8/17 ≈ 0.471
      └── Some((8, 8)): 2/10 ≈ 0.200
  ├── Some((4, 3)): 1412/2617 ≈ 0.540
    ├── Some((3, 0)): 133/255 ≈ 0.522
      ├── Some((0, 0)): 6/18 ≈ 0.333
      ├── Some((0, 1)): 4/15 ≈ 0.267
      ├── Some((0, 2)): 14/28 ≈ 0.500
      ├── Some((0, 3)): 21/36 ≈ 0.583
      ├── Some((0, 4)): 17/31 ≈ 0.548
      ├── Some((0, 5)): 18/32 ≈ 0.562
      ├── Some((0, 6)): 17/31 ≈ 0.548
      ├── Some((0, 7)): 19/33 ≈ 0.576
      └── Some((0, 8)): 16/30 ≈ 0.533
    ├── Some((3, 1)): 141/267 ≈ 0.528
      ├── Some((1, 0)): 17/31 ≈ 0.548
      ├── Some((1, 1)): 22/37 ≈ 0.595
      ├── Some((1, 2)): 10/23 ≈ 0.435
      ├── Some((1, 3)): 16/30 ≈ 0.533
      ├── Some((1, 4)): 20/35 ≈ 0.571
      ├── Some((1, 5)): 9/22 ≈ 0.409
      ├── Some((1, 6)): 9/22 ≈ 0.409
      ├── Some((1, 7)): 21/36 ≈ 0.583
      └── Some((1, 8)): 16/30 ≈ 0.533
    ├── Some((3, 2)): 159/294 ≈ 0.541
      ├── Some((2, 0)): 23/39 ≈ 0.590
      ├── Some((2, 1)): 11/25 ≈ 0.440
      ├── Some((2, 2)): 11/25 ≈ 0.440
      ├── Some((2, 3)): 38/55 ≈ 0.691
      ├── Some((2, 4)): 16/31 ≈ 0.516
      ├── Some((2, 5)): 6/19 ≈ 0.316
      ├── Some((2, 6)): 17/32 ≈ 0.531
      ├── Some((2, 7)): 24/40 ≈ 0.600
      └── Some((2, 8)): 13/27 ≈ 0.481
    ├── Some((3, 3)): 244/420 ≈ 0.581
      ├── Some((3, 0)): 36/59 ≈ 0.610
      ├── Some((3, 1)): 20/40 ≈ 0.500
      ├── Some((3, 2)): 12/30 ≈ 0.400
      ├── Some((3, 4)): 26/47 ≈ 0.553
      ├── Some((3, 5)): 40/64 ≈ 0.625
      ├── Some((3, 6)): 66/94 ≈ 0.702
      ├── Some((3, 7)): 26/47 ≈ 0.553
      └── Some((3, 8)): 18/38 ≈ 0.474
    ├── Some((3, 4)): 148/278 ≈ 0.532
      ├── Some((4, 0)): 18/34 ≈ 0.529
      ├── Some((4, 1)): 25/43 ≈ 0.581
      ├── Some((4, 2)): 19/36 ≈ 0.528
      ├── Some((4, 4)): 12/27 ≈ 0.444
      ├── Some((4, 5)): 11/26 ≈ 0.423
      ├── Some((4, 6)): 29/47 ≈ 0.617
      ├── Some((4, 7)): 23/40 ≈ 0.575
      └── Some((4, 8)): 10/24 ≈ 0.417
    ├── Some((3, 5)): 139/264 ≈ 0.527
      ├── Some((5, 0)): 11/24 ≈ 0.458
      ├── Some((5, 1)): 16/30 ≈ 0.533
      ├── Some((5, 2)): 25/40 ≈ 0.625
      ├── Some((5, 3)): 17/31 ≈ 0.548
      ├── Some((5, 4)): 12/25 ≈ 0.480
      ├── Some((5, 5)): 17/31 ≈ 0.548
      ├── Some((5, 6)): 10/23 ≈ 0.435
      ├── Some((5, 7)): 12/26 ≈ 0.462
      └── Some((5, 8)): 18/33 ≈ 0.545
    ├── Some((3, 6)): 169/310 ≈ 0.545
      ├── Some((6, 0)): 26/45 ≈ 0.578
      ├── Some((6, 1)): 18/35 ≈ 0.514
      ├── Some((6, 2)): 19/36 ≈ 0.528
      ├── Some((6, 3)): 15/31 ≈ 0.484
      ├── Some((6, 5)): 25/44 ≈ 0.568
      ├── Some((6, 6)): 19/36 ≈ 0.528
      ├── Some((6, 7)): 16/33 ≈ 0.485
      └── Some((6, 8)): 30/49 ≈ 0.612
    ├── Some((3, 7)): 146/275 ≈ 0.531
      ├── Some((7, 0)): 10/23 ≈ 0.435
      ├── Some((7, 1)): 13/27 ≈ 0.481
      ├── Some((7, 2)): 15/29 ≈ 0.517
      ├── Some((7, 3)): 16/31 ≈ 0.516
      ├── Some((7, 4)): 26/42 ≈ 0.619
      ├── Some((7, 5)): 27/43 ≈ 0.628
      ├── Some((7, 6)): 2/13 ≈ 0.154
      ├── Some((7, 7)): 15/29 ≈ 0.517
      └── Some((7, 8)): 22/37 ≈ 0.595
    └── Some((3, 8)): 132/253 ≈ 0.522
      ├── Some((8, 0)): 12/25 ≈ 0.480
      ├── Some((8, 1)): 14/27 ≈ 0.519
      ├── Some((8, 2)): 26/41 ≈ 0.634
      ├── Some((8, 3)): 13/26 ≈ 0.500
      ├── Some((8, 4)): 15/29 ≈ 0.517
      ├── Some((8, 5)): 16/30 ≈ 0.533
      ├── Some((8, 6)): 1/11 ≈ 0.091
      ├── Some((8, 7)): 24/39 ≈ 0.615
      └── Some((8, 8)): 11/24 ≈ 0.458
  ├── Some((4, 4)): 486/1006 ≈ 0.483
    ├── Some((4, 0)): 51/112 ≈ 0.455
      ├── Some((0, 0)): 3/9 ≈ 0.333
      ├── Some((0, 1)): 3/9 ≈ 0.333
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 9/16 ≈ 0.562
      ├── Some((0, 4)): 9/16 ≈ 0.562
      ├── Some((0, 5)): 3/10 ≈ 0.300
      ├── Some((0, 6)): 5/12 ≈ 0.417
      ├── Some((0, 7)): 0/6 ≈ 0.000
      └── Some((0, 8)): 13/20 ≈ 0.650
    ├── Some((4, 1)): 121/216 ≈ 0.560
      ├── Some((1, 0)): 11/21 ≈ 0.524
      ├── Some((1, 1)): 8/18 ≈ 0.444
      ├── Some((1, 2)): 15/26 ≈ 0.577
      ├── Some((1, 3)): 11/21 ≈ 0.524
      ├── Some((1, 4)): 17/28 ≈ 0.607
      ├── Some((1, 5)): 11/22 ≈ 0.500
      ├── Some((1, 6)): 20/31 ≈ 0.645
      ├── Some((1, 7)): 10/20 ≈ 0.500
      └── Some((1, 8)): 17/28 ≈ 0.607
    ├── Some((4, 2)): 29/77 ≈ 0.377
      ├── Some((2, 0)): 0/5 ≈ 0.000
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 0/5 ≈ 0.000
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 7/12 ≈ 0.583
      ├── Some((2, 6)): 0/5 ≈ 0.000
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 9/14 ≈ 0.643
    ├── Some((4, 3)): 33/84 ≈ 0.393
      ├── Some((3, 0)): 7/13 ≈ 0.538
      ├── Some((3, 1)): 1/7 ≈ 0.143
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 0/5 ≈ 0.000
      ├── Some((3, 4)): 0/5 ≈ 0.000
      ├── Some((3, 5)): 0/5 ≈ 0.000
      ├── Some((3, 6)): 6/12 ≈ 0.500
      ├── Some((3, 7)): 12/18 ≈ 0.667
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((4, 5)): 21/64 ≈ 0.328
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 6/11 ≈ 0.545
      ├── Some((5, 3)): 5/10 ≈ 0.500
      ├── Some((5, 4)): 0/4 ≈ 0.000
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 2/7 ≈ 0.286
      ├── Some((5, 7)): 1/6 ≈ 0.167
      └── Some((5, 8)): 0/4 ≈ 0.000
    ├── Some((4, 6)): 59/124 ≈ 0.476
      ├── Some((6, 0)): 11/19 ≈ 0.579
      ├── Some((6, 1)): 2/9 ≈ 0.222
      ├── Some((6, 2)): 5/13 ≈ 0.385
      ├── Some((6, 3)): 11/19 ≈ 0.579
      ├── Some((6, 5)): 14/23 ≈ 0.609
      ├── Some((6, 6)): 6/14 ≈ 0.429
      ├── Some((6, 7)): 7/15 ≈ 0.467
      └── Some((6, 8)): 3/11 ≈ 0.273
    ├── Some((4, 7)): 89/169 ≈ 0.527
      ├── Some((7, 0)): 12/21 ≈ 0.571
      ├── Some((7, 1)): 10/19 ≈ 0.526
      ├── Some((7, 2)): 13/22 ≈ 0.591
      ├── Some((7, 3)): 6/14 ≈ 0.429
      ├── Some((7, 4)): 8/17 ≈ 0.471
      ├── Some((7, 5)): 8/17 ≈ 0.471
      ├── Some((7, 6)): 7/16 ≈ 0.438
      ├── Some((7, 7)): 14/23 ≈ 0.609
      └── Some((7, 8)): 10/19 ≈ 0.526
    └── Some((4, 8)): 82/159 ≈ 0.516
      ├── Some((8, 0)): 6/14 ≈ 0.429
      ├── Some((8, 1)): 7/15 ≈ 0.467
      ├── Some((8, 2)): 4/12 ≈ 0.333
      ├── Some((8, 3)): 17/26 ≈ 0.654
      ├── Some((8, 4)): 8/16 ≈ 0.500
      ├── Some((8, 5)): 13/22 ≈ 0.591
      ├── Some((8, 6)): 11/20 ≈ 0.550
      ├── Some((8, 7)): 9/18 ≈ 0.500
      └── Some((8, 8)): 7/15 ≈ 0.467
  ├── Some((4, 5)): 963/1845 ≈ 0.522
    ├── Some((5, 0)): 120/225 ≈ 0.533
      ├── Some((0, 0)): 20/32 ≈ 0.625
      ├── Some((0, 1)): 29/42 ≈ 0.690
      ├── Some((0, 2)): 13/25 ≈ 0.520
      ├── Some((0, 3)): 11/22 ≈ 0.500
      ├── Some((0, 4)): 12/24 ≈ 0.500
      ├── Some((0, 5)): 13/25 ≈ 0.520
      ├── Some((0, 6)): 5/15 ≈ 0.333
      ├── Some((0, 7)): 8/19 ≈ 0.421
      └── Some((0, 8)): 9/20 ≈ 0.450
    ├── Some((5, 1)): 103/200 ≈ 0.515
      ├── Some((1, 0)): 10/21 ≈ 0.476
      ├── Some((1, 1)): 8/18 ≈ 0.444
      ├── Some((1, 2)): 12/23 ≈ 0.522
      ├── Some((1, 3)): 22/34 ≈ 0.647
      ├── Some((1, 4)): 7/17 ≈ 0.412
      ├── Some((1, 5)): 9/19 ≈ 0.474
      ├── Some((1, 6)): 9/19 ≈ 0.474
      ├── Some((1, 7)): 11/22 ≈ 0.500
      └── Some((1, 8)): 15/26 ≈ 0.577
    ├── Some((5, 2)): 106/204 ≈ 0.520
      ├── Some((2, 0)): 10/21 ≈ 0.476
      ├── Some((2, 1)): 6/16 ≈ 0.375
      ├── Some((2, 2)): 7/17 ≈ 0.412
      ├── Some((2, 3)): 10/21 ≈ 0.476
      ├── Some((2, 4)): 10/21 ≈ 0.476
      ├── Some((2, 5)): 10/21 ≈ 0.476
      ├── Some((2, 6)): 23/35 ≈ 0.657
      ├── Some((2, 7)): 17/28 ≈ 0.607
      └── Some((2, 8)): 12/23 ≈ 0.522
    ├── Some((5, 3)): 157/280 ≈ 0.561
      ├── Some((3, 0)): 26/41 ≈ 0.634
      ├── Some((3, 1)): 10/23 ≈ 0.435
      ├── Some((3, 2)): 19/33 ≈ 0.576
      ├── Some((3, 3)): 21/35 ≈ 0.600
      ├── Some((3, 4)): 15/28 ≈ 0.536
      ├── Some((3, 5)): 17/31 ≈ 0.548
      ├── Some((3, 6)): 5/16 ≈ 0.312
      ├── Some((3, 7)): 24/39 ≈ 0.615
      └── Some((3, 8)): 19/33 ≈ 0.576
    ├── Some((5, 4)): 137/250 ≈ 0.548
      ├── Some((4, 0)): 24/39 ≈ 0.615
      ├── Some((4, 1)): 32/48 ≈ 0.667
      ├── Some((4, 2)): 7/19 ≈ 0.368
      ├── Some((4, 3)): 12/26 ≈ 0.462
      ├── Some((4, 4)): 25/40 ≈ 0.625
      ├── Some((4, 6)): 5/17 ≈ 0.294
      ├── Some((4, 7)): 16/30 ≈ 0.533
      └── Some((4, 8)): 16/30 ≈ 0.533
    ├── Some((5, 5)): 88/177 ≈ 0.497
      ├── Some((5, 0)): 27/39 ≈ 0.692
      ├── Some((5, 1)): 8/19 ≈ 0.421
      ├── Some((5, 2)): 15/27 ≈ 0.556
      ├── Some((5, 3)): 6/16 ≈ 0.375
      ├── Some((5, 4)): 6/16 ≈ 0.375
      ├── Some((5, 6)): 9/20 ≈ 0.450
      ├── Some((5, 7)): 10/21 ≈ 0.476
      └── Some((5, 8)): 7/18 ≈ 0.389
    ├── Some((5, 6)): 56/127 ≈ 0.441
      ├── Some((6, 0)): 4/12 ≈ 0.333
      ├── Some((6, 1)): 8/17 ≈ 0.471
      ├── Some((6, 2)): 3/11 ≈ 0.273
      ├── Some((6, 3)): 10/19 ≈ 0.526
      ├── Some((6, 5)): 11/20 ≈ 0.550
      ├── Some((6, 6)): 5/14 ≈ 0.357
      ├── Some((6, 7)): 4/12 ≈ 0.333
      └── Some((6, 8)): 11/21 ≈ 0.524
    ├── Some((5, 7)): 127/235 ≈ 0.540
      ├── Some((7, 0)): 19/32 ≈ 0.594
      ├── Some((7, 1)): 9/20 ≈ 0.450
      ├── Some((7, 2)): 14/26 ≈ 0.538
      ├── Some((7, 3)): 13/25 ≈ 0.520
      ├── Some((7, 4)): 14/26 ≈ 0.538
      ├── Some((7, 5)): 6/17 ≈ 0.353
      ├── Some((7, 6)): 28/41 ≈ 0.683
      ├── Some((7, 7)): 11/23 ≈ 0.478
      └── Some((7, 8)): 12/24 ≈ 0.500
    └── Some((5, 8)): 68/146 ≈ 0.466
      ├── Some((8, 0)): 9/18 ≈ 0.500
      ├── Some((8, 1)): 10/19 ≈ 0.526
      ├── Some((8, 2)): 6/14 ≈ 0.429
      ├── Some((8, 3)): 8/17 ≈ 0.471
      ├── Some((8, 4)): 3/11 ≈ 0.273
      ├── Some((8, 5)): 6/15 ≈ 0.400
      ├── Some((8, 6)): 3/11 ≈ 0.273
      ├── Some((8, 7)): 12/21 ≈ 0.571
      └── Some((8, 8)): 10/19 ≈ 0.526
  ├── Some((4, 6)): 1127/2128 ≈ 0.530
    ├── Some((6, 0)): 100/203 ≈ 0.493
      ├── Some((0, 0)): 3/13 ≈ 0.231
      ├── Some((0, 1)): 6/16 ≈ 0.375
      ├── Some((0, 2)): 5/15 ≈ 0.333
      ├── Some((0, 3)): 23/36 ≈ 0.639
      ├── Some((0, 4)): 12/24 ≈ 0.500
      ├── Some((0, 5)): 13/25 ≈ 0.520
      ├── Some((0, 6)): 7/18 ≈ 0.389
      ├── Some((0, 7)): 24/37 ≈ 0.649
      └── Some((0, 8)): 7/18 ≈ 0.389
    ├── Some((6, 1)): 122/238 ≈ 0.513
      ├── Some((1, 0)): 14/27 ≈ 0.519
      ├── Some((1, 1)): 6/17 ≈ 0.353
      ├── Some((1, 2)): 14/27 ≈ 0.519
      ├── Some((1, 3)): 8/20 ≈ 0.400
      ├── Some((1, 4)): 8/20 ≈ 0.400
      ├── Some((1, 5)): 14/27 ≈ 0.519
      ├── Some((1, 6)): 18/31 ≈ 0.581
      ├── Some((1, 7)): 19/33 ≈ 0.576
      └── Some((1, 8)): 21/35 ≈ 0.600
    ├── Some((6, 2)): 109/218 ≈ 0.500
      ├── Some((2, 0)): 5/16 ≈ 0.312
      ├── Some((2, 1)): 14/27 ≈ 0.519
      ├── Some((2, 2)): 15/28 ≈ 0.536
      ├── Some((2, 3)): 20/33 ≈ 0.606
      ├── Some((2, 4)): 8/19 ≈ 0.421
      ├── Some((2, 5)): 15/28 ≈ 0.536
      ├── Some((2, 6)): 17/30 ≈ 0.567
      ├── Some((2, 7)): 2/12 ≈ 0.167
      └── Some((2, 8)): 12/24 ≈ 0.500
    ├── Some((6, 3)): 105/211 ≈ 0.498
      ├── Some((3, 0)): 11/23 ≈ 0.478
      ├── Some((3, 1)): 1/10 ≈ 0.100
      ├── Some((3, 2)): 19/32 ≈ 0.594
      ├── Some((3, 3)): 15/27 ≈ 0.556
      ├── Some((3, 4)): 14/26 ≈ 0.538
      ├── Some((3, 5)): 5/16 ≈ 0.312
      ├── Some((3, 6)): 20/33 ≈ 0.606
      ├── Some((3, 7)): 9/20 ≈ 0.450
      └── Some((3, 8)): 11/23 ≈ 0.478
    ├── Some((6, 5)): 158/292 ≈ 0.541
      ├── Some((5, 0)): 41/59 ≈ 0.695
      ├── Some((5, 1)): 4/16 ≈ 0.250
      ├── Some((5, 2)): 24/40 ≈ 0.600
      ├── Some((5, 3)): 18/33 ≈ 0.545
      ├── Some((5, 4)): 3/14 ≈ 0.214
      ├── Some((5, 5)): 18/33 ≈ 0.545
      ├── Some((5, 6)): 15/30 ≈ 0.500
      ├── Some((5, 7)): 19/35 ≈ 0.543
      └── Some((5, 8)): 16/31 ≈ 0.516
    ├── Some((6, 6)): 156/289 ≈ 0.540
      ├── Some((6, 0)): 28/49 ≈ 0.571
      ├── Some((6, 1)): 10/26 ≈ 0.385
      ├── Some((6, 2)): 8/23 ≈ 0.348
      ├── Some((6, 3)): 23/42 ≈ 0.548
      ├── Some((6, 5)): 16/34 ≈ 0.471
      ├── Some((6, 7)): 25/45 ≈ 0.556
      └── Some((6, 8)): 46/69 ≈ 0.667
    ├── Some((6, 7)): 158/293 ≈ 0.539
      ├── Some((7, 0)): 15/30 ≈ 0.500
      ├── Some((7, 1)): 21/37 ≈ 0.568
      ├── Some((7, 2)): 17/32 ≈ 0.531
      ├── Some((7, 3)): 10/24 ≈ 0.417
      ├── Some((7, 4)): 29/46 ≈ 0.630
      ├── Some((7, 5)): 14/28 ≈ 0.500
      ├── Some((7, 6)): 14/28 ≈ 0.500
      ├── Some((7, 7)): 17/32 ≈ 0.531
      └── Some((7, 8)): 20/35 ≈ 0.571
    └── Some((6, 8)): 219/383 ≈ 0.572
      ├── Some((8, 0)): 30/49 ≈ 0.612
      ├── Some((8, 1)): 22/40 ≈ 0.550
      ├── Some((8, 2)): 23/41 ≈ 0.561
      ├── Some((8, 3)): 39/59 ≈ 0.661
      ├── Some((8, 4)): 18/35 ≈ 0.514
      ├── Some((8, 5)): 34/54 ≈ 0.630
      ├── Some((8, 6)): 22/40 ≈ 0.550
      ├── Some((8, 7)): 19/37 ≈ 0.514
      └── Some((8, 8)): 11/27 ≈ 0.407
  ├── Some((4, 7)): 1397/2591 ≈ 0.539
    ├── Some((7, 0)): 180/325 ≈ 0.554
      ├── Some((0, 0)): 19/35 ≈ 0.543
      ├── Some((0, 1)): 19/35 ≈ 0.543
      ├── Some((0, 2)): 27/44 ≈ 0.614
      ├── Some((0, 3)): 13/28 ≈ 0.464
      ├── Some((0, 4)): 13/28 ≈ 0.464
      ├── Some((0, 5)): 18/34 ≈ 0.529
      ├── Some((0, 6)): 20/36 ≈ 0.556
      ├── Some((0, 7)): 23/40 ≈ 0.575
      └── Some((0, 8)): 27/44 ≈ 0.614
    ├── Some((7, 1)): 122/238 ≈ 0.513
      ├── Some((1, 0)): 22/36 ≈ 0.611
      ├── Some((1, 1)): 14/27 ≈ 0.519
      ├── Some((1, 2)): 10/22 ≈ 0.455
      ├── Some((1, 3)): 21/35 ≈ 0.600
      ├── Some((1, 4)): 24/38 ≈ 0.632
      ├── Some((1, 5)): 9/21 ≈ 0.429
      ├── Some((1, 6)): 9/21 ≈ 0.429
      ├── Some((1, 7)): 6/18 ≈ 0.333
      └── Some((1, 8)): 7/19 ≈ 0.368
    ├── Some((7, 2)): 191/342 ≈ 0.558
      ├── Some((2, 0)): 14/30 ≈ 0.467
      ├── Some((2, 1)): 35/54 ≈ 0.648
      ├── Some((2, 2)): 18/34 ≈ 0.529
      ├── Some((2, 3)): 16/32 ≈ 0.500
      ├── Some((2, 4)): 16/32 ≈ 0.500
      ├── Some((2, 5)): 10/25 ≈ 0.400
      ├── Some((2, 6)): 28/46 ≈ 0.609
      ├── Some((2, 7)): 30/48 ≈ 0.625
      └── Some((2, 8)): 23/40 ≈ 0.575
    ├── Some((7, 3)): 184/331 ≈ 0.556
      ├── Some((3, 0)): 19/35 ≈ 0.543
      ├── Some((3, 1)): 26/43 ≈ 0.605
      ├── Some((3, 2)): 23/40 ≈ 0.575
      ├── Some((3, 3)): 8/22 ≈ 0.364
      ├── Some((3, 4)): 18/34 ≈ 0.529
      ├── Some((3, 5)): 26/43 ≈ 0.605
      ├── Some((3, 6)): 28/46 ≈ 0.609
      ├── Some((3, 7)): 22/39 ≈ 0.564
      └── Some((3, 8)): 13/28 ≈ 0.464
    ├── Some((7, 4)): 137/261 ≈ 0.525
      ├── Some((4, 0)): 25/42 ≈ 0.595
      ├── Some((4, 1)): 23/40 ≈ 0.575
      ├── Some((4, 2)): 10/24 ≈ 0.417
      ├── Some((4, 3)): 11/25 ≈ 0.440
      ├── Some((4, 4)): 12/26 ≈ 0.462
      ├── Some((4, 5)): 25/42 ≈ 0.595
      ├── Some((4, 6)): 8/21 ≈ 0.381
      └── Some((4, 8)): 23/40 ≈ 0.575
    ├── Some((7, 5)): 180/325 ≈ 0.554
      ├── Some((5, 0)): 17/33 ≈ 0.515
      ├── Some((5, 1)): 12/27 ≈ 0.444
      ├── Some((5, 2)): 19/35 ≈ 0.543
      ├── Some((5, 3)): 34/52 ≈ 0.654
      ├── Some((5, 4)): 39/58 ≈ 0.672
      ├── Some((5, 5)): 16/32 ≈ 0.500
      ├── Some((5, 6)): 20/36 ≈ 0.556
      ├── Some((5, 7)): 7/20 ≈ 0.350
      └── Some((5, 8)): 15/31 ≈ 0.484
    ├── Some((7, 6)): 144/271 ≈ 0.531
      ├── Some((6, 0)): 15/30 ≈ 0.500
      ├── Some((6, 1)): 17/33 ≈ 0.515
      ├── Some((6, 2)): 20/36 ≈ 0.556
      ├── Some((6, 3)): 21/37 ≈ 0.568
      ├── Some((6, 5)): 22/39 ≈ 0.564
      ├── Some((6, 6)): 17/33 ≈ 0.515
      ├── Some((6, 7)): 9/23 ≈ 0.391
      └── Some((6, 8)): 22/39 ≈ 0.564
    ├── Some((7, 7)): 138/262 ≈ 0.527
      ├── Some((7, 0)): 20/36 ≈ 0.556
      ├── Some((7, 1)): 18/34 ≈ 0.529
      ├── Some((7, 2)): 9/23 ≈ 0.391
      ├── Some((7, 3)): 9/23 ≈ 0.391
      ├── Some((7, 4)): 14/29 ≈ 0.483
      ├── Some((7, 5)): 13/28 ≈ 0.464
      ├── Some((7, 6)): 18/34 ≈ 0.529
      └── Some((7, 8)): 36/54 ≈ 0.667
    └── Some((7, 8)): 120/235 ≈ 0.511
      ├── Some((8, 0)): 15/28 ≈ 0.536
      ├── Some((8, 1)): 9/21 ≈ 0.429
      ├── Some((8, 2)): 14/27 ≈ 0.519
      ├── Some((8, 3)): 19/33 ≈ 0.576
      ├── Some((8, 4)): 13/26 ≈ 0.500
      ├── Some((8, 5)): 14/27 ≈ 0.519
      ├── Some((8, 6)): 8/20 ≈ 0.400
      ├── Some((8, 7)): 11/23 ≈ 0.478
      └── Some((8, 8)): 16/29 ≈ 0.552
  └── Some((4, 8)): 725/1430 ≈ 0.507
    ├── Some((8, 0)): 70/143 ≈ 0.490
      ├── Some((0, 0)): 9/17 ≈ 0.529
      ├── Some((0, 1)): 13/21 ≈ 0.619
      ├── Some((0, 2)): 6/14 ≈ 0.429
      ├── Some((0, 3)): 9/17 ≈ 0.529
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 10/18 ≈ 0.556
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 10/18 ≈ 0.556
      └── Some((0, 8)): 4/12 ≈ 0.333
    ├── Some((8, 1)): 91/175 ≈ 0.520
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 1)): 10/20 ≈ 0.500
      ├── Some((1, 2)): 7/16 ≈ 0.438
      ├── Some((1, 3)): 6/15 ≈ 0.400
      ├── Some((1, 4)): 3/11 ≈ 0.273
      ├── Some((1, 5)): 9/18 ≈ 0.500
      ├── Some((1, 6)): 8/17 ≈ 0.471
      ├── Some((1, 7)): 20/30 ≈ 0.667
      └── Some((1, 8)): 18/28 ≈ 0.643
    ├── Some((8, 2)): 121/219 ≈ 0.553
      ├── Some((2, 0)): 18/29 ≈ 0.621
      ├── Some((2, 1)): 9/19 ≈ 0.474
      ├── Some((2, 2)): 9/19 ≈ 0.474
      ├── Some((2, 3)): 9/20 ≈ 0.450
      ├── Some((2, 4)): 15/26 ≈ 0.577
      ├── Some((2, 5)): 14/25 ≈ 0.560
      ├── Some((2, 6)): 18/29 ≈ 0.621
      ├── Some((2, 7)): 13/24 ≈ 0.542
      └── Some((2, 8)): 16/27 ≈ 0.593
    ├── Some((8, 3)): 46/106 ≈ 0.434
      ├── Some((3, 0)): 5/12 ≈ 0.417
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 6/13 ≈ 0.462
      ├── Some((3, 3)): 9/16 ≈ 0.562
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 2/8 ≈ 0.250
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((8, 4)): 111/204 ≈ 0.544
      ├── Some((4, 0)): 18/30 ≈ 0.600
      ├── Some((4, 1)): 21/33 ≈ 0.636
      ├── Some((4, 2)): 13/24 ≈ 0.542
      ├── Some((4, 3)): 13/25 ≈ 0.520
      ├── Some((4, 4)): 11/22 ≈ 0.500
      ├── Some((4, 5)): 12/23 ≈ 0.522
      ├── Some((4, 6)): 15/27 ≈ 0.556
      └── Some((4, 7)): 8/19 ≈ 0.421
    ├── Some((8, 5)): 52/116 ≈ 0.448
      ├── Some((5, 0)): 11/19 ≈ 0.579
      ├── Some((5, 1)): 1/7 ≈ 0.143
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 7/14 ≈ 0.500
      ├── Some((5, 6)): 2/9 ≈ 0.222
      ├── Some((5, 7)): 8/15 ≈ 0.533
      └── Some((5, 8)): 8/15 ≈ 0.533
    ├── Some((8, 6)): 76/153 ≈ 0.497
      ├── Some((6, 0)): 10/20 ≈ 0.500
      ├── Some((6, 1)): 12/22 ≈ 0.545
      ├── Some((6, 2)): 5/14 ≈ 0.357
      ├── Some((6, 3)): 9/18 ≈ 0.500
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 9/19 ≈ 0.474
      ├── Some((6, 7)): 6/15 ≈ 0.400
      └── Some((6, 8)): 16/26 ≈ 0.615
    ├── Some((8, 7)): 81/160 ≈ 0.506
      ├── Some((7, 0)): 8/17 ≈ 0.471
      ├── Some((7, 1)): 10/19 ≈ 0.526
      ├── Some((7, 2)): 10/19 ≈ 0.526
      ├── Some((7, 3)): 14/23 ≈ 0.609
      ├── Some((7, 4)): 5/13 ≈ 0.385
      ├── Some((7, 5)): 10/19 ≈ 0.526
      ├── Some((7, 6)): 13/22 ≈ 0.591
      ├── Some((7, 7)): 5/13 ≈ 0.385
      └── Some((7, 8)): 5/14 ≈ 0.357
    └── Some((8, 8)): 76/153 ≈ 0.497
      ├── Some((8, 0)): 9/18 ≈ 0.500
      ├── Some((8, 1)): 14/24 ≈ 0.583
      ├── Some((8, 2)): 9/19 ≈ 0.474
      ├── Some((8, 3)): 3/11 ≈ 0.273
      ├── Some((8, 4)): 11/21 ≈ 0.524
      ├── Some((8, 5)): 5/14 ≈ 0.357
      ├── Some((8, 6)): 14/24 ≈ 0.583
      └── Some((8, 7)): 11/21 ≈ 0.524
├── Some((6, 5)): 10891/20499 ≈ 0.531
  ├── Some((5, 0)): 1533/2835 ≈ 0.541
    ├── Some((0, 0)): 162/303 ≈ 0.535
      ├── Some((0, 1)): 22/40 ≈ 0.550
      ├── Some((0, 2)): 24/42 ≈ 0.571
      ├── Some((0, 3)): 20/38 ≈ 0.526
      ├── Some((0, 4)): 13/29 ≈ 0.448
      ├── Some((0, 5)): 31/51 ≈ 0.608
      ├── Some((0, 6)): 21/39 ≈ 0.538
      ├── Some((0, 7)): 12/28 ≈ 0.429
      └── Some((0, 8)): 18/35 ≈ 0.514
    ├── Some((0, 1)): 144/275 ≈ 0.524
      ├── Some((1, 0)): 24/40 ≈ 0.600
      ├── Some((1, 1)): 13/27 ≈ 0.481
      ├── Some((1, 2)): 14/28 ≈ 0.500
      ├── Some((1, 3)): 13/27 ≈ 0.481
      ├── Some((1, 4)): 13/27 ≈ 0.481
      ├── Some((1, 5)): 19/34 ≈ 0.559
      ├── Some((1, 6)): 16/31 ≈ 0.516
      ├── Some((1, 7)): 16/31 ≈ 0.516
      └── Some((1, 8)): 15/29 ≈ 0.517
    ├── Some((0, 2)): 202/363 ≈ 0.556
      ├── Some((2, 0)): 30/49 ≈ 0.612
      ├── Some((2, 1)): 14/30 ≈ 0.467
      ├── Some((2, 2)): 11/27 ≈ 0.407
      ├── Some((2, 3)): 22/40 ≈ 0.550
      ├── Some((2, 4)): 16/33 ≈ 0.485
      ├── Some((2, 5)): 29/48 ≈ 0.604
      ├── Some((2, 6)): 35/55 ≈ 0.636
      ├── Some((2, 7)): 15/32 ≈ 0.469
      └── Some((2, 8)): 29/48 ≈ 0.604
    ├── Some((0, 3)): 196/354 ≈ 0.554
      ├── Some((3, 0)): 23/41 ≈ 0.561
      ├── Some((3, 1)): 14/30 ≈ 0.467
      ├── Some((3, 2)): 53/75 ≈ 0.707
      ├── Some((3, 3)): 23/41 ≈ 0.561
      ├── Some((3, 4)): 20/37 ≈ 0.541
      ├── Some((3, 5)): 27/46 ≈ 0.587
      ├── Some((3, 6)): 12/28 ≈ 0.429
      ├── Some((3, 7)): 14/30 ≈ 0.467
      └── Some((3, 8)): 10/25 ≈ 0.400
    ├── Some((0, 4)): 128/250 ≈ 0.512
      ├── Some((4, 0)): 16/30 ≈ 0.533
      ├── Some((4, 1)): 13/26 ≈ 0.500
      ├── Some((4, 2)): 14/28 ≈ 0.500
      ├── Some((4, 3)): 7/19 ≈ 0.368
      ├── Some((4, 4)): 13/27 ≈ 0.481
      ├── Some((4, 5)): 17/31 ≈ 0.548
      ├── Some((4, 6)): 18/32 ≈ 0.562
      ├── Some((4, 7)): 18/32 ≈ 0.562
      └── Some((4, 8)): 11/24 ≈ 0.458
    ├── Some((0, 5)): 144/275 ≈ 0.524
      ├── Some((5, 1)): 17/33 ≈ 0.515
      ├── Some((5, 2)): 22/39 ≈ 0.564
      ├── Some((5, 3)): 19/36 ≈ 0.528
      ├── Some((5, 4)): 20/37 ≈ 0.541
      ├── Some((5, 5)): 10/25 ≈ 0.400
      ├── Some((5, 6)): 20/37 ≈ 0.541
      ├── Some((5, 7)): 13/28 ≈ 0.464
      └── Some((5, 8)): 22/39 ≈ 0.564
    ├── Some((0, 6)): 177/325 ≈ 0.545
      ├── Some((6, 0)): 35/56 ≈ 0.625
      ├── Some((6, 1)): 27/47 ≈ 0.574
      ├── Some((6, 2)): 21/39 ≈ 0.538
      ├── Some((6, 3)): 21/39 ≈ 0.538
      ├── Some((6, 4)): 31/51 ≈ 0.608
      ├── Some((6, 6)): 10/26 ≈ 0.385
      ├── Some((6, 7)): 13/29 ≈ 0.448
      └── Some((6, 8)): 19/37 ≈ 0.514
    ├── Some((0, 7)): 175/322 ≈ 0.543
      ├── Some((7, 0)): 26/43 ≈ 0.605
      ├── Some((7, 1)): 31/49 ≈ 0.633
      ├── Some((7, 2)): 14/29 ≈ 0.483
      ├── Some((7, 3)): 15/31 ≈ 0.484
      ├── Some((7, 4)): 14/29 ≈ 0.483
      ├── Some((7, 5)): 10/24 ≈ 0.417
      ├── Some((7, 6)): 11/26 ≈ 0.423
      ├── Some((7, 7)): 27/45 ≈ 0.600
      └── Some((7, 8)): 27/45 ≈ 0.600
    └── Some((0, 8)): 205/367 ≈ 0.559
      ├── Some((8, 0)): 33/52 ≈ 0.635
      ├── Some((8, 1)): 23/41 ≈ 0.561
      ├── Some((8, 2)): 14/30 ≈ 0.467
      ├── Some((8, 3)): 17/34 ≈ 0.500
      ├── Some((8, 4)): 27/46 ≈ 0.587
      ├── Some((8, 5)): 17/34 ≈ 0.500
      ├── Some((8, 6)): 28/47 ≈ 0.596
      ├── Some((8, 7)): 30/49 ≈ 0.612
      └── Some((8, 8)): 16/33 ≈ 0.485
  ├── Some((5, 1)): 878/1705 ≈ 0.515
    ├── Some((1, 0)): 37/95 ≈ 0.389
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 3/9 ≈ 0.333
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 4/10 ≈ 0.400
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((1, 1)): 95/186 ≈ 0.511
      ├── Some((1, 0)): 7/18 ≈ 0.389
      ├── Some((1, 2)): 6/16 ≈ 0.375
      ├── Some((1, 3)): 15/27 ≈ 0.556
      ├── Some((1, 4)): 11/22 ≈ 0.500
      ├── Some((1, 5)): 14/26 ≈ 0.538
      ├── Some((1, 6)): 19/31 ≈ 0.613
      ├── Some((1, 7)): 14/26 ≈ 0.538
      └── Some((1, 8)): 8/19 ≈ 0.421
    ├── Some((1, 2)): 78/160 ≈ 0.488
      ├── Some((2, 0)): 8/17 ≈ 0.471
      ├── Some((2, 1)): 10/20 ≈ 0.500
      ├── Some((2, 2)): 3/11 ≈ 0.273
      ├── Some((2, 3)): 22/32 ≈ 0.688
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 10/20 ≈ 0.500
      ├── Some((2, 6)): 10/20 ≈ 0.500
      ├── Some((2, 7)): 8/17 ≈ 0.471
      └── Some((2, 8)): 0/7 ≈ 0.000
    ├── Some((1, 3)): 126/233 ≈ 0.541
      ├── Some((3, 0)): 4/14 ≈ 0.286
      ├── Some((3, 1)): 28/41 ≈ 0.683
      ├── Some((3, 2)): 13/25 ≈ 0.520
      ├── Some((3, 3)): 17/30 ≈ 0.567
      ├── Some((3, 4)): 14/26 ≈ 0.538
      ├── Some((3, 5)): 12/24 ≈ 0.500
      ├── Some((3, 6)): 23/36 ≈ 0.639
      ├── Some((3, 7)): 6/17 ≈ 0.353
      └── Some((3, 8)): 8/19 ≈ 0.421
    ├── Some((1, 4)): 147/264 ≈ 0.557
      ├── Some((4, 0)): 5/16 ≈ 0.312
      ├── Some((4, 1)): 27/41 ≈ 0.659
      ├── Some((4, 2)): 4/15 ≈ 0.267
      ├── Some((4, 3)): 16/29 ≈ 0.552
      ├── Some((4, 4)): 20/33 ≈ 0.606
      ├── Some((4, 5)): 22/36 ≈ 0.611
      ├── Some((4, 6)): 23/37 ≈ 0.622
      ├── Some((4, 7)): 20/34 ≈ 0.588
      └── Some((4, 8)): 10/22 ≈ 0.455
    ├── Some((1, 5)): 66/142 ≈ 0.465
      ├── Some((5, 0)): 10/20 ≈ 0.500
      ├── Some((5, 2)): 4/13 ≈ 0.308
      ├── Some((5, 3)): 13/23 ≈ 0.565
      ├── Some((5, 4)): 11/21 ≈ 0.524
      ├── Some((5, 5)): 6/15 ≈ 0.400
      ├── Some((5, 6)): 16/27 ≈ 0.593
      ├── Some((5, 7)): 3/12 ≈ 0.250
      └── Some((5, 8)): 2/10 ≈ 0.200
    ├── Some((1, 6)): 103/198 ≈ 0.520
      ├── Some((6, 0)): 18/31 ≈ 0.581
      ├── Some((6, 1)): 15/27 ≈ 0.556
      ├── Some((6, 2)): 8/19 ≈ 0.421
      ├── Some((6, 3)): 15/27 ≈ 0.556
      ├── Some((6, 4)): 14/26 ≈ 0.538
      ├── Some((6, 6)): 9/20 ≈ 0.450
      ├── Some((6, 7)): 16/28 ≈ 0.571
      └── Some((6, 8)): 8/19 ≈ 0.421
    ├── Some((1, 7)): 127/234 ≈ 0.543
      ├── Some((7, 0)): 11/22 ≈ 0.500
      ├── Some((7, 1)): 13/25 ≈ 0.520
      ├── Some((7, 2)): 8/19 ≈ 0.421
      ├── Some((7, 3)): 26/39 ≈ 0.667
      ├── Some((7, 4)): 14/26 ≈ 0.538
      ├── Some((7, 5)): 12/24 ≈ 0.500
      ├── Some((7, 6)): 21/33 ≈ 0.636
      ├── Some((7, 7)): 7/18 ≈ 0.389
      └── Some((7, 8)): 15/27 ≈ 0.556
    └── Some((1, 8)): 99/192 ≈ 0.516
      ├── Some((8, 0)): 9/19 ≈ 0.474
      ├── Some((8, 1)): 16/27 ≈ 0.593
      ├── Some((8, 2)): 7/17 ≈ 0.412
      ├── Some((8, 3)): 11/21 ≈ 0.524
      ├── Some((8, 4)): 10/20 ≈ 0.500
      ├── Some((8, 5)): 8/18 ≈ 0.444
      ├── Some((8, 6)): 10/20 ≈ 0.500
      ├── Some((8, 7)): 16/27 ≈ 0.593
      └── Some((8, 8)): 11/22 ≈ 0.500
  ├── Some((5, 2)): 908/1757 ≈ 0.517
    ├── Some((2, 0)): 68/145 ≈ 0.469
      ├── Some((0, 0)): 12/21 ≈ 0.571
      ├── Some((0, 1)): 6/14 ≈ 0.429
      ├── Some((0, 2)): 9/18 ≈ 0.500
      ├── Some((0, 3)): 9/18 ≈ 0.500
      ├── Some((0, 4)): 4/12 ≈ 0.333
      ├── Some((0, 5)): 14/23 ≈ 0.609
      ├── Some((0, 6)): 6/15 ≈ 0.400
      ├── Some((0, 7)): 3/11 ≈ 0.273
      └── Some((0, 8)): 4/12 ≈ 0.333
    ├── Some((2, 1)): 91/180 ≈ 0.506
      ├── Some((1, 0)): 6/15 ≈ 0.400
      ├── Some((1, 1)): 7/17 ≈ 0.412
      ├── Some((1, 2)): 16/27 ≈ 0.593
      ├── Some((1, 3)): 14/24 ≈ 0.583
      ├── Some((1, 4)): 18/29 ≈ 0.621
      ├── Some((1, 5)): 12/22 ≈ 0.545
      ├── Some((1, 6)): 6/15 ≈ 0.400
      ├── Some((1, 7)): 4/13 ≈ 0.308
      └── Some((1, 8)): 7/17 ≈ 0.412
    ├── Some((2, 2)): 110/209 ≈ 0.526
      ├── Some((2, 0)): 23/37 ≈ 0.622
      ├── Some((2, 1)): 19/32 ≈ 0.594
      ├── Some((2, 3)): 15/28 ≈ 0.536
      ├── Some((2, 4)): 8/19 ≈ 0.421
      ├── Some((2, 5)): 7/18 ≈ 0.389
      ├── Some((2, 6)): 9/21 ≈ 0.429
      ├── Some((2, 7)): 9/21 ≈ 0.429
      └── Some((2, 8)): 19/32 ≈ 0.594
    ├── Some((2, 3)): 118/221 ≈ 0.534
      ├── Some((3, 0)): 20/32 ≈ 0.625
      ├── Some((3, 1)): 4/14 ≈ 0.286
      ├── Some((3, 2)): 10/21 ≈ 0.476
      ├── Some((3, 3)): 6/16 ≈ 0.375
      ├── Some((3, 4)): 9/20 ≈ 0.450
      ├── Some((3, 5)): 11/22 ≈ 0.500
      ├── Some((3, 6)): 17/29 ≈ 0.586
      ├── Some((3, 7)): 15/27 ≈ 0.556
      └── Some((3, 8)): 26/39 ≈ 0.667
    ├── Some((2, 4)): 88/176 ≈ 0.500
      ├── Some((4, 0)): 5/14 ≈ 0.357
      ├── Some((4, 1)): 19/30 ≈ 0.633
      ├── Some((4, 2)): 2/10 ≈ 0.200
      ├── Some((4, 3)): 14/24 ≈ 0.583
      ├── Some((4, 4)): 10/20 ≈ 0.500
      ├── Some((4, 5)): 10/20 ≈ 0.500
      ├── Some((4, 6)): 13/23 ≈ 0.565
      ├── Some((4, 7)): 6/16 ≈ 0.375
      └── Some((4, 8)): 8/18 ≈ 0.444
    ├── Some((2, 5)): 126/233 ≈ 0.541
      ├── Some((5, 0)): 10/22 ≈ 0.455
      ├── Some((5, 1)): 16/30 ≈ 0.533
      ├── Some((5, 3)): 21/35 ≈ 0.600
      ├── Some((5, 4)): 9/21 ≈ 0.429
      ├── Some((5, 5)): 20/34 ≈ 0.588
      ├── Some((5, 6)): 23/37 ≈ 0.622
      ├── Some((5, 7)): 17/31 ≈ 0.548
      └── Some((5, 8)): 10/22 ≈ 0.455
    ├── Some((2, 6)): 101/196 ≈ 0.515
      ├── Some((6, 0)): 10/22 ≈ 0.455
      ├── Some((6, 1)): 12/24 ≈ 0.500
      ├── Some((6, 2)): 16/28 ≈ 0.571
      ├── Some((6, 3)): 12/24 ≈ 0.500
      ├── Some((6, 4)): 15/27 ≈ 0.556
      ├── Some((6, 6)): 12/24 ≈ 0.500
      ├── Some((6, 7)): 15/27 ≈ 0.556
      └── Some((6, 8)): 8/19 ≈ 0.421
    ├── Some((2, 7)): 103/199 ≈ 0.518
      ├── Some((7, 0)): 17/28 ≈ 0.607
      ├── Some((7, 1)): 13/24 ≈ 0.542
      ├── Some((7, 2)): 10/20 ≈ 0.500
      ├── Some((7, 3)): 6/16 ≈ 0.375
      ├── Some((7, 4)): 12/23 ≈ 0.522
      ├── Some((7, 5)): 11/22 ≈ 0.500
      ├── Some((7, 6)): 17/28 ≈ 0.607
      ├── Some((7, 7)): 8/18 ≈ 0.444
      └── Some((7, 8)): 9/19 ≈ 0.474
    └── Some((2, 8)): 102/197 ≈ 0.518
      ├── Some((8, 0)): 18/29 ≈ 0.621
      ├── Some((8, 1)): 9/19 ≈ 0.474
      ├── Some((8, 2)): 13/24 ≈ 0.542
      ├── Some((8, 3)): 18/29 ≈ 0.621
      ├── Some((8, 4)): 9/19 ≈ 0.474
      ├── Some((8, 5)): 9/19 ≈ 0.474
      ├── Some((8, 6)): 10/21 ≈ 0.476
      ├── Some((8, 7)): 9/19 ≈ 0.474
      └── Some((8, 8)): 7/17 ≈ 0.412
  ├── Some((5, 3)): 1424/2648 ≈ 0.538
    ├── Some((3, 0)): 143/271 ≈ 0.528
      ├── Some((0, 0)): 19/34 ≈ 0.559
      ├── Some((0, 1)): 17/32 ≈ 0.531
      ├── Some((0, 2)): 24/39 ≈ 0.615
      ├── Some((0, 3)): 20/35 ≈ 0.571
      ├── Some((0, 4)): 16/30 ≈ 0.533
      ├── Some((0, 5)): 14/28 ≈ 0.500
      ├── Some((0, 6)): 10/23 ≈ 0.435
      ├── Some((0, 7)): 8/21 ≈ 0.381
      └── Some((0, 8)): 14/28 ≈ 0.500
    ├── Some((3, 1)): 148/279 ≈ 0.530
      ├── Some((1, 0)): 11/25 ≈ 0.440
      ├── Some((1, 1)): 21/36 ≈ 0.583
      ├── Some((1, 2)): 12/26 ≈ 0.462
      ├── Some((1, 3)): 8/21 ≈ 0.381
      ├── Some((1, 4)): 26/42 ≈ 0.619
      ├── Some((1, 5)): 21/36 ≈ 0.583
      ├── Some((1, 6)): 8/21 ≈ 0.381
      ├── Some((1, 7)): 19/34 ≈ 0.559
      └── Some((1, 8)): 22/37 ≈ 0.595
    ├── Some((3, 2)): 135/259 ≈ 0.521
      ├── Some((2, 0)): 21/36 ≈ 0.583
      ├── Some((2, 1)): 7/19 ≈ 0.368
      ├── Some((2, 2)): 22/37 ≈ 0.595
      ├── Some((2, 3)): 21/36 ≈ 0.583
      ├── Some((2, 4)): 13/27 ≈ 0.481
      ├── Some((2, 5)): 21/36 ≈ 0.583
      ├── Some((2, 6)): 5/17 ≈ 0.294
      ├── Some((2, 7)): 12/25 ≈ 0.480
      └── Some((2, 8)): 12/25 ≈ 0.480
    ├── Some((3, 3)): 120/236 ≈ 0.508
      ├── Some((3, 0)): 12/26 ≈ 0.462
      ├── Some((3, 1)): 17/32 ≈ 0.531
      ├── Some((3, 2)): 24/40 ≈ 0.600
      ├── Some((3, 4)): 17/32 ≈ 0.531
      ├── Some((3, 5)): 17/32 ≈ 0.531
      ├── Some((3, 6)): 15/29 ≈ 0.517
      ├── Some((3, 7)): 7/19 ≈ 0.368
      └── Some((3, 8)): 11/25 ≈ 0.440
    ├── Some((3, 4)): 151/284 ≈ 0.532
      ├── Some((4, 0)): 23/39 ≈ 0.590
      ├── Some((4, 1)): 18/33 ≈ 0.545
      ├── Some((4, 2)): 13/27 ≈ 0.481
      ├── Some((4, 3)): 12/26 ≈ 0.462
      ├── Some((4, 4)): 6/19 ≈ 0.316
      ├── Some((4, 5)): 16/31 ≈ 0.516
      ├── Some((4, 6)): 18/33 ≈ 0.545
      ├── Some((4, 7)): 32/49 ≈ 0.653
      └── Some((4, 8)): 12/26 ≈ 0.462
    ├── Some((3, 5)): 168/309 ≈ 0.544
      ├── Some((5, 0)): 29/48 ≈ 0.604
      ├── Some((5, 1)): 11/27 ≈ 0.407
      ├── Some((5, 2)): 28/47 ≈ 0.596
      ├── Some((5, 4)): 30/50 ≈ 0.600
      ├── Some((5, 5)): 23/41 ≈ 0.561
      ├── Some((5, 6)): 14/30 ≈ 0.467
      ├── Some((5, 7)): 10/25 ≈ 0.400
      └── Some((5, 8)): 22/40 ≈ 0.550
    ├── Some((3, 6)): 182/330 ≈ 0.552
      ├── Some((6, 0)): 31/51 ≈ 0.608
      ├── Some((6, 1)): 24/43 ≈ 0.558
      ├── Some((6, 2)): 20/38 ≈ 0.526
      ├── Some((6, 3)): 14/31 ≈ 0.452
      ├── Some((6, 4)): 25/44 ≈ 0.568
      ├── Some((6, 6)): 33/53 ≈ 0.623
      ├── Some((6, 7)): 17/34 ≈ 0.500
      └── Some((6, 8)): 17/35 ≈ 0.486
    ├── Some((3, 7)): 144/273 ≈ 0.527
      ├── Some((7, 0)): 15/29 ≈ 0.517
      ├── Some((7, 1)): 5/17 ≈ 0.294
      ├── Some((7, 2)): 18/33 ≈ 0.545
      ├── Some((7, 3)): 24/40 ≈ 0.600
      ├── Some((7, 4)): 32/49 ≈ 0.653
      ├── Some((7, 5)): 8/21 ≈ 0.381
      ├── Some((7, 6)): 19/34 ≈ 0.559
      ├── Some((7, 7)): 10/23 ≈ 0.435
      └── Some((7, 8)): 12/26 ≈ 0.462
    └── Some((3, 8)): 233/406 ≈ 0.574
      ├── Some((8, 0)): 21/39 ≈ 0.538
      ├── Some((8, 1)): 18/36 ≈ 0.500
      ├── Some((8, 2)): 28/48 ≈ 0.583
      ├── Some((8, 3)): 22/41 ≈ 0.537
      ├── Some((8, 4)): 33/53 ≈ 0.623
      ├── Some((8, 5)): 26/45 ≈ 0.578
      ├── Some((8, 6)): 21/39 ≈ 0.538
      ├── Some((8, 7)): 43/65 ≈ 0.662
      └── Some((8, 8)): 21/39 ≈ 0.538
  ├── Some((5, 4)): 1964/3568 ≈ 0.550
    ├── Some((4, 0)): 159/306 ≈ 0.520
      ├── Some((0, 0)): 13/29 ≈ 0.448
      ├── Some((0, 1)): 27/45 ≈ 0.600
      ├── Some((0, 2)): 12/27 ≈ 0.444
      ├── Some((0, 3)): 14/30 ≈ 0.467
      ├── Some((0, 4)): 18/35 ≈ 0.514
      ├── Some((0, 5)): 30/49 ≈ 0.612
      ├── Some((0, 6)): 6/19 ≈ 0.316
      ├── Some((0, 7)): 16/32 ≈ 0.500
      └── Some((0, 8)): 22/39 ≈ 0.564
    ├── Some((4, 1)): 239/429 ≈ 0.557
      ├── Some((1, 0)): 22/42 ≈ 0.524
      ├── Some((1, 1)): 21/41 ≈ 0.512
      ├── Some((1, 2)): 30/52 ≈ 0.577
      ├── Some((1, 3)): 17/36 ≈ 0.472
      ├── Some((1, 4)): 34/57 ≈ 0.596
      ├── Some((1, 5)): 22/42 ≈ 0.524
      ├── Some((1, 6)): 31/53 ≈ 0.585
      ├── Some((1, 7)): 43/67 ≈ 0.642
      └── Some((1, 8)): 19/38 ≈ 0.500
    ├── Some((4, 2)): 180/339 ≈ 0.531
      ├── Some((2, 0)): 10/25 ≈ 0.400
      ├── Some((2, 1)): 23/41 ≈ 0.561
      ├── Some((2, 2)): 23/41 ≈ 0.561
      ├── Some((2, 3)): 24/43 ≈ 0.558
      ├── Some((2, 4)): 31/51 ≈ 0.608
      ├── Some((2, 5)): 11/27 ≈ 0.407
      ├── Some((2, 6)): 16/33 ≈ 0.485
      ├── Some((2, 7)): 21/39 ≈ 0.538
      └── Some((2, 8)): 20/38 ≈ 0.526
    ├── Some((4, 3)): 236/424 ≈ 0.557
      ├── Some((3, 0)): 31/53 ≈ 0.585
      ├── Some((3, 1)): 22/42 ≈ 0.524
      ├── Some((3, 2)): 11/28 ≈ 0.393
      ├── Some((3, 3)): 30/52 ≈ 0.577
      ├── Some((3, 4)): 23/44 ≈ 0.523
      ├── Some((3, 5)): 26/47 ≈ 0.553
      ├── Some((3, 6)): 12/30 ≈ 0.400
      ├── Some((3, 7)): 35/58 ≈ 0.603
      └── Some((3, 8)): 45/69 ≈ 0.652
    ├── Some((4, 4)): 189/353 ≈ 0.535
      ├── Some((4, 0)): 33/56 ≈ 0.589
      ├── Some((4, 1)): 20/40 ≈ 0.500
      ├── Some((4, 2)): 15/33 ≈ 0.455
      ├── Some((4, 3)): 25/46 ≈ 0.543
      ├── Some((4, 5)): 31/53 ≈ 0.585
      ├── Some((4, 6)): 15/33 ≈ 0.455
      ├── Some((4, 7)): 29/51 ≈ 0.569
      └── Some((4, 8)): 20/40 ≈ 0.500
    ├── Some((4, 5)): 300/520 ≈ 0.577
      ├── Some((5, 0)): 47/77 ≈ 0.610
      ├── Some((5, 1)): 59/91 ≈ 0.648
      ├── Some((5, 2)): 28/53 ≈ 0.528
      ├── Some((5, 3)): 28/54 ≈ 0.519
      ├── Some((5, 5)): 19/42 ≈ 0.452
      ├── Some((5, 6)): 39/67 ≈ 0.582
      ├── Some((5, 7)): 44/73 ≈ 0.603
      └── Some((5, 8)): 35/62 ≈ 0.565
    ├── Some((4, 6)): 155/300 ≈ 0.517
      ├── Some((6, 0)): 22/41 ≈ 0.537
      ├── Some((6, 1)): 17/35 ≈ 0.486
      ├── Some((6, 2)): 25/44 ≈ 0.568
      ├── Some((6, 3)): 22/41 ≈ 0.537
      ├── Some((6, 4)): 15/32 ≈ 0.469
      ├── Some((6, 6)): 28/48 ≈ 0.583
      ├── Some((6, 7)): 12/28 ≈ 0.429
      └── Some((6, 8)): 13/30 ≈ 0.433
    ├── Some((4, 7)): 183/343 ≈ 0.534
      ├── Some((7, 0)): 27/46 ≈ 0.587
      ├── Some((7, 1)): 27/46 ≈ 0.587
      ├── Some((7, 2)): 8/23 ≈ 0.348
      ├── Some((7, 3)): 21/39 ≈ 0.538
      ├── Some((7, 4)): 26/45 ≈ 0.578
      ├── Some((7, 5)): 17/34 ≈ 0.500
      ├── Some((7, 6)): 19/37 ≈ 0.514
      ├── Some((7, 7)): 24/43 ≈ 0.558
      └── Some((7, 8)): 13/29 ≈ 0.448
    └── Some((4, 8)): 322/553 ≈ 0.582
      ├── Some((8, 0)): 24/47 ≈ 0.511
      ├── Some((8, 1)): 44/72 ≈ 0.611
      ├── Some((8, 2)): 23/46 ≈ 0.500
      ├── Some((8, 3)): 16/37 ≈ 0.432
      ├── Some((8, 4)): 12/31 ≈ 0.387
      ├── Some((8, 5)): 45/73 ≈ 0.616
      ├── Some((8, 6)): 66/97 ≈ 0.680
      ├── Some((8, 7)): 38/65 ≈ 0.585
      └── Some((8, 8)): 54/84 ≈ 0.643
  ├── Some((5, 5)): 943/1818 ≈ 0.519
    ├── Some((5, 0)): 100/200 ≈ 0.500
      ├── Some((0, 0)): 17/29 ≈ 0.586
      ├── Some((0, 1)): 11/22 ≈ 0.500
      ├── Some((0, 2)): 4/14 ≈ 0.286
      ├── Some((0, 3)): 12/23 ≈ 0.522
      ├── Some((0, 4)): 14/26 ≈ 0.538
      ├── Some((0, 5)): 17/29 ≈ 0.586
      ├── Some((0, 6)): 4/14 ≈ 0.286
      ├── Some((0, 7)): 6/16 ≈ 0.375
      └── Some((0, 8)): 14/26 ≈ 0.538
    ├── Some((5, 1)): 142/264 ≈ 0.538
      ├── Some((1, 0)): 24/39 ≈ 0.615
      ├── Some((1, 1)): 27/42 ≈ 0.643
      ├── Some((1, 2)): 26/41 ≈ 0.634
      ├── Some((1, 3)): 13/27 ≈ 0.481
      ├── Some((1, 4)): 23/38 ≈ 0.605
      ├── Some((1, 5)): 6/18 ≈ 0.333
      ├── Some((1, 6)): 7/19 ≈ 0.368
      ├── Some((1, 7)): 4/15 ≈ 0.267
      └── Some((1, 8)): 11/24 ≈ 0.458
    ├── Some((5, 2)): 146/270 ≈ 0.541
      ├── Some((2, 0)): 20/35 ≈ 0.571
      ├── Some((2, 1)): 18/32 ≈ 0.562
      ├── Some((2, 2)): 23/38 ≈ 0.605
      ├── Some((2, 3)): 1/11 ≈ 0.091
      ├── Some((2, 4)): 17/31 ≈ 0.548
      ├── Some((2, 5)): 20/35 ≈ 0.571
      ├── Some((2, 6)): 24/39 ≈ 0.615
      ├── Some((2, 7)): 10/23 ≈ 0.435
      └── Some((2, 8)): 12/25 ≈ 0.480
    ├── Some((5, 3)): 110/216 ≈ 0.509
      ├── Some((3, 0)): 18/30 ≈ 0.600
      ├── Some((3, 1)): 11/23 ≈ 0.478
      ├── Some((3, 2)): 18/30 ≈ 0.600
      ├── Some((3, 3)): 12/24 ≈ 0.500
      ├── Some((3, 4)): 15/27 ≈ 0.556
      ├── Some((3, 5)): 5/15 ≈ 0.333
      ├── Some((3, 6)): 8/19 ≈ 0.421
      ├── Some((3, 7)): 10/22 ≈ 0.455
      └── Some((3, 8)): 13/25 ≈ 0.520
    ├── Some((5, 4)): 139/260 ≈ 0.535
      ├── Some((4, 0)): 14/27 ≈ 0.519
      ├── Some((4, 1)): 13/26 ≈ 0.500
      ├── Some((4, 2)): 13/26 ≈ 0.500
      ├── Some((4, 3)): 23/37 ≈ 0.622
      ├── Some((4, 4)): 15/28 ≈ 0.536
      ├── Some((4, 5)): 22/36 ≈ 0.611
      ├── Some((4, 6)): 10/23 ≈ 0.435
      ├── Some((4, 7)): 18/32 ≈ 0.562
      └── Some((4, 8)): 11/24 ≈ 0.458
    ├── Some((5, 6)): 123/235 ≈ 0.523
      ├── Some((6, 0)): 15/29 ≈ 0.517
      ├── Some((6, 1)): 26/41 ≈ 0.634
      ├── Some((6, 2)): 14/28 ≈ 0.500
      ├── Some((6, 3)): 14/28 ≈ 0.500
      ├── Some((6, 4)): 7/19 ≈ 0.368
      ├── Some((6, 6)): 19/33 ≈ 0.576
      ├── Some((6, 7)): 19/34 ≈ 0.559
      └── Some((6, 8)): 9/22 ≈ 0.409
    ├── Some((5, 7)): 86/178 ≈ 0.483
      ├── Some((7, 0)): 7/17 ≈ 0.412
      ├── Some((7, 1)): 6/16 ≈ 0.375
      ├── Some((7, 2)): 7/17 ≈ 0.412
      ├── Some((7, 3)): 10/20 ≈ 0.500
      ├── Some((7, 4)): 19/30 ≈ 0.633
      ├── Some((7, 5)): 18/29 ≈ 0.621
      ├── Some((7, 6)): 4/13 ≈ 0.308
      ├── Some((7, 7)): 6/16 ≈ 0.375
      └── Some((7, 8)): 9/19 ≈ 0.474
    └── Some((5, 8)): 96/194 ≈ 0.495
      ├── Some((8, 0)): 7/17 ≈ 0.412
      ├── Some((8, 1)): 11/22 ≈ 0.500
      ├── Some((8, 2)): 7/17 ≈ 0.412
      ├── Some((8, 3)): 19/31 ≈ 0.613
      ├── Some((8, 4)): 5/15 ≈ 0.333
      ├── Some((8, 5)): 15/27 ≈ 0.556
      ├── Some((8, 6)): 10/21 ≈ 0.476
      ├── Some((8, 7)): 19/31 ≈ 0.613
      └── Some((8, 8)): 3/12 ≈ 0.250
  ├── Some((5, 6)): 1246/2343 ≈ 0.532
    ├── Some((6, 0)): 68/155 ≈ 0.439
      ├── Some((0, 0)): 9/19 ≈ 0.474
      ├── Some((0, 1)): 8/17 ≈ 0.471
      ├── Some((0, 2)): 8/18 ≈ 0.444
      ├── Some((0, 3)): 3/12 ≈ 0.250
      ├── Some((0, 4)): 9/19 ≈ 0.474
      ├── Some((0, 5)): 1/9 ≈ 0.111
      ├── Some((0, 6)): 11/21 ≈ 0.524
      ├── Some((0, 7)): 8/18 ≈ 0.444
      └── Some((0, 8)): 11/21 ≈ 0.524
    ├── Some((6, 1)): 152/288 ≈ 0.528
      ├── Some((1, 0)): 12/26 ≈ 0.462
      ├── Some((1, 1)): 12/26 ≈ 0.462
      ├── Some((1, 2)): 27/43 ≈ 0.628
      ├── Some((1, 3)): 10/24 ≈ 0.417
      ├── Some((1, 4)): 10/24 ≈ 0.417
      ├── Some((1, 5)): 15/30 ≈ 0.500
      ├── Some((1, 6)): 21/37 ≈ 0.568
      ├── Some((1, 7)): 30/47 ≈ 0.638
      └── Some((1, 8)): 15/30 ≈ 0.500
    ├── Some((6, 2)): 130/254 ≈ 0.512
      ├── Some((2, 0)): 22/37 ≈ 0.595
      ├── Some((2, 1)): 4/15 ≈ 0.267
      ├── Some((2, 2)): 11/24 ≈ 0.458
      ├── Some((2, 3)): 20/35 ≈ 0.571
      ├── Some((2, 4)): 11/25 ≈ 0.440
      ├── Some((2, 5)): 19/34 ≈ 0.559
      ├── Some((2, 6)): 7/19 ≈ 0.368
      ├── Some((2, 7)): 25/41 ≈ 0.610
      └── Some((2, 8)): 10/23 ≈ 0.435
    ├── Some((6, 3)): 136/263 ≈ 0.517
      ├── Some((3, 0)): 10/23 ≈ 0.435
      ├── Some((3, 1)): 10/23 ≈ 0.435
      ├── Some((3, 2)): 22/37 ≈ 0.595
      ├── Some((3, 3)): 10/23 ≈ 0.435
      ├── Some((3, 4)): 19/34 ≈ 0.559
      ├── Some((3, 5)): 12/25 ≈ 0.480
      ├── Some((3, 6)): 16/30 ≈ 0.533
      ├── Some((3, 7)): 18/33 ≈ 0.545
      └── Some((3, 8)): 19/34 ≈ 0.559
    ├── Some((6, 4)): 166/309 ≈ 0.537
      ├── Some((4, 0)): 22/39 ≈ 0.564
      ├── Some((4, 1)): 19/35 ≈ 0.543
      ├── Some((4, 2)): 4/16 ≈ 0.250
      ├── Some((4, 3)): 24/41 ≈ 0.585
      ├── Some((4, 4)): 25/42 ≈ 0.595
      ├── Some((4, 5)): 24/41 ≈ 0.585
      ├── Some((4, 6)): 8/22 ≈ 0.364
      ├── Some((4, 7)): 27/44 ≈ 0.614
      └── Some((4, 8)): 13/28 ≈ 0.464
    ├── Some((6, 6)): 208/373 ≈ 0.558
      ├── Some((6, 0)): 17/37 ≈ 0.459
      ├── Some((6, 1)): 32/56 ≈ 0.571
      ├── Some((6, 2)): 41/67 ≈ 0.612
      ├── Some((6, 3)): 31/55 ≈ 0.564
      ├── Some((6, 4)): 14/33 ≈ 0.424
      ├── Some((6, 7)): 28/52 ≈ 0.538
      └── Some((6, 8)): 45/72 ≈ 0.625
    ├── Some((6, 7)): 178/327 ≈ 0.544
      ├── Some((7, 0)): 38/57 ≈ 0.667
      ├── Some((7, 1)): 13/28 ≈ 0.464
      ├── Some((7, 2)): 16/32 ≈ 0.500
      ├── Some((7, 3)): 18/35 ≈ 0.514
      ├── Some((7, 4)): 18/35 ≈ 0.514
      ├── Some((7, 5)): 21/38 ≈ 0.553
      ├── Some((7, 6)): 28/46 ≈ 0.609
      ├── Some((7, 7)): 16/32 ≈ 0.500
      └── Some((7, 8)): 9/23 ≈ 0.391
    └── Some((6, 8)): 208/373 ≈ 0.558
      ├── Some((8, 0)): 36/56 ≈ 0.643
      ├── Some((8, 1)): 17/34 ≈ 0.500
      ├── Some((8, 2)): 23/42 ≈ 0.548
      ├── Some((8, 3)): 32/52 ≈ 0.615
      ├── Some((8, 4)): 15/32 ≈ 0.469
      ├── Some((8, 5)): 26/45 ≈ 0.578
      ├── Some((8, 6)): 21/39 ≈ 0.538
      ├── Some((8, 7)): 13/29 ≈ 0.448
      └── Some((8, 8)): 24/43 ≈ 0.558
  ├── Some((5, 7)): 915/1770 ≈ 0.517
    ├── Some((7, 0)): 112/213 ≈ 0.526
      ├── Some((0, 0)): 12/23 ≈ 0.522
      ├── Some((0, 1)): 6/16 ≈ 0.375
      ├── Some((0, 2)): 19/31 ≈ 0.613
      ├── Some((0, 3)): 8/19 ≈ 0.421
      ├── Some((0, 4)): 29/42 ≈ 0.690
      ├── Some((0, 5)): 8/19 ≈ 0.421
      ├── Some((0, 6)): 8/19 ≈ 0.421
      ├── Some((0, 7)): 4/14 ≈ 0.286
      └── Some((0, 8)): 17/29 ≈ 0.586
    ├── Some((7, 1)): 73/153 ≈ 0.477
      ├── Some((1, 0)): 5/13 ≈ 0.385
      ├── Some((1, 1)): 3/11 ≈ 0.273
      ├── Some((1, 2)): 14/23 ≈ 0.609
      ├── Some((1, 3)): 9/18 ≈ 0.500
      ├── Some((1, 4)): 8/17 ≈ 0.471
      ├── Some((1, 5)): 10/19 ≈ 0.526
      ├── Some((1, 6)): 8/17 ≈ 0.471
      ├── Some((1, 7)): 6/15 ≈ 0.400
      └── Some((1, 8)): 10/19 ≈ 0.526
    ├── Some((7, 2)): 146/263 ≈ 0.555
      ├── Some((2, 0)): 13/26 ≈ 0.500
      ├── Some((2, 1)): 9/21 ≈ 0.429
      ├── Some((2, 2)): 21/34 ≈ 0.618
      ├── Some((2, 3)): 15/28 ≈ 0.536
      ├── Some((2, 4)): 24/38 ≈ 0.632
      ├── Some((2, 5)): 15/28 ≈ 0.536
      ├── Some((2, 6)): 15/28 ≈ 0.536
      ├── Some((2, 7)): 24/38 ≈ 0.632
      └── Some((2, 8)): 9/21 ≈ 0.429
    ├── Some((7, 3)): 102/198 ≈ 0.515
      ├── Some((3, 0)): 9/20 ≈ 0.450
      ├── Some((3, 1)): 16/27 ≈ 0.593
      ├── Some((3, 2)): 8/18 ≈ 0.444
      ├── Some((3, 3)): 19/30 ≈ 0.633
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 10/21 ≈ 0.476
      ├── Some((3, 6)): 8/18 ≈ 0.444
      ├── Some((3, 7)): 14/25 ≈ 0.560
      └── Some((3, 8)): 9/20 ≈ 0.450
    ├── Some((7, 4)): 66/142 ≈ 0.465
      ├── Some((4, 0)): 10/19 ≈ 0.526
      ├── Some((4, 1)): 5/13 ≈ 0.385
      ├── Some((4, 2)): 6/14 ≈ 0.429
      ├── Some((4, 3)): 15/24 ≈ 0.625
      ├── Some((4, 4)): 5/13 ≈ 0.385
      ├── Some((4, 5)): 3/11 ≈ 0.273
      ├── Some((4, 6)): 8/17 ≈ 0.471
      ├── Some((4, 7)): 7/15 ≈ 0.467
      └── Some((4, 8)): 7/15 ≈ 0.467
    ├── Some((7, 5)): 73/153 ≈ 0.477
      ├── Some((5, 0)): 18/29 ≈ 0.621
      ├── Some((5, 1)): 11/21 ≈ 0.524
      ├── Some((5, 2)): 13/24 ≈ 0.542
      ├── Some((5, 3)): 4/13 ≈ 0.308
      ├── Some((5, 4)): 1/9 ≈ 0.111
      ├── Some((5, 5)): 9/19 ≈ 0.474
      ├── Some((5, 6)): 10/20 ≈ 0.500
      └── Some((5, 8)): 7/17 ≈ 0.412
    ├── Some((7, 6)): 122/228 ≈ 0.535
      ├── Some((6, 0)): 18/32 ≈ 0.562
      ├── Some((6, 1)): 17/31 ≈ 0.548
      ├── Some((6, 2)): 17/31 ≈ 0.548
      ├── Some((6, 3)): 24/38 ≈ 0.632
      ├── Some((6, 4)): 10/23 ≈ 0.435
      ├── Some((6, 6)): 4/15 ≈ 0.267
      ├── Some((6, 7)): 26/41 ≈ 0.634
      └── Some((6, 8)): 5/16 ≈ 0.312
    ├── Some((7, 7)): 146/263 ≈ 0.555
      ├── Some((7, 0)): 17/32 ≈ 0.531
      ├── Some((7, 1)): 21/36 ≈ 0.583
      ├── Some((7, 2)): 33/49 ≈ 0.673
      ├── Some((7, 3)): 9/22 ≈ 0.409
      ├── Some((7, 4)): 12/26 ≈ 0.462
      ├── Some((7, 5)): 18/33 ≈ 0.545
      ├── Some((7, 6)): 16/30 ≈ 0.533
      └── Some((7, 8)): 19/34 ≈ 0.559
    └── Some((7, 8)): 75/156 ≈ 0.481
      ├── Some((8, 0)): 11/20 ≈ 0.550
      ├── Some((8, 1)): 8/17 ≈ 0.471
      ├── Some((8, 2)): 4/12 ≈ 0.333
      ├── Some((8, 3)): 10/19 ≈ 0.526
      ├── Some((8, 4)): 7/16 ≈ 0.438
      ├── Some((8, 5)): 13/23 ≈ 0.565
      ├── Some((8, 6)): 9/18 ≈ 0.500
      ├── Some((8, 7)): 9/18 ≈ 0.500
      └── Some((8, 8)): 4/12 ≈ 0.333
  └── Some((5, 8)): 1079/2054 ≈ 0.525
    ├── Some((8, 0)): 121/230 ≈ 0.526
      ├── Some((0, 0)): 7/18 ≈ 0.389
      ├── Some((0, 1)): 7/18 ≈ 0.389
      ├── Some((0, 2)): 13/25 ≈ 0.520
      ├── Some((0, 3)): 24/37 ≈ 0.649
      ├── Some((0, 4)): 9/20 ≈ 0.450
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 19/32 ≈ 0.594
      ├── Some((0, 7)): 19/32 ≈ 0.594
      └── Some((0, 8)): 11/23 ≈ 0.478
    ├── Some((8, 1)): 195/340 ≈ 0.574
      ├── Some((1, 0)): 35/53 ≈ 0.660
      ├── Some((1, 1)): 12/27 ≈ 0.444
      ├── Some((1, 2)): 36/54 ≈ 0.667
      ├── Some((1, 3)): 8/21 ≈ 0.381
      ├── Some((1, 4)): 26/43 ≈ 0.605
      ├── Some((1, 5)): 22/38 ≈ 0.579
      ├── Some((1, 6)): 24/41 ≈ 0.585
      ├── Some((1, 7)): 21/37 ≈ 0.568
      └── Some((1, 8)): 11/25 ≈ 0.440
    ├── Some((8, 2)): 81/169 ≈ 0.479
      ├── Some((2, 0)): 5/14 ≈ 0.357
      ├── Some((2, 1)): 7/17 ≈ 0.412
      ├── Some((2, 2)): 10/20 ≈ 0.500
      ├── Some((2, 3)): 1/9 ≈ 0.111
      ├── Some((2, 4)): 12/22 ≈ 0.545
      ├── Some((2, 5)): 14/24 ≈ 0.583
      ├── Some((2, 6)): 9/19 ≈ 0.474
      ├── Some((2, 7)): 13/23 ≈ 0.565
      └── Some((2, 8)): 10/20 ≈ 0.500
    ├── Some((8, 3)): 131/245 ≈ 0.535
      ├── Some((3, 0)): 21/35 ≈ 0.600
      ├── Some((3, 1)): 12/24 ≈ 0.500
      ├── Some((3, 2)): 18/31 ≈ 0.581
      ├── Some((3, 3)): 17/30 ≈ 0.567
      ├── Some((3, 4)): 10/22 ≈ 0.455
      ├── Some((3, 5)): 6/17 ≈ 0.353
      ├── Some((3, 6)): 10/22 ≈ 0.455
      ├── Some((3, 7)): 14/27 ≈ 0.519
      └── Some((3, 8)): 22/36 ≈ 0.611
    ├── Some((8, 4)): 117/224 ≈ 0.522
      ├── Some((4, 0)): 15/27 ≈ 0.556
      ├── Some((4, 1)): 8/19 ≈ 0.421
      ├── Some((4, 2)): 4/14 ≈ 0.286
      ├── Some((4, 3)): 20/33 ≈ 0.606
      ├── Some((4, 4)): 6/17 ≈ 0.353
      ├── Some((4, 5)): 14/26 ≈ 0.538
      ├── Some((4, 6)): 21/34 ≈ 0.618
      ├── Some((4, 7)): 23/36 ≈ 0.639
      └── Some((4, 8)): 6/17 ≈ 0.353
    ├── Some((8, 5)): 110/214 ≈ 0.514
      ├── Some((5, 0)): 18/32 ≈ 0.562
      ├── Some((5, 1)): 12/25 ≈ 0.480
      ├── Some((5, 2)): 20/34 ≈ 0.588
      ├── Some((5, 3)): 15/28 ≈ 0.536
      ├── Some((5, 4)): 10/22 ≈ 0.455
      ├── Some((5, 5)): 13/26 ≈ 0.500
      ├── Some((5, 6)): 6/17 ≈ 0.353
      └── Some((5, 7)): 16/29 ≈ 0.552
    ├── Some((8, 6)): 103/203 ≈ 0.507
      ├── Some((6, 0)): 19/32 ≈ 0.594
      ├── Some((6, 1)): 9/21 ≈ 0.429
      ├── Some((6, 2)): 15/28 ≈ 0.536
      ├── Some((6, 3)): 17/30 ≈ 0.567
      ├── Some((6, 4)): 15/28 ≈ 0.536
      ├── Some((6, 6)): 10/22 ≈ 0.455
      ├── Some((6, 7)): 4/14 ≈ 0.286
      └── Some((6, 8)): 14/27 ≈ 0.519
    ├── Some((8, 7)): 79/166 ≈ 0.476
      ├── Some((7, 0)): 12/22 ≈ 0.545
      ├── Some((7, 1)): 14/25 ≈ 0.560
      ├── Some((7, 2)): 1/9 ≈ 0.111
      ├── Some((7, 3)): 16/27 ≈ 0.593
      ├── Some((7, 4)): 6/15 ≈ 0.400
      ├── Some((7, 5)): 6/15 ≈ 0.400
      ├── Some((7, 6)): 2/10 ≈ 0.200
      ├── Some((7, 7)): 10/20 ≈ 0.500
      └── Some((7, 8)): 12/22 ≈ 0.545
    └── Some((8, 8)): 142/262 ≈ 0.542
      ├── Some((8, 0)): 21/37 ≈ 0.568
      ├── Some((8, 1)): 19/34 ≈ 0.559
      ├── Some((8, 2)): 20/35 ≈ 0.571
      ├── Some((8, 3)): 11/25 ≈ 0.440
      ├── Some((8, 4)): 2/13 ≈ 0.154
      ├── Some((8, 5)): 20/36 ≈ 0.556
      ├── Some((8, 6)): 16/31 ≈ 0.516
      └── Some((8, 7)): 33/50 ≈ 0.660
├── Some((6, 6)): 8117/15455 ≈ 0.525
  ├── Some((6, 0)): 1274/2380 ≈ 0.535
    ├── Some((0, 0)): 169/306 ≈ 0.552
      ├── Some((0, 1)): 22/40 ≈ 0.550
      ├── Some((0, 2)): 26/44 ≈ 0.591
      ├── Some((0, 3)): 18/35 ≈ 0.514
      ├── Some((0, 4)): 12/27 ≈ 0.444
      ├── Some((0, 5)): 15/31 ≈ 0.484
      ├── Some((0, 6)): 27/45 ≈ 0.600
      ├── Some((0, 7)): 21/38 ≈ 0.553
      └── Some((0, 8)): 27/45 ≈ 0.600
    ├── Some((0, 1)): 176/316 ≈ 0.557
      ├── Some((1, 0)): 14/29 ≈ 0.483
      ├── Some((1, 1)): 19/34 ≈ 0.559
      ├── Some((1, 2)): 31/48 ≈ 0.646
      ├── Some((1, 3)): 15/30 ≈ 0.500
      ├── Some((1, 4)): 15/30 ≈ 0.500
      ├── Some((1, 5)): 24/40 ≈ 0.600
      ├── Some((1, 6)): 26/42 ≈ 0.619
      ├── Some((1, 7)): 15/30 ≈ 0.500
      └── Some((1, 8)): 17/32 ≈ 0.531
    ├── Some((0, 2)): 163/297 ≈ 0.549
      ├── Some((2, 0)): 18/33 ≈ 0.545
      ├── Some((2, 1)): 13/27 ≈ 0.481
      ├── Some((2, 2)): 19/34 ≈ 0.559
      ├── Some((2, 3)): 15/29 ≈ 0.517
      ├── Some((2, 4)): 11/25 ≈ 0.440
      ├── Some((2, 5)): 27/43 ≈ 0.628
      ├── Some((2, 6)): 23/38 ≈ 0.605
      ├── Some((2, 7)): 25/41 ≈ 0.610
      └── Some((2, 8)): 12/26 ≈ 0.462
    ├── Some((0, 3)): 74/161 ≈ 0.460
      ├── Some((3, 0)): 12/22 ≈ 0.545
      ├── Some((3, 1)): 3/12 ≈ 0.250
      ├── Some((3, 2)): 8/18 ≈ 0.444
      ├── Some((3, 3)): 6/15 ≈ 0.400
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 18/29 ≈ 0.621
      ├── Some((3, 6)): 4/13 ≈ 0.308
      ├── Some((3, 7)): 5/14 ≈ 0.357
      └── Some((3, 8)): 9/19 ≈ 0.474
    ├── Some((0, 4)): 158/290 ≈ 0.545
      ├── Some((4, 0)): 9/22 ≈ 0.409
      ├── Some((4, 1)): 36/53 ≈ 0.679
      ├── Some((4, 2)): 15/29 ≈ 0.517
      ├── Some((4, 3)): 18/33 ≈ 0.545
      ├── Some((4, 4)): 14/28 ≈ 0.500
      ├── Some((4, 5)): 21/36 ≈ 0.583
      ├── Some((4, 6)): 8/21 ≈ 0.381
      ├── Some((4, 7)): 21/36 ≈ 0.583
      └── Some((4, 8)): 16/31 ≈ 0.516
    ├── Some((0, 5)): 106/211 ≈ 0.502
      ├── Some((5, 0)): 15/27 ≈ 0.556
      ├── Some((5, 1)): 8/19 ≈ 0.421
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 3)): 9/20 ≈ 0.450
      ├── Some((5, 4)): 14/26 ≈ 0.538
      ├── Some((5, 5)): 15/27 ≈ 0.556
      ├── Some((5, 6)): 17/29 ≈ 0.586
      ├── Some((5, 7)): 9/20 ≈ 0.450
      └── Some((5, 8)): 7/18 ≈ 0.389
    ├── Some((0, 6)): 143/267 ≈ 0.536
      ├── Some((6, 1)): 14/30 ≈ 0.467
      ├── Some((6, 2)): 31/51 ≈ 0.608
      ├── Some((6, 3)): 16/33 ≈ 0.485
      ├── Some((6, 4)): 32/52 ≈ 0.615
      ├── Some((6, 5)): 11/26 ≈ 0.423
      ├── Some((6, 7)): 24/42 ≈ 0.571
      └── Some((6, 8)): 15/32 ≈ 0.469
    ├── Some((0, 7)): 133/252 ≈ 0.528
      ├── Some((7, 0)): 18/32 ≈ 0.562
      ├── Some((7, 1)): 4/15 ≈ 0.267
      ├── Some((7, 2)): 13/26 ≈ 0.500
      ├── Some((7, 3)): 16/30 ≈ 0.533
      ├── Some((7, 4)): 18/32 ≈ 0.562
      ├── Some((7, 5)): 17/31 ≈ 0.548
      ├── Some((7, 6)): 14/27 ≈ 0.519
      ├── Some((7, 7)): 10/22 ≈ 0.455
      └── Some((7, 8)): 22/36 ≈ 0.611
    └── Some((0, 8)): 151/279 ≈ 0.541
      ├── Some((8, 0)): 21/36 ≈ 0.583
      ├── Some((8, 1)): 28/44 ≈ 0.636
      ├── Some((8, 2)): 6/18 ≈ 0.333
      ├── Some((8, 3)): 12/26 ≈ 0.462
      ├── Some((8, 4)): 18/33 ≈ 0.545
      ├── Some((8, 5)): 24/39 ≈ 0.615
      ├── Some((8, 6)): 14/28 ≈ 0.500
      ├── Some((8, 7)): 20/35 ≈ 0.571
      └── Some((8, 8)): 7/19 ≈ 0.368
  ├── Some((6, 1)): 1288/2405 ≈ 0.536
    ├── Some((1, 0)): 124/239 ≈ 0.519
      ├── Some((0, 0)): 7/19 ≈ 0.368
      ├── Some((0, 1)): 19/33 ≈ 0.576
      ├── Some((0, 2)): 13/26 ≈ 0.500
      ├── Some((0, 3)): 6/17 ≈ 0.353
      ├── Some((0, 4)): 9/21 ≈ 0.429
      ├── Some((0, 5)): 22/36 ≈ 0.611
      ├── Some((0, 6)): 21/35 ≈ 0.600
      ├── Some((0, 7)): 9/21 ≈ 0.429
      └── Some((0, 8)): 17/30 ≈ 0.567
    ├── Some((1, 1)): 82/174 ≈ 0.471
      ├── Some((1, 0)): 17/30 ≈ 0.567
      ├── Some((1, 2)): 15/27 ≈ 0.556
      ├── Some((1, 3)): 5/15 ≈ 0.333
      ├── Some((1, 4)): 10/22 ≈ 0.455
      ├── Some((1, 5)): 2/11 ≈ 0.182
      ├── Some((1, 6)): 9/20 ≈ 0.450
      ├── Some((1, 7)): 8/19 ≈ 0.421
      └── Some((1, 8)): 16/29 ≈ 0.552
    ├── Some((1, 2)): 171/310 ≈ 0.552
      ├── Some((2, 0)): 16/31 ≈ 0.516
      ├── Some((2, 1)): 18/33 ≈ 0.545
      ├── Some((2, 2)): 3/15 ≈ 0.200
      ├── Some((2, 3)): 18/33 ≈ 0.545
      ├── Some((2, 4)): 18/34 ≈ 0.529
      ├── Some((2, 5)): 19/35 ≈ 0.543
      ├── Some((2, 6)): 15/30 ≈ 0.500
      ├── Some((2, 7)): 26/43 ≈ 0.605
      └── Some((2, 8)): 37/55 ≈ 0.673
    ├── Some((1, 3)): 127/244 ≈ 0.520
      ├── Some((3, 0)): 14/27 ≈ 0.519
      ├── Some((3, 1)): 16/30 ≈ 0.533
      ├── Some((3, 2)): 12/25 ≈ 0.480
      ├── Some((3, 3)): 25/39 ≈ 0.641
      ├── Some((3, 4)): 10/22 ≈ 0.455
      ├── Some((3, 5)): 20/34 ≈ 0.588
      ├── Some((3, 6)): 20/34 ≈ 0.588
      ├── Some((3, 7)): 9/21 ≈ 0.429
      └── Some((3, 8)): 1/11 ≈ 0.091
    ├── Some((1, 4)): 233/401 ≈ 0.581
      ├── Some((4, 0)): 23/41 ≈ 0.561
      ├── Some((4, 1)): 35/55 ≈ 0.636
      ├── Some((4, 2)): 26/45 ≈ 0.578
      ├── Some((4, 3)): 19/37 ≈ 0.514
      ├── Some((4, 4)): 29/48 ≈ 0.604
      ├── Some((4, 5)): 13/29 ≈ 0.448
      ├── Some((4, 6)): 21/39 ≈ 0.538
      ├── Some((4, 7)): 36/56 ≈ 0.643
      └── Some((4, 8)): 31/50 ≈ 0.620
    ├── Some((1, 5)): 104/208 ≈ 0.500
      ├── Some((5, 0)): 7/18 ≈ 0.389
      ├── Some((5, 1)): 7/18 ≈ 0.389
      ├── Some((5, 2)): 21/34 ≈ 0.618
      ├── Some((5, 3)): 11/23 ≈ 0.478
      ├── Some((5, 4)): 19/31 ≈ 0.613
      ├── Some((5, 5)): 5/15 ≈ 0.333
      ├── Some((5, 6)): 19/32 ≈ 0.594
      ├── Some((5, 7)): 10/21 ≈ 0.476
      └── Some((5, 8)): 5/15 ≈ 0.333
    ├── Some((1, 6)): 146/272 ≈ 0.537
      ├── Some((6, 0)): 39/60 ≈ 0.650
      ├── Some((6, 2)): 18/36 ≈ 0.500
      ├── Some((6, 3)): 20/38 ≈ 0.526
      ├── Some((6, 4)): 21/39 ≈ 0.538
      ├── Some((6, 5)): 11/27 ≈ 0.407
      ├── Some((6, 7)): 17/34 ≈ 0.500
      └── Some((6, 8)): 19/37 ≈ 0.514
    ├── Some((1, 7)): 130/248 ≈ 0.524
      ├── Some((7, 0)): 20/34 ≈ 0.588
      ├── Some((7, 1)): 11/24 ≈ 0.458
      ├── Some((7, 2)): 12/25 ≈ 0.480
      ├── Some((7, 3)): 20/34 ≈ 0.588
      ├── Some((7, 4)): 5/16 ≈ 0.312
      ├── Some((7, 5)): 22/36 ≈ 0.611
      ├── Some((7, 6)): 10/23 ≈ 0.435
      ├── Some((7, 7)): 14/27 ≈ 0.519
      └── Some((7, 8)): 15/28 ≈ 0.536
    └── Some((1, 8)): 170/308 ≈ 0.552
      ├── Some((8, 0)): 16/31 ≈ 0.516
      ├── Some((8, 1)): 18/33 ≈ 0.545
      ├── Some((8, 2)): 35/53 ≈ 0.660
      ├── Some((8, 3)): 19/35 ≈ 0.543
      ├── Some((8, 4)): 8/21 ≈ 0.381
      ├── Some((8, 5)): 17/32 ≈ 0.531
      ├── Some((8, 6)): 23/39 ≈ 0.590
      ├── Some((8, 7)): 17/32 ≈ 0.531
      └── Some((8, 8)): 16/31 ≈ 0.516
  ├── Some((6, 2)): 982/1877 ≈ 0.523
    ├── Some((2, 0)): 141/257 ≈ 0.549
      ├── Some((0, 0)): 17/30 ≈ 0.567
      ├── Some((0, 1)): 16/29 ≈ 0.552
      ├── Some((0, 2)): 15/28 ≈ 0.536
      ├── Some((0, 3)): 14/27 ≈ 0.519
      ├── Some((0, 4)): 9/21 ≈ 0.429
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 21/34 ≈ 0.618
      ├── Some((0, 7)): 18/31 ≈ 0.581
      └── Some((0, 8)): 19/32 ≈ 0.594
    ├── Some((2, 1)): 124/231 ≈ 0.537
      ├── Some((1, 0)): 5/16 ≈ 0.312
      ├── Some((1, 1)): 8/19 ≈ 0.421
      ├── Some((1, 2)): 12/24 ≈ 0.500
      ├── Some((1, 3)): 23/36 ≈ 0.639
      ├── Some((1, 4)): 15/27 ≈ 0.556
      ├── Some((1, 5)): 15/27 ≈ 0.556
      ├── Some((1, 6)): 17/29 ≈ 0.586
      ├── Some((1, 7)): 15/27 ≈ 0.556
      └── Some((1, 8)): 13/25 ≈ 0.520
    ├── Some((2, 2)): 152/273 ≈ 0.557
      ├── Some((2, 0)): 14/29 ≈ 0.483
      ├── Some((2, 1)): 13/27 ≈ 0.481
      ├── Some((2, 3)): 25/41 ≈ 0.610
      ├── Some((2, 4)): 13/27 ≈ 0.481
      ├── Some((2, 5)): 13/27 ≈ 0.481
      ├── Some((2, 6)): 25/41 ≈ 0.610
      ├── Some((2, 7)): 27/43 ≈ 0.628
      └── Some((2, 8)): 21/37 ≈ 0.568
    ├── Some((2, 3)): 68/146 ≈ 0.466
      ├── Some((3, 0)): 12/21 ≈ 0.571
      ├── Some((3, 1)): 2/10 ≈ 0.200
      ├── Some((3, 2)): 19/28 ≈ 0.679
      ├── Some((3, 3)): 5/13 ≈ 0.385
      ├── Some((3, 4)): 5/13 ≈ 0.385
      ├── Some((3, 5)): 11/20 ≈ 0.550
      ├── Some((3, 6)): 3/11 ≈ 0.273
      ├── Some((3, 7)): 5/14 ≈ 0.357
      └── Some((3, 8)): 6/15 ≈ 0.400
    ├── Some((2, 4)): 100/195 ≈ 0.513
      ├── Some((4, 0)): 10/20 ≈ 0.500
      ├── Some((4, 1)): 7/17 ≈ 0.412
      ├── Some((4, 2)): 12/23 ≈ 0.522
      ├── Some((4, 3)): 16/27 ≈ 0.593
      ├── Some((4, 4)): 11/22 ≈ 0.500
      ├── Some((4, 5)): 8/18 ≈ 0.444
      ├── Some((4, 6)): 17/28 ≈ 0.607
      ├── Some((4, 7)): 6/16 ≈ 0.375
      └── Some((4, 8)): 12/23 ≈ 0.522
    ├── Some((2, 5)): 81/166 ≈ 0.488
      ├── Some((5, 0)): 8/17 ≈ 0.471
      ├── Some((5, 1)): 7/16 ≈ 0.438
      ├── Some((5, 2)): 4/13 ≈ 0.308
      ├── Some((5, 3)): 16/26 ≈ 0.615
      ├── Some((5, 4)): 8/17 ≈ 0.471
      ├── Some((5, 5)): 9/19 ≈ 0.474
      ├── Some((5, 6)): 7/16 ≈ 0.438
      ├── Some((5, 7)): 10/20 ≈ 0.500
      └── Some((5, 8)): 11/21 ≈ 0.524
    ├── Some((2, 6)): 114/216 ≈ 0.528
      ├── Some((6, 0)): 14/28 ≈ 0.500
      ├── Some((6, 1)): 5/17 ≈ 0.294
      ├── Some((6, 3)): 21/37 ≈ 0.568
      ├── Some((6, 4)): 25/41 ≈ 0.610
      ├── Some((6, 5)): 15/30 ≈ 0.500
      ├── Some((6, 7)): 14/28 ≈ 0.500
      └── Some((6, 8)): 19/34 ≈ 0.559
    ├── Some((2, 7)): 87/176 ≈ 0.494
      ├── Some((7, 0)): 9/19 ≈ 0.474
      ├── Some((7, 1)): 7/17 ≈ 0.412
      ├── Some((7, 2)): 11/21 ≈ 0.524
      ├── Some((7, 3)): 6/15 ≈ 0.400
      ├── Some((7, 4)): 9/19 ≈ 0.474
      ├── Some((7, 5)): 19/30 ≈ 0.633
      ├── Some((7, 6)): 10/20 ≈ 0.500
      ├── Some((7, 7)): 5/14 ≈ 0.357
      └── Some((7, 8)): 10/20 ≈ 0.500
    └── Some((2, 8)): 114/216 ≈ 0.528
      ├── Some((8, 0)): 17/29 ≈ 0.586
      ├── Some((8, 1)): 11/22 ≈ 0.500
      ├── Some((8, 2)): 7/17 ≈ 0.412
      ├── Some((8, 3)): 15/27 ≈ 0.556
      ├── Some((8, 4)): 7/17 ≈ 0.412
      ├── Some((8, 5)): 12/23 ≈ 0.522
      ├── Some((8, 6)): 13/24 ≈ 0.542
      ├── Some((8, 7)): 18/30 ≈ 0.600
      └── Some((8, 8)): 14/26 ≈ 0.538
  ├── Some((6, 3)): 830/1613 ≈ 0.515
    ├── Some((3, 0)): 52/118 ≈ 0.441
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 9/17 ≈ 0.529
      ├── Some((0, 2)): 3/10 ≈ 0.300
      ├── Some((0, 3)): 5/12 ≈ 0.417
      ├── Some((0, 4)): 10/18 ≈ 0.556
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 6/13 ≈ 0.462
      ├── Some((0, 7)): 4/11 ≈ 0.364
      └── Some((0, 8)): 5/12 ≈ 0.417
    ├── Some((3, 1)): 99/191 ≈ 0.518
      ├── Some((1, 0)): 4/13 ≈ 0.308
      ├── Some((1, 1)): 18/29 ≈ 0.621
      ├── Some((1, 2)): 9/19 ≈ 0.474
      ├── Some((1, 3)): 7/17 ≈ 0.412
      ├── Some((1, 4)): 20/31 ≈ 0.645
      ├── Some((1, 5)): 14/25 ≈ 0.560
      ├── Some((1, 6)): 5/14 ≈ 0.357
      ├── Some((1, 7)): 12/22 ≈ 0.545
      └── Some((1, 8)): 10/20 ≈ 0.500
    ├── Some((3, 2)): 54/122 ≈ 0.443
      ├── Some((2, 0)): 12/20 ≈ 0.600
      ├── Some((2, 1)): 5/12 ≈ 0.417
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 6/14 ≈ 0.429
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 7/15 ≈ 0.467
      ├── Some((2, 7)): 5/13 ≈ 0.385
      └── Some((2, 8)): 4/11 ≈ 0.364
    ├── Some((3, 3)): 51/117 ≈ 0.436
      ├── Some((3, 0)): 2/10 ≈ 0.200
      ├── Some((3, 1)): 2/10 ≈ 0.200
      ├── Some((3, 2)): 15/24 ≈ 0.625
      ├── Some((3, 4)): 7/15 ≈ 0.467
      ├── Some((3, 5)): 0/7 ≈ 0.000
      ├── Some((3, 6)): 6/14 ≈ 0.429
      ├── Some((3, 7)): 14/23 ≈ 0.609
      └── Some((3, 8)): 5/13 ≈ 0.385
    ├── Some((3, 4)): 83/166 ≈ 0.500
      ├── Some((4, 0)): 7/16 ≈ 0.438
      ├── Some((4, 1)): 18/28 ≈ 0.643
      ├── Some((4, 2)): 6/15 ≈ 0.400
      ├── Some((4, 3)): 12/21 ≈ 0.571
      ├── Some((4, 4)): 8/17 ≈ 0.471
      ├── Some((4, 5)): 9/18 ≈ 0.500
      ├── Some((4, 6)): 6/15 ≈ 0.400
      ├── Some((4, 7)): 7/16 ≈ 0.438
      └── Some((4, 8)): 10/19 ≈ 0.526
    ├── Some((3, 5)): 100/192 ≈ 0.521
      ├── Some((5, 0)): 8/18 ≈ 0.444
      ├── Some((5, 1)): 8/18 ≈ 0.444
      ├── Some((5, 2)): 10/20 ≈ 0.500
      ├── Some((5, 3)): 13/23 ≈ 0.565
      ├── Some((5, 4)): 15/26 ≈ 0.577
      ├── Some((5, 5)): 12/22 ≈ 0.545
      ├── Some((5, 6)): 7/17 ≈ 0.412
      ├── Some((5, 7)): 15/26 ≈ 0.577
      └── Some((5, 8)): 11/21 ≈ 0.524
    ├── Some((3, 6)): 157/275 ≈ 0.571
      ├── Some((6, 0)): 25/42 ≈ 0.595
      ├── Some((6, 1)): 7/20 ≈ 0.350
      ├── Some((6, 2)): 27/45 ≈ 0.600
      ├── Some((6, 4)): 19/35 ≈ 0.543
      ├── Some((6, 5)): 30/48 ≈ 0.625
      ├── Some((6, 7)): 28/46 ≈ 0.609
      └── Some((6, 8)): 21/38 ≈ 0.553
    ├── Some((3, 7)): 83/166 ≈ 0.500
      ├── Some((7, 0)): 3/11 ≈ 0.273
      ├── Some((7, 1)): 6/15 ≈ 0.400
      ├── Some((7, 2)): 10/19 ≈ 0.526
      ├── Some((7, 3)): 7/16 ≈ 0.438
      ├── Some((7, 4)): 11/20 ≈ 0.550
      ├── Some((7, 5)): 9/18 ≈ 0.500
      ├── Some((7, 6)): 12/21 ≈ 0.571
      ├── Some((7, 7)): 12/22 ≈ 0.545
      └── Some((7, 8)): 13/23 ≈ 0.565
    └── Some((3, 8)): 150/265 ≈ 0.566
      ├── Some((8, 0)): 18/31 ≈ 0.581
      ├── Some((8, 1)): 10/22 ≈ 0.455
      ├── Some((8, 2)): 19/32 ≈ 0.594
      ├── Some((8, 3)): 16/29 ≈ 0.552
      ├── Some((8, 4)): 12/25 ≈ 0.480
      ├── Some((8, 5)): 6/17 ≈ 0.353
      ├── Some((8, 6)): 8/20 ≈ 0.400
      ├── Some((8, 7)): 31/45 ≈ 0.689
      └── Some((8, 8)): 29/43 ≈ 0.674
  ├── Some((6, 4)): 1046/1988 ≈ 0.526
    ├── Some((4, 0)): 100/197 ≈ 0.508
      ├── Some((0, 0)): 10/21 ≈ 0.476
      ├── Some((0, 1)): 19/30 ≈ 0.633
      ├── Some((0, 2)): 13/24 ≈ 0.542
      ├── Some((0, 3)): 5/15 ≈ 0.333
      ├── Some((0, 4)): 4/14 ≈ 0.286
      ├── Some((0, 5)): 8/18 ≈ 0.444
      ├── Some((0, 6)): 9/20 ≈ 0.450
      ├── Some((0, 7)): 19/31 ≈ 0.613
      └── Some((0, 8)): 12/23 ≈ 0.522
    ├── Some((4, 1)): 50/119 ≈ 0.420
      ├── Some((1, 0)): 15/24 ≈ 0.625
      ├── Some((1, 1)): 2/9 ≈ 0.222
      ├── Some((1, 2)): 7/15 ≈ 0.467
      ├── Some((1, 3)): 8/16 ≈ 0.500
      ├── Some((1, 4)): 4/12 ≈ 0.333
      ├── Some((1, 5)): 8/16 ≈ 0.500
      ├── Some((1, 6)): 2/9 ≈ 0.222
      ├── Some((1, 7)): 2/9 ≈ 0.222
      └── Some((1, 8)): 1/8 ≈ 0.125
    ├── Some((4, 2)): 87/177 ≈ 0.492
      ├── Some((2, 0)): 4/13 ≈ 0.308
      ├── Some((2, 1)): 10/20 ≈ 0.500
      ├── Some((2, 2)): 17/28 ≈ 0.607
      ├── Some((2, 3)): 21/32 ≈ 0.656
      ├── Some((2, 4)): 2/11 ≈ 0.182
      ├── Some((2, 5)): 8/18 ≈ 0.444
      ├── Some((2, 6)): 16/27 ≈ 0.593
      ├── Some((2, 7)): 5/14 ≈ 0.357
      └── Some((2, 8)): 4/13 ≈ 0.308
    ├── Some((4, 3)): 165/294 ≈ 0.561
      ├── Some((3, 0)): 26/41 ≈ 0.634
      ├── Some((3, 1)): 16/30 ≈ 0.533
      ├── Some((3, 2)): 11/24 ≈ 0.458
      ├── Some((3, 3)): 28/44 ≈ 0.636
      ├── Some((3, 4)): 13/27 ≈ 0.481
      ├── Some((3, 5)): 16/30 ≈ 0.533
      ├── Some((3, 6)): 21/36 ≈ 0.583
      ├── Some((3, 7)): 11/24 ≈ 0.458
      └── Some((3, 8)): 22/37 ≈ 0.595
    ├── Some((4, 4)): 175/309 ≈ 0.566
      ├── Some((4, 0)): 32/51 ≈ 0.627
      ├── Some((4, 1)): 24/42 ≈ 0.571
      ├── Some((4, 2)): 24/42 ≈ 0.571
      ├── Some((4, 3)): 31/49 ≈ 0.633
      ├── Some((4, 5)): 9/23 ≈ 0.391
      ├── Some((4, 6)): 37/56 ≈ 0.661
      ├── Some((4, 7)): 5/18 ≈ 0.278
      └── Some((4, 8)): 12/27 ≈ 0.444
    ├── Some((4, 5)): 114/218 ≈ 0.523
      ├── Some((5, 0)): 10/21 ≈ 0.476
      ├── Some((5, 1)): 11/23 ≈ 0.478
      ├── Some((5, 2)): 10/21 ≈ 0.476
      ├── Some((5, 3)): 19/31 ≈ 0.613
      ├── Some((5, 4)): 9/20 ≈ 0.450
      ├── Some((5, 5)): 14/26 ≈ 0.538
      ├── Some((5, 6)): 8/19 ≈ 0.421
      ├── Some((5, 7)): 17/29 ≈ 0.586
      └── Some((5, 8)): 15/27 ≈ 0.556
    ├── Some((4, 6)): 97/192 ≈ 0.505
      ├── Some((6, 0)): 8/21 ≈ 0.381
      ├── Some((6, 1)): 12/25 ≈ 0.480
      ├── Some((6, 2)): 25/41 ≈ 0.610
      ├── Some((6, 3)): 20/35 ≈ 0.571
      ├── Some((6, 5)): 17/31 ≈ 0.548
      ├── Some((6, 7)): 7/19 ≈ 0.368
      └── Some((6, 8)): 7/19 ≈ 0.368
    ├── Some((4, 7)): 122/230 ≈ 0.530
      ├── Some((7, 0)): 8/19 ≈ 0.421
      ├── Some((7, 1)): 8/19 ≈ 0.421
      ├── Some((7, 2)): 15/28 ≈ 0.536
      ├── Some((7, 3)): 26/39 ≈ 0.667
      ├── Some((7, 4)): 14/26 ≈ 0.538
      ├── Some((7, 5)): 15/28 ≈ 0.536
      ├── Some((7, 6)): 8/19 ≈ 0.421
      ├── Some((7, 7)): 13/25 ≈ 0.520
      └── Some((7, 8)): 14/26 ≈ 0.538
    └── Some((4, 8)): 136/251 ≈ 0.542
      ├── Some((8, 0)): 14/27 ≈ 0.519
      ├── Some((8, 1)): 18/31 ≈ 0.581
      ├── Some((8, 2)): 13/26 ≈ 0.500
      ├── Some((8, 3)): 16/29 ≈ 0.552
      ├── Some((8, 4)): 24/38 ≈ 0.632
      ├── Some((8, 5)): 24/38 ≈ 0.632
      ├── Some((8, 6)): 16/29 ≈ 0.552
      ├── Some((8, 7)): 3/13 ≈ 0.231
      └── Some((8, 8)): 7/19 ≈ 0.368
  ├── Some((6, 5)): 687/1362 ≈ 0.504
    ├── Some((5, 0)): 108/199 ≈ 0.543
      ├── Some((0, 0)): 16/26 ≈ 0.615
      ├── Some((0, 1)): 10/20 ≈ 0.500
      ├── Some((0, 2)): 8/18 ≈ 0.444
      ├── Some((0, 3)): 12/22 ≈ 0.545
      ├── Some((0, 4)): 7/17 ≈ 0.412
      ├── Some((0, 5)): 13/23 ≈ 0.565
      ├── Some((0, 6)): 7/17 ≈ 0.412
      ├── Some((0, 7)): 15/25 ≈ 0.600
      └── Some((0, 8)): 19/30 ≈ 0.633
    ├── Some((5, 1)): 93/177 ≈ 0.525
      ├── Some((1, 0)): 6/15 ≈ 0.400
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 2)): 5/14 ≈ 0.357
      ├── Some((1, 3)): 15/25 ≈ 0.600
      ├── Some((1, 4)): 18/28 ≈ 0.643
      ├── Some((1, 5)): 10/19 ≈ 0.526
      ├── Some((1, 6)): 18/28 ≈ 0.643
      ├── Some((1, 7)): 4/13 ≈ 0.308
      └── Some((1, 8)): 5/14 ≈ 0.357
    ├── Some((5, 2)): 90/172 ≈ 0.523
      ├── Some((2, 0)): 12/21 ≈ 0.571
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 11/20 ≈ 0.550
      ├── Some((2, 3)): 11/20 ≈ 0.550
      ├── Some((2, 4)): 9/18 ≈ 0.500
      ├── Some((2, 5)): 9/18 ≈ 0.500
      ├── Some((2, 6)): 15/25 ≈ 0.600
      ├── Some((2, 7)): 3/11 ≈ 0.273
      └── Some((2, 8)): 12/21 ≈ 0.571
    ├── Some((5, 3)): 79/156 ≈ 0.506
      ├── Some((3, 0)): 2/10 ≈ 0.200
      ├── Some((3, 1)): 7/15 ≈ 0.467
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 8/16 ≈ 0.500
      ├── Some((3, 4)): 7/15 ≈ 0.467
      ├── Some((3, 5)): 15/24 ≈ 0.625
      ├── Some((3, 6)): 10/19 ≈ 0.526
      ├── Some((3, 7)): 9/18 ≈ 0.500
      └── Some((3, 8)): 13/22 ≈ 0.591
    ├── Some((5, 4)): 66/136 ≈ 0.485
      ├── Some((4, 0)): 4/11 ≈ 0.364
      ├── Some((4, 1)): 6/14 ≈ 0.429
      ├── Some((4, 2)): 8/16 ≈ 0.500
      ├── Some((4, 3)): 8/16 ≈ 0.500
      ├── Some((4, 4)): 3/10 ≈ 0.300
      ├── Some((4, 5)): 10/18 ≈ 0.556
      ├── Some((4, 6)): 4/12 ≈ 0.333
      ├── Some((4, 7)): 13/21 ≈ 0.619
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((5, 5)): 73/147 ≈ 0.497
      ├── Some((5, 0)): 2/10 ≈ 0.200
      ├── Some((5, 1)): 6/15 ≈ 0.400
      ├── Some((5, 2)): 18/28 ≈ 0.643
      ├── Some((5, 3)): 8/17 ≈ 0.471
      ├── Some((5, 4)): 18/28 ≈ 0.643
      ├── Some((5, 6)): 3/11 ≈ 0.273
      ├── Some((5, 7)): 5/14 ≈ 0.357
      └── Some((5, 8)): 13/23 ≈ 0.565
    ├── Some((5, 6)): 28/76 ≈ 0.368
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 4/11 ≈ 0.364
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 3/10 ≈ 0.300
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 7)): 2/8 ≈ 0.250
      └── Some((6, 8)): 2/8 ≈ 0.250
    ├── Some((5, 7)): 109/200 ≈ 0.545
      ├── Some((7, 0)): 9/19 ≈ 0.474
      ├── Some((7, 1)): 5/14 ≈ 0.357
      ├── Some((7, 2)): 16/27 ≈ 0.593
      ├── Some((7, 3)): 27/38 ≈ 0.711
      ├── Some((7, 4)): 6/16 ≈ 0.375
      ├── Some((7, 5)): 13/23 ≈ 0.565
      ├── Some((7, 6)): 11/21 ≈ 0.524
      ├── Some((7, 7)): 11/21 ≈ 0.524
      └── Some((7, 8)): 10/20 ≈ 0.500
    └── Some((5, 8)): 41/98 ≈ 0.418
      ├── Some((8, 0)): 2/8 ≈ 0.250
      ├── Some((8, 1)): 3/9 ≈ 0.333
      ├── Some((8, 2)): 2/8 ≈ 0.250
      ├── Some((8, 3)): 8/14 ≈ 0.571
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 5/11 ≈ 0.455
      ├── Some((8, 7)): 8/15 ≈ 0.533
      └── Some((8, 8)): 1/7 ≈ 0.143
  ├── Some((6, 7)): 775/1517 ≈ 0.511
    ├── Some((7, 0)): 118/216 ≈ 0.546
      ├── Some((0, 0)): 10/21 ≈ 0.476
      ├── Some((0, 1)): 13/24 ≈ 0.542
      ├── Some((0, 2)): 22/34 ≈ 0.647
      ├── Some((0, 3)): 11/22 ≈ 0.500
      ├── Some((0, 4)): 2/11 ≈ 0.182
      ├── Some((0, 5)): 23/35 ≈ 0.657
      ├── Some((0, 6)): 19/30 ≈ 0.633
      ├── Some((0, 7)): 5/15 ≈ 0.333
      └── Some((0, 8)): 12/23 ≈ 0.522
    ├── Some((7, 1)): 79/158 ≈ 0.500
      ├── Some((1, 0)): 17/26 ≈ 0.654
      ├── Some((1, 1)): 8/17 ≈ 0.471
      ├── Some((1, 2)): 7/16 ≈ 0.438
      ├── Some((1, 3)): 1/8 ≈ 0.125
      ├── Some((1, 4)): 15/24 ≈ 0.625
      ├── Some((1, 5)): 7/16 ≈ 0.438
      ├── Some((1, 6)): 6/15 ≈ 0.400
      ├── Some((1, 7)): 10/19 ≈ 0.526
      └── Some((1, 8)): 7/16 ≈ 0.438
    ├── Some((7, 2)): 83/165 ≈ 0.503
      ├── Some((2, 0)): 21/31 ≈ 0.677
      ├── Some((2, 1)): 11/20 ≈ 0.550
      ├── Some((2, 2)): 10/19 ≈ 0.526
      ├── Some((2, 3)): 9/18 ≈ 0.500
      ├── Some((2, 4)): 9/18 ≈ 0.500
      ├── Some((2, 5)): 9/18 ≈ 0.500
      ├── Some((2, 6)): 4/13 ≈ 0.308
      ├── Some((2, 7)): 3/11 ≈ 0.273
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((7, 3)): 84/166 ≈ 0.506
      ├── Some((3, 0)): 13/23 ≈ 0.565
      ├── Some((3, 1)): 19/29 ≈ 0.655
      ├── Some((3, 2)): 3/11 ≈ 0.273
      ├── Some((3, 3)): 3/11 ≈ 0.273
      ├── Some((3, 4)): 2/10 ≈ 0.200
      ├── Some((3, 5)): 7/16 ≈ 0.438
      ├── Some((3, 6)): 12/21 ≈ 0.571
      ├── Some((3, 7)): 11/20 ≈ 0.550
      └── Some((3, 8)): 14/24 ≈ 0.583
    ├── Some((7, 4)): 79/158 ≈ 0.500
      ├── Some((4, 0)): 10/19 ≈ 0.526
      ├── Some((4, 1)): 11/20 ≈ 0.550
      ├── Some((4, 2)): 17/26 ≈ 0.654
      ├── Some((4, 3)): 8/17 ≈ 0.471
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 8/17 ≈ 0.471
      └── Some((4, 8)): 5/13 ≈ 0.385
    ├── Some((7, 5)): 105/197 ≈ 0.533
      ├── Some((5, 0)): 9/19 ≈ 0.474
      ├── Some((5, 1)): 12/22 ≈ 0.545
      ├── Some((5, 2)): 5/14 ≈ 0.357
      ├── Some((5, 3)): 4/13 ≈ 0.308
      ├── Some((5, 4)): 4/13 ≈ 0.308
      ├── Some((5, 5)): 12/23 ≈ 0.522
      ├── Some((5, 6)): 17/28 ≈ 0.607
      ├── Some((5, 7)): 21/32 ≈ 0.656
      └── Some((5, 8)): 21/32 ≈ 0.656
    ├── Some((7, 6)): 53/118 ≈ 0.449
      ├── Some((6, 0)): 9/19 ≈ 0.474
      ├── Some((6, 1)): 1/9 ≈ 0.111
      ├── Some((6, 2)): 6/15 ≈ 0.400
      ├── Some((6, 3)): 15/25 ≈ 0.600
      ├── Some((6, 4)): 4/13 ≈ 0.308
      ├── Some((6, 5)): 8/17 ≈ 0.471
      └── Some((6, 8)): 9/19 ≈ 0.474
    ├── Some((7, 7)): 58/126 ≈ 0.460
      ├── Some((7, 0)): 10/19 ≈ 0.526
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 5/13 ≈ 0.385
      ├── Some((7, 3)): 10/19 ≈ 0.526
      ├── Some((7, 4)): 9/18 ≈ 0.500
      ├── Some((7, 5)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 12/21 ≈ 0.571
      └── Some((7, 8)): 3/11 ≈ 0.273
    └── Some((7, 8)): 115/212 ≈ 0.542
      ├── Some((8, 0)): 12/23 ≈ 0.522
      ├── Some((8, 1)): 20/31 ≈ 0.645
      ├── Some((8, 2)): 6/16 ≈ 0.375
      ├── Some((8, 3)): 16/27 ≈ 0.593
      ├── Some((8, 4)): 17/28 ≈ 0.607
      ├── Some((8, 5)): 10/21 ≈ 0.476
      ├── Some((8, 6)): 13/24 ≈ 0.542
      ├── Some((8, 7)): 12/23 ≈ 0.522
      └── Some((8, 8)): 8/18 ≈ 0.444
  └── Some((6, 8)): 1234/2312 ≈ 0.534
    ├── Some((8, 0)): 120/231 ≈ 0.519
      ├── Some((0, 0)): 8/19 ≈ 0.421
      ├── Some((0, 1)): 13/25 ≈ 0.520
      ├── Some((0, 2)): 15/28 ≈ 0.536
      ├── Some((0, 3)): 16/29 ≈ 0.552
      ├── Some((0, 4)): 10/22 ≈ 0.455
      ├── Some((0, 5)): 14/26 ≈ 0.538
      ├── Some((0, 6)): 12/24 ≈ 0.500
      ├── Some((0, 7)): 15/28 ≈ 0.536
      └── Some((0, 8)): 16/29 ≈ 0.552
    ├── Some((8, 1)): 122/234 ≈ 0.521
      ├── Some((1, 0)): 15/28 ≈ 0.536
      ├── Some((1, 1)): 7/18 ≈ 0.389
      ├── Some((1, 2)): 9/21 ≈ 0.429
      ├── Some((1, 3)): 15/28 ≈ 0.536
      ├── Some((1, 4)): 21/34 ≈ 0.618
      ├── Some((1, 5)): 12/24 ≈ 0.500
      ├── Some((1, 6)): 13/25 ≈ 0.520
      ├── Some((1, 7)): 21/34 ≈ 0.618
      └── Some((1, 8)): 9/21 ≈ 0.429
    ├── Some((8, 2)): 156/286 ≈ 0.545
      ├── Some((2, 0)): 29/45 ≈ 0.644
      ├── Some((2, 1)): 4/16 ≈ 0.250
      ├── Some((2, 2)): 1/11 ≈ 0.091
      ├── Some((2, 3)): 34/51 ≈ 0.667
      ├── Some((2, 4)): 9/22 ≈ 0.409
      ├── Some((2, 5)): 15/30 ≈ 0.500
      ├── Some((2, 6)): 26/42 ≈ 0.619
      ├── Some((2, 7)): 19/34 ≈ 0.559
      └── Some((2, 8)): 19/34 ≈ 0.559
    ├── Some((8, 3)): 172/309 ≈ 0.557
      ├── Some((3, 0)): 26/42 ≈ 0.619
      ├── Some((3, 1)): 34/51 ≈ 0.667
      ├── Some((3, 2)): 16/31 ≈ 0.516
      ├── Some((3, 3)): 14/28 ≈ 0.500
      ├── Some((3, 4)): 13/27 ≈ 0.481
      ├── Some((3, 5)): 18/33 ≈ 0.545
      ├── Some((3, 6)): 15/30 ≈ 0.500
      ├── Some((3, 7)): 11/25 ≈ 0.440
      └── Some((3, 8)): 25/41 ≈ 0.610
    ├── Some((8, 4)): 98/198 ≈ 0.495
      ├── Some((4, 0)): 13/25 ≈ 0.520
      ├── Some((4, 1)): 17/29 ≈ 0.586
      ├── Some((4, 2)): 3/12 ≈ 0.250
      ├── Some((4, 3)): 18/30 ≈ 0.600
      ├── Some((4, 4)): 11/22 ≈ 0.500
      ├── Some((4, 5)): 14/26 ≈ 0.538
      ├── Some((4, 6)): 4/14 ≈ 0.286
      ├── Some((4, 7)): 6/16 ≈ 0.375
      └── Some((4, 8)): 12/23 ≈ 0.522
    ├── Some((8, 5)): 164/298 ≈ 0.550
      ├── Some((5, 0)): 10/23 ≈ 0.435
      ├── Some((5, 1)): 26/42 ≈ 0.619
      ├── Some((5, 2)): 14/28 ≈ 0.500
      ├── Some((5, 3)): 9/22 ≈ 0.409
      ├── Some((5, 4)): 13/27 ≈ 0.481
      ├── Some((5, 5)): 17/32 ≈ 0.531
      ├── Some((5, 6)): 31/48 ≈ 0.646
      ├── Some((5, 7)): 18/33 ≈ 0.545
      └── Some((5, 8)): 26/42 ≈ 0.619
    ├── Some((8, 6)): 158/289 ≈ 0.547
      ├── Some((6, 0)): 31/52 ≈ 0.596
      ├── Some((6, 1)): 17/35 ≈ 0.486
      ├── Some((6, 2)): 10/26 ≈ 0.385
      ├── Some((6, 3)): 32/53 ≈ 0.604
      ├── Some((6, 4)): 20/38 ≈ 0.526
      ├── Some((6, 5)): 11/27 ≈ 0.407
      └── Some((6, 7)): 36/57 ≈ 0.632
    ├── Some((8, 7)): 157/287 ≈ 0.547
      ├── Some((7, 0)): 18/33 ≈ 0.545
      ├── Some((7, 1)): 25/40 ≈ 0.625
      ├── Some((7, 2)): 15/29 ≈ 0.517
      ├── Some((7, 3)): 13/27 ≈ 0.481
      ├── Some((7, 4)): 11/24 ≈ 0.458
      ├── Some((7, 5)): 9/22 ≈ 0.409
      ├── Some((7, 6)): 20/35 ≈ 0.571
      ├── Some((7, 7)): 16/30 ≈ 0.533
      └── Some((7, 8)): 30/46 ≈ 0.652
    └── Some((8, 8)): 86/179 ≈ 0.480
      ├── Some((8, 0)): 9/20 ≈ 0.450
      ├── Some((8, 1)): 7/18 ≈ 0.389
      ├── Some((8, 2)): 10/22 ≈ 0.455
      ├── Some((8, 3)): 9/20 ≈ 0.450
      ├── Some((8, 4)): 8/19 ≈ 0.421
      ├── Some((8, 5)): 20/33 ≈ 0.606
      ├── Some((8, 6)): 13/25 ≈ 0.520
      └── Some((8, 7)): 9/21 ≈ 0.429
├── Some((6, 7)): 10061/18993 ≈ 0.530
  ├── Some((7, 0)): 928/1783 ≈ 0.520
    ├── Some((0, 0)): 83/168 ≈ 0.494
      ├── Some((0, 1)): 10/21 ≈ 0.476
      ├── Some((0, 2)): 6/16 ≈ 0.375
      ├── Some((0, 3)): 4/13 ≈ 0.308
      ├── Some((0, 4)): 22/34 ≈ 0.647
      ├── Some((0, 5)): 13/24 ≈ 0.542
      ├── Some((0, 6)): 4/13 ≈ 0.308
      ├── Some((0, 7)): 11/22 ≈ 0.500
      └── Some((0, 8)): 13/24 ≈ 0.542
    ├── Some((0, 1)): 119/222 ≈ 0.536
      ├── Some((1, 0)): 9/20 ≈ 0.450
      ├── Some((1, 1)): 13/24 ≈ 0.542
      ├── Some((1, 2)): 18/30 ≈ 0.600
      ├── Some((1, 3)): 12/23 ≈ 0.522
      ├── Some((1, 4)): 23/35 ≈ 0.657
      ├── Some((1, 5)): 16/28 ≈ 0.571
      ├── Some((1, 6)): 5/15 ≈ 0.333
      ├── Some((1, 7)): 14/26 ≈ 0.538
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((0, 2)): 84/170 ≈ 0.494
      ├── Some((2, 0)): 17/27 ≈ 0.630
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 12/22 ≈ 0.545
      ├── Some((2, 3)): 5/14 ≈ 0.357
      ├── Some((2, 4)): 8/18 ≈ 0.444
      ├── Some((2, 5)): 5/14 ≈ 0.357
      ├── Some((2, 6)): 13/23 ≈ 0.565
      ├── Some((2, 7)): 2/10 ≈ 0.200
      └── Some((2, 8)): 14/24 ≈ 0.583
    ├── Some((0, 3)): 104/200 ≈ 0.520
      ├── Some((3, 0)): 16/27 ≈ 0.593
      ├── Some((3, 1)): 10/21 ≈ 0.476
      ├── Some((3, 2)): 11/22 ≈ 0.500
      ├── Some((3, 3)): 4/13 ≈ 0.308
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 16/27 ≈ 0.593
      ├── Some((3, 6)): 14/25 ≈ 0.560
      ├── Some((3, 7)): 9/20 ≈ 0.450
      └── Some((3, 8)): 15/26 ≈ 0.577
    ├── Some((0, 4)): 98/191 ≈ 0.513
      ├── Some((4, 0)): 5/14 ≈ 0.357
      ├── Some((4, 1)): 3/12 ≈ 0.250
      ├── Some((4, 2)): 3/12 ≈ 0.250
      ├── Some((4, 3)): 10/20 ≈ 0.500
      ├── Some((4, 4)): 12/23 ≈ 0.522
      ├── Some((4, 5)): 14/25 ≈ 0.560
      ├── Some((4, 6)): 19/30 ≈ 0.633
      ├── Some((4, 7)): 15/26 ≈ 0.577
      └── Some((4, 8)): 17/28 ≈ 0.607
    ├── Some((0, 5)): 148/265 ≈ 0.558
      ├── Some((5, 0)): 14/27 ≈ 0.519
      ├── Some((5, 1)): 7/19 ≈ 0.368
      ├── Some((5, 2)): 20/34 ≈ 0.588
      ├── Some((5, 3)): 17/30 ≈ 0.567
      ├── Some((5, 4)): 21/35 ≈ 0.600
      ├── Some((5, 5)): 18/31 ≈ 0.581
      ├── Some((5, 6)): 28/42 ≈ 0.667
      ├── Some((5, 7)): 6/17 ≈ 0.353
      └── Some((5, 8)): 16/29 ≈ 0.552
    ├── Some((0, 6)): 161/284 ≈ 0.567
      ├── Some((6, 0)): 24/40 ≈ 0.600
      ├── Some((6, 1)): 12/26 ≈ 0.462
      ├── Some((6, 2)): 15/30 ≈ 0.500
      ├── Some((6, 3)): 20/36 ≈ 0.556
      ├── Some((6, 4)): 13/27 ≈ 0.481
      ├── Some((6, 5)): 16/31 ≈ 0.516
      ├── Some((6, 6)): 16/31 ≈ 0.516
      └── Some((6, 8)): 44/62 ≈ 0.710
    ├── Some((0, 7)): 81/165 ≈ 0.491
      ├── Some((7, 1)): 2/11 ≈ 0.182
      ├── Some((7, 2)): 7/17 ≈ 0.412
      ├── Some((7, 3)): 14/25 ≈ 0.560
      ├── Some((7, 4)): 11/22 ≈ 0.500
      ├── Some((7, 5)): 10/20 ≈ 0.500
      ├── Some((7, 6)): 11/22 ≈ 0.500
      ├── Some((7, 7)): 19/30 ≈ 0.633
      └── Some((7, 8)): 7/17 ≈ 0.412
    └── Some((0, 8)): 50/117 ≈ 0.427
      ├── Some((8, 0)): 7/15 ≈ 0.467
      ├── Some((8, 1)): 0/6 ≈ 0.000
      ├── Some((8, 2)): 9/17 ≈ 0.529
      ├── Some((8, 3)): 11/19 ≈ 0.579
      ├── Some((8, 4)): 1/8 ≈ 0.125
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 6/13 ≈ 0.462
      └── Some((8, 8)): 4/11 ≈ 0.364
  ├── Some((7, 1)): 1047/1989 ≈ 0.526
    ├── Some((1, 0)): 78/163 ≈ 0.479
      ├── Some((0, 0)): 5/14 ≈ 0.357
      ├── Some((0, 1)): 11/21 ≈ 0.524
      ├── Some((0, 2)): 19/29 ≈ 0.655
      ├── Some((0, 3)): 1/9 ≈ 0.111
      ├── Some((0, 4)): 8/18 ≈ 0.444
      ├── Some((0, 5)): 6/15 ≈ 0.400
      ├── Some((0, 6)): 7/16 ≈ 0.438
      ├── Some((0, 7)): 14/24 ≈ 0.583
      └── Some((0, 8)): 7/16 ≈ 0.438
    ├── Some((1, 1)): 89/180 ≈ 0.494
      ├── Some((1, 0)): 13/25 ≈ 0.520
      ├── Some((1, 2)): 8/19 ≈ 0.421
      ├── Some((1, 3)): 17/29 ≈ 0.586
      ├── Some((1, 4)): 18/30 ≈ 0.600
      ├── Some((1, 5)): 9/20 ≈ 0.450
      ├── Some((1, 6)): 10/21 ≈ 0.476
      ├── Some((1, 7)): 6/16 ≈ 0.375
      └── Some((1, 8)): 8/19 ≈ 0.421
    ├── Some((1, 2)): 124/233 ≈ 0.532
      ├── Some((2, 0)): 11/23 ≈ 0.478
      ├── Some((2, 1)): 6/17 ≈ 0.353
      ├── Some((2, 2)): 12/24 ≈ 0.500
      ├── Some((2, 3)): 17/30 ≈ 0.567
      ├── Some((2, 4)): 8/19 ≈ 0.421
      ├── Some((2, 5)): 9/21 ≈ 0.429
      ├── Some((2, 6)): 13/25 ≈ 0.520
      ├── Some((2, 7)): 18/31 ≈ 0.581
      └── Some((2, 8)): 29/42 ≈ 0.690
    ├── Some((1, 3)): 153/276 ≈ 0.554
      ├── Some((3, 0)): 13/26 ≈ 0.500
      ├── Some((3, 1)): 8/20 ≈ 0.400
      ├── Some((3, 2)): 15/29 ≈ 0.517
      ├── Some((3, 3)): 14/28 ≈ 0.500
      ├── Some((3, 4)): 18/32 ≈ 0.562
      ├── Some((3, 5)): 33/48 ≈ 0.688
      ├── Some((3, 6)): 11/24 ≈ 0.458
      ├── Some((3, 7)): 5/16 ≈ 0.312
      └── Some((3, 8)): 36/52 ≈ 0.692
    ├── Some((1, 4)): 148/269 ≈ 0.550
      ├── Some((4, 0)): 3/14 ≈ 0.214
      ├── Some((4, 1)): 14/27 ≈ 0.519
      ├── Some((4, 2)): 8/20 ≈ 0.400
      ├── Some((4, 3)): 12/25 ≈ 0.480
      ├── Some((4, 4)): 14/27 ≈ 0.519
      ├── Some((4, 5)): 26/41 ≈ 0.634
      ├── Some((4, 6)): 22/36 ≈ 0.611
      ├── Some((4, 7)): 26/41 ≈ 0.634
      └── Some((4, 8)): 23/37 ≈ 0.622
    ├── Some((1, 5)): 131/244 ≈ 0.537
      ├── Some((5, 0)): 9/21 ≈ 0.429
      ├── Some((5, 1)): 13/26 ≈ 0.500
      ├── Some((5, 2)): 19/32 ≈ 0.594
      ├── Some((5, 3)): 23/37 ≈ 0.622
      ├── Some((5, 4)): 7/18 ≈ 0.389
      ├── Some((5, 5)): 5/16 ≈ 0.312
      ├── Some((5, 6)): 30/44 ≈ 0.682
      ├── Some((5, 7)): 17/30 ≈ 0.567
      └── Some((5, 8)): 7/19 ≈ 0.368
    ├── Some((1, 6)): 63/140 ≈ 0.450
      ├── Some((6, 0)): 2/10 ≈ 0.200
      ├── Some((6, 1)): 5/14 ≈ 0.357
      ├── Some((6, 2)): 4/13 ≈ 0.308
      ├── Some((6, 3)): 3/12 ≈ 0.250
      ├── Some((6, 4)): 8/18 ≈ 0.444
      ├── Some((6, 5)): 8/18 ≈ 0.444
      ├── Some((6, 6)): 15/26 ≈ 0.577
      └── Some((6, 8)): 17/28 ≈ 0.607
    ├── Some((1, 7)): 187/326 ≈ 0.574
      ├── Some((7, 0)): 9/24 ≈ 0.375
      ├── Some((7, 2)): 13/29 ≈ 0.448
      ├── Some((7, 3)): 47/67 ≈ 0.701
      ├── Some((7, 4)): 27/45 ≈ 0.600
      ├── Some((7, 5)): 17/33 ≈ 0.515
      ├── Some((7, 6)): 32/51 ≈ 0.627
      ├── Some((7, 7)): 24/42 ≈ 0.571
      └── Some((7, 8)): 17/34 ≈ 0.500
    └── Some((1, 8)): 74/157 ≈ 0.471
      ├── Some((8, 0)): 4/13 ≈ 0.308
      ├── Some((8, 1)): 9/19 ≈ 0.474
      ├── Some((8, 2)): 6/15 ≈ 0.400
      ├── Some((8, 3)): 14/24 ≈ 0.583
      ├── Some((8, 4)): 16/26 ≈ 0.615
      ├── Some((8, 5)): 0/7 ≈ 0.000
      ├── Some((8, 6)): 6/15 ≈ 0.400
      ├── Some((8, 7)): 8/17 ≈ 0.471
      └── Some((8, 8)): 10/20 ≈ 0.500
  ├── Some((7, 2)): 1225/2296 ≈ 0.534
    ├── Some((2, 0)): 154/282 ≈ 0.546
      ├── Some((0, 0)): 21/36 ≈ 0.583
      ├── Some((0, 1)): 24/39 ≈ 0.615
      ├── Some((0, 2)): 11/24 ≈ 0.458
      ├── Some((0, 3)): 22/37 ≈ 0.595
      ├── Some((0, 4)): 13/27 ≈ 0.481
      ├── Some((0, 5)): 12/26 ≈ 0.462
      ├── Some((0, 6)): 15/29 ≈ 0.517
      ├── Some((0, 7)): 7/19 ≈ 0.368
      └── Some((0, 8)): 28/44 ≈ 0.636
    ├── Some((2, 1)): 169/305 ≈ 0.554
      ├── Some((1, 0)): 19/35 ≈ 0.543
      ├── Some((1, 1)): 13/27 ≈ 0.481
      ├── Some((1, 2)): 9/22 ≈ 0.409
      ├── Some((1, 3)): 15/30 ≈ 0.500
      ├── Some((1, 4)): 29/46 ≈ 0.630
      ├── Some((1, 5)): 9/22 ≈ 0.409
      ├── Some((1, 6)): 16/31 ≈ 0.516
      ├── Some((1, 7)): 22/38 ≈ 0.579
      └── Some((1, 8)): 36/53 ≈ 0.679
    ├── Some((2, 2)): 104/207 ≈ 0.502
      ├── Some((2, 0)): 11/23 ≈ 0.478
      ├── Some((2, 1)): 19/33 ≈ 0.576
      ├── Some((2, 3)): 7/19 ≈ 0.368
      ├── Some((2, 4)): 11/23 ≈ 0.478
      ├── Some((2, 5)): 28/43 ≈ 0.651
      ├── Some((2, 6)): 11/24 ≈ 0.458
      ├── Some((2, 7)): 7/19 ≈ 0.368
      └── Some((2, 8)): 10/22 ≈ 0.455
    ├── Some((2, 3)): 106/210 ≈ 0.505
      ├── Some((3, 0)): 14/26 ≈ 0.538
      ├── Some((3, 1)): 17/29 ≈ 0.586
      ├── Some((3, 2)): 11/22 ≈ 0.500
      ├── Some((3, 3)): 12/24 ≈ 0.500
      ├── Some((3, 4)): 20/32 ≈ 0.625
      ├── Some((3, 5)): 6/17 ≈ 0.353
      ├── Some((3, 6)): 5/15 ≈ 0.333
      ├── Some((3, 7)): 13/25 ≈ 0.520
      └── Some((3, 8)): 8/19 ≈ 0.421
    ├── Some((2, 4)): 206/359 ≈ 0.574
      ├── Some((4, 0)): 31/49 ≈ 0.633
      ├── Some((4, 1)): 15/31 ≈ 0.484
      ├── Some((4, 2)): 15/31 ≈ 0.484
      ├── Some((4, 3)): 41/60 ≈ 0.683
      ├── Some((4, 4)): 22/39 ≈ 0.564
      ├── Some((4, 5)): 19/35 ≈ 0.543
      ├── Some((4, 6)): 10/25 ≈ 0.400
      ├── Some((4, 7)): 36/55 ≈ 0.655
      └── Some((4, 8)): 17/33 ≈ 0.515
    ├── Some((2, 5)): 106/210 ≈ 0.505
      ├── Some((5, 0)): 16/28 ≈ 0.571
      ├── Some((5, 1)): 8/19 ≈ 0.421
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 17/29 ≈ 0.586
      ├── Some((5, 4)): 16/28 ≈ 0.571
      ├── Some((5, 5)): 6/17 ≈ 0.353
      ├── Some((5, 6)): 4/14 ≈ 0.286
      ├── Some((5, 7)): 12/24 ≈ 0.500
      └── Some((5, 8)): 16/28 ≈ 0.571
    ├── Some((2, 6)): 152/280 ≈ 0.543
      ├── Some((6, 0)): 27/45 ≈ 0.600
      ├── Some((6, 1)): 20/36 ≈ 0.556
      ├── Some((6, 2)): 21/38 ≈ 0.553
      ├── Some((6, 3)): 24/41 ≈ 0.585
      ├── Some((6, 4)): 18/34 ≈ 0.529
      ├── Some((6, 5)): 26/43 ≈ 0.605
      ├── Some((6, 6)): 7/20 ≈ 0.350
      └── Some((6, 8)): 8/22 ≈ 0.364
    ├── Some((2, 7)): 84/176 ≈ 0.477
      ├── Some((7, 0)): 7/18 ≈ 0.389
      ├── Some((7, 1)): 3/13 ≈ 0.231
      ├── Some((7, 3)): 8/19 ≈ 0.421
      ├── Some((7, 4)): 28/42 ≈ 0.667
      ├── Some((7, 5)): 14/26 ≈ 0.538
      ├── Some((7, 6)): 11/23 ≈ 0.478
      ├── Some((7, 7)): 5/15 ≈ 0.333
      └── Some((7, 8)): 8/19 ≈ 0.421
    └── Some((2, 8)): 143/266 ≈ 0.538
      ├── Some((8, 0)): 24/39 ≈ 0.615
      ├── Some((8, 1)): 6/18 ≈ 0.333
      ├── Some((8, 2)): 8/20 ≈ 0.400
      ├── Some((8, 3)): 9/22 ≈ 0.409
      ├── Some((8, 4)): 29/45 ≈ 0.644
      ├── Some((8, 5)): 25/40 ≈ 0.625
      ├── Some((8, 6)): 18/32 ≈ 0.562
      ├── Some((8, 7)): 17/31 ≈ 0.548
      └── Some((8, 8)): 6/18 ≈ 0.333
  ├── Some((7, 3)): 1590/2919 ≈ 0.545
    ├── Some((3, 0)): 107/218 ≈ 0.491
      ├── Some((0, 0)): 9/21 ≈ 0.429
      ├── Some((0, 1)): 15/28 ≈ 0.536
      ├── Some((0, 2)): 11/23 ≈ 0.478
      ├── Some((0, 3)): 17/30 ≈ 0.567
      ├── Some((0, 4)): 13/26 ≈ 0.500
      ├── Some((0, 5)): 9/21 ≈ 0.429
      ├── Some((0, 6)): 12/24 ≈ 0.500
      ├── Some((0, 7)): 11/23 ≈ 0.478
      └── Some((0, 8)): 9/21 ≈ 0.429
    ├── Some((3, 1)): 189/343 ≈ 0.551
      ├── Some((1, 0)): 23/41 ≈ 0.561
      ├── Some((1, 1)): 25/43 ≈ 0.581
      ├── Some((1, 2)): 24/42 ≈ 0.571
      ├── Some((1, 3)): 21/38 ≈ 0.553
      ├── Some((1, 4)): 9/23 ≈ 0.391
      ├── Some((1, 5)): 29/47 ≈ 0.617
      ├── Some((1, 6)): 21/38 ≈ 0.553
      ├── Some((1, 7)): 22/39 ≈ 0.564
      └── Some((1, 8)): 15/31 ≈ 0.484
    ├── Some((3, 2)): 193/349 ≈ 0.553
      ├── Some((2, 0)): 21/38 ≈ 0.553
      ├── Some((2, 1)): 23/41 ≈ 0.561
      ├── Some((2, 2)): 17/34 ≈ 0.500
      ├── Some((2, 3)): 19/36 ≈ 0.528
      ├── Some((2, 4)): 31/50 ≈ 0.620
      ├── Some((2, 5)): 11/26 ≈ 0.423
      ├── Some((2, 6)): 13/29 ≈ 0.448
      ├── Some((2, 7)): 22/40 ≈ 0.550
      └── Some((2, 8)): 35/54 ≈ 0.648
    ├── Some((3, 3)): 149/283 ≈ 0.527
      ├── Some((3, 0)): 11/26 ≈ 0.423
      ├── Some((3, 1)): 20/37 ≈ 0.541
      ├── Some((3, 2)): 13/29 ≈ 0.448
      ├── Some((3, 4)): 21/38 ≈ 0.553
      ├── Some((3, 5)): 21/38 ≈ 0.553
      ├── Some((3, 6)): 13/29 ≈ 0.448
      ├── Some((3, 7)): 17/34 ≈ 0.500
      └── Some((3, 8)): 32/51 ≈ 0.627
    ├── Some((3, 4)): 210/374 ≈ 0.561
      ├── Some((4, 0)): 10/25 ≈ 0.400
      ├── Some((4, 1)): 27/46 ≈ 0.587
      ├── Some((4, 2)): 25/44 ≈ 0.568
      ├── Some((4, 3)): 22/40 ≈ 0.550
      ├── Some((4, 4)): 21/39 ≈ 0.538
      ├── Some((4, 5)): 28/47 ≈ 0.596
      ├── Some((4, 6)): 26/45 ≈ 0.578
      ├── Some((4, 7)): 16/33 ≈ 0.485
      └── Some((4, 8)): 34/54 ≈ 0.630
    ├── Some((3, 5)): 214/380 ≈ 0.563
      ├── Some((5, 0)): 12/28 ≈ 0.429
      ├── Some((5, 1)): 12/28 ≈ 0.429
      ├── Some((5, 2)): 37/58 ≈ 0.638
      ├── Some((5, 3)): 22/41 ≈ 0.537
      ├── Some((5, 4)): 24/43 ≈ 0.558
      ├── Some((5, 5)): 37/58 ≈ 0.638
      ├── Some((5, 6)): 20/38 ≈ 0.526
      ├── Some((5, 7)): 40/61 ≈ 0.656
      └── Some((5, 8)): 9/24 ≈ 0.375
    ├── Some((3, 6)): 165/307 ≈ 0.537
      ├── Some((6, 0)): 22/40 ≈ 0.550
      ├── Some((6, 1)): 29/49 ≈ 0.592
      ├── Some((6, 2)): 14/30 ≈ 0.467
      ├── Some((6, 3)): 40/61 ≈ 0.656
      ├── Some((6, 4)): 12/28 ≈ 0.429
      ├── Some((6, 5)): 9/24 ≈ 0.375
      ├── Some((6, 6)): 19/37 ≈ 0.514
      └── Some((6, 8)): 19/37 ≈ 0.514
    ├── Some((3, 7)): 163/304 ≈ 0.536
      ├── Some((7, 0)): 14/30 ≈ 0.467
      ├── Some((7, 1)): 26/45 ≈ 0.578
      ├── Some((7, 2)): 28/47 ≈ 0.596
      ├── Some((7, 4)): 17/34 ≈ 0.500
      ├── Some((7, 5)): 10/25 ≈ 0.400
      ├── Some((7, 6)): 20/38 ≈ 0.526
      ├── Some((7, 7)): 19/37 ≈ 0.514
      └── Some((7, 8)): 28/47 ≈ 0.596
    └── Some((3, 8)): 200/360 ≈ 0.556
      ├── Some((8, 0)): 31/50 ≈ 0.620
      ├── Some((8, 1)): 27/46 ≈ 0.587
      ├── Some((8, 2)): 8/23 ≈ 0.348
      ├── Some((8, 3)): 25/43 ≈ 0.581
      ├── Some((8, 4)): 24/42 ≈ 0.571
      ├── Some((8, 5)): 24/42 ≈ 0.571
      ├── Some((8, 6)): 15/31 ≈ 0.484
      ├── Some((8, 7)): 29/48 ≈ 0.604
      └── Some((8, 8)): 17/34 ≈ 0.500
  ├── Some((7, 4)): 1292/2411 ≈ 0.536
    ├── Some((4, 0)): 91/188 ≈ 0.484
      ├── Some((0, 0)): 9/20 ≈ 0.450
      ├── Some((0, 1)): 7/17 ≈ 0.412
      ├── Some((0, 2)): 11/22 ≈ 0.500
      ├── Some((0, 3)): 6/16 ≈ 0.375
      ├── Some((0, 4)): 12/23 ≈ 0.522
      ├── Some((0, 5)): 9/20 ≈ 0.450
      ├── Some((0, 6)): 6/16 ≈ 0.375
      ├── Some((0, 7)): 16/28 ≈ 0.571
      └── Some((0, 8)): 14/25 ≈ 0.560
    ├── Some((4, 1)): 143/268 ≈ 0.534
      ├── Some((1, 0)): 15/29 ≈ 0.517
      ├── Some((1, 1)): 23/38 ≈ 0.605
      ├── Some((1, 2)): 11/24 ≈ 0.458
      ├── Some((1, 3)): 10/23 ≈ 0.435
      ├── Some((1, 4)): 14/28 ≈ 0.500
      ├── Some((1, 5)): 13/26 ≈ 0.500
      ├── Some((1, 6)): 13/27 ≈ 0.481
      ├── Some((1, 7)): 12/25 ≈ 0.480
      └── Some((1, 8)): 31/47 ≈ 0.660
    ├── Some((4, 2)): 145/271 ≈ 0.535
      ├── Some((2, 0)): 17/31 ≈ 0.548
      ├── Some((2, 1)): 25/40 ≈ 0.625
      ├── Some((2, 2)): 22/37 ≈ 0.595
      ├── Some((2, 3)): 8/21 ≈ 0.381
      ├── Some((2, 4)): 25/40 ≈ 0.625
      ├── Some((2, 5)): 12/26 ≈ 0.462
      ├── Some((2, 6)): 12/26 ≈ 0.462
      ├── Some((2, 7)): 6/18 ≈ 0.333
      └── Some((2, 8)): 17/31 ≈ 0.548
    ├── Some((4, 3)): 166/302 ≈ 0.550
      ├── Some((3, 0)): 30/47 ≈ 0.638
      ├── Some((3, 1)): 10/24 ≈ 0.417
      ├── Some((3, 2)): 45/63 ≈ 0.714
      ├── Some((3, 3)): 13/27 ≈ 0.481
      ├── Some((3, 4)): 16/31 ≈ 0.516
      ├── Some((3, 5)): 12/26 ≈ 0.462
      ├── Some((3, 6)): 10/24 ≈ 0.417
      ├── Some((3, 7)): 13/28 ≈ 0.464
      └── Some((3, 8)): 16/31 ≈ 0.516
    ├── Some((4, 4)): 158/290 ≈ 0.545
      ├── Some((4, 0)): 5/18 ≈ 0.278
      ├── Some((4, 1)): 9/23 ≈ 0.391
      ├── Some((4, 2)): 12/27 ≈ 0.444
      ├── Some((4, 3)): 36/55 ≈ 0.655
      ├── Some((4, 5)): 13/29 ≈ 0.448
      ├── Some((4, 6)): 26/44 ≈ 0.591
      ├── Some((4, 7)): 23/41 ≈ 0.561
      └── Some((4, 8)): 33/52 ≈ 0.635
    ├── Some((4, 5)): 229/395 ≈ 0.580
      ├── Some((5, 0)): 27/46 ≈ 0.587
      ├── Some((5, 1)): 23/41 ≈ 0.561
      ├── Some((5, 2)): 35/55 ≈ 0.636
      ├── Some((5, 3)): 26/45 ≈ 0.578
      ├── Some((5, 4)): 29/48 ≈ 0.604
      ├── Some((5, 5)): 29/48 ≈ 0.604
      ├── Some((5, 6)): 12/28 ≈ 0.429
      ├── Some((5, 7)): 22/40 ≈ 0.550
      └── Some((5, 8)): 25/43 ≈ 0.581
    ├── Some((4, 6)): 139/261 ≈ 0.533
      ├── Some((6, 0)): 31/48 ≈ 0.646
      ├── Some((6, 1)): 14/29 ≈ 0.483
      ├── Some((6, 2)): 12/26 ≈ 0.462
      ├── Some((6, 3)): 9/23 ≈ 0.391
      ├── Some((6, 4)): 31/49 ≈ 0.633
      ├── Some((6, 5)): 11/25 ≈ 0.440
      ├── Some((6, 6)): 11/25 ≈ 0.440
      └── Some((6, 8)): 19/35 ≈ 0.543
    ├── Some((4, 7)): 145/271 ≈ 0.535
      ├── Some((7, 0)): 22/39 ≈ 0.564
      ├── Some((7, 1)): 31/49 ≈ 0.633
      ├── Some((7, 2)): 19/35 ≈ 0.543
      ├── Some((7, 3)): 16/31 ≈ 0.516
      ├── Some((7, 5)): 13/28 ≈ 0.464
      ├── Some((7, 6)): 13/28 ≈ 0.464
      ├── Some((7, 7)): 6/19 ≈ 0.316
      └── Some((7, 8)): 24/41 ≈ 0.585
    └── Some((4, 8)): 76/164 ≈ 0.463
      ├── Some((8, 0)): 7/17 ≈ 0.412
      ├── Some((8, 1)): 11/21 ≈ 0.524
      ├── Some((8, 2)): 5/14 ≈ 0.357
      ├── Some((8, 3)): 7/17 ≈ 0.412
      ├── Some((8, 4)): 4/13 ≈ 0.308
      ├── Some((8, 5)): 14/24 ≈ 0.583
      ├── Some((8, 6)): 14/25 ≈ 0.560
      ├── Some((8, 7)): 1/9 ≈ 0.111
      └── Some((8, 8)): 13/23 ≈ 0.565
  ├── Some((7, 5)): 939/1803 ≈ 0.521
    ├── Some((5, 0)): 93/183 ≈ 0.508
      ├── Some((0, 0)): 7/17 ≈ 0.412
      ├── Some((0, 1)): 11/21 ≈ 0.524
      ├── Some((0, 2)): 4/13 ≈ 0.308
      ├── Some((0, 3)): 6/16 ≈ 0.375
      ├── Some((0, 4)): 14/24 ≈ 0.583
      ├── Some((0, 5)): 12/22 ≈ 0.545
      ├── Some((0, 6)): 13/23 ≈ 0.565
      ├── Some((0, 7)): 10/20 ≈ 0.500
      └── Some((0, 8)): 15/26 ≈ 0.577
    ├── Some((5, 1)): 112/212 ≈ 0.528
      ├── Some((1, 0)): 10/21 ≈ 0.476
      ├── Some((1, 1)): 16/28 ≈ 0.571
      ├── Some((1, 2)): 12/23 ≈ 0.522
      ├── Some((1, 3)): 12/23 ≈ 0.522
      ├── Some((1, 4)): 17/29 ≈ 0.586
      ├── Some((1, 5)): 2/11 ≈ 0.182
      ├── Some((1, 6)): 16/28 ≈ 0.571
      ├── Some((1, 7)): 14/25 ≈ 0.560
      └── Some((1, 8)): 12/23 ≈ 0.522
    ├── Some((5, 2)): 105/202 ≈ 0.520
      ├── Some((2, 0)): 7/17 ≈ 0.412
      ├── Some((2, 1)): 14/25 ≈ 0.560
      ├── Some((2, 2)): 9/20 ≈ 0.450
      ├── Some((2, 3)): 7/17 ≈ 0.412
      ├── Some((2, 4)): 14/25 ≈ 0.560
      ├── Some((2, 5)): 30/42 ≈ 0.714
      ├── Some((2, 6)): 11/22 ≈ 0.500
      ├── Some((2, 7)): 7/17 ≈ 0.412
      └── Some((2, 8)): 6/16 ≈ 0.375
    ├── Some((5, 3)): 131/240 ≈ 0.546
      ├── Some((3, 0)): 10/22 ≈ 0.455
      ├── Some((3, 1)): 5/16 ≈ 0.312
      ├── Some((3, 2)): 21/34 ≈ 0.618
      ├── Some((3, 3)): 15/27 ≈ 0.556
      ├── Some((3, 4)): 18/31 ≈ 0.581
      ├── Some((3, 5)): 8/19 ≈ 0.421
      ├── Some((3, 6)): 12/24 ≈ 0.500
      ├── Some((3, 7)): 26/39 ≈ 0.667
      └── Some((3, 8)): 15/27 ≈ 0.556
    ├── Some((5, 4)): 107/204 ≈ 0.525
      ├── Some((4, 0)): 2/11 ≈ 0.182
      ├── Some((4, 1)): 20/31 ≈ 0.645
      ├── Some((4, 2)): 14/25 ≈ 0.560
      ├── Some((4, 3)): 14/25 ≈ 0.560
      ├── Some((4, 4)): 4/14 ≈ 0.286
      ├── Some((4, 5)): 13/24 ≈ 0.542
      ├── Some((4, 6)): 11/22 ≈ 0.500
      ├── Some((4, 7)): 18/29 ≈ 0.621
      └── Some((4, 8)): 11/22 ≈ 0.500
    ├── Some((5, 5)): 83/168 ≈ 0.494
      ├── Some((5, 0)): 6/16 ≈ 0.375
      ├── Some((5, 1)): 6/16 ≈ 0.375
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 18/29 ≈ 0.621
      ├── Some((5, 4)): 8/18 ≈ 0.444
      ├── Some((5, 6)): 10/20 ≈ 0.500
      ├── Some((5, 7)): 11/22 ≈ 0.500
      └── Some((5, 8)): 13/24 ≈ 0.542
    ├── Some((5, 6)): 98/191 ≈ 0.513
      ├── Some((6, 0)): 7/18 ≈ 0.389
      ├── Some((6, 1)): 12/24 ≈ 0.500
      ├── Some((6, 2)): 2/11 ≈ 0.182
      ├── Some((6, 3)): 15/27 ≈ 0.556
      ├── Some((6, 4)): 11/23 ≈ 0.478
      ├── Some((6, 5)): 16/28 ≈ 0.571
      ├── Some((6, 6)): 14/26 ≈ 0.538
      └── Some((6, 8)): 20/33 ≈ 0.606
    ├── Some((5, 7)): 105/202 ≈ 0.520
      ├── Some((7, 0)): 22/35 ≈ 0.629
      ├── Some((7, 1)): 8/19 ≈ 0.421
      ├── Some((7, 2)): 10/22 ≈ 0.455
      ├── Some((7, 3)): 10/22 ≈ 0.455
      ├── Some((7, 4)): 17/29 ≈ 0.586
      ├── Some((7, 6)): 12/24 ≈ 0.500
      ├── Some((7, 7)): 7/18 ≈ 0.389
      └── Some((7, 8)): 19/32 ≈ 0.594
    └── Some((5, 8)): 104/200 ≈ 0.520
      ├── Some((8, 0)): 5/15 ≈ 0.333
      ├── Some((8, 1)): 13/24 ≈ 0.542
      ├── Some((8, 2)): 13/24 ≈ 0.542
      ├── Some((8, 3)): 17/28 ≈ 0.607
      ├── Some((8, 4)): 3/12 ≈ 0.250
      ├── Some((8, 5)): 14/25 ≈ 0.560
      ├── Some((8, 6)): 12/23 ≈ 0.522
      ├── Some((8, 7)): 12/23 ≈ 0.522
      └── Some((8, 8)): 14/25 ≈ 0.560
  ├── Some((7, 6)): 1028/1957 ≈ 0.525
    ├── Some((6, 0)): 153/282 ≈ 0.543
      ├── Some((0, 0)): 2/13 ≈ 0.154
      ├── Some((0, 1)): 24/40 ≈ 0.600
      ├── Some((0, 2)): 11/24 ≈ 0.458
      ├── Some((0, 3)): 11/24 ≈ 0.458
      ├── Some((0, 4)): 30/46 ≈ 0.652
      ├── Some((0, 5)): 14/28 ≈ 0.500
      ├── Some((0, 6)): 19/34 ≈ 0.559
      ├── Some((0, 7)): 27/43 ≈ 0.628
      └── Some((0, 8)): 15/29 ≈ 0.517
    ├── Some((6, 1)): 93/190 ≈ 0.489
      ├── Some((1, 0)): 20/32 ≈ 0.625
      ├── Some((1, 1)): 14/25 ≈ 0.560
      ├── Some((1, 2)): 8/19 ≈ 0.421
      ├── Some((1, 3)): 9/20 ≈ 0.450
      ├── Some((1, 4)): 14/26 ≈ 0.538
      ├── Some((1, 5)): 3/12 ≈ 0.250
      ├── Some((1, 6)): 2/11 ≈ 0.182
      ├── Some((1, 7)): 13/24 ≈ 0.542
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((6, 2)): 108/213 ≈ 0.507
      ├── Some((2, 0)): 5/16 ≈ 0.312
      ├── Some((2, 1)): 15/27 ≈ 0.556
      ├── Some((2, 2)): 13/25 ≈ 0.520
      ├── Some((2, 3)): 4/14 ≈ 0.286
      ├── Some((2, 4)): 5/16 ≈ 0.312
      ├── Some((2, 5)): 21/34 ≈ 0.618
      ├── Some((2, 6)): 23/36 ≈ 0.639
      ├── Some((2, 7)): 13/25 ≈ 0.520
      └── Some((2, 8)): 8/19 ≈ 0.421
    ├── Some((6, 3)): 145/270 ≈ 0.537
      ├── Some((3, 0)): 31/47 ≈ 0.660
      ├── Some((3, 1)): 3/14 ≈ 0.214
      ├── Some((3, 2)): 18/32 ≈ 0.562
      ├── Some((3, 3)): 15/29 ≈ 0.517
      ├── Some((3, 4)): 9/22 ≈ 0.409
      ├── Some((3, 5)): 14/28 ≈ 0.500
      ├── Some((3, 6)): 15/29 ≈ 0.517
      ├── Some((3, 7)): 10/23 ≈ 0.435
      └── Some((3, 8)): 30/45 ≈ 0.667
    ├── Some((6, 4)): 112/219 ≈ 0.511
      ├── Some((4, 0)): 13/25 ≈ 0.520
      ├── Some((4, 1)): 16/28 ≈ 0.571
      ├── Some((4, 2)): 11/23 ≈ 0.478
      ├── Some((4, 3)): 17/30 ≈ 0.567
      ├── Some((4, 4)): 7/18 ≈ 0.389
      ├── Some((4, 5)): 12/24 ≈ 0.500
      ├── Some((4, 6)): 9/20 ≈ 0.450
      ├── Some((4, 7)): 7/18 ≈ 0.389
      └── Some((4, 8)): 19/32 ≈ 0.594
    ├── Some((6, 5)): 143/267 ≈ 0.536
      ├── Some((5, 0)): 14/27 ≈ 0.519
      ├── Some((5, 1)): 23/38 ≈ 0.605
      ├── Some((5, 2)): 13/26 ≈ 0.500
      ├── Some((5, 3)): 9/22 ≈ 0.409
      ├── Some((5, 4)): 14/27 ≈ 0.519
      ├── Some((5, 5)): 17/31 ≈ 0.548
      ├── Some((5, 6)): 17/31 ≈ 0.548
      ├── Some((5, 7)): 12/25 ≈ 0.480
      └── Some((5, 8)): 24/39 ≈ 0.615
    ├── Some((6, 6)): 160/292 ≈ 0.548
      ├── Some((6, 0)): 26/46 ≈ 0.565
      ├── Some((6, 1)): 23/42 ≈ 0.548
      ├── Some((6, 2)): 31/51 ≈ 0.608
      ├── Some((6, 3)): 25/44 ≈ 0.568
      ├── Some((6, 4)): 15/32 ≈ 0.469
      ├── Some((6, 5)): 28/48 ≈ 0.583
      └── Some((6, 8)): 12/28 ≈ 0.429
    └── Some((6, 8)): 114/223 ≈ 0.511
      ├── Some((8, 0)): 8/19 ≈ 0.421
      ├── Some((8, 1)): 15/27 ≈ 0.556
      ├── Some((8, 2)): 18/31 ≈ 0.581
      ├── Some((8, 3)): 18/31 ≈ 0.581
      ├── Some((8, 4)): 9/21 ≈ 0.429
      ├── Some((8, 5)): 9/21 ≈ 0.429
      ├── Some((8, 6)): 10/22 ≈ 0.455
      ├── Some((8, 7)): 18/31 ≈ 0.581
      └── Some((8, 8)): 8/19 ≈ 0.421
  ├── Some((7, 7)): 905/1743 ≈ 0.519
    ├── Some((7, 0)): 118/226 ≈ 0.522
      ├── Some((0, 0)): 25/38 ≈ 0.658
      ├── Some((0, 1)): 7/18 ≈ 0.389
      ├── Some((0, 2)): 12/24 ≈ 0.500
      ├── Some((0, 3)): 12/24 ≈ 0.500
      ├── Some((0, 4)): 12/24 ≈ 0.500
      ├── Some((0, 5)): 8/19 ≈ 0.421
      ├── Some((0, 6)): 16/29 ≈ 0.552
      ├── Some((0, 7)): 11/23 ≈ 0.478
      └── Some((0, 8)): 14/26 ≈ 0.538
    ├── Some((7, 1)): 130/244 ≈ 0.533
      ├── Some((1, 0)): 5/16 ≈ 0.312
      ├── Some((1, 1)): 16/29 ≈ 0.552
      ├── Some((1, 2)): 11/23 ≈ 0.478
      ├── Some((1, 3)): 10/22 ≈ 0.455
      ├── Some((1, 4)): 19/32 ≈ 0.594
      ├── Some((1, 5)): 20/34 ≈ 0.588
      ├── Some((1, 6)): 12/25 ≈ 0.480
      ├── Some((1, 7)): 11/23 ≈ 0.478
      └── Some((1, 8)): 25/39 ≈ 0.641
    ├── Some((7, 2)): 60/136 ≈ 0.441
      ├── Some((2, 0)): 6/14 ≈ 0.429
      ├── Some((2, 1)): 11/20 ≈ 0.550
      ├── Some((2, 2)): 2/10 ≈ 0.200
      ├── Some((2, 3)): 3/11 ≈ 0.273
      ├── Some((2, 4)): 8/17 ≈ 0.471
      ├── Some((2, 5)): 3/11 ≈ 0.273
      ├── Some((2, 6)): 11/20 ≈ 0.550
      ├── Some((2, 7)): 1/8 ≈ 0.125
      └── Some((2, 8)): 15/24 ≈ 0.625
    ├── Some((7, 3)): 140/260 ≈ 0.538
      ├── Some((3, 0)): 29/44 ≈ 0.659
      ├── Some((3, 1)): 3/14 ≈ 0.214
      ├── Some((3, 2)): 12/25 ≈ 0.480
      ├── Some((3, 3)): 15/28 ≈ 0.536
      ├── Some((3, 4)): 19/33 ≈ 0.576
      ├── Some((3, 5)): 9/21 ≈ 0.429
      ├── Some((3, 6)): 21/35 ≈ 0.600
      ├── Some((3, 7)): 22/36 ≈ 0.611
      └── Some((3, 8)): 10/23 ≈ 0.435
    ├── Some((7, 4)): 45/111 ≈ 0.405
      ├── Some((4, 0)): 6/14 ≈ 0.429
      ├── Some((4, 1)): 9/17 ≈ 0.529
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 5/12 ≈ 0.417
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 5/12 ≈ 0.417
      ├── Some((4, 6)): 4/11 ≈ 0.364
      ├── Some((4, 7)): 3/10 ≈ 0.300
      └── Some((4, 8)): 3/10 ≈ 0.300
    ├── Some((7, 5)): 150/274 ≈ 0.547
      ├── Some((5, 0)): 18/32 ≈ 0.562
      ├── Some((5, 1)): 12/25 ≈ 0.480
      ├── Some((5, 2)): 20/34 ≈ 0.588
      ├── Some((5, 3)): 18/32 ≈ 0.562
      ├── Some((5, 4)): 23/38 ≈ 0.605
      ├── Some((5, 5)): 9/21 ≈ 0.429
      ├── Some((5, 6)): 13/26 ≈ 0.500
      ├── Some((5, 7)): 19/33 ≈ 0.576
      └── Some((5, 8)): 18/32 ≈ 0.562
    ├── Some((7, 6)): 148/271 ≈ 0.546
      ├── Some((6, 0)): 16/31 ≈ 0.516
      ├── Some((6, 1)): 19/35 ≈ 0.543
      ├── Some((6, 2)): 16/31 ≈ 0.516
      ├── Some((6, 3)): 21/37 ≈ 0.568
      ├── Some((6, 4)): 21/37 ≈ 0.568
      ├── Some((6, 5)): 3/14 ≈ 0.214
      ├── Some((6, 6)): 37/55 ≈ 0.673
      └── Some((6, 8)): 15/30 ≈ 0.500
    └── Some((7, 8)): 114/220 ≈ 0.518
      ├── Some((8, 0)): 14/26 ≈ 0.538
      ├── Some((8, 1)): 22/35 ≈ 0.629
      ├── Some((8, 2)): 18/31 ≈ 0.581
      ├── Some((8, 3)): 12/24 ≈ 0.500
      ├── Some((8, 4)): 9/20 ≈ 0.450
      ├── Some((8, 5)): 4/14 ≈ 0.286
      ├── Some((8, 6)): 8/19 ≈ 0.421
      ├── Some((8, 7)): 15/27 ≈ 0.556
      └── Some((8, 8)): 11/23 ≈ 0.478
  └── Some((7, 8)): 1106/2091 ≈ 0.529
    ├── Some((8, 0)): 69/150 ≈ 0.460
      ├── Some((0, 0)): 8/17 ≈ 0.471
      ├── Some((0, 1)): 13/23 ≈ 0.565
      ├── Some((0, 2)): 7/16 ≈ 0.438
      ├── Some((0, 3)): 10/19 ≈ 0.526
      ├── Some((0, 4)): 4/13 ≈ 0.308
      ├── Some((0, 5)): 8/17 ≈ 0.471
      ├── Some((0, 6)): 3/11 ≈ 0.273
      ├── Some((0, 7)): 8/17 ≈ 0.471
      └── Some((0, 8)): 7/16 ≈ 0.438
    ├── Some((8, 1)): 149/272 ≈ 0.548
      ├── Some((1, 0)): 21/35 ≈ 0.600
      ├── Some((1, 1)): 19/33 ≈ 0.576
      ├── Some((1, 2)): 9/22 ≈ 0.409
      ├── Some((1, 3)): 8/20 ≈ 0.400
      ├── Some((1, 4)): 27/42 ≈ 0.643
      ├── Some((1, 5)): 16/30 ≈ 0.533
      ├── Some((1, 6)): 16/30 ≈ 0.533
      ├── Some((1, 7)): 7/19 ≈ 0.368
      └── Some((1, 8)): 25/40 ≈ 0.625
    ├── Some((8, 2)): 155/281 ≈ 0.552
      ├── Some((2, 0)): 0/9 ≈ 0.000
      ├── Some((2, 1)): 17/31 ≈ 0.548
      ├── Some((2, 2)): 15/29 ≈ 0.517
      ├── Some((2, 3)): 16/30 ≈ 0.533
      ├── Some((2, 4)): 16/30 ≈ 0.533
      ├── Some((2, 5)): 22/37 ≈ 0.595
      ├── Some((2, 6)): 19/34 ≈ 0.559
      ├── Some((2, 7)): 32/48 ≈ 0.667
      └── Some((2, 8)): 18/32 ≈ 0.562
    ├── Some((8, 3)): 126/238 ≈ 0.529
      ├── Some((3, 0)): 21/34 ≈ 0.618
      ├── Some((3, 1)): 8/20 ≈ 0.400
      ├── Some((3, 2)): 12/24 ≈ 0.500
      ├── Some((3, 3)): 15/28 ≈ 0.536
      ├── Some((3, 4)): 19/32 ≈ 0.594
      ├── Some((3, 5)): 9/21 ≈ 0.429
      ├── Some((3, 6)): 7/18 ≈ 0.389
      ├── Some((3, 7)): 15/28 ≈ 0.536
      └── Some((3, 8)): 19/32 ≈ 0.594
    ├── Some((8, 4)): 106/208 ≈ 0.510
      ├── Some((4, 0)): 13/24 ≈ 0.542
      ├── Some((4, 1)): 8/19 ≈ 0.421
      ├── Some((4, 2)): 6/16 ≈ 0.375
      ├── Some((4, 3)): 7/18 ≈ 0.389
      ├── Some((4, 4)): 17/29 ≈ 0.586
      ├── Some((4, 5)): 25/37 ≈ 0.676
      ├── Some((4, 6)): 10/21 ≈ 0.476
      ├── Some((4, 7)): 7/18 ≈ 0.389
      └── Some((4, 8)): 13/25 ≈ 0.520
    ├── Some((8, 5)): 58/133 ≈ 0.436
      ├── Some((5, 0)): 15/24 ≈ 0.625
      ├── Some((5, 1)): 2/10 ≈ 0.200
      ├── Some((5, 2)): 10/19 ≈ 0.526
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 4/12 ≈ 0.333
      ├── Some((5, 5)): 3/11 ≈ 0.273
      ├── Some((5, 6)): 9/18 ≈ 0.500
      ├── Some((5, 7)): 3/11 ≈ 0.273
      └── Some((5, 8)): 4/12 ≈ 0.333
    ├── Some((8, 6)): 211/363 ≈ 0.581
      ├── Some((6, 0)): 26/45 ≈ 0.578
      ├── Some((6, 1)): 35/56 ≈ 0.625
      ├── Some((6, 2)): 44/66 ≈ 0.667
      ├── Some((6, 3)): 38/59 ≈ 0.644
      ├── Some((6, 4)): 21/39 ≈ 0.538
      ├── Some((6, 5)): 9/24 ≈ 0.375
      ├── Some((6, 6)): 17/35 ≈ 0.486
      └── Some((6, 8)): 20/38 ≈ 0.526
    ├── Some((8, 7)): 113/218 ≈ 0.518
      ├── Some((7, 0)): 9/21 ≈ 0.429
      ├── Some((7, 1)): 14/27 ≈ 0.519
      ├── Some((7, 2)): 11/24 ≈ 0.458
      ├── Some((7, 3)): 8/20 ≈ 0.400
      ├── Some((7, 4)): 11/24 ≈ 0.458
      ├── Some((7, 5)): 22/36 ≈ 0.611
      ├── Some((7, 6)): 27/41 ≈ 0.659
      └── Some((7, 7)): 11/24 ≈ 0.458
    └── Some((8, 8)): 119/227 ≈ 0.524
      ├── Some((8, 0)): 12/25 ≈ 0.480
      ├── Some((8, 1)): 15/28 ≈ 0.536
      ├── Some((8, 2)): 15/29 ≈ 0.517
      ├── Some((8, 3)): 19/33 ≈ 0.576
      ├── Some((8, 4)): 7/19 ≈ 0.368
      ├── Some((8, 5)): 19/33 ≈ 0.576
      ├── Some((8, 6)): 14/27 ≈ 0.519
      └── Some((8, 7)): 18/32 ≈ 0.562
├── Some((6, 8)): 6970/13360 ≈ 0.522
  ├── Some((8, 0)): 891/1686 ≈ 0.528
    ├── Some((0, 0)): 90/175 ≈ 0.514
      ├── Some((0, 1)): 14/25 ≈ 0.560
      ├── Some((0, 2)): 12/23 ≈ 0.522
      ├── Some((0, 3)): 4/13 ≈ 0.308
      ├── Some((0, 4)): 8/18 ≈ 0.444
      ├── Some((0, 5)): 11/22 ≈ 0.500
      ├── Some((0, 6)): 21/33 ≈ 0.636
      ├── Some((0, 7)): 10/21 ≈ 0.476
      └── Some((0, 8)): 9/19 ≈ 0.474
    ├── Some((0, 1)): 117/214 ≈ 0.547
      ├── Some((1, 0)): 5/15 ≈ 0.333
      ├── Some((1, 1)): 28/39 ≈ 0.718
      ├── Some((1, 2)): 12/23 ≈ 0.522
      ├── Some((1, 3)): 11/22 ≈ 0.500
      ├── Some((1, 4)): 14/25 ≈ 0.560
      ├── Some((1, 5)): 17/28 ≈ 0.607
      ├── Some((1, 6)): 11/22 ≈ 0.500
      ├── Some((1, 7)): 13/24 ≈ 0.542
      └── Some((1, 8)): 5/15 ≈ 0.333
    ├── Some((0, 2)): 114/210 ≈ 0.543
      ├── Some((2, 0)): 5/15 ≈ 0.333
      ├── Some((2, 1)): 13/24 ≈ 0.542
      ├── Some((2, 2)): 21/32 ≈ 0.656
      ├── Some((2, 3)): 15/26 ≈ 0.577
      ├── Some((2, 4)): 4/13 ≈ 0.308
      ├── Some((2, 5)): 27/39 ≈ 0.692
      ├── Some((2, 6)): 5/15 ≈ 0.333
      ├── Some((2, 7)): 13/24 ≈ 0.542
      └── Some((2, 8)): 10/21 ≈ 0.476
    ├── Some((0, 3)): 148/259 ≈ 0.571
      ├── Some((3, 0)): 12/24 ≈ 0.500
      ├── Some((3, 1)): 27/40 ≈ 0.675
      ├── Some((3, 2)): 1/10 ≈ 0.100
      ├── Some((3, 3)): 15/27 ≈ 0.556
      ├── Some((3, 4)): 16/29 ≈ 0.552
      ├── Some((3, 5)): 27/40 ≈ 0.675
      ├── Some((3, 6)): 12/24 ≈ 0.500
      ├── Some((3, 7)): 19/32 ≈ 0.594
      └── Some((3, 8)): 19/32 ≈ 0.594
    ├── Some((0, 4)): 78/157 ≈ 0.497
      ├── Some((4, 0)): 8/17 ≈ 0.471
      ├── Some((4, 1)): 15/24 ≈ 0.625
      ├── Some((4, 2)): 1/8 ≈ 0.125
      ├── Some((4, 3)): 4/12 ≈ 0.333
      ├── Some((4, 4)): 13/22 ≈ 0.591
      ├── Some((4, 5)): 5/14 ≈ 0.357
      ├── Some((4, 6)): 14/23 ≈ 0.609
      ├── Some((4, 7)): 11/20 ≈ 0.550
      └── Some((4, 8)): 7/16 ≈ 0.438
    ├── Some((0, 5)): 64/135 ≈ 0.474
      ├── Some((5, 0)): 11/19 ≈ 0.579
      ├── Some((5, 1)): 9/17 ≈ 0.529
      ├── Some((5, 2)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 3/10 ≈ 0.300
      ├── Some((5, 4)): 4/12 ≈ 0.333
      ├── Some((5, 5)): 3/10 ≈ 0.300
      ├── Some((5, 6)): 8/16 ≈ 0.500
      ├── Some((5, 7)): 7/15 ≈ 0.467
      └── Some((5, 8)): 9/17 ≈ 0.529
    ├── Some((0, 6)): 111/205 ≈ 0.541
      ├── Some((6, 0)): 13/25 ≈ 0.520
      ├── Some((6, 1)): 26/39 ≈ 0.667
      ├── Some((6, 2)): 4/14 ≈ 0.286
      ├── Some((6, 3)): 13/25 ≈ 0.520
      ├── Some((6, 4)): 18/30 ≈ 0.600
      ├── Some((6, 5)): 19/32 ≈ 0.594
      ├── Some((6, 6)): 8/19 ≈ 0.421
      └── Some((6, 7)): 9/20 ≈ 0.450
    ├── Some((0, 7)): 66/138 ≈ 0.478
      ├── Some((7, 0)): 13/21 ≈ 0.619
      ├── Some((7, 1)): 9/17 ≈ 0.529
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 4/12 ≈ 0.333
      ├── Some((7, 4)): 7/15 ≈ 0.467
      ├── Some((7, 5)): 9/17 ≈ 0.529
      ├── Some((7, 6)): 8/16 ≈ 0.500
      ├── Some((7, 7)): 6/14 ≈ 0.429
      └── Some((7, 8)): 7/15 ≈ 0.467
    └── Some((0, 8)): 102/192 ≈ 0.531
      ├── Some((8, 1)): 2/11 ≈ 0.182
      ├── Some((8, 2)): 20/32 ≈ 0.625
      ├── Some((8, 3)): 12/23 ≈ 0.522
      ├── Some((8, 4)): 27/40 ≈ 0.675
      ├── Some((8, 5)): 4/14 ≈ 0.286
      ├── Some((8, 6)): 7/18 ≈ 0.389
      ├── Some((8, 7)): 9/20 ≈ 0.450
      └── Some((8, 8)): 21/33 ≈ 0.636
  ├── Some((8, 1)): 1043/1945 ≈ 0.536
    ├── Some((1, 0)): 180/310 ≈ 0.581
      ├── Some((0, 0)): 18/32 ≈ 0.562
      ├── Some((0, 1)): 24/39 ≈ 0.615
      ├── Some((0, 2)): 39/55 ≈ 0.709
      ├── Some((0, 3)): 24/39 ≈ 0.615
      ├── Some((0, 4)): 8/21 ≈ 0.381
      ├── Some((0, 5)): 16/30 ≈ 0.533
      ├── Some((0, 6)): 12/25 ≈ 0.480
      ├── Some((0, 7)): 18/32 ≈ 0.562
      └── Some((0, 8)): 21/36 ≈ 0.583
    ├── Some((1, 1)): 113/213 ≈ 0.531
      ├── Some((1, 0)): 15/28 ≈ 0.536
      ├── Some((1, 2)): 24/38 ≈ 0.632
      ├── Some((1, 3)): 8/20 ≈ 0.400
      ├── Some((1, 4)): 20/33 ≈ 0.606
      ├── Some((1, 5)): 13/25 ≈ 0.520
      ├── Some((1, 6)): 12/24 ≈ 0.500
      ├── Some((1, 7)): 14/27 ≈ 0.519
      └── Some((1, 8)): 6/17 ≈ 0.353
    ├── Some((1, 2)): 110/208 ≈ 0.529
      ├── Some((2, 0)): 20/32 ≈ 0.625
      ├── Some((2, 1)): 10/21 ≈ 0.476
      ├── Some((2, 2)): 10/21 ≈ 0.476
      ├── Some((2, 3)): 12/23 ≈ 0.522
      ├── Some((2, 4)): 13/24 ≈ 0.542
      ├── Some((2, 5)): 10/21 ≈ 0.476
      ├── Some((2, 6)): 1/9 ≈ 0.111
      ├── Some((2, 7)): 23/35 ≈ 0.657
      └── Some((2, 8)): 10/21 ≈ 0.476
    ├── Some((1, 3)): 75/155 ≈ 0.484
      ├── Some((3, 0)): 2/10 ≈ 0.200
      ├── Some((3, 1)): 4/12 ≈ 0.333
      ├── Some((3, 2)): 8/17 ≈ 0.471
      ├── Some((3, 3)): 2/10 ≈ 0.200
      ├── Some((3, 4)): 8/17 ≈ 0.471
      ├── Some((3, 5)): 21/31 ≈ 0.677
      ├── Some((3, 6)): 11/20 ≈ 0.550
      ├── Some((3, 7)): 13/23 ≈ 0.565
      └── Some((3, 8)): 5/14 ≈ 0.357
    ├── Some((1, 4)): 118/220 ≈ 0.536
      ├── Some((4, 0)): 11/22 ≈ 0.500
      ├── Some((4, 1)): 13/24 ≈ 0.542
      ├── Some((4, 2)): 13/24 ≈ 0.542
      ├── Some((4, 3)): 14/26 ≈ 0.538
      ├── Some((4, 4)): 8/19 ≈ 0.421
      ├── Some((4, 5)): 17/29 ≈ 0.586
      ├── Some((4, 6)): 8/19 ≈ 0.421
      ├── Some((4, 7)): 7/17 ≈ 0.412
      └── Some((4, 8)): 27/39 ≈ 0.692
    ├── Some((1, 5)): 44/106 ≈ 0.415
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 1)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 4/11 ≈ 0.364
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 15/22 ≈ 0.682
      ├── Some((5, 5)): 2/8 ≈ 0.250
      ├── Some((5, 6)): 2/9 ≈ 0.222
      ├── Some((5, 7)): 0/6 ≈ 0.000
      └── Some((5, 8)): 5/12 ≈ 0.417
    ├── Some((1, 6)): 156/276 ≈ 0.565
      ├── Some((6, 0)): 12/26 ≈ 0.462
      ├── Some((6, 1)): 11/25 ≈ 0.440
      ├── Some((6, 2)): 22/37 ≈ 0.595
      ├── Some((6, 3)): 22/37 ≈ 0.595
      ├── Some((6, 4)): 15/29 ≈ 0.517
      ├── Some((6, 5)): 27/43 ≈ 0.628
      ├── Some((6, 6)): 31/47 ≈ 0.660
      └── Some((6, 7)): 16/31 ≈ 0.516
    ├── Some((1, 7)): 133/242 ≈ 0.550
      ├── Some((7, 0)): 11/23 ≈ 0.478
      ├── Some((7, 1)): 21/34 ≈ 0.618
      ├── Some((7, 2)): 19/32 ≈ 0.594
      ├── Some((7, 3)): 14/26 ≈ 0.538
      ├── Some((7, 4)): 8/19 ≈ 0.421
      ├── Some((7, 5)): 17/29 ≈ 0.586
      ├── Some((7, 6)): 13/25 ≈ 0.520
      ├── Some((7, 7)): 12/24 ≈ 0.500
      └── Some((7, 8)): 17/29 ≈ 0.586
    └── Some((1, 8)): 114/214 ≈ 0.533
      ├── Some((8, 0)): 12/24 ≈ 0.500
      ├── Some((8, 2)): 26/40 ≈ 0.650
      ├── Some((8, 3)): 9/21 ≈ 0.429
      ├── Some((8, 4)): 7/18 ≈ 0.389
      ├── Some((8, 5)): 15/28 ≈ 0.536
      ├── Some((8, 6)): 22/35 ≈ 0.629
      ├── Some((8, 7)): 17/30 ≈ 0.567
      └── Some((8, 8)): 6/17 ≈ 0.353
  ├── Some((8, 2)): 687/1336 ≈ 0.514
    ├── Some((2, 0)): 98/180 ≈ 0.544
      ├── Some((0, 0)): 11/20 ≈ 0.550
      ├── Some((0, 1)): 10/19 ≈ 0.526
      ├── Some((0, 2)): 10/19 ≈ 0.526
      ├── Some((0, 3)): 9/18 ≈ 0.500
      ├── Some((0, 4)): 18/27 ≈ 0.667
      ├── Some((0, 5)): 11/20 ≈ 0.550
      ├── Some((0, 6)): 8/17 ≈ 0.471
      ├── Some((0, 7)): 9/18 ≈ 0.500
      └── Some((0, 8)): 12/21 ≈ 0.571
    ├── Some((2, 1)): 79/153 ≈ 0.516
      ├── Some((1, 0)): 5/13 ≈ 0.385
      ├── Some((1, 1)): 9/17 ≈ 0.529
      ├── Some((1, 2)): 8/16 ≈ 0.500
      ├── Some((1, 3)): 14/22 ≈ 0.636
      ├── Some((1, 4)): 8/16 ≈ 0.500
      ├── Some((1, 5)): 8/16 ≈ 0.500
      ├── Some((1, 6)): 6/14 ≈ 0.429
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 15/24 ≈ 0.625
    ├── Some((2, 2)): 65/132 ≈ 0.492
      ├── Some((2, 0)): 11/20 ≈ 0.550
      ├── Some((2, 1)): 1/8 ≈ 0.125
      ├── Some((2, 3)): 6/14 ≈ 0.429
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 3/11 ≈ 0.273
      ├── Some((2, 6)): 13/22 ≈ 0.591
      ├── Some((2, 7)): 5/13 ≈ 0.385
      └── Some((2, 8)): 16/25 ≈ 0.640
    ├── Some((2, 3)): 85/161 ≈ 0.528
      ├── Some((3, 0)): 12/21 ≈ 0.571
      ├── Some((3, 1)): 8/16 ≈ 0.500
      ├── Some((3, 2)): 16/25 ≈ 0.640
      ├── Some((3, 3)): 13/22 ≈ 0.591
      ├── Some((3, 4)): 6/14 ≈ 0.429
      ├── Some((3, 5)): 6/14 ≈ 0.429
      ├── Some((3, 6)): 8/16 ≈ 0.500
      ├── Some((3, 7)): 9/18 ≈ 0.500
      └── Some((3, 8)): 6/14 ≈ 0.429
    ├── Some((2, 4)): 56/118 ≈ 0.475
      ├── Some((4, 0)): 10/17 ≈ 0.588
      ├── Some((4, 1)): 14/21 ≈ 0.667
      ├── Some((4, 2)): 2/8 ≈ 0.250
      ├── Some((4, 3)): 2/9 ≈ 0.222
      ├── Some((4, 4)): 1/7 ≈ 0.143
      ├── Some((4, 5)): 10/17 ≈ 0.588
      ├── Some((4, 6)): 2/9 ≈ 0.222
      ├── Some((4, 7)): 8/15 ≈ 0.533
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((2, 5)): 101/185 ≈ 0.546
      ├── Some((5, 0)): 8/17 ≈ 0.471
      ├── Some((5, 1)): 4/13 ≈ 0.308
      ├── Some((5, 2)): 7/16 ≈ 0.438
      ├── Some((5, 3)): 14/24 ≈ 0.583
      ├── Some((5, 4)): 11/20 ≈ 0.550
      ├── Some((5, 5)): 12/21 ≈ 0.571
      ├── Some((5, 6)): 13/22 ≈ 0.591
      ├── Some((5, 7)): 10/19 ≈ 0.526
      └── Some((5, 8)): 22/32 ≈ 0.688
    ├── Some((2, 6)): 64/131 ≈ 0.489
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 13/22 ≈ 0.591
      ├── Some((6, 2)): 7/15 ≈ 0.467
      ├── Some((6, 3)): 13/22 ≈ 0.591
      ├── Some((6, 4)): 6/14 ≈ 0.429
      ├── Some((6, 5)): 2/10 ≈ 0.200
      ├── Some((6, 6)): 7/15 ≈ 0.467
      └── Some((6, 7)): 8/17 ≈ 0.471
    ├── Some((2, 7)): 47/105 ≈ 0.448
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 3/9 ≈ 0.333
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 5/12 ≈ 0.417
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 2/8 ≈ 0.250
      ├── Some((7, 6)): 12/18 ≈ 0.667
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((2, 8)): 91/170 ≈ 0.535
      ├── Some((8, 0)): 17/28 ≈ 0.607
      ├── Some((8, 1)): 14/24 ≈ 0.583
      ├── Some((8, 3)): 11/21 ≈ 0.524
      ├── Some((8, 4)): 13/23 ≈ 0.565
      ├── Some((8, 5)): 6/15 ≈ 0.400
      ├── Some((8, 6)): 9/19 ≈ 0.474
      ├── Some((8, 7)): 6/15 ≈ 0.400
      └── Some((8, 8)): 14/24 ≈ 0.583
  ├── Some((8, 3)): 1106/2052 ≈ 0.539
    ├── Some((3, 0)): 136/248 ≈ 0.548
      ├── Some((0, 0)): 20/33 ≈ 0.606
      ├── Some((0, 1)): 6/17 ≈ 0.353
      ├── Some((0, 2)): 14/27 ≈ 0.519
      ├── Some((0, 3)): 12/24 ≈ 0.500
      ├── Some((0, 4)): 11/23 ≈ 0.478
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 13/25 ≈ 0.520
      ├── Some((0, 7)): 20/33 ≈ 0.606
      └── Some((0, 8)): 27/41 ≈ 0.659
    ├── Some((3, 1)): 122/228 ≈ 0.535
      ├── Some((1, 0)): 15/27 ≈ 0.556
      ├── Some((1, 1)): 12/24 ≈ 0.500
      ├── Some((1, 2)): 15/27 ≈ 0.556
      ├── Some((1, 3)): 16/28 ≈ 0.571
      ├── Some((1, 4)): 20/32 ≈ 0.625
      ├── Some((1, 5)): 21/34 ≈ 0.618
      ├── Some((1, 6)): 5/15 ≈ 0.333
      ├── Some((1, 7)): 9/20 ≈ 0.450
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((3, 2)): 140/254 ≈ 0.551
      ├── Some((2, 0)): 14/26 ≈ 0.538
      ├── Some((2, 1)): 24/37 ≈ 0.649
      ├── Some((2, 2)): 12/24 ≈ 0.500
      ├── Some((2, 3)): 11/23 ≈ 0.478
      ├── Some((2, 4)): 15/28 ≈ 0.536
      ├── Some((2, 5)): 9/21 ≈ 0.429
      ├── Some((2, 6)): 16/29 ≈ 0.552
      ├── Some((2, 7)): 22/35 ≈ 0.629
      └── Some((2, 8)): 17/30 ≈ 0.567
    ├── Some((3, 3)): 196/335 ≈ 0.585
      ├── Some((3, 0)): 19/36 ≈ 0.528
      ├── Some((3, 1)): 27/45 ≈ 0.600
      ├── Some((3, 2)): 25/42 ≈ 0.595
      ├── Some((3, 4)): 35/54 ≈ 0.648
      ├── Some((3, 5)): 26/44 ≈ 0.591
      ├── Some((3, 6)): 17/33 ≈ 0.515
      ├── Some((3, 7)): 18/34 ≈ 0.529
      └── Some((3, 8)): 28/46 ≈ 0.609
    ├── Some((3, 4)): 84/170 ≈ 0.494
      ├── Some((4, 0)): 11/21 ≈ 0.524
      ├── Some((4, 1)): 12/22 ≈ 0.545
      ├── Some((4, 2)): 7/16 ≈ 0.438
      ├── Some((4, 3)): 7/16 ≈ 0.438
      ├── Some((4, 4)): 8/17 ≈ 0.471
      ├── Some((4, 5)): 15/25 ≈ 0.600
      ├── Some((4, 6)): 5/14 ≈ 0.357
      ├── Some((4, 7)): 9/18 ≈ 0.500
      └── Some((4, 8)): 10/20 ≈ 0.500
    ├── Some((3, 5)): 105/202 ≈ 0.520
      ├── Some((5, 0)): 19/31 ≈ 0.613
      ├── Some((5, 1)): 13/24 ≈ 0.542
      ├── Some((5, 2)): 12/23 ≈ 0.522
      ├── Some((5, 3)): 24/36 ≈ 0.667
      ├── Some((5, 4)): 10/21 ≈ 0.476
      ├── Some((5, 5)): 14/26 ≈ 0.538
      ├── Some((5, 6)): 6/16 ≈ 0.375
      ├── Some((5, 7)): 6/16 ≈ 0.375
      └── Some((5, 8)): 0/8 ≈ 0.000
    ├── Some((3, 6)): 116/219 ≈ 0.530
      ├── Some((6, 0)): 16/29 ≈ 0.552
      ├── Some((6, 1)): 21/35 ≈ 0.600
      ├── Some((6, 2)): 14/27 ≈ 0.519
      ├── Some((6, 3)): 16/29 ≈ 0.552
      ├── Some((6, 4)): 12/25 ≈ 0.480
      ├── Some((6, 5)): 6/17 ≈ 0.353
      ├── Some((6, 6)): 12/25 ≈ 0.480
      └── Some((6, 7)): 18/31 ≈ 0.581
    ├── Some((3, 7)): 50/117 ≈ 0.427
      ├── Some((7, 0)): 5/12 ≈ 0.417
      ├── Some((7, 1)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 5/13 ≈ 0.385
      ├── Some((7, 3)): 7/15 ≈ 0.467
      ├── Some((7, 4)): 7/15 ≈ 0.467
      ├── Some((7, 5)): 0/6 ≈ 0.000
      ├── Some((7, 6)): 8/16 ≈ 0.500
      ├── Some((7, 7)): 1/8 ≈ 0.125
      └── Some((7, 8)): 11/19 ≈ 0.579
    └── Some((3, 8)): 156/278 ≈ 0.561
      ├── Some((8, 0)): 27/43 ≈ 0.628
      ├── Some((8, 1)): 24/40 ≈ 0.600
      ├── Some((8, 2)): 18/33 ≈ 0.545
      ├── Some((8, 4)): 22/38 ≈ 0.579
      ├── Some((8, 5)): 12/26 ≈ 0.462
      ├── Some((8, 6)): 21/36 ≈ 0.583
      ├── Some((8, 7)): 25/41 ≈ 0.610
      └── Some((8, 8)): 7/20 ≈ 0.350
  ├── Some((8, 4)): 608/1199 ≈ 0.507
    ├── Some((4, 0)): 97/176 ≈ 0.551
      ├── Some((0, 0)): 12/21 ≈ 0.571
      ├── Some((0, 1)): 5/13 ≈ 0.385
      ├── Some((0, 2)): 17/26 ≈ 0.654
      ├── Some((0, 3)): 3/11 ≈ 0.273
      ├── Some((0, 4)): 8/17 ≈ 0.471
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 12/21 ≈ 0.571
      ├── Some((0, 7)): 29/38 ≈ 0.763
      └── Some((0, 8)): 2/10 ≈ 0.200
    ├── Some((4, 1)): 35/84 ≈ 0.417
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 8/14 ≈ 0.571
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 4/10 ≈ 0.400
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 8/14 ≈ 0.571
    ├── Some((4, 2)): 74/143 ≈ 0.517
      ├── Some((2, 0)): 10/18 ≈ 0.556
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 9/17 ≈ 0.529
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 14/22 ≈ 0.636
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 10/18 ≈ 0.556
      └── Some((2, 8)): 7/15 ≈ 0.467
    ├── Some((4, 3)): 93/171 ≈ 0.544
      ├── Some((3, 0)): 17/26 ≈ 0.654
      ├── Some((3, 1)): 13/22 ≈ 0.591
      ├── Some((3, 2)): 6/14 ≈ 0.429
      ├── Some((3, 3)): 10/19 ≈ 0.526
      ├── Some((3, 4)): 8/16 ≈ 0.500
      ├── Some((3, 5)): 15/24 ≈ 0.625
      ├── Some((3, 6)): 8/17 ≈ 0.471
      ├── Some((3, 7)): 12/21 ≈ 0.571
      └── Some((3, 8)): 3/11 ≈ 0.273
    ├── Some((4, 4)): 60/123 ≈ 0.488
      ├── Some((4, 0)): 3/11 ≈ 0.273
      ├── Some((4, 1)): 4/12 ≈ 0.333
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 18/26 ≈ 0.692
      ├── Some((4, 5)): 4/12 ≈ 0.333
      ├── Some((4, 6)): 15/23 ≈ 0.652
      ├── Some((4, 7)): 6/14 ≈ 0.429
      └── Some((4, 8)): 2/9 ≈ 0.222
    ├── Some((4, 5)): 75/145 ≈ 0.517
      ├── Some((5, 0)): 12/20 ≈ 0.600
      ├── Some((5, 1)): 3/10 ≈ 0.300
      ├── Some((5, 2)): 15/23 ≈ 0.652
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 7/15 ≈ 0.467
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 6/14 ≈ 0.429
      └── Some((5, 8)): 15/23 ≈ 0.652
    ├── Some((4, 6)): 78/149 ≈ 0.523
      ├── Some((6, 0)): 9/18 ≈ 0.500
      ├── Some((6, 1)): 12/21 ≈ 0.571
      ├── Some((6, 2)): 19/28 ≈ 0.679
      ├── Some((6, 3)): 14/23 ≈ 0.609
      ├── Some((6, 4)): 8/17 ≈ 0.471
      ├── Some((6, 5)): 6/14 ≈ 0.429
      ├── Some((6, 6)): 4/12 ≈ 0.333
      └── Some((6, 7)): 6/15 ≈ 0.400
    ├── Some((4, 7)): 48/104 ≈ 0.462
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 9/16 ≈ 0.562
      ├── Some((7, 2)): 6/12 ≈ 0.500
      ├── Some((7, 3)): 6/12 ≈ 0.500
      ├── Some((7, 4)): 5/11 ≈ 0.455
      ├── Some((7, 5)): 6/12 ≈ 0.500
      ├── Some((7, 6)): 3/9 ≈ 0.333
      ├── Some((7, 7)): 5/11 ≈ 0.455
      └── Some((7, 8)): 5/11 ≈ 0.455
    └── Some((4, 8)): 47/103 ≈ 0.456
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 12/20 ≈ 0.600
      ├── Some((8, 3)): 1/7 ≈ 0.143
      ├── Some((8, 5)): 1/7 ≈ 0.143
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 10/17 ≈ 0.588
      └── Some((8, 8)): 4/11 ≈ 0.364
  ├── Some((8, 5)): 704/1365 ≈ 0.516
    ├── Some((5, 0)): 102/187 ≈ 0.545
      ├── Some((0, 0)): 9/18 ≈ 0.500
      ├── Some((0, 1)): 7/16 ≈ 0.438
      ├── Some((0, 2)): 11/20 ≈ 0.550
      ├── Some((0, 3)): 10/19 ≈ 0.526
      ├── Some((0, 4)): 17/27 ≈ 0.630
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 19/29 ≈ 0.655
      ├── Some((0, 7)): 13/23 ≈ 0.565
      └── Some((0, 8)): 7/16 ≈ 0.438
    ├── Some((5, 1)): 138/239 ≈ 0.577
      ├── Some((1, 0)): 9/20 ≈ 0.450
      ├── Some((1, 1)): 11/22 ≈ 0.500
      ├── Some((1, 2)): 16/28 ≈ 0.571
      ├── Some((1, 3)): 11/22 ≈ 0.500
      ├── Some((1, 4)): 34/46 ≈ 0.739
      ├── Some((1, 5)): 4/14 ≈ 0.286
      ├── Some((1, 6)): 28/40 ≈ 0.700
      ├── Some((1, 7)): 14/25 ≈ 0.560
      └── Some((1, 8)): 10/21 ≈ 0.476
    ├── Some((5, 2)): 54/116 ≈ 0.466
      ├── Some((2, 0)): 3/10 ≈ 0.300
      ├── Some((2, 1)): 8/15 ≈ 0.533
      ├── Some((2, 2)): 3/10 ≈ 0.300
      ├── Some((2, 3)): 7/14 ≈ 0.500
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 2/8 ≈ 0.250
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 9/16 ≈ 0.562
      └── Some((2, 8)): 11/18 ≈ 0.611
    ├── Some((5, 3)): 42/98 ≈ 0.429
      ├── Some((3, 0)): 10/16 ≈ 0.625
      ├── Some((3, 1)): 2/8 ≈ 0.250
      ├── Some((3, 2)): 5/11 ≈ 0.455
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 2/8 ≈ 0.250
      ├── Some((3, 5)): 2/8 ≈ 0.250
      ├── Some((3, 6)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((5, 4)): 58/122 ≈ 0.475
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 8/16 ≈ 0.500
      ├── Some((4, 2)): 2/9 ≈ 0.222
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 4)): 13/21 ≈ 0.619
      ├── Some((4, 5)): 5/12 ≈ 0.417
      ├── Some((4, 6)): 7/14 ≈ 0.500
      ├── Some((4, 7)): 7/14 ≈ 0.500
      └── Some((4, 8)): 0/6 ≈ 0.000
    ├── Some((5, 5)): 111/200 ≈ 0.555
      ├── Some((5, 0)): 13/24 ≈ 0.542
      ├── Some((5, 1)): 5/15 ≈ 0.333
      ├── Some((5, 2)): 14/26 ≈ 0.538
      ├── Some((5, 3)): 5/15 ≈ 0.333
      ├── Some((5, 4)): 34/46 ≈ 0.739
      ├── Some((5, 6)): 22/34 ≈ 0.647
      ├── Some((5, 7)): 9/20 ≈ 0.450
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((5, 6)): 101/186 ≈ 0.543
      ├── Some((6, 0)): 5/15 ≈ 0.333
      ├── Some((6, 1)): 13/24 ≈ 0.542
      ├── Some((6, 2)): 17/28 ≈ 0.607
      ├── Some((6, 3)): 4/13 ≈ 0.308
      ├── Some((6, 4)): 6/16 ≈ 0.375
      ├── Some((6, 5)): 14/25 ≈ 0.560
      ├── Some((6, 6)): 9/20 ≈ 0.450
      └── Some((6, 7)): 32/44 ≈ 0.727
    ├── Some((5, 7)): 47/106 ≈ 0.443
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 13/20 ≈ 0.650
      ├── Some((7, 2)): 4/10 ≈ 0.400
      ├── Some((7, 3)): 7/14 ≈ 0.500
      ├── Some((7, 4)): 5/12 ≈ 0.417
      ├── Some((7, 5)): 1/7 ≈ 0.143
      ├── Some((7, 6)): 6/13 ≈ 0.462
      ├── Some((7, 7)): 0/6 ≈ 0.000
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((5, 8)): 50/110 ≈ 0.455
      ├── Some((8, 0)): 10/18 ≈ 0.556
      ├── Some((8, 1)): 3/10 ≈ 0.300
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 15/23 ≈ 0.652
      ├── Some((8, 4)): 6/13 ≈ 0.462
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 3/10 ≈ 0.300
      └── Some((8, 8)): 1/8 ≈ 0.125
  ├── Some((8, 6)): 856/1627 ≈ 0.526
    ├── Some((6, 0)): 109/207 ≈ 0.527
      ├── Some((0, 0)): 2/11 ≈ 0.182
      ├── Some((0, 1)): 3/12 ≈ 0.250
      ├── Some((0, 2)): 12/23 ≈ 0.522
      ├── Some((0, 3)): 14/25 ≈ 0.560
      ├── Some((0, 4)): 18/30 ≈ 0.600
      ├── Some((0, 5)): 12/23 ≈ 0.522
      ├── Some((0, 6)): 17/28 ≈ 0.607
      ├── Some((0, 7)): 9/20 ≈ 0.450
      └── Some((0, 8)): 22/34 ≈ 0.647
    ├── Some((6, 1)): 46/110 ≈ 0.418
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 7/14 ≈ 0.500
      ├── Some((1, 2)): 3/10 ≈ 0.300
      ├── Some((1, 3)): 0/6 ≈ 0.000
      ├── Some((1, 4)): 8/15 ≈ 0.533
      ├── Some((1, 5)): 10/18 ≈ 0.556
      ├── Some((1, 6)): 3/10 ≈ 0.300
      ├── Some((1, 7)): 3/10 ≈ 0.300
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((6, 2)): 57/128 ≈ 0.445
      ├── Some((2, 0)): 6/14 ≈ 0.429
      ├── Some((2, 1)): 5/13 ≈ 0.385
      ├── Some((2, 2)): 11/19 ≈ 0.579
      ├── Some((2, 3)): 4/12 ≈ 0.333
      ├── Some((2, 4)): 9/17 ≈ 0.529
      ├── Some((2, 5)): 8/16 ≈ 0.500
      ├── Some((2, 6)): 4/12 ≈ 0.333
      ├── Some((2, 7)): 1/8 ≈ 0.125
      └── Some((2, 8)): 8/16 ≈ 0.500
    ├── Some((6, 3)): 128/236 ≈ 0.542
      ├── Some((3, 0)): 14/26 ≈ 0.538
      ├── Some((3, 1)): 4/14 ≈ 0.286
      ├── Some((3, 2)): 13/25 ≈ 0.520
      ├── Some((3, 3)): 18/30 ≈ 0.600
      ├── Some((3, 4)): 21/34 ≈ 0.618
      ├── Some((3, 5)): 13/25 ≈ 0.520
      ├── Some((3, 6)): 19/32 ≈ 0.594
      ├── Some((3, 7)): 12/24 ≈ 0.500
      └── Some((3, 8)): 13/25 ≈ 0.520
    ├── Some((6, 4)): 146/262 ≈ 0.557
      ├── Some((4, 0)): 34/48 ≈ 0.708
      ├── Some((4, 1)): 8/20 ≈ 0.400
      ├── Some((4, 2)): 15/28 ≈ 0.536
      ├── Some((4, 3)): 14/27 ≈ 0.519
      ├── Some((4, 4)): 10/22 ≈ 0.455
      ├── Some((4, 5)): 24/38 ≈ 0.632
      ├── Some((4, 6)): 17/30 ≈ 0.567
      ├── Some((4, 7)): 16/29 ≈ 0.552
      └── Some((4, 8)): 7/19 ≈ 0.368
    ├── Some((6, 5)): 154/274 ≈ 0.562
      ├── Some((5, 0)): 11/24 ≈ 0.458
      ├── Some((5, 1)): 7/19 ≈ 0.368
      ├── Some((5, 2)): 25/39 ≈ 0.641
      ├── Some((5, 3)): 23/37 ≈ 0.622
      ├── Some((5, 4)): 16/29 ≈ 0.552
      ├── Some((5, 5)): 17/30 ≈ 0.567
      ├── Some((5, 6)): 26/40 ≈ 0.650
      ├── Some((5, 7)): 10/22 ≈ 0.455
      └── Some((5, 8)): 19/33 ≈ 0.576
    ├── Some((6, 6)): 85/171 ≈ 0.497
      ├── Some((6, 0)): 15/28 ≈ 0.536
      ├── Some((6, 1)): 8/20 ≈ 0.400
      ├── Some((6, 2)): 13/25 ≈ 0.520
      ├── Some((6, 3)): 15/28 ≈ 0.536
      ├── Some((6, 4)): 13/25 ≈ 0.520
      ├── Some((6, 5)): 11/23 ≈ 0.478
      └── Some((6, 7)): 9/21 ≈ 0.429
    └── Some((6, 7)): 130/238 ≈ 0.546
      ├── Some((7, 0)): 16/28 ≈ 0.571
      ├── Some((7, 1)): 9/20 ≈ 0.450
      ├── Some((7, 2)): 14/26 ≈ 0.538
      ├── Some((7, 3)): 12/24 ≈ 0.500
      ├── Some((7, 4)): 24/37 ≈ 0.649
      ├── Some((7, 5)): 12/24 ≈ 0.500
      ├── Some((7, 6)): 18/31 ≈ 0.581
      ├── Some((7, 7)): 8/19 ≈ 0.421
      └── Some((7, 8)): 16/28 ≈ 0.571
  ├── Some((8, 7)): 566/1125 ≈ 0.503
    ├── Some((7, 0)): 31/77 ≈ 0.403
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 4/9 ≈ 0.444
      ├── Some((0, 3)): 6/11 ≈ 0.545
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 0/5 ≈ 0.000
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((7, 1)): 55/114 ≈ 0.482
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 0/6 ≈ 0.000
      ├── Some((1, 2)): 10/17 ≈ 0.588
      ├── Some((1, 3)): 3/9 ≈ 0.333
      ├── Some((1, 4)): 13/20 ≈ 0.650
      ├── Some((1, 5)): 4/11 ≈ 0.364
      ├── Some((1, 6)): 8/15 ≈ 0.533
      ├── Some((1, 7)): 9/16 ≈ 0.562
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((7, 2)): 100/179 ≈ 0.559
      ├── Some((2, 0)): 14/23 ≈ 0.609
      ├── Some((2, 1)): 12/21 ≈ 0.571
      ├── Some((2, 2)): 16/25 ≈ 0.640
      ├── Some((2, 3)): 7/15 ≈ 0.467
      ├── Some((2, 4)): 12/21 ≈ 0.571
      ├── Some((2, 5)): 4/12 ≈ 0.333
      ├── Some((2, 6)): 14/23 ≈ 0.609
      ├── Some((2, 7)): 11/20 ≈ 0.550
      └── Some((2, 8)): 10/18 ≈ 0.556
    ├── Some((7, 3)): 80/150 ≈ 0.533
      ├── Some((3, 0)): 2/9 ≈ 0.222
      ├── Some((3, 1)): 13/21 ≈ 0.619
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 8/16 ≈ 0.500
      ├── Some((3, 4)): 12/20 ≈ 0.600
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 13/21 ≈ 0.619
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 11/19 ≈ 0.579
    ├── Some((7, 4)): 34/82 ≈ 0.415
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 1/6 ≈ 0.167
      ├── Some((4, 4)): 6/11 ≈ 0.545
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((7, 5)): 52/109 ≈ 0.477
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 2/8 ≈ 0.250
      ├── Some((5, 2)): 5/12 ≈ 0.417
      ├── Some((5, 3)): 1/7 ≈ 0.143
      ├── Some((5, 4)): 2/8 ≈ 0.250
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 14/20 ≈ 0.700
      ├── Some((5, 7)): 12/19 ≈ 0.632
      └── Some((5, 8)): 3/9 ≈ 0.333
    ├── Some((7, 6)): 67/132 ≈ 0.508
      ├── Some((6, 0)): 3/11 ≈ 0.273
      ├── Some((6, 1)): 9/17 ≈ 0.529
      ├── Some((6, 2)): 3/11 ≈ 0.273
      ├── Some((6, 3)): 12/20 ≈ 0.600
      ├── Some((6, 4)): 11/19 ≈ 0.579
      ├── Some((6, 5)): 8/16 ≈ 0.500
      ├── Some((6, 6)): 12/20 ≈ 0.600
      └── Some((6, 7)): 9/17 ≈ 0.529
    ├── Some((7, 7)): 77/146 ≈ 0.527
      ├── Some((7, 0)): 11/20 ≈ 0.550
      ├── Some((7, 1)): 6/14 ≈ 0.429
      ├── Some((7, 2)): 7/15 ≈ 0.467
      ├── Some((7, 3)): 9/18 ≈ 0.500
      ├── Some((7, 4)): 14/23 ≈ 0.609
      ├── Some((7, 5)): 7/15 ≈ 0.467
      ├── Some((7, 6)): 8/16 ≈ 0.500
      └── Some((7, 8)): 15/24 ≈ 0.625
    └── Some((7, 8)): 69/135 ≈ 0.511
      ├── Some((8, 0)): 11/19 ≈ 0.579
      ├── Some((8, 1)): 13/22 ≈ 0.591
      ├── Some((8, 2)): 3/11 ≈ 0.273
      ├── Some((8, 3)): 8/16 ≈ 0.500
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 11/20 ≈ 0.550
      ├── Some((8, 6)): 8/16 ≈ 0.500
      └── Some((8, 8)): 9/17 ≈ 0.529
  └── Some((8, 8)): 508/1024 ≈ 0.496
    ├── Some((8, 0)): 104/187 ≈ 0.556
      ├── Some((0, 0)): 16/26 ≈ 0.615
      ├── Some((0, 1)): 18/28 ≈ 0.643
      ├── Some((0, 2)): 16/26 ≈ 0.615
      ├── Some((0, 3)): 10/19 ≈ 0.526
      ├── Some((0, 4)): 5/14 ≈ 0.357
      ├── Some((0, 5)): 12/21 ≈ 0.571
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 10/19 ≈ 0.526
      └── Some((0, 8)): 12/21 ≈ 0.571
    ├── Some((8, 1)): 62/126 ≈ 0.492
      ├── Some((1, 0)): 9/16 ≈ 0.562
      ├── Some((1, 1)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 4/11 ≈ 0.364
      ├── Some((1, 3)): 8/15 ≈ 0.533
      ├── Some((1, 4)): 3/10 ≈ 0.300
      ├── Some((1, 5)): 9/17 ≈ 0.529
      ├── Some((1, 6)): 8/15 ≈ 0.533
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 8/15 ≈ 0.533
    ├── Some((8, 2)): 33/81 ≈ 0.407
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 0/5 ≈ 0.000
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 4/9 ≈ 0.444
      ├── Some((2, 5)): 6/12 ≈ 0.500
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 7/12 ≈ 0.583
      └── Some((2, 8)): 6/12 ≈ 0.500
    ├── Some((8, 3)): 65/131 ≈ 0.496
      ├── Some((3, 0)): 9/17 ≈ 0.529
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 12/20 ≈ 0.600
      ├── Some((3, 3)): 3/10 ≈ 0.300
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 5/12 ≈ 0.417
      ├── Some((3, 7)): 10/18 ≈ 0.556
      └── Some((3, 8)): 8/15 ≈ 0.533
    ├── Some((8, 4)): 51/109 ≈ 0.468
      ├── Some((4, 0)): 1/7 ≈ 0.143
      ├── Some((4, 1)): 1/7 ≈ 0.143
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 10/16 ≈ 0.625
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 11/17 ≈ 0.647
      ├── Some((4, 7)): 3/9 ≈ 0.333
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((8, 5)): 65/131 ≈ 0.496
      ├── Some((5, 0)): 8/16 ≈ 0.500
      ├── Some((5, 1)): 14/22 ≈ 0.636
      ├── Some((5, 2)): 2/9 ≈ 0.222
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 5/12 ≈ 0.417
      ├── Some((5, 5)): 11/19 ≈ 0.579
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 7/14 ≈ 0.500
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((8, 6)): 61/125 ≈ 0.488
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 8/16 ≈ 0.500
      ├── Some((6, 2)): 12/20 ≈ 0.600
      ├── Some((6, 3)): 11/19 ≈ 0.579
      ├── Some((6, 4)): 7/15 ≈ 0.467
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 8/16 ≈ 0.500
      └── Some((6, 7)): 4/12 ≈ 0.333
    └── Some((8, 7)): 67/133 ≈ 0.504
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 6/13 ≈ 0.462
      ├── Some((7, 3)): 7/14 ≈ 0.500
      ├── Some((7, 4)): 2/9 ≈ 0.222
      ├── Some((7, 5)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 17/24 ≈ 0.708
      ├── Some((7, 7)): 7/14 ≈ 0.500
      └── Some((7, 8)): 7/15 ≈ 0.467
├── Some((7, 0)): 5028/9794 ≈ 0.513
  ├── Some((0, 0)): 634/1220 ≈ 0.520
    ├── Some((0, 1)): 65/132 ≈ 0.492
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 2/9 ≈ 0.222
      ├── Some((1, 3)): 10/18 ≈ 0.556
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 10/18 ≈ 0.556
      ├── Some((1, 7)): 6/13 ≈ 0.462
      └── Some((1, 8)): 11/19 ≈ 0.579
    ├── Some((0, 2)): 35/86 ≈ 0.407
      ├── Some((2, 0)): 3/8 ≈ 0.375
      ├── Some((2, 1)): 1/6 ≈ 0.167
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 0/5 ≈ 0.000
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 8/14 ≈ 0.571
      └── Some((2, 8)): 7/13 ≈ 0.538
    ├── Some((0, 3)): 39/92 ≈ 0.424
      ├── Some((3, 0)): 1/6 ≈ 0.167
      ├── Some((3, 1)): 1/7 ≈ 0.143
      ├── Some((3, 2)): 8/14 ≈ 0.571
      ├── Some((3, 3)): 7/13 ≈ 0.538
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 0/5 ≈ 0.000
      ├── Some((3, 6)): 7/13 ≈ 0.538
      ├── Some((3, 7)): 9/15 ≈ 0.600
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((0, 4)): 106/192 ≈ 0.552
      ├── Some((4, 0)): 26/36 ≈ 0.722
      ├── Some((4, 1)): 4/13 ≈ 0.308
      ├── Some((4, 2)): 14/24 ≈ 0.583
      ├── Some((4, 3)): 8/17 ≈ 0.471
      ├── Some((4, 4)): 7/16 ≈ 0.438
      ├── Some((4, 5)): 8/18 ≈ 0.444
      ├── Some((4, 6)): 16/26 ≈ 0.615
      ├── Some((4, 7)): 6/15 ≈ 0.400
      └── Some((4, 8)): 16/26 ≈ 0.615
    ├── Some((0, 5)): 105/191 ≈ 0.550
      ├── Some((5, 0)): 10/19 ≈ 0.526
      ├── Some((5, 1)): 11/21 ≈ 0.524
      ├── Some((5, 2)): 7/16 ≈ 0.438
      ├── Some((5, 3)): 28/38 ≈ 0.737
      ├── Some((5, 4)): 10/20 ≈ 0.500
      ├── Some((5, 5)): 2/10 ≈ 0.200
      ├── Some((5, 6)): 6/15 ≈ 0.400
      ├── Some((5, 7)): 14/24 ≈ 0.583
      └── Some((5, 8)): 17/27 ≈ 0.630
    ├── Some((0, 6)): 99/182 ≈ 0.544
      ├── Some((6, 0)): 5/14 ≈ 0.357
      ├── Some((6, 1)): 20/30 ≈ 0.667
      ├── Some((6, 2)): 8/17 ≈ 0.471
      ├── Some((6, 3)): 9/18 ≈ 0.500
      ├── Some((6, 4)): 3/11 ≈ 0.273
      ├── Some((6, 5)): 10/19 ≈ 0.526
      ├── Some((6, 6)): 11/20 ≈ 0.550
      ├── Some((6, 7)): 18/28 ≈ 0.643
      └── Some((6, 8)): 14/24 ≈ 0.583
    ├── Some((0, 7)): 103/188 ≈ 0.548
      ├── Some((7, 1)): 12/22 ≈ 0.545
      ├── Some((7, 2)): 20/31 ≈ 0.645
      ├── Some((7, 3)): 11/21 ≈ 0.524
      ├── Some((7, 4)): 17/28 ≈ 0.607
      ├── Some((7, 5)): 7/17 ≈ 0.412
      ├── Some((7, 6)): 12/23 ≈ 0.522
      ├── Some((7, 7)): 16/27 ≈ 0.593
      └── Some((7, 8)): 8/18 ≈ 0.444
    └── Some((0, 8)): 81/156 ≈ 0.519
      ├── Some((8, 0)): 9/17 ≈ 0.529
      ├── Some((8, 1)): 3/11 ≈ 0.273
      ├── Some((8, 2)): 14/23 ≈ 0.609
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 4/12 ≈ 0.333
      ├── Some((8, 6)): 12/21 ≈ 0.571
      ├── Some((8, 7)): 17/26 ≈ 0.654
      └── Some((8, 8)): 9/17 ≈ 0.529
  ├── Some((0, 1)): 922/1708 ≈ 0.540
    ├── Some((1, 0)): 120/216 ≈ 0.556
      ├── Some((0, 0)): 15/27 ≈ 0.556
      ├── Some((0, 2)): 16/28 ≈ 0.571
      ├── Some((0, 3)): 10/21 ≈ 0.476
      ├── Some((0, 4)): 26/39 ≈ 0.667
      ├── Some((0, 5)): 14/26 ≈ 0.538
      ├── Some((0, 6)): 12/24 ≈ 0.500
      ├── Some((0, 7)): 10/21 ≈ 0.476
      └── Some((0, 8)): 17/29 ≈ 0.586
    ├── Some((1, 1)): 106/195 ≈ 0.544
      ├── Some((1, 0)): 8/18 ≈ 0.444
      ├── Some((1, 2)): 20/32 ≈ 0.625
      ├── Some((1, 3)): 16/27 ≈ 0.593
      ├── Some((1, 4)): 9/20 ≈ 0.450
      ├── Some((1, 5)): 13/24 ≈ 0.542
      ├── Some((1, 6)): 8/19 ≈ 0.421
      ├── Some((1, 7)): 10/21 ≈ 0.476
      └── Some((1, 8)): 21/33 ≈ 0.636
    ├── Some((1, 2)): 72/145 ≈ 0.497
      ├── Some((2, 0)): 11/19 ≈ 0.579
      ├── Some((2, 1)): 4/12 ≈ 0.333
      ├── Some((2, 2)): 6/14 ≈ 0.429
      ├── Some((2, 3)): 4/12 ≈ 0.333
      ├── Some((2, 4)): 5/13 ≈ 0.385
      ├── Some((2, 5)): 13/22 ≈ 0.591
      ├── Some((2, 6)): 10/18 ≈ 0.556
      ├── Some((2, 7)): 10/18 ≈ 0.556
      └── Some((2, 8)): 8/16 ≈ 0.500
    ├── Some((1, 3)): 86/166 ≈ 0.518
      ├── Some((3, 0)): 6/15 ≈ 0.400
      ├── Some((3, 1)): 8/17 ≈ 0.471
      ├── Some((3, 2)): 8/17 ≈ 0.471
      ├── Some((3, 3)): 15/24 ≈ 0.625
      ├── Some((3, 4)): 12/21 ≈ 0.571
      ├── Some((3, 5)): 10/19 ≈ 0.526
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 13/22 ≈ 0.591
      └── Some((3, 8)): 8/17 ≈ 0.471
    ├── Some((1, 4)): 110/201 ≈ 0.547
      ├── Some((4, 0)): 4/13 ≈ 0.308
      ├── Some((4, 1)): 15/25 ≈ 0.600
      ├── Some((4, 2)): 8/18 ≈ 0.444
      ├── Some((4, 3)): 13/23 ≈ 0.565
      ├── Some((4, 4)): 9/19 ≈ 0.474
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 14/24 ≈ 0.583
      ├── Some((4, 7)): 15/26 ≈ 0.577
      └── Some((4, 8)): 22/33 ≈ 0.667
    ├── Some((1, 5)): 113/205 ≈ 0.551
      ├── Some((5, 0)): 9/19 ≈ 0.474
      ├── Some((5, 1)): 17/28 ≈ 0.607
      ├── Some((5, 2)): 9/19 ≈ 0.474
      ├── Some((5, 3)): 9/19 ≈ 0.474
      ├── Some((5, 4)): 13/23 ≈ 0.565
      ├── Some((5, 5)): 13/23 ≈ 0.565
      ├── Some((5, 6)): 6/16 ≈ 0.375
      ├── Some((5, 7)): 21/32 ≈ 0.656
      └── Some((5, 8)): 15/25 ≈ 0.600
    ├── Some((1, 6)): 99/185 ≈ 0.535
      ├── Some((6, 0)): 7/16 ≈ 0.438
      ├── Some((6, 1)): 16/26 ≈ 0.615
      ├── Some((6, 2)): 12/22 ≈ 0.545
      ├── Some((6, 3)): 9/18 ≈ 0.500
      ├── Some((6, 4)): 5/14 ≈ 0.357
      ├── Some((6, 5)): 8/17 ≈ 0.471
      ├── Some((6, 6)): 18/28 ≈ 0.643
      ├── Some((6, 7)): 12/22 ≈ 0.545
      └── Some((6, 8)): 11/21 ≈ 0.524
    ├── Some((1, 7)): 86/166 ≈ 0.518
      ├── Some((7, 1)): 13/24 ≈ 0.542
      ├── Some((7, 2)): 10/20 ≈ 0.500
      ├── Some((7, 3)): 10/20 ≈ 0.500
      ├── Some((7, 4)): 12/22 ≈ 0.545
      ├── Some((7, 5)): 12/22 ≈ 0.545
      ├── Some((7, 6)): 22/33 ≈ 0.667
      ├── Some((7, 7)): 2/11 ≈ 0.182
      └── Some((7, 8)): 4/13 ≈ 0.308
    └── Some((1, 8)): 129/228 ≈ 0.566
      ├── Some((8, 0)): 14/25 ≈ 0.560
      ├── Some((8, 1)): 1/10 ≈ 0.100
      ├── Some((8, 2)): 30/42 ≈ 0.714
      ├── Some((8, 3)): 11/22 ≈ 0.500
      ├── Some((8, 4)): 4/14 ≈ 0.286
      ├── Some((8, 5)): 14/25 ≈ 0.560
      ├── Some((8, 6)): 18/29 ≈ 0.621
      ├── Some((8, 7)): 15/26 ≈ 0.577
      └── Some((8, 8)): 22/34 ≈ 0.647
  ├── Some((0, 2)): 742/1404 ≈ 0.528
    ├── Some((2, 0)): 74/144 ≈ 0.514
      ├── Some((0, 0)): 2/10 ≈ 0.200
      ├── Some((0, 1)): 15/24 ≈ 0.625
      ├── Some((0, 3)): 12/21 ≈ 0.571
      ├── Some((0, 4)): 10/19 ≈ 0.526
      ├── Some((0, 5)): 12/21 ≈ 0.571
      ├── Some((0, 6)): 7/16 ≈ 0.438
      ├── Some((0, 7)): 9/18 ≈ 0.500
      └── Some((0, 8)): 6/14 ≈ 0.429
    ├── Some((2, 1)): 77/149 ≈ 0.517
      ├── Some((1, 0)): 2/9 ≈ 0.222
      ├── Some((1, 1)): 2/9 ≈ 0.222
      ├── Some((1, 2)): 6/14 ≈ 0.429
      ├── Some((1, 3)): 9/17 ≈ 0.529
      ├── Some((1, 4)): 19/28 ≈ 0.679
      ├── Some((1, 5)): 11/19 ≈ 0.579
      ├── Some((1, 6)): 11/20 ≈ 0.550
      ├── Some((1, 7)): 10/18 ≈ 0.556
      └── Some((1, 8)): 6/14 ≈ 0.429
    ├── Some((2, 2)): 144/243 ≈ 0.593
      ├── Some((2, 0)): 20/33 ≈ 0.606
      ├── Some((2, 1)): 18/30 ≈ 0.600
      ├── Some((2, 3)): 26/39 ≈ 0.667
      ├── Some((2, 4)): 21/34 ≈ 0.618
      ├── Some((2, 5)): 17/29 ≈ 0.586
      ├── Some((2, 6)): 15/27 ≈ 0.556
      ├── Some((2, 7)): 14/26 ≈ 0.538
      └── Some((2, 8)): 12/24 ≈ 0.500
    ├── Some((2, 3)): 65/131 ≈ 0.496
      ├── Some((3, 0)): 5/12 ≈ 0.417
      ├── Some((3, 1)): 3/10 ≈ 0.300
      ├── Some((3, 2)): 4/11 ≈ 0.364
      ├── Some((3, 3)): 11/19 ≈ 0.579
      ├── Some((3, 4)): 10/18 ≈ 0.556
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 11/19 ≈ 0.579
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((2, 4)): 72/141 ≈ 0.511
      ├── Some((4, 0)): 2/9 ≈ 0.222
      ├── Some((4, 1)): 4/11 ≈ 0.364
      ├── Some((4, 2)): 10/18 ≈ 0.556
      ├── Some((4, 3)): 6/14 ≈ 0.429
      ├── Some((4, 4)): 3/10 ≈ 0.300
      ├── Some((4, 5)): 14/22 ≈ 0.636
      ├── Some((4, 6)): 16/24 ≈ 0.667
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 7/15 ≈ 0.467
    ├── Some((2, 5)): 51/110 ≈ 0.464
      ├── Some((5, 0)): 12/19 ≈ 0.632
      ├── Some((5, 1)): 7/14 ≈ 0.500
      ├── Some((5, 2)): 1/7 ≈ 0.143
      ├── Some((5, 3)): 9/16 ≈ 0.562
      ├── Some((5, 4)): 4/10 ≈ 0.400
      ├── Some((5, 5)): 0/6 ≈ 0.000
      ├── Some((5, 6)): 10/17 ≈ 0.588
      ├── Some((5, 7)): 1/7 ≈ 0.143
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((2, 6)): 65/131 ≈ 0.496
      ├── Some((6, 0)): 6/13 ≈ 0.462
      ├── Some((6, 1)): 12/20 ≈ 0.600
      ├── Some((6, 2)): 8/15 ≈ 0.533
      ├── Some((6, 3)): 2/9 ≈ 0.222
      ├── Some((6, 4)): 10/18 ≈ 0.556
      ├── Some((6, 5)): 7/14 ≈ 0.500
      ├── Some((6, 6)): 5/12 ≈ 0.417
      ├── Some((6, 7)): 6/13 ≈ 0.462
      └── Some((6, 8)): 8/16 ≈ 0.500
    ├── Some((2, 7)): 97/177 ≈ 0.548
      ├── Some((7, 1)): 21/32 ≈ 0.656
      ├── Some((7, 2)): 14/25 ≈ 0.560
      ├── Some((7, 3)): 5/14 ≈ 0.357
      ├── Some((7, 4)): 20/31 ≈ 0.645
      ├── Some((7, 5)): 13/23 ≈ 0.565
      ├── Some((7, 6)): 16/27 ≈ 0.593
      ├── Some((7, 7)): 2/10 ≈ 0.200
      └── Some((7, 8)): 5/14 ≈ 0.357
    └── Some((2, 8)): 97/177 ≈ 0.548
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 1)): 9/17 ≈ 0.529
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 8/16 ≈ 0.500
      ├── Some((8, 4)): 14/23 ≈ 0.609
      ├── Some((8, 5)): 10/19 ≈ 0.526
      ├── Some((8, 6)): 11/20 ≈ 0.550
      ├── Some((8, 7)): 11/20 ≈ 0.550
      └── Some((8, 8)): 15/24 ≈ 0.625
  ├── Some((0, 3)): 278/600 ≈ 0.463
    ├── Some((3, 0)): 22/54 ≈ 0.407
      ├── Some((0, 0)): 1/5 ≈ 0.200
      ├── Some((0, 1)): 1/5 ≈ 0.200
      ├── Some((0, 2)): 2/6 ≈ 0.333
      ├── Some((0, 4)): 5/9 ≈ 0.556
      ├── Some((0, 5)): 6/9 ≈ 0.667
      ├── Some((0, 6)): 0/4 ≈ 0.000
      ├── Some((0, 7)): 2/6 ≈ 0.333
      └── Some((0, 8)): 5/9 ≈ 0.556
    ├── Some((3, 1)): 26/60 ≈ 0.433
      ├── Some((1, 0)): 3/7 ≈ 0.429
      ├── Some((1, 1)): 3/7 ≈ 0.429
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 4/7 ≈ 0.571
      ├── Some((1, 5)): 1/5 ≈ 0.200
      ├── Some((1, 6)): 4/7 ≈ 0.571
      ├── Some((1, 7)): 3/7 ≈ 0.429
      └── Some((1, 8)): 4/7 ≈ 0.571
    ├── Some((3, 2)): 25/58 ≈ 0.431
      ├── Some((2, 0)): 2/6 ≈ 0.333
      ├── Some((2, 1)): 2/6 ≈ 0.333
      ├── Some((2, 2)): 1/5 ≈ 0.200
      ├── Some((2, 3)): 3/7 ≈ 0.429
      ├── Some((2, 4)): 9/11 ≈ 0.818
      ├── Some((2, 5)): 0/4 ≈ 0.000
      ├── Some((2, 6)): 4/7 ≈ 0.571
      ├── Some((2, 7)): 2/6 ≈ 0.333
      └── Some((2, 8)): 1/5 ≈ 0.200
    ├── Some((3, 3)): 32/68 ≈ 0.471
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 6/10 ≈ 0.600
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 7/11 ≈ 0.636
      ├── Some((3, 7)): 4/8 ≈ 0.500
      └── Some((3, 8)): 1/5 ≈ 0.200
    ├── Some((3, 4)): 28/63 ≈ 0.444
      ├── Some((4, 0)): 4/8 ≈ 0.500
      ├── Some((4, 1)): 4/8 ≈ 0.500
      ├── Some((4, 2)): 2/6 ≈ 0.333
      ├── Some((4, 3)): 8/11 ≈ 0.727
      ├── Some((4, 4)): 0/4 ≈ 0.000
      ├── Some((4, 5)): 1/5 ≈ 0.200
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 2/6 ≈ 0.333
      └── Some((4, 8)): 5/9 ≈ 0.556
    ├── Some((3, 5)): 30/65 ≈ 0.462
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 4/8 ≈ 0.500
      ├── Some((5, 2)): 3/7 ≈ 0.429
      ├── Some((5, 3)): 5/9 ≈ 0.556
      ├── Some((5, 4)): 7/10 ≈ 0.700
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 4/8 ≈ 0.500
      ├── Some((5, 7)): 1/5 ≈ 0.200
      └── Some((5, 8)): 3/7 ≈ 0.429
    ├── Some((3, 6)): 35/73 ≈ 0.479
      ├── Some((6, 0)): 0/4 ≈ 0.000
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 6/10 ≈ 0.600
      ├── Some((6, 3)): 4/8 ≈ 0.500
      ├── Some((6, 4)): 6/10 ≈ 0.600
      ├── Some((6, 5)): 0/4 ≈ 0.000
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 6/10 ≈ 0.600
    ├── Some((3, 7)): 40/79 ≈ 0.506
      ├── Some((7, 1)): 0/5 ≈ 0.000
      ├── Some((7, 2)): 7/12 ≈ 0.583
      ├── Some((7, 3)): 5/10 ≈ 0.500
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 11/15 ≈ 0.733
      ├── Some((7, 7)): 4/9 ≈ 0.444
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((3, 8)): 40/79 ≈ 0.506
      ├── Some((8, 0)): 5/9 ≈ 0.556
      ├── Some((8, 1)): 5/9 ≈ 0.556
      ├── Some((8, 2)): 6/10 ≈ 0.600
      ├── Some((8, 3)): 6/10 ≈ 0.600
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 7/11 ≈ 0.636
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((0, 4)): 440/886 ≈ 0.497
    ├── Some((4, 0)): 69/127 ≈ 0.543
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 10/18 ≈ 0.556
      ├── Some((0, 2)): 3/10 ≈ 0.300
      ├── Some((0, 3)): 11/19 ≈ 0.579
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 8/15 ≈ 0.533
      ├── Some((0, 7)): 8/15 ≈ 0.533
      └── Some((0, 8)): 16/23 ≈ 0.696
    ├── Some((4, 1)): 67/124 ≈ 0.540
      ├── Some((1, 0)): 20/26 ≈ 0.769
      ├── Some((1, 1)): 5/11 ≈ 0.455
      ├── Some((1, 2)): 0/6 ≈ 0.000
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 18/24 ≈ 0.750
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 9/16 ≈ 0.562
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 0/6 ≈ 0.000
    ├── Some((4, 2)): 43/90 ≈ 0.478
      ├── Some((2, 0)): 6/11 ≈ 0.545
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 6/11 ≈ 0.545
      ├── Some((2, 4)): 2/7 ≈ 0.286
      ├── Some((2, 5)): 8/13 ≈ 0.615
      ├── Some((2, 6)): 4/9 ≈ 0.444
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 6/11 ≈ 0.545
    ├── Some((4, 3)): 24/62 ≈ 0.387
      ├── Some((3, 0)): 2/6 ≈ 0.333
      ├── Some((3, 1)): 3/7 ≈ 0.429
      ├── Some((3, 2)): 5/9 ≈ 0.556
      ├── Some((3, 3)): 2/6 ≈ 0.333
      ├── Some((3, 4)): 0/4 ≈ 0.000
      ├── Some((3, 5)): 3/7 ≈ 0.429
      ├── Some((3, 6)): 1/5 ≈ 0.200
      ├── Some((3, 7)): 5/9 ≈ 0.556
      └── Some((3, 8)): 3/8 ≈ 0.375
    ├── Some((4, 4)): 70/129 ≈ 0.543
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 7/14 ≈ 0.500
      ├── Some((4, 2)): 5/12 ≈ 0.417
      ├── Some((4, 3)): 13/21 ≈ 0.619
      ├── Some((4, 5)): 10/18 ≈ 0.556
      ├── Some((4, 6)): 9/16 ≈ 0.562
      ├── Some((4, 7)): 12/20 ≈ 0.600
      └── Some((4, 8)): 8/15 ≈ 0.533
    ├── Some((4, 5)): 49/99 ≈ 0.495
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 7/12 ≈ 0.583
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 9/14 ≈ 0.643
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 7/12 ≈ 0.583
      └── Some((5, 8)): 2/7 ≈ 0.286
    ├── Some((4, 6)): 35/78 ≈ 0.449
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 6/11 ≈ 0.545
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 7/11 ≈ 0.636
      ├── Some((6, 7)): 5/10 ≈ 0.500
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((4, 7)): 28/68 ≈ 0.412
      ├── Some((7, 1)): 2/7 ≈ 0.286
      ├── Some((7, 2)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 0/4 ≈ 0.000
      ├── Some((7, 4)): 6/11 ≈ 0.545
      ├── Some((7, 5)): 1/6 ≈ 0.167
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 5/10 ≈ 0.500
      └── Some((7, 8)): 6/11 ≈ 0.545
    └── Some((4, 8)): 55/108 ≈ 0.509
      ├── Some((8, 0)): 1/6 ≈ 0.167
      ├── Some((8, 1)): 8/14 ≈ 0.571
      ├── Some((8, 2)): 9/15 ≈ 0.600
      ├── Some((8, 3)): 12/18 ≈ 0.667
      ├── Some((8, 4)): 1/7 ≈ 0.143
      ├── Some((8, 5)): 7/13 ≈ 0.538
      ├── Some((8, 6)): 7/13 ≈ 0.538
      ├── Some((8, 7)): 5/11 ≈ 0.455
      └── Some((8, 8)): 4/10 ≈ 0.400
  ├── Some((0, 5)): 500/990 ≈ 0.505
    ├── Some((5, 0)): 31/74 ≈ 0.419
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 3/8 ≈ 0.375
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 6/12 ≈ 0.500
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((5, 1)): 20/57 ≈ 0.351
      ├── Some((1, 0)): 1/5 ≈ 0.200
      ├── Some((1, 1)): 2/6 ≈ 0.333
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 3/7 ≈ 0.429
      ├── Some((1, 5)): 2/6 ≈ 0.333
      ├── Some((1, 6)): 3/7 ≈ 0.429
      ├── Some((1, 7)): 2/6 ≈ 0.333
      └── Some((1, 8)): 3/7 ≈ 0.429
    ├── Some((5, 2)): 40/88 ≈ 0.455
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 2/7 ≈ 0.286
      ├── Some((2, 2)): 9/14 ≈ 0.643
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 6/11 ≈ 0.545
      ├── Some((2, 5)): 6/12 ≈ 0.500
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 7/12 ≈ 0.583
      └── Some((2, 8)): 6/12 ≈ 0.500
    ├── Some((5, 3)): 100/173 ≈ 0.578
      ├── Some((3, 0)): 17/25 ≈ 0.680
      ├── Some((3, 1)): 10/18 ≈ 0.556
      ├── Some((3, 2)): 4/12 ≈ 0.333
      ├── Some((3, 3)): 2/9 ≈ 0.222
      ├── Some((3, 4)): 19/27 ≈ 0.704
      ├── Some((3, 5)): 17/26 ≈ 0.654
      ├── Some((3, 6)): 9/17 ≈ 0.529
      ├── Some((3, 7)): 13/22 ≈ 0.591
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((5, 4)): 47/98 ≈ 0.480
      ├── Some((4, 0)): 9/15 ≈ 0.600
      ├── Some((4, 1)): 9/15 ≈ 0.600
      ├── Some((4, 2)): 8/14 ≈ 0.571
      ├── Some((4, 3)): 1/6 ≈ 0.167
      ├── Some((4, 4)): 7/13 ≈ 0.538
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 3/9 ≈ 0.333
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((5, 5)): 104/179 ≈ 0.581
      ├── Some((5, 0)): 6/15 ≈ 0.400
      ├── Some((5, 1)): 7/16 ≈ 0.438
      ├── Some((5, 2)): 3/11 ≈ 0.273
      ├── Some((5, 3)): 20/30 ≈ 0.667
      ├── Some((5, 4)): 10/19 ≈ 0.526
      ├── Some((5, 6)): 15/24 ≈ 0.625
      ├── Some((5, 7)): 20/30 ≈ 0.667
      └── Some((5, 8)): 23/33 ≈ 0.697
    ├── Some((5, 6)): 35/81 ≈ 0.432
      ├── Some((6, 0)): 4/9 ≈ 0.444
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 0/5 ≈ 0.000
      ├── Some((6, 3)): 8/13 ≈ 0.615
      ├── Some((6, 4)): 4/9 ≈ 0.444
      ├── Some((6, 5)): 9/14 ≈ 0.643
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 5/11 ≈ 0.455
      └── Some((6, 8)): 0/5 ≈ 0.000
    ├── Some((5, 7)): 58/114 ≈ 0.509
      ├── Some((7, 1)): 12/19 ≈ 0.632
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 8/15 ≈ 0.533
      ├── Some((7, 4)): 9/16 ≈ 0.562
      ├── Some((7, 5)): 0/6 ≈ 0.000
      ├── Some((7, 6)): 5/12 ≈ 0.417
      ├── Some((7, 7)): 12/20 ≈ 0.600
      └── Some((7, 8)): 8/15 ≈ 0.533
    └── Some((5, 8)): 65/125 ≈ 0.520
      ├── Some((8, 0)): 17/23 ≈ 0.739
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 1/7 ≈ 0.143
      ├── Some((8, 3)): 5/12 ≈ 0.417
      ├── Some((8, 4)): 10/17 ≈ 0.588
      ├── Some((8, 5)): 2/8 ≈ 0.250
      ├── Some((8, 6)): 14/21 ≈ 0.667
      ├── Some((8, 7)): 3/9 ≈ 0.333
      └── Some((8, 8)): 5/12 ≈ 0.417
  ├── Some((0, 6)): 580/1128 ≈ 0.514
    ├── Some((6, 0)): 72/137 ≈ 0.526
      ├── Some((0, 0)): 4/12 ≈ 0.333
      ├── Some((0, 1)): 7/15 ≈ 0.467
      ├── Some((0, 2)): 4/12 ≈ 0.333
      ├── Some((0, 3)): 6/14 ≈ 0.429
      ├── Some((0, 4)): 14/23 ≈ 0.609
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 7)): 10/18 ≈ 0.556
      └── Some((0, 8)): 18/26 ≈ 0.692
    ├── Some((6, 1)): 49/103 ≈ 0.476
      ├── Some((1, 0)): 7/13 ≈ 0.538
      ├── Some((1, 1)): 1/6 ≈ 0.167
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 9/15 ≈ 0.600
      ├── Some((1, 4)): 4/10 ≈ 0.400
      ├── Some((1, 5)): 1/7 ≈ 0.143
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 8/14 ≈ 0.571
      └── Some((1, 8)): 7/13 ≈ 0.538
    ├── Some((6, 2)): 78/145 ≈ 0.538
      ├── Some((2, 0)): 10/18 ≈ 0.556
      ├── Some((2, 1)): 16/23 ≈ 0.696
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 2/9 ≈ 0.222
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 13/20 ≈ 0.650
      ├── Some((2, 6)): 9/17 ≈ 0.529
      ├── Some((2, 7)): 12/20 ≈ 0.600
      └── Some((2, 8)): 4/11 ≈ 0.364
    ├── Some((6, 3)): 79/146 ≈ 0.541
      ├── Some((3, 0)): 13/21 ≈ 0.619
      ├── Some((3, 1)): 6/13 ≈ 0.462
      ├── Some((3, 2)): 5/12 ≈ 0.417
      ├── Some((3, 3)): 12/20 ≈ 0.600
      ├── Some((3, 4)): 4/11 ≈ 0.364
      ├── Some((3, 5)): 10/18 ≈ 0.556
      ├── Some((3, 6)): 16/23 ≈ 0.696
      ├── Some((3, 7)): 7/15 ≈ 0.467
      └── Some((3, 8)): 5/12 ≈ 0.417
    ├── Some((6, 4)): 94/168 ≈ 0.560
      ├── Some((4, 0)): 12/21 ≈ 0.571
      ├── Some((4, 1)): 6/14 ≈ 0.429
      ├── Some((4, 2)): 17/25 ≈ 0.680
      ├── Some((4, 3)): 20/28 ≈ 0.714
      ├── Some((4, 4)): 4/12 ≈ 0.333
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 12/21 ≈ 0.571
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((6, 5)): 42/93 ≈ 0.452
      ├── Some((5, 0)): 6/11 ≈ 0.545
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 7/12 ≈ 0.583
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 5/11 ≈ 0.455
    ├── Some((6, 6)): 36/83 ≈ 0.434
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 8/14 ≈ 0.571
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 1/6 ≈ 0.167
      ├── Some((6, 5)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 7/13 ≈ 0.538
      └── Some((6, 8)): 4/10 ≈ 0.400
    ├── Some((6, 7)): 70/134 ≈ 0.522
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 11/19 ≈ 0.579
      ├── Some((7, 3)): 7/15 ≈ 0.467
      ├── Some((7, 4)): 7/15 ≈ 0.467
      ├── Some((7, 5)): 5/13 ≈ 0.385
      ├── Some((7, 6)): 12/20 ≈ 0.600
      ├── Some((7, 7)): 7/15 ≈ 0.467
      └── Some((7, 8)): 13/21 ≈ 0.619
    └── Some((6, 8)): 59/118 ≈ 0.500
      ├── Some((8, 0)): 5/12 ≈ 0.417
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 16/22 ≈ 0.727
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 8/15 ≈ 0.533
      ├── Some((8, 5)): 2/8 ≈ 0.250
      ├── Some((8, 6)): 4/10 ≈ 0.400
      ├── Some((8, 7)): 10/17 ≈ 0.588
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((0, 7)): 610/1179 ≈ 0.517
    ├── Some((7, 1)): 108/193 ≈ 0.560
      ├── Some((1, 0)): 13/23 ≈ 0.565
      ├── Some((1, 1)): 17/27 ≈ 0.630
      ├── Some((1, 2)): 7/16 ≈ 0.438
      ├── Some((1, 3)): 17/27 ≈ 0.630
      ├── Some((1, 4)): 28/38 ≈ 0.737
      ├── Some((1, 5)): 6/15 ≈ 0.400
      ├── Some((1, 6)): 10/19 ≈ 0.526
      ├── Some((1, 7)): 5/14 ≈ 0.357
      └── Some((1, 8)): 4/13 ≈ 0.308
    ├── Some((7, 2)): 70/138 ≈ 0.507
      ├── Some((2, 0)): 5/12 ≈ 0.417
      ├── Some((2, 1)): 8/16 ≈ 0.500
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 10/18 ≈ 0.556
      ├── Some((2, 4)): 3/10 ≈ 0.300
      ├── Some((2, 5)): 16/24 ≈ 0.667
      ├── Some((2, 6)): 14/22 ≈ 0.636
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 3/10 ≈ 0.300
    ├── Some((7, 3)): 84/159 ≈ 0.528
      ├── Some((3, 0)): 22/30 ≈ 0.733
      ├── Some((3, 1)): 16/25 ≈ 0.640
      ├── Some((3, 2)): 2/9 ≈ 0.222
      ├── Some((3, 3)): 12/21 ≈ 0.571
      ├── Some((3, 4)): 4/12 ≈ 0.333
      ├── Some((3, 5)): 5/13 ≈ 0.385
      ├── Some((3, 6)): 10/19 ≈ 0.526
      ├── Some((3, 7)): 7/15 ≈ 0.467
      └── Some((3, 8)): 6/14 ≈ 0.429
    ├── Some((7, 4)): 68/135 ≈ 0.504
      ├── Some((4, 0)): 2/9 ≈ 0.222
      ├── Some((4, 1)): 2/9 ≈ 0.222
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 13/21 ≈ 0.619
      ├── Some((4, 4)): 4/11 ≈ 0.364
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 3/10 ≈ 0.300
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 17/25 ≈ 0.680
    ├── Some((7, 5)): 89/166 ≈ 0.536
      ├── Some((5, 0)): 12/21 ≈ 0.571
      ├── Some((5, 1)): 5/13 ≈ 0.385
      ├── Some((5, 2)): 11/20 ≈ 0.550
      ├── Some((5, 3)): 10/18 ≈ 0.556
      ├── Some((5, 4)): 11/20 ≈ 0.550
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 10/19 ≈ 0.526
      ├── Some((5, 7)): 12/21 ≈ 0.571
      └── Some((5, 8)): 8/16 ≈ 0.500
    ├── Some((7, 6)): 61/125 ≈ 0.488
      ├── Some((6, 0)): 1/8 ≈ 0.125
      ├── Some((6, 1)): 8/15 ≈ 0.533
      ├── Some((6, 2)): 13/20 ≈ 0.650
      ├── Some((6, 3)): 13/21 ≈ 0.619
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 6/13 ≈ 0.462
      ├── Some((6, 6)): 3/10 ≈ 0.300
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 4/11 ≈ 0.364
    ├── Some((7, 7)): 51/110 ≈ 0.464
      ├── Some((7, 1)): 5/13 ≈ 0.385
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 10/19 ≈ 0.526
      ├── Some((7, 4)): 5/13 ≈ 0.385
      ├── Some((7, 5)): 5/13 ≈ 0.385
      ├── Some((7, 6)): 3/11 ≈ 0.273
      └── Some((7, 8)): 15/24 ≈ 0.625
    └── Some((7, 8)): 79/152 ≈ 0.520
      ├── Some((8, 0)): 8/16 ≈ 0.500
      ├── Some((8, 1)): 8/16 ≈ 0.500
      ├── Some((8, 2)): 6/14 ≈ 0.429
      ├── Some((8, 3)): 4/12 ≈ 0.333
      ├── Some((8, 4)): 12/20 ≈ 0.600
      ├── Some((8, 5)): 15/24 ≈ 0.625
      ├── Some((8, 6)): 6/14 ≈ 0.429
      ├── Some((8, 7)): 11/19 ≈ 0.579
      └── Some((8, 8)): 8/16 ≈ 0.500
  └── Some((0, 8)): 322/678 ≈ 0.475
    ├── Some((8, 0)): 31/68 ≈ 0.456
      ├── Some((0, 0)): 3/8 ≈ 0.375
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 9/13 ≈ 0.692
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 6/10 ≈ 0.600
      ├── Some((0, 5)): 1/5 ≈ 0.200
      ├── Some((0, 6)): 1/5 ≈ 0.200
      └── Some((0, 7)): 3/8 ≈ 0.375
    ├── Some((8, 1)): 28/64 ≈ 0.438
      ├── Some((1, 0)): 5/9 ≈ 0.556
      ├── Some((1, 1)): 2/6 ≈ 0.333
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 3/7 ≈ 0.429
      ├── Some((1, 4)): 5/9 ≈ 0.556
      ├── Some((1, 5)): 1/5 ≈ 0.200
      ├── Some((1, 6)): 3/7 ≈ 0.429
      ├── Some((1, 7)): 2/6 ≈ 0.333
      └── Some((1, 8)): 5/9 ≈ 0.556
    ├── Some((8, 2)): 38/79 ≈ 0.481
      ├── Some((2, 0)): 4/8 ≈ 0.500
      ├── Some((2, 1)): 7/11 ≈ 0.636
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 4/8 ≈ 0.500
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 2/7 ≈ 0.286
      ├── Some((2, 7)): 6/10 ≈ 0.600
      └── Some((2, 8)): 4/9 ≈ 0.444
    ├── Some((8, 3)): 21/54 ≈ 0.389
      ├── Some((3, 0)): 0/4 ≈ 0.000
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 1/5 ≈ 0.200
      ├── Some((3, 3)): 2/6 ≈ 0.333
      ├── Some((3, 4)): 3/6 ≈ 0.500
      ├── Some((3, 5)): 2/6 ≈ 0.333
      ├── Some((3, 6)): 3/6 ≈ 0.500
      ├── Some((3, 7)): 6/9 ≈ 0.667
      └── Some((3, 8)): 3/6 ≈ 0.500
    ├── Some((8, 4)): 42/84 ≈ 0.500
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 5/10 ≈ 0.500
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 6/11 ≈ 0.545
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 0/4 ≈ 0.000
      ├── Some((4, 6)): 4/9 ≈ 0.444
      ├── Some((4, 7)): 4/9 ≈ 0.444
      └── Some((4, 8)): 10/14 ≈ 0.714
    ├── Some((8, 5)): 35/74 ≈ 0.473
      ├── Some((5, 0)): 4/8 ≈ 0.500
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 4/8 ≈ 0.500
      ├── Some((5, 3)): 4/8 ≈ 0.500
      ├── Some((5, 4)): 1/5 ≈ 0.200
      ├── Some((5, 5)): 4/9 ≈ 0.444
      ├── Some((5, 6)): 8/12 ≈ 0.667
      ├── Some((5, 7)): 2/7 ≈ 0.286
      └── Some((5, 8)): 5/9 ≈ 0.556
    ├── Some((8, 6)): 39/80 ≈ 0.488
      ├── Some((6, 0)): 0/4 ≈ 0.000
      ├── Some((6, 1)): 6/10 ≈ 0.600
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 4/9 ≈ 0.444
      ├── Some((6, 4)): 6/10 ≈ 0.600
      ├── Some((6, 5)): 6/11 ≈ 0.545
      ├── Some((6, 6)): 7/11 ≈ 0.636
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((8, 7)): 41/83 ≈ 0.494
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 13/18 ≈ 0.722
      ├── Some((7, 6)): 4/10 ≈ 0.400
      ├── Some((7, 7)): 1/6 ≈ 0.167
      └── Some((7, 8)): 8/13 ≈ 0.615
    └── Some((8, 8)): 47/91 ≈ 0.516
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 7/12 ≈ 0.583
      ├── Some((8, 2)): 7/13 ≈ 0.538
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 11/16 ≈ 0.688
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 2/7 ≈ 0.286
      └── Some((8, 7)): 7/13 ≈ 0.538
├── Some((7, 1)): 5424/10523 ≈ 0.515
  ├── Some((1, 0)): 534/1052 ≈ 0.508
    ├── Some((0, 0)): 63/122 ≈ 0.516
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 4/11 ≈ 0.364
      ├── Some((0, 4)): 6/13 ≈ 0.462
      ├── Some((0, 5)): 13/21 ≈ 0.619
      ├── Some((0, 6)): 7/15 ≈ 0.467
      ├── Some((0, 7)): 3/10 ≈ 0.300
      └── Some((0, 8)): 16/24 ≈ 0.667
    ├── Some((0, 1)): 75/140 ≈ 0.536
      ├── Some((1, 1)): 14/23 ≈ 0.609
      ├── Some((1, 2)): 8/16 ≈ 0.500
      ├── Some((1, 3)): 7/15 ≈ 0.467
      ├── Some((1, 4)): 8/16 ≈ 0.500
      ├── Some((1, 5)): 11/19 ≈ 0.579
      ├── Some((1, 6)): 8/16 ≈ 0.500
      ├── Some((1, 7)): 12/20 ≈ 0.600
      └── Some((1, 8)): 6/14 ≈ 0.429
    ├── Some((0, 2)): 56/112 ≈ 0.500
      ├── Some((2, 0)): 4/10 ≈ 0.400
      ├── Some((2, 1)): 8/14 ≈ 0.571
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 10/16 ≈ 0.625
      ├── Some((2, 4)): 3/9 ≈ 0.333
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 6/12 ≈ 0.500
      ├── Some((2, 7)): 8/15 ≈ 0.533
      └── Some((2, 8)): 8/15 ≈ 0.533
    ├── Some((0, 3)): 36/83 ≈ 0.434
      ├── Some((3, 0)): 7/12 ≈ 0.583
      ├── Some((3, 1)): 7/12 ≈ 0.583
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 7/13 ≈ 0.538
      ├── Some((3, 6)): 3/8 ≈ 0.375
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 1/6 ≈ 0.167
    ├── Some((0, 4)): 87/156 ≈ 0.558
      ├── Some((4, 0)): 17/24 ≈ 0.708
      ├── Some((4, 1)): 9/17 ≈ 0.529
      ├── Some((4, 2)): 10/18 ≈ 0.556
      ├── Some((4, 3)): 11/19 ≈ 0.579
      ├── Some((4, 4)): 5/12 ≈ 0.417
      ├── Some((4, 5)): 3/10 ≈ 0.300
      ├── Some((4, 6)): 10/18 ≈ 0.556
      ├── Some((4, 7)): 14/21 ≈ 0.667
      └── Some((4, 8)): 8/16 ≈ 0.500
    ├── Some((0, 5)): 53/108 ≈ 0.491
      ├── Some((5, 0)): 12/18 ≈ 0.667
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 6/12 ≈ 0.500
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 6/12 ≈ 0.500
      └── Some((5, 8)): 4/10 ≈ 0.400
    ├── Some((0, 6)): 63/122 ≈ 0.516
      ├── Some((6, 0)): 11/17 ≈ 0.647
      ├── Some((6, 1)): 9/15 ≈ 0.600
      ├── Some((6, 2)): 8/15 ≈ 0.533
      ├── Some((6, 3)): 9/16 ≈ 0.562
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 3/9 ≈ 0.333
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 8/15 ≈ 0.533
      └── Some((6, 8)): 7/14 ≈ 0.500
    ├── Some((0, 7)): 52/107 ≈ 0.486
      ├── Some((7, 0)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 12/19 ≈ 0.632
      ├── Some((7, 3)): 9/16 ≈ 0.562
      ├── Some((7, 4)): 8/15 ≈ 0.533
      ├── Some((7, 5)): 2/8 ≈ 0.250
      ├── Some((7, 6)): 8/15 ≈ 0.533
      ├── Some((7, 7)): 3/10 ≈ 0.300
      └── Some((7, 8)): 4/11 ≈ 0.364
    └── Some((0, 8)): 48/101 ≈ 0.475
      ├── Some((8, 0)): 11/17 ≈ 0.647
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 1/6 ≈ 0.167
      ├── Some((8, 5)): 7/13 ≈ 0.538
      ├── Some((8, 6)): 6/12 ≈ 0.500
      ├── Some((8, 7)): 1/7 ≈ 0.143
      └── Some((8, 8)): 9/15 ≈ 0.600
  ├── Some((1, 1)): 367/761 ≈ 0.482
    ├── Some((1, 0)): 33/76 ≈ 0.434
      ├── Some((0, 0)): 5/10 ≈ 0.500
      ├── Some((0, 1)): 6/10 ≈ 0.600
      ├── Some((0, 2)): 0/4 ≈ 0.000
      ├── Some((0, 3)): 6/11 ≈ 0.545
      ├── Some((0, 4)): 6/11 ≈ 0.545
      ├── Some((0, 5)): 0/4 ≈ 0.000
      ├── Some((0, 6)): 2/7 ≈ 0.286
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 5/10 ≈ 0.500
    ├── Some((1, 2)): 54/107 ≈ 0.505
      ├── Some((2, 0)): 4/10 ≈ 0.400
      ├── Some((2, 1)): 8/14 ≈ 0.571
      ├── Some((2, 2)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 8/14 ≈ 0.571
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 9/14 ≈ 0.643
      ├── Some((2, 7)): 8/14 ≈ 0.571
      └── Some((2, 8)): 8/14 ≈ 0.571
    ├── Some((1, 3)): 66/124 ≈ 0.532
      ├── Some((3, 0)): 10/16 ≈ 0.625
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 6/13 ≈ 0.462
      ├── Some((3, 3)): 5/11 ≈ 0.455
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 9/16 ≈ 0.562
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 10/16 ≈ 0.625
    ├── Some((1, 4)): 38/84 ≈ 0.452
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 9/14 ≈ 0.643
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 4/9 ≈ 0.444
      ├── Some((4, 6)): 5/10 ≈ 0.500
      ├── Some((4, 7)): 7/12 ≈ 0.583
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((1, 5)): 30/71 ≈ 0.423
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 1/5 ≈ 0.200
      ├── Some((5, 2)): 5/9 ≈ 0.556
      ├── Some((5, 3)): 4/8 ≈ 0.500
      ├── Some((5, 4)): 2/7 ≈ 0.286
      ├── Some((5, 5)): 7/11 ≈ 0.636
      ├── Some((5, 6)): 4/9 ≈ 0.444
      ├── Some((5, 7)): 0/4 ≈ 0.000
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((1, 6)): 60/116 ≈ 0.517
      ├── Some((6, 0)): 11/17 ≈ 0.647
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 9/15 ≈ 0.600
      └── Some((6, 8)): 10/16 ≈ 0.625
    ├── Some((1, 7)): 54/107 ≈ 0.505
      ├── Some((7, 0)): 1/7 ≈ 0.143
      ├── Some((7, 2)): 6/13 ≈ 0.462
      ├── Some((7, 3)): 10/17 ≈ 0.588
      ├── Some((7, 4)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 3/9 ≈ 0.333
      ├── Some((7, 6)): 11/18 ≈ 0.611
      ├── Some((7, 7)): 11/18 ≈ 0.611
      └── Some((7, 8)): 7/14 ≈ 0.500
    └── Some((1, 8)): 32/75 ≈ 0.427
      ├── Some((8, 0)): 7/12 ≈ 0.583
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 5/10 ≈ 0.500
      ├── Some((8, 3)): 7/12 ≈ 0.583
      ├── Some((8, 4)): 1/6 ≈ 0.167
      ├── Some((8, 5)): 4/9 ≈ 0.444
      ├── Some((8, 6)): 0/4 ≈ 0.000
      ├── Some((8, 7)): 4/9 ≈ 0.444
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((1, 2)): 418/850 ≈ 0.492
    ├── Some((2, 0)): 75/135 ≈ 0.556
      ├── Some((0, 0)): 5/12 ≈ 0.417
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 18/24 ≈ 0.750
      ├── Some((0, 4)): 15/21 ≈ 0.714
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 9/16 ≈ 0.562
      └── Some((0, 8)): 5/12 ≈ 0.417
    ├── Some((2, 1)): 32/74 ≈ 0.432
      ├── Some((1, 0)): 3/8 ≈ 0.375
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 5/10 ≈ 0.500
      ├── Some((1, 5)): 5/11 ≈ 0.455
      ├── Some((1, 6)): 5/11 ≈ 0.455
      ├── Some((1, 7)): 7/12 ≈ 0.583
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((2, 2)): 22/58 ≈ 0.379
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 6/11 ≈ 0.545
      ├── Some((2, 3)): 0/4 ≈ 0.000
      ├── Some((2, 4)): 4/9 ≈ 0.444
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 1/5 ≈ 0.200
      ├── Some((2, 7)): 5/10 ≈ 0.500
      └── Some((2, 8)): 0/4 ≈ 0.000
    ├── Some((2, 3)): 53/105 ≈ 0.505
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 7/13 ≈ 0.538
      ├── Some((3, 2)): 10/15 ≈ 0.667
      ├── Some((3, 3)): 7/13 ≈ 0.538
      ├── Some((3, 4)): 3/9 ≈ 0.333
      ├── Some((3, 5)): 7/13 ≈ 0.538
      ├── Some((3, 6)): 7/13 ≈ 0.538
      ├── Some((3, 7)): 2/7 ≈ 0.286
      └── Some((3, 8)): 6/12 ≈ 0.500
    ├── Some((2, 4)): 33/75 ≈ 0.440
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 4/9 ≈ 0.444
      ├── Some((4, 2)): 0/4 ≈ 0.000
      ├── Some((4, 3)): 5/9 ≈ 0.556
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 5/9 ≈ 0.556
      ├── Some((4, 6)): 2/7 ≈ 0.286
      ├── Some((4, 7)): 4/9 ≈ 0.444
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((2, 5)): 57/110 ≈ 0.518
      ├── Some((5, 0)): 3/9 ≈ 0.333
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 5/11 ≈ 0.455
      ├── Some((5, 3)): 8/14 ≈ 0.571
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 15/20 ≈ 0.750
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 9/15 ≈ 0.600
      └── Some((5, 8)): 1/7 ≈ 0.143
    ├── Some((2, 6)): 18/52 ≈ 0.346
      ├── Some((6, 0)): 1/5 ≈ 0.200
      ├── Some((6, 1)): 0/4 ≈ 0.000
      ├── Some((6, 2)): 4/7 ≈ 0.571
      ├── Some((6, 3)): 3/6 ≈ 0.500
      ├── Some((6, 4)): 0/4 ≈ 0.000
      ├── Some((6, 5)): 2/6 ≈ 0.333
      ├── Some((6, 6)): 3/7 ≈ 0.429
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 4/7 ≈ 0.571
    ├── Some((2, 7)): 76/137 ≈ 0.555
      ├── Some((7, 0)): 8/16 ≈ 0.500
      ├── Some((7, 2)): 4/11 ≈ 0.364
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 9/17 ≈ 0.529
      ├── Some((7, 5)): 11/19 ≈ 0.579
      ├── Some((7, 6)): 7/14 ≈ 0.500
      ├── Some((7, 7)): 12/20 ≈ 0.600
      └── Some((7, 8)): 15/22 ≈ 0.682
    └── Some((2, 8)): 52/103 ≈ 0.505
      ├── Some((8, 0)): 8/13 ≈ 0.615
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 15/20 ≈ 0.750
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 3/9 ≈ 0.333
      ├── Some((8, 5)): 7/13 ≈ 0.538
      ├── Some((8, 6)): 7/13 ≈ 0.538
      ├── Some((8, 7)): 1/6 ≈ 0.167
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((1, 3)): 767/1451 ≈ 0.529
    ├── Some((3, 0)): 80/154 ≈ 0.519
      ├── Some((0, 0)): 4/12 ≈ 0.333
      ├── Some((0, 1)): 10/18 ≈ 0.556
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 14/23 ≈ 0.609
      ├── Some((0, 4)): 8/16 ≈ 0.500
      ├── Some((0, 5)): 10/18 ≈ 0.556
      ├── Some((0, 6)): 7/15 ≈ 0.467
      ├── Some((0, 7)): 10/18 ≈ 0.556
      └── Some((0, 8)): 7/15 ≈ 0.467
    ├── Some((3, 1)): 111/199 ≈ 0.558
      ├── Some((1, 0)): 16/27 ≈ 0.593
      ├── Some((1, 1)): 16/27 ≈ 0.593
      ├── Some((1, 2)): 24/36 ≈ 0.667
      ├── Some((1, 4)): 19/31 ≈ 0.613
      ├── Some((1, 5)): 15/26 ≈ 0.577
      ├── Some((1, 6)): 10/21 ≈ 0.476
      ├── Some((1, 7)): 9/20 ≈ 0.450
      └── Some((1, 8)): 1/10 ≈ 0.100
    ├── Some((3, 2)): 95/176 ≈ 0.540
      ├── Some((2, 0)): 14/23 ≈ 0.609
      ├── Some((2, 1)): 10/19 ≈ 0.526
      ├── Some((2, 2)): 9/18 ≈ 0.500
      ├── Some((2, 3)): 5/13 ≈ 0.385
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 10/19 ≈ 0.526
      ├── Some((2, 6)): 14/23 ≈ 0.609
      ├── Some((2, 7)): 13/22 ≈ 0.591
      └── Some((2, 8)): 14/23 ≈ 0.609
    ├── Some((3, 3)): 134/231 ≈ 0.580
      ├── Some((3, 0)): 26/39 ≈ 0.667
      ├── Some((3, 1)): 20/33 ≈ 0.606
      ├── Some((3, 2)): 16/28 ≈ 0.571
      ├── Some((3, 4)): 7/18 ≈ 0.389
      ├── Some((3, 5)): 25/38 ≈ 0.658
      ├── Some((3, 6)): 10/21 ≈ 0.476
      ├── Some((3, 7)): 17/29 ≈ 0.586
      └── Some((3, 8)): 12/24 ≈ 0.500
    ├── Some((3, 4)): 68/137 ≈ 0.496
      ├── Some((4, 0)): 4/11 ≈ 0.364
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 2/9 ≈ 0.222
      ├── Some((4, 3)): 19/27 ≈ 0.704
      ├── Some((4, 4)): 9/17 ≈ 0.529
      ├── Some((4, 5)): 9/17 ≈ 0.529
      ├── Some((4, 6)): 11/19 ≈ 0.579
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 1/8 ≈ 0.125
    ├── Some((3, 5)): 87/164 ≈ 0.530
      ├── Some((5, 0)): 6/14 ≈ 0.429
      ├── Some((5, 1)): 12/21 ≈ 0.571
      ├── Some((5, 2)): 23/32 ≈ 0.719
      ├── Some((5, 3)): 11/20 ≈ 0.550
      ├── Some((5, 4)): 11/20 ≈ 0.550
      ├── Some((5, 5)): 6/14 ≈ 0.429
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 3/11 ≈ 0.273
      └── Some((5, 8)): 7/16 ≈ 0.438
    ├── Some((3, 6)): 43/99 ≈ 0.434
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 9/16 ≈ 0.562
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 2/8 ≈ 0.250
      ├── Some((6, 4)): 13/19 ≈ 0.684
      ├── Some((6, 5)): 0/6 ≈ 0.000
      ├── Some((6, 6)): 4/10 ≈ 0.400
      ├── Some((6, 7)): 5/11 ≈ 0.455
      └── Some((6, 8)): 1/7 ≈ 0.143
    ├── Some((3, 7)): 76/148 ≈ 0.514
      ├── Some((7, 0)): 16/26 ≈ 0.615
      ├── Some((7, 2)): 13/22 ≈ 0.591
      ├── Some((7, 3)): 2/10 ≈ 0.200
      ├── Some((7, 4)): 15/25 ≈ 0.600
      ├── Some((7, 5)): 8/17 ≈ 0.471
      ├── Some((7, 6)): 10/19 ≈ 0.526
      ├── Some((7, 7)): 8/17 ≈ 0.471
      └── Some((7, 8)): 3/11 ≈ 0.273
    └── Some((3, 8)): 72/142 ≈ 0.507
      ├── Some((8, 0)): 5/12 ≈ 0.417
      ├── Some((8, 1)): 11/19 ≈ 0.579
      ├── Some((8, 2)): 6/13 ≈ 0.462
      ├── Some((8, 3)): 5/12 ≈ 0.417
      ├── Some((8, 4)): 8/16 ≈ 0.500
      ├── Some((8, 5)): 10/18 ≈ 0.556
      ├── Some((8, 6)): 8/16 ≈ 0.500
      ├── Some((8, 7)): 13/21 ≈ 0.619
      └── Some((8, 8)): 6/14 ≈ 0.429
  ├── Some((1, 4)): 640/1235 ≈ 0.518
    ├── Some((4, 0)): 90/164 ≈ 0.549
      ├── Some((0, 0)): 12/20 ≈ 0.600
      ├── Some((0, 1)): 11/19 ≈ 0.579
      ├── Some((0, 2)): 5/13 ≈ 0.385
      ├── Some((0, 3)): 8/16 ≈ 0.500
      ├── Some((0, 4)): 7/15 ≈ 0.467
      ├── Some((0, 5)): 5/13 ≈ 0.385
      ├── Some((0, 6)): 13/21 ≈ 0.619
      ├── Some((0, 7)): 13/22 ≈ 0.591
      └── Some((0, 8)): 16/24 ≈ 0.667
    ├── Some((4, 1)): 56/115 ≈ 0.487
      ├── Some((1, 0)): 3/10 ≈ 0.300
      ├── Some((1, 1)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 6/13 ≈ 0.462
      ├── Some((1, 3)): 3/10 ≈ 0.300
      ├── Some((1, 5)): 15/23 ≈ 0.652
      ├── Some((1, 6)): 9/17 ≈ 0.529
      ├── Some((1, 7)): 9/17 ≈ 0.529
      └── Some((1, 8)): 5/12 ≈ 0.417
    ├── Some((4, 2)): 65/129 ≈ 0.504
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 2)): 16/24 ≈ 0.667
      ├── Some((2, 3)): 18/25 ≈ 0.720
      ├── Some((2, 4)): 4/11 ≈ 0.364
      ├── Some((2, 5)): 2/9 ≈ 0.222
      ├── Some((2, 6)): 9/17 ≈ 0.529
      ├── Some((2, 7)): 0/6 ≈ 0.000
      └── Some((2, 8)): 6/13 ≈ 0.462
    ├── Some((4, 3)): 83/154 ≈ 0.539
      ├── Some((3, 0)): 8/16 ≈ 0.500
      ├── Some((3, 1)): 7/15 ≈ 0.467
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 16/24 ≈ 0.667
      ├── Some((3, 4)): 14/22 ≈ 0.636
      ├── Some((3, 5)): 8/16 ≈ 0.500
      ├── Some((3, 6)): 7/15 ≈ 0.467
      ├── Some((3, 7)): 4/11 ≈ 0.364
      └── Some((3, 8)): 10/18 ≈ 0.556
    ├── Some((4, 4)): 71/137 ≈ 0.518
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 12/20 ≈ 0.600
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 14/23 ≈ 0.609
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 2/9 ≈ 0.222
      └── Some((4, 8)): 16/25 ≈ 0.640
    ├── Some((4, 5)): 92/167 ≈ 0.551
      ├── Some((5, 0)): 13/22 ≈ 0.591
      ├── Some((5, 1)): 0/7 ≈ 0.000
      ├── Some((5, 2)): 20/29 ≈ 0.690
      ├── Some((5, 3)): 6/14 ≈ 0.429
      ├── Some((5, 4)): 16/25 ≈ 0.640
      ├── Some((5, 5)): 4/12 ≈ 0.333
      ├── Some((5, 6)): 19/28 ≈ 0.679
      ├── Some((5, 7)): 3/11 ≈ 0.273
      └── Some((5, 8)): 10/18 ≈ 0.556
    ├── Some((4, 6)): 39/90 ≈ 0.433
      ├── Some((6, 0)): 7/13 ≈ 0.538
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 7/13 ≈ 0.538
      ├── Some((6, 4)): 1/6 ≈ 0.167
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 3/9 ≈ 0.333
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((4, 7)): 65/129 ≈ 0.504
      ├── Some((7, 0)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 15/23 ≈ 0.652
      ├── Some((7, 3)): 6/14 ≈ 0.429
      ├── Some((7, 4)): 4/12 ≈ 0.333
      ├── Some((7, 5)): 3/10 ≈ 0.300
      ├── Some((7, 6)): 14/22 ≈ 0.636
      ├── Some((7, 7)): 9/17 ≈ 0.529
      └── Some((7, 8)): 7/15 ≈ 0.467
    └── Some((4, 8)): 79/149 ≈ 0.530
      ├── Some((8, 0)): 13/21 ≈ 0.619
      ├── Some((8, 1)): 9/17 ≈ 0.529
      ├── Some((8, 2)): 12/20 ≈ 0.600
      ├── Some((8, 3)): 9/17 ≈ 0.529
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 7/14 ≈ 0.500
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 9/17 ≈ 0.529
      └── Some((8, 8)): 11/19 ≈ 0.579
  ├── Some((1, 5)): 594/1156 ≈ 0.514
    ├── Some((5, 0)): 82/152 ≈ 0.539
      ├── Some((0, 0)): 13/21 ≈ 0.619
      ├── Some((0, 1)): 2/9 ≈ 0.222
      ├── Some((0, 2)): 15/23 ≈ 0.652
      ├── Some((0, 3)): 15/23 ≈ 0.652
      ├── Some((0, 4)): 3/10 ≈ 0.300
      ├── Some((0, 5)): 2/9 ≈ 0.222
      ├── Some((0, 6)): 11/19 ≈ 0.579
      ├── Some((0, 7)): 7/15 ≈ 0.467
      └── Some((0, 8)): 14/22 ≈ 0.636
    ├── Some((5, 1)): 62/123 ≈ 0.504
      ├── Some((1, 0)): 13/21 ≈ 0.619
      ├── Some((1, 1)): 8/16 ≈ 0.500
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 3)): 6/13 ≈ 0.462
      ├── Some((1, 4)): 5/12 ≈ 0.417
      ├── Some((1, 6)): 3/10 ≈ 0.300
      ├── Some((1, 7)): 11/19 ≈ 0.579
      └── Some((1, 8)): 9/17 ≈ 0.529
    ├── Some((5, 2)): 46/99 ≈ 0.465
      ├── Some((2, 0)): 4/10 ≈ 0.400
      ├── Some((2, 1)): 8/14 ≈ 0.571
      ├── Some((2, 2)): 10/15 ≈ 0.667
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 6/12 ≈ 0.500
      ├── Some((2, 5)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 2/7 ≈ 0.286
      └── Some((2, 8)): 2/8 ≈ 0.250
    ├── Some((5, 3)): 93/167 ≈ 0.557
      ├── Some((3, 0)): 15/24 ≈ 0.625
      ├── Some((3, 1)): 8/16 ≈ 0.500
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 6/14 ≈ 0.429
      ├── Some((3, 4)): 10/18 ≈ 0.556
      ├── Some((3, 5)): 19/28 ≈ 0.679
      ├── Some((3, 6)): 10/18 ≈ 0.556
      ├── Some((3, 7)): 7/15 ≈ 0.467
      └── Some((3, 8)): 9/17 ≈ 0.529
    ├── Some((5, 4)): 46/99 ≈ 0.465
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 9/15 ≈ 0.600
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 7/13 ≈ 0.538
      ├── Some((4, 6)): 2/7 ≈ 0.286
      ├── Some((4, 7)): 7/13 ≈ 0.538
      └── Some((4, 8)): 5/11 ≈ 0.455
    ├── Some((5, 5)): 59/118 ≈ 0.500
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 1)): 7/14 ≈ 0.500
      ├── Some((5, 2)): 7/14 ≈ 0.500
      ├── Some((5, 3)): 11/19 ≈ 0.579
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 12/20 ≈ 0.600
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 2/9 ≈ 0.222
    ├── Some((5, 6)): 73/139 ≈ 0.525
      ├── Some((6, 0)): 9/17 ≈ 0.529
      ├── Some((6, 1)): 14/21 ≈ 0.667
      ├── Some((6, 2)): 14/21 ≈ 0.667
      ├── Some((6, 3)): 5/12 ≈ 0.417
      ├── Some((6, 4)): 2/9 ≈ 0.222
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 3/10 ≈ 0.300
      ├── Some((6, 7)): 10/18 ≈ 0.556
      └── Some((6, 8)): 11/19 ≈ 0.579
    ├── Some((5, 7)): 57/115 ≈ 0.496
      ├── Some((7, 0)): 11/19 ≈ 0.579
      ├── Some((7, 2)): 6/13 ≈ 0.462
      ├── Some((7, 3)): 8/15 ≈ 0.533
      ├── Some((7, 4)): 9/16 ≈ 0.562
      ├── Some((7, 5)): 8/15 ≈ 0.533
      ├── Some((7, 6)): 9/16 ≈ 0.562
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 2/9 ≈ 0.222
    └── Some((5, 8)): 76/143 ≈ 0.531
      ├── Some((8, 0)): 5/12 ≈ 0.417
      ├── Some((8, 1)): 13/21 ≈ 0.619
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 14/21 ≈ 0.667
      ├── Some((8, 4)): 9/17 ≈ 0.529
      ├── Some((8, 5)): 7/14 ≈ 0.500
      ├── Some((8, 6)): 7/14 ≈ 0.500
      ├── Some((8, 7)): 7/14 ≈ 0.500
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((1, 6)): 839/1573 ≈ 0.533
    ├── Some((6, 0)): 90/171 ≈ 0.526
      ├── Some((0, 0)): 5/14 ≈ 0.357
      ├── Some((0, 1)): 8/17 ≈ 0.471
      ├── Some((0, 2)): 8/17 ≈ 0.471
      ├── Some((0, 3)): 8/17 ≈ 0.471
      ├── Some((0, 4)): 5/14 ≈ 0.357
      ├── Some((0, 5)): 10/19 ≈ 0.526
      ├── Some((0, 6)): 12/21 ≈ 0.571
      ├── Some((0, 7)): 13/22 ≈ 0.591
      └── Some((0, 8)): 20/29 ≈ 0.690
    ├── Some((6, 1)): 99/184 ≈ 0.538
      ├── Some((1, 0)): 13/24 ≈ 0.542
      ├── Some((1, 1)): 10/20 ≈ 0.500
      ├── Some((1, 2)): 4/13 ≈ 0.308
      ├── Some((1, 3)): 16/27 ≈ 0.593
      ├── Some((1, 4)): 11/22 ≈ 0.500
      ├── Some((1, 5)): 5/15 ≈ 0.333
      ├── Some((1, 7)): 20/31 ≈ 0.645
      └── Some((1, 8)): 20/31 ≈ 0.645
    ├── Some((6, 2)): 143/246 ≈ 0.581
      ├── Some((2, 0)): 7/17 ≈ 0.412
      ├── Some((2, 1)): 19/31 ≈ 0.613
      ├── Some((2, 2)): 18/30 ≈ 0.600
      ├── Some((2, 3)): 16/28 ≈ 0.571
      ├── Some((2, 4)): 15/26 ≈ 0.577
      ├── Some((2, 5)): 26/38 ≈ 0.684
      ├── Some((2, 6)): 12/23 ≈ 0.522
      ├── Some((2, 7)): 10/21 ≈ 0.476
      └── Some((2, 8)): 19/31 ≈ 0.613
    ├── Some((6, 3)): 80/156 ≈ 0.513
      ├── Some((3, 0)): 15/24 ≈ 0.625
      ├── Some((3, 1)): 2/10 ≈ 0.200
      ├── Some((3, 2)): 10/19 ≈ 0.526
      ├── Some((3, 3)): 16/25 ≈ 0.640
      ├── Some((3, 4)): 10/19 ≈ 0.526
      ├── Some((3, 5)): 6/14 ≈ 0.429
      ├── Some((3, 6)): 4/12 ≈ 0.333
      ├── Some((3, 7)): 8/16 ≈ 0.500
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((6, 4)): 77/152 ≈ 0.507
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 6/14 ≈ 0.429
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 11/20 ≈ 0.550
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 10/18 ≈ 0.556
      ├── Some((4, 6)): 9/17 ≈ 0.529
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 11/20 ≈ 0.550
    ├── Some((6, 5)): 142/245 ≈ 0.580
      ├── Some((5, 0)): 16/28 ≈ 0.571
      ├── Some((5, 1)): 5/15 ≈ 0.333
      ├── Some((5, 2)): 24/36 ≈ 0.667
      ├── Some((5, 3)): 17/29 ≈ 0.586
      ├── Some((5, 4)): 28/40 ≈ 0.700
      ├── Some((5, 5)): 13/24 ≈ 0.542
      ├── Some((5, 6)): 17/29 ≈ 0.586
      ├── Some((5, 7)): 7/17 ≈ 0.412
      └── Some((5, 8)): 15/26 ≈ 0.577
    ├── Some((6, 6)): 91/172 ≈ 0.529
      ├── Some((6, 0)): 13/23 ≈ 0.565
      ├── Some((6, 1)): 18/29 ≈ 0.621
      ├── Some((6, 2)): 11/21 ≈ 0.524
      ├── Some((6, 3)): 15/26 ≈ 0.577
      ├── Some((6, 4)): 13/23 ≈ 0.565
      ├── Some((6, 5)): 2/10 ≈ 0.200
      ├── Some((6, 7)): 8/18 ≈ 0.444
      └── Some((6, 8)): 11/21 ≈ 0.524
    ├── Some((6, 7)): 66/135 ≈ 0.489
      ├── Some((7, 0)): 4/12 ≈ 0.333
      ├── Some((7, 2)): 4/12 ≈ 0.333
      ├── Some((7, 3)): 14/23 ≈ 0.609
      ├── Some((7, 4)): 12/21 ≈ 0.571
      ├── Some((7, 5)): 8/17 ≈ 0.471
      ├── Some((7, 6)): 4/12 ≈ 0.333
      ├── Some((7, 7)): 8/17 ≈ 0.471
      └── Some((7, 8)): 11/20 ≈ 0.550
    └── Some((6, 8)): 50/111 ≈ 0.450
      ├── Some((8, 0)): 3/9 ≈ 0.333
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 1/7 ≈ 0.143
      ├── Some((8, 3)): 6/13 ≈ 0.462
      ├── Some((8, 4)): 4/11 ≈ 0.364
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 8/15 ≈ 0.533
      ├── Some((8, 7)): 5/12 ≈ 0.417
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((1, 7)): 647/1247 ≈ 0.519
    ├── Some((7, 0)): 57/120 ≈ 0.475
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 2)): 12/19 ≈ 0.632
      ├── Some((0, 3)): 4/11 ≈ 0.364
      ├── Some((0, 4)): 0/6 ≈ 0.000
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 16/23 ≈ 0.696
      ├── Some((0, 7)): 3/10 ≈ 0.300
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((7, 2)): 98/181 ≈ 0.541
      ├── Some((2, 0)): 6/15 ≈ 0.400
      ├── Some((2, 1)): 18/28 ≈ 0.643
      ├── Some((2, 2)): 6/15 ≈ 0.400
      ├── Some((2, 3)): 15/25 ≈ 0.600
      ├── Some((2, 4)): 12/21 ≈ 0.571
      ├── Some((2, 5)): 12/21 ≈ 0.571
      ├── Some((2, 6)): 8/17 ≈ 0.471
      ├── Some((2, 7)): 13/22 ≈ 0.591
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((7, 3)): 69/139 ≈ 0.496
      ├── Some((3, 0)): 4/11 ≈ 0.364
      ├── Some((3, 1)): 4/11 ≈ 0.364
      ├── Some((3, 2)): 7/15 ≈ 0.467
      ├── Some((3, 3)): 17/25 ≈ 0.680
      ├── Some((3, 4)): 9/17 ≈ 0.529
      ├── Some((3, 5)): 10/18 ≈ 0.556
      ├── Some((3, 6)): 5/12 ≈ 0.417
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((7, 4)): 68/137 ≈ 0.496
      ├── Some((4, 0)): 11/19 ≈ 0.579
      ├── Some((4, 1)): 0/6 ≈ 0.000
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 12/20 ≈ 0.600
      ├── Some((4, 4)): 4/11 ≈ 0.364
      ├── Some((4, 5)): 10/18 ≈ 0.556
      ├── Some((4, 6)): 9/17 ≈ 0.529
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 10/18 ≈ 0.556
    ├── Some((7, 5)): 114/204 ≈ 0.559
      ├── Some((5, 0)): 9/19 ≈ 0.474
      ├── Some((5, 1)): 17/27 ≈ 0.630
      ├── Some((5, 2)): 8/18 ≈ 0.444
      ├── Some((5, 3)): 8/18 ≈ 0.444
      ├── Some((5, 4)): 16/26 ≈ 0.615
      ├── Some((5, 5)): 14/24 ≈ 0.583
      ├── Some((5, 6)): 6/15 ≈ 0.400
      ├── Some((5, 7)): 17/27 ≈ 0.630
      └── Some((5, 8)): 19/29 ≈ 0.655
    ├── Some((7, 6)): 57/120 ≈ 0.475
      ├── Some((6, 0)): 2/9 ≈ 0.222
      ├── Some((6, 1)): 10/17 ≈ 0.588
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 3)): 11/18 ≈ 0.611
      ├── Some((6, 4)): 3/10 ≈ 0.300
      ├── Some((6, 5)): 8/15 ≈ 0.533
      ├── Some((6, 6)): 5/12 ≈ 0.417
      ├── Some((6, 7)): 6/13 ≈ 0.462
      └── Some((6, 8)): 4/11 ≈ 0.364
    ├── Some((7, 7)): 95/177 ≈ 0.537
      ├── Some((7, 0)): 12/24 ≈ 0.500
      ├── Some((7, 2)): 18/30 ≈ 0.600
      ├── Some((7, 3)): 21/34 ≈ 0.618
      ├── Some((7, 4)): 10/21 ≈ 0.476
      ├── Some((7, 5)): 14/26 ≈ 0.538
      ├── Some((7, 6)): 10/21 ≈ 0.476
      └── Some((7, 8)): 9/20 ≈ 0.450
    └── Some((7, 8)): 89/168 ≈ 0.530
      ├── Some((8, 0)): 13/22 ≈ 0.591
      ├── Some((8, 1)): 4/12 ≈ 0.333
      ├── Some((8, 2)): 2/10 ≈ 0.200
      ├── Some((8, 3)): 15/24 ≈ 0.625
      ├── Some((8, 4)): 14/23 ≈ 0.609
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 10/19 ≈ 0.526
      ├── Some((8, 7)): 13/22 ≈ 0.591
      └── Some((8, 8)): 11/20 ≈ 0.550
  └── Some((1, 8)): 618/1197 ≈ 0.516
    ├── Some((8, 0)): 86/158 ≈ 0.544
      ├── Some((0, 0)): 15/24 ≈ 0.625
      ├── Some((0, 1)): 16/24 ≈ 0.667
      ├── Some((0, 2)): 12/20 ≈ 0.600
      ├── Some((0, 3)): 3/11 ≈ 0.273
      ├── Some((0, 4)): 16/24 ≈ 0.667
      ├── Some((0, 5)): 6/14 ≈ 0.429
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 2/9 ≈ 0.222
      └── Some((0, 8)): 11/19 ≈ 0.579
    ├── Some((8, 1)): 64/127 ≈ 0.504
      ├── Some((1, 0)): 4/12 ≈ 0.333
      ├── Some((1, 1)): 22/31 ≈ 0.710
      ├── Some((1, 2)): 10/18 ≈ 0.556
      ├── Some((1, 3)): 9/17 ≈ 0.529
      ├── Some((1, 4)): 2/9 ≈ 0.222
      ├── Some((1, 5)): 9/17 ≈ 0.529
      ├── Some((1, 6)): 6/14 ≈ 0.429
      └── Some((1, 7)): 1/8 ≈ 0.125
    ├── Some((8, 2)): 85/157 ≈ 0.541
      ├── Some((2, 0)): 4/12 ≈ 0.333
      ├── Some((2, 1)): 10/18 ≈ 0.556
      ├── Some((2, 2)): 10/18 ≈ 0.556
      ├── Some((2, 3)): 11/19 ≈ 0.579
      ├── Some((2, 4)): 11/19 ≈ 0.579
      ├── Some((2, 5)): 3/10 ≈ 0.300
      ├── Some((2, 6)): 13/21 ≈ 0.619
      ├── Some((2, 7)): 12/20 ≈ 0.600
      └── Some((2, 8)): 11/19 ≈ 0.579
    ├── Some((8, 3)): 40/91 ≈ 0.440
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 6/12 ≈ 0.500
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 6/12 ≈ 0.500
      ├── Some((3, 4)): 8/13 ≈ 0.615
      ├── Some((3, 5)): 4/10 ≈ 0.400
      ├── Some((3, 6)): 3/8 ≈ 0.375
      ├── Some((3, 7)): 1/6 ≈ 0.167
      └── Some((3, 8)): 4/10 ≈ 0.400
    ├── Some((8, 4)): 51/107 ≈ 0.477
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 1)): 5/11 ≈ 0.455
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 7/13 ≈ 0.538
      ├── Some((4, 4)): 7/13 ≈ 0.538
      ├── Some((4, 5)): 10/16 ≈ 0.625
      ├── Some((4, 6)): 4/10 ≈ 0.400
      ├── Some((4, 7)): 8/15 ≈ 0.533
      └── Some((4, 8)): 2/8 ≈ 0.250
    ├── Some((8, 5)): 97/174 ≈ 0.557
      ├── Some((5, 0)): 1/8 ≈ 0.125
      ├── Some((5, 1)): 8/16 ≈ 0.500
      ├── Some((5, 2)): 24/32 ≈ 0.750
      ├── Some((5, 3)): 13/22 ≈ 0.591
      ├── Some((5, 4)): 9/18 ≈ 0.500
      ├── Some((5, 5)): 16/25 ≈ 0.640
      ├── Some((5, 6)): 9/18 ≈ 0.500
      ├── Some((5, 7)): 12/21 ≈ 0.571
      └── Some((5, 8)): 5/13 ≈ 0.385
    ├── Some((8, 6)): 85/157 ≈ 0.541
      ├── Some((6, 0)): 5/13 ≈ 0.385
      ├── Some((6, 1)): 6/14 ≈ 0.429
      ├── Some((6, 2)): 2/9 ≈ 0.222
      ├── Some((6, 3)): 16/25 ≈ 0.640
      ├── Some((6, 4)): 11/19 ≈ 0.579
      ├── Some((6, 5)): 10/18 ≈ 0.556
      ├── Some((6, 6)): 10/18 ≈ 0.556
      ├── Some((6, 7)): 18/26 ≈ 0.692
      └── Some((6, 8)): 6/14 ≈ 0.429
    ├── Some((8, 7)): 31/77 ≈ 0.403
      ├── Some((7, 0)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 1/6 ≈ 0.167
      ├── Some((7, 4)): 7/13 ≈ 0.538
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 2/8 ≈ 0.250
      ├── Some((7, 7)): 8/14 ≈ 0.571
      └── Some((7, 8)): 1/6 ≈ 0.167
    └── Some((8, 8)): 79/148 ≈ 0.534
      ├── Some((8, 0)): 15/24 ≈ 0.625
      ├── Some((8, 1)): 12/21 ≈ 0.571
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 10/19 ≈ 0.526
      ├── Some((8, 4)): 2/10 ≈ 0.200
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 12/21 ≈ 0.571
      └── Some((8, 7)): 12/21 ≈ 0.571
├── Some((7, 2)): 3416/6807 ≈ 0.502
  ├── Some((2, 0)): 375/749 ≈ 0.501
    ├── Some((0, 0)): 41/83 ≈ 0.494
      ├── Some((0, 1)): 2/7 ≈ 0.286
      ├── Some((0, 2)): 7/12 ≈ 0.583
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 7/12 ≈ 0.583
      └── Some((0, 8)): 8/13 ≈ 0.615
    ├── Some((0, 1)): 54/100 ≈ 0.540
      ├── Some((1, 0)): 6/11 ≈ 0.545
      ├── Some((1, 1)): 10/15 ≈ 0.667
      ├── Some((1, 2)): 5/10 ≈ 0.500
      ├── Some((1, 3)): 10/15 ≈ 0.667
      ├── Some((1, 4)): 4/9 ≈ 0.444
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 2/7 ≈ 0.286
      ├── Some((1, 7)): 5/10 ≈ 0.500
      └── Some((1, 8)): 10/15 ≈ 0.667
    ├── Some((0, 2)): 20/52 ≈ 0.385
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 2/6 ≈ 0.333
      ├── Some((2, 3)): 4/7 ≈ 0.571
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 2/6 ≈ 0.333
      ├── Some((2, 6)): 4/8 ≈ 0.500
      ├── Some((2, 7)): 2/6 ≈ 0.333
      └── Some((2, 8)): 4/8 ≈ 0.500
    ├── Some((0, 3)): 44/87 ≈ 0.506
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 9/13 ≈ 0.692
      ├── Some((3, 2)): 5/10 ≈ 0.500
      ├── Some((3, 3)): 4/9 ≈ 0.444
      ├── Some((3, 4)): 1/6 ≈ 0.167
      ├── Some((3, 5)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 7/11 ≈ 0.636
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 5/10 ≈ 0.500
    ├── Some((0, 4)): 46/89 ≈ 0.517
      ├── Some((4, 0)): 8/12 ≈ 0.667
      ├── Some((4, 1)): 1/6 ≈ 0.167
      ├── Some((4, 2)): 7/12 ≈ 0.583
      ├── Some((4, 3)): 8/12 ≈ 0.667
      ├── Some((4, 4)): 7/12 ≈ 0.583
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 2/7 ≈ 0.286
      ├── Some((4, 7)): 8/12 ≈ 0.667
      └── Some((4, 8)): 3/8 ≈ 0.375
    ├── Some((0, 5)): 36/75 ≈ 0.480
      ├── Some((5, 0)): 9/13 ≈ 0.692
      ├── Some((5, 1)): 4/8 ≈ 0.500
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 6/10 ≈ 0.600
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 4/8 ≈ 0.500
      ├── Some((5, 6)): 4/8 ≈ 0.500
      ├── Some((5, 7)): 0/4 ≈ 0.000
      └── Some((5, 8)): 4/8 ≈ 0.500
    ├── Some((0, 6)): 70/122 ≈ 0.574
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 10/16 ≈ 0.625
      ├── Some((6, 2)): 14/19 ≈ 0.737
      ├── Some((6, 3)): 11/17 ≈ 0.647
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 16/21 ≈ 0.762
    ├── Some((0, 7)): 39/80 ≈ 0.488
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 3)): 7/12 ≈ 0.583
      ├── Some((7, 4)): 2/7 ≈ 0.286
      ├── Some((7, 5)): 7/12 ≈ 0.583
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 8/13 ≈ 0.615
    └── Some((0, 8)): 25/60 ≈ 0.417
      ├── Some((8, 0)): 1/5 ≈ 0.200
      ├── Some((8, 1)): 2/6 ≈ 0.333
      ├── Some((8, 2)): 7/10 ≈ 0.700
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 6/9 ≈ 0.667
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 1/5 ≈ 0.200
      └── Some((8, 8)): 3/7 ≈ 0.429
  ├── Some((2, 1)): 442/864 ≈ 0.512
    ├── Some((1, 0)): 39/82 ≈ 0.476
      ├── Some((0, 0)): 0/4 ≈ 0.000
      ├── Some((0, 1)): 6/11 ≈ 0.545
      ├── Some((0, 2)): 1/6 ≈ 0.167
      ├── Some((0, 3)): 5/10 ≈ 0.500
      ├── Some((0, 4)): 5/10 ≈ 0.500
      ├── Some((0, 5)): 4/9 ≈ 0.444
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 9/13 ≈ 0.692
      └── Some((0, 8)): 8/12 ≈ 0.667
    ├── Some((1, 1)): 76/133 ≈ 0.571
      ├── Some((1, 0)): 13/20 ≈ 0.650
      ├── Some((1, 2)): 6/13 ≈ 0.462
      ├── Some((1, 3)): 11/18 ≈ 0.611
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 14/21 ≈ 0.667
      ├── Some((1, 6)): 8/15 ≈ 0.533
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 9/16 ≈ 0.562
    ├── Some((1, 2)): 79/138 ≈ 0.572
      ├── Some((2, 0)): 4/11 ≈ 0.364
      ├── Some((2, 2)): 9/17 ≈ 0.529
      ├── Some((2, 3)): 13/21 ≈ 0.619
      ├── Some((2, 4)): 19/26 ≈ 0.731
      ├── Some((2, 5)): 15/22 ≈ 0.682
      ├── Some((2, 6)): 10/18 ≈ 0.556
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 2/9 ≈ 0.222
    ├── Some((1, 3)): 34/75 ≈ 0.453
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 4/9 ≈ 0.444
      ├── Some((3, 2)): 4/9 ≈ 0.444
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 2/7 ≈ 0.286
      ├── Some((3, 5)): 7/11 ≈ 0.636
      ├── Some((3, 6)): 0/4 ≈ 0.000
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 6/10 ≈ 0.600
    ├── Some((1, 4)): 47/93 ≈ 0.505
      ├── Some((4, 0)): 1/6 ≈ 0.167
      ├── Some((4, 1)): 3/8 ≈ 0.375
      ├── Some((4, 2)): 3/8 ≈ 0.375
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 10/15 ≈ 0.667
      ├── Some((4, 5)): 9/14 ≈ 0.643
      ├── Some((4, 6)): 7/12 ≈ 0.583
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 2/7 ≈ 0.286
    ├── Some((1, 5)): 46/92 ≈ 0.500
      ├── Some((5, 0)): 5/10 ≈ 0.500
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 5/10 ≈ 0.500
      ├── Some((5, 3)): 5/10 ≈ 0.500
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 0/5 ≈ 0.000
      ├── Some((5, 6)): 4/9 ≈ 0.444
      ├── Some((5, 7)): 15/20 ≈ 0.750
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((1, 6)): 41/85 ≈ 0.482
      ├── Some((6, 0)): 6/10 ≈ 0.600
      ├── Some((6, 1)): 6/11 ≈ 0.545
      ├── Some((6, 2)): 3/8 ≈ 0.375
      ├── Some((6, 3)): 6/11 ≈ 0.545
      ├── Some((6, 4)): 6/11 ≈ 0.545
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 4/9 ≈ 0.444
    ├── Some((1, 7)): 49/96 ≈ 0.510
      ├── Some((7, 0)): 11/16 ≈ 0.688
      ├── Some((7, 1)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 7/13 ≈ 0.538
      ├── Some((7, 4)): 2/8 ≈ 0.250
      ├── Some((7, 5)): 11/16 ≈ 0.688
      ├── Some((7, 6)): 6/12 ≈ 0.500
      ├── Some((7, 7)): 3/9 ≈ 0.333
      └── Some((7, 8)): 4/10 ≈ 0.400
    └── Some((1, 8)): 30/69 ≈ 0.435
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 3/8 ≈ 0.375
      ├── Some((8, 2)): 4/8 ≈ 0.500
      ├── Some((8, 3)): 2/6 ≈ 0.333
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 6/10 ≈ 0.600
      ├── Some((8, 6)): 5/9 ≈ 0.556
      ├── Some((8, 7)): 2/7 ≈ 0.286
      └── Some((8, 8)): 4/8 ≈ 0.500
  ├── Some((2, 2)): 502/965 ≈ 0.520
    ├── Some((2, 0)): 78/142 ≈ 0.549
      ├── Some((0, 0)): 5/12 ≈ 0.417
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 2)): 0/6 ≈ 0.000
      ├── Some((0, 3)): 10/17 ≈ 0.588
      ├── Some((0, 4)): 11/19 ≈ 0.579
      ├── Some((0, 5)): 9/16 ≈ 0.562
      ├── Some((0, 6)): 9/16 ≈ 0.562
      ├── Some((0, 7)): 9/16 ≈ 0.562
      └── Some((0, 8)): 16/23 ≈ 0.696
    ├── Some((2, 1)): 58/114 ≈ 0.509
      ├── Some((1, 0)): 12/18 ≈ 0.667
      ├── Some((1, 1)): 2/8 ≈ 0.250
      ├── Some((1, 2)): 8/15 ≈ 0.533
      ├── Some((1, 3)): 6/12 ≈ 0.500
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 3/9 ≈ 0.333
      ├── Some((1, 6)): 11/17 ≈ 0.647
      ├── Some((1, 7)): 10/16 ≈ 0.625
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((2, 3)): 71/132 ≈ 0.538
      ├── Some((3, 0)): 11/18 ≈ 0.611
      ├── Some((3, 1)): 12/19 ≈ 0.632
      ├── Some((3, 2)): 2/8 ≈ 0.250
      ├── Some((3, 3)): 3/10 ≈ 0.300
      ├── Some((3, 4)): 2/8 ≈ 0.250
      ├── Some((3, 5)): 15/21 ≈ 0.714
      ├── Some((3, 6)): 15/22 ≈ 0.682
      ├── Some((3, 7)): 4/11 ≈ 0.364
      └── Some((3, 8)): 7/14 ≈ 0.500
    ├── Some((2, 4)): 44/94 ≈ 0.468
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 1)): 7/13 ≈ 0.538
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 7/13 ≈ 0.538
      ├── Some((4, 4)): 6/12 ≈ 0.500
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 10/15 ≈ 0.667
      ├── Some((4, 7)): 2/7 ≈ 0.286
      └── Some((4, 8)): 1/6 ≈ 0.167
    ├── Some((2, 5)): 71/133 ≈ 0.534
      ├── Some((5, 0)): 4/11 ≈ 0.364
      ├── Some((5, 1)): 12/19 ≈ 0.632
      ├── Some((5, 2)): 7/14 ≈ 0.500
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 13/20 ≈ 0.650
      ├── Some((5, 5)): 3/10 ≈ 0.300
      ├── Some((5, 6)): 19/26 ≈ 0.731
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 2/8 ≈ 0.250
    ├── Some((2, 6)): 56/111 ≈ 0.505
      ├── Some((6, 0)): 10/16 ≈ 0.625
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 8/14 ≈ 0.571
      ├── Some((6, 5)): 8/14 ≈ 0.571
      ├── Some((6, 6)): 4/10 ≈ 0.400
      ├── Some((6, 7)): 8/14 ≈ 0.571
      └── Some((6, 8)): 5/11 ≈ 0.455
    ├── Some((2, 7)): 62/120 ≈ 0.517
      ├── Some((7, 0)): 13/20 ≈ 0.650
      ├── Some((7, 1)): 13/20 ≈ 0.650
      ├── Some((7, 3)): 8/15 ≈ 0.533
      ├── Some((7, 4)): 10/18 ≈ 0.556
      ├── Some((7, 5)): 10/18 ≈ 0.556
      ├── Some((7, 6)): 4/11 ≈ 0.364
      ├── Some((7, 7)): 1/7 ≈ 0.143
      └── Some((7, 8)): 3/10 ≈ 0.300
    └── Some((2, 8)): 61/118 ≈ 0.517
      ├── Some((8, 0)): 10/16 ≈ 0.625
      ├── Some((8, 1)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 1/7 ≈ 0.143
      ├── Some((8, 3)): 10/16 ≈ 0.625
      ├── Some((8, 4)): 6/12 ≈ 0.500
      ├── Some((8, 5)): 7/14 ≈ 0.500
      ├── Some((8, 6)): 6/12 ≈ 0.500
      ├── Some((8, 7)): 5/11 ≈ 0.455
      └── Some((8, 8)): 8/14 ≈ 0.571
  ├── Some((2, 3)): 264/557 ≈ 0.474
    ├── Some((3, 0)): 49/89 ≈ 0.551
      ├── Some((0, 0)): 5/9 ≈ 0.556
      ├── Some((0, 1)): 5/10 ≈ 0.500
      ├── Some((0, 2)): 5/10 ≈ 0.500
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 8/12 ≈ 0.667
      ├── Some((0, 5)): 3/8 ≈ 0.375
      ├── Some((0, 6)): 6/10 ≈ 0.600
      ├── Some((0, 7)): 6/10 ≈ 0.600
      └── Some((0, 8)): 6/10 ≈ 0.600
    ├── Some((3, 1)): 41/78 ≈ 0.526
      ├── Some((1, 0)): 9/13 ≈ 0.692
      ├── Some((1, 1)): 2/6 ≈ 0.333
      ├── Some((1, 2)): 3/7 ≈ 0.429
      ├── Some((1, 3)): 1/5 ≈ 0.200
      ├── Some((1, 4)): 5/9 ≈ 0.556
      ├── Some((1, 5)): 4/8 ≈ 0.500
      ├── Some((1, 6)): 5/9 ≈ 0.556
      ├── Some((1, 7)): 8/12 ≈ 0.667
      └── Some((1, 8)): 3/8 ≈ 0.375
    ├── Some((3, 2)): 34/69 ≈ 0.493
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 4/8 ≈ 0.500
      ├── Some((2, 2)): 5/9 ≈ 0.556
      ├── Some((2, 4)): 5/9 ≈ 0.556
      ├── Some((2, 5)): 4/8 ≈ 0.500
      ├── Some((2, 6)): 11/15 ≈ 0.733
      ├── Some((2, 7)): 1/5 ≈ 0.200
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((3, 3)): 12/37 ≈ 0.324
      ├── Some((3, 0)): 0/3 ≈ 0.000
      ├── Some((3, 1)): 2/5 ≈ 0.400
      ├── Some((3, 2)): 2/5 ≈ 0.400
      ├── Some((3, 4)): 2/6 ≈ 0.333
      ├── Some((3, 5)): 0/3 ≈ 0.000
      ├── Some((3, 6)): 0/3 ≈ 0.000
      ├── Some((3, 7)): 1/4 ≈ 0.250
      └── Some((3, 8)): 4/7 ≈ 0.571
    ├── Some((3, 4)): 24/55 ≈ 0.436
      ├── Some((4, 0)): 0/3 ≈ 0.000
      ├── Some((4, 1)): 4/7 ≈ 0.571
      ├── Some((4, 2)): 2/6 ≈ 0.333
      ├── Some((4, 3)): 4/7 ≈ 0.571
      ├── Some((4, 4)): 3/6 ≈ 0.500
      ├── Some((4, 5)): 3/6 ≈ 0.500
      ├── Some((4, 6)): 2/6 ≈ 0.333
      ├── Some((4, 7)): 5/8 ≈ 0.625
      └── Some((4, 8)): 1/5 ≈ 0.200
    ├── Some((3, 5)): 26/57 ≈ 0.456
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 4/7 ≈ 0.571
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 3/6 ≈ 0.500
      ├── Some((5, 4)): 5/8 ≈ 0.625
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 2/6 ≈ 0.333
      ├── Some((5, 7)): 3/6 ≈ 0.500
      └── Some((5, 8)): 4/7 ≈ 0.571
    ├── Some((3, 6)): 15/41 ≈ 0.366
      ├── Some((6, 0)): 3/5 ≈ 0.600
      ├── Some((6, 1)): 0/3 ≈ 0.000
      ├── Some((6, 2)): 1/4 ≈ 0.250
      ├── Some((6, 3)): 1/4 ≈ 0.250
      ├── Some((6, 4)): 4/6 ≈ 0.667
      ├── Some((6, 5)): 0/3 ≈ 0.000
      ├── Some((6, 6)): 2/5 ≈ 0.400
      ├── Some((6, 7)): 3/6 ≈ 0.500
      └── Some((6, 8)): 1/4 ≈ 0.250
    ├── Some((3, 7)): 37/73 ≈ 0.507
      ├── Some((7, 0)): 5/9 ≈ 0.556
      ├── Some((7, 1)): 1/5 ≈ 0.200
      ├── Some((7, 3)): 7/11 ≈ 0.636
      ├── Some((7, 4)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 6/10 ≈ 0.600
      ├── Some((7, 6)): 6/10 ≈ 0.600
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 5/10 ≈ 0.500
    └── Some((3, 8)): 26/57 ≈ 0.456
      ├── Some((8, 0)): 3/6 ≈ 0.500
      ├── Some((8, 1)): 4/7 ≈ 0.571
      ├── Some((8, 2)): 3/6 ≈ 0.500
      ├── Some((8, 3)): 2/6 ≈ 0.333
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 3/6 ≈ 0.500
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 3/6 ≈ 0.500
      └── Some((8, 8)): 3/7 ≈ 0.429
  ├── Some((2, 4)): 302/623 ≈ 0.485
    ├── Some((4, 0)): 38/75 ≈ 0.507
      ├── Some((0, 0)): 7/11 ≈ 0.636
      ├── Some((0, 1)): 3/7 ≈ 0.429
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 8/12 ≈ 0.667
      ├── Some((0, 4)): 6/10 ≈ 0.600
      ├── Some((0, 5)): 0/4 ≈ 0.000
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 5/9 ≈ 0.556
    ├── Some((4, 1)): 31/66 ≈ 0.470
      ├── Some((1, 0)): 3/7 ≈ 0.429
      ├── Some((1, 1)): 4/8 ≈ 0.500
      ├── Some((1, 2)): 1/5 ≈ 0.200
      ├── Some((1, 3)): 6/9 ≈ 0.667
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 4/8 ≈ 0.500
      ├── Some((1, 6)): 3/7 ≈ 0.429
      ├── Some((1, 7)): 1/5 ≈ 0.200
      └── Some((1, 8)): 4/8 ≈ 0.500
    ├── Some((4, 2)): 41/80 ≈ 0.512
      ├── Some((2, 0)): 5/10 ≈ 0.500
      ├── Some((2, 1)): 4/9 ≈ 0.444
      ├── Some((2, 2)): 5/10 ≈ 0.500
      ├── Some((2, 3)): 10/14 ≈ 0.714
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 3/8 ≈ 0.375
      ├── Some((2, 7)): 4/9 ≈ 0.444
      └── Some((2, 8)): 6/11 ≈ 0.545
    ├── Some((4, 3)): 23/54 ≈ 0.426
      ├── Some((3, 0)): 0/3 ≈ 0.000
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 4/7 ≈ 0.571
      ├── Some((3, 3)): 1/5 ≈ 0.200
      ├── Some((3, 4)): 2/5 ≈ 0.400
      ├── Some((3, 5)): 5/8 ≈ 0.625
      ├── Some((3, 6)): 2/6 ≈ 0.333
      ├── Some((3, 7)): 5/8 ≈ 0.625
      └── Some((3, 8)): 2/6 ≈ 0.333
    ├── Some((4, 4)): 57/101 ≈ 0.564
      ├── Some((4, 0)): 13/18 ≈ 0.722
      ├── Some((4, 1)): 7/12 ≈ 0.583
      ├── Some((4, 2)): 7/12 ≈ 0.583
      ├── Some((4, 3)): 5/11 ≈ 0.455
      ├── Some((4, 5)): 7/13 ≈ 0.538
      ├── Some((4, 6)): 3/9 ≈ 0.333
      ├── Some((4, 7)): 10/15 ≈ 0.667
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((4, 5)): 31/66 ≈ 0.470
      ├── Some((5, 0)): 0/4 ≈ 0.000
      ├── Some((5, 1)): 3/7 ≈ 0.429
      ├── Some((5, 2)): 6/9 ≈ 0.667
      ├── Some((5, 3)): 2/6 ≈ 0.333
      ├── Some((5, 4)): 8/11 ≈ 0.727
      ├── Some((5, 5)): 4/8 ≈ 0.500
      ├── Some((5, 6)): 4/8 ≈ 0.500
      ├── Some((5, 7)): 4/8 ≈ 0.500
      └── Some((5, 8)): 0/4 ≈ 0.000
    ├── Some((4, 6)): 32/67 ≈ 0.478
      ├── Some((6, 0)): 3/7 ≈ 0.429
      ├── Some((6, 1)): 2/6 ≈ 0.333
      ├── Some((6, 2)): 1/5 ≈ 0.200
      ├── Some((6, 3)): 4/8 ≈ 0.500
      ├── Some((6, 4)): 2/6 ≈ 0.333
      ├── Some((6, 5)): 5/9 ≈ 0.556
      ├── Some((6, 6)): 3/7 ≈ 0.429
      ├── Some((6, 7)): 6/9 ≈ 0.667
      └── Some((6, 8)): 5/9 ≈ 0.556
    ├── Some((4, 7)): 26/59 ≈ 0.441
      ├── Some((7, 0)): 1/5 ≈ 0.200
      ├── Some((7, 1)): 3/7 ≈ 0.429
      ├── Some((7, 3)): 6/10 ≈ 0.600
      ├── Some((7, 4)): 2/6 ≈ 0.333
      ├── Some((7, 5)): 1/5 ≈ 0.200
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 2/6 ≈ 0.333
      └── Some((7, 8)): 7/11 ≈ 0.636
    └── Some((4, 8)): 23/54 ≈ 0.426
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 0/3 ≈ 0.000
      ├── Some((8, 2)): 3/6 ≈ 0.500
      ├── Some((8, 3)): 2/6 ≈ 0.333
      ├── Some((8, 4)): 2/6 ≈ 0.333
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 0/3 ≈ 0.000
      ├── Some((8, 7)): 4/7 ≈ 0.571
      └── Some((8, 8)): 9/11 ≈ 0.818
  ├── Some((2, 5)): 362/727 ≈ 0.498
    ├── Some((5, 0)): 38/78 ≈ 0.487
      ├── Some((0, 0)): 4/9 ≈ 0.444
      ├── Some((0, 1)): 5/9 ≈ 0.556
      ├── Some((0, 2)): 8/12 ≈ 0.667
      ├── Some((0, 3)): 6/10 ≈ 0.600
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 6/10 ≈ 0.600
      ├── Some((0, 6)): 5/9 ≈ 0.556
      ├── Some((0, 7)): 1/6 ≈ 0.167
      └── Some((0, 8)): 0/4 ≈ 0.000
    ├── Some((5, 1)): 48/92 ≈ 0.522
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 0/5 ≈ 0.000
      ├── Some((1, 2)): 14/18 ≈ 0.778
      ├── Some((1, 3)): 8/12 ≈ 0.667
      ├── Some((1, 4)): 0/5 ≈ 0.000
      ├── Some((1, 5)): 6/11 ≈ 0.545
      ├── Some((1, 6)): 8/13 ≈ 0.615
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 8/13 ≈ 0.615
    ├── Some((5, 2)): 44/86 ≈ 0.512
      ├── Some((2, 0)): 5/11 ≈ 0.455
      ├── Some((2, 1)): 1/6 ≈ 0.167
      ├── Some((2, 2)): 19/23 ≈ 0.826
      ├── Some((2, 3)): 7/12 ≈ 0.583
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 2/7 ≈ 0.286
      └── Some((2, 8)): 4/9 ≈ 0.444
    ├── Some((5, 3)): 30/66 ≈ 0.455
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 2/6 ≈ 0.333
      ├── Some((3, 2)): 1/5 ≈ 0.200
      ├── Some((3, 3)): 3/7 ≈ 0.429
      ├── Some((3, 4)): 3/7 ≈ 0.429
      ├── Some((3, 5)): 2/6 ≈ 0.333
      ├── Some((3, 6)): 6/10 ≈ 0.600
      ├── Some((3, 7)): 4/8 ≈ 0.500
      └── Some((3, 8)): 2/6 ≈ 0.333
    ├── Some((5, 4)): 41/82 ≈ 0.500
      ├── Some((4, 0)): 3/8 ≈ 0.375
      ├── Some((4, 1)): 5/9 ≈ 0.556
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 1/6 ≈ 0.167
      ├── Some((4, 4)): 5/9 ≈ 0.556
      ├── Some((4, 5)): 6/10 ≈ 0.600
      ├── Some((4, 6)): 5/10 ≈ 0.500
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 4/9 ≈ 0.444
    ├── Some((5, 5)): 34/72 ≈ 0.472
      ├── Some((5, 0)): 3/8 ≈ 0.375
      ├── Some((5, 1)): 6/10 ≈ 0.600
      ├── Some((5, 2)): 7/11 ≈ 0.636
      ├── Some((5, 3)): 3/8 ≈ 0.375
      ├── Some((5, 4)): 8/12 ≈ 0.667
      ├── Some((5, 6)): 3/8 ≈ 0.375
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 1/6 ≈ 0.167
    ├── Some((5, 6)): 62/110 ≈ 0.564
      ├── Some((6, 0)): 7/12 ≈ 0.583
      ├── Some((6, 1)): 10/15 ≈ 0.667
      ├── Some((6, 2)): 13/18 ≈ 0.722
      ├── Some((6, 3)): 6/11 ≈ 0.545
      ├── Some((6, 4)): 6/11 ≈ 0.545
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 3/8 ≈ 0.375
      ├── Some((6, 7)): 5/11 ≈ 0.455
      └── Some((6, 8)): 6/12 ≈ 0.500
    ├── Some((5, 7)): 43/85 ≈ 0.506
      ├── Some((7, 0)): 2/7 ≈ 0.286
      ├── Some((7, 1)): 4/9 ≈ 0.444
      ├── Some((7, 3)): 9/14 ≈ 0.643
      ├── Some((7, 4)): 1/6 ≈ 0.167
      ├── Some((7, 5)): 4/9 ≈ 0.444
      ├── Some((7, 6)): 10/15 ≈ 0.667
      ├── Some((7, 7)): 6/12 ≈ 0.500
      └── Some((7, 8)): 6/12 ≈ 0.500
    └── Some((5, 8)): 22/55 ≈ 0.400
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 3/6 ≈ 0.500
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 5/8 ≈ 0.625
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 0/4 ≈ 0.000
      ├── Some((8, 7)): 5/8 ≈ 0.625
      └── Some((8, 8)): 3/7 ≈ 0.429
  ├── Some((2, 6)): 335/680 ≈ 0.493
    ├── Some((6, 0)): 27/61 ≈ 0.443
      ├── Some((0, 0)): 4/7 ≈ 0.571
      ├── Some((0, 1)): 1/5 ≈ 0.200
      ├── Some((0, 2)): 3/7 ≈ 0.429
      ├── Some((0, 3)): 1/5 ≈ 0.200
      ├── Some((0, 4)): 5/8 ≈ 0.625
      ├── Some((0, 5)): 3/7 ≈ 0.429
      ├── Some((0, 6)): 2/6 ≈ 0.333
      ├── Some((0, 7)): 4/7 ≈ 0.571
      └── Some((0, 8)): 4/8 ≈ 0.500
    ├── Some((6, 1)): 46/88 ≈ 0.523
      ├── Some((1, 0)): 5/10 ≈ 0.500
      ├── Some((1, 1)): 8/12 ≈ 0.667
      ├── Some((1, 2)): 6/10 ≈ 0.600
      ├── Some((1, 3)): 4/9 ≈ 0.444
      ├── Some((1, 4)): 14/17 ≈ 0.824
      ├── Some((1, 5)): 3/8 ≈ 0.375
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 1/6 ≈ 0.167
      └── Some((1, 8)): 2/7 ≈ 0.286
    ├── Some((6, 2)): 55/100 ≈ 0.550
      ├── Some((2, 0)): 10/15 ≈ 0.667
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 8/14 ≈ 0.571
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 7)): 10/15 ≈ 0.667
      └── Some((2, 8)): 11/16 ≈ 0.688
    ├── Some((6, 3)): 16/45 ≈ 0.356
      ├── Some((3, 0)): 3/6 ≈ 0.500
      ├── Some((3, 1)): 3/6 ≈ 0.500
      ├── Some((3, 2)): 2/5 ≈ 0.400
      ├── Some((3, 3)): 2/5 ≈ 0.400
      ├── Some((3, 4)): 2/5 ≈ 0.400
      ├── Some((3, 5)): 1/4 ≈ 0.250
      ├── Some((3, 6)): 0/3 ≈ 0.000
      ├── Some((3, 7)): 1/5 ≈ 0.200
      └── Some((3, 8)): 1/5 ≈ 0.200
    ├── Some((6, 4)): 38/77 ≈ 0.494
      ├── Some((4, 0)): 6/10 ≈ 0.600
      ├── Some((4, 1)): 4/8 ≈ 0.500
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 6/10 ≈ 0.600
      ├── Some((4, 4)): 2/7 ≈ 0.286
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 7/11 ≈ 0.636
      └── Some((4, 8)): 1/5 ≈ 0.200
    ├── Some((6, 5)): 36/74 ≈ 0.486
      ├── Some((5, 0)): 8/12 ≈ 0.667
      ├── Some((5, 1)): 3/7 ≈ 0.429
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 7/11 ≈ 0.636
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 2/6 ≈ 0.333
      ├── Some((5, 6)): 5/9 ≈ 0.556
      ├── Some((5, 7)): 1/5 ≈ 0.200
      └── Some((5, 8)): 5/9 ≈ 0.556
    ├── Some((6, 6)): 55/100 ≈ 0.550
      ├── Some((6, 0)): 10/15 ≈ 0.667
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 9/15 ≈ 0.600
      ├── Some((6, 3)): 3/9 ≈ 0.333
      ├── Some((6, 4)): 10/15 ≈ 0.667
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 7)): 10/15 ≈ 0.667
      └── Some((6, 8)): 6/12 ≈ 0.500
    ├── Some((6, 7)): 33/70 ≈ 0.471
      ├── Some((7, 0)): 4/9 ≈ 0.444
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 3)): 6/10 ≈ 0.600
      ├── Some((7, 4)): 0/4 ≈ 0.000
      ├── Some((7, 5)): 6/10 ≈ 0.600
      ├── Some((7, 6)): 1/6 ≈ 0.167
      ├── Some((7, 7)): 5/10 ≈ 0.500
      └── Some((7, 8)): 6/10 ≈ 0.600
    └── Some((6, 8)): 29/64 ≈ 0.453
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 1/5 ≈ 0.200
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 5/9 ≈ 0.556
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 12/15 ≈ 0.800
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 3/7 ≈ 0.429
      └── Some((8, 8)): 1/5 ≈ 0.200
  ├── Some((2, 7)): 329/670 ≈ 0.491
    ├── Some((7, 0)): 23/57 ≈ 0.404
      ├── Some((0, 0)): 2/6 ≈ 0.333
      ├── Some((0, 1)): 3/6 ≈ 0.500
      ├── Some((0, 2)): 3/6 ≈ 0.500
      ├── Some((0, 3)): 3/7 ≈ 0.429
      ├── Some((0, 4)): 1/5 ≈ 0.200
      ├── Some((0, 5)): 2/6 ≈ 0.333
      ├── Some((0, 6)): 4/7 ≈ 0.571
      ├── Some((0, 7)): 3/7 ≈ 0.429
      └── Some((0, 8)): 2/6 ≈ 0.333
    ├── Some((7, 1)): 45/90 ≈ 0.500
      ├── Some((1, 0)): 8/13 ≈ 0.615
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 1/6 ≈ 0.167
      ├── Some((1, 3)): 5/10 ≈ 0.500
      ├── Some((1, 4)): 7/12 ≈ 0.583
      ├── Some((1, 5)): 5/10 ≈ 0.500
      ├── Some((1, 6)): 9/13 ≈ 0.692
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 6/11 ≈ 0.545
    ├── Some((7, 3)): 34/74 ≈ 0.459
      ├── Some((3, 0)): 9/13 ≈ 0.692
      ├── Some((3, 1)): 0/4 ≈ 0.000
      ├── Some((3, 2)): 1/5 ≈ 0.200
      ├── Some((3, 3)): 9/13 ≈ 0.692
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 1/6 ≈ 0.167
      ├── Some((3, 6)): 8/12 ≈ 0.667
      ├── Some((3, 7)): 1/6 ≈ 0.167
      └── Some((3, 8)): 1/6 ≈ 0.167
    ├── Some((7, 4)): 28/65 ≈ 0.431
      ├── Some((4, 0)): 4/8 ≈ 0.500
      ├── Some((4, 1)): 5/9 ≈ 0.556
      ├── Some((4, 2)): 4/8 ≈ 0.500
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 0/4 ≈ 0.000
      ├── Some((4, 5)): 2/6 ≈ 0.333
      ├── Some((4, 6)): 4/8 ≈ 0.500
      ├── Some((4, 7)): 6/10 ≈ 0.600
      └── Some((4, 8)): 2/6 ≈ 0.333
    ├── Some((7, 5)): 42/85 ≈ 0.494
      ├── Some((5, 0)): 5/10 ≈ 0.500
      ├── Some((5, 1)): 4/9 ≈ 0.444
      ├── Some((5, 2)): 10/14 ≈ 0.714
      ├── Some((5, 3)): 2/7 ≈ 0.286
      ├── Some((5, 4)): 2/7 ≈ 0.286
      ├── Some((5, 5)): 0/4 ≈ 0.000
      ├── Some((5, 6)): 6/11 ≈ 0.545
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 7/11 ≈ 0.636
    ├── Some((7, 6)): 38/80 ≈ 0.475
      ├── Some((6, 0)): 3/8 ≈ 0.375
      ├── Some((6, 1)): 5/10 ≈ 0.500
      ├── Some((6, 2)): 6/10 ≈ 0.600
      ├── Some((6, 3)): 11/15 ≈ 0.733
      ├── Some((6, 4)): 4/9 ≈ 0.444
      ├── Some((6, 5)): 1/6 ≈ 0.167
      ├── Some((6, 6)): 3/8 ≈ 0.375
      ├── Some((6, 7)): 0/4 ≈ 0.000
      └── Some((6, 8)): 4/9 ≈ 0.444
    ├── Some((7, 7)): 73/128 ≈ 0.570
      ├── Some((7, 0)): 17/25 ≈ 0.680
      ├── Some((7, 1)): 4/11 ≈ 0.364
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 18/26 ≈ 0.692
      ├── Some((7, 5)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 9/17 ≈ 0.529
      └── Some((7, 8)): 11/19 ≈ 0.579
    └── Some((7, 8)): 45/90 ≈ 0.500
      ├── Some((8, 0)): 1/6 ≈ 0.167
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 10/14 ≈ 0.714
      ├── Some((8, 3)): 9/14 ≈ 0.643
      ├── Some((8, 4)): 9/14 ≈ 0.643
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 3/8 ≈ 0.375
      ├── Some((8, 7)): 5/10 ≈ 0.500
      └── Some((8, 8)): 0/5 ≈ 0.000
  └── Some((2, 8)): 505/971 ≈ 0.520
    ├── Some((8, 0)): 44/91 ≈ 0.484
      ├── Some((0, 0)): 8/13 ≈ 0.615
      ├── Some((0, 1)): 1/6 ≈ 0.167
      ├── Some((0, 2)): 0/5 ≈ 0.000
      ├── Some((0, 3)): 7/12 ≈ 0.583
      ├── Some((0, 4)): 11/16 ≈ 0.688
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 6/12 ≈ 0.500
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 7/12 ≈ 0.583
    ├── Some((8, 1)): 63/118 ≈ 0.534
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 0/6 ≈ 0.000
      ├── Some((1, 2)): 8/15 ≈ 0.533
      ├── Some((1, 3)): 11/17 ≈ 0.647
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 11/17 ≈ 0.647
      ├── Some((1, 6)): 4/10 ≈ 0.400
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 16/22 ≈ 0.727
    ├── Some((8, 2)): 59/112 ≈ 0.527
      ├── Some((2, 0)): 11/18 ≈ 0.611
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 10/17 ≈ 0.588
      ├── Some((2, 4)): 2/8 ≈ 0.250
      ├── Some((2, 5)): 13/20 ≈ 0.650
      ├── Some((2, 6)): 4/10 ≈ 0.400
      └── Some((2, 7)): 9/16 ≈ 0.562
    ├── Some((8, 3)): 27/66 ≈ 0.409
      ├── Some((3, 0)): 1/5 ≈ 0.200
      ├── Some((3, 1)): 6/10 ≈ 0.600
      ├── Some((3, 2)): 4/8 ≈ 0.500
      ├── Some((3, 3)): 3/8 ≈ 0.375
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 2/7 ≈ 0.286
      ├── Some((3, 6)): 1/5 ≈ 0.200
      ├── Some((3, 7)): 0/4 ≈ 0.000
      └── Some((3, 8)): 6/10 ≈ 0.600
    ├── Some((8, 4)): 76/135 ≈ 0.563
      ├── Some((4, 0)): 0/6 ≈ 0.000
      ├── Some((4, 1)): 16/22 ≈ 0.727
      ├── Some((4, 2)): 7/14 ≈ 0.500
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 4)): 2/8 ≈ 0.250
      ├── Some((4, 5)): 16/22 ≈ 0.727
      ├── Some((4, 6)): 13/19 ≈ 0.684
      ├── Some((4, 7)): 10/17 ≈ 0.588
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((8, 5)): 74/133 ≈ 0.556
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 7/14 ≈ 0.500
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 8/15 ≈ 0.533
      ├── Some((5, 6)): 11/17 ≈ 0.647
      ├── Some((5, 7)): 11/17 ≈ 0.647
      └── Some((5, 8)): 10/16 ≈ 0.625
    ├── Some((8, 6)): 46/94 ≈ 0.489
      ├── Some((6, 0)): 7/12 ≈ 0.583
      ├── Some((6, 1)): 2/7 ≈ 0.286
      ├── Some((6, 2)): 7/12 ≈ 0.583
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 7/13 ≈ 0.538
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 10/15 ≈ 0.667
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((8, 7)): 65/120 ≈ 0.542
      ├── Some((7, 0)): 7/14 ≈ 0.500
      ├── Some((7, 1)): 14/21 ≈ 0.667
      ├── Some((7, 3)): 3/10 ≈ 0.300
      ├── Some((7, 4)): 1/7 ≈ 0.143
      ├── Some((7, 5)): 11/18 ≈ 0.611
      ├── Some((7, 6)): 13/20 ≈ 0.650
      ├── Some((7, 7)): 6/13 ≈ 0.462
      └── Some((7, 8)): 9/16 ≈ 0.562
    └── Some((8, 8)): 51/101 ≈ 0.505
      ├── Some((8, 0)): 8/14 ≈ 0.571
      ├── Some((8, 1)): 8/14 ≈ 0.571
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 8/15 ≈ 0.533
      ├── Some((8, 4)): 12/18 ≈ 0.667
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 2/8 ≈ 0.250
      └── Some((8, 7)): 6/12 ≈ 0.500
├── Some((7, 3)): 5095/9917 ≈ 0.514
  ├── Some((3, 0)): 535/1049 ≈ 0.510
    ├── Some((0, 0)): 53/107 ≈ 0.495
      ├── Some((0, 1)): 1/7 ≈ 0.143
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 7/14 ≈ 0.500
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 4/11 ≈ 0.364
      ├── Some((0, 6)): 5/12 ≈ 0.417
      ├── Some((0, 7)): 17/23 ≈ 0.739
      └── Some((0, 8)): 8/15 ≈ 0.533
    ├── Some((0, 1)): 40/88 ≈ 0.455
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 4/9 ≈ 0.444
      ├── Some((1, 2)): 2/7 ≈ 0.286
      ├── Some((1, 3)): 8/13 ≈ 0.615
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 7/12 ≈ 0.583
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((0, 2)): 68/129 ≈ 0.527
      ├── Some((2, 0)): 9/16 ≈ 0.562
      ├── Some((2, 1)): 7/14 ≈ 0.500
      ├── Some((2, 2)): 11/18 ≈ 0.611
      ├── Some((2, 3)): 3/9 ≈ 0.333
      ├── Some((2, 4)): 4/11 ≈ 0.364
      ├── Some((2, 5)): 7/14 ≈ 0.500
      ├── Some((2, 6)): 11/18 ≈ 0.611
      ├── Some((2, 7)): 2/8 ≈ 0.250
      └── Some((2, 8)): 14/20 ≈ 0.700
    ├── Some((0, 3)): 53/107 ≈ 0.495
      ├── Some((3, 1)): 9/16 ≈ 0.562
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 3/10 ≈ 0.300
      ├── Some((3, 6)): 16/23 ≈ 0.696
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((0, 4)): 77/142 ≈ 0.542
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 9/16 ≈ 0.562
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 4)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 18/25 ≈ 0.720
      ├── Some((4, 6)): 2/9 ≈ 0.222
      ├── Some((4, 7)): 11/19 ≈ 0.579
      └── Some((4, 8)): 14/21 ≈ 0.667
    ├── Some((0, 5)): 50/103 ≈ 0.485
      ├── Some((5, 0)): 2/7 ≈ 0.286
      ├── Some((5, 1)): 8/14 ≈ 0.571
      ├── Some((5, 2)): 9/15 ≈ 0.600
      ├── Some((5, 3)): 8/14 ≈ 0.571
      ├── Some((5, 4)): 5/11 ≈ 0.455
      ├── Some((5, 5)): 5/11 ≈ 0.455
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 7/13 ≈ 0.538
      └── Some((5, 8)): 2/7 ≈ 0.286
    ├── Some((0, 6)): 87/156 ≈ 0.558
      ├── Some((6, 0)): 12/20 ≈ 0.600
      ├── Some((6, 1)): 21/28 ≈ 0.750
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 10/18 ≈ 0.556
      ├── Some((6, 4)): 3/10 ≈ 0.300
      ├── Some((6, 5)): 13/21 ≈ 0.619
      ├── Some((6, 6)): 9/17 ≈ 0.529
      ├── Some((6, 7)): 8/16 ≈ 0.500
      └── Some((6, 8)): 5/13 ≈ 0.385
    ├── Some((0, 7)): 55/110 ≈ 0.500
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 7/14 ≈ 0.500
      ├── Some((7, 2)): 7/14 ≈ 0.500
      ├── Some((7, 4)): 2/8 ≈ 0.250
      ├── Some((7, 5)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 13/20 ≈ 0.650
      ├── Some((7, 7)): 8/15 ≈ 0.533
      └── Some((7, 8)): 9/16 ≈ 0.562
    └── Some((0, 8)): 52/106 ≈ 0.491
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 3/9 ≈ 0.333
      ├── Some((8, 2)): 6/12 ≈ 0.500
      ├── Some((8, 3)): 4/10 ≈ 0.400
      ├── Some((8, 4)): 10/16 ≈ 0.625
      ├── Some((8, 5)): 4/10 ≈ 0.400
      ├── Some((8, 6)): 7/13 ≈ 0.538
      ├── Some((8, 7)): 7/13 ≈ 0.538
      └── Some((8, 8)): 6/12 ≈ 0.500
  ├── Some((3, 1)): 696/1324 ≈ 0.526
    ├── Some((1, 0)): 39/91 ≈ 0.429
      ├── Some((0, 0)): 12/18 ≈ 0.667
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 6/12 ≈ 0.500
      ├── Some((0, 4)): 2/8 ≈ 0.250
      ├── Some((0, 5)): 7/13 ≈ 0.538
      ├── Some((0, 6)): 1/6 ≈ 0.167
      ├── Some((0, 7)): 0/5 ≈ 0.000
      └── Some((0, 8)): 1/7 ≈ 0.143
    ├── Some((1, 1)): 75/144 ≈ 0.521
      ├── Some((1, 0)): 8/17 ≈ 0.471
      ├── Some((1, 2)): 18/27 ≈ 0.667
      ├── Some((1, 3)): 14/23 ≈ 0.609
      ├── Some((1, 4)): 11/20 ≈ 0.550
      ├── Some((1, 5)): 4/12 ≈ 0.333
      ├── Some((1, 6)): 4/12 ≈ 0.333
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 9/18 ≈ 0.500
    ├── Some((1, 2)): 113/198 ≈ 0.571
      ├── Some((2, 0)): 9/18 ≈ 0.500
      ├── Some((2, 1)): 17/27 ≈ 0.630
      ├── Some((2, 2)): 8/17 ≈ 0.471
      ├── Some((2, 3)): 7/16 ≈ 0.438
      ├── Some((2, 4)): 12/22 ≈ 0.545
      ├── Some((2, 5)): 24/34 ≈ 0.706
      ├── Some((2, 6)): 10/19 ≈ 0.526
      ├── Some((2, 7)): 7/16 ≈ 0.438
      └── Some((2, 8)): 18/28 ≈ 0.643
    ├── Some((1, 3)): 103/184 ≈ 0.560
      ├── Some((3, 0)): 15/25 ≈ 0.600
      ├── Some((3, 2)): 8/18 ≈ 0.444
      ├── Some((3, 3)): 17/27 ≈ 0.630
      ├── Some((3, 4)): 24/35 ≈ 0.686
      ├── Some((3, 5)): 7/17 ≈ 0.412
      ├── Some((3, 6)): 12/22 ≈ 0.545
      ├── Some((3, 7)): 9/19 ≈ 0.474
      └── Some((3, 8)): 10/20 ≈ 0.500
    ├── Some((1, 4)): 45/100 ≈ 0.450
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 6/12 ≈ 0.500
      ├── Some((4, 2)): 8/14 ≈ 0.571
      ├── Some((4, 3)): 2/8 ≈ 0.250
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 5/11 ≈ 0.455
      ├── Some((4, 6)): 9/15 ≈ 0.600
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 3/9 ≈ 0.333
    ├── Some((1, 5)): 79/150 ≈ 0.527
      ├── Some((5, 0)): 10/18 ≈ 0.556
      ├── Some((5, 1)): 12/20 ≈ 0.600
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 11/19 ≈ 0.579
      ├── Some((5, 4)): 4/12 ≈ 0.333
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 12/20 ≈ 0.600
      ├── Some((5, 7)): 13/21 ≈ 0.619
      └── Some((5, 8)): 1/8 ≈ 0.125
    ├── Some((1, 6)): 86/160 ≈ 0.538
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 6/14 ≈ 0.429
      ├── Some((6, 2)): 12/20 ≈ 0.600
      ├── Some((6, 3)): 5/13 ≈ 0.385
      ├── Some((6, 4)): 16/25 ≈ 0.640
      ├── Some((6, 5)): 9/17 ≈ 0.529
      ├── Some((6, 6)): 8/16 ≈ 0.500
      ├── Some((6, 7)): 11/19 ≈ 0.579
      └── Some((6, 8)): 12/20 ≈ 0.600
    ├── Some((1, 7)): 70/137 ≈ 0.511
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 10/19 ≈ 0.526
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 4)): 9/17 ≈ 0.529
      ├── Some((7, 5)): 8/16 ≈ 0.500
      ├── Some((7, 6)): 12/21 ≈ 0.571
      ├── Some((7, 7)): 2/9 ≈ 0.222
      └── Some((7, 8)): 11/20 ≈ 0.550
    └── Some((1, 8)): 85/159 ≈ 0.535
      ├── Some((8, 0)): 18/27 ≈ 0.667
      ├── Some((8, 1)): 9/17 ≈ 0.529
      ├── Some((8, 2)): 22/31 ≈ 0.710
      ├── Some((8, 3)): 4/12 ≈ 0.333
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 6/14 ≈ 0.429
      ├── Some((8, 7)): 9/17 ≈ 0.529
      └── Some((8, 8)): 4/12 ≈ 0.333
  ├── Some((3, 2)): 632/1215 ≈ 0.520
    ├── Some((2, 0)): 27/71 ≈ 0.380
      ├── Some((0, 0)): 7/12 ≈ 0.583
      ├── Some((0, 1)): 0/4 ≈ 0.000
      ├── Some((0, 2)): 5/10 ≈ 0.500
      ├── Some((0, 3)): 1/6 ≈ 0.167
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 2/7 ≈ 0.286
      ├── Some((0, 6)): 8/13 ≈ 0.615
      ├── Some((0, 7)): 0/4 ≈ 0.000
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((2, 1)): 59/119 ≈ 0.496
      ├── Some((1, 0)): 7/14 ≈ 0.500
      ├── Some((1, 1)): 10/17 ≈ 0.588
      ├── Some((1, 2)): 14/21 ≈ 0.667
      ├── Some((1, 3)): 3/9 ≈ 0.333
      ├── Some((1, 4)): 8/15 ≈ 0.533
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 1/7 ≈ 0.143
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 11/18 ≈ 0.611
    ├── Some((2, 2)): 55/113 ≈ 0.487
      ├── Some((2, 0)): 4/11 ≈ 0.364
      ├── Some((2, 1)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 5/12 ≈ 0.417
      ├── Some((2, 4)): 12/20 ≈ 0.600
      ├── Some((2, 5)): 13/21 ≈ 0.619
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 4/11 ≈ 0.364
    ├── Some((2, 3)): 51/107 ≈ 0.477
      ├── Some((3, 0)): 5/12 ≈ 0.417
      ├── Some((3, 1)): 15/22 ≈ 0.682
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 6/13 ≈ 0.462
      ├── Some((3, 5)): 4/11 ≈ 0.364
      ├── Some((3, 6)): 8/15 ≈ 0.533
      ├── Some((3, 7)): 3/10 ≈ 0.300
      └── Some((3, 8)): 7/14 ≈ 0.500
    ├── Some((2, 4)): 49/105 ≈ 0.467
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 5/11 ≈ 0.455
      ├── Some((4, 2)): 11/17 ≈ 0.647
      ├── Some((4, 3)): 0/6 ≈ 0.000
      ├── Some((4, 4)): 4/10 ≈ 0.400
      ├── Some((4, 5)): 10/17 ≈ 0.588
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((2, 5)): 112/195 ≈ 0.574
      ├── Some((5, 0)): 13/22 ≈ 0.591
      ├── Some((5, 1)): 27/36 ≈ 0.750
      ├── Some((5, 2)): 14/24 ≈ 0.583
      ├── Some((5, 3)): 6/15 ≈ 0.400
      ├── Some((5, 4)): 20/30 ≈ 0.667
      ├── Some((5, 5)): 6/15 ≈ 0.400
      ├── Some((5, 6)): 7/16 ≈ 0.438
      ├── Some((5, 7)): 7/16 ≈ 0.438
      └── Some((5, 8)): 11/20 ≈ 0.550
    ├── Some((2, 6)): 93/168 ≈ 0.554
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 7/15 ≈ 0.467
      ├── Some((6, 2)): 10/18 ≈ 0.556
      ├── Some((6, 3)): 12/21 ≈ 0.571
      ├── Some((6, 4)): 19/28 ≈ 0.679
      ├── Some((6, 5)): 7/15 ≈ 0.467
      ├── Some((6, 6)): 5/13 ≈ 0.385
      ├── Some((6, 7)): 15/24 ≈ 0.625
      └── Some((6, 8)): 10/18 ≈ 0.556
    ├── Some((2, 7)): 93/168 ≈ 0.554
      ├── Some((7, 0)): 14/23 ≈ 0.609
      ├── Some((7, 1)): 17/27 ≈ 0.630
      ├── Some((7, 2)): 3/11 ≈ 0.273
      ├── Some((7, 4)): 7/16 ≈ 0.438
      ├── Some((7, 5)): 19/29 ≈ 0.655
      ├── Some((7, 6)): 7/16 ≈ 0.438
      ├── Some((7, 7)): 16/26 ≈ 0.615
      └── Some((7, 8)): 10/19 ≈ 0.526
    └── Some((2, 8)): 93/168 ≈ 0.554
      ├── Some((8, 0)): 10/18 ≈ 0.556
      ├── Some((8, 1)): 8/16 ≈ 0.500
      ├── Some((8, 2)): 11/19 ≈ 0.579
      ├── Some((8, 3)): 4/12 ≈ 0.333
      ├── Some((8, 4)): 12/21 ≈ 0.571
      ├── Some((8, 5)): 13/22 ≈ 0.591
      ├── Some((8, 6)): 17/26 ≈ 0.654
      ├── Some((8, 7)): 8/16 ≈ 0.500
      └── Some((8, 8)): 9/17 ≈ 0.529
  ├── Some((3, 3)): 570/1109 ≈ 0.514
    ├── Some((3, 0)): 73/142 ≈ 0.514
      ├── Some((0, 0)): 9/17 ≈ 0.529
      ├── Some((0, 1)): 9/17 ≈ 0.529
      ├── Some((0, 2)): 12/20 ≈ 0.600
      ├── Some((0, 3)): 14/21 ≈ 0.667
      ├── Some((0, 4)): 2/9 ≈ 0.222
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 6)): 11/19 ≈ 0.579
      ├── Some((0, 7)): 2/9 ≈ 0.222
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((3, 1)): 81/153 ≈ 0.529
      ├── Some((1, 0)): 9/17 ≈ 0.529
      ├── Some((1, 1)): 12/20 ≈ 0.600
      ├── Some((1, 2)): 9/17 ≈ 0.529
      ├── Some((1, 3)): 13/21 ≈ 0.619
      ├── Some((1, 4)): 7/15 ≈ 0.467
      ├── Some((1, 5)): 16/24 ≈ 0.667
      ├── Some((1, 6)): 4/12 ≈ 0.333
      ├── Some((1, 7)): 5/13 ≈ 0.385
      └── Some((1, 8)): 5/13 ≈ 0.385
    ├── Some((3, 2)): 40/92 ≈ 0.435
      ├── Some((2, 0)): 7/13 ≈ 0.538
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 1/6 ≈ 0.167
      ├── Some((2, 4)): 5/11 ≈ 0.455
      ├── Some((2, 5)): 8/13 ≈ 0.615
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 6/12 ≈ 0.500
    ├── Some((3, 4)): 72/140 ≈ 0.514
      ├── Some((4, 0)): 4/11 ≈ 0.364
      ├── Some((4, 1)): 16/24 ≈ 0.667
      ├── Some((4, 2)): 11/19 ≈ 0.579
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 4)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 8/16 ≈ 0.500
      ├── Some((4, 6)): 5/12 ≈ 0.417
      ├── Some((4, 7)): 10/18 ≈ 0.556
      └── Some((4, 8)): 5/12 ≈ 0.417
    ├── Some((3, 5)): 77/147 ≈ 0.524
      ├── Some((5, 0)): 4/11 ≈ 0.364
      ├── Some((5, 1)): 12/20 ≈ 0.600
      ├── Some((5, 2)): 17/25 ≈ 0.680
      ├── Some((5, 3)): 4/11 ≈ 0.364
      ├── Some((5, 4)): 8/16 ≈ 0.500
      ├── Some((5, 5)): 12/20 ≈ 0.600
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 8/16 ≈ 0.500
      └── Some((5, 8)): 4/12 ≈ 0.333
    ├── Some((3, 6)): 52/110 ≈ 0.473
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 2/8 ≈ 0.250
      ├── Some((6, 2)): 3/9 ≈ 0.333
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 9/16 ≈ 0.562
      ├── Some((6, 6)): 5/11 ≈ 0.455
      ├── Some((6, 7)): 6/13 ≈ 0.462
      └── Some((6, 8)): 11/18 ≈ 0.611
    ├── Some((3, 7)): 59/121 ≈ 0.488
      ├── Some((7, 0)): 5/13 ≈ 0.385
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 4)): 21/29 ≈ 0.724
      ├── Some((7, 5)): 7/15 ≈ 0.467
      ├── Some((7, 6)): 2/9 ≈ 0.222
      ├── Some((7, 7)): 8/16 ≈ 0.500
      └── Some((7, 8)): 5/13 ≈ 0.385
    └── Some((3, 8)): 116/203 ≈ 0.571
      ├── Some((8, 0)): 9/18 ≈ 0.500
      ├── Some((8, 1)): 16/26 ≈ 0.615
      ├── Some((8, 2)): 12/21 ≈ 0.571
      ├── Some((8, 3)): 18/28 ≈ 0.643
      ├── Some((8, 4)): 22/32 ≈ 0.688
      ├── Some((8, 5)): 6/15 ≈ 0.400
      ├── Some((8, 6)): 7/16 ≈ 0.438
      ├── Some((8, 7)): 13/23 ≈ 0.565
      └── Some((8, 8)): 13/23 ≈ 0.565
  ├── Some((3, 4)): 662/1266 ≈ 0.523
    ├── Some((4, 0)): 72/139 ≈ 0.518
      ├── Some((0, 0)): 9/17 ≈ 0.529
      ├── Some((0, 1)): 7/14 ≈ 0.500
      ├── Some((0, 2)): 13/20 ≈ 0.650
      ├── Some((0, 3)): 11/19 ≈ 0.579
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 7/14 ≈ 0.500
      ├── Some((0, 7)): 9/17 ≈ 0.529
      └── Some((0, 8)): 3/10 ≈ 0.300
    ├── Some((4, 1)): 74/142 ≈ 0.521
      ├── Some((1, 0)): 3/10 ≈ 0.300
      ├── Some((1, 1)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 9/17 ≈ 0.529
      ├── Some((1, 3)): 12/20 ≈ 0.600
      ├── Some((1, 4)): 9/17 ≈ 0.529
      ├── Some((1, 5)): 6/14 ≈ 0.429
      ├── Some((1, 6)): 19/26 ≈ 0.731
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 4/11 ≈ 0.364
    ├── Some((4, 2)): 67/132 ≈ 0.508
      ├── Some((2, 0)): 10/17 ≈ 0.588
      ├── Some((2, 1)): 11/19 ≈ 0.579
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 8/15 ≈ 0.533
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 8/15 ≈ 0.533
      ├── Some((2, 7)): 8/15 ≈ 0.533
      └── Some((2, 8)): 5/12 ≈ 0.417
    ├── Some((4, 3)): 80/150 ≈ 0.533
      ├── Some((3, 0)): 9/18 ≈ 0.500
      ├── Some((3, 1)): 17/26 ≈ 0.654
      ├── Some((3, 2)): 9/18 ≈ 0.500
      ├── Some((3, 3)): 15/24 ≈ 0.625
      ├── Some((3, 5)): 14/23 ≈ 0.609
      ├── Some((3, 6)): 3/11 ≈ 0.273
      ├── Some((3, 7)): 6/14 ≈ 0.429
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((4, 4)): 130/221 ≈ 0.588
      ├── Some((4, 0)): 20/32 ≈ 0.625
      ├── Some((4, 1)): 20/32 ≈ 0.625
      ├── Some((4, 2)): 15/26 ≈ 0.577
      ├── Some((4, 3)): 30/42 ≈ 0.714
      ├── Some((4, 5)): 10/21 ≈ 0.476
      ├── Some((4, 6)): 13/24 ≈ 0.542
      ├── Some((4, 7)): 15/27 ≈ 0.556
      └── Some((4, 8)): 6/16 ≈ 0.375
    ├── Some((4, 5)): 104/185 ≈ 0.562
      ├── Some((5, 0)): 20/29 ≈ 0.690
      ├── Some((5, 1)): 17/26 ≈ 0.654
      ├── Some((5, 2)): 12/21 ≈ 0.571
      ├── Some((5, 3)): 2/10 ≈ 0.200
      ├── Some((5, 4)): 8/17 ≈ 0.471
      ├── Some((5, 5)): 19/28 ≈ 0.679
      ├── Some((5, 6)): 10/19 ≈ 0.526
      ├── Some((5, 7)): 11/20 ≈ 0.550
      └── Some((5, 8)): 5/14 ≈ 0.357
    ├── Some((4, 6)): 51/108 ≈ 0.472
      ├── Some((6, 0)): 5/11 ≈ 0.455
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 5/12 ≈ 0.417
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 13/19 ≈ 0.684
      ├── Some((6, 5)): 2/8 ≈ 0.250
      ├── Some((6, 6)): 9/16 ≈ 0.562
      ├── Some((6, 7)): 1/7 ≈ 0.143
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((4, 7)): 51/108 ≈ 0.472
      ├── Some((7, 0)): 7/14 ≈ 0.500
      ├── Some((7, 1)): 2/9 ≈ 0.222
      ├── Some((7, 2)): 7/14 ≈ 0.500
      ├── Some((7, 4)): 3/10 ≈ 0.300
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 11/18 ≈ 0.611
      ├── Some((7, 7)): 9/16 ≈ 0.562
      └── Some((7, 8)): 6/13 ≈ 0.462
    └── Some((4, 8)): 33/80 ≈ 0.412
      ├── Some((8, 0)): 2/7 ≈ 0.286
      ├── Some((8, 1)): 7/12 ≈ 0.583
      ├── Some((8, 2)): 0/5 ≈ 0.000
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 4/9 ≈ 0.444
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 9/14 ≈ 0.643
      └── Some((8, 8)): 4/10 ≈ 0.400
  ├── Some((3, 5)): 553/1080 ≈ 0.512
    ├── Some((5, 0)): 85/154 ≈ 0.552
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 9/17 ≈ 0.529
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 4/11 ≈ 0.364
      ├── Some((0, 4)): 9/17 ≈ 0.529
      ├── Some((0, 5)): 12/20 ≈ 0.600
      ├── Some((0, 6)): 14/22 ≈ 0.636
      ├── Some((0, 7)): 11/19 ≈ 0.579
      └── Some((0, 8)): 15/22 ≈ 0.682
    ├── Some((5, 1)): 74/139 ≈ 0.532
      ├── Some((1, 0)): 9/17 ≈ 0.529
      ├── Some((1, 1)): 6/13 ≈ 0.462
      ├── Some((1, 2)): 19/26 ≈ 0.731
      ├── Some((1, 3)): 7/14 ≈ 0.500
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 8/15 ≈ 0.533
      ├── Some((1, 7)): 8/16 ≈ 0.500
      └── Some((1, 8)): 2/9 ≈ 0.222
    ├── Some((5, 2)): 43/94 ≈ 0.457
      ├── Some((2, 0)): 11/16 ≈ 0.688
      ├── Some((2, 1)): 3/9 ≈ 0.333
      ├── Some((2, 2)): 6/12 ≈ 0.500
      ├── Some((2, 3)): 9/15 ≈ 0.600
      ├── Some((2, 4)): 1/6 ≈ 0.167
      ├── Some((2, 5)): 2/8 ≈ 0.250
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 1/6 ≈ 0.167
    ├── Some((5, 3)): 41/91 ≈ 0.451
      ├── Some((3, 0)): 7/13 ≈ 0.538
      ├── Some((3, 1)): 7/13 ≈ 0.538
      ├── Some((3, 2)): 7/13 ≈ 0.538
      ├── Some((3, 3)): 3/9 ≈ 0.333
      ├── Some((3, 4)): 8/15 ≈ 0.533
      ├── Some((3, 6)): 4/10 ≈ 0.400
      ├── Some((3, 7)): 3/9 ≈ 0.333
      └── Some((3, 8)): 2/8 ≈ 0.250
    ├── Some((5, 4)): 59/117 ≈ 0.504
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 2/8 ≈ 0.250
      ├── Some((4, 2)): 12/19 ≈ 0.632
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 4)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 8/15 ≈ 0.533
      ├── Some((4, 6)): 3/9 ≈ 0.333
      ├── Some((4, 7)): 14/20 ≈ 0.700
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((5, 5)): 66/128 ≈ 0.516
      ├── Some((5, 0)): 6/14 ≈ 0.429
      ├── Some((5, 1)): 2/9 ≈ 0.222
      ├── Some((5, 2)): 13/21 ≈ 0.619
      ├── Some((5, 3)): 9/17 ≈ 0.529
      ├── Some((5, 4)): 1/8 ≈ 0.125
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 17/25 ≈ 0.680
      └── Some((5, 8)): 10/18 ≈ 0.556
    ├── Some((5, 6)): 11/43 ≈ 0.256
      ├── Some((6, 0)): 2/5 ≈ 0.400
      ├── Some((6, 1)): 1/5 ≈ 0.200
      ├── Some((6, 2)): 0/3 ≈ 0.000
      ├── Some((6, 3)): 0/3 ≈ 0.000
      ├── Some((6, 4)): 0/3 ≈ 0.000
      ├── Some((6, 5)): 1/5 ≈ 0.200
      ├── Some((6, 6)): 2/6 ≈ 0.333
      ├── Some((6, 7)): 3/6 ≈ 0.500
      └── Some((6, 8)): 2/6 ≈ 0.333
    ├── Some((5, 7)): 106/184 ≈ 0.576
      ├── Some((7, 0)): 7/16 ≈ 0.438
      ├── Some((7, 1)): 16/26 ≈ 0.615
      ├── Some((7, 2)): 16/26 ≈ 0.615
      ├── Some((7, 4)): 12/22 ≈ 0.545
      ├── Some((7, 5)): 14/24 ≈ 0.583
      ├── Some((7, 6)): 23/33 ≈ 0.697
      ├── Some((7, 7)): 9/18 ≈ 0.500
      └── Some((7, 8)): 9/18 ≈ 0.500
    └── Some((5, 8)): 67/129 ≈ 0.519
      ├── Some((8, 0)): 15/22 ≈ 0.682
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 2/8 ≈ 0.250
      ├── Some((8, 3)): 2/9 ≈ 0.222
      ├── Some((8, 4)): 2/9 ≈ 0.222
      ├── Some((8, 5)): 12/19 ≈ 0.632
      ├── Some((8, 6)): 11/18 ≈ 0.611
      ├── Some((8, 7)): 10/17 ≈ 0.588
      └── Some((8, 8)): 6/13 ≈ 0.462
  ├── Some((3, 6)): 444/891 ≈ 0.498
    ├── Some((6, 0)): 48/98 ≈ 0.490
      ├── Some((0, 0)): 6/12 ≈ 0.500
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 12/17 ≈ 0.706
      ├── Some((0, 5)): 5/11 ≈ 0.455
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 5/11 ≈ 0.455
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((6, 1)): 49/99 ≈ 0.495
      ├── Some((1, 0)): 2/8 ≈ 0.250
      ├── Some((1, 1)): 1/6 ≈ 0.167
      ├── Some((1, 2)): 6/12 ≈ 0.500
      ├── Some((1, 3)): 1/6 ≈ 0.167
      ├── Some((1, 4)): 16/21 ≈ 0.762
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 11/16 ≈ 0.688
      ├── Some((1, 7)): 6/12 ≈ 0.500
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((6, 2)): 46/95 ≈ 0.484
      ├── Some((2, 0)): 8/14 ≈ 0.571
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 8/14 ≈ 0.571
      ├── Some((2, 3)): 11/16 ≈ 0.688
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 0/5 ≈ 0.000
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 11/16 ≈ 0.688
      └── Some((2, 8)): 0/5 ≈ 0.000
    ├── Some((6, 3)): 27/66 ≈ 0.409
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 5/10 ≈ 0.500
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 3)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 7)): 5/10 ≈ 0.500
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((6, 4)): 22/59 ≈ 0.373
      ├── Some((4, 0)): 1/5 ≈ 0.200
      ├── Some((4, 1)): 1/5 ≈ 0.200
      ├── Some((4, 2)): 4/8 ≈ 0.500
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 2/6 ≈ 0.333
      ├── Some((4, 5)): 3/7 ≈ 0.429
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 4/8 ≈ 0.500
      └── Some((4, 8)): 5/9 ≈ 0.556
    ├── Some((6, 5)): 66/123 ≈ 0.537
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 5/11 ≈ 0.455
      ├── Some((5, 2)): 9/16 ≈ 0.562
      ├── Some((5, 3)): 10/16 ≈ 0.625
      ├── Some((5, 4)): 12/18 ≈ 0.667
      ├── Some((5, 5)): 2/8 ≈ 0.250
      ├── Some((5, 6)): 5/11 ≈ 0.455
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 13/19 ≈ 0.684
    ├── Some((6, 6)): 81/144 ≈ 0.562
      ├── Some((6, 0)): 6/14 ≈ 0.429
      ├── Some((6, 1)): 13/21 ≈ 0.619
      ├── Some((6, 2)): 20/28 ≈ 0.714
      ├── Some((6, 3)): 10/18 ≈ 0.556
      ├── Some((6, 4)): 13/21 ≈ 0.619
      ├── Some((6, 5)): 3/10 ≈ 0.300
      ├── Some((6, 7)): 8/16 ≈ 0.500
      └── Some((6, 8)): 7/15 ≈ 0.467
    ├── Some((6, 7)): 29/69 ≈ 0.420
      ├── Some((7, 0)): 1/5 ≈ 0.200
      ├── Some((7, 1)): 1/6 ≈ 0.167
      ├── Some((7, 2)): 2/7 ≈ 0.286
      ├── Some((7, 4)): 6/11 ≈ 0.545
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 5/10 ≈ 0.500
      ├── Some((7, 7)): 2/7 ≈ 0.286
      └── Some((7, 8)): 6/11 ≈ 0.545
    └── Some((6, 8)): 76/137 ≈ 0.555
      ├── Some((8, 0)): 12/18 ≈ 0.667
      ├── Some((8, 1)): 12/18 ≈ 0.667
      ├── Some((8, 2)): 7/14 ≈ 0.500
      ├── Some((8, 3)): 1/7 ≈ 0.143
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 11/18 ≈ 0.611
      ├── Some((8, 6)): 8/15 ≈ 0.533
      ├── Some((8, 7)): 12/19 ≈ 0.632
      └── Some((8, 8)): 8/15 ≈ 0.533
  ├── Some((3, 7)): 498/985 ≈ 0.506
    ├── Some((7, 0)): 80/149 ≈ 0.537
      ├── Some((0, 0)): 4/11 ≈ 0.364
      ├── Some((0, 1)): 15/23 ≈ 0.652
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 15/23 ≈ 0.652
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 7/15 ≈ 0.467
      ├── Some((0, 7)): 8/16 ≈ 0.500
      └── Some((0, 8)): 11/19 ≈ 0.579
    ├── Some((7, 1)): 47/101 ≈ 0.465
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 8/14 ≈ 0.571
      ├── Some((1, 2)): 3/9 ≈ 0.333
      ├── Some((1, 3)): 1/7 ≈ 0.143
      ├── Some((1, 4)): 6/12 ≈ 0.500
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 2/8 ≈ 0.250
      └── Some((1, 8)): 13/19 ≈ 0.684
    ├── Some((7, 2)): 35/83 ≈ 0.422
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 6/12 ≈ 0.500
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 7/12 ≈ 0.583
      ├── Some((2, 4)): 0/5 ≈ 0.000
      ├── Some((2, 5)): 4/9 ≈ 0.444
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 9/14 ≈ 0.643
      └── Some((2, 8)): 1/6 ≈ 0.167
    ├── Some((7, 4)): 58/117 ≈ 0.496
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 4/10 ≈ 0.400
      ├── Some((4, 3)): 7/14 ≈ 0.500
      ├── Some((4, 4)): 9/16 ≈ 0.562
      ├── Some((4, 5)): 11/17 ≈ 0.647
      ├── Some((4, 6)): 10/17 ≈ 0.588
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 2/8 ≈ 0.250
    ├── Some((7, 5)): 53/110 ≈ 0.482
      ├── Some((5, 0)): 10/17 ≈ 0.588
      ├── Some((5, 1)): 3/9 ≈ 0.333
      ├── Some((5, 2)): 7/14 ≈ 0.500
      ├── Some((5, 3)): 3/9 ≈ 0.333
      ├── Some((5, 4)): 8/15 ≈ 0.533
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 3/9 ≈ 0.333
      ├── Some((5, 7)): 3/9 ≈ 0.333
      └── Some((5, 8)): 11/17 ≈ 0.647
    ├── Some((7, 6)): 74/141 ≈ 0.525
      ├── Some((6, 0)): 6/13 ≈ 0.462
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 13/20 ≈ 0.650
      ├── Some((6, 3)): 11/19 ≈ 0.579
      ├── Some((6, 4)): 11/19 ≈ 0.579
      ├── Some((6, 5)): 5/12 ≈ 0.417
      ├── Some((6, 6)): 13/21 ≈ 0.619
      ├── Some((6, 7)): 1/8 ≈ 0.125
      └── Some((6, 8)): 7/14 ≈ 0.500
    ├── Some((7, 7)): 85/156 ≈ 0.545
      ├── Some((7, 0)): 12/22 ≈ 0.545
      ├── Some((7, 1)): 18/29 ≈ 0.621
      ├── Some((7, 2)): 12/22 ≈ 0.545
      ├── Some((7, 4)): 5/14 ≈ 0.357
      ├── Some((7, 5)): 17/28 ≈ 0.607
      ├── Some((7, 6)): 6/15 ≈ 0.400
      └── Some((7, 8)): 15/25 ≈ 0.600
    └── Some((7, 8)): 65/127 ≈ 0.512
      ├── Some((8, 0)): 7/14 ≈ 0.500
      ├── Some((8, 1)): 13/19 ≈ 0.684
      ├── Some((8, 2)): 3/9 ≈ 0.333
      ├── Some((8, 3)): 7/14 ≈ 0.500
      ├── Some((8, 4)): 8/15 ≈ 0.533
      ├── Some((8, 5)): 4/11 ≈ 0.364
      ├── Some((8, 6)): 5/12 ≈ 0.417
      ├── Some((8, 7)): 6/13 ≈ 0.462
      └── Some((8, 8)): 12/19 ≈ 0.632
  └── Some((3, 8)): 505/997 ≈ 0.507
    ├── Some((8, 0)): 81/146 ≈ 0.555
      ├── Some((0, 0)): 14/21 ≈ 0.667
      ├── Some((0, 1)): 11/19 ≈ 0.579
      ├── Some((0, 2)): 13/20 ≈ 0.650
      ├── Some((0, 3)): 3/10 ≈ 0.300
      ├── Some((0, 4)): 10/18 ≈ 0.556
      ├── Some((0, 5)): 16/23 ≈ 0.696
      ├── Some((0, 6)): 3/10 ≈ 0.300
      ├── Some((0, 7)): 7/14 ≈ 0.500
      └── Some((0, 8)): 3/10 ≈ 0.300
    ├── Some((8, 1)): 32/75 ≈ 0.427
      ├── Some((1, 0)): 1/6 ≈ 0.167
      ├── Some((1, 1)): 5/10 ≈ 0.500
      ├── Some((1, 2)): 0/4 ≈ 0.000
      ├── Some((1, 3)): 8/13 ≈ 0.615
      ├── Some((1, 4)): 0/4 ≈ 0.000
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 5/10 ≈ 0.500
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 10/14 ≈ 0.714
    ├── Some((8, 2)): 37/83 ≈ 0.446
      ├── Some((2, 0)): 6/11 ≈ 0.545
      ├── Some((2, 1)): 7/12 ≈ 0.583
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 5/10 ≈ 0.500
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 5/10 ≈ 0.500
      └── Some((2, 8)): 6/11 ≈ 0.545
    ├── Some((8, 3)): 52/105 ≈ 0.495
      ├── Some((3, 0)): 4/10 ≈ 0.400
      ├── Some((3, 1)): 12/19 ≈ 0.632
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 6/13 ≈ 0.462
      ├── Some((3, 4)): 7/14 ≈ 0.500
      ├── Some((3, 5)): 1/7 ≈ 0.143
      ├── Some((3, 6)): 11/18 ≈ 0.611
      └── Some((3, 7)): 7/14 ≈ 0.500
    ├── Some((8, 4)): 69/130 ≈ 0.531
      ├── Some((4, 0)): 9/16 ≈ 0.562
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 8/15 ≈ 0.533
      ├── Some((4, 3)): 9/16 ≈ 0.562
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 8/15 ≈ 0.533
      ├── Some((4, 6)): 11/18 ≈ 0.611
      ├── Some((4, 7)): 2/8 ≈ 0.250
      └── Some((4, 8)): 10/17 ≈ 0.588
    ├── Some((8, 5)): 70/131 ≈ 0.534
      ├── Some((5, 0)): 5/12 ≈ 0.417
      ├── Some((5, 1)): 10/16 ≈ 0.625
      ├── Some((5, 2)): 11/17 ≈ 0.647
      ├── Some((5, 3)): 10/17 ≈ 0.588
      ├── Some((5, 4)): 9/16 ≈ 0.562
      ├── Some((5, 5)): 8/15 ≈ 0.533
      ├── Some((5, 6)): 8/15 ≈ 0.533
      ├── Some((5, 7)): 2/8 ≈ 0.250
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((8, 6)): 56/111 ≈ 0.505
      ├── Some((6, 0)): 3/9 ≈ 0.333
      ├── Some((6, 1)): 9/15 ≈ 0.600
      ├── Some((6, 2)): 7/13 ≈ 0.538
      ├── Some((6, 3)): 6/12 ≈ 0.500
      ├── Some((6, 4)): 2/8 ≈ 0.250
      ├── Some((6, 5)): 9/15 ≈ 0.600
      ├── Some((6, 6)): 6/12 ≈ 0.500
      ├── Some((6, 7)): 6/12 ≈ 0.500
      └── Some((6, 8)): 8/14 ≈ 0.571
    ├── Some((8, 7)): 55/110 ≈ 0.500
      ├── Some((7, 0)): 1/7 ≈ 0.143
      ├── Some((7, 1)): 7/14 ≈ 0.500
      ├── Some((7, 2)): 7/14 ≈ 0.500
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 1/7 ≈ 0.143
      ├── Some((7, 6)): 7/14 ≈ 0.500
      ├── Some((7, 7)): 16/24 ≈ 0.667
      └── Some((7, 8)): 8/15 ≈ 0.533
    └── Some((8, 8)): 52/105 ≈ 0.495
      ├── Some((8, 0)): 5/11 ≈ 0.455
      ├── Some((8, 1)): 6/12 ≈ 0.500
      ├── Some((8, 2)): 4/10 ≈ 0.400
      ├── Some((8, 3)): 9/16 ≈ 0.562
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 9/16 ≈ 0.562
      ├── Some((8, 6)): 9/16 ≈ 0.562
      └── Some((8, 7)): 6/13 ≈ 0.462
├── Some((7, 4)): 4541/8895 ≈ 0.511
  ├── Some((4, 0)): 484/955 ≈ 0.507
    ├── Some((0, 0)): 53/105 ≈ 0.505
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 2)): 7/14 ≈ 0.500
      ├── Some((0, 3)): 4/10 ≈ 0.400
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 5/11 ≈ 0.455
      ├── Some((0, 7)): 11/17 ≈ 0.647
      └── Some((0, 8)): 9/16 ≈ 0.562
    ├── Some((0, 1)): 62/118 ≈ 0.525
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 1/7 ≈ 0.143
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 3)): 9/15 ≈ 0.600
      ├── Some((1, 4)): 11/17 ≈ 0.647
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 16/22 ≈ 0.727
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((0, 2)): 26/65 ≈ 0.400
      ├── Some((2, 0)): 5/9 ≈ 0.556
      ├── Some((2, 1)): 6/10 ≈ 0.600
      ├── Some((2, 2)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 4/8 ≈ 0.500
      ├── Some((2, 4)): 2/6 ≈ 0.333
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 0/4 ≈ 0.000
      ├── Some((2, 7)): 2/7 ≈ 0.286
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((0, 3)): 70/130 ≈ 0.538
      ├── Some((3, 0)): 11/17 ≈ 0.647
      ├── Some((3, 1)): 11/18 ≈ 0.611
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 4/10 ≈ 0.400
      ├── Some((3, 4)): 10/17 ≈ 0.588
      ├── Some((3, 5)): 4/10 ≈ 0.400
      ├── Some((3, 6)): 10/17 ≈ 0.588
      ├── Some((3, 7)): 5/12 ≈ 0.417
      └── Some((3, 8)): 11/18 ≈ 0.611
    ├── Some((0, 4)): 40/87 ≈ 0.460
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 4/10 ≈ 0.400
      ├── Some((4, 3)): 7/13 ≈ 0.538
      ├── Some((4, 4)): 7/13 ≈ 0.538
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 6/12 ≈ 0.500
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 5/11 ≈ 0.455
    ├── Some((0, 5)): 59/114 ≈ 0.518
      ├── Some((5, 0)): 4/10 ≈ 0.400
      ├── Some((5, 1)): 9/15 ≈ 0.600
      ├── Some((5, 2)): 7/13 ≈ 0.538
      ├── Some((5, 3)): 11/17 ≈ 0.647
      ├── Some((5, 4)): 4/10 ≈ 0.400
      ├── Some((5, 5)): 7/13 ≈ 0.538
      ├── Some((5, 6)): 2/8 ≈ 0.250
      ├── Some((5, 7)): 7/13 ≈ 0.538
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((0, 6)): 69/128 ≈ 0.539
      ├── Some((6, 0)): 7/14 ≈ 0.500
      ├── Some((6, 1)): 1/7 ≈ 0.143
      ├── Some((6, 2)): 10/17 ≈ 0.588
      ├── Some((6, 3)): 2/8 ≈ 0.250
      ├── Some((6, 4)): 12/18 ≈ 0.667
      ├── Some((6, 5)): 6/13 ≈ 0.462
      ├── Some((6, 6)): 8/15 ≈ 0.533
      ├── Some((6, 7)): 12/18 ≈ 0.667
      └── Some((6, 8)): 10/17 ≈ 0.588
    ├── Some((0, 7)): 44/92 ≈ 0.478
      ├── Some((7, 0)): 4/10 ≈ 0.400
      ├── Some((7, 1)): 7/13 ≈ 0.538
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 6/12 ≈ 0.500
      ├── Some((7, 5)): 18/23 ≈ 0.783
      ├── Some((7, 6)): 1/7 ≈ 0.143
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 2/8 ≈ 0.250
    └── Some((0, 8)): 60/115 ≈ 0.522
      ├── Some((8, 0)): 7/13 ≈ 0.538
      ├── Some((8, 1)): 4/10 ≈ 0.400
      ├── Some((8, 2)): 9/15 ≈ 0.600
      ├── Some((8, 3)): 6/12 ≈ 0.500
      ├── Some((8, 4)): 7/13 ≈ 0.538
      ├── Some((8, 5)): 6/12 ≈ 0.500
      ├── Some((8, 6)): 2/8 ≈ 0.250
      ├── Some((8, 7)): 8/14 ≈ 0.571
      └── Some((8, 8)): 11/17 ≈ 0.647
  ├── Some((4, 1)): 692/1309 ≈ 0.529
    ├── Some((1, 0)): 63/126 ≈ 0.500
      ├── Some((0, 0)): 2/8 ≈ 0.250
      ├── Some((0, 1)): 5/12 ≈ 0.417
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 5/12 ≈ 0.417
      ├── Some((0, 4)): 11/18 ≈ 0.611
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 10/17 ≈ 0.588
      ├── Some((0, 7)): 9/16 ≈ 0.562
      └── Some((0, 8)): 9/16 ≈ 0.562
    ├── Some((1, 1)): 88/162 ≈ 0.543
      ├── Some((1, 0)): 8/17 ≈ 0.471
      ├── Some((1, 2)): 7/16 ≈ 0.438
      ├── Some((1, 3)): 10/19 ≈ 0.526
      ├── Some((1, 4)): 10/19 ≈ 0.526
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 19/29 ≈ 0.655
      ├── Some((1, 7)): 9/18 ≈ 0.500
      └── Some((1, 8)): 12/22 ≈ 0.545
    ├── Some((1, 2)): 92/167 ≈ 0.551
      ├── Some((2, 0)): 6/14 ≈ 0.429
      ├── Some((2, 1)): 9/17 ≈ 0.529
      ├── Some((2, 2)): 6/14 ≈ 0.429
      ├── Some((2, 3)): 15/24 ≈ 0.625
      ├── Some((2, 4)): 12/20 ≈ 0.600
      ├── Some((2, 5)): 6/14 ≈ 0.429
      ├── Some((2, 6)): 13/22 ≈ 0.591
      ├── Some((2, 7)): 14/23 ≈ 0.609
      └── Some((2, 8)): 10/18 ≈ 0.556
    ├── Some((1, 3)): 65/129 ≈ 0.504
      ├── Some((3, 0)): 10/17 ≈ 0.588
      ├── Some((3, 1)): 11/18 ≈ 0.611
      ├── Some((3, 2)): 4/11 ≈ 0.364
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 9/16 ≈ 0.562
      ├── Some((3, 6)): 2/9 ≈ 0.222
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 9/16 ≈ 0.562
    ├── Some((1, 4)): 43/96 ≈ 0.448
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 2/8 ≈ 0.250
      ├── Some((4, 4)): 5/11 ≈ 0.455
      ├── Some((4, 5)): 11/18 ≈ 0.611
      ├── Some((4, 6)): 6/13 ≈ 0.462
      ├── Some((4, 7)): 6/13 ≈ 0.462
      └── Some((4, 8)): 5/12 ≈ 0.417
    ├── Some((1, 5)): 104/184 ≈ 0.565
      ├── Some((5, 0)): 4/12 ≈ 0.333
      ├── Some((5, 1)): 20/30 ≈ 0.667
      ├── Some((5, 2)): 7/16 ≈ 0.438
      ├── Some((5, 3)): 12/21 ≈ 0.571
      ├── Some((5, 4)): 4/12 ≈ 0.333
      ├── Some((5, 5)): 15/24 ≈ 0.625
      ├── Some((5, 6)): 10/19 ≈ 0.526
      ├── Some((5, 7)): 15/24 ≈ 0.625
      └── Some((5, 8)): 16/25 ≈ 0.640
    ├── Some((1, 6)): 112/195 ≈ 0.574
      ├── Some((6, 0)): 27/36 ≈ 0.750
      ├── Some((6, 1)): 10/19 ≈ 0.526
      ├── Some((6, 2)): 7/16 ≈ 0.438
      ├── Some((6, 3)): 17/27 ≈ 0.630
      ├── Some((6, 4)): 5/14 ≈ 0.357
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 19/29 ≈ 0.655
      ├── Some((6, 7)): 15/25 ≈ 0.600
      └── Some((6, 8)): 2/10 ≈ 0.200
    ├── Some((1, 7)): 49/105 ≈ 0.467
      ├── Some((7, 0)): 2/8 ≈ 0.250
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 5/12 ≈ 0.417
      ├── Some((7, 3)): 3/10 ≈ 0.300
      ├── Some((7, 5)): 8/15 ≈ 0.533
      ├── Some((7, 6)): 8/15 ≈ 0.533
      ├── Some((7, 7)): 8/15 ≈ 0.533
      └── Some((7, 8)): 9/16 ≈ 0.562
    └── Some((1, 8)): 76/144 ≈ 0.528
      ├── Some((8, 0)): 14/22 ≈ 0.636
      ├── Some((8, 1)): 7/14 ≈ 0.500
      ├── Some((8, 2)): 5/12 ≈ 0.417
      ├── Some((8, 3)): 10/18 ≈ 0.556
      ├── Some((8, 4)): 1/8 ≈ 0.125
      ├── Some((8, 5)): 18/25 ≈ 0.720
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 9/17 ≈ 0.529
      └── Some((8, 8)): 8/16 ≈ 0.500
  ├── Some((4, 2)): 477/943 ≈ 0.506
    ├── Some((2, 0)): 32/74 ≈ 0.432
      ├── Some((0, 0)): 5/9 ≈ 0.556
      ├── Some((0, 1)): 3/8 ≈ 0.375
      ├── Some((0, 2)): 5/9 ≈ 0.556
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 1/5 ≈ 0.200
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 1/5 ≈ 0.200
      └── Some((0, 8)): 4/9 ≈ 0.444
    ├── Some((2, 1)): 54/107 ≈ 0.505
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 5/11 ≈ 0.455
      ├── Some((1, 2)): 16/21 ≈ 0.762
      ├── Some((1, 3)): 9/15 ≈ 0.600
      ├── Some((1, 4)): 9/15 ≈ 0.600
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 1/6 ≈ 0.167
      ├── Some((1, 7)): 7/13 ≈ 0.538
      └── Some((1, 8)): 1/7 ≈ 0.143
    ├── Some((2, 2)): 62/118 ≈ 0.525
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 3/10 ≈ 0.300
      ├── Some((2, 3)): 9/16 ≈ 0.562
      ├── Some((2, 4)): 11/18 ≈ 0.611
      ├── Some((2, 5)): 12/19 ≈ 0.632
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 8/15 ≈ 0.533
      └── Some((2, 8)): 7/14 ≈ 0.500
    ├── Some((2, 3)): 56/110 ≈ 0.509
      ├── Some((3, 0)): 9/15 ≈ 0.600
      ├── Some((3, 1)): 5/11 ≈ 0.455
      ├── Some((3, 2)): 5/11 ≈ 0.455
      ├── Some((3, 3)): 9/15 ≈ 0.600
      ├── Some((3, 4)): 7/13 ≈ 0.538
      ├── Some((3, 5)): 5/11 ≈ 0.455
      ├── Some((3, 6)): 8/14 ≈ 0.571
      ├── Some((3, 7)): 7/13 ≈ 0.538
      └── Some((3, 8)): 0/6 ≈ 0.000
    ├── Some((2, 4)): 79/142 ≈ 0.556
      ├── Some((4, 0)): 16/24 ≈ 0.667
      ├── Some((4, 1)): 13/21 ≈ 0.619
      ├── Some((4, 3)): 10/18 ≈ 0.556
      ├── Some((4, 4)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 4/11 ≈ 0.364
      ├── Some((4, 6)): 12/20 ≈ 0.600
      ├── Some((4, 7)): 9/17 ≈ 0.529
      └── Some((4, 8)): 8/16 ≈ 0.500
    ├── Some((2, 5)): 54/107 ≈ 0.505
      ├── Some((5, 0)): 8/14 ≈ 0.571
      ├── Some((5, 1)): 12/18 ≈ 0.667
      ├── Some((5, 2)): 5/11 ≈ 0.455
      ├── Some((5, 3)): 7/13 ≈ 0.538
      ├── Some((5, 4)): 13/18 ≈ 0.722
      ├── Some((5, 5)): 1/7 ≈ 0.143
      ├── Some((5, 6)): 0/5 ≈ 0.000
      ├── Some((5, 7)): 5/11 ≈ 0.455
      └── Some((5, 8)): 3/9 ≈ 0.333
    ├── Some((2, 6)): 80/143 ≈ 0.559
      ├── Some((6, 0)): 6/13 ≈ 0.462
      ├── Some((6, 1)): 10/17 ≈ 0.588
      ├── Some((6, 2)): 11/18 ≈ 0.611
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 11/18 ≈ 0.611
      ├── Some((6, 5)): 9/16 ≈ 0.562
      ├── Some((6, 6)): 11/18 ≈ 0.611
      ├── Some((6, 7)): 10/17 ≈ 0.588
      └── Some((6, 8)): 8/15 ≈ 0.533
    ├── Some((2, 7)): 33/76 ≈ 0.434
      ├── Some((7, 0)): 1/6 ≈ 0.167
      ├── Some((7, 1)): 7/13 ≈ 0.538
      ├── Some((7, 2)): 8/13 ≈ 0.615
      ├── Some((7, 3)): 4/10 ≈ 0.400
      ├── Some((7, 5)): 3/8 ≈ 0.375
      ├── Some((7, 6)): 3/8 ≈ 0.375
      ├── Some((7, 7)): 4/10 ≈ 0.400
      └── Some((7, 8)): 2/7 ≈ 0.286
    └── Some((2, 8)): 26/65 ≈ 0.400
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 2/6 ≈ 0.333
      ├── Some((8, 2)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 2/6 ≈ 0.333
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 6/10 ≈ 0.600
      ├── Some((8, 6)): 4/8 ≈ 0.500
      ├── Some((8, 7)): 3/8 ≈ 0.375
      └── Some((8, 8)): 4/8 ≈ 0.500
  ├── Some((4, 3)): 705/1331 ≈ 0.530
    ├── Some((3, 0)): 87/161 ≈ 0.540
      ├── Some((0, 0)): 9/17 ≈ 0.529
      ├── Some((0, 1)): 10/18 ≈ 0.556
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 2/9 ≈ 0.222
      ├── Some((0, 4)): 14/23 ≈ 0.609
      ├── Some((0, 5)): 14/23 ≈ 0.609
      ├── Some((0, 6)): 12/21 ≈ 0.571
      ├── Some((0, 7)): 9/17 ≈ 0.529
      └── Some((0, 8)): 6/14 ≈ 0.429
    ├── Some((3, 1)): 72/139 ≈ 0.518
      ├── Some((1, 0)): 4/11 ≈ 0.364
      ├── Some((1, 1)): 11/19 ≈ 0.579
      ├── Some((1, 2)): 6/13 ≈ 0.462
      ├── Some((1, 3)): 4/11 ≈ 0.364
      ├── Some((1, 4)): 12/20 ≈ 0.600
      ├── Some((1, 5)): 8/15 ≈ 0.533
      ├── Some((1, 6)): 7/14 ≈ 0.500
      ├── Some((1, 7)): 9/17 ≈ 0.529
      └── Some((1, 8)): 10/18 ≈ 0.556
    ├── Some((3, 2)): 70/136 ≈ 0.515
      ├── Some((2, 0)): 9/16 ≈ 0.562
      ├── Some((2, 1)): 9/16 ≈ 0.562
      ├── Some((2, 2)): 7/14 ≈ 0.500
      ├── Some((2, 3)): 10/18 ≈ 0.556
      ├── Some((2, 4)): 5/12 ≈ 0.417
      ├── Some((2, 5)): 4/11 ≈ 0.364
      ├── Some((2, 6)): 9/16 ≈ 0.562
      ├── Some((2, 7)): 12/20 ≈ 0.600
      └── Some((2, 8)): 5/12 ≈ 0.417
    ├── Some((3, 3)): 112/196 ≈ 0.571
      ├── Some((3, 0)): 14/25 ≈ 0.560
      ├── Some((3, 1)): 14/25 ≈ 0.560
      ├── Some((3, 2)): 21/32 ≈ 0.656
      ├── Some((3, 4)): 21/32 ≈ 0.656
      ├── Some((3, 5)): 17/28 ≈ 0.607
      ├── Some((3, 6)): 11/21 ≈ 0.524
      ├── Some((3, 7)): 3/12 ≈ 0.250
      └── Some((3, 8)): 10/20 ≈ 0.500
    ├── Some((3, 4)): 36/85 ≈ 0.424
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 6/12 ≈ 0.500
      ├── Some((4, 2)): 0/5 ≈ 0.000
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 6/12 ≈ 0.500
      ├── Some((4, 6)): 5/11 ≈ 0.455
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((3, 5)): 89/164 ≈ 0.543
      ├── Some((5, 0)): 8/16 ≈ 0.500
      ├── Some((5, 1)): 2/10 ≈ 0.200
      ├── Some((5, 2)): 15/24 ≈ 0.625
      ├── Some((5, 3)): 0/7 ≈ 0.000
      ├── Some((5, 4)): 20/29 ≈ 0.690
      ├── Some((5, 5)): 13/22 ≈ 0.591
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 14/23 ≈ 0.609
      └── Some((5, 8)): 9/17 ≈ 0.529
    ├── Some((3, 6)): 109/192 ≈ 0.568
      ├── Some((6, 0)): 18/28 ≈ 0.643
      ├── Some((6, 1)): 7/16 ≈ 0.438
      ├── Some((6, 2)): 10/19 ≈ 0.526
      ├── Some((6, 3)): 26/35 ≈ 0.743
      ├── Some((6, 4)): 6/15 ≈ 0.400
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 15/25 ≈ 0.600
      ├── Some((6, 7)): 5/14 ≈ 0.357
      └── Some((6, 8)): 12/21 ≈ 0.571
    ├── Some((3, 7)): 92/168 ≈ 0.548
      ├── Some((7, 0)): 21/31 ≈ 0.677
      ├── Some((7, 1)): 2/10 ≈ 0.200
      ├── Some((7, 2)): 4/13 ≈ 0.308
      ├── Some((7, 3)): 14/24 ≈ 0.583
      ├── Some((7, 5)): 27/38 ≈ 0.711
      ├── Some((7, 6)): 3/12 ≈ 0.250
      ├── Some((7, 7)): 14/24 ≈ 0.583
      └── Some((7, 8)): 6/15 ≈ 0.400
    └── Some((3, 8)): 38/89 ≈ 0.427
      ├── Some((8, 0)): 0/5 ≈ 0.000
      ├── Some((8, 1)): 9/14 ≈ 0.643
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 3/9 ≈ 0.333
      ├── Some((8, 4)): 4/10 ≈ 0.400
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 6/12 ≈ 0.500
      ├── Some((8, 7)): 5/11 ≈ 0.455
      └── Some((8, 8)): 3/9 ≈ 0.333
  ├── Some((4, 4)): 440/879 ≈ 0.501
    ├── Some((4, 0)): 47/99 ≈ 0.475
      ├── Some((0, 0)): 5/11 ≈ 0.455
      ├── Some((0, 1)): 7/13 ≈ 0.538
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 1/6 ≈ 0.167
      ├── Some((0, 4)): 1/6 ≈ 0.167
      ├── Some((0, 5)): 3/9 ≈ 0.333
      ├── Some((0, 6)): 7/13 ≈ 0.538
      ├── Some((0, 7)): 10/15 ≈ 0.667
      └── Some((0, 8)): 10/16 ≈ 0.625
    ├── Some((4, 1)): 100/174 ≈ 0.575
      ├── Some((1, 0)): 18/27 ≈ 0.667
      ├── Some((1, 1)): 5/13 ≈ 0.385
      ├── Some((1, 2)): 7/15 ≈ 0.467
      ├── Some((1, 3)): 8/16 ≈ 0.500
      ├── Some((1, 4)): 9/17 ≈ 0.529
      ├── Some((1, 5)): 21/29 ≈ 0.724
      ├── Some((1, 6)): 18/27 ≈ 0.667
      ├── Some((1, 7)): 2/9 ≈ 0.222
      └── Some((1, 8)): 11/20 ≈ 0.550
    ├── Some((4, 2)): 36/82 ≈ 0.439
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 9/14 ≈ 0.643
      ├── Some((2, 2)): 4/9 ≈ 0.444
      ├── Some((2, 3)): 2/7 ≈ 0.286
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 2/7 ≈ 0.286
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 7/12 ≈ 0.583
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((4, 3)): 63/122 ≈ 0.516
      ├── Some((3, 0)): 20/26 ≈ 0.769
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 6/13 ≈ 0.462
      ├── Some((3, 3)): 8/15 ≈ 0.533
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 3/9 ≈ 0.333
      ├── Some((3, 6)): 5/11 ≈ 0.455
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 6/13 ≈ 0.462
    ├── Some((4, 5)): 27/68 ≈ 0.397
      ├── Some((5, 0)): 2/7 ≈ 0.286
      ├── Some((5, 1)): 4/9 ≈ 0.444
      ├── Some((5, 2)): 1/5 ≈ 0.200
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 7/11 ≈ 0.636
      ├── Some((5, 5)): 1/6 ≈ 0.167
      ├── Some((5, 6)): 2/7 ≈ 0.286
      ├── Some((5, 7)): 7/11 ≈ 0.636
      └── Some((5, 8)): 1/6 ≈ 0.167
    ├── Some((4, 6)): 70/132 ≈ 0.530
      ├── Some((6, 0)): 4/11 ≈ 0.364
      ├── Some((6, 1)): 6/13 ≈ 0.462
      ├── Some((6, 2)): 13/20 ≈ 0.650
      ├── Some((6, 3)): 7/14 ≈ 0.500
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 1/7 ≈ 0.143
      ├── Some((6, 6)): 15/22 ≈ 0.682
      ├── Some((6, 7)): 9/16 ≈ 0.562
      └── Some((6, 8)): 9/16 ≈ 0.562
    ├── Some((4, 7)): 66/126 ≈ 0.524
      ├── Some((7, 0)): 5/12 ≈ 0.417
      ├── Some((7, 1)): 11/19 ≈ 0.579
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 3/10 ≈ 0.300
      ├── Some((7, 6)): 15/23 ≈ 0.652
      ├── Some((7, 7)): 7/14 ≈ 0.500
      └── Some((7, 8)): 9/17 ≈ 0.529
    └── Some((4, 8)): 31/75 ≈ 0.413
      ├── Some((8, 0)): 4/9 ≈ 0.444
      ├── Some((8, 1)): 4/9 ≈ 0.444
      ├── Some((8, 2)): 3/8 ≈ 0.375
      ├── Some((8, 3)): 5/9 ≈ 0.556
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 5/10 ≈ 0.500
      ├── Some((8, 6)): 0/4 ≈ 0.000
      ├── Some((8, 7)): 3/8 ≈ 0.375
      └── Some((8, 8)): 3/8 ≈ 0.375
  ├── Some((4, 5)): 657/1250 ≈ 0.526
    ├── Some((5, 0)): 70/135 ≈ 0.519
      ├── Some((0, 0)): 13/21 ≈ 0.619
      ├── Some((0, 1)): 16/23 ≈ 0.696
      ├── Some((0, 2)): 4/11 ≈ 0.364
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 5/12 ≈ 0.417
      ├── Some((0, 6)): 8/16 ≈ 0.500
      ├── Some((0, 7)): 2/9 ≈ 0.222
      └── Some((0, 8)): 7/14 ≈ 0.500
    ├── Some((5, 1)): 74/141 ≈ 0.525
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 9/17 ≈ 0.529
      ├── Some((1, 3)): 4/11 ≈ 0.364
      ├── Some((1, 4)): 13/21 ≈ 0.619
      ├── Some((1, 5)): 8/16 ≈ 0.500
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 16/24 ≈ 0.667
      └── Some((1, 8)): 6/13 ≈ 0.462
    ├── Some((5, 2)): 50/105 ≈ 0.476
      ├── Some((2, 0)): 3/9 ≈ 0.333
      ├── Some((2, 1)): 2/8 ≈ 0.250
      ├── Some((2, 2)): 10/17 ≈ 0.588
      ├── Some((2, 3)): 1/7 ≈ 0.143
      ├── Some((2, 4)): 0/6 ≈ 0.000
      ├── Some((2, 5)): 4/10 ≈ 0.400
      ├── Some((2, 6)): 11/17 ≈ 0.647
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 14/20 ≈ 0.700
    ├── Some((5, 3)): 65/128 ≈ 0.508
      ├── Some((3, 0)): 4/11 ≈ 0.364
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 13/20 ≈ 0.650
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 6/13 ≈ 0.462
      ├── Some((3, 5)): 11/18 ≈ 0.611
      ├── Some((3, 6)): 4/11 ≈ 0.364
      ├── Some((3, 7)): 9/16 ≈ 0.562
      └── Some((3, 8)): 5/12 ≈ 0.417
    ├── Some((5, 4)): 54/111 ≈ 0.486
      ├── Some((4, 0)): 9/16 ≈ 0.562
      ├── Some((4, 1)): 12/19 ≈ 0.632
      ├── Some((4, 2)): 7/14 ≈ 0.500
      ├── Some((4, 3)): 2/9 ≈ 0.222
      ├── Some((4, 4)): 2/9 ≈ 0.222
      ├── Some((4, 6)): 12/19 ≈ 0.632
      ├── Some((4, 7)): 7/14 ≈ 0.500
      └── Some((4, 8)): 3/10 ≈ 0.300
    ├── Some((5, 5)): 95/170 ≈ 0.559
      ├── Some((5, 0)): 18/28 ≈ 0.643
      ├── Some((5, 1)): 17/27 ≈ 0.630
      ├── Some((5, 2)): 9/18 ≈ 0.500
      ├── Some((5, 3)): 7/16 ≈ 0.438
      ├── Some((5, 4)): 13/22 ≈ 0.591
      ├── Some((5, 6)): 8/17 ≈ 0.471
      ├── Some((5, 7)): 9/18 ≈ 0.500
      └── Some((5, 8)): 13/23 ≈ 0.565
    ├── Some((5, 6)): 106/186 ≈ 0.570
      ├── Some((6, 0)): 20/29 ≈ 0.690
      ├── Some((6, 1)): 18/27 ≈ 0.667
      ├── Some((6, 2)): 6/14 ≈ 0.429
      ├── Some((6, 3)): 7/16 ≈ 0.438
      ├── Some((6, 4)): 9/18 ≈ 0.500
      ├── Some((6, 5)): 13/22 ≈ 0.591
      ├── Some((6, 6)): 16/25 ≈ 0.640
      ├── Some((6, 7)): 13/22 ≈ 0.591
      └── Some((6, 8)): 4/12 ≈ 0.333
    ├── Some((5, 7)): 51/107 ≈ 0.477
      ├── Some((7, 0)): 16/24 ≈ 0.667
      ├── Some((7, 1)): 9/17 ≈ 0.529
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 6/13 ≈ 0.462
      ├── Some((7, 5)): 8/15 ≈ 0.533
      ├── Some((7, 6)): 1/7 ≈ 0.143
      ├── Some((7, 7)): 6/13 ≈ 0.462
      └── Some((7, 8)): 1/7 ≈ 0.143
    └── Some((5, 8)): 92/166 ≈ 0.554
      ├── Some((8, 0)): 14/23 ≈ 0.609
      ├── Some((8, 1)): 12/20 ≈ 0.600
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 13/22 ≈ 0.591
      ├── Some((8, 4)): 12/20 ≈ 0.600
      ├── Some((8, 5)): 2/9 ≈ 0.222
      ├── Some((8, 6)): 8/16 ≈ 0.500
      ├── Some((8, 7)): 12/20 ≈ 0.600
      └── Some((8, 8)): 11/19 ≈ 0.579
  ├── Some((4, 6)): 335/695 ≈ 0.482
    ├── Some((6, 0)): 14/43 ≈ 0.326
      ├── Some((0, 0)): 2/5 ≈ 0.400
      ├── Some((0, 1)): 3/6 ≈ 0.500
      ├── Some((0, 2)): 1/4 ≈ 0.250
      ├── Some((0, 3)): 0/3 ≈ 0.000
      ├── Some((0, 4)): 4/7 ≈ 0.571
      ├── Some((0, 5)): 0/3 ≈ 0.000
      ├── Some((0, 6)): 1/4 ≈ 0.250
      ├── Some((0, 7)): 1/5 ≈ 0.200
      └── Some((0, 8)): 2/5 ≈ 0.400
    ├── Some((6, 1)): 59/108 ≈ 0.546
      ├── Some((1, 0)): 8/14 ≈ 0.571
      ├── Some((1, 1)): 14/19 ≈ 0.737
      ├── Some((1, 2)): 11/16 ≈ 0.688
      ├── Some((1, 3)): 0/5 ≈ 0.000
      ├── Some((1, 4)): 8/14 ≈ 0.571
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 9/14 ≈ 0.643
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((6, 2)): 44/88 ≈ 0.500
      ├── Some((2, 0)): 6/10 ≈ 0.600
      ├── Some((2, 1)): 6/11 ≈ 0.545
      ├── Some((2, 2)): 7/11 ≈ 0.636
      ├── Some((2, 3)): 4/9 ≈ 0.444
      ├── Some((2, 4)): 3/8 ≈ 0.375
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 6/11 ≈ 0.545
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((6, 3)): 14/43 ≈ 0.326
      ├── Some((3, 0)): 2/5 ≈ 0.400
      ├── Some((3, 1)): 0/3 ≈ 0.000
      ├── Some((3, 2)): 0/3 ≈ 0.000
      ├── Some((3, 3)): 1/4 ≈ 0.250
      ├── Some((3, 4)): 2/5 ≈ 0.400
      ├── Some((3, 5)): 2/5 ≈ 0.400
      ├── Some((3, 6)): 4/7 ≈ 0.571
      ├── Some((3, 7)): 1/5 ≈ 0.200
      └── Some((3, 8)): 2/5 ≈ 0.400
    ├── Some((6, 4)): 36/76 ≈ 0.474
      ├── Some((4, 0)): 6/11 ≈ 0.545
      ├── Some((4, 1)): 6/11 ≈ 0.545
      ├── Some((4, 2)): 5/10 ≈ 0.500
      ├── Some((4, 3)): 1/6 ≈ 0.167
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 7/11 ≈ 0.636
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((6, 5)): 32/70 ≈ 0.457
      ├── Some((5, 0)): 0/4 ≈ 0.000
      ├── Some((5, 1)): 2/6 ≈ 0.333
      ├── Some((5, 2)): 3/8 ≈ 0.375
      ├── Some((5, 3)): 3/8 ≈ 0.375
      ├── Some((5, 4)): 4/8 ≈ 0.500
      ├── Some((5, 5)): 4/8 ≈ 0.500
      ├── Some((5, 6)): 5/9 ≈ 0.556
      ├── Some((5, 7)): 6/10 ≈ 0.600
      └── Some((5, 8)): 4/8 ≈ 0.500
    ├── Some((6, 6)): 36/76 ≈ 0.474
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 12/16 ≈ 0.750
      ├── Some((6, 3)): 5/10 ≈ 0.500
      ├── Some((6, 4)): 1/6 ≈ 0.167
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 9/14 ≈ 0.643
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((6, 7)): 36/76 ≈ 0.474
      ├── Some((7, 0)): 1/6 ≈ 0.167
      ├── Some((7, 1)): 7/12 ≈ 0.583
      ├── Some((7, 2)): 8/13 ≈ 0.615
      ├── Some((7, 3)): 4/9 ≈ 0.444
      ├── Some((7, 5)): 2/7 ≈ 0.286
      ├── Some((7, 6)): 2/7 ≈ 0.286
      ├── Some((7, 7)): 5/10 ≈ 0.500
      └── Some((7, 8)): 6/11 ≈ 0.545
    └── Some((6, 8)): 63/114 ≈ 0.553
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 8/14 ≈ 0.571
      ├── Some((8, 2)): 13/18 ≈ 0.722
      ├── Some((8, 3)): 7/13 ≈ 0.538
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 7/13 ≈ 0.538
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 7/13 ≈ 0.538
      └── Some((8, 8)): 13/18 ≈ 0.722
  ├── Some((4, 7)): 359/737 ≈ 0.487
    ├── Some((7, 0)): 41/86 ≈ 0.477
      ├── Some((0, 0)): 9/14 ≈ 0.643
      ├── Some((0, 1)): 5/10 ≈ 0.500
      ├── Some((0, 2)): 8/13 ≈ 0.615
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 3/8 ≈ 0.375
      ├── Some((0, 5)): 6/11 ≈ 0.545
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 0/5 ≈ 0.000
      └── Some((0, 8)): 2/7 ≈ 0.286
    ├── Some((7, 1)): 59/112 ≈ 0.527
      ├── Some((1, 0)): 4/10 ≈ 0.400
      ├── Some((1, 1)): 3/9 ≈ 0.333
      ├── Some((1, 2)): 8/14 ≈ 0.571
      ├── Some((1, 3)): 8/14 ≈ 0.571
      ├── Some((1, 4)): 11/16 ≈ 0.688
      ├── Some((1, 5)): 3/9 ≈ 0.333
      ├── Some((1, 6)): 9/14 ≈ 0.643
      ├── Some((1, 7)): 5/11 ≈ 0.455
      └── Some((1, 8)): 8/14 ≈ 0.571
    ├── Some((7, 2)): 49/98 ≈ 0.500
      ├── Some((2, 0)): 2/7 ≈ 0.286
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 3/9 ≈ 0.333
      ├── Some((2, 3)): 0/5 ≈ 0.000
      ├── Some((2, 4)): 7/13 ≈ 0.538
      ├── Some((2, 5)): 9/14 ≈ 0.643
      ├── Some((2, 6)): 9/14 ≈ 0.643
      ├── Some((2, 7)): 7/13 ≈ 0.538
      └── Some((2, 8)): 9/14 ≈ 0.643
    ├── Some((7, 3)): 27/66 ≈ 0.409
      ├── Some((3, 0)): 2/6 ≈ 0.333
      ├── Some((3, 1)): 7/11 ≈ 0.636
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 5/9 ≈ 0.556
      ├── Some((3, 4)): 1/5 ≈ 0.200
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 1/5 ≈ 0.200
      ├── Some((3, 7)): 6/10 ≈ 0.600
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((7, 5)): 50/100 ≈ 0.500
      ├── Some((5, 0)): 10/15 ≈ 0.667
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 6/12 ≈ 0.500
      ├── Some((5, 3)): 9/14 ≈ 0.643
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 6/12 ≈ 0.500
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 6/12 ≈ 0.500
    ├── Some((7, 6)): 51/101 ≈ 0.505
      ├── Some((6, 0)): 11/16 ≈ 0.688
      ├── Some((6, 1)): 0/5 ≈ 0.000
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 8/13 ≈ 0.615
      ├── Some((6, 4)): 11/16 ≈ 0.688
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 6/12 ≈ 0.500
    ├── Some((7, 7)): 51/101 ≈ 0.505
      ├── Some((7, 0)): 4/11 ≈ 0.364
      ├── Some((7, 1)): 2/9 ≈ 0.222
      ├── Some((7, 2)): 14/22 ≈ 0.636
      ├── Some((7, 3)): 9/16 ≈ 0.562
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 10/17 ≈ 0.588
      └── Some((7, 8)): 5/12 ≈ 0.417
    └── Some((7, 8)): 31/72 ≈ 0.431
      ├── Some((8, 0)): 2/7 ≈ 0.286
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 8/12 ≈ 0.667
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 3/8 ≈ 0.375
      ├── Some((8, 6)): 5/10 ≈ 0.500
      ├── Some((8, 7)): 3/8 ≈ 0.375
      └── Some((8, 8)): 6/10 ≈ 0.600
  └── Some((4, 8)): 392/795 ≈ 0.493
    ├── Some((8, 0)): 42/86 ≈ 0.488
      ├── Some((0, 0)): 6/11 ≈ 0.545
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 7/12 ≈ 0.583
      ├── Some((0, 3)): 0/5 ≈ 0.000
      ├── Some((0, 4)): 4/9 ≈ 0.444
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 5/10 ≈ 0.500
      ├── Some((0, 7)): 2/7 ≈ 0.286
      └── Some((0, 8)): 8/12 ≈ 0.667
    ├── Some((8, 1)): 39/82 ≈ 0.476
      ├── Some((1, 0)): 9/13 ≈ 0.692
      ├── Some((1, 1)): 4/9 ≈ 0.444
      ├── Some((1, 2)): 6/10 ≈ 0.600
      ├── Some((1, 3)): 5/10 ≈ 0.500
      ├── Some((1, 4)): 5/10 ≈ 0.500
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 5/10 ≈ 0.500
      ├── Some((1, 7)): 0/4 ≈ 0.000
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((8, 2)): 66/120 ≈ 0.550
      ├── Some((2, 0)): 9/15 ≈ 0.600
      ├── Some((2, 1)): 6/12 ≈ 0.500
      ├── Some((2, 2)): 7/13 ≈ 0.538
      ├── Some((2, 3)): 5/11 ≈ 0.455
      ├── Some((2, 4)): 1/7 ≈ 0.143
      ├── Some((2, 5)): 6/12 ≈ 0.500
      ├── Some((2, 6)): 14/20 ≈ 0.700
      ├── Some((2, 7)): 7/13 ≈ 0.538
      └── Some((2, 8)): 10/16 ≈ 0.625
    ├── Some((8, 3)): 72/128 ≈ 0.562
      ├── Some((3, 0)): 6/13 ≈ 0.462
      ├── Some((3, 1)): 10/16 ≈ 0.625
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 16/22 ≈ 0.727
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 11/17 ≈ 0.647
      ├── Some((3, 6)): 9/15 ≈ 0.600
      ├── Some((3, 7)): 2/8 ≈ 0.250
      └── Some((3, 8)): 11/17 ≈ 0.647
    ├── Some((8, 4)): 51/99 ≈ 0.515
      ├── Some((4, 0)): 3/9 ≈ 0.333
      ├── Some((4, 1)): 6/12 ≈ 0.500
      ├── Some((4, 2)): 5/11 ≈ 0.455
      ├── Some((4, 3)): 15/21 ≈ 0.714
      ├── Some((4, 4)): 1/7 ≈ 0.143
      ├── Some((4, 5)): 9/15 ≈ 0.600
      ├── Some((4, 6)): 4/10 ≈ 0.400
      └── Some((4, 7)): 7/13 ≈ 0.538
    ├── Some((8, 5)): 28/66 ≈ 0.424
      ├── Some((5, 0)): 5/9 ≈ 0.556
      ├── Some((5, 1)): 6/10 ≈ 0.600
      ├── Some((5, 2)): 6/10 ≈ 0.600
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 2/6 ≈ 0.333
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 4/8 ≈ 0.500
      ├── Some((5, 7)): 2/7 ≈ 0.286
      └── Some((5, 8)): 1/5 ≈ 0.200
    ├── Some((8, 6)): 45/91 ≈ 0.495
      ├── Some((6, 0)): 6/11 ≈ 0.545
      ├── Some((6, 1)): 8/13 ≈ 0.615
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 8/13 ≈ 0.615
      ├── Some((6, 4)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 6/11 ≈ 0.545
      ├── Some((6, 7)): 6/11 ≈ 0.545
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((8, 7)): 27/65 ≈ 0.415
      ├── Some((7, 0)): 1/5 ≈ 0.200
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 6/11 ≈ 0.545
      ├── Some((7, 3)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 6/11 ≈ 0.545
      ├── Some((7, 6)): 1/6 ≈ 0.167
      ├── Some((7, 7)): 7/11 ≈ 0.636
      └── Some((7, 8)): 0/4 ≈ 0.000
    └── Some((8, 8)): 22/57 ≈ 0.386
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 0/4 ≈ 0.000
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 4/9 ≈ 0.444
      └── Some((8, 7)): 8/12 ≈ 0.667
├── Some((7, 5)): 8375/15925 ≈ 0.526
  ├── Some((5, 0)): 975/1849 ≈ 0.527
    ├── Some((0, 0)): 90/178 ≈ 0.506
      ├── Some((0, 1)): 15/26 ≈ 0.577
      ├── Some((0, 2)): 13/24 ≈ 0.542
      ├── Some((0, 3)): 19/31 ≈ 0.613
      ├── Some((0, 4)): 11/22 ≈ 0.500
      ├── Some((0, 5)): 10/21 ≈ 0.476
      ├── Some((0, 6)): 9/20 ≈ 0.450
      ├── Some((0, 7)): 11/22 ≈ 0.500
      └── Some((0, 8)): 2/11 ≈ 0.182
    ├── Some((0, 1)): 105/201 ≈ 0.522
      ├── Some((1, 0)): 12/23 ≈ 0.522
      ├── Some((1, 1)): 16/27 ≈ 0.593
      ├── Some((1, 2)): 10/21 ≈ 0.476
      ├── Some((1, 3)): 14/25 ≈ 0.560
      ├── Some((1, 4)): 19/31 ≈ 0.613
      ├── Some((1, 5)): 3/12 ≈ 0.250
      ├── Some((1, 6)): 17/28 ≈ 0.607
      ├── Some((1, 7)): 6/16 ≈ 0.375
      └── Some((1, 8)): 7/17 ≈ 0.412
    ├── Some((0, 2)): 147/263 ≈ 0.559
      ├── Some((2, 0)): 19/32 ≈ 0.594
      ├── Some((2, 1)): 29/43 ≈ 0.674
      ├── Some((2, 2)): 11/23 ≈ 0.478
      ├── Some((2, 3)): 15/28 ≈ 0.536
      ├── Some((2, 4)): 13/26 ≈ 0.500
      ├── Some((2, 5)): 9/21 ≈ 0.429
      ├── Some((2, 6)): 12/24 ≈ 0.500
      ├── Some((2, 7)): 24/38 ≈ 0.632
      └── Some((2, 8)): 14/27 ≈ 0.519
    ├── Some((0, 3)): 73/152 ≈ 0.480
      ├── Some((3, 0)): 5/13 ≈ 0.385
      ├── Some((3, 1)): 4/12 ≈ 0.333
      ├── Some((3, 2)): 10/19 ≈ 0.526
      ├── Some((3, 3)): 5/14 ≈ 0.357
      ├── Some((3, 4)): 18/27 ≈ 0.667
      ├── Some((3, 5)): 10/19 ≈ 0.526
      ├── Some((3, 6)): 8/17 ≈ 0.471
      ├── Some((3, 7)): 9/18 ≈ 0.500
      └── Some((3, 8)): 4/12 ≈ 0.333
    ├── Some((0, 4)): 100/194 ≈ 0.515
      ├── Some((4, 0)): 8/18 ≈ 0.444
      ├── Some((4, 1)): 10/20 ≈ 0.500
      ├── Some((4, 2)): 11/21 ≈ 0.524
      ├── Some((4, 3)): 19/30 ≈ 0.633
      ├── Some((4, 4)): 14/25 ≈ 0.560
      ├── Some((4, 5)): 11/22 ≈ 0.500
      ├── Some((4, 6)): 6/16 ≈ 0.375
      ├── Some((4, 7)): 4/13 ≈ 0.308
      └── Some((4, 8)): 17/28 ≈ 0.607
    ├── Some((0, 5)): 80/163 ≈ 0.491
      ├── Some((5, 1)): 4/13 ≈ 0.308
      ├── Some((5, 2)): 16/27 ≈ 0.593
      ├── Some((5, 3)): 9/19 ≈ 0.474
      ├── Some((5, 4)): 9/19 ≈ 0.474
      ├── Some((5, 5)): 12/23 ≈ 0.522
      ├── Some((5, 6)): 9/19 ≈ 0.474
      ├── Some((5, 7)): 9/19 ≈ 0.474
      └── Some((5, 8)): 12/23 ≈ 0.522
    ├── Some((0, 6)): 161/283 ≈ 0.569
      ├── Some((6, 0)): 15/28 ≈ 0.536
      ├── Some((6, 1)): 16/29 ≈ 0.552
      ├── Some((6, 2)): 27/42 ≈ 0.643
      ├── Some((6, 3)): 27/42 ≈ 0.643
      ├── Some((6, 4)): 18/32 ≈ 0.562
      ├── Some((6, 5)): 13/26 ≈ 0.500
      ├── Some((6, 6)): 15/28 ≈ 0.536
      ├── Some((6, 7)): 10/22 ≈ 0.455
      └── Some((6, 8)): 19/33 ≈ 0.576
    ├── Some((0, 7)): 122/226 ≈ 0.540
      ├── Some((7, 0)): 26/41 ≈ 0.634
      ├── Some((7, 1)): 26/41 ≈ 0.634
      ├── Some((7, 2)): 10/22 ≈ 0.455
      ├── Some((7, 3)): 13/26 ≈ 0.500
      ├── Some((7, 4)): 17/31 ≈ 0.548
      ├── Some((7, 6)): 3/13 ≈ 0.231
      ├── Some((7, 7)): 6/17 ≈ 0.353
      └── Some((7, 8)): 20/34 ≈ 0.588
    └── Some((0, 8)): 96/188 ≈ 0.511
      ├── Some((8, 0)): 4/13 ≈ 0.308
      ├── Some((8, 1)): 9/19 ≈ 0.474
      ├── Some((8, 2)): 10/20 ≈ 0.500
      ├── Some((8, 3)): 16/27 ≈ 0.593
      ├── Some((8, 4)): 6/16 ≈ 0.375
      ├── Some((8, 5)): 16/27 ≈ 0.593
      ├── Some((8, 6)): 5/14 ≈ 0.357
      ├── Some((8, 7)): 19/30 ≈ 0.633
      └── Some((8, 8)): 11/21 ≈ 0.524
  ├── Some((5, 1)): 577/1157 ≈ 0.499
    ├── Some((1, 0)): 59/122 ≈ 0.484
      ├── Some((0, 0)): 12/19 ≈ 0.632
      ├── Some((0, 1)): 9/16 ≈ 0.562
      ├── Some((0, 2)): 5/12 ≈ 0.417
      ├── Some((0, 3)): 2/9 ≈ 0.222
      ├── Some((0, 4)): 5/12 ≈ 0.417
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 8/15 ≈ 0.533
      ├── Some((0, 7)): 5/12 ≈ 0.417
      └── Some((0, 8)): 6/13 ≈ 0.462
    ├── Some((1, 1)): 63/128 ≈ 0.492
      ├── Some((1, 0)): 3/11 ≈ 0.273
      ├── Some((1, 2)): 7/15 ≈ 0.467
      ├── Some((1, 3)): 16/25 ≈ 0.640
      ├── Some((1, 4)): 12/20 ≈ 0.600
      ├── Some((1, 5)): 6/14 ≈ 0.429
      ├── Some((1, 6)): 6/14 ≈ 0.429
      ├── Some((1, 7)): 6/14 ≈ 0.429
      └── Some((1, 8)): 6/14 ≈ 0.429
    ├── Some((1, 2)): 81/154 ≈ 0.526
      ├── Some((2, 0)): 10/18 ≈ 0.556
      ├── Some((2, 1)): 13/21 ≈ 0.619
      ├── Some((2, 2)): 9/17 ≈ 0.529
      ├── Some((2, 3)): 12/20 ≈ 0.600
      ├── Some((2, 4)): 13/21 ≈ 0.619
      ├── Some((2, 5)): 4/12 ≈ 0.333
      ├── Some((2, 6)): 1/8 ≈ 0.125
      ├── Some((2, 7)): 13/22 ≈ 0.591
      └── Some((2, 8)): 6/14 ≈ 0.429
    ├── Some((1, 3)): 33/82 ≈ 0.402
      ├── Some((3, 0)): 5/11 ≈ 0.455
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 0/5 ≈ 0.000
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 7/13 ≈ 0.538
      ├── Some((3, 7)): 4/10 ≈ 0.400
      └── Some((3, 8)): 3/8 ≈ 0.375
    ├── Some((1, 4)): 34/83 ≈ 0.410
      ├── Some((4, 0)): 1/6 ≈ 0.167
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 4/10 ≈ 0.400
      ├── Some((4, 4)): 8/14 ≈ 0.571
      ├── Some((4, 5)): 1/6 ≈ 0.167
      ├── Some((4, 6)): 1/6 ≈ 0.167
      ├── Some((4, 7)): 9/14 ≈ 0.643
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((1, 5)): 89/165 ≈ 0.539
      ├── Some((5, 0)): 17/27 ≈ 0.630
      ├── Some((5, 2)): 15/25 ≈ 0.600
      ├── Some((5, 3)): 9/18 ≈ 0.500
      ├── Some((5, 4)): 6/15 ≈ 0.400
      ├── Some((5, 5)): 5/14 ≈ 0.357
      ├── Some((5, 6)): 18/28 ≈ 0.643
      ├── Some((5, 7)): 10/19 ≈ 0.526
      └── Some((5, 8)): 9/18 ≈ 0.500
    ├── Some((1, 6)): 98/178 ≈ 0.551
      ├── Some((6, 0)): 4/12 ≈ 0.333
      ├── Some((6, 1)): 21/30 ≈ 0.700
      ├── Some((6, 2)): 8/17 ≈ 0.471
      ├── Some((6, 3)): 12/21 ≈ 0.571
      ├── Some((6, 4)): 16/25 ≈ 0.640
      ├── Some((6, 5)): 10/19 ≈ 0.526
      ├── Some((6, 6)): 4/12 ≈ 0.333
      ├── Some((6, 7)): 10/19 ≈ 0.526
      └── Some((6, 8)): 13/22 ≈ 0.591
    ├── Some((1, 7)): 45/100 ≈ 0.450
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 4/10 ≈ 0.400
      ├── Some((7, 3)): 9/16 ≈ 0.562
      ├── Some((7, 4)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 8/15 ≈ 0.533
      ├── Some((7, 7)): 2/8 ≈ 0.250
      └── Some((7, 8)): 4/11 ≈ 0.364
    └── Some((1, 8)): 74/144 ≈ 0.514
      ├── Some((8, 0)): 15/23 ≈ 0.652
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 12/20 ≈ 0.600
      ├── Some((8, 3)): 5/12 ≈ 0.417
      ├── Some((8, 4)): 2/9 ≈ 0.222
      ├── Some((8, 5)): 11/19 ≈ 0.579
      ├── Some((8, 6)): 12/20 ≈ 0.600
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 6/14 ≈ 0.429
  ├── Some((5, 2)): 1378/2537 ≈ 0.543
    ├── Some((2, 0)): 114/223 ≈ 0.511
      ├── Some((0, 0)): 16/29 ≈ 0.552
      ├── Some((0, 1)): 21/34 ≈ 0.618
      ├── Some((0, 2)): 18/31 ≈ 0.581
      ├── Some((0, 3)): 8/19 ≈ 0.421
      ├── Some((0, 4)): 17/30 ≈ 0.567
      ├── Some((0, 5)): 5/16 ≈ 0.312
      ├── Some((0, 6)): 10/22 ≈ 0.455
      ├── Some((0, 7)): 4/14 ≈ 0.286
      └── Some((0, 8)): 14/27 ≈ 0.519
    ├── Some((2, 1)): 138/259 ≈ 0.533
      ├── Some((1, 0)): 24/39 ≈ 0.615
      ├── Some((1, 1)): 22/36 ≈ 0.611
      ├── Some((1, 2)): 12/25 ≈ 0.480
      ├── Some((1, 3)): 13/26 ≈ 0.500
      ├── Some((1, 4)): 9/21 ≈ 0.429
      ├── Some((1, 5)): 5/16 ≈ 0.312
      ├── Some((1, 6)): 20/34 ≈ 0.588
      ├── Some((1, 7)): 18/32 ≈ 0.562
      └── Some((1, 8)): 15/29 ≈ 0.517
    ├── Some((2, 2)): 114/223 ≈ 0.511
      ├── Some((2, 0)): 20/34 ≈ 0.588
      ├── Some((2, 1)): 13/26 ≈ 0.500
      ├── Some((2, 3)): 10/23 ≈ 0.435
      ├── Some((2, 4)): 12/25 ≈ 0.480
      ├── Some((2, 5)): 9/22 ≈ 0.409
      ├── Some((2, 6)): 18/32 ≈ 0.562
      ├── Some((2, 7)): 11/24 ≈ 0.458
      └── Some((2, 8)): 21/36 ≈ 0.583
    ├── Some((2, 3)): 195/344 ≈ 0.567
      ├── Some((3, 0)): 19/35 ≈ 0.543
      ├── Some((3, 1)): 13/28 ≈ 0.464
      ├── Some((3, 2)): 14/29 ≈ 0.483
      ├── Some((3, 3)): 21/38 ≈ 0.553
      ├── Some((3, 4)): 29/47 ≈ 0.617
      ├── Some((3, 5)): 17/33 ≈ 0.515
      ├── Some((3, 6)): 23/40 ≈ 0.575
      ├── Some((3, 7)): 30/48 ≈ 0.625
      └── Some((3, 8)): 28/45 ≈ 0.622
    ├── Some((2, 4)): 157/288 ≈ 0.545
      ├── Some((4, 0)): 12/26 ≈ 0.462
      ├── Some((4, 1)): 25/40 ≈ 0.625
      ├── Some((4, 2)): 17/32 ≈ 0.531
      ├── Some((4, 3)): 16/30 ≈ 0.533
      ├── Some((4, 4)): 10/23 ≈ 0.435
      ├── Some((4, 5)): 12/26 ≈ 0.462
      ├── Some((4, 6)): 13/27 ≈ 0.481
      ├── Some((4, 7)): 29/45 ≈ 0.644
      └── Some((4, 8)): 23/38 ≈ 0.605
    ├── Some((2, 5)): 156/287 ≈ 0.544
      ├── Some((5, 0)): 12/27 ≈ 0.444
      ├── Some((5, 1)): 13/28 ≈ 0.464
      ├── Some((5, 3)): 26/43 ≈ 0.605
      ├── Some((5, 4)): 25/42 ≈ 0.595
      ├── Some((5, 5)): 16/32 ≈ 0.500
      ├── Some((5, 6)): 25/42 ≈ 0.595
      ├── Some((5, 7)): 24/41 ≈ 0.585
      └── Some((5, 8)): 15/31 ≈ 0.484
    ├── Some((2, 6)): 222/384 ≈ 0.578
      ├── Some((6, 0)): 29/48 ≈ 0.604
      ├── Some((6, 1)): 16/32 ≈ 0.500
      ├── Some((6, 2)): 33/52 ≈ 0.635
      ├── Some((6, 3)): 27/45 ≈ 0.600
      ├── Some((6, 4)): 19/36 ≈ 0.528
      ├── Some((6, 5)): 17/34 ≈ 0.500
      ├── Some((6, 6)): 30/49 ≈ 0.612
      ├── Some((6, 7)): 26/44 ≈ 0.591
      └── Some((6, 8)): 25/43 ≈ 0.581
    ├── Some((2, 7)): 137/258 ≈ 0.531
      ├── Some((7, 0)): 19/35 ≈ 0.543
      ├── Some((7, 1)): 1/12 ≈ 0.083
      ├── Some((7, 2)): 5/17 ≈ 0.294
      ├── Some((7, 3)): 22/39 ≈ 0.564
      ├── Some((7, 4)): 11/25 ≈ 0.440
      ├── Some((7, 6)): 33/51 ≈ 0.647
      ├── Some((7, 7)): 20/36 ≈ 0.556
      └── Some((7, 8)): 25/42 ≈ 0.595
    └── Some((2, 8)): 145/270 ≈ 0.537
      ├── Some((8, 0)): 12/25 ≈ 0.480
      ├── Some((8, 1)): 29/45 ≈ 0.644
      ├── Some((8, 2)): 19/34 ≈ 0.559
      ├── Some((8, 3)): 14/28 ≈ 0.500
      ├── Some((8, 4)): 19/34 ≈ 0.559
      ├── Some((8, 5)): 24/39 ≈ 0.615
      ├── Some((8, 6)): 6/18 ≈ 0.333
      ├── Some((8, 7)): 17/31 ≈ 0.548
      └── Some((8, 8)): 4/15 ≈ 0.267
  ├── Some((5, 3)): 1053/1983 ≈ 0.531
    ├── Some((3, 0)): 54/124 ≈ 0.435
      ├── Some((0, 0)): 3/11 ≈ 0.273
      ├── Some((0, 1)): 2/9 ≈ 0.222
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 10/18 ≈ 0.556
      ├── Some((0, 4)): 11/19 ≈ 0.579
      ├── Some((0, 5)): 9/17 ≈ 0.529
      ├── Some((0, 6)): 2/9 ≈ 0.222
      ├── Some((0, 7)): 2/9 ≈ 0.222
      └── Some((0, 8)): 5/13 ≈ 0.385
    ├── Some((3, 1)): 106/205 ≈ 0.517
      ├── Some((1, 0)): 14/26 ≈ 0.538
      ├── Some((1, 1)): 7/17 ≈ 0.412
      ├── Some((1, 2)): 3/12 ≈ 0.250
      ├── Some((1, 3)): 13/24 ≈ 0.542
      ├── Some((1, 4)): 12/23 ≈ 0.522
      ├── Some((1, 5)): 17/29 ≈ 0.586
      ├── Some((1, 6)): 18/30 ≈ 0.600
      ├── Some((1, 7)): 13/24 ≈ 0.542
      └── Some((1, 8)): 8/19 ≈ 0.421
    ├── Some((3, 2)): 154/276 ≈ 0.558
      ├── Some((2, 0)): 13/26 ≈ 0.500
      ├── Some((2, 1)): 19/33 ≈ 0.576
      ├── Some((2, 2)): 23/37 ≈ 0.622
      ├── Some((2, 3)): 15/28 ≈ 0.536
      ├── Some((2, 4)): 20/34 ≈ 0.588
      ├── Some((2, 5)): 25/40 ≈ 0.625
      ├── Some((2, 6)): 14/27 ≈ 0.519
      ├── Some((2, 7)): 6/18 ≈ 0.333
      └── Some((2, 8)): 18/32 ≈ 0.562
    ├── Some((3, 3)): 137/251 ≈ 0.546
      ├── Some((3, 0)): 32/48 ≈ 0.667
      ├── Some((3, 1)): 12/25 ≈ 0.480
      ├── Some((3, 2)): 11/24 ≈ 0.458
      ├── Some((3, 4)): 14/28 ≈ 0.500
      ├── Some((3, 5)): 12/25 ≈ 0.480
      ├── Some((3, 6)): 18/33 ≈ 0.545
      ├── Some((3, 7)): 19/34 ≈ 0.559
      └── Some((3, 8)): 18/33 ≈ 0.545
    ├── Some((3, 4)): 149/269 ≈ 0.554
      ├── Some((4, 0)): 25/39 ≈ 0.641
      ├── Some((4, 1)): 22/36 ≈ 0.611
      ├── Some((4, 2)): 22/36 ≈ 0.611
      ├── Some((4, 3)): 15/28 ≈ 0.536
      ├── Some((4, 4)): 18/32 ≈ 0.562
      ├── Some((4, 5)): 14/27 ≈ 0.519
      ├── Some((4, 6)): 8/20 ≈ 0.400
      ├── Some((4, 7)): 8/20 ≈ 0.400
      └── Some((4, 8)): 17/30 ≈ 0.567
    ├── Some((3, 5)): 101/198 ≈ 0.510
      ├── Some((5, 0)): 8/19 ≈ 0.421
      ├── Some((5, 1)): 13/25 ≈ 0.520
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 4)): 8/19 ≈ 0.421
      ├── Some((5, 5)): 15/27 ≈ 0.556
      ├── Some((5, 6)): 15/28 ≈ 0.536
      ├── Some((5, 7)): 14/26 ≈ 0.538
      └── Some((5, 8)): 16/29 ≈ 0.552
    ├── Some((3, 6)): 151/272 ≈ 0.555
      ├── Some((6, 0)): 16/30 ≈ 0.533
      ├── Some((6, 1)): 14/27 ≈ 0.519
      ├── Some((6, 2)): 27/42 ≈ 0.643
      ├── Some((6, 3)): 15/28 ≈ 0.536
      ├── Some((6, 4)): 7/19 ≈ 0.368
      ├── Some((6, 5)): 29/44 ≈ 0.659
      ├── Some((6, 6)): 20/34 ≈ 0.588
      ├── Some((6, 7)): 7/19 ≈ 0.368
      └── Some((6, 8)): 15/28 ≈ 0.536
    ├── Some((3, 7)): 41/103 ≈ 0.398
      ├── Some((7, 0)): 4/11 ≈ 0.364
      ├── Some((7, 1)): 6/14 ≈ 0.429
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 3/10 ≈ 0.300
      ├── Some((7, 4)): 10/18 ≈ 0.556
      ├── Some((7, 6)): 4/12 ≈ 0.333
      ├── Some((7, 7)): 4/12 ≈ 0.333
      └── Some((7, 8)): 2/9 ≈ 0.222
    └── Some((3, 8)): 159/284 ≈ 0.560
      ├── Some((8, 0)): 20/34 ≈ 0.588
      ├── Some((8, 1)): 14/27 ≈ 0.519
      ├── Some((8, 2)): 24/39 ≈ 0.615
      ├── Some((8, 3)): 16/30 ≈ 0.533
      ├── Some((8, 4)): 19/33 ≈ 0.576
      ├── Some((8, 5)): 27/42 ≈ 0.643
      ├── Some((8, 6)): 12/25 ≈ 0.480
      ├── Some((8, 7)): 14/27 ≈ 0.519
      └── Some((8, 8)): 13/26 ≈ 0.500
  ├── Some((5, 4)): 1330/2455 ≈ 0.542
    ├── Some((4, 0)): 144/268 ≈ 0.537
      ├── Some((0, 0)): 18/33 ≈ 0.545
      ├── Some((0, 1)): 21/36 ≈ 0.583
      ├── Some((0, 2)): 17/31 ≈ 0.548
      ├── Some((0, 3)): 12/25 ≈ 0.480
      ├── Some((0, 4)): 11/24 ≈ 0.458
      ├── Some((0, 5)): 1/11 ≈ 0.091
      ├── Some((0, 6)): 19/34 ≈ 0.559
      ├── Some((0, 7)): 32/48 ≈ 0.667
      └── Some((0, 8)): 12/25 ≈ 0.480
    ├── Some((4, 1)): 112/219 ≈ 0.511
      ├── Some((1, 0)): 19/32 ≈ 0.594
      ├── Some((1, 1)): 11/23 ≈ 0.478
      ├── Some((1, 2)): 14/26 ≈ 0.538
      ├── Some((1, 3)): 15/27 ≈ 0.556
      ├── Some((1, 4)): 14/26 ≈ 0.538
      ├── Some((1, 5)): 7/18 ≈ 0.389
      ├── Some((1, 6)): 3/13 ≈ 0.231
      ├── Some((1, 7)): 15/28 ≈ 0.536
      └── Some((1, 8)): 13/25 ≈ 0.520
    ├── Some((4, 2)): 214/371 ≈ 0.577
      ├── Some((2, 0)): 31/50 ≈ 0.620
      ├── Some((2, 1)): 16/32 ≈ 0.500
      ├── Some((2, 2)): 23/41 ≈ 0.561
      ├── Some((2, 3)): 22/39 ≈ 0.564
      ├── Some((2, 4)): 20/37 ≈ 0.541
      ├── Some((2, 5)): 11/26 ≈ 0.423
      ├── Some((2, 6)): 48/69 ≈ 0.696
      ├── Some((2, 7)): 16/32 ≈ 0.500
      └── Some((2, 8)): 26/44 ≈ 0.591
    ├── Some((4, 3)): 112/219 ≈ 0.511
      ├── Some((3, 0)): 5/16 ≈ 0.312
      ├── Some((3, 1)): 11/23 ≈ 0.478
      ├── Some((3, 2)): 12/24 ≈ 0.500
      ├── Some((3, 3)): 16/28 ≈ 0.571
      ├── Some((3, 4)): 22/35 ≈ 0.629
      ├── Some((3, 5)): 16/28 ≈ 0.571
      ├── Some((3, 6)): 9/20 ≈ 0.450
      ├── Some((3, 7)): 8/19 ≈ 0.421
      └── Some((3, 8)): 13/25 ≈ 0.520
    ├── Some((4, 4)): 208/362 ≈ 0.575
      ├── Some((4, 0)): 26/45 ≈ 0.578
      ├── Some((4, 1)): 15/32 ≈ 0.469
      ├── Some((4, 2)): 28/48 ≈ 0.583
      ├── Some((4, 3)): 28/48 ≈ 0.583
      ├── Some((4, 5)): 33/54 ≈ 0.611
      ├── Some((4, 6)): 38/59 ≈ 0.644
      ├── Some((4, 7)): 31/51 ≈ 0.608
      └── Some((4, 8)): 9/24 ≈ 0.375
    ├── Some((4, 5)): 125/239 ≈ 0.523
      ├── Some((5, 0)): 17/31 ≈ 0.548
      ├── Some((5, 1)): 18/33 ≈ 0.545
      ├── Some((5, 2)): 23/38 ≈ 0.605
      ├── Some((5, 3)): 12/26 ≈ 0.462
      ├── Some((5, 5)): 18/33 ≈ 0.545
      ├── Some((5, 6)): 7/19 ≈ 0.368
      ├── Some((5, 7)): 21/36 ≈ 0.583
      └── Some((5, 8)): 9/22 ≈ 0.409
    ├── Some((4, 6)): 132/249 ≈ 0.530
      ├── Some((6, 0)): 14/27 ≈ 0.519
      ├── Some((6, 1)): 25/39 ≈ 0.641
      ├── Some((6, 2)): 11/24 ≈ 0.458
      ├── Some((6, 3)): 0/9 ≈ 0.000
      ├── Some((6, 4)): 14/27 ≈ 0.519
      ├── Some((6, 5)): 9/21 ≈ 0.429
      ├── Some((6, 6)): 17/31 ≈ 0.548
      ├── Some((6, 7)): 20/34 ≈ 0.588
      └── Some((6, 8)): 22/36 ≈ 0.611
    ├── Some((4, 7)): 120/231 ≈ 0.519
      ├── Some((7, 0)): 12/25 ≈ 0.480
      ├── Some((7, 1)): 30/46 ≈ 0.652
      ├── Some((7, 2)): 20/35 ≈ 0.571
      ├── Some((7, 3)): 3/14 ≈ 0.214
      ├── Some((7, 4)): 27/43 ≈ 0.628
      ├── Some((7, 6)): 14/28 ≈ 0.500
      ├── Some((7, 7)): 8/21 ≈ 0.381
      └── Some((7, 8)): 6/18 ≈ 0.333
    └── Some((4, 8)): 163/296 ≈ 0.551
      ├── Some((8, 0)): 12/26 ≈ 0.462
      ├── Some((8, 1)): 3/14 ≈ 0.214
      ├── Some((8, 2)): 37/55 ≈ 0.673
      ├── Some((8, 3)): 24/40 ≈ 0.600
      ├── Some((8, 4)): 9/22 ≈ 0.409
      ├── Some((8, 5)): 25/41 ≈ 0.610
      ├── Some((8, 6)): 16/31 ≈ 0.516
      ├── Some((8, 7)): 25/41 ≈ 0.610
      └── Some((8, 8)): 11/25 ≈ 0.440
  ├── Some((5, 5)): 806/1557 ≈ 0.518
    ├── Some((5, 0)): 111/210 ≈ 0.529
      ├── Some((0, 0)): 9/20 ≈ 0.450
      ├── Some((0, 1)): 17/28 ≈ 0.607
      ├── Some((0, 2)): 17/29 ≈ 0.586
      ├── Some((0, 3)): 9/20 ≈ 0.450
      ├── Some((0, 4)): 1/10 ≈ 0.100
      ├── Some((0, 5)): 20/32 ≈ 0.625
      ├── Some((0, 6)): 15/26 ≈ 0.577
      ├── Some((0, 7)): 16/27 ≈ 0.593
      └── Some((0, 8)): 7/17 ≈ 0.412
    ├── Some((5, 1)): 126/233 ≈ 0.541
      ├── Some((1, 0)): 14/26 ≈ 0.538
      ├── Some((1, 1)): 11/23 ≈ 0.478
      ├── Some((1, 2)): 6/17 ≈ 0.353
      ├── Some((1, 3)): 11/23 ≈ 0.478
      ├── Some((1, 4)): 17/29 ≈ 0.586
      ├── Some((1, 5)): 21/33 ≈ 0.636
      ├── Some((1, 6)): 20/32 ≈ 0.625
      ├── Some((1, 7)): 12/24 ≈ 0.500
      └── Some((1, 8)): 13/25 ≈ 0.520
    ├── Some((5, 2)): 98/191 ≈ 0.513
      ├── Some((2, 0)): 11/22 ≈ 0.500
      ├── Some((2, 1)): 4/13 ≈ 0.308
      ├── Some((2, 2)): 19/30 ≈ 0.633
      ├── Some((2, 3)): 13/24 ≈ 0.542
      ├── Some((2, 4)): 10/20 ≈ 0.500
      ├── Some((2, 5)): 10/20 ≈ 0.500
      ├── Some((2, 6)): 2/11 ≈ 0.182
      ├── Some((2, 7)): 13/24 ≈ 0.542
      └── Some((2, 8)): 15/26 ≈ 0.577
    ├── Some((5, 3)): 100/194 ≈ 0.515
      ├── Some((3, 0)): 5/14 ≈ 0.357
      ├── Some((3, 1)): 10/20 ≈ 0.500
      ├── Some((3, 2)): 6/16 ≈ 0.375
      ├── Some((3, 3)): 18/29 ≈ 0.621
      ├── Some((3, 4)): 15/26 ≈ 0.577
      ├── Some((3, 5)): 7/17 ≈ 0.412
      ├── Some((3, 6)): 14/25 ≈ 0.560
      ├── Some((3, 7)): 12/22 ≈ 0.545
      └── Some((3, 8)): 13/24 ≈ 0.542
    ├── Some((5, 4)): 68/145 ≈ 0.469
      ├── Some((4, 0)): 14/23 ≈ 0.609
      ├── Some((4, 1)): 2/10 ≈ 0.200
      ├── Some((4, 2)): 6/14 ≈ 0.429
      ├── Some((4, 3)): 9/18 ≈ 0.500
      ├── Some((4, 4)): 5/13 ≈ 0.385
      ├── Some((4, 5)): 3/11 ≈ 0.273
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 18/27 ≈ 0.667
      └── Some((4, 8)): 6/15 ≈ 0.400
    ├── Some((5, 6)): 118/221 ≈ 0.534
      ├── Some((6, 0)): 12/24 ≈ 0.500
      ├── Some((6, 1)): 20/32 ≈ 0.625
      ├── Some((6, 2)): 8/19 ≈ 0.421
      ├── Some((6, 3)): 6/16 ≈ 0.375
      ├── Some((6, 4)): 6/16 ≈ 0.375
      ├── Some((6, 5)): 16/28 ≈ 0.571
      ├── Some((6, 6)): 15/27 ≈ 0.556
      ├── Some((6, 7)): 16/28 ≈ 0.571
      └── Some((6, 8)): 18/30 ≈ 0.600
    ├── Some((5, 7)): 50/116 ≈ 0.431
      ├── Some((7, 0)): 4/12 ≈ 0.333
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 6/14 ≈ 0.429
      ├── Some((7, 3)): 10/19 ≈ 0.526
      ├── Some((7, 4)): 2/9 ≈ 0.222
      ├── Some((7, 6)): 12/21 ≈ 0.571
      ├── Some((7, 7)): 6/14 ≈ 0.429
      └── Some((7, 8)): 3/11 ≈ 0.273
    └── Some((5, 8)): 135/246 ≈ 0.549
      ├── Some((8, 0)): 12/24 ≈ 0.500
      ├── Some((8, 1)): 24/37 ≈ 0.649
      ├── Some((8, 2)): 20/33 ≈ 0.606
      ├── Some((8, 3)): 23/36 ≈ 0.639
      ├── Some((8, 4)): 15/28 ≈ 0.536
      ├── Some((8, 5)): 8/19 ≈ 0.421
      ├── Some((8, 6)): 10/22 ≈ 0.455
      ├── Some((8, 7)): 14/27 ≈ 0.519
      └── Some((8, 8)): 8/19 ≈ 0.421
  ├── Some((5, 6)): 906/1730 ≈ 0.524
    ├── Some((6, 0)): 87/172 ≈ 0.506
      ├── Some((0, 0)): 17/27 ≈ 0.630
      ├── Some((0, 1)): 8/17 ≈ 0.471
      ├── Some((0, 2)): 8/17 ≈ 0.471
      ├── Some((0, 3)): 4/13 ≈ 0.308
      ├── Some((0, 4)): 3/11 ≈ 0.273
      ├── Some((0, 5)): 10/20 ≈ 0.500
      ├── Some((0, 6)): 7/16 ≈ 0.438
      ├── Some((0, 7)): 15/25 ≈ 0.600
      └── Some((0, 8)): 15/25 ≈ 0.600
    ├── Some((6, 1)): 102/194 ≈ 0.526
      ├── Some((1, 0)): 11/21 ≈ 0.524
      ├── Some((1, 1)): 13/23 ≈ 0.565
      ├── Some((1, 2)): 16/27 ≈ 0.593
      ├── Some((1, 3)): 15/25 ≈ 0.600
      ├── Some((1, 4)): 5/14 ≈ 0.357
      ├── Some((1, 5)): 19/30 ≈ 0.633
      ├── Some((1, 6)): 9/19 ≈ 0.474
      ├── Some((1, 7)): 7/17 ≈ 0.412
      └── Some((1, 8)): 7/17 ≈ 0.412
    ├── Some((6, 2)): 114/212 ≈ 0.538
      ├── Some((2, 0)): 15/26 ≈ 0.577
      ├── Some((2, 1)): 17/29 ≈ 0.586
      ├── Some((2, 2)): 10/21 ≈ 0.476
      ├── Some((2, 3)): 11/22 ≈ 0.500
      ├── Some((2, 4)): 3/12 ≈ 0.250
      ├── Some((2, 5)): 7/17 ≈ 0.412
      ├── Some((2, 6)): 13/24 ≈ 0.542
      ├── Some((2, 7)): 16/27 ≈ 0.593
      └── Some((2, 8)): 21/33 ≈ 0.636
    ├── Some((6, 3)): 76/155 ≈ 0.490
      ├── Some((3, 0)): 11/20 ≈ 0.550
      ├── Some((3, 1)): 11/20 ≈ 0.550
      ├── Some((3, 2)): 8/17 ≈ 0.471
      ├── Some((3, 3)): 7/16 ≈ 0.438
      ├── Some((3, 4)): 13/22 ≈ 0.591
      ├── Some((3, 5)): 8/17 ≈ 0.471
      ├── Some((3, 6)): 15/24 ≈ 0.625
      ├── Some((3, 7)): 1/8 ≈ 0.125
      └── Some((3, 8)): 2/10 ≈ 0.200
    ├── Some((6, 4)): 88/174 ≈ 0.506
      ├── Some((4, 0)): 7/16 ≈ 0.438
      ├── Some((4, 1)): 12/22 ≈ 0.545
      ├── Some((4, 2)): 9/18 ≈ 0.500
      ├── Some((4, 3)): 9/18 ≈ 0.500
      ├── Some((4, 4)): 5/14 ≈ 0.357
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 5/14 ≈ 0.357
      ├── Some((4, 7)): 18/28 ≈ 0.643
      └── Some((4, 8)): 14/24 ≈ 0.583
    ├── Some((6, 5)): 95/184 ≈ 0.516
      ├── Some((5, 0)): 9/20 ≈ 0.450
      ├── Some((5, 1)): 18/30 ≈ 0.600
      ├── Some((5, 2)): 12/23 ≈ 0.522
      ├── Some((5, 3)): 12/23 ≈ 0.522
      ├── Some((5, 4)): 17/29 ≈ 0.586
      ├── Some((5, 5)): 7/17 ≈ 0.412
      ├── Some((5, 7)): 4/14 ≈ 0.286
      └── Some((5, 8)): 15/27 ≈ 0.556
    ├── Some((6, 6)): 89/175 ≈ 0.509
      ├── Some((6, 0)): 12/23 ≈ 0.522
      ├── Some((6, 1)): 19/31 ≈ 0.613
      ├── Some((6, 2)): 14/25 ≈ 0.560
      ├── Some((6, 3)): 18/30 ≈ 0.600
      ├── Some((6, 4)): 11/22 ≈ 0.500
      ├── Some((6, 5)): 0/8 ≈ 0.000
      ├── Some((6, 7)): 11/22 ≈ 0.500
      └── Some((6, 8)): 4/13 ≈ 0.308
    ├── Some((6, 7)): 121/222 ≈ 0.545
      ├── Some((7, 0)): 15/28 ≈ 0.536
      ├── Some((7, 1)): 6/17 ≈ 0.353
      ├── Some((7, 2)): 8/19 ≈ 0.421
      ├── Some((7, 3)): 14/27 ≈ 0.519
      ├── Some((7, 4)): 25/39 ≈ 0.641
      ├── Some((7, 6)): 21/34 ≈ 0.618
      ├── Some((7, 7)): 15/28 ≈ 0.536
      └── Some((7, 8)): 16/29 ≈ 0.552
    └── Some((6, 8)): 134/241 ≈ 0.556
      ├── Some((8, 0)): 11/23 ≈ 0.478
      ├── Some((8, 1)): 31/45 ≈ 0.689
      ├── Some((8, 2)): 23/36 ≈ 0.639
      ├── Some((8, 3)): 20/33 ≈ 0.606
      ├── Some((8, 4)): 26/39 ≈ 0.667
      ├── Some((8, 5)): 8/19 ≈ 0.421
      ├── Some((8, 6)): 2/12 ≈ 0.167
      ├── Some((8, 7)): 8/19 ≈ 0.421
      └── Some((8, 8)): 4/14 ≈ 0.286
  ├── Some((5, 7)): 615/1224 ≈ 0.502
    ├── Some((7, 0)): 85/166 ≈ 0.512
      ├── Some((0, 0)): 19/28 ≈ 0.679
      ├── Some((0, 1)): 12/21 ≈ 0.571
      ├── Some((0, 2)): 9/18 ≈ 0.500
      ├── Some((0, 3)): 7/16 ≈ 0.438
      ├── Some((0, 4)): 6/15 ≈ 0.400
      ├── Some((0, 5)): 11/20 ≈ 0.550
      ├── Some((0, 6)): 8/17 ≈ 0.471
      ├── Some((0, 7)): 8/17 ≈ 0.471
      └── Some((0, 8)): 5/13 ≈ 0.385
    ├── Some((7, 1)): 93/177 ≈ 0.525
      ├── Some((1, 0)): 8/17 ≈ 0.471
      ├── Some((1, 1)): 15/25 ≈ 0.600
      ├── Some((1, 2)): 6/15 ≈ 0.400
      ├── Some((1, 3)): 8/17 ≈ 0.471
      ├── Some((1, 4)): 7/16 ≈ 0.438
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 17/27 ≈ 0.630
      ├── Some((1, 7)): 13/23 ≈ 0.565
      └── Some((1, 8)): 5/14 ≈ 0.357
    ├── Some((7, 2)): 59/126 ≈ 0.468
      ├── Some((2, 0)): 10/18 ≈ 0.556
      ├── Some((2, 1)): 4/11 ≈ 0.364
      ├── Some((2, 2)): 6/13 ≈ 0.462
      ├── Some((2, 3)): 3/10 ≈ 0.300
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 10/18 ≈ 0.556
      ├── Some((2, 6)): 6/13 ≈ 0.462
      ├── Some((2, 7)): 6/13 ≈ 0.462
      └── Some((2, 8)): 4/11 ≈ 0.364
    ├── Some((7, 3)): 104/194 ≈ 0.536
      ├── Some((3, 0)): 11/21 ≈ 0.524
      ├── Some((3, 1)): 6/15 ≈ 0.400
      ├── Some((3, 2)): 6/15 ≈ 0.400
      ├── Some((3, 3)): 10/20 ≈ 0.500
      ├── Some((3, 4)): 9/19 ≈ 0.474
      ├── Some((3, 5)): 11/21 ≈ 0.524
      ├── Some((3, 6)): 8/18 ≈ 0.444
      ├── Some((3, 7)): 18/29 ≈ 0.621
      └── Some((3, 8)): 24/35 ≈ 0.686
    ├── Some((7, 4)): 35/88 ≈ 0.398
      ├── Some((4, 0)): 5/11 ≈ 0.455
      ├── Some((4, 1)): 9/15 ≈ 0.600
      ├── Some((4, 2)): 0/5 ≈ 0.000
      ├── Some((4, 3)): 3/9 ≈ 0.333
      ├── Some((4, 4)): 3/9 ≈ 0.333
      ├── Some((4, 5)): 2/8 ≈ 0.250
      ├── Some((4, 6)): 7/13 ≈ 0.538
      ├── Some((4, 7)): 4/10 ≈ 0.400
      └── Some((4, 8)): 1/7 ≈ 0.143
    ├── Some((7, 6)): 102/191 ≈ 0.534
      ├── Some((6, 0)): 14/24 ≈ 0.583
      ├── Some((6, 1)): 17/27 ≈ 0.630
      ├── Some((6, 2)): 3/12 ≈ 0.250
      ├── Some((6, 3)): 20/31 ≈ 0.645
      ├── Some((6, 4)): 7/17 ≈ 0.412
      ├── Some((6, 5)): 6/15 ≈ 0.400
      ├── Some((6, 6)): 10/20 ≈ 0.500
      ├── Some((6, 7)): 9/19 ≈ 0.474
      └── Some((6, 8)): 15/25 ≈ 0.600
    ├── Some((7, 7)): 88/170 ≈ 0.518
      ├── Some((7, 0)): 4/14 ≈ 0.286
      ├── Some((7, 1)): 21/34 ≈ 0.618
      ├── Some((7, 2)): 16/28 ≈ 0.571
      ├── Some((7, 3)): 9/20 ≈ 0.450
      ├── Some((7, 4)): 10/21 ≈ 0.476
      ├── Some((7, 6)): 19/32 ≈ 0.594
      └── Some((7, 8)): 9/20 ≈ 0.450
    └── Some((7, 8)): 49/111 ≈ 0.441
      ├── Some((8, 0)): 9/16 ≈ 0.562
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 4/11 ≈ 0.364
      ├── Some((8, 5)): 8/15 ≈ 0.533
      ├── Some((8, 6)): 6/13 ≈ 0.462
      ├── Some((8, 7)): 2/9 ≈ 0.222
      └── Some((8, 8)): 8/15 ≈ 0.533
  └── Some((5, 8)): 734/1432 ≈ 0.513
    ├── Some((8, 0)): 111/203 ≈ 0.547
      ├── Some((0, 0)): 15/25 ≈ 0.600
      ├── Some((0, 1)): 4/13 ≈ 0.308
      ├── Some((0, 2)): 13/23 ≈ 0.565
      ├── Some((0, 3)): 7/17 ≈ 0.412
      ├── Some((0, 4)): 25/36 ≈ 0.694
      ├── Some((0, 5)): 16/27 ≈ 0.593
      ├── Some((0, 6)): 6/16 ≈ 0.375
      ├── Some((0, 7)): 13/23 ≈ 0.565
      └── Some((0, 8)): 12/22 ≈ 0.545
    ├── Some((8, 1)): 62/130 ≈ 0.477
      ├── Some((1, 0)): 16/24 ≈ 0.667
      ├── Some((1, 1)): 8/16 ≈ 0.500
      ├── Some((1, 2)): 6/14 ≈ 0.429
      ├── Some((1, 3)): 12/20 ≈ 0.600
      ├── Some((1, 4)): 3/10 ≈ 0.300
      ├── Some((1, 5)): 9/17 ≈ 0.529
      ├── Some((1, 6)): 4/11 ≈ 0.364
      ├── Some((1, 7)): 4/11 ≈ 0.364
      └── Some((1, 8)): 0/6 ≈ 0.000
    ├── Some((8, 2)): 128/227 ≈ 0.564
      ├── Some((2, 0)): 14/25 ≈ 0.560
      ├── Some((2, 1)): 14/25 ≈ 0.560
      ├── Some((2, 2)): 24/36 ≈ 0.667
      ├── Some((2, 3)): 12/23 ≈ 0.522
      ├── Some((2, 4)): 12/23 ≈ 0.522
      ├── Some((2, 5)): 7/17 ≈ 0.412
      ├── Some((2, 6)): 18/29 ≈ 0.621
      ├── Some((2, 7)): 13/24 ≈ 0.542
      └── Some((2, 8)): 13/24 ≈ 0.542
    ├── Some((8, 3)): 76/151 ≈ 0.503
      ├── Some((3, 0)): 15/24 ≈ 0.625
      ├── Some((3, 1)): 2/9 ≈ 0.222
      ├── Some((3, 2)): 7/15 ≈ 0.467
      ├── Some((3, 3)): 9/18 ≈ 0.500
      ├── Some((3, 4)): 5/13 ≈ 0.385
      ├── Some((3, 5)): 9/18 ≈ 0.500
      ├── Some((3, 6)): 7/15 ≈ 0.467
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 16/25 ≈ 0.640
    ├── Some((8, 4)): 65/135 ≈ 0.481
      ├── Some((4, 0)): 6/14 ≈ 0.429
      ├── Some((4, 1)): 10/18 ≈ 0.556
      ├── Some((4, 2)): 7/15 ≈ 0.467
      ├── Some((4, 3)): 11/19 ≈ 0.579
      ├── Some((4, 4)): 3/10 ≈ 0.300
      ├── Some((4, 5)): 6/14 ≈ 0.429
      ├── Some((4, 6)): 10/18 ≈ 0.556
      ├── Some((4, 7)): 4/11 ≈ 0.364
      └── Some((4, 8)): 7/15 ≈ 0.467
    ├── Some((8, 5)): 81/159 ≈ 0.509
      ├── Some((5, 0)): 4/13 ≈ 0.308
      ├── Some((5, 1)): 11/21 ≈ 0.524
      ├── Some((5, 2)): 11/21 ≈ 0.524
      ├── Some((5, 3)): 15/25 ≈ 0.600
      ├── Some((5, 4)): 7/16 ≈ 0.438
      ├── Some((5, 5)): 7/16 ≈ 0.438
      ├── Some((5, 6)): 6/15 ≈ 0.400
      └── Some((5, 7)): 20/31 ≈ 0.645
    ├── Some((8, 6)): 66/136 ≈ 0.485
      ├── Some((6, 0)): 3/10 ≈ 0.300
      ├── Some((6, 1)): 9/17 ≈ 0.529
      ├── Some((6, 2)): 8/16 ≈ 0.500
      ├── Some((6, 3)): 13/21 ≈ 0.619
      ├── Some((6, 4)): 7/15 ≈ 0.467
      ├── Some((6, 5)): 3/10 ≈ 0.300
      ├── Some((6, 6)): 4/11 ≈ 0.364
      ├── Some((6, 7)): 12/20 ≈ 0.600
      └── Some((6, 8)): 7/15 ≈ 0.467
    ├── Some((8, 7)): 72/145 ≈ 0.497
      ├── Some((7, 0)): 13/22 ≈ 0.591
      ├── Some((7, 1)): 7/16 ≈ 0.438
      ├── Some((7, 2)): 5/14 ≈ 0.357
      ├── Some((7, 3)): 6/15 ≈ 0.400
      ├── Some((7, 4)): 9/18 ≈ 0.500
      ├── Some((7, 6)): 15/25 ≈ 0.600
      ├── Some((7, 7)): 8/17 ≈ 0.471
      └── Some((7, 8)): 8/17 ≈ 0.471
    └── Some((8, 8)): 72/145 ≈ 0.497
      ├── Some((8, 0)): 9/18 ≈ 0.500
      ├── Some((8, 1)): 8/17 ≈ 0.471
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 7/16 ≈ 0.438
      ├── Some((8, 4)): 11/20 ≈ 0.550
      ├── Some((8, 5)): 8/17 ≈ 0.471
      ├── Some((8, 6)): 4/13 ≈ 0.308
      └── Some((8, 7)): 15/25 ≈ 0.600
├── Some((7, 6)): 3396/6770 ≈ 0.502
  ├── Some((6, 0)): 349/705 ≈ 0.495
    ├── Some((0, 0)): 27/62 ≈ 0.435
      ├── Some((0, 1)): 4/9 ≈ 0.444
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 11/15 ≈ 0.733
      ├── Some((0, 4)): 5/10 ≈ 0.500
      ├── Some((0, 5)): 0/4 ≈ 0.000
      ├── Some((0, 6)): 3/8 ≈ 0.375
      ├── Some((0, 7)): 1/5 ≈ 0.200
      └── Some((0, 8)): 1/5 ≈ 0.200
    ├── Some((0, 1)): 81/136 ≈ 0.596
      ├── Some((1, 0)): 6/12 ≈ 0.500
      ├── Some((1, 1)): 11/17 ≈ 0.647
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 17/23 ≈ 0.739
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 9/15 ≈ 0.600
      ├── Some((1, 7)): 12/18 ≈ 0.667
      └── Some((1, 8)): 9/15 ≈ 0.600
    ├── Some((0, 2)): 53/98 ≈ 0.541
      ├── Some((2, 0)): 1/6 ≈ 0.167
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 2)): 1/6 ≈ 0.167
      ├── Some((2, 3)): 6/11 ≈ 0.545
      ├── Some((2, 4)): 10/15 ≈ 0.667
      ├── Some((2, 5)): 10/15 ≈ 0.667
      ├── Some((2, 6)): 5/10 ≈ 0.500
      ├── Some((2, 7)): 6/11 ≈ 0.545
      └── Some((2, 8)): 10/15 ≈ 0.667
    ├── Some((0, 3)): 27/62 ≈ 0.435
      ├── Some((3, 0)): 3/7 ≈ 0.429
      ├── Some((3, 1)): 6/9 ≈ 0.667
      ├── Some((3, 2)): 1/5 ≈ 0.200
      ├── Some((3, 3)): 6/10 ≈ 0.600
      ├── Some((3, 4)): 2/6 ≈ 0.333
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 2/6 ≈ 0.333
      ├── Some((3, 7)): 7/10 ≈ 0.700
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((0, 4)): 22/55 ≈ 0.400
      ├── Some((4, 0)): 3/6 ≈ 0.500
      ├── Some((4, 1)): 3/6 ≈ 0.500
      ├── Some((4, 2)): 3/6 ≈ 0.500
      ├── Some((4, 3)): 1/5 ≈ 0.200
      ├── Some((4, 4)): 1/5 ≈ 0.200
      ├── Some((4, 5)): 3/7 ≈ 0.429
      ├── Some((4, 6)): 3/7 ≈ 0.429
      ├── Some((4, 7)): 4/7 ≈ 0.571
      └── Some((4, 8)): 1/5 ≈ 0.200
    ├── Some((0, 5)): 43/85 ≈ 0.506
      ├── Some((5, 0)): 12/16 ≈ 0.750
      ├── Some((5, 1)): 2/7 ≈ 0.286
      ├── Some((5, 2)): 7/11 ≈ 0.636
      ├── Some((5, 3)): 7/11 ≈ 0.636
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 3/8 ≈ 0.375
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 2/7 ≈ 0.286
    ├── Some((0, 6)): 29/65 ≈ 0.446
      ├── Some((6, 1)): 4/8 ≈ 0.500
      ├── Some((6, 2)): 4/8 ≈ 0.500
      ├── Some((6, 3)): 4/8 ≈ 0.500
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 3/8 ≈ 0.375
      ├── Some((6, 6)): 6/10 ≈ 0.600
      ├── Some((6, 7)): 3/8 ≈ 0.375
      └── Some((6, 8)): 4/9 ≈ 0.444
    ├── Some((0, 7)): 47/90 ≈ 0.522
      ├── Some((7, 0)): 4/10 ≈ 0.400
      ├── Some((7, 1)): 5/11 ≈ 0.455
      ├── Some((7, 2)): 5/11 ≈ 0.455
      ├── Some((7, 3)): 6/11 ≈ 0.545
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 7/12 ≈ 0.583
      ├── Some((7, 7)): 6/11 ≈ 0.545
      └── Some((7, 8)): 10/15 ≈ 0.667
    └── Some((0, 8)): 20/51 ≈ 0.392
      ├── Some((8, 0)): 1/5 ≈ 0.200
      ├── Some((8, 1)): 2/5 ≈ 0.400
      ├── Some((8, 2)): 7/10 ≈ 0.700
      ├── Some((8, 3)): 2/5 ≈ 0.400
      ├── Some((8, 4)): 1/5 ≈ 0.200
      ├── Some((8, 5)): 1/5 ≈ 0.200
      ├── Some((8, 6)): 2/5 ≈ 0.400
      ├── Some((8, 7)): 4/7 ≈ 0.571
      └── Some((8, 8)): 0/3 ≈ 0.000
  ├── Some((6, 1)): 356/717 ≈ 0.497
    ├── Some((1, 0)): 33/70 ≈ 0.471
      ├── Some((0, 0)): 4/8 ≈ 0.500
      ├── Some((0, 1)): 1/5 ≈ 0.200
      ├── Some((0, 2)): 1/5 ≈ 0.200
      ├── Some((0, 3)): 5/9 ≈ 0.556
      ├── Some((0, 4)): 12/16 ≈ 0.750
      ├── Some((0, 5)): 4/8 ≈ 0.500
      ├── Some((0, 6)): 1/5 ≈ 0.200
      ├── Some((0, 7)): 4/9 ≈ 0.444
      └── Some((0, 8)): 0/4 ≈ 0.000
    ├── Some((1, 1)): 54/100 ≈ 0.540
      ├── Some((1, 0)): 8/14 ≈ 0.571
      ├── Some((1, 2)): 0/5 ≈ 0.000
      ├── Some((1, 3)): 12/17 ≈ 0.706
      ├── Some((1, 4)): 9/15 ≈ 0.600
      ├── Some((1, 5)): 2/8 ≈ 0.250
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 8/14 ≈ 0.571
      └── Some((1, 8)): 8/14 ≈ 0.571
    ├── Some((1, 2)): 52/97 ≈ 0.536
      ├── Some((2, 0)): 6/11 ≈ 0.545
      ├── Some((2, 1)): 1/6 ≈ 0.167
      ├── Some((2, 2)): 1/6 ≈ 0.167
      ├── Some((2, 3)): 5/10 ≈ 0.500
      ├── Some((2, 4)): 5/10 ≈ 0.500
      ├── Some((2, 5)): 9/14 ≈ 0.643
      ├── Some((2, 6)): 5/10 ≈ 0.500
      ├── Some((2, 7)): 10/15 ≈ 0.667
      └── Some((2, 8)): 9/14 ≈ 0.643
    ├── Some((1, 3)): 45/87 ≈ 0.517
      ├── Some((3, 0)): 4/9 ≈ 0.444
      ├── Some((3, 1)): 3/8 ≈ 0.375
      ├── Some((3, 2)): 1/6 ≈ 0.167
      ├── Some((3, 3)): 8/12 ≈ 0.667
      ├── Some((3, 4)): 8/12 ≈ 0.667
      ├── Some((3, 5)): 10/14 ≈ 0.714
      ├── Some((3, 6)): 3/8 ≈ 0.375
      ├── Some((3, 7)): 6/10 ≈ 0.600
      └── Some((3, 8)): 2/7 ≈ 0.286
    ├── Some((1, 4)): 51/96 ≈ 0.531
      ├── Some((4, 0)): 11/15 ≈ 0.733
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 0/5 ≈ 0.000
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 6/11 ≈ 0.545
      ├── Some((4, 5)): 5/10 ≈ 0.500
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 11/16 ≈ 0.688
      └── Some((4, 8)): 10/15 ≈ 0.667
    ├── Some((1, 5)): 15/44 ≈ 0.341
      ├── Some((5, 0)): 0/3 ≈ 0.000
      ├── Some((5, 1)): 3/6 ≈ 0.500
      ├── Some((5, 2)): 3/6 ≈ 0.500
      ├── Some((5, 3)): 0/3 ≈ 0.000
      ├── Some((5, 4)): 3/6 ≈ 0.500
      ├── Some((5, 5)): 1/5 ≈ 0.200
      ├── Some((5, 6)): 0/3 ≈ 0.000
      ├── Some((5, 7)): 3/6 ≈ 0.500
      └── Some((5, 8)): 2/5 ≈ 0.400
    ├── Some((1, 6)): 33/71 ≈ 0.465
      ├── Some((6, 0)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 2/7 ≈ 0.286
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 5/10 ≈ 0.500
      ├── Some((6, 5)): 7/11 ≈ 0.636
      ├── Some((6, 6)): 0/4 ≈ 0.000
      ├── Some((6, 7)): 6/11 ≈ 0.545
      └── Some((6, 8)): 7/11 ≈ 0.636
    ├── Some((1, 7)): 39/79 ≈ 0.494
      ├── Some((7, 0)): 1/6 ≈ 0.167
      ├── Some((7, 1)): 7/12 ≈ 0.583
      ├── Some((7, 2)): 8/12 ≈ 0.667
      ├── Some((7, 3)): 7/12 ≈ 0.583
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 7/12 ≈ 0.583
      ├── Some((7, 7)): 3/8 ≈ 0.375
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((1, 8)): 34/72 ≈ 0.472
      ├── Some((8, 0)): 4/8 ≈ 0.500
      ├── Some((8, 1)): 4/8 ≈ 0.500
      ├── Some((8, 2)): 2/6 ≈ 0.333
      ├── Some((8, 3)): 6/10 ≈ 0.600
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 2/7 ≈ 0.286
      ├── Some((8, 6)): 5/9 ≈ 0.556
      ├── Some((8, 7)): 4/8 ≈ 0.500
      └── Some((8, 8)): 4/8 ≈ 0.500
  ├── Some((6, 2)): 379/756 ≈ 0.501
    ├── Some((2, 0)): 32/70 ≈ 0.457
      ├── Some((0, 0)): 10/14 ≈ 0.714
      ├── Some((0, 1)): 3/8 ≈ 0.375
      ├── Some((0, 2)): 4/8 ≈ 0.500
      ├── Some((0, 3)): 2/6 ≈ 0.333
      ├── Some((0, 4)): 0/4 ≈ 0.000
      ├── Some((0, 5)): 3/8 ≈ 0.375
      ├── Some((0, 6)): 1/5 ≈ 0.200
      ├── Some((0, 7)): 4/8 ≈ 0.500
      └── Some((0, 8)): 4/8 ≈ 0.500
    ├── Some((2, 1)): 38/78 ≈ 0.487
      ├── Some((1, 0)): 10/14 ≈ 0.714
      ├── Some((1, 1)): 1/5 ≈ 0.200
      ├── Some((1, 2)): 9/13 ≈ 0.692
      ├── Some((1, 3)): 4/9 ≈ 0.444
      ├── Some((1, 4)): 6/10 ≈ 0.600
      ├── Some((1, 5)): 0/4 ≈ 0.000
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 3/8 ≈ 0.375
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((2, 2)): 38/79 ≈ 0.481
      ├── Some((2, 0)): 4/9 ≈ 0.444
      ├── Some((2, 1)): 14/19 ≈ 0.737
      ├── Some((2, 3)): 6/11 ≈ 0.545
      ├── Some((2, 4)): 2/7 ≈ 0.286
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 1/6 ≈ 0.167
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((2, 3)): 48/92 ≈ 0.522
      ├── Some((3, 0)): 9/14 ≈ 0.643
      ├── Some((3, 1)): 5/10 ≈ 0.500
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 1/6 ≈ 0.167
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 3/8 ≈ 0.375
      ├── Some((3, 6)): 6/11 ≈ 0.545
      ├── Some((3, 7)): 6/11 ≈ 0.545
      └── Some((3, 8)): 10/14 ≈ 0.714
    ├── Some((2, 4)): 42/84 ≈ 0.500
      ├── Some((4, 0)): 5/9 ≈ 0.556
      ├── Some((4, 1)): 8/12 ≈ 0.667
      ├── Some((4, 2)): 4/9 ≈ 0.444
      ├── Some((4, 3)): 3/8 ≈ 0.375
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 5/10 ≈ 0.500
      ├── Some((4, 7)): 5/10 ≈ 0.500
      └── Some((4, 8)): 6/10 ≈ 0.600
    ├── Some((2, 5)): 47/91 ≈ 0.516
      ├── Some((5, 0)): 5/10 ≈ 0.500
      ├── Some((5, 1)): 9/13 ≈ 0.692
      ├── Some((5, 2)): 3/8 ≈ 0.375
      ├── Some((5, 3)): 0/5 ≈ 0.000
      ├── Some((5, 4)): 8/12 ≈ 0.667
      ├── Some((5, 5)): 5/10 ≈ 0.500
      ├── Some((5, 6)): 5/10 ≈ 0.500
      ├── Some((5, 7)): 5/10 ≈ 0.500
      └── Some((5, 8)): 7/12 ≈ 0.583
    ├── Some((2, 6)): 43/86 ≈ 0.500
      ├── Some((6, 0)): 2/7 ≈ 0.286
      ├── Some((6, 1)): 8/13 ≈ 0.615
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 9/14 ≈ 0.643
      ├── Some((6, 5)): 5/11 ≈ 0.455
      ├── Some((6, 6)): 4/10 ≈ 0.400
      ├── Some((6, 7)): 10/15 ≈ 0.667
      └── Some((6, 8)): 3/8 ≈ 0.375
    ├── Some((2, 7)): 77/132 ≈ 0.583
      ├── Some((7, 0)): 11/18 ≈ 0.611
      ├── Some((7, 1)): 9/16 ≈ 0.562
      ├── Some((7, 2)): 19/25 ≈ 0.760
      ├── Some((7, 3)): 7/14 ≈ 0.500
      ├── Some((7, 4)): 3/10 ≈ 0.300
      ├── Some((7, 5)): 15/22 ≈ 0.682
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 8/15 ≈ 0.533
    └── Some((2, 8)): 14/43 ≈ 0.326
      ├── Some((8, 0)): 5/8 ≈ 0.625
      ├── Some((8, 1)): 0/3 ≈ 0.000
      ├── Some((8, 2)): 0/3 ≈ 0.000
      ├── Some((8, 3)): 2/5 ≈ 0.400
      ├── Some((8, 4)): 2/5 ≈ 0.400
      ├── Some((8, 5)): 1/4 ≈ 0.250
      ├── Some((8, 6)): 2/5 ≈ 0.400
      ├── Some((8, 7)): 1/4 ≈ 0.250
      └── Some((8, 8)): 1/5 ≈ 0.200
  ├── Some((6, 3)): 324/661 ≈ 0.490
    ├── Some((3, 0)): 48/90 ≈ 0.533
      ├── Some((0, 0)): 10/14 ≈ 0.714
      ├── Some((0, 1)): 5/10 ≈ 0.500
      ├── Some((0, 2)): 6/11 ≈ 0.545
      ├── Some((0, 3)): 2/7 ≈ 0.286
      ├── Some((0, 4)): 0/4 ≈ 0.000
      ├── Some((0, 5)): 5/10 ≈ 0.500
      ├── Some((0, 6)): 6/11 ≈ 0.545
      ├── Some((0, 7)): 7/11 ≈ 0.636
      └── Some((0, 8)): 7/11 ≈ 0.636
    ├── Some((3, 1)): 37/75 ≈ 0.493
      ├── Some((1, 0)): 5/9 ≈ 0.556
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 5/9 ≈ 0.556
      ├── Some((1, 3)): 4/8 ≈ 0.500
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 8/12 ≈ 0.667
      ├── Some((1, 7)): 5/9 ≈ 0.556
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((3, 2)): 25/58 ≈ 0.431
      ├── Some((2, 0)): 4/7 ≈ 0.571
      ├── Some((2, 1)): 4/7 ≈ 0.571
      ├── Some((2, 2)): 3/6 ≈ 0.500
      ├── Some((2, 3)): 2/6 ≈ 0.333
      ├── Some((2, 4)): 3/7 ≈ 0.429
      ├── Some((2, 5)): 3/7 ≈ 0.429
      ├── Some((2, 6)): 2/6 ≈ 0.333
      ├── Some((2, 7)): 4/7 ≈ 0.571
      └── Some((2, 8)): 0/4 ≈ 0.000
    ├── Some((3, 3)): 35/72 ≈ 0.486
      ├── Some((3, 0)): 6/10 ≈ 0.600
      ├── Some((3, 1)): 10/14 ≈ 0.714
      ├── Some((3, 2)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 6/10 ≈ 0.600
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 6/11 ≈ 0.545
    ├── Some((3, 4)): 46/87 ≈ 0.529
      ├── Some((4, 0)): 7/11 ≈ 0.636
      ├── Some((4, 1)): 5/9 ≈ 0.556
      ├── Some((4, 2)): 6/10 ≈ 0.600
      ├── Some((4, 3)): 4/9 ≈ 0.444
      ├── Some((4, 4)): 3/8 ≈ 0.375
      ├── Some((4, 5)): 8/12 ≈ 0.667
      ├── Some((4, 6)): 3/8 ≈ 0.375
      ├── Some((4, 7)): 5/9 ≈ 0.556
      └── Some((4, 8)): 5/10 ≈ 0.500
    ├── Some((3, 5)): 37/75 ≈ 0.493
      ├── Some((5, 0)): 3/7 ≈ 0.429
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 2/6 ≈ 0.333
      ├── Some((5, 3)): 5/9 ≈ 0.556
      ├── Some((5, 4)): 8/12 ≈ 0.667
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 4/8 ≈ 0.500
      ├── Some((5, 7)): 4/8 ≈ 0.500
      └── Some((5, 8)): 4/8 ≈ 0.500
    ├── Some((3, 6)): 42/82 ≈ 0.512
      ├── Some((6, 0)): 6/11 ≈ 0.545
      ├── Some((6, 1)): 8/13 ≈ 0.615
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 4)): 3/8 ≈ 0.375
      ├── Some((6, 5)): 14/18 ≈ 0.778
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((3, 7)): 28/62 ≈ 0.452
      ├── Some((7, 0)): 7/11 ≈ 0.636
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 3/8 ≈ 0.375
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 3/8 ≈ 0.375
      ├── Some((7, 5)): 4/8 ≈ 0.500
      ├── Some((7, 7)): 2/6 ≈ 0.333
      └── Some((7, 8)): 4/8 ≈ 0.500
    └── Some((3, 8)): 26/59 ≈ 0.441
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 0/4 ≈ 0.000
      ├── Some((8, 3)): 1/5 ≈ 0.200
      ├── Some((8, 4)): 4/7 ≈ 0.571
      ├── Some((8, 5)): 6/9 ≈ 0.667
      ├── Some((8, 6)): 9/12 ≈ 0.750
      ├── Some((8, 7)): 0/4 ≈ 0.000
      └── Some((8, 8)): 3/7 ≈ 0.429
  ├── Some((6, 4)): 345/698 ≈ 0.494
    ├── Some((4, 0)): 41/82 ≈ 0.500
      ├── Some((0, 0)): 2/7 ≈ 0.286
      ├── Some((0, 1)): 5/9 ≈ 0.556
      ├── Some((0, 2)): 7/11 ≈ 0.636
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 6/10 ≈ 0.600
      ├── Some((0, 5)): 1/6 ≈ 0.167
      ├── Some((0, 6)): 4/9 ≈ 0.444
      ├── Some((0, 7)): 5/10 ≈ 0.500
      └── Some((0, 8)): 7/11 ≈ 0.636
    ├── Some((4, 1)): 22/55 ≈ 0.400
      ├── Some((1, 0)): 4/7 ≈ 0.571
      ├── Some((1, 1)): 1/5 ≈ 0.200
      ├── Some((1, 2)): 2/6 ≈ 0.333
      ├── Some((1, 3)): 2/6 ≈ 0.333
      ├── Some((1, 4)): 2/6 ≈ 0.333
      ├── Some((1, 5)): 4/7 ≈ 0.571
      ├── Some((1, 6)): 3/6 ≈ 0.500
      ├── Some((1, 7)): 3/7 ≈ 0.429
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((4, 2)): 60/108 ≈ 0.556
      ├── Some((2, 0)): 6/11 ≈ 0.545
      ├── Some((2, 1)): 11/16 ≈ 0.688
      ├── Some((2, 2)): 2/7 ≈ 0.286
      ├── Some((2, 3)): 9/14 ≈ 0.643
      ├── Some((2, 4)): 9/14 ≈ 0.643
      ├── Some((2, 5)): 8/13 ≈ 0.615
      ├── Some((2, 6)): 5/11 ≈ 0.455
      ├── Some((2, 7)): 4/10 ≈ 0.400
      └── Some((2, 8)): 5/11 ≈ 0.455
    ├── Some((4, 3)): 32/70 ≈ 0.457
      ├── Some((3, 0)): 4/8 ≈ 0.500
      ├── Some((3, 1)): 5/9 ≈ 0.556
      ├── Some((3, 2)): 6/10 ≈ 0.600
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 4)): 6/10 ≈ 0.600
      ├── Some((3, 5)): 3/7 ≈ 0.429
      ├── Some((3, 6)): 3/7 ≈ 0.429
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 2/6 ≈ 0.333
    ├── Some((4, 4)): 69/120 ≈ 0.575
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 9/16 ≈ 0.562
      ├── Some((4, 2)): 3/9 ≈ 0.333
      ├── Some((4, 3)): 15/21 ≈ 0.714
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 11/17 ≈ 0.647
      └── Some((4, 8)): 13/19 ≈ 0.684
    ├── Some((4, 5)): 3/24 ≈ 0.125
      ├── Some((5, 0)): 0/2 ≈ 0.000
      ├── Some((5, 1)): 0/2 ≈ 0.000
      ├── Some((5, 2)): 0/2 ≈ 0.000
      ├── Some((5, 3)): 0/2 ≈ 0.000
      ├── Some((5, 4)): 1/3 ≈ 0.333
      ├── Some((5, 5)): 0/3 ≈ 0.000
      ├── Some((5, 6)): 1/3 ≈ 0.333
      ├── Some((5, 7)): 0/3 ≈ 0.000
      └── Some((5, 8)): 0/3 ≈ 0.000
    ├── Some((4, 6)): 48/92 ≈ 0.522
      ├── Some((6, 0)): 9/14 ≈ 0.643
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 5)): 9/15 ≈ 0.600
      ├── Some((6, 6)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 11/16 ≈ 0.688
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((4, 7)): 22/55 ≈ 0.400
      ├── Some((7, 0)): 2/6 ≈ 0.333
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 0/4 ≈ 0.000
      ├── Some((7, 3)): 5/9 ≈ 0.556
      ├── Some((7, 4)): 3/7 ≈ 0.429
      ├── Some((7, 5)): 3/7 ≈ 0.429
      ├── Some((7, 7)): 3/7 ≈ 0.429
      └── Some((7, 8)): 3/8 ≈ 0.375
    └── Some((4, 8)): 47/91 ≈ 0.516
      ├── Some((8, 0)): 6/10 ≈ 0.600
      ├── Some((8, 1)): 5/10 ≈ 0.500
      ├── Some((8, 2)): 5/10 ≈ 0.500
      ├── Some((8, 3)): 5/10 ≈ 0.500
      ├── Some((8, 4)): 5/10 ≈ 0.500
      ├── Some((8, 5)): 5/10 ≈ 0.500
      ├── Some((8, 6)): 6/11 ≈ 0.545
      ├── Some((8, 7)): 3/8 ≈ 0.375
      └── Some((8, 8)): 6/11 ≈ 0.545
  ├── Some((6, 5)): 421/828 ≈ 0.508
    ├── Some((5, 0)): 50/97 ≈ 0.515
      ├── Some((0, 0)): 8/13 ≈ 0.615
      ├── Some((0, 1)): 10/15 ≈ 0.667
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 3/8 ≈ 0.375
      ├── Some((0, 4)): 0/5 ≈ 0.000
      ├── Some((0, 5)): 3/8 ≈ 0.375
      ├── Some((0, 6)): 3/9 ≈ 0.333
      ├── Some((0, 7)): 9/14 ≈ 0.643
      └── Some((0, 8)): 11/16 ≈ 0.688
    ├── Some((5, 1)): 57/106 ≈ 0.538
      ├── Some((1, 0)): 8/13 ≈ 0.615
      ├── Some((1, 1)): 2/7 ≈ 0.286
      ├── Some((1, 2)): 3/8 ≈ 0.375
      ├── Some((1, 3)): 8/13 ≈ 0.615
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 12/17 ≈ 0.706
      ├── Some((1, 6)): 6/12 ≈ 0.500
      ├── Some((1, 7)): 4/10 ≈ 0.400
      └── Some((1, 8)): 11/16 ≈ 0.688
    ├── Some((5, 2)): 26/62 ≈ 0.419
      ├── Some((2, 0)): 4/8 ≈ 0.500
      ├── Some((2, 1)): 1/5 ≈ 0.200
      ├── Some((2, 2)): 3/7 ≈ 0.429
      ├── Some((2, 3)): 4/8 ≈ 0.500
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 4/8 ≈ 0.500
      ├── Some((2, 7)): 4/8 ≈ 0.500
      └── Some((2, 8)): 3/7 ≈ 0.429
    ├── Some((5, 3)): 49/95 ≈ 0.516
      ├── Some((3, 0)): 10/15 ≈ 0.667
      ├── Some((3, 1)): 3/8 ≈ 0.375
      ├── Some((3, 2)): 7/12 ≈ 0.583
      ├── Some((3, 3)): 7/12 ≈ 0.583
      ├── Some((3, 4)): 4/9 ≈ 0.444
      ├── Some((3, 5)): 7/12 ≈ 0.583
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 5/11 ≈ 0.455
    ├── Some((5, 4)): 58/108 ≈ 0.537
      ├── Some((4, 0)): 6/12 ≈ 0.500
      ├── Some((4, 1)): 6/12 ≈ 0.500
      ├── Some((4, 2)): 7/12 ≈ 0.583
      ├── Some((4, 3)): 7/12 ≈ 0.583
      ├── Some((4, 4)): 5/11 ≈ 0.455
      ├── Some((4, 5)): 8/13 ≈ 0.615
      ├── Some((4, 6)): 8/13 ≈ 0.615
      ├── Some((4, 7)): 8/13 ≈ 0.615
      └── Some((4, 8)): 3/9 ≈ 0.333
    ├── Some((5, 5)): 41/84 ≈ 0.488
      ├── Some((5, 0)): 7/12 ≈ 0.583
      ├── Some((5, 1)): 7/12 ≈ 0.583
      ├── Some((5, 2)): 4/10 ≈ 0.400
      ├── Some((5, 3)): 13/18 ≈ 0.722
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 6)): 0/5 ≈ 0.000
      ├── Some((5, 7)): 1/6 ≈ 0.167
      └── Some((5, 8)): 3/8 ≈ 0.375
    ├── Some((5, 6)): 44/88 ≈ 0.500
      ├── Some((6, 0)): 13/18 ≈ 0.722
      ├── Some((6, 1)): 8/13 ≈ 0.615
      ├── Some((6, 2)): 5/11 ≈ 0.455
      ├── Some((6, 3)): 3/8 ≈ 0.375
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 4/9 ≈ 0.444
      ├── Some((6, 7)): 1/6 ≈ 0.167
      └── Some((6, 8)): 4/10 ≈ 0.400
    ├── Some((5, 7)): 35/75 ≈ 0.467
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 5/10 ≈ 0.500
      ├── Some((7, 2)): 4/9 ≈ 0.444
      ├── Some((7, 3)): 5/10 ≈ 0.500
      ├── Some((7, 4)): 5/10 ≈ 0.500
      ├── Some((7, 5)): 8/13 ≈ 0.615
      ├── Some((7, 7)): 6/11 ≈ 0.545
      └── Some((7, 8)): 2/7 ≈ 0.286
    └── Some((5, 8)): 61/112 ≈ 0.545
      ├── Some((8, 0)): 8/14 ≈ 0.571
      ├── Some((8, 1)): 10/15 ≈ 0.667
      ├── Some((8, 2)): 5/11 ≈ 0.455
      ├── Some((8, 3)): 13/18 ≈ 0.722
      ├── Some((8, 4)): 2/8 ≈ 0.250
      ├── Some((8, 5)): 5/11 ≈ 0.455
      ├── Some((8, 6)): 2/8 ≈ 0.250
      ├── Some((8, 7)): 9/14 ≈ 0.643
      └── Some((8, 8)): 6/12 ≈ 0.500
  ├── Some((6, 6)): 231/498 ≈ 0.464
    ├── Some((6, 0)): 44/83 ≈ 0.530
      ├── Some((0, 0)): 1/5 ≈ 0.200
      ├── Some((0, 1)): 5/9 ≈ 0.556
      ├── Some((0, 2)): 4/9 ≈ 0.444
      ├── Some((0, 3)): 4/9 ≈ 0.444
      ├── Some((0, 4)): 10/14 ≈ 0.714
      ├── Some((0, 5)): 5/9 ≈ 0.556
      ├── Some((0, 6)): 5/9 ≈ 0.556
      ├── Some((0, 7)): 5/9 ≈ 0.556
      └── Some((0, 8)): 5/9 ≈ 0.556
    ├── Some((6, 1)): 30/64 ≈ 0.469
      ├── Some((1, 0)): 4/7 ≈ 0.571
      ├── Some((1, 1)): 3/7 ≈ 0.429
      ├── Some((1, 2)): 4/7 ≈ 0.571
      ├── Some((1, 3)): 4/8 ≈ 0.500
      ├── Some((1, 4)): 4/8 ≈ 0.500
      ├── Some((1, 5)): 6/9 ≈ 0.667
      ├── Some((1, 6)): 4/8 ≈ 0.500
      ├── Some((1, 7)): 1/5 ≈ 0.200
      └── Some((1, 8)): 0/4 ≈ 0.000
    ├── Some((6, 2)): 26/58 ≈ 0.448
      ├── Some((2, 0)): 7/10 ≈ 0.700
      ├── Some((2, 1)): 4/7 ≈ 0.571
      ├── Some((2, 2)): 3/6 ≈ 0.500
      ├── Some((2, 3)): 2/6 ≈ 0.333
      ├── Some((2, 4)): 2/6 ≈ 0.333
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 3/6 ≈ 0.500
      ├── Some((2, 7)): 1/5 ≈ 0.200
      └── Some((2, 8)): 3/6 ≈ 0.500
    ├── Some((6, 3)): 27/60 ≈ 0.450
      ├── Some((3, 0)): 4/7 ≈ 0.571
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 2/6 ≈ 0.333
      ├── Some((3, 3)): 0/4 ≈ 0.000
      ├── Some((3, 4)): 2/6 ≈ 0.333
      ├── Some((3, 5)): 0/4 ≈ 0.000
      ├── Some((3, 6)): 10/12 ≈ 0.833
      ├── Some((3, 7)): 3/7 ≈ 0.429
      └── Some((3, 8)): 4/8 ≈ 0.500
    ├── Some((6, 4)): 13/39 ≈ 0.333
      ├── Some((4, 0)): 0/3 ≈ 0.000
      ├── Some((4, 1)): 1/4 ≈ 0.250
      ├── Some((4, 2)): 0/3 ≈ 0.000
      ├── Some((4, 3)): 3/5 ≈ 0.600
      ├── Some((4, 4)): 2/4 ≈ 0.500
      ├── Some((4, 5)): 2/5 ≈ 0.400
      ├── Some((4, 6)): 2/5 ≈ 0.400
      ├── Some((4, 7)): 2/5 ≈ 0.400
      └── Some((4, 8)): 1/4 ≈ 0.250
    ├── Some((6, 5)): 34/70 ≈ 0.486
      ├── Some((5, 0)): 1/5 ≈ 0.200
      ├── Some((5, 1)): 4/8 ≈ 0.500
      ├── Some((5, 2)): 6/9 ≈ 0.667
      ├── Some((5, 3)): 0/4 ≈ 0.000
      ├── Some((5, 4)): 4/8 ≈ 0.500
      ├── Some((5, 5)): 6/10 ≈ 0.600
      ├── Some((5, 6)): 6/10 ≈ 0.600
      ├── Some((5, 7)): 1/5 ≈ 0.200
      └── Some((5, 8)): 6/10 ≈ 0.600
    ├── Some((6, 7)): 22/52 ≈ 0.423
      ├── Some((7, 0)): 5/8 ≈ 0.625
      ├── Some((7, 1)): 2/6 ≈ 0.333
      ├── Some((7, 2)): 3/6 ≈ 0.500
      ├── Some((7, 3)): 2/6 ≈ 0.333
      ├── Some((7, 4)): 3/6 ≈ 0.500
      ├── Some((7, 5)): 1/5 ≈ 0.200
      ├── Some((7, 7)): 3/7 ≈ 0.429
      └── Some((7, 8)): 3/7 ≈ 0.429
    └── Some((6, 8)): 35/71 ≈ 0.493
      ├── Some((8, 0)): 2/6 ≈ 0.333
      ├── Some((8, 1)): 5/9 ≈ 0.556
      ├── Some((8, 2)): 6/10 ≈ 0.600
      ├── Some((8, 3)): 5/9 ≈ 0.556
      ├── Some((8, 4)): 11/14 ≈ 0.786
      ├── Some((8, 5)): 2/6 ≈ 0.333
      ├── Some((8, 6)): 0/4 ≈ 0.000
      ├── Some((8, 7)): 1/5 ≈ 0.200
      └── Some((8, 8)): 3/7 ≈ 0.429
  ├── Some((6, 7)): 372/744 ≈ 0.500
    ├── Some((7, 0)): 30/69 ≈ 0.435
      ├── Some((0, 0)): 6/10 ≈ 0.600
      ├── Some((0, 1)): 0/4 ≈ 0.000
      ├── Some((0, 2)): 3/7 ≈ 0.429
      ├── Some((0, 3)): 4/8 ≈ 0.500
      ├── Some((0, 4)): 3/7 ≈ 0.429
      ├── Some((0, 5)): 3/7 ≈ 0.429
      ├── Some((0, 6)): 5/9 ≈ 0.556
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 3/8 ≈ 0.375
    ├── Some((7, 1)): 44/90 ≈ 0.489
      ├── Some((1, 0)): 4/9 ≈ 0.444
      ├── Some((1, 1)): 7/12 ≈ 0.583
      ├── Some((1, 2)): 6/11 ≈ 0.545
      ├── Some((1, 3)): 2/7 ≈ 0.286
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 4/9 ≈ 0.444
      ├── Some((1, 6)): 6/11 ≈ 0.545
      ├── Some((1, 7)): 8/13 ≈ 0.615
      └── Some((1, 8)): 4/9 ≈ 0.444
    ├── Some((7, 2)): 28/66 ≈ 0.424
      ├── Some((2, 0)): 2/6 ≈ 0.333
      ├── Some((2, 1)): 4/8 ≈ 0.500
      ├── Some((2, 2)): 4/8 ≈ 0.500
      ├── Some((2, 3)): 3/8 ≈ 0.375
      ├── Some((2, 4)): 6/10 ≈ 0.600
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 0/4 ≈ 0.000
      ├── Some((2, 7)): 1/5 ≈ 0.200
      └── Some((2, 8)): 4/8 ≈ 0.500
    ├── Some((7, 3)): 62/115 ≈ 0.539
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 13/18 ≈ 0.722
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 8/14 ≈ 0.571
      ├── Some((3, 4)): 6/12 ≈ 0.500
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 13/18 ≈ 0.722
      └── Some((3, 8)): 6/12 ≈ 0.500
    ├── Some((7, 4)): 69/125 ≈ 0.552
      ├── Some((4, 0)): 7/13 ≈ 0.538
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 10/16 ≈ 0.625
      ├── Some((4, 3)): 11/17 ≈ 0.647
      ├── Some((4, 4)): 11/17 ≈ 0.647
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 7/13 ≈ 0.538
      ├── Some((4, 7)): 9/15 ≈ 0.600
      └── Some((4, 8)): 7/14 ≈ 0.500
    ├── Some((7, 5)): 43/88 ≈ 0.489
      ├── Some((5, 0)): 9/14 ≈ 0.643
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 2/7 ≈ 0.286
      ├── Some((5, 3)): 7/12 ≈ 0.583
      ├── Some((5, 4)): 1/6 ≈ 0.167
      ├── Some((5, 5)): 2/7 ≈ 0.286
      ├── Some((5, 6)): 6/11 ≈ 0.545
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 6/11 ≈ 0.545
    ├── Some((7, 7)): 60/113 ≈ 0.531
      ├── Some((7, 0)): 14/22 ≈ 0.636
      ├── Some((7, 1)): 5/12 ≈ 0.417
      ├── Some((7, 2)): 6/13 ≈ 0.462
      ├── Some((7, 3)): 9/16 ≈ 0.562
      ├── Some((7, 4)): 11/19 ≈ 0.579
      ├── Some((7, 5)): 4/11 ≈ 0.364
      └── Some((7, 8)): 11/19 ≈ 0.579
    └── Some((7, 8)): 35/77 ≈ 0.455
      ├── Some((8, 0)): 4/8 ≈ 0.500
      ├── Some((8, 1)): 7/11 ≈ 0.636
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 3)): 4/9 ≈ 0.444
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 4/9 ≈ 0.444
      ├── Some((8, 6)): 4/9 ≈ 0.444
      ├── Some((8, 7)): 1/5 ≈ 0.200
      └── Some((8, 8)): 5/9 ≈ 0.556
  └── Some((6, 8)): 619/1162 ≈ 0.533
    ├── Some((8, 0)): 61/119 ≈ 0.513
      ├── Some((0, 0)): 10/17 ≈ 0.588
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 3/9 ≈ 0.333
      ├── Some((0, 3)): 12/18 ≈ 0.667
      ├── Some((0, 4)): 7/14 ≈ 0.500
      ├── Some((0, 5)): 9/16 ≈ 0.562
      ├── Some((0, 6)): 2/8 ≈ 0.250
      ├── Some((0, 7)): 4/10 ≈ 0.400
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((8, 1)): 40/88 ≈ 0.455
      ├── Some((1, 0)): 0/5 ≈ 0.000
      ├── Some((1, 1)): 1/6 ≈ 0.167
      ├── Some((1, 2)): 4/10 ≈ 0.400
      ├── Some((1, 3)): 6/12 ≈ 0.500
      ├── Some((1, 4)): 0/5 ≈ 0.000
      ├── Some((1, 5)): 8/13 ≈ 0.615
      ├── Some((1, 6)): 8/13 ≈ 0.615
      ├── Some((1, 7)): 8/13 ≈ 0.615
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((8, 2)): 76/140 ≈ 0.543
      ├── Some((2, 0)): 2/9 ≈ 0.222
      ├── Some((2, 1)): 13/20 ≈ 0.650
      ├── Some((2, 2)): 4/11 ≈ 0.364
      ├── Some((2, 3)): 11/18 ≈ 0.611
      ├── Some((2, 4)): 12/19 ≈ 0.632
      ├── Some((2, 5)): 2/9 ≈ 0.222
      ├── Some((2, 6)): 13/20 ≈ 0.650
      ├── Some((2, 7)): 11/18 ≈ 0.611
      └── Some((2, 8)): 8/15 ≈ 0.533
    ├── Some((8, 3)): 85/153 ≈ 0.556
      ├── Some((3, 0)): 14/21 ≈ 0.667
      ├── Some((3, 1)): 6/13 ≈ 0.462
      ├── Some((3, 2)): 13/21 ≈ 0.619
      ├── Some((3, 3)): 14/22 ≈ 0.636
      ├── Some((3, 4)): 8/16 ≈ 0.500
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 10/18 ≈ 0.556
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 7/14 ≈ 0.500
    ├── Some((8, 4)): 36/82 ≈ 0.439
      ├── Some((4, 0)): 4/9 ≈ 0.444
      ├── Some((4, 1)): 6/11 ≈ 0.545
      ├── Some((4, 2)): 2/7 ≈ 0.286
      ├── Some((4, 3)): 1/6 ≈ 0.167
      ├── Some((4, 4)): 6/12 ≈ 0.500
      ├── Some((4, 5)): 2/7 ≈ 0.286
      ├── Some((4, 6)): 4/9 ≈ 0.444
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 7/12 ≈ 0.583
    ├── Some((8, 5)): 56/112 ≈ 0.500
      ├── Some((5, 0)): 10/17 ≈ 0.588
      ├── Some((5, 1)): 3/9 ≈ 0.333
      ├── Some((5, 2)): 1/7 ≈ 0.143
      ├── Some((5, 3)): 15/21 ≈ 0.714
      ├── Some((5, 4)): 3/9 ≈ 0.333
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 11/18 ≈ 0.611
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 4/10 ≈ 0.400
    ├── Some((8, 6)): 141/228 ≈ 0.618
      ├── Some((6, 0)): 12/22 ≈ 0.545
      ├── Some((6, 1)): 14/25 ≈ 0.560
      ├── Some((6, 2)): 17/28 ≈ 0.607
      ├── Some((6, 3)): 14/25 ≈ 0.560
      ├── Some((6, 4)): 18/29 ≈ 0.621
      ├── Some((6, 5)): 32/43 ≈ 0.744
      ├── Some((6, 6)): 10/20 ≈ 0.500
      └── Some((6, 7)): 24/35 ≈ 0.686
    ├── Some((8, 7)): 66/126 ≈ 0.524
      ├── Some((7, 0)): 13/21 ≈ 0.619
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 3/10 ≈ 0.300
      ├── Some((7, 3)): 4/11 ≈ 0.364
      ├── Some((7, 4)): 4/11 ≈ 0.364
      ├── Some((7, 5)): 12/20 ≈ 0.600
      ├── Some((7, 7)): 18/26 ≈ 0.692
      └── Some((7, 8)): 6/13 ≈ 0.462
    └── Some((8, 8)): 57/113 ≈ 0.504
      ├── Some((8, 0)): 13/20 ≈ 0.650
      ├── Some((8, 1)): 2/8 ≈ 0.250
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 9/16 ≈ 0.562
      ├── Some((8, 4)): 10/17 ≈ 0.588
      ├── Some((8, 5)): 7/14 ≈ 0.500
      ├── Some((8, 6)): 11/18 ≈ 0.611
      └── Some((8, 7)): 2/9 ≈ 0.222
├── Some((7, 7)): 4542/8897 ≈ 0.511
  ├── Some((7, 0)): 551/1085 ≈ 0.508
    ├── Some((0, 0)): 65/126 ≈ 0.516
      ├── Some((0, 1)): 4/11 ≈ 0.364
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 7/15 ≈ 0.467
      ├── Some((0, 4)): 5/12 ≈ 0.417
      ├── Some((0, 5)): 6/13 ≈ 0.462
      ├── Some((0, 6)): 13/21 ≈ 0.619
      ├── Some((0, 7)): 16/24 ≈ 0.667
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((0, 1)): 35/82 ≈ 0.427
      ├── Some((1, 0)): 5/11 ≈ 0.455
      ├── Some((1, 1)): 9/14 ≈ 0.643
      ├── Some((1, 2)): 1/6 ≈ 0.167
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 8/13 ≈ 0.615
      ├── Some((1, 5)): 2/7 ≈ 0.286
      ├── Some((1, 6)): 2/7 ≈ 0.286
      ├── Some((1, 7)): 4/9 ≈ 0.444
      └── Some((1, 8)): 1/6 ≈ 0.167
    ├── Some((0, 2)): 52/107 ≈ 0.486
      ├── Some((2, 0)): 0/6 ≈ 0.000
      ├── Some((2, 1)): 9/15 ≈ 0.600
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 6/12 ≈ 0.500
      ├── Some((2, 4)): 8/14 ≈ 0.571
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 10/16 ≈ 0.625
      ├── Some((2, 7)): 3/9 ≈ 0.333
      └── Some((2, 8)): 8/14 ≈ 0.571
    ├── Some((0, 3)): 63/123 ≈ 0.512
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 11/18 ≈ 0.611
      ├── Some((3, 2)): 3/9 ≈ 0.333
      ├── Some((3, 3)): 3/10 ≈ 0.300
      ├── Some((3, 4)): 8/15 ≈ 0.533
      ├── Some((3, 5)): 4/11 ≈ 0.364
      ├── Some((3, 6)): 16/22 ≈ 0.727
      ├── Some((3, 7)): 9/16 ≈ 0.562
      └── Some((3, 8)): 5/12 ≈ 0.417
    ├── Some((0, 4)): 62/122 ≈ 0.508
      ├── Some((4, 0)): 10/17 ≈ 0.588
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 6/13 ≈ 0.462
      ├── Some((4, 3)): 4/10 ≈ 0.400
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 13/19 ≈ 0.684
      ├── Some((4, 6)): 10/17 ≈ 0.588
      ├── Some((4, 7)): 8/15 ≈ 0.533
      └── Some((4, 8)): 1/7 ≈ 0.143
    ├── Some((0, 5)): 61/121 ≈ 0.504
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 6/13 ≈ 0.462
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 12/18 ≈ 0.667
      ├── Some((5, 5)): 4/10 ≈ 0.400
      ├── Some((5, 6)): 4/10 ≈ 0.400
      ├── Some((5, 7)): 9/16 ≈ 0.562
      └── Some((5, 8)): 10/17 ≈ 0.588
    ├── Some((0, 6)): 46/98 ≈ 0.469
      ├── Some((6, 0)): 1/6 ≈ 0.167
      ├── Some((6, 1)): 3/9 ≈ 0.333
      ├── Some((6, 2)): 4/10 ≈ 0.400
      ├── Some((6, 3)): 5/11 ≈ 0.455
      ├── Some((6, 4)): 6/12 ≈ 0.500
      ├── Some((6, 5)): 8/14 ≈ 0.571
      ├── Some((6, 6)): 3/9 ≈ 0.333
      ├── Some((6, 7)): 4/10 ≈ 0.400
      └── Some((6, 8)): 11/16 ≈ 0.688
    ├── Some((0, 7)): 100/176 ≈ 0.568
      ├── Some((7, 1)): 16/27 ≈ 0.593
      ├── Some((7, 2)): 8/18 ≈ 0.444
      ├── Some((7, 3)): 18/29 ≈ 0.621
      ├── Some((7, 4)): 18/30 ≈ 0.600
      ├── Some((7, 5)): 16/27 ≈ 0.593
      ├── Some((7, 6)): 16/27 ≈ 0.593
      └── Some((7, 8)): 7/17 ≈ 0.412
    └── Some((0, 8)): 67/129 ≈ 0.519
      ├── Some((8, 0)): 12/19 ≈ 0.632
      ├── Some((8, 1)): 11/18 ≈ 0.611
      ├── Some((8, 2)): 6/13 ≈ 0.462
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 15/22 ≈ 0.682
      ├── Some((8, 5)): 6/13 ≈ 0.462
      ├── Some((8, 6)): 9/16 ≈ 0.562
      ├── Some((8, 7)): 4/11 ≈ 0.364
      └── Some((8, 8)): 2/8 ≈ 0.250
  ├── Some((7, 1)): 545/1074 ≈ 0.507
    ├── Some((1, 0)): 64/125 ≈ 0.512
      ├── Some((0, 0)): 10/17 ≈ 0.588
      ├── Some((0, 1)): 1/7 ≈ 0.143
      ├── Some((0, 2)): 8/15 ≈ 0.533
      ├── Some((0, 3)): 6/13 ≈ 0.462
      ├── Some((0, 4)): 10/17 ≈ 0.588
      ├── Some((0, 5)): 7/14 ≈ 0.500
      ├── Some((0, 6)): 6/13 ≈ 0.462
      ├── Some((0, 7)): 10/17 ≈ 0.588
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((1, 1)): 141/232 ≈ 0.608
      ├── Some((1, 0)): 19/30 ≈ 0.633
      ├── Some((1, 2)): 28/40 ≈ 0.700
      ├── Some((1, 3)): 13/24 ≈ 0.542
      ├── Some((1, 4)): 23/35 ≈ 0.657
      ├── Some((1, 5)): 9/20 ≈ 0.450
      ├── Some((1, 6)): 10/21 ≈ 0.476
      ├── Some((1, 7)): 12/23 ≈ 0.522
      └── Some((1, 8)): 26/38 ≈ 0.684
    ├── Some((1, 2)): 54/111 ≈ 0.486
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 10/17 ≈ 0.588
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 2/8 ≈ 0.250
      ├── Some((2, 4)): 10/17 ≈ 0.588
      ├── Some((2, 5)): 2/8 ≈ 0.250
      ├── Some((2, 6)): 1/7 ≈ 0.143
      ├── Some((2, 7)): 14/20 ≈ 0.700
      └── Some((2, 8)): 3/9 ≈ 0.333
    ├── Some((1, 3)): 43/94 ≈ 0.457
      ├── Some((3, 0)): 10/15 ≈ 0.667
      ├── Some((3, 1)): 6/12 ≈ 0.500
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 0/5 ≈ 0.000
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 2/8 ≈ 0.250
      ├── Some((3, 6)): 1/6 ≈ 0.167
      ├── Some((3, 7)): 7/13 ≈ 0.538
      └── Some((3, 8)): 7/13 ≈ 0.538
    ├── Some((1, 4)): 51/106 ≈ 0.481
      ├── Some((4, 0)): 2/8 ≈ 0.250
      ├── Some((4, 1)): 3/9 ≈ 0.333
      ├── Some((4, 2)): 2/8 ≈ 0.250
      ├── Some((4, 3)): 14/20 ≈ 0.700
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 3/9 ≈ 0.333
      ├── Some((4, 6)): 3/9 ≈ 0.333
      ├── Some((4, 7)): 12/18 ≈ 0.667
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((1, 5)): 26/68 ≈ 0.382
      ├── Some((5, 0)): 6/10 ≈ 0.600
      ├── Some((5, 1)): 4/9 ≈ 0.444
      ├── Some((5, 2)): 5/9 ≈ 0.556
      ├── Some((5, 3)): 1/5 ≈ 0.200
      ├── Some((5, 4)): 3/8 ≈ 0.375
      ├── Some((5, 5)): 0/4 ≈ 0.000
      ├── Some((5, 6)): 2/7 ≈ 0.286
      ├── Some((5, 7)): 3/8 ≈ 0.375
      └── Some((5, 8)): 2/7 ≈ 0.286
    ├── Some((1, 6)): 43/94 ≈ 0.457
      ├── Some((6, 0)): 6/12 ≈ 0.500
      ├── Some((6, 1)): 5/11 ≈ 0.455
      ├── Some((6, 2)): 6/12 ≈ 0.500
      ├── Some((6, 3)): 1/6 ≈ 0.167
      ├── Some((6, 4)): 10/15 ≈ 0.667
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 2/7 ≈ 0.286
      ├── Some((6, 7)): 7/13 ≈ 0.538
      └── Some((6, 8)): 4/10 ≈ 0.400
    ├── Some((1, 7)): 58/116 ≈ 0.500
      ├── Some((7, 0)): 13/22 ≈ 0.591
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 10/19 ≈ 0.526
      ├── Some((7, 5)): 3/11 ≈ 0.273
      ├── Some((7, 6)): 2/9 ≈ 0.222
      └── Some((7, 8)): 12/21 ≈ 0.571
    └── Some((1, 8)): 65/127 ≈ 0.512
      ├── Some((8, 0)): 4/10 ≈ 0.400
      ├── Some((8, 1)): 5/12 ≈ 0.417
      ├── Some((8, 2)): 12/19 ≈ 0.632
      ├── Some((8, 3)): 6/13 ≈ 0.462
      ├── Some((8, 4)): 6/13 ≈ 0.462
      ├── Some((8, 5)): 9/16 ≈ 0.562
      ├── Some((8, 6)): 6/13 ≈ 0.462
      ├── Some((8, 7)): 9/16 ≈ 0.562
      └── Some((8, 8)): 7/14 ≈ 0.500
  ├── Some((7, 2)): 657/1268 ≈ 0.518
    ├── Some((2, 0)): 80/151 ≈ 0.530
      ├── Some((0, 0)): 6/14 ≈ 0.429
      ├── Some((0, 1)): 11/19 ≈ 0.579
      ├── Some((0, 2)): 12/20 ≈ 0.600
      ├── Some((0, 3)): 4/11 ≈ 0.364
      ├── Some((0, 4)): 9/17 ≈ 0.529
      ├── Some((0, 5)): 13/21 ≈ 0.619
      ├── Some((0, 6)): 4/11 ≈ 0.364
      ├── Some((0, 7)): 10/18 ≈ 0.556
      └── Some((0, 8)): 11/19 ≈ 0.579
    ├── Some((2, 1)): 57/118 ≈ 0.483
      ├── Some((1, 0)): 4/11 ≈ 0.364
      ├── Some((1, 1)): 2/8 ≈ 0.250
      ├── Some((1, 2)): 7/14 ≈ 0.500
      ├── Some((1, 3)): 8/15 ≈ 0.533
      ├── Some((1, 4)): 6/13 ≈ 0.462
      ├── Some((1, 5)): 4/11 ≈ 0.364
      ├── Some((1, 6)): 13/20 ≈ 0.650
      ├── Some((1, 7)): 9/16 ≈ 0.562
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((2, 2)): 85/158 ≈ 0.538
      ├── Some((2, 0)): 12/21 ≈ 0.571
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 3)): 4/12 ≈ 0.333
      ├── Some((2, 4)): 8/17 ≈ 0.471
      ├── Some((2, 5)): 15/25 ≈ 0.600
      ├── Some((2, 6)): 12/21 ≈ 0.571
      ├── Some((2, 7)): 13/23 ≈ 0.565
      └── Some((2, 8)): 12/21 ≈ 0.571
    ├── Some((2, 3)): 67/132 ≈ 0.508
      ├── Some((3, 0)): 10/17 ≈ 0.588
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 11/18 ≈ 0.611
      ├── Some((3, 3)): 12/19 ≈ 0.632
      ├── Some((3, 4)): 2/9 ≈ 0.222
      ├── Some((3, 5)): 2/9 ≈ 0.222
      ├── Some((3, 6)): 7/14 ≈ 0.500
      ├── Some((3, 7)): 11/19 ≈ 0.579
      └── Some((3, 8)): 7/14 ≈ 0.500
    ├── Some((2, 4)): 63/126 ≈ 0.500
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 6/13 ≈ 0.462
      ├── Some((4, 2)): 2/9 ≈ 0.222
      ├── Some((4, 3)): 9/16 ≈ 0.562
      ├── Some((4, 4)): 7/14 ≈ 0.500
      ├── Some((4, 5)): 14/21 ≈ 0.667
      ├── Some((4, 6)): 8/15 ≈ 0.533
      ├── Some((4, 7)): 0/6 ≈ 0.000
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((2, 5)): 86/160 ≈ 0.538
      ├── Some((5, 0)): 14/23 ≈ 0.609
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 12/20 ≈ 0.600
      ├── Some((5, 3)): 12/20 ≈ 0.600
      ├── Some((5, 4)): 12/20 ≈ 0.600
      ├── Some((5, 5)): 2/9 ≈ 0.222
      ├── Some((5, 6)): 13/22 ≈ 0.591
      ├── Some((5, 7)): 11/19 ≈ 0.579
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((2, 6)): 92/168 ≈ 0.548
      ├── Some((6, 0)): 9/17 ≈ 0.529
      ├── Some((6, 1)): 4/12 ≈ 0.333
      ├── Some((6, 2)): 8/16 ≈ 0.500
      ├── Some((6, 3)): 8/16 ≈ 0.500
      ├── Some((6, 4)): 15/24 ≈ 0.625
      ├── Some((6, 5)): 13/22 ≈ 0.591
      ├── Some((6, 6)): 17/26 ≈ 0.654
      ├── Some((6, 7)): 12/21 ≈ 0.571
      └── Some((6, 8)): 5/13 ≈ 0.385
    ├── Some((2, 7)): 49/106 ≈ 0.462
      ├── Some((7, 0)): 10/18 ≈ 0.556
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 3)): 10/18 ≈ 0.556
      ├── Some((7, 4)): 11/20 ≈ 0.550
      ├── Some((7, 5)): 3/11 ≈ 0.273
      ├── Some((7, 6)): 1/8 ≈ 0.125
      └── Some((7, 8)): 7/15 ≈ 0.467
    └── Some((2, 8)): 78/148 ≈ 0.527
      ├── Some((8, 0)): 2/9 ≈ 0.222
      ├── Some((8, 1)): 16/24 ≈ 0.667
      ├── Some((8, 2)): 4/12 ≈ 0.333
      ├── Some((8, 3)): 16/24 ≈ 0.667
      ├── Some((8, 4)): 16/24 ≈ 0.667
      ├── Some((8, 5)): 9/17 ≈ 0.529
      ├── Some((8, 6)): 6/14 ≈ 0.429
      ├── Some((8, 7)): 7/15 ≈ 0.467
      └── Some((8, 8)): 1/8 ≈ 0.125
  ├── Some((7, 3)): 302/646 ≈ 0.467
    ├── Some((3, 0)): 21/53 ≈ 0.396
      ├── Some((0, 0)): 1/5 ≈ 0.200
      ├── Some((0, 1)): 1/5 ≈ 0.200
      ├── Some((0, 2)): 0/3 ≈ 0.000
      ├── Some((0, 3)): 8/11 ≈ 0.727
      ├── Some((0, 4)): 2/6 ≈ 0.333
      ├── Some((0, 5)): 1/5 ≈ 0.200
      ├── Some((0, 6)): 4/7 ≈ 0.571
      ├── Some((0, 7)): 0/4 ≈ 0.000
      └── Some((0, 8)): 3/6 ≈ 0.500
    ├── Some((3, 1)): 44/87 ≈ 0.506
      ├── Some((1, 0)): 5/10 ≈ 0.500
      ├── Some((1, 1)): 8/12 ≈ 0.667
      ├── Some((1, 2)): 6/11 ≈ 0.545
      ├── Some((1, 3)): 3/8 ≈ 0.375
      ├── Some((1, 4)): 2/7 ≈ 0.286
      ├── Some((1, 5)): 7/12 ≈ 0.583
      ├── Some((1, 6)): 3/8 ≈ 0.375
      ├── Some((1, 7)): 9/13 ≈ 0.692
      └── Some((1, 8)): 0/5 ≈ 0.000
    ├── Some((3, 2)): 29/65 ≈ 0.446
      ├── Some((2, 0)): 3/7 ≈ 0.429
      ├── Some((2, 1)): 7/11 ≈ 0.636
      ├── Some((2, 2)): 1/5 ≈ 0.200
      ├── Some((2, 3)): 6/10 ≈ 0.600
      ├── Some((2, 4)): 2/6 ≈ 0.333
      ├── Some((2, 5)): 1/5 ≈ 0.200
      ├── Some((2, 6)): 2/6 ≈ 0.333
      ├── Some((2, 7)): 2/6 ≈ 0.333
      └── Some((2, 8)): 4/8 ≈ 0.500
    ├── Some((3, 3)): 49/94 ≈ 0.521
      ├── Some((3, 0)): 9/14 ≈ 0.643
      ├── Some((3, 1)): 8/13 ≈ 0.615
      ├── Some((3, 2)): 8/13 ≈ 0.615
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 3/9 ≈ 0.333
      ├── Some((3, 7)): 2/7 ≈ 0.286
      └── Some((3, 8)): 8/14 ≈ 0.571
    ├── Some((3, 4)): 24/58 ≈ 0.414
      ├── Some((4, 0)): 2/6 ≈ 0.333
      ├── Some((4, 1)): 6/9 ≈ 0.667
      ├── Some((4, 2)): 2/6 ≈ 0.333
      ├── Some((4, 3)): 3/6 ≈ 0.500
      ├── Some((4, 4)): 1/5 ≈ 0.200
      ├── Some((4, 5)): 4/7 ≈ 0.571
      ├── Some((4, 6)): 3/7 ≈ 0.429
      ├── Some((4, 7)): 0/4 ≈ 0.000
      └── Some((4, 8)): 3/7 ≈ 0.429
    ├── Some((3, 5)): 52/98 ≈ 0.531
      ├── Some((5, 0)): 5/11 ≈ 0.455
      ├── Some((5, 1)): 3/8 ≈ 0.375
      ├── Some((5, 2)): 3/8 ≈ 0.375
      ├── Some((5, 3)): 6/11 ≈ 0.545
      ├── Some((5, 4)): 11/16 ≈ 0.688
      ├── Some((5, 5)): 3/8 ≈ 0.375
      ├── Some((5, 6)): 9/14 ≈ 0.643
      ├── Some((5, 7)): 7/12 ≈ 0.583
      └── Some((5, 8)): 4/9 ≈ 0.444
    ├── Some((3, 6)): 34/73 ≈ 0.466
      ├── Some((6, 0)): 5/9 ≈ 0.556
      ├── Some((6, 1)): 0/4 ≈ 0.000
      ├── Some((6, 2)): 6/10 ≈ 0.600
      ├── Some((6, 3)): 1/5 ≈ 0.200
      ├── Some((6, 4)): 5/9 ≈ 0.556
      ├── Some((6, 5)): 5/9 ≈ 0.556
      ├── Some((6, 6)): 5/10 ≈ 0.500
      ├── Some((6, 7)): 4/9 ≈ 0.444
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((3, 7)): 20/52 ≈ 0.385
      ├── Some((7, 0)): 0/4 ≈ 0.000
      ├── Some((7, 1)): 3/8 ≈ 0.375
      ├── Some((7, 2)): 7/12 ≈ 0.583
      ├── Some((7, 4)): 8/12 ≈ 0.667
      ├── Some((7, 5)): 0/4 ≈ 0.000
      ├── Some((7, 6)): 1/5 ≈ 0.200
      └── Some((7, 8)): 1/6 ≈ 0.167
    └── Some((3, 8)): 29/65 ≈ 0.446
      ├── Some((8, 0)): 4/8 ≈ 0.500
      ├── Some((8, 1)): 3/7 ≈ 0.429
      ├── Some((8, 2)): 2/6 ≈ 0.333
      ├── Some((8, 3)): 7/11 ≈ 0.636
      ├── Some((8, 4)): 3/7 ≈ 0.429
      ├── Some((8, 5)): 6/10 ≈ 0.600
      ├── Some((8, 6)): 2/6 ≈ 0.333
      ├── Some((8, 7)): 0/4 ≈ 0.000
      └── Some((8, 8)): 1/5 ≈ 0.200
  ├── Some((7, 4)): 819/1545 ≈ 0.530
    ├── Some((4, 0)): 101/187 ≈ 0.540
      ├── Some((0, 0)): 10/19 ≈ 0.526
      ├── Some((0, 1)): 14/24 ≈ 0.583
      ├── Some((0, 2)): 5/14 ≈ 0.357
      ├── Some((0, 3)): 9/18 ≈ 0.500
      ├── Some((0, 4)): 12/22 ≈ 0.545
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 10/19 ≈ 0.526
      ├── Some((0, 7)): 17/27 ≈ 0.630
      └── Some((0, 8)): 15/25 ≈ 0.600
    ├── Some((4, 1)): 50/111 ≈ 0.450
      ├── Some((1, 0)): 3/9 ≈ 0.333
      ├── Some((1, 1)): 9/16 ≈ 0.562
      ├── Some((1, 2)): 3/10 ≈ 0.300
      ├── Some((1, 3)): 3/10 ≈ 0.300
      ├── Some((1, 4)): 11/18 ≈ 0.611
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 6/13 ≈ 0.462
      └── Some((1, 8)): 2/8 ≈ 0.250
    ├── Some((4, 2)): 113/204 ≈ 0.554
      ├── Some((2, 0)): 9/19 ≈ 0.474
      ├── Some((2, 1)): 5/14 ≈ 0.357
      ├── Some((2, 2)): 21/32 ≈ 0.656
      ├── Some((2, 3)): 9/19 ≈ 0.474
      ├── Some((2, 4)): 22/33 ≈ 0.667
      ├── Some((2, 5)): 11/21 ≈ 0.524
      ├── Some((2, 6)): 13/23 ≈ 0.565
      ├── Some((2, 7)): 19/29 ≈ 0.655
      └── Some((2, 8)): 4/13 ≈ 0.308
    ├── Some((4, 3)): 92/174 ≈ 0.529
      ├── Some((3, 0)): 9/18 ≈ 0.500
      ├── Some((3, 1)): 6/15 ≈ 0.400
      ├── Some((3, 2)): 22/32 ≈ 0.688
      ├── Some((3, 3)): 10/19 ≈ 0.526
      ├── Some((3, 4)): 12/21 ≈ 0.571
      ├── Some((3, 5)): 10/19 ≈ 0.526
      ├── Some((3, 6)): 13/23 ≈ 0.565
      ├── Some((3, 7)): 4/12 ≈ 0.333
      └── Some((3, 8)): 5/14 ≈ 0.357
    ├── Some((4, 4)): 140/243 ≈ 0.576
      ├── Some((4, 0)): 17/30 ≈ 0.567
      ├── Some((4, 1)): 33/47 ≈ 0.702
      ├── Some((4, 2)): 8/20 ≈ 0.400
      ├── Some((4, 3)): 15/28 ≈ 0.536
      ├── Some((4, 5)): 23/36 ≈ 0.639
      ├── Some((4, 6)): 18/31 ≈ 0.581
      ├── Some((4, 7)): 6/17 ≈ 0.353
      └── Some((4, 8)): 20/33 ≈ 0.606
    ├── Some((4, 5)): 97/181 ≈ 0.536
      ├── Some((5, 0)): 1/9 ≈ 0.111
      ├── Some((5, 1)): 2/10 ≈ 0.200
      ├── Some((5, 2)): 16/26 ≈ 0.615
      ├── Some((5, 3)): 13/23 ≈ 0.565
      ├── Some((5, 4)): 10/19 ≈ 0.526
      ├── Some((5, 5)): 13/23 ≈ 0.565
      ├── Some((5, 6)): 9/18 ≈ 0.500
      ├── Some((5, 7)): 18/28 ≈ 0.643
      └── Some((5, 8)): 14/24 ≈ 0.583
    ├── Some((4, 6)): 76/150 ≈ 0.507
      ├── Some((6, 0)): 11/19 ≈ 0.579
      ├── Some((6, 1)): 7/15 ≈ 0.467
      ├── Some((6, 2)): 3/11 ≈ 0.273
      ├── Some((6, 3)): 8/16 ≈ 0.500
      ├── Some((6, 4)): 9/17 ≈ 0.529
      ├── Some((6, 5)): 14/23 ≈ 0.609
      ├── Some((6, 6)): 12/21 ≈ 0.571
      ├── Some((6, 7)): 4/12 ≈ 0.333
      └── Some((6, 8)): 7/15 ≈ 0.467
    ├── Some((4, 7)): 104/191 ≈ 0.545
      ├── Some((7, 0)): 12/24 ≈ 0.500
      ├── Some((7, 1)): 22/35 ≈ 0.629
      ├── Some((7, 2)): 16/29 ≈ 0.552
      ├── Some((7, 3)): 9/21 ≈ 0.429
      ├── Some((7, 5)): 24/38 ≈ 0.632
      ├── Some((7, 6)): 12/24 ≈ 0.500
      └── Some((7, 8)): 8/19 ≈ 0.421
    └── Some((4, 8)): 45/103 ≈ 0.437
      ├── Some((8, 0)): 2/8 ≈ 0.250
      ├── Some((8, 1)): 5/11 ≈ 0.455
      ├── Some((8, 2)): 8/15 ≈ 0.533
      ├── Some((8, 3)): 5/11 ≈ 0.455
      ├── Some((8, 4)): 7/14 ≈ 0.500
      ├── Some((8, 5)): 9/16 ≈ 0.562
      ├── Some((8, 6)): 3/9 ≈ 0.333
      ├── Some((8, 7)): 2/8 ≈ 0.250
      └── Some((8, 8)): 4/10 ≈ 0.400
  ├── Some((7, 5)): 443/896 ≈ 0.494
    ├── Some((5, 0)): 67/126 ≈ 0.532
      ├── Some((0, 0)): 6/13 ≈ 0.462
      ├── Some((0, 1)): 5/11 ≈ 0.455
      ├── Some((0, 2)): 9/16 ≈ 0.562
      ├── Some((0, 3)): 9/16 ≈ 0.562
      ├── Some((0, 4)): 5/11 ≈ 0.455
      ├── Some((0, 5)): 8/15 ≈ 0.533
      ├── Some((0, 6)): 10/16 ≈ 0.625
      ├── Some((0, 7)): 10/16 ≈ 0.625
      └── Some((0, 8)): 5/11 ≈ 0.455
    ├── Some((5, 1)): 58/113 ≈ 0.513
      ├── Some((1, 0)): 12/18 ≈ 0.667
      ├── Some((1, 1)): 3/9 ≈ 0.333
      ├── Some((1, 2)): 3/9 ≈ 0.333
      ├── Some((1, 3)): 8/14 ≈ 0.571
      ├── Some((1, 4)): 2/8 ≈ 0.250
      ├── Some((1, 5)): 3/9 ≈ 0.333
      ├── Some((1, 6)): 11/17 ≈ 0.647
      ├── Some((1, 7)): 8/14 ≈ 0.571
      └── Some((1, 8)): 8/14 ≈ 0.571
    ├── Some((5, 2)): 50/101 ≈ 0.495
      ├── Some((2, 0)): 7/13 ≈ 0.538
      ├── Some((2, 1)): 9/14 ≈ 0.643
      ├── Some((2, 2)): 4/10 ≈ 0.400
      ├── Some((2, 3)): 3/9 ≈ 0.333
      ├── Some((2, 4)): 6/12 ≈ 0.500
      ├── Some((2, 5)): 3/9 ≈ 0.333
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 11/16 ≈ 0.688
      └── Some((2, 8)): 2/7 ≈ 0.286
    ├── Some((5, 3)): 31/73 ≈ 0.425
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 1/5 ≈ 0.200
      ├── Some((3, 2)): 10/14 ≈ 0.714
      ├── Some((3, 3)): 2/7 ≈ 0.286
      ├── Some((3, 4)): 3/8 ≈ 0.375
      ├── Some((3, 5)): 6/10 ≈ 0.600
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 5/10 ≈ 0.500
      └── Some((3, 8)): 0/4 ≈ 0.000
    ├── Some((5, 4)): 80/144 ≈ 0.556
      ├── Some((4, 0)): 13/20 ≈ 0.650
      ├── Some((4, 1)): 6/13 ≈ 0.462
      ├── Some((4, 2)): 8/15 ≈ 0.533
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 13/20 ≈ 0.650
      ├── Some((4, 5)): 16/23 ≈ 0.696
      ├── Some((4, 6)): 8/15 ≈ 0.533
      ├── Some((4, 7)): 4/11 ≈ 0.364
      └── Some((4, 8)): 9/16 ≈ 0.562
    ├── Some((5, 5)): 57/112 ≈ 0.509
      ├── Some((5, 0)): 1/7 ≈ 0.143
      ├── Some((5, 1)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 6/13 ≈ 0.462
      ├── Some((5, 4)): 9/16 ≈ 0.562
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 12/19 ≈ 0.632
      └── Some((5, 8)): 10/17 ≈ 0.588
    ├── Some((5, 6)): 14/46 ≈ 0.304
      ├── Some((6, 0)): 0/3 ≈ 0.000
      ├── Some((6, 1)): 1/5 ≈ 0.200
      ├── Some((6, 2)): 3/7 ≈ 0.429
      ├── Some((6, 3)): 4/7 ≈ 0.571
      ├── Some((6, 4)): 1/5 ≈ 0.200
      ├── Some((6, 5)): 0/3 ≈ 0.000
      ├── Some((6, 6)): 0/3 ≈ 0.000
      ├── Some((6, 7)): 1/5 ≈ 0.200
      └── Some((6, 8)): 3/7 ≈ 0.429
    ├── Some((5, 7)): 59/114 ≈ 0.518
      ├── Some((7, 0)): 3/10 ≈ 0.300
      ├── Some((7, 1)): 2/9 ≈ 0.222
      ├── Some((7, 2)): 12/20 ≈ 0.600
      ├── Some((7, 3)): 11/19 ≈ 0.579
      ├── Some((7, 4)): 15/23 ≈ 0.652
      ├── Some((7, 6)): 10/18 ≈ 0.556
      └── Some((7, 8)): 6/14 ≈ 0.429
    └── Some((5, 8)): 26/66 ≈ 0.394
      ├── Some((8, 0)): 1/5 ≈ 0.200
      ├── Some((8, 1)): 0/4 ≈ 0.000
      ├── Some((8, 2)): 3/8 ≈ 0.375
      ├── Some((8, 3)): 3/8 ≈ 0.375
      ├── Some((8, 4)): 2/7 ≈ 0.286
      ├── Some((8, 5)): 6/10 ≈ 0.600
      ├── Some((8, 6)): 4/8 ≈ 0.500
      ├── Some((8, 7)): 7/11 ≈ 0.636
      └── Some((8, 8)): 0/4 ≈ 0.000
  ├── Some((7, 6)): 689/1323 ≈ 0.521
    ├── Some((6, 0)): 73/142 ≈ 0.514
      ├── Some((0, 0)): 5/12 ≈ 0.417
      ├── Some((0, 1)): 6/13 ≈ 0.462
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 18/26 ≈ 0.692
      ├── Some((0, 4)): 8/16 ≈ 0.500
      ├── Some((0, 5)): 7/15 ≈ 0.467
      ├── Some((0, 6)): 6/14 ≈ 0.429
      ├── Some((0, 7)): 8/16 ≈ 0.500
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((6, 1)): 77/148 ≈ 0.520
      ├── Some((1, 0)): 10/18 ≈ 0.556
      ├── Some((1, 1)): 8/16 ≈ 0.500
      ├── Some((1, 2)): 10/18 ≈ 0.556
      ├── Some((1, 3)): 15/23 ≈ 0.652
      ├── Some((1, 4)): 9/17 ≈ 0.529
      ├── Some((1, 5)): 6/14 ≈ 0.429
      ├── Some((1, 6)): 7/15 ≈ 0.467
      ├── Some((1, 7)): 4/11 ≈ 0.364
      └── Some((1, 8)): 7/15 ≈ 0.467
    ├── Some((6, 2)): 119/208 ≈ 0.572
      ├── Some((2, 0)): 10/20 ≈ 0.500
      ├── Some((2, 1)): 7/16 ≈ 0.438
      ├── Some((2, 2)): 14/24 ≈ 0.583
      ├── Some((2, 3)): 19/29 ≈ 0.655
      ├── Some((2, 4)): 11/21 ≈ 0.524
      ├── Some((2, 5)): 18/28 ≈ 0.643
      ├── Some((2, 6)): 13/23 ≈ 0.565
      ├── Some((2, 7)): 8/17 ≈ 0.471
      └── Some((2, 8)): 19/29 ≈ 0.655
    ├── Some((6, 3)): 95/174 ≈ 0.546
      ├── Some((3, 0)): 5/13 ≈ 0.385
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 2)): 6/15 ≈ 0.400
      ├── Some((3, 3)): 9/18 ≈ 0.500
      ├── Some((3, 4)): 12/21 ≈ 0.571
      ├── Some((3, 5)): 11/20 ≈ 0.550
      ├── Some((3, 6)): 20/29 ≈ 0.690
      ├── Some((3, 7)): 11/20 ≈ 0.550
      └── Some((3, 8)): 15/24 ≈ 0.625
    ├── Some((6, 4)): 41/94 ≈ 0.436
      ├── Some((4, 0)): 6/12 ≈ 0.500
      ├── Some((4, 1)): 5/11 ≈ 0.455
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 3/9 ≈ 0.333
      ├── Some((4, 4)): 1/6 ≈ 0.167
      ├── Some((4, 5)): 1/6 ≈ 0.167
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 8/14 ≈ 0.571
      └── Some((4, 8)): 9/15 ≈ 0.600
    ├── Some((6, 5)): 80/153 ≈ 0.523
      ├── Some((5, 0)): 10/18 ≈ 0.556
      ├── Some((5, 1)): 16/25 ≈ 0.640
      ├── Some((5, 2)): 13/21 ≈ 0.619
      ├── Some((5, 3)): 4/12 ≈ 0.333
      ├── Some((5, 4)): 12/20 ≈ 0.600
      ├── Some((5, 5)): 9/17 ≈ 0.529
      ├── Some((5, 6)): 3/11 ≈ 0.273
      ├── Some((5, 7)): 5/13 ≈ 0.385
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((6, 6)): 45/100 ≈ 0.450
      ├── Some((6, 0)): 2/8 ≈ 0.250
      ├── Some((6, 1)): 5/12 ≈ 0.417
      ├── Some((6, 2)): 1/7 ≈ 0.143
      ├── Some((6, 3)): 6/13 ≈ 0.462
      ├── Some((6, 4)): 9/16 ≈ 0.562
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 7)): 12/19 ≈ 0.632
      └── Some((6, 8)): 6/13 ≈ 0.462
    ├── Some((6, 7)): 66/132 ≈ 0.500
      ├── Some((7, 0)): 18/28 ≈ 0.643
      ├── Some((7, 1)): 14/24 ≈ 0.583
      ├── Some((7, 2)): 5/14 ≈ 0.357
      ├── Some((7, 3)): 4/13 ≈ 0.308
      ├── Some((7, 4)): 8/17 ≈ 0.471
      ├── Some((7, 5)): 8/17 ≈ 0.471
      └── Some((7, 8)): 9/18 ≈ 0.500
    └── Some((6, 8)): 93/171 ≈ 0.544
      ├── Some((8, 0)): 20/29 ≈ 0.690
      ├── Some((8, 1)): 11/20 ≈ 0.550
      ├── Some((8, 2)): 7/15 ≈ 0.467
      ├── Some((8, 3)): 9/18 ≈ 0.500
      ├── Some((8, 4)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 6/14 ≈ 0.429
      ├── Some((8, 6)): 12/21 ≈ 0.571
      ├── Some((8, 7)): 9/18 ≈ 0.500
      └── Some((8, 8)): 13/22 ≈ 0.591
  └── Some((7, 8)): 536/1059 ≈ 0.506
    ├── Some((8, 0)): 38/86 ≈ 0.442
      ├── Some((0, 0)): 1/6 ≈ 0.167
      ├── Some((0, 1)): 3/8 ≈ 0.375
      ├── Some((0, 2)): 3/8 ≈ 0.375
      ├── Some((0, 3)): 6/12 ≈ 0.500
      ├── Some((0, 4)): 3/9 ≈ 0.333
      ├── Some((0, 5)): 10/15 ≈ 0.667
      ├── Some((0, 6)): 8/13 ≈ 0.615
      ├── Some((0, 7)): 0/5 ≈ 0.000
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((8, 1)): 67/129 ≈ 0.519
      ├── Some((1, 0)): 12/18 ≈ 0.667
      ├── Some((1, 1)): 9/16 ≈ 0.562
      ├── Some((1, 2)): 6/13 ≈ 0.462
      ├── Some((1, 3)): 6/13 ≈ 0.462
      ├── Some((1, 4)): 7/14 ≈ 0.500
      ├── Some((1, 5)): 5/12 ≈ 0.417
      ├── Some((1, 6)): 6/13 ≈ 0.462
      ├── Some((1, 7)): 12/19 ≈ 0.632
      └── Some((1, 8)): 4/10 ≈ 0.400
    ├── Some((8, 2)): 58/116 ≈ 0.500
      ├── Some((2, 0)): 0/6 ≈ 0.000
      ├── Some((2, 1)): 10/17 ≈ 0.588
      ├── Some((2, 2)): 10/17 ≈ 0.588
      ├── Some((2, 3)): 3/9 ≈ 0.333
      ├── Some((2, 4)): 1/7 ≈ 0.143
      ├── Some((2, 5)): 11/17 ≈ 0.647
      ├── Some((2, 6)): 7/14 ≈ 0.500
      ├── Some((2, 7)): 12/18 ≈ 0.667
      └── Some((2, 8)): 4/10 ≈ 0.400
    ├── Some((8, 3)): 71/134 ≈ 0.530
      ├── Some((3, 0)): 6/13 ≈ 0.462
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 8/15 ≈ 0.533
      ├── Some((3, 3)): 11/18 ≈ 0.611
      ├── Some((3, 4)): 2/8 ≈ 0.250
      ├── Some((3, 5)): 5/12 ≈ 0.417
      ├── Some((3, 6)): 15/22 ≈ 0.682
      ├── Some((3, 7)): 6/13 ≈ 0.462
      └── Some((3, 8)): 13/20 ≈ 0.650
    ├── Some((8, 4)): 56/113 ≈ 0.496
      ├── Some((4, 0)): 4/10 ≈ 0.400
      ├── Some((4, 1)): 12/18 ≈ 0.667
      ├── Some((4, 2)): 10/16 ≈ 0.625
      ├── Some((4, 3)): 4/10 ≈ 0.400
      ├── Some((4, 4)): 6/12 ≈ 0.500
      ├── Some((4, 5)): 7/14 ≈ 0.500
      ├── Some((4, 6)): 2/8 ≈ 0.250
      ├── Some((4, 7)): 5/11 ≈ 0.455
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((8, 5)): 52/107 ≈ 0.486
      ├── Some((5, 0)): 9/15 ≈ 0.600
      ├── Some((5, 1)): 11/17 ≈ 0.647
      ├── Some((5, 2)): 6/12 ≈ 0.500
      ├── Some((5, 3)): 8/15 ≈ 0.533
      ├── Some((5, 4)): 6/12 ≈ 0.500
      ├── Some((5, 5)): 5/11 ≈ 0.455
      ├── Some((5, 6)): 1/7 ≈ 0.143
      ├── Some((5, 7)): 2/8 ≈ 0.250
      └── Some((5, 8)): 3/9 ≈ 0.333
    ├── Some((8, 6)): 51/105 ≈ 0.486
      ├── Some((6, 0)): 5/11 ≈ 0.455
      ├── Some((6, 1)): 7/13 ≈ 0.538
      ├── Some((6, 2)): 11/17 ≈ 0.647
      ├── Some((6, 3)): 4/10 ≈ 0.400
      ├── Some((6, 4)): 3/9 ≈ 0.333
      ├── Some((6, 5)): 6/12 ≈ 0.500
      ├── Some((6, 6)): 7/13 ≈ 0.538
      ├── Some((6, 7)): 7/13 ≈ 0.538
      └── Some((6, 8)): 1/6 ≈ 0.167
    ├── Some((8, 7)): 56/113 ≈ 0.496
      ├── Some((7, 0)): 11/19 ≈ 0.579
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 10/18 ≈ 0.556
      ├── Some((7, 3)): 4/12 ≈ 0.333
      ├── Some((7, 4)): 6/14 ≈ 0.429
      ├── Some((7, 5)): 8/16 ≈ 0.500
      └── Some((7, 6)): 10/18 ≈ 0.556
    └── Some((8, 8)): 86/155 ≈ 0.555
      ├── Some((8, 0)): 10/19 ≈ 0.526
      ├── Some((8, 1)): 9/18 ≈ 0.500
      ├── Some((8, 2)): 17/26 ≈ 0.654
      ├── Some((8, 3)): 7/15 ≈ 0.467
      ├── Some((8, 4)): 9/18 ≈ 0.500
      ├── Some((8, 5)): 8/16 ≈ 0.500
      ├── Some((8, 6)): 20/29 ≈ 0.690
      └── Some((8, 7)): 5/13 ≈ 0.385
├── Some((7, 8)): 5502/10667 ≈ 0.516
  ├── Some((8, 0)): 686/1315 ≈ 0.522
    ├── Some((0, 0)): 34/83 ≈ 0.410
      ├── Some((0, 1)): 7/14 ≈ 0.500
      ├── Some((0, 2)): 2/8 ≈ 0.250
      ├── Some((0, 3)): 5/11 ≈ 0.455
      ├── Some((0, 4)): 0/5 ≈ 0.000
      ├── Some((0, 5)): 1/7 ≈ 0.143
      ├── Some((0, 6)): 6/12 ≈ 0.500
      ├── Some((0, 7)): 1/7 ≈ 0.143
      └── Some((0, 8)): 12/18 ≈ 0.667
    ├── Some((0, 1)): 67/133 ≈ 0.504
      ├── Some((1, 0)): 3/10 ≈ 0.300
      ├── Some((1, 1)): 10/18 ≈ 0.556
      ├── Some((1, 2)): 4/11 ≈ 0.364
      ├── Some((1, 3)): 8/15 ≈ 0.533
      ├── Some((1, 4)): 5/12 ≈ 0.417
      ├── Some((1, 5)): 13/21 ≈ 0.619
      ├── Some((1, 6)): 14/22 ≈ 0.636
      ├── Some((1, 7)): 4/11 ≈ 0.364
      └── Some((1, 8)): 5/12 ≈ 0.417
    ├── Some((0, 2)): 75/145 ≈ 0.517
      ├── Some((2, 0)): 3/10 ≈ 0.300
      ├── Some((2, 1)): 4/11 ≈ 0.364
      ├── Some((2, 2)): 9/17 ≈ 0.529
      ├── Some((2, 3)): 7/15 ≈ 0.467
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 15/23 ≈ 0.652
      ├── Some((2, 6)): 5/13 ≈ 0.385
      ├── Some((2, 7)): 13/21 ≈ 0.619
      └── Some((2, 8)): 8/16 ≈ 0.500
    ├── Some((0, 3)): 81/153 ≈ 0.529
      ├── Some((3, 0)): 16/24 ≈ 0.667
      ├── Some((3, 1)): 4/12 ≈ 0.333
      ├── Some((3, 2)): 3/11 ≈ 0.273
      ├── Some((3, 3)): 7/15 ≈ 0.467
      ├── Some((3, 4)): 16/24 ≈ 0.667
      ├── Some((3, 5)): 7/15 ≈ 0.467
      ├── Some((3, 6)): 8/16 ≈ 0.500
      ├── Some((3, 7)): 12/20 ≈ 0.600
      └── Some((3, 8)): 7/15 ≈ 0.467
    ├── Some((0, 4)): 79/151 ≈ 0.523
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 8/16 ≈ 0.500
      ├── Some((4, 2)): 9/17 ≈ 0.529
      ├── Some((4, 3)): 9/17 ≈ 0.529
      ├── Some((4, 4)): 9/17 ≈ 0.529
      ├── Some((4, 5)): 9/17 ≈ 0.529
      ├── Some((4, 6)): 6/14 ≈ 0.429
      ├── Some((4, 7)): 8/16 ≈ 0.500
      └── Some((4, 8)): 13/21 ≈ 0.619
    ├── Some((0, 5)): 83/156 ≈ 0.532
      ├── Some((5, 0)): 10/18 ≈ 0.556
      ├── Some((5, 1)): 9/17 ≈ 0.529
      ├── Some((5, 2)): 4/12 ≈ 0.333
      ├── Some((5, 3)): 12/20 ≈ 0.600
      ├── Some((5, 4)): 6/14 ≈ 0.429
      ├── Some((5, 5)): 14/23 ≈ 0.609
      ├── Some((5, 6)): 6/14 ≈ 0.429
      ├── Some((5, 7)): 4/12 ≈ 0.333
      └── Some((5, 8)): 17/25 ≈ 0.680
    ├── Some((0, 6)): 60/123 ≈ 0.488
      ├── Some((6, 0)): 3/10 ≈ 0.300
      ├── Some((6, 1)): 17/24 ≈ 0.708
      ├── Some((6, 2)): 7/14 ≈ 0.500
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 6/13 ≈ 0.462
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 8/15 ≈ 0.533
      ├── Some((6, 7)): 4/11 ≈ 0.364
      └── Some((6, 8)): 2/9 ≈ 0.222
    ├── Some((0, 7)): 81/153 ≈ 0.529
      ├── Some((7, 0)): 8/17 ≈ 0.471
      ├── Some((7, 1)): 5/13 ≈ 0.385
      ├── Some((7, 2)): 12/21 ≈ 0.571
      ├── Some((7, 3)): 7/16 ≈ 0.438
      ├── Some((7, 4)): 8/17 ≈ 0.471
      ├── Some((7, 5)): 12/21 ≈ 0.571
      ├── Some((7, 6)): 22/31 ≈ 0.710
      └── Some((7, 7)): 7/16 ≈ 0.438
    └── Some((0, 8)): 126/217 ≈ 0.581
      ├── Some((8, 1)): 17/29 ≈ 0.586
      ├── Some((8, 2)): 10/21 ≈ 0.476
      ├── Some((8, 3)): 3/12 ≈ 0.250
      ├── Some((8, 4)): 11/22 ≈ 0.500
      ├── Some((8, 5)): 16/28 ≈ 0.571
      ├── Some((8, 6)): 19/31 ≈ 0.613
      ├── Some((8, 7)): 30/42 ≈ 0.714
      └── Some((8, 8)): 19/31 ≈ 0.613
  ├── Some((8, 1)): 556/1091 ≈ 0.510
    ├── Some((1, 0)): 55/112 ≈ 0.491
      ├── Some((0, 0)): 4/10 ≈ 0.400
      ├── Some((0, 1)): 8/15 ≈ 0.533
      ├── Some((0, 2)): 7/13 ≈ 0.538
      ├── Some((0, 3)): 9/15 ≈ 0.600
      ├── Some((0, 4)): 8/15 ≈ 0.533
      ├── Some((0, 5)): 7/13 ≈ 0.538
      ├── Some((0, 6)): 6/12 ≈ 0.500
      ├── Some((0, 7)): 3/9 ≈ 0.333
      └── Some((0, 8)): 3/9 ≈ 0.333
    ├── Some((1, 1)): 90/161 ≈ 0.559
      ├── Some((1, 0)): 10/19 ≈ 0.526
      ├── Some((1, 2)): 10/19 ≈ 0.526
      ├── Some((1, 3)): 10/19 ≈ 0.526
      ├── Some((1, 4)): 6/14 ≈ 0.429
      ├── Some((1, 5)): 13/22 ≈ 0.591
      ├── Some((1, 6)): 18/27 ≈ 0.667
      ├── Some((1, 7)): 7/16 ≈ 0.438
      └── Some((1, 8)): 15/24 ≈ 0.625
    ├── Some((1, 2)): 50/104 ≈ 0.481
      ├── Some((2, 0)): 3/9 ≈ 0.333
      ├── Some((2, 1)): 5/11 ≈ 0.455
      ├── Some((2, 2)): 7/13 ≈ 0.538
      ├── Some((2, 3)): 2/8 ≈ 0.250
      ├── Some((2, 4)): 7/13 ≈ 0.538
      ├── Some((2, 5)): 13/18 ≈ 0.722
      ├── Some((2, 6)): 7/13 ≈ 0.538
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 1/7 ≈ 0.143
    ├── Some((1, 3)): 82/150 ≈ 0.547
      ├── Some((3, 0)): 12/20 ≈ 0.600
      ├── Some((3, 1)): 5/12 ≈ 0.417
      ├── Some((3, 2)): 13/20 ≈ 0.650
      ├── Some((3, 3)): 9/16 ≈ 0.562
      ├── Some((3, 4)): 9/17 ≈ 0.529
      ├── Some((3, 5)): 7/14 ≈ 0.500
      ├── Some((3, 6)): 12/20 ≈ 0.600
      ├── Some((3, 7)): 12/20 ≈ 0.600
      └── Some((3, 8)): 3/10 ≈ 0.300
    ├── Some((1, 4)): 42/92 ≈ 0.457
      ├── Some((4, 0)): 1/6 ≈ 0.167
      ├── Some((4, 1)): 2/7 ≈ 0.286
      ├── Some((4, 2)): 6/12 ≈ 0.500
      ├── Some((4, 3)): 8/13 ≈ 0.615
      ├── Some((4, 4)): 7/13 ≈ 0.538
      ├── Some((4, 5)): 4/10 ≈ 0.400
      ├── Some((4, 6)): 3/9 ≈ 0.333
      ├── Some((4, 7)): 11/16 ≈ 0.688
      └── Some((4, 8)): 0/5 ≈ 0.000
    ├── Some((1, 5)): 70/133 ≈ 0.526
      ├── Some((5, 0)): 10/17 ≈ 0.588
      ├── Some((5, 1)): 7/14 ≈ 0.500
      ├── Some((5, 2)): 11/18 ≈ 0.611
      ├── Some((5, 3)): 3/10 ≈ 0.300
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 6)): 8/15 ≈ 0.533
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 11/18 ≈ 0.611
    ├── Some((1, 6)): 67/129 ≈ 0.519
      ├── Some((6, 0)): 1/7 ≈ 0.143
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 8/15 ≈ 0.533
      ├── Some((6, 3)): 6/13 ≈ 0.462
      ├── Some((6, 4)): 3/10 ≈ 0.300
      ├── Some((6, 5)): 11/18 ≈ 0.611
      ├── Some((6, 6)): 8/15 ≈ 0.533
      ├── Some((6, 7)): 7/14 ≈ 0.500
      └── Some((6, 8)): 15/22 ≈ 0.682
    ├── Some((1, 7)): 47/100 ≈ 0.470
      ├── Some((7, 0)): 6/13 ≈ 0.462
      ├── Some((7, 1)): 6/13 ≈ 0.462
      ├── Some((7, 2)): 1/7 ≈ 0.143
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 13/19 ≈ 0.684
      ├── Some((7, 5)): 1/7 ≈ 0.143
      ├── Some((7, 6)): 10/17 ≈ 0.588
      └── Some((7, 7)): 8/15 ≈ 0.533
    └── Some((1, 8)): 53/109 ≈ 0.486
      ├── Some((8, 0)): 8/15 ≈ 0.533
      ├── Some((8, 2)): 10/17 ≈ 0.588
      ├── Some((8, 3)): 2/8 ≈ 0.250
      ├── Some((8, 4)): 11/18 ≈ 0.611
      ├── Some((8, 5)): 9/16 ≈ 0.562
      ├── Some((8, 6)): 4/11 ≈ 0.364
      ├── Some((8, 7)): 7/14 ≈ 0.500
      └── Some((8, 8)): 2/9 ≈ 0.222
  ├── Some((8, 2)): 435/881 ≈ 0.494
    ├── Some((2, 0)): 66/123 ≈ 0.537
      ├── Some((0, 0)): 7/13 ≈ 0.538
      ├── Some((0, 1)): 9/15 ≈ 0.600
      ├── Some((0, 2)): 4/10 ≈ 0.400
      ├── Some((0, 3)): 10/16 ≈ 0.625
      ├── Some((0, 4)): 7/14 ≈ 0.500
      ├── Some((0, 5)): 8/14 ≈ 0.571
      ├── Some((0, 6)): 8/14 ≈ 0.571
      ├── Some((0, 7)): 6/12 ≈ 0.500
      └── Some((0, 8)): 7/14 ≈ 0.500
    ├── Some((2, 1)): 28/68 ≈ 0.412
      ├── Some((1, 0)): 2/6 ≈ 0.333
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 7/11 ≈ 0.636
      ├── Some((1, 3)): 1/5 ≈ 0.200
      ├── Some((1, 4)): 3/8 ≈ 0.375
      ├── Some((1, 5)): 4/8 ≈ 0.500
      ├── Some((1, 6)): 1/5 ≈ 0.200
      ├── Some((1, 7)): 2/7 ≈ 0.286
      └── Some((1, 8)): 5/9 ≈ 0.556
    ├── Some((2, 2)): 36/80 ≈ 0.450
      ├── Some((2, 0)): 4/10 ≈ 0.400
      ├── Some((2, 1)): 3/8 ≈ 0.375
      ├── Some((2, 3)): 7/12 ≈ 0.583
      ├── Some((2, 4)): 7/12 ≈ 0.583
      ├── Some((2, 5)): 3/8 ≈ 0.375
      ├── Some((2, 6)): 4/10 ≈ 0.400
      ├── Some((2, 7)): 5/11 ≈ 0.455
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((2, 3)): 68/126 ≈ 0.540
      ├── Some((3, 0)): 11/17 ≈ 0.647
      ├── Some((3, 1)): 11/17 ≈ 0.647
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 10/17 ≈ 0.588
      ├── Some((3, 4)): 4/10 ≈ 0.400
      ├── Some((3, 5)): 9/16 ≈ 0.562
      ├── Some((3, 6)): 13/19 ≈ 0.684
      ├── Some((3, 7)): 1/7 ≈ 0.143
      └── Some((3, 8)): 5/12 ≈ 0.417
    ├── Some((2, 4)): 56/109 ≈ 0.514
      ├── Some((4, 0)): 9/15 ≈ 0.600
      ├── Some((4, 1)): 4/10 ≈ 0.400
      ├── Some((4, 2)): 10/15 ≈ 0.667
      ├── Some((4, 3)): 6/12 ≈ 0.500
      ├── Some((4, 4)): 10/16 ≈ 0.625
      ├── Some((4, 5)): 7/13 ≈ 0.538
      ├── Some((4, 6)): 0/5 ≈ 0.000
      ├── Some((4, 7)): 6/12 ≈ 0.500
      └── Some((4, 8)): 4/10 ≈ 0.400
    ├── Some((2, 5)): 54/107 ≈ 0.505
      ├── Some((5, 0)): 2/8 ≈ 0.250
      ├── Some((5, 1)): 6/12 ≈ 0.500
      ├── Some((5, 2)): 10/15 ≈ 0.667
      ├── Some((5, 3)): 5/11 ≈ 0.455
      ├── Some((5, 4)): 8/14 ≈ 0.571
      ├── Some((5, 5)): 6/12 ≈ 0.500
      ├── Some((5, 6)): 5/11 ≈ 0.455
      ├── Some((5, 7)): 4/10 ≈ 0.400
      └── Some((5, 8)): 7/13 ≈ 0.538
    ├── Some((2, 6)): 42/89 ≈ 0.472
      ├── Some((6, 0)): 4/10 ≈ 0.400
      ├── Some((6, 1)): 7/12 ≈ 0.583
      ├── Some((6, 2)): 1/6 ≈ 0.167
      ├── Some((6, 3)): 11/16 ≈ 0.688
      ├── Some((6, 4)): 1/6 ≈ 0.167
      ├── Some((6, 5)): 2/7 ≈ 0.286
      ├── Some((6, 6)): 8/13 ≈ 0.615
      ├── Some((6, 7)): 8/13 ≈ 0.615
      └── Some((6, 8)): 0/5 ≈ 0.000
    ├── Some((2, 7)): 59/114 ≈ 0.518
      ├── Some((7, 0)): 9/16 ≈ 0.562
      ├── Some((7, 1)): 4/10 ≈ 0.400
      ├── Some((7, 2)): 9/16 ≈ 0.562
      ├── Some((7, 3)): 4/11 ≈ 0.364
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 6/13 ≈ 0.462
      ├── Some((7, 6)): 14/20 ≈ 0.700
      └── Some((7, 7)): 6/13 ≈ 0.462
    └── Some((2, 8)): 25/64 ≈ 0.391
      ├── Some((8, 0)): 3/8 ≈ 0.375
      ├── Some((8, 1)): 1/5 ≈ 0.200
      ├── Some((8, 3)): 2/7 ≈ 0.286
      ├── Some((8, 4)): 5/10 ≈ 0.500
      ├── Some((8, 5)): 6/11 ≈ 0.545
      ├── Some((8, 6)): 2/7 ≈ 0.286
      ├── Some((8, 7)): 4/9 ≈ 0.444
      └── Some((8, 8)): 1/6 ≈ 0.167
  ├── Some((8, 3)): 350/731 ≈ 0.479
    ├── Some((3, 0)): 37/79 ≈ 0.468
      ├── Some((0, 0)): 3/8 ≈ 0.375
      ├── Some((0, 1)): 8/12 ≈ 0.667
      ├── Some((0, 2)): 5/9 ≈ 0.556
      ├── Some((0, 3)): 1/6 ≈ 0.167
      ├── Some((0, 4)): 6/10 ≈ 0.600
      ├── Some((0, 5)): 3/8 ≈ 0.375
      ├── Some((0, 6)): 7/11 ≈ 0.636
      ├── Some((0, 7)): 3/8 ≈ 0.375
      └── Some((0, 8)): 1/6 ≈ 0.167
    ├── Some((3, 1)): 59/109 ≈ 0.541
      ├── Some((1, 0)): 7/12 ≈ 0.583
      ├── Some((1, 1)): 10/15 ≈ 0.667
      ├── Some((1, 2)): 3/9 ≈ 0.333
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 5/11 ≈ 0.455
      ├── Some((1, 5)): 6/12 ≈ 0.500
      ├── Some((1, 6)): 8/13 ≈ 0.615
      ├── Some((1, 7)): 7/12 ≈ 0.583
      └── Some((1, 8)): 7/13 ≈ 0.538
    ├── Some((3, 2)): 30/68 ≈ 0.441
      ├── Some((2, 0)): 0/4 ≈ 0.000
      ├── Some((2, 1)): 3/7 ≈ 0.429
      ├── Some((2, 2)): 3/7 ≈ 0.429
      ├── Some((2, 3)): 9/13 ≈ 0.692
      ├── Some((2, 4)): 1/5 ≈ 0.200
      ├── Some((2, 5)): 3/7 ≈ 0.429
      ├── Some((2, 6)): 7/11 ≈ 0.636
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 1/5 ≈ 0.200
    ├── Some((3, 3)): 34/74 ≈ 0.459
      ├── Some((3, 0)): 2/7 ≈ 0.286
      ├── Some((3, 1)): 2/7 ≈ 0.286
      ├── Some((3, 2)): 6/11 ≈ 0.545
      ├── Some((3, 4)): 7/11 ≈ 0.636
      ├── Some((3, 5)): 4/9 ≈ 0.444
      ├── Some((3, 6)): 3/8 ≈ 0.375
      ├── Some((3, 7)): 4/9 ≈ 0.444
      └── Some((3, 8)): 6/11 ≈ 0.545
    ├── Some((3, 4)): 29/67 ≈ 0.433
      ├── Some((4, 0)): 2/6 ≈ 0.333
      ├── Some((4, 1)): 6/10 ≈ 0.600
      ├── Some((4, 2)): 8/12 ≈ 0.667
      ├── Some((4, 3)): 2/6 ≈ 0.333
      ├── Some((4, 4)): 3/7 ≈ 0.429
      ├── Some((4, 5)): 2/6 ≈ 0.333
      ├── Some((4, 6)): 1/5 ≈ 0.200
      ├── Some((4, 7)): 3/8 ≈ 0.375
      └── Some((4, 8)): 2/6 ≈ 0.333
    ├── Some((3, 5)): 47/93 ≈ 0.505
      ├── Some((5, 0)): 2/7 ≈ 0.286
      ├── Some((5, 1)): 4/10 ≈ 0.400
      ├── Some((5, 2)): 3/8 ≈ 0.375
      ├── Some((5, 3)): 4/10 ≈ 0.400
      ├── Some((5, 4)): 6/11 ≈ 0.545
      ├── Some((5, 5)): 1/6 ≈ 0.167
      ├── Some((5, 6)): 17/21 ≈ 0.810
      ├── Some((5, 7)): 6/11 ≈ 0.545
      └── Some((5, 8)): 3/8 ≈ 0.375
    ├── Some((3, 6)): 40/83 ≈ 0.482
      ├── Some((6, 0)): 6/11 ≈ 0.545
      ├── Some((6, 1)): 4/9 ≈ 0.444
      ├── Some((6, 2)): 7/11 ≈ 0.636
      ├── Some((6, 3)): 2/7 ≈ 0.286
      ├── Some((6, 4)): 0/4 ≈ 0.000
      ├── Some((6, 5)): 5/10 ≈ 0.500
      ├── Some((6, 6)): 6/11 ≈ 0.545
      ├── Some((6, 7)): 7/12 ≈ 0.583
      └── Some((6, 8)): 2/7 ≈ 0.286
    ├── Some((3, 7)): 47/93 ≈ 0.505
      ├── Some((7, 0)): 3/9 ≈ 0.333
      ├── Some((7, 1)): 8/14 ≈ 0.571
      ├── Some((7, 2)): 2/8 ≈ 0.250
      ├── Some((7, 3)): 2/8 ≈ 0.250
      ├── Some((7, 4)): 6/12 ≈ 0.500
      ├── Some((7, 5)): 5/11 ≈ 0.455
      ├── Some((7, 6)): 10/15 ≈ 0.667
      └── Some((7, 7)): 10/15 ≈ 0.667
    └── Some((3, 8)): 27/64 ≈ 0.422
      ├── Some((8, 0)): 5/9 ≈ 0.556
      ├── Some((8, 1)): 2/7 ≈ 0.286
      ├── Some((8, 2)): 2/7 ≈ 0.286
      ├── Some((8, 4)): 4/9 ≈ 0.444
      ├── Some((8, 5)): 0/4 ≈ 0.000
      ├── Some((8, 6)): 4/9 ≈ 0.444
      ├── Some((8, 7)): 7/11 ≈ 0.636
      └── Some((8, 8)): 2/7 ≈ 0.286
  ├── Some((8, 4)): 670/1287 ≈ 0.521
    ├── Some((4, 0)): 59/121 ≈ 0.488
      ├── Some((0, 0)): 10/17 ≈ 0.588
      ├── Some((0, 1)): 11/18 ≈ 0.611
      ├── Some((0, 2)): 6/13 ≈ 0.462
      ├── Some((0, 3)): 1/7 ≈ 0.143
      ├── Some((0, 4)): 9/16 ≈ 0.562
      ├── Some((0, 5)): 9/16 ≈ 0.562
      ├── Some((0, 6)): 6/13 ≈ 0.462
      ├── Some((0, 7)): 3/10 ≈ 0.300
      └── Some((0, 8)): 3/10 ≈ 0.300
    ├── Some((4, 1)): 77/147 ≈ 0.524
      ├── Some((1, 0)): 6/14 ≈ 0.429
      ├── Some((1, 1)): 3/10 ≈ 0.300
      ├── Some((1, 2)): 5/12 ≈ 0.417
      ├── Some((1, 3)): 13/21 ≈ 0.619
      ├── Some((1, 4)): 10/18 ≈ 0.556
      ├── Some((1, 5)): 13/21 ≈ 0.619
      ├── Some((1, 6)): 8/16 ≈ 0.500
      ├── Some((1, 7)): 5/12 ≈ 0.417
      └── Some((1, 8)): 14/22 ≈ 0.636
    ├── Some((4, 2)): 75/144 ≈ 0.521
      ├── Some((2, 0)): 3/10 ≈ 0.300
      ├── Some((2, 1)): 10/18 ≈ 0.556
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 3/10 ≈ 0.300
      ├── Some((2, 4)): 9/17 ≈ 0.529
      ├── Some((2, 5)): 22/29 ≈ 0.759
      ├── Some((2, 6)): 10/18 ≈ 0.556
      ├── Some((2, 7)): 5/13 ≈ 0.385
      └── Some((2, 8)): 8/16 ≈ 0.500
    ├── Some((4, 3)): 74/142 ≈ 0.521
      ├── Some((3, 0)): 9/17 ≈ 0.529
      ├── Some((3, 1)): 6/13 ≈ 0.462
      ├── Some((3, 2)): 2/9 ≈ 0.222
      ├── Some((3, 3)): 8/15 ≈ 0.533
      ├── Some((3, 4)): 13/21 ≈ 0.619
      ├── Some((3, 5)): 8/15 ≈ 0.533
      ├── Some((3, 6)): 6/13 ≈ 0.462
      ├── Some((3, 7)): 11/19 ≈ 0.579
      └── Some((3, 8)): 11/19 ≈ 0.579
    ├── Some((4, 4)): 67/132 ≈ 0.508
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 5/13 ≈ 0.385
      ├── Some((4, 2)): 2/9 ≈ 0.222
      ├── Some((4, 3)): 16/25 ≈ 0.640
      ├── Some((4, 5)): 9/17 ≈ 0.529
      ├── Some((4, 6)): 9/17 ≈ 0.529
      ├── Some((4, 7)): 14/23 ≈ 0.609
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((4, 5)): 69/135 ≈ 0.511
      ├── Some((5, 0)): 8/15 ≈ 0.533
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 12/20 ≈ 0.600
      ├── Some((5, 3)): 11/19 ≈ 0.579
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 3/10 ≈ 0.300
      ├── Some((5, 6)): 13/21 ≈ 0.619
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 5/12 ≈ 0.417
    ├── Some((4, 6)): 99/178 ≈ 0.556
      ├── Some((6, 0)): 14/23 ≈ 0.609
      ├── Some((6, 1)): 6/14 ≈ 0.429
      ├── Some((6, 2)): 11/20 ≈ 0.550
      ├── Some((6, 3)): 9/18 ≈ 0.500
      ├── Some((6, 4)): 13/22 ≈ 0.591
      ├── Some((6, 5)): 6/14 ≈ 0.429
      ├── Some((6, 6)): 15/24 ≈ 0.625
      ├── Some((6, 7)): 13/22 ≈ 0.591
      └── Some((6, 8)): 11/20 ≈ 0.550
    ├── Some((4, 7)): 81/153 ≈ 0.529
      ├── Some((7, 0)): 22/32 ≈ 0.688
      ├── Some((7, 1)): 4/12 ≈ 0.333
      ├── Some((7, 2)): 6/15 ≈ 0.400
      ├── Some((7, 3)): 4/12 ≈ 0.333
      ├── Some((7, 4)): 8/17 ≈ 0.471
      ├── Some((7, 5)): 2/10 ≈ 0.200
      ├── Some((7, 6)): 16/25 ≈ 0.640
      └── Some((7, 7)): 19/29 ≈ 0.655
    └── Some((4, 8)): 68/134 ≈ 0.507
      ├── Some((8, 0)): 11/20 ≈ 0.550
      ├── Some((8, 1)): 9/17 ≈ 0.529
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 5/13 ≈ 0.385
      ├── Some((8, 5)): 7/15 ≈ 0.467
      ├── Some((8, 6)): 8/16 ≈ 0.500
      ├── Some((8, 7)): 6/14 ≈ 0.429
      └── Some((8, 8)): 13/22 ≈ 0.591
  ├── Some((8, 5)): 662/1274 ≈ 0.520
    ├── Some((5, 0)): 115/201 ≈ 0.572
      ├── Some((0, 0)): 12/22 ≈ 0.545
      ├── Some((0, 1)): 10/19 ≈ 0.526
      ├── Some((0, 2)): 22/32 ≈ 0.688
      ├── Some((0, 3)): 9/18 ≈ 0.500
      ├── Some((0, 4)): 10/19 ≈ 0.526
      ├── Some((0, 5)): 14/24 ≈ 0.583
      ├── Some((0, 6)): 7/16 ≈ 0.438
      ├── Some((0, 7)): 20/30 ≈ 0.667
      └── Some((0, 8)): 11/20 ≈ 0.550
    ├── Some((5, 1)): 56/116 ≈ 0.483
      ├── Some((1, 0)): 3/9 ≈ 0.333
      ├── Some((1, 1)): 6/13 ≈ 0.462
      ├── Some((1, 2)): 9/16 ≈ 0.562
      ├── Some((1, 3)): 3/9 ≈ 0.333
      ├── Some((1, 4)): 11/18 ≈ 0.611
      ├── Some((1, 5)): 11/18 ≈ 0.611
      ├── Some((1, 6)): 2/8 ≈ 0.250
      ├── Some((1, 7)): 8/15 ≈ 0.533
      └── Some((1, 8)): 3/9 ≈ 0.333
    ├── Some((5, 2)): 64/128 ≈ 0.500
      ├── Some((2, 0)): 4/11 ≈ 0.364
      ├── Some((2, 1)): 12/20 ≈ 0.600
      ├── Some((2, 2)): 9/16 ≈ 0.562
      ├── Some((2, 3)): 6/13 ≈ 0.462
      ├── Some((2, 4)): 11/19 ≈ 0.579
      ├── Some((2, 5)): 8/15 ≈ 0.533
      ├── Some((2, 6)): 0/6 ≈ 0.000
      ├── Some((2, 7)): 10/17 ≈ 0.588
      └── Some((2, 8)): 3/10 ≈ 0.300
    ├── Some((5, 3)): 65/129 ≈ 0.504
      ├── Some((3, 0)): 7/14 ≈ 0.500
      ├── Some((3, 1)): 8/15 ≈ 0.533
      ├── Some((3, 2)): 12/20 ≈ 0.600
      ├── Some((3, 3)): 7/14 ≈ 0.500
      ├── Some((3, 4)): 0/6 ≈ 0.000
      ├── Some((3, 5)): 2/9 ≈ 0.222
      ├── Some((3, 6)): 3/10 ≈ 0.300
      ├── Some((3, 7)): 9/17 ≈ 0.529
      └── Some((3, 8)): 16/23 ≈ 0.696
    ├── Some((5, 4)): 73/141 ≈ 0.518
      ├── Some((4, 0)): 5/12 ≈ 0.417
      ├── Some((4, 1)): 3/10 ≈ 0.300
      ├── Some((4, 2)): 12/20 ≈ 0.600
      ├── Some((4, 3)): 3/10 ≈ 0.300
      ├── Some((4, 4)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 8/15 ≈ 0.533
      ├── Some((4, 6)): 13/21 ≈ 0.619
      ├── Some((4, 7)): 13/21 ≈ 0.619
      └── Some((4, 8)): 10/18 ≈ 0.556
    ├── Some((5, 5)): 72/140 ≈ 0.514
      ├── Some((5, 0)): 2/9 ≈ 0.222
      ├── Some((5, 1)): 7/15 ≈ 0.467
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 16/25 ≈ 0.640
      ├── Some((5, 4)): 10/19 ≈ 0.526
      ├── Some((5, 6)): 12/21 ≈ 0.571
      ├── Some((5, 7)): 9/18 ≈ 0.500
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((5, 6)): 61/123 ≈ 0.496
      ├── Some((6, 0)): 5/12 ≈ 0.417
      ├── Some((6, 1)): 4/10 ≈ 0.400
      ├── Some((6, 2)): 6/13 ≈ 0.462
      ├── Some((6, 3)): 10/17 ≈ 0.588
      ├── Some((6, 4)): 6/13 ≈ 0.462
      ├── Some((6, 5)): 8/15 ≈ 0.533
      ├── Some((6, 6)): 7/14 ≈ 0.500
      ├── Some((6, 7)): 9/16 ≈ 0.562
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((5, 7)): 109/192 ≈ 0.568
      ├── Some((7, 0)): 19/30 ≈ 0.633
      ├── Some((7, 1)): 4/13 ≈ 0.308
      ├── Some((7, 2)): 12/22 ≈ 0.545
      ├── Some((7, 3)): 8/18 ≈ 0.444
      ├── Some((7, 4)): 7/17 ≈ 0.412
      ├── Some((7, 5)): 12/22 ≈ 0.545
      ├── Some((7, 6)): 20/31 ≈ 0.645
      └── Some((7, 7)): 27/38 ≈ 0.711
    └── Some((5, 8)): 47/103 ≈ 0.456
      ├── Some((8, 0)): 9/16 ≈ 0.562
      ├── Some((8, 1)): 6/13 ≈ 0.462
      ├── Some((8, 2)): 11/18 ≈ 0.611
      ├── Some((8, 3)): 2/9 ≈ 0.222
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 6)): 9/16 ≈ 0.562
      ├── Some((8, 7)): 5/12 ≈ 0.417
      └── Some((8, 8)): 0/6 ≈ 0.000
  ├── Some((8, 6)): 805/1518 ≈ 0.530
    ├── Some((6, 0)): 118/210 ≈ 0.562
      ├── Some((0, 0)): 17/27 ≈ 0.630
      ├── Some((0, 1)): 22/33 ≈ 0.667
      ├── Some((0, 2)): 8/18 ≈ 0.444
      ├── Some((0, 3)): 4/13 ≈ 0.308
      ├── Some((0, 4)): 18/29 ≈ 0.621
      ├── Some((0, 5)): 9/19 ≈ 0.474
      ├── Some((0, 6)): 16/26 ≈ 0.615
      ├── Some((0, 7)): 8/18 ≈ 0.444
      └── Some((0, 8)): 16/26 ≈ 0.615
    ├── Some((6, 1)): 85/163 ≈ 0.521
      ├── Some((1, 0)): 14/23 ≈ 0.609
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 2)): 6/14 ≈ 0.429
      ├── Some((1, 3)): 11/20 ≈ 0.550
      ├── Some((1, 4)): 15/24 ≈ 0.625
      ├── Some((1, 5)): 9/17 ≈ 0.529
      ├── Some((1, 6)): 6/14 ≈ 0.429
      ├── Some((1, 7)): 4/12 ≈ 0.333
      └── Some((1, 8)): 9/18 ≈ 0.500
    ├── Some((6, 2)): 76/149 ≈ 0.510
      ├── Some((2, 0)): 8/16 ≈ 0.500
      ├── Some((2, 1)): 8/16 ≈ 0.500
      ├── Some((2, 2)): 11/19 ≈ 0.579
      ├── Some((2, 3)): 13/21 ≈ 0.619
      ├── Some((2, 4)): 5/13 ≈ 0.385
      ├── Some((2, 5)): 14/22 ≈ 0.636
      ├── Some((2, 6)): 6/14 ≈ 0.429
      ├── Some((2, 7)): 8/16 ≈ 0.500
      └── Some((2, 8)): 3/11 ≈ 0.273
    ├── Some((6, 3)): 100/184 ≈ 0.543
      ├── Some((3, 0)): 14/24 ≈ 0.583
      ├── Some((3, 1)): 7/16 ≈ 0.438
      ├── Some((3, 2)): 7/16 ≈ 0.438
      ├── Some((3, 3)): 8/17 ≈ 0.471
      ├── Some((3, 4)): 16/26 ≈ 0.615
      ├── Some((3, 5)): 14/24 ≈ 0.583
      ├── Some((3, 6)): 18/28 ≈ 0.643
      ├── Some((3, 7)): 12/21 ≈ 0.571
      └── Some((3, 8)): 3/11 ≈ 0.273
    ├── Some((6, 4)): 66/134 ≈ 0.493
      ├── Some((4, 0)): 8/16 ≈ 0.500
      ├── Some((4, 1)): 15/23 ≈ 0.652
      ├── Some((4, 2)): 8/16 ≈ 0.500
      ├── Some((4, 3)): 4/11 ≈ 0.364
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 9/17 ≈ 0.529
      ├── Some((4, 7)): 4/11 ≈ 0.364
      └── Some((4, 8)): 4/11 ≈ 0.364
    ├── Some((6, 5)): 83/160 ≈ 0.519
      ├── Some((5, 0)): 6/14 ≈ 0.429
      ├── Some((5, 1)): 14/23 ≈ 0.609
      ├── Some((5, 2)): 12/21 ≈ 0.571
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 13/22 ≈ 0.591
      ├── Some((5, 5)): 5/13 ≈ 0.385
      ├── Some((5, 6)): 9/18 ≈ 0.500
      ├── Some((5, 7)): 10/19 ≈ 0.526
      └── Some((5, 8)): 6/14 ≈ 0.429
    ├── Some((6, 6)): 96/179 ≈ 0.536
      ├── Some((6, 0)): 14/24 ≈ 0.583
      ├── Some((6, 1)): 15/26 ≈ 0.577
      ├── Some((6, 2)): 16/27 ≈ 0.593
      ├── Some((6, 3)): 17/28 ≈ 0.607
      ├── Some((6, 4)): 8/18 ≈ 0.444
      ├── Some((6, 5)): 6/16 ≈ 0.375
      ├── Some((6, 7)): 10/20 ≈ 0.500
      └── Some((6, 8)): 9/19 ≈ 0.474
    ├── Some((6, 7)): 114/204 ≈ 0.559
      ├── Some((7, 0)): 10/21 ≈ 0.476
      ├── Some((7, 1)): 17/28 ≈ 0.607
      ├── Some((7, 2)): 17/28 ≈ 0.607
      ├── Some((7, 3)): 20/32 ≈ 0.625
      ├── Some((7, 4)): 20/32 ≈ 0.625
      ├── Some((7, 5)): 7/17 ≈ 0.412
      ├── Some((7, 6)): 13/24 ≈ 0.542
      └── Some((7, 7)): 10/21 ≈ 0.476
    └── Some((6, 8)): 66/134 ≈ 0.493
      ├── Some((8, 0)): 2/9 ≈ 0.222
      ├── Some((8, 1)): 19/28 ≈ 0.679
      ├── Some((8, 2)): 9/18 ≈ 0.500
      ├── Some((8, 3)): 6/14 ≈ 0.429
      ├── Some((8, 4)): 10/19 ≈ 0.526
      ├── Some((8, 5)): 6/14 ≈ 0.429
      ├── Some((8, 7)): 11/20 ≈ 0.550
      └── Some((8, 8)): 3/11 ≈ 0.273
  ├── Some((8, 7)): 755/1433 ≈ 0.527
    ├── Some((7, 0)): 92/176 ≈ 0.523
      ├── Some((0, 0)): 9/18 ≈ 0.500
      ├── Some((0, 1)): 10/19 ≈ 0.526
      ├── Some((0, 2)): 16/26 ≈ 0.615
      ├── Some((0, 3)): 10/19 ≈ 0.526
      ├── Some((0, 4)): 4/13 ≈ 0.308
      ├── Some((0, 5)): 5/14 ≈ 0.357
      ├── Some((0, 6)): 8/17 ≈ 0.471
      ├── Some((0, 7)): 19/29 ≈ 0.655
      └── Some((0, 8)): 11/20 ≈ 0.550
    ├── Some((7, 1)): 29/79 ≈ 0.367
      ├── Some((1, 0)): 2/7 ≈ 0.286
      ├── Some((1, 1)): 3/8 ≈ 0.375
      ├── Some((1, 2)): 1/6 ≈ 0.167
      ├── Some((1, 3)): 5/11 ≈ 0.455
      ├── Some((1, 4)): 3/9 ≈ 0.333
      ├── Some((1, 5)): 1/6 ≈ 0.167
      ├── Some((1, 6)): 3/9 ≈ 0.333
      ├── Some((1, 7)): 3/9 ≈ 0.333
      └── Some((1, 8)): 7/13 ≈ 0.538
    ├── Some((7, 2)): 96/182 ≈ 0.527
      ├── Some((2, 0)): 6/15 ≈ 0.400
      ├── Some((2, 1)): 8/17 ≈ 0.471
      ├── Some((2, 2)): 12/22 ≈ 0.545
      ├── Some((2, 3)): 10/19 ≈ 0.526
      ├── Some((2, 4)): 14/24 ≈ 0.583
      ├── Some((2, 5)): 13/23 ≈ 0.565
      ├── Some((2, 6)): 17/27 ≈ 0.630
      ├── Some((2, 7)): 6/15 ≈ 0.400
      └── Some((2, 8)): 10/19 ≈ 0.526
    ├── Some((7, 3)): 105/195 ≈ 0.538
      ├── Some((3, 0)): 8/18 ≈ 0.444
      ├── Some((3, 1)): 13/23 ≈ 0.565
      ├── Some((3, 2)): 16/26 ≈ 0.615
      ├── Some((3, 3)): 9/19 ≈ 0.474
      ├── Some((3, 4)): 12/22 ≈ 0.545
      ├── Some((3, 5)): 9/19 ≈ 0.474
      ├── Some((3, 6)): 15/25 ≈ 0.600
      ├── Some((3, 7)): 10/20 ≈ 0.500
      └── Some((3, 8)): 12/22 ≈ 0.545
    ├── Some((7, 4)): 105/195 ≈ 0.538
      ├── Some((4, 0)): 9/19 ≈ 0.474
      ├── Some((4, 1)): 8/18 ≈ 0.444
      ├── Some((4, 2)): 13/23 ≈ 0.565
      ├── Some((4, 3)): 11/21 ≈ 0.524
      ├── Some((4, 4)): 12/22 ≈ 0.545
      ├── Some((4, 5)): 14/24 ≈ 0.583
      ├── Some((4, 6)): 9/19 ≈ 0.474
      ├── Some((4, 7)): 13/23 ≈ 0.565
      └── Some((4, 8)): 15/25 ≈ 0.600
    ├── Some((7, 5)): 114/209 ≈ 0.545
      ├── Some((5, 0)): 4/13 ≈ 0.308
      ├── Some((5, 1)): 21/32 ≈ 0.656
      ├── Some((5, 2)): 6/16 ≈ 0.375
      ├── Some((5, 3)): 12/23 ≈ 0.522
      ├── Some((5, 4)): 23/34 ≈ 0.676
      ├── Some((5, 5)): 9/19 ≈ 0.474
      ├── Some((5, 6)): 22/33 ≈ 0.667
      ├── Some((5, 7)): 5/15 ≈ 0.333
      └── Some((5, 8)): 12/23 ≈ 0.522
    ├── Some((7, 6)): 110/203 ≈ 0.542
      ├── Some((6, 0)): 15/26 ≈ 0.577
      ├── Some((6, 1)): 14/24 ≈ 0.583
      ├── Some((6, 2)): 10/20 ≈ 0.500
      ├── Some((6, 3)): 9/19 ≈ 0.474
      ├── Some((6, 4)): 7/17 ≈ 0.412
      ├── Some((6, 5)): 16/27 ≈ 0.593
      ├── Some((6, 6)): 16/27 ≈ 0.593
      ├── Some((6, 7)): 9/19 ≈ 0.474
      └── Some((6, 8)): 13/23 ≈ 0.565
    └── Some((7, 7)): 103/193 ≈ 0.534
      ├── Some((7, 0)): 15/28 ≈ 0.536
      ├── Some((7, 1)): 26/40 ≈ 0.650
      ├── Some((7, 2)): 17/30 ≈ 0.567
      ├── Some((7, 3)): 13/26 ≈ 0.500
      ├── Some((7, 4)): 16/29 ≈ 0.552
      ├── Some((7, 5)): 11/24 ≈ 0.458
      └── Some((7, 6)): 4/15 ≈ 0.267
  └── Some((8, 8)): 582/1136 ≈ 0.512
    ├── Some((8, 0)): 84/159 ≈ 0.528
      ├── Some((0, 0)): 11/19 ≈ 0.579
      ├── Some((0, 1)): 8/16 ≈ 0.500
      ├── Some((0, 2)): 11/20 ≈ 0.550
      ├── Some((0, 3)): 1/8 ≈ 0.125
      ├── Some((0, 4)): 3/11 ≈ 0.273
      ├── Some((0, 5)): 11/20 ≈ 0.550
      ├── Some((0, 6)): 5/13 ≈ 0.385
      ├── Some((0, 7)): 16/25 ≈ 0.640
      └── Some((0, 8)): 17/26 ≈ 0.654
    ├── Some((8, 1)): 61/125 ≈ 0.488
      ├── Some((1, 0)): 9/16 ≈ 0.562
      ├── Some((1, 1)): 5/12 ≈ 0.417
      ├── Some((1, 2)): 5/12 ≈ 0.417
      ├── Some((1, 3)): 2/9 ≈ 0.222
      ├── Some((1, 4)): 5/12 ≈ 0.417
      ├── Some((1, 5)): 6/13 ≈ 0.462
      ├── Some((1, 6)): 9/16 ≈ 0.562
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 13/20 ≈ 0.650
    ├── Some((8, 2)): 35/85 ≈ 0.412
      ├── Some((2, 0)): 0/5 ≈ 0.000
      ├── Some((2, 1)): 4/10 ≈ 0.400
      ├── Some((2, 2)): 5/11 ≈ 0.455
      ├── Some((2, 3)): 3/8 ≈ 0.375
      ├── Some((2, 4)): 4/10 ≈ 0.400
      ├── Some((2, 5)): 7/12 ≈ 0.583
      ├── Some((2, 6)): 6/12 ≈ 0.500
      ├── Some((2, 7)): 3/8 ≈ 0.375
      └── Some((2, 8)): 3/8 ≈ 0.375
    ├── Some((8, 3)): 94/174 ≈ 0.540
      ├── Some((3, 0)): 10/19 ≈ 0.526
      ├── Some((3, 1)): 9/18 ≈ 0.500
      ├── Some((3, 2)): 7/16 ≈ 0.438
      ├── Some((3, 3)): 13/22 ≈ 0.591
      ├── Some((3, 4)): 14/23 ≈ 0.609
      ├── Some((3, 5)): 7/16 ≈ 0.438
      ├── Some((3, 6)): 0/7 ≈ 0.000
      ├── Some((3, 7)): 19/28 ≈ 0.679
      └── Some((3, 8)): 15/24 ≈ 0.625
    ├── Some((8, 4)): 71/140 ≈ 0.507
      ├── Some((4, 0)): 8/16 ≈ 0.500
      ├── Some((4, 1)): 3/10 ≈ 0.300
      ├── Some((4, 2)): 2/9 ≈ 0.222
      ├── Some((4, 3)): 13/21 ≈ 0.619
      ├── Some((4, 4)): 6/13 ≈ 0.462
      ├── Some((4, 5)): 12/20 ≈ 0.600
      ├── Some((4, 6)): 12/20 ≈ 0.600
      ├── Some((4, 7)): 6/13 ≈ 0.462
      └── Some((4, 8)): 9/17 ≈ 0.529
    ├── Some((8, 5)): 61/126 ≈ 0.484
      ├── Some((5, 0)): 6/13 ≈ 0.462
      ├── Some((5, 1)): 1/8 ≈ 0.125
      ├── Some((5, 2)): 9/16 ≈ 0.562
      ├── Some((5, 3)): 10/17 ≈ 0.588
      ├── Some((5, 4)): 11/19 ≈ 0.579
      ├── Some((5, 5)): 6/13 ≈ 0.462
      ├── Some((5, 6)): 6/13 ≈ 0.462
      ├── Some((5, 7)): 3/10 ≈ 0.300
      └── Some((5, 8)): 9/16 ≈ 0.562
    ├── Some((8, 6)): 130/225 ≈ 0.578
      ├── Some((6, 0)): 10/20 ≈ 0.500
      ├── Some((6, 1)): 6/16 ≈ 0.375
      ├── Some((6, 2)): 10/20 ≈ 0.500
      ├── Some((6, 3)): 16/27 ≈ 0.593
      ├── Some((6, 4)): 10/20 ≈ 0.500
      ├── Some((6, 5)): 10/21 ≈ 0.476
      ├── Some((6, 6)): 16/27 ≈ 0.593
      ├── Some((6, 7)): 21/32 ≈ 0.656
      └── Some((6, 8)): 30/41 ≈ 0.732
    └── Some((8, 7)): 45/101 ≈ 0.446
      ├── Some((7, 0)): 8/15 ≈ 0.533
      ├── Some((7, 1)): 4/11 ≈ 0.364
      ├── Some((7, 2)): 8/15 ≈ 0.533
      ├── Some((7, 3)): 3/10 ≈ 0.300
      ├── Some((7, 4)): 7/14 ≈ 0.500
      ├── Some((7, 5)): 5/12 ≈ 0.417
      ├── Some((7, 6)): 6/13 ≈ 0.462
      └── Some((7, 7)): 3/10 ≈ 0.300
├── Some((8, 0)): 10628/20022 ≈ 0.531
  ├── Some((0, 0)): 1542/2846 ≈ 0.542
    ├── Some((0, 1)): 152/293 ≈ 0.519
      ├── Some((1, 0)): 15/31 ≈ 0.484
      ├── Some((1, 1)): 9/23 ≈ 0.391
      ├── Some((1, 2)): 21/38 ≈ 0.553
      ├── Some((1, 3)): 12/27 ≈ 0.444
      ├── Some((1, 4)): 19/35 ≈ 0.543
      ├── Some((1, 5)): 2/13 ≈ 0.154
      ├── Some((1, 6)): 32/50 ≈ 0.640
      ├── Some((1, 7)): 19/35 ≈ 0.543
      └── Some((1, 8)): 23/40 ≈ 0.575
    ├── Some((0, 2)): 194/358 ≈ 0.542
      ├── Some((2, 0)): 24/43 ≈ 0.558
      ├── Some((2, 1)): 19/37 ≈ 0.514
      ├── Some((2, 2)): 21/39 ≈ 0.538
      ├── Some((2, 3)): 31/51 ≈ 0.608
      ├── Some((2, 4)): 13/30 ≈ 0.433
      ├── Some((2, 5)): 18/36 ≈ 0.500
      ├── Some((2, 6)): 21/39 ≈ 0.538
      ├── Some((2, 7)): 38/59 ≈ 0.644
      └── Some((2, 8)): 8/23 ≈ 0.348
    ├── Some((0, 3)): 156/300 ≈ 0.520
      ├── Some((3, 0)): 27/45 ≈ 0.600
      ├── Some((3, 1)): 19/36 ≈ 0.528
      ├── Some((3, 2)): 10/24 ≈ 0.417
      ├── Some((3, 3)): 20/37 ≈ 0.541
      ├── Some((3, 4)): 9/23 ≈ 0.391
      ├── Some((3, 5)): 20/37 ≈ 0.541
      ├── Some((3, 6)): 31/49 ≈ 0.633
      ├── Some((3, 7)): 3/15 ≈ 0.200
      └── Some((3, 8)): 17/33 ≈ 0.515
    ├── Some((0, 4)): 195/360 ≈ 0.542
      ├── Some((4, 0)): 13/30 ≈ 0.433
      ├── Some((4, 1)): 32/52 ≈ 0.615
      ├── Some((4, 2)): 27/47 ≈ 0.574
      ├── Some((4, 3)): 8/23 ≈ 0.348
      ├── Some((4, 4)): 10/26 ≈ 0.385
      ├── Some((4, 5)): 26/45 ≈ 0.578
      ├── Some((4, 6)): 28/48 ≈ 0.583
      ├── Some((4, 7)): 31/51 ≈ 0.608
      └── Some((4, 8)): 19/37 ≈ 0.514
    ├── Some((0, 5)): 159/304 ≈ 0.523
      ├── Some((5, 0)): 24/41 ≈ 0.585
      ├── Some((5, 1)): 34/53 ≈ 0.642
      ├── Some((5, 2)): 11/26 ≈ 0.423
      ├── Some((5, 3)): 18/34 ≈ 0.529
      ├── Some((5, 4)): 7/21 ≈ 0.333
      ├── Some((5, 5)): 19/36 ≈ 0.528
      ├── Some((5, 6)): 11/26 ≈ 0.423
      ├── Some((5, 7)): 29/47 ≈ 0.617
      └── Some((5, 8)): 6/19 ≈ 0.316
    ├── Some((0, 6)): 219/396 ≈ 0.553
      ├── Some((6, 0)): 21/40 ≈ 0.525
      ├── Some((6, 1)): 37/59 ≈ 0.627
      ├── Some((6, 2)): 31/52 ≈ 0.596
      ├── Some((6, 3)): 16/34 ≈ 0.471
      ├── Some((6, 4)): 19/37 ≈ 0.514
      ├── Some((6, 5)): 18/36 ≈ 0.500
      ├── Some((6, 6)): 17/35 ≈ 0.486
      ├── Some((6, 7)): 36/58 ≈ 0.621
      └── Some((6, 8)): 24/44 ≈ 0.545
    ├── Some((0, 7)): 204/373 ≈ 0.547
      ├── Some((7, 0)): 32/53 ≈ 0.604
      ├── Some((7, 1)): 23/42 ≈ 0.548
      ├── Some((7, 2)): 31/52 ≈ 0.596
      ├── Some((7, 3)): 12/28 ≈ 0.429
      ├── Some((7, 4)): 23/42 ≈ 0.548
      ├── Some((7, 5)): 12/29 ≈ 0.414
      ├── Some((7, 6)): 28/48 ≈ 0.583
      ├── Some((7, 7)): 6/20 ≈ 0.300
      └── Some((7, 8)): 37/58 ≈ 0.638
    └── Some((0, 8)): 262/461 ≈ 0.568
      ├── Some((8, 1)): 28/52 ≈ 0.538
      ├── Some((8, 2)): 52/81 ≈ 0.642
      ├── Some((8, 3)): 42/69 ≈ 0.609
      ├── Some((8, 4)): 30/54 ≈ 0.556
      ├── Some((8, 5)): 27/51 ≈ 0.529
      ├── Some((8, 6)): 30/55 ≈ 0.545
      ├── Some((8, 7)): 38/64 ≈ 0.594
      └── Some((8, 8)): 14/34 ≈ 0.412
  ├── Some((0, 1)): 1243/2334 ≈ 0.533
    ├── Some((1, 0)): 137/258 ≈ 0.531
      ├── Some((0, 0)): 5/17 ≈ 0.294
      ├── Some((0, 2)): 17/32 ≈ 0.531
      ├── Some((0, 3)): 18/34 ≈ 0.529
      ├── Some((0, 4)): 16/31 ≈ 0.516
      ├── Some((0, 5)): 30/47 ≈ 0.638
      ├── Some((0, 6)): 24/40 ≈ 0.600
      ├── Some((0, 7)): 16/31 ≈ 0.516
      └── Some((0, 8)): 11/25 ≈ 0.440
    ├── Some((1, 1)): 141/264 ≈ 0.534
      ├── Some((1, 0)): 9/23 ≈ 0.391
      ├── Some((1, 2)): 29/46 ≈ 0.630
      ├── Some((1, 3)): 21/37 ≈ 0.568
      ├── Some((1, 4)): 8/21 ≈ 0.381
      ├── Some((1, 5)): 12/26 ≈ 0.462
      ├── Some((1, 6)): 17/32 ≈ 0.531
      ├── Some((1, 7)): 18/34 ≈ 0.529
      └── Some((1, 8)): 27/44 ≈ 0.614
    ├── Some((1, 2)): 114/223 ≈ 0.511
      ├── Some((2, 0)): 12/24 ≈ 0.500
      ├── Some((2, 1)): 6/17 ≈ 0.353
      ├── Some((2, 2)): 13/25 ≈ 0.520
      ├── Some((2, 3)): 22/36 ≈ 0.611
      ├── Some((2, 4)): 8/20 ≈ 0.400
      ├── Some((2, 5)): 4/14 ≈ 0.286
      ├── Some((2, 6)): 13/25 ≈ 0.520
      ├── Some((2, 7)): 14/27 ≈ 0.519
      └── Some((2, 8)): 21/34 ≈ 0.618
    ├── Some((1, 3)): 141/264 ≈ 0.534
      ├── Some((3, 0)): 16/30 ≈ 0.533
      ├── Some((3, 1)): 13/26 ≈ 0.500
      ├── Some((3, 2)): 31/46 ≈ 0.674
      ├── Some((3, 3)): 12/25 ≈ 0.480
      ├── Some((3, 4)): 13/26 ≈ 0.500
      ├── Some((3, 5)): 12/25 ≈ 0.480
      ├── Some((3, 6)): 9/22 ≈ 0.409
      ├── Some((3, 7)): 16/30 ≈ 0.533
      └── Some((3, 8)): 19/33 ≈ 0.576
    ├── Some((1, 4)): 99/200 ≈ 0.495
      ├── Some((4, 0)): 6/17 ≈ 0.353
      ├── Some((4, 1)): 14/26 ≈ 0.538
      ├── Some((4, 2)): 5/15 ≈ 0.333
      ├── Some((4, 3)): 10/21 ≈ 0.476
      ├── Some((4, 4)): 15/27 ≈ 0.556
      ├── Some((4, 5)): 20/32 ≈ 0.625
      ├── Some((4, 6)): 4/14 ≈ 0.286
      ├── Some((4, 7)): 15/27 ≈ 0.556
      └── Some((4, 8)): 9/20 ≈ 0.450
    ├── Some((1, 5)): 181/324 ≈ 0.559
      ├── Some((5, 0)): 27/44 ≈ 0.614
      ├── Some((5, 1)): 11/25 ≈ 0.440
      ├── Some((5, 2)): 20/36 ≈ 0.556
      ├── Some((5, 3)): 15/30 ≈ 0.500
      ├── Some((5, 4)): 9/23 ≈ 0.391
      ├── Some((5, 5)): 24/41 ≈ 0.585
      ├── Some((5, 6)): 26/43 ≈ 0.605
      ├── Some((5, 7)): 16/31 ≈ 0.516
      └── Some((5, 8)): 32/50 ≈ 0.640
    ├── Some((1, 6)): 130/248 ≈ 0.524
      ├── Some((6, 0)): 22/36 ≈ 0.611
      ├── Some((6, 1)): 15/28 ≈ 0.536
      ├── Some((6, 2)): 11/24 ≈ 0.458
      ├── Some((6, 3)): 15/28 ≈ 0.536
      ├── Some((6, 4)): 11/24 ≈ 0.458
      ├── Some((6, 5)): 9/21 ≈ 0.429
      ├── Some((6, 6)): 16/29 ≈ 0.552
      ├── Some((6, 7)): 16/30 ≈ 0.533
      └── Some((6, 8)): 14/27 ≈ 0.519
    ├── Some((1, 7)): 102/205 ≈ 0.498
      ├── Some((7, 0)): 13/25 ≈ 0.520
      ├── Some((7, 1)): 7/18 ≈ 0.389
      ├── Some((7, 2)): 16/29 ≈ 0.552
      ├── Some((7, 3)): 15/27 ≈ 0.556
      ├── Some((7, 4)): 2/11 ≈ 0.182
      ├── Some((7, 5)): 23/36 ≈ 0.639
      ├── Some((7, 6)): 9/20 ≈ 0.450
      ├── Some((7, 7)): 12/24 ≈ 0.500
      └── Some((7, 8)): 4/14 ≈ 0.286
    └── Some((1, 8)): 197/347 ≈ 0.568
      ├── Some((8, 1)): 39/60 ≈ 0.650
      ├── Some((8, 2)): 33/53 ≈ 0.623
      ├── Some((8, 3)): 21/39 ≈ 0.538
      ├── Some((8, 4)): 22/40 ≈ 0.550
      ├── Some((8, 5)): 22/41 ≈ 0.537
      ├── Some((8, 6)): 31/51 ≈ 0.608
      ├── Some((8, 7)): 20/38 ≈ 0.526
      └── Some((8, 8)): 9/24 ≈ 0.375
  ├── Some((0, 2)): 914/1765 ≈ 0.518
    ├── Some((2, 0)): 80/164 ≈ 0.488
      ├── Some((0, 0)): 7/17 ≈ 0.412
      ├── Some((0, 1)): 11/22 ≈ 0.500
      ├── Some((0, 3)): 6/16 ≈ 0.375
      ├── Some((0, 4)): 12/23 ≈ 0.522
      ├── Some((0, 5)): 13/24 ≈ 0.542
      ├── Some((0, 6)): 11/22 ≈ 0.500
      ├── Some((0, 7)): 9/19 ≈ 0.474
      └── Some((0, 8)): 10/20 ≈ 0.500
    ├── Some((2, 1)): 85/171 ≈ 0.497
      ├── Some((1, 0)): 7/17 ≈ 0.412
      ├── Some((1, 1)): 7/17 ≈ 0.412
      ├── Some((1, 2)): 14/24 ≈ 0.583
      ├── Some((1, 3)): 2/10 ≈ 0.200
      ├── Some((1, 4)): 24/35 ≈ 0.686
      ├── Some((1, 5)): 2/10 ≈ 0.200
      ├── Some((1, 6)): 18/28 ≈ 0.643
      ├── Some((1, 7)): 6/15 ≈ 0.400
      └── Some((1, 8)): 5/14 ≈ 0.357
    ├── Some((2, 2)): 135/246 ≈ 0.549
      ├── Some((2, 0)): 16/30 ≈ 0.533
      ├── Some((2, 1)): 13/26 ≈ 0.500
      ├── Some((2, 3)): 9/21 ≈ 0.429
      ├── Some((2, 4)): 24/39 ≈ 0.615
      ├── Some((2, 5)): 21/35 ≈ 0.600
      ├── Some((2, 6)): 15/29 ≈ 0.517
      ├── Some((2, 7)): 19/33 ≈ 0.576
      └── Some((2, 8)): 18/32 ≈ 0.562
    ├── Some((2, 3)): 107/205 ≈ 0.522
      ├── Some((3, 0)): 9/19 ≈ 0.474
      ├── Some((3, 1)): 9/20 ≈ 0.450
      ├── Some((3, 2)): 9/20 ≈ 0.450
      ├── Some((3, 3)): 12/23 ≈ 0.522
      ├── Some((3, 4)): 6/16 ≈ 0.375
      ├── Some((3, 5)): 24/36 ≈ 0.667
      ├── Some((3, 6)): 14/25 ≈ 0.560
      ├── Some((3, 7)): 11/22 ≈ 0.500
      └── Some((3, 8)): 12/23 ≈ 0.522
    ├── Some((2, 4)): 150/268 ≈ 0.560
      ├── Some((4, 0)): 21/35 ≈ 0.600
      ├── Some((4, 1)): 17/30 ≈ 0.567
      ├── Some((4, 2)): 13/26 ≈ 0.500
      ├── Some((4, 3)): 26/40 ≈ 0.650
      ├── Some((4, 4)): 22/36 ≈ 0.611
      ├── Some((4, 5)): 16/29 ≈ 0.552
      ├── Some((4, 6)): 19/32 ≈ 0.594
      ├── Some((4, 7)): 5/16 ≈ 0.312
      └── Some((4, 8)): 11/23 ≈ 0.478
    ├── Some((2, 5)): 87/174 ≈ 0.500
      ├── Some((5, 0)): 12/22 ≈ 0.545
      ├── Some((5, 1)): 14/24 ≈ 0.583
      ├── Some((5, 2)): 6/15 ≈ 0.400
      ├── Some((5, 3)): 7/16 ≈ 0.438
      ├── Some((5, 4)): 13/23 ≈ 0.565
      ├── Some((5, 5)): 4/13 ≈ 0.308
      ├── Some((5, 6)): 11/21 ≈ 0.524
      ├── Some((5, 7)): 14/24 ≈ 0.583
      └── Some((5, 8)): 6/15 ≈ 0.400
    ├── Some((2, 6)): 56/126 ≈ 0.444
      ├── Some((6, 0)): 3/10 ≈ 0.300
      ├── Some((6, 1)): 3/10 ≈ 0.300
      ├── Some((6, 2)): 9/17 ≈ 0.529
      ├── Some((6, 3)): 8/16 ≈ 0.500
      ├── Some((6, 4)): 9/17 ≈ 0.529
      ├── Some((6, 5)): 5/13 ≈ 0.385
      ├── Some((6, 6)): 7/15 ≈ 0.467
      ├── Some((6, 7)): 2/9 ≈ 0.222
      └── Some((6, 8)): 10/18 ≈ 0.556
    ├── Some((2, 7)): 93/184 ≈ 0.505
      ├── Some((7, 0)): 19/30 ≈ 0.633
      ├── Some((7, 1)): 5/14 ≈ 0.357
      ├── Some((7, 2)): 11/21 ≈ 0.524
      ├── Some((7, 3)): 9/19 ≈ 0.474
      ├── Some((7, 4)): 5/15 ≈ 0.333
      ├── Some((7, 5)): 14/25 ≈ 0.560
      ├── Some((7, 6)): 14/25 ≈ 0.560
      ├── Some((7, 7)): 11/21 ≈ 0.524
      └── Some((7, 8)): 4/13 ≈ 0.308
    └── Some((2, 8)): 121/226 ≈ 0.535
      ├── Some((8, 1)): 5/16 ≈ 0.312
      ├── Some((8, 2)): 10/22 ≈ 0.455
      ├── Some((8, 3)): 20/34 ≈ 0.588
      ├── Some((8, 4)): 13/26 ≈ 0.500
      ├── Some((8, 5)): 19/33 ≈ 0.576
      ├── Some((8, 6)): 16/29 ≈ 0.552
      ├── Some((8, 7)): 24/38 ≈ 0.632
      └── Some((8, 8)): 14/27 ≈ 0.519
  ├── Some((0, 3)): 1064/2025 ≈ 0.525
    ├── Some((3, 0)): 148/270 ≈ 0.548
      ├── Some((0, 0)): 29/46 ≈ 0.630
      ├── Some((0, 1)): 23/39 ≈ 0.590
      ├── Some((0, 2)): 12/26 ≈ 0.462
      ├── Some((0, 4)): 16/31 ≈ 0.516
      ├── Some((0, 5)): 21/37 ≈ 0.568
      ├── Some((0, 6)): 6/19 ≈ 0.316
      ├── Some((0, 7)): 27/44 ≈ 0.614
      └── Some((0, 8)): 13/27 ≈ 0.481
    ├── Some((3, 1)): 189/331 ≈ 0.571
      ├── Some((1, 0)): 15/30 ≈ 0.500
      ├── Some((1, 1)): 11/25 ≈ 0.440
      ├── Some((1, 2)): 8/21 ≈ 0.381
      ├── Some((1, 3)): 15/30 ≈ 0.500
      ├── Some((1, 4)): 34/52 ≈ 0.654
      ├── Some((1, 5)): 24/41 ≈ 0.585
      ├── Some((1, 6)): 28/45 ≈ 0.622
      ├── Some((1, 7)): 15/30 ≈ 0.500
      └── Some((1, 8)): 38/56 ≈ 0.679
    ├── Some((3, 2)): 66/145 ≈ 0.455
      ├── Some((2, 0)): 5/14 ≈ 0.357
      ├── Some((2, 1)): 9/18 ≈ 0.500
      ├── Some((2, 2)): 16/26 ≈ 0.615
      ├── Some((2, 3)): 8/17 ≈ 0.471
      ├── Some((2, 4)): 1/9 ≈ 0.111
      ├── Some((2, 5)): 11/20 ≈ 0.550
      ├── Some((2, 6)): 5/14 ≈ 0.357
      ├── Some((2, 7)): 10/19 ≈ 0.526
      └── Some((2, 8)): 0/7 ≈ 0.000
    ├── Some((3, 3)): 101/200 ≈ 0.505
      ├── Some((3, 0)): 10/22 ≈ 0.455
      ├── Some((3, 1)): 19/32 ≈ 0.594
      ├── Some((3, 2)): 13/26 ≈ 0.500
      ├── Some((3, 4)): 24/38 ≈ 0.632
      ├── Some((3, 5)): 3/13 ≈ 0.231
      ├── Some((3, 6)): 9/21 ≈ 0.429
      ├── Some((3, 7)): 16/29 ≈ 0.552
      └── Some((3, 8)): 7/18 ≈ 0.389
    ├── Some((3, 4)): 93/187 ≈ 0.497
      ├── Some((4, 0)): 11/21 ≈ 0.524
      ├── Some((4, 1)): 7/17 ≈ 0.412
      ├── Some((4, 2)): 1/9 ≈ 0.111
      ├── Some((4, 3)): 11/22 ≈ 0.500
      ├── Some((4, 4)): 17/28 ≈ 0.607
      ├── Some((4, 5)): 9/19 ≈ 0.474
      ├── Some((4, 6)): 11/22 ≈ 0.500
      ├── Some((4, 7)): 12/23 ≈ 0.522
      └── Some((4, 8)): 14/25 ≈ 0.560
    ├── Some((3, 5)): 156/282 ≈ 0.553
      ├── Some((5, 0)): 18/32 ≈ 0.562
      ├── Some((5, 1)): 18/32 ≈ 0.562
      ├── Some((5, 2)): 29/45 ≈ 0.644
      ├── Some((5, 3)): 23/38 ≈ 0.605
      ├── Some((5, 4)): 16/30 ≈ 0.533
      ├── Some((5, 5)): 10/23 ≈ 0.435
      ├── Some((5, 6)): 20/35 ≈ 0.571
      ├── Some((5, 7)): 3/14 ≈ 0.214
      └── Some((5, 8)): 18/32 ≈ 0.562
    ├── Some((3, 6)): 75/159 ≈ 0.472
      ├── Some((6, 0)): 18/28 ≈ 0.643
      ├── Some((6, 1)): 17/27 ≈ 0.630
      ├── Some((6, 2)): 12/22 ≈ 0.545
      ├── Some((6, 3)): 4/13 ≈ 0.308
      ├── Some((6, 4)): 5/14 ≈ 0.357
      ├── Some((6, 5)): 1/9 ≈ 0.111
      ├── Some((6, 6)): 1/9 ≈ 0.111
      ├── Some((6, 7)): 12/22 ≈ 0.545
      └── Some((6, 8)): 5/14 ≈ 0.357
    ├── Some((3, 7)): 136/253 ≈ 0.538
      ├── Some((7, 0)): 10/22 ≈ 0.455
      ├── Some((7, 1)): 20/34 ≈ 0.588
      ├── Some((7, 2)): 10/22 ≈ 0.455
      ├── Some((7, 3)): 18/32 ≈ 0.562
      ├── Some((7, 4)): 12/25 ≈ 0.480
      ├── Some((7, 5)): 22/36 ≈ 0.611
      ├── Some((7, 6)): 2/12 ≈ 0.167
      ├── Some((7, 7)): 20/34 ≈ 0.588
      └── Some((7, 8)): 21/35 ≈ 0.600
    └── Some((3, 8)): 99/197 ≈ 0.503
      ├── Some((8, 1)): 5/16 ≈ 0.312
      ├── Some((8, 2)): 11/23 ≈ 0.478
      ├── Some((8, 3)): 8/20 ≈ 0.400
      ├── Some((8, 4)): 14/27 ≈ 0.519
      ├── Some((8, 5)): 4/14 ≈ 0.286
      ├── Some((8, 6)): 18/31 ≈ 0.581
      ├── Some((8, 7)): 24/38 ≈ 0.632
      └── Some((8, 8)): 14/27 ≈ 0.519
  ├── Some((0, 4)): 879/1704 ≈ 0.516
    ├── Some((4, 0)): 85/171 ≈ 0.497
      ├── Some((0, 0)): 12/23 ≈ 0.522
      ├── Some((0, 1)): 18/30 ≈ 0.600
      ├── Some((0, 2)): 4/13 ≈ 0.308
      ├── Some((0, 3)): 4/13 ≈ 0.308
      ├── Some((0, 5)): 14/25 ≈ 0.560
      ├── Some((0, 6)): 9/20 ≈ 0.450
      ├── Some((0, 7)): 10/21 ≈ 0.476
      └── Some((0, 8)): 14/25 ≈ 0.560
    ├── Some((4, 1)): 67/143 ≈ 0.469
      ├── Some((1, 0)): 11/20 ≈ 0.550
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 2)): 5/13 ≈ 0.385
      ├── Some((1, 3)): 2/9 ≈ 0.222
      ├── Some((1, 4)): 13/22 ≈ 0.591
      ├── Some((1, 5)): 2/10 ≈ 0.200
      ├── Some((1, 6)): 9/18 ≈ 0.500
      ├── Some((1, 7)): 8/16 ≈ 0.500
      └── Some((1, 8)): 6/14 ≈ 0.429
    ├── Some((4, 2)): 139/251 ≈ 0.554
      ├── Some((2, 0)): 21/34 ≈ 0.618
      ├── Some((2, 1)): 18/31 ≈ 0.581
      ├── Some((2, 2)): 7/18 ≈ 0.389
      ├── Some((2, 3)): 20/33 ≈ 0.606
      ├── Some((2, 4)): 18/31 ≈ 0.581
      ├── Some((2, 5)): 19/32 ≈ 0.594
      ├── Some((2, 6)): 11/23 ≈ 0.478
      ├── Some((2, 7)): 9/20 ≈ 0.450
      └── Some((2, 8)): 16/28 ≈ 0.571
    ├── Some((4, 3)): 107/204 ≈ 0.525
      ├── Some((3, 0)): 15/26 ≈ 0.577
      ├── Some((3, 1)): 19/30 ≈ 0.633
      ├── Some((3, 2)): 12/23 ≈ 0.522
      ├── Some((3, 3)): 9/19 ≈ 0.474
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 9/20 ≈ 0.450
      ├── Some((3, 6)): 13/24 ≈ 0.542
      ├── Some((3, 7)): 5/15 ≈ 0.333
      └── Some((3, 8)): 17/28 ≈ 0.607
    ├── Some((4, 4)): 44/106 ≈ 0.415
      ├── Some((4, 0)): 2/9 ≈ 0.222
      ├── Some((4, 1)): 6/14 ≈ 0.429
      ├── Some((4, 2)): 6/14 ≈ 0.429
      ├── Some((4, 3)): 11/19 ≈ 0.579
      ├── Some((4, 5)): 3/10 ≈ 0.300
      ├── Some((4, 6)): 2/9 ≈ 0.222
      ├── Some((4, 7)): 6/14 ≈ 0.429
      └── Some((4, 8)): 8/16 ≈ 0.500
    ├── Some((4, 5)): 90/178 ≈ 0.506
      ├── Some((5, 0)): 7/16 ≈ 0.438
      ├── Some((5, 1)): 5/14 ≈ 0.357
      ├── Some((5, 2)): 11/21 ≈ 0.524
      ├── Some((5, 3)): 14/24 ≈ 0.583
      ├── Some((5, 4)): 14/24 ≈ 0.583
      ├── Some((5, 5)): 12/22 ≈ 0.545
      ├── Some((5, 6)): 3/12 ≈ 0.250
      ├── Some((5, 7)): 12/22 ≈ 0.545
      └── Some((5, 8)): 12/22 ≈ 0.545
    ├── Some((4, 6)): 91/180 ≈ 0.506
      ├── Some((6, 0)): 6/15 ≈ 0.400
      ├── Some((6, 1)): 10/20 ≈ 0.500
      ├── Some((6, 2)): 16/27 ≈ 0.593
      ├── Some((6, 3)): 13/23 ≈ 0.565
      ├── Some((6, 4)): 11/21 ≈ 0.524
      ├── Some((6, 5)): 19/30 ≈ 0.633
      ├── Some((6, 6)): 2/10 ≈ 0.200
      ├── Some((6, 7)): 9/19 ≈ 0.474
      └── Some((6, 8)): 5/14 ≈ 0.357
    ├── Some((4, 7)): 101/195 ≈ 0.518
      ├── Some((7, 0)): 9/19 ≈ 0.474
      ├── Some((7, 1)): 9/19 ≈ 0.474
      ├── Some((7, 2)): 7/17 ≈ 0.412
      ├── Some((7, 3)): 13/24 ≈ 0.542
      ├── Some((7, 4)): 11/21 ≈ 0.524
      ├── Some((7, 5)): 12/23 ≈ 0.522
      ├── Some((7, 6)): 10/20 ≈ 0.500
      ├── Some((7, 7)): 12/23 ≈ 0.522
      └── Some((7, 8)): 17/28 ≈ 0.607
    └── Some((4, 8)): 155/275 ≈ 0.564
      ├── Some((8, 1)): 19/34 ≈ 0.559
      ├── Some((8, 2)): 16/30 ≈ 0.533
      ├── Some((8, 3)): 20/35 ≈ 0.571
      ├── Some((8, 4)): 25/41 ≈ 0.610
      ├── Some((8, 5)): 13/27 ≈ 0.481
      ├── Some((8, 6)): 18/33 ≈ 0.545
      ├── Some((8, 7)): 23/38 ≈ 0.605
      └── Some((8, 8)): 21/36 ≈ 0.583
  ├── Some((0, 5)): 978/1876 ≈ 0.521
    ├── Some((5, 0)): 82/168 ≈ 0.488
      ├── Some((0, 0)): 11/22 ≈ 0.500
      ├── Some((0, 1)): 19/31 ≈ 0.613
      ├── Some((0, 2)): 6/16 ≈ 0.375
      ├── Some((0, 3)): 7/17 ≈ 0.412
      ├── Some((0, 4)): 3/12 ≈ 0.250
      ├── Some((0, 6)): 8/18 ≈ 0.444
      ├── Some((0, 7)): 17/29 ≈ 0.586
      └── Some((0, 8)): 11/22 ≈ 0.500
    ├── Some((5, 1)): 125/233 ≈ 0.536
      ├── Some((1, 0)): 12/24 ≈ 0.500
      ├── Some((1, 1)): 21/34 ≈ 0.618
      ├── Some((1, 2)): 6/17 ≈ 0.353
      ├── Some((1, 3)): 6/17 ≈ 0.353
      ├── Some((1, 4)): 21/34 ≈ 0.618
      ├── Some((1, 5)): 16/28 ≈ 0.571
      ├── Some((1, 6)): 12/24 ≈ 0.500
      ├── Some((1, 7)): 21/34 ≈ 0.618
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((5, 2)): 91/182 ≈ 0.500
      ├── Some((2, 0)): 9/19 ≈ 0.474
      ├── Some((2, 1)): 5/15 ≈ 0.333
      ├── Some((2, 2)): 8/18 ≈ 0.444
      ├── Some((2, 3)): 10/20 ≈ 0.500
      ├── Some((2, 4)): 8/18 ≈ 0.444
      ├── Some((2, 5)): 11/21 ≈ 0.524
      ├── Some((2, 6)): 1/9 ≈ 0.111
      ├── Some((2, 7)): 25/36 ≈ 0.694
      └── Some((2, 8)): 14/25 ≈ 0.560
    ├── Some((5, 3)): 104/202 ≈ 0.515
      ├── Some((3, 0)): 21/33 ≈ 0.636
      ├── Some((3, 1)): 13/24 ≈ 0.542
      ├── Some((3, 2)): 11/22 ≈ 0.500
      ├── Some((3, 3)): 12/23 ≈ 0.522
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 12/23 ≈ 0.522
      ├── Some((3, 6)): 4/14 ≈ 0.286
      ├── Some((3, 7)): 10/21 ≈ 0.476
      └── Some((3, 8)): 12/23 ≈ 0.522
    ├── Some((5, 4)): 115/218 ≈ 0.528
      ├── Some((4, 0)): 16/28 ≈ 0.571
      ├── Some((4, 1)): 11/23 ≈ 0.478
      ├── Some((4, 2)): 5/15 ≈ 0.333
      ├── Some((4, 3)): 16/28 ≈ 0.571
      ├── Some((4, 4)): 22/35 ≈ 0.629
      ├── Some((4, 5)): 1/10 ≈ 0.100
      ├── Some((4, 6)): 19/31 ≈ 0.613
      ├── Some((4, 7)): 8/19 ≈ 0.421
      └── Some((4, 8)): 16/28 ≈ 0.571
    ├── Some((5, 5)): 104/202 ≈ 0.515
      ├── Some((5, 0)): 11/23 ≈ 0.478
      ├── Some((5, 1)): 25/39 ≈ 0.641
      ├── Some((5, 2)): 13/26 ≈ 0.500
      ├── Some((5, 3)): 14/27 ≈ 0.519
      ├── Some((5, 4)): 4/14 ≈ 0.286
      ├── Some((5, 6)): 9/21 ≈ 0.429
      ├── Some((5, 7)): 6/17 ≈ 0.353
      └── Some((5, 8)): 21/34 ≈ 0.618
    ├── Some((5, 6)): 101/197 ≈ 0.513
      ├── Some((6, 0)): 16/27 ≈ 0.593
      ├── Some((6, 1)): 9/19 ≈ 0.474
      ├── Some((6, 2)): 11/22 ≈ 0.500
      ├── Some((6, 3)): 4/13 ≈ 0.308
      ├── Some((6, 4)): 9/20 ≈ 0.450
      ├── Some((6, 5)): 13/24 ≈ 0.542
      ├── Some((6, 6)): 18/29 ≈ 0.621
      ├── Some((6, 7)): 7/17 ≈ 0.412
      └── Some((6, 8)): 14/25 ≈ 0.560
    ├── Some((5, 7)): 130/240 ≈ 0.542
      ├── Some((7, 0)): 7/18 ≈ 0.389
      ├── Some((7, 1)): 7/18 ≈ 0.389
      ├── Some((7, 2)): 8/19 ≈ 0.421
      ├── Some((7, 3)): 10/22 ≈ 0.455
      ├── Some((7, 4)): 26/40 ≈ 0.650
      ├── Some((7, 5)): 11/23 ≈ 0.478
      ├── Some((7, 6)): 21/34 ≈ 0.618
      ├── Some((7, 7)): 33/47 ≈ 0.702
      └── Some((7, 8)): 7/18 ≈ 0.389
    └── Some((5, 8)): 125/233 ≈ 0.536
      ├── Some((8, 1)): 12/25 ≈ 0.480
      ├── Some((8, 2)): 20/34 ≈ 0.588
      ├── Some((8, 3)): 13/26 ≈ 0.500
      ├── Some((8, 4)): 5/16 ≈ 0.312
      ├── Some((8, 5)): 24/39 ≈ 0.615
      ├── Some((8, 6)): 21/35 ≈ 0.600
      ├── Some((8, 7)): 19/33 ≈ 0.576
      └── Some((8, 8)): 11/24 ≈ 0.458
  ├── Some((0, 6)): 1344/2508 ≈ 0.536
    ├── Some((6, 0)): 185/332 ≈ 0.557
      ├── Some((0, 0)): 30/50 ≈ 0.600
      ├── Some((0, 1)): 41/62 ≈ 0.661
      ├── Some((0, 2)): 23/41 ≈ 0.561
      ├── Some((0, 3)): 23/42 ≈ 0.548
      ├── Some((0, 4)): 22/40 ≈ 0.550
      ├── Some((0, 5)): 10/25 ≈ 0.400
      ├── Some((0, 7)): 15/32 ≈ 0.469
      └── Some((0, 8)): 21/39 ≈ 0.538
    ├── Some((6, 1)): 159/294 ≈ 0.541
      ├── Some((1, 0)): 23/39 ≈ 0.590
      ├── Some((1, 1)): 6/19 ≈ 0.316
      ├── Some((1, 2)): 25/41 ≈ 0.610
      ├── Some((1, 3)): 9/22 ≈ 0.409
      ├── Some((1, 4)): 25/41 ≈ 0.610
      ├── Some((1, 5)): 9/22 ≈ 0.409
      ├── Some((1, 6)): 25/41 ≈ 0.610
      ├── Some((1, 7)): 19/35 ≈ 0.543
      └── Some((1, 8)): 18/33 ≈ 0.545
    ├── Some((6, 2)): 158/292 ≈ 0.541
      ├── Some((2, 0)): 16/31 ≈ 0.516
      ├── Some((2, 1)): 16/31 ≈ 0.516
      ├── Some((2, 2)): 19/34 ≈ 0.559
      ├── Some((2, 3)): 21/36 ≈ 0.583
      ├── Some((2, 4)): 26/42 ≈ 0.619
      ├── Some((2, 5)): 6/18 ≈ 0.333
      ├── Some((2, 6)): 15/30 ≈ 0.500
      ├── Some((2, 7)): 18/33 ≈ 0.545
      └── Some((2, 8)): 21/36 ≈ 0.583
    ├── Some((6, 3)): 118/231 ≈ 0.511
      ├── Some((3, 0)): 18/31 ≈ 0.581
      ├── Some((3, 1)): 13/26 ≈ 0.500
      ├── Some((3, 2)): 7/18 ≈ 0.389
      ├── Some((3, 3)): 29/43 ≈ 0.674
      ├── Some((3, 4)): 14/27 ≈ 0.519
      ├── Some((3, 5)): 6/17 ≈ 0.353
      ├── Some((3, 6)): 14/27 ≈ 0.519
      ├── Some((3, 7)): 13/26 ≈ 0.500
      └── Some((3, 8)): 4/15 ≈ 0.267
    ├── Some((6, 4)): 159/294 ≈ 0.541
      ├── Some((4, 0)): 19/35 ≈ 0.543
      ├── Some((4, 1)): 9/22 ≈ 0.409
      ├── Some((4, 2)): 17/32 ≈ 0.531
      ├── Some((4, 3)): 38/56 ≈ 0.679
      ├── Some((4, 4)): 17/32 ≈ 0.531
      ├── Some((4, 5)): 24/40 ≈ 0.600
      ├── Some((4, 6)): 16/31 ≈ 0.516
      ├── Some((4, 7)): 7/20 ≈ 0.350
      └── Some((4, 8)): 11/25 ≈ 0.440
    ├── Some((6, 5)): 121/236 ≈ 0.513
      ├── Some((5, 0)): 19/33 ≈ 0.576
      ├── Some((5, 1)): 17/30 ≈ 0.567
      ├── Some((5, 2)): 8/20 ≈ 0.400
      ├── Some((5, 3)): 8/20 ≈ 0.400
      ├── Some((5, 4)): 15/28 ≈ 0.536
      ├── Some((5, 5)): 15/28 ≈ 0.536
      ├── Some((5, 6)): 16/29 ≈ 0.552
      ├── Some((5, 7)): 17/31 ≈ 0.548
      └── Some((5, 8)): 5/16 ≈ 0.312
    ├── Some((6, 6)): 140/265 ≈ 0.528
      ├── Some((6, 0)): 21/37 ≈ 0.568
      ├── Some((6, 1)): 6/19 ≈ 0.316
      ├── Some((6, 2)): 20/36 ≈ 0.556
      ├── Some((6, 3)): 18/34 ≈ 0.529
      ├── Some((6, 4)): 21/37 ≈ 0.568
      ├── Some((6, 5)): 17/33 ≈ 0.515
      ├── Some((6, 7)): 11/25 ≈ 0.440
      └── Some((6, 8)): 26/43 ≈ 0.605
    ├── Some((6, 7)): 191/341 ≈ 0.560
      ├── Some((7, 0)): 11/26 ≈ 0.423
      ├── Some((7, 1)): 15/31 ≈ 0.484
      ├── Some((7, 2)): 22/39 ≈ 0.564
      ├── Some((7, 3)): 25/42 ≈ 0.595
      ├── Some((7, 4)): 15/31 ≈ 0.484
      ├── Some((7, 5)): 19/35 ≈ 0.543
      ├── Some((7, 6)): 32/50 ≈ 0.640
      ├── Some((7, 7)): 24/41 ≈ 0.585
      └── Some((7, 8)): 27/45 ≈ 0.600
    └── Some((6, 8)): 112/222 ≈ 0.505
      ├── Some((8, 1)): 7/19 ≈ 0.368
      ├── Some((8, 2)): 11/24 ≈ 0.458
      ├── Some((8, 3)): 23/38 ≈ 0.605
      ├── Some((8, 4)): 15/29 ≈ 0.517
      ├── Some((8, 5)): 17/32 ≈ 0.531
      ├── Some((8, 6)): 18/33 ≈ 0.545
      ├── Some((8, 7)): 11/24 ≈ 0.458
      └── Some((8, 8)): 9/22 ≈ 0.409
  ├── Some((0, 7)): 1766/3228 ≈ 0.547
    ├── Some((7, 0)): 179/333 ≈ 0.538
      ├── Some((0, 0)): 21/40 ≈ 0.525
      ├── Some((0, 1)): 24/44 ≈ 0.545
      ├── Some((0, 2)): 54/79 ≈ 0.684
      ├── Some((0, 3)): 14/31 ≈ 0.452
      ├── Some((0, 4)): 5/19 ≈ 0.263
      ├── Some((0, 5)): 14/32 ≈ 0.438
      ├── Some((0, 6)): 25/45 ≈ 0.556
      └── Some((0, 8)): 22/42 ≈ 0.524
    ├── Some((7, 1)): 223/400 ≈ 0.558
      ├── Some((1, 0)): 39/61 ≈ 0.639
      ├── Some((1, 1)): 24/44 ≈ 0.545
      ├── Some((1, 2)): 31/52 ≈ 0.596
      ├── Some((1, 3)): 20/39 ≈ 0.513
      ├── Some((1, 4)): 17/35 ≈ 0.486
      ├── Some((1, 5)): 19/38 ≈ 0.500
      ├── Some((1, 6)): 31/52 ≈ 0.596
      ├── Some((1, 7)): 12/29 ≈ 0.414
      └── Some((1, 8)): 29/49 ≈ 0.592
    ├── Some((7, 2)): 236/419 ≈ 0.563
      ├── Some((2, 0)): 26/46 ≈ 0.565
      ├── Some((2, 1)): 30/51 ≈ 0.588
      ├── Some((2, 2)): 23/43 ≈ 0.535
      ├── Some((2, 3)): 22/42 ≈ 0.524
      ├── Some((2, 4)): 36/58 ≈ 0.621
      ├── Some((2, 5)): 21/40 ≈ 0.525
      ├── Some((2, 6)): 14/32 ≈ 0.438
      ├── Some((2, 7)): 24/44 ≈ 0.545
      └── Some((2, 8)): 39/62 ≈ 0.629
    ├── Some((7, 3)): 243/430 ≈ 0.565
      ├── Some((3, 0)): 38/61 ≈ 0.623
      ├── Some((3, 1)): 9/26 ≈ 0.346
      ├── Some((3, 2)): 26/47 ≈ 0.553
      ├── Some((3, 3)): 23/43 ≈ 0.535
      ├── Some((3, 4)): 15/33 ≈ 0.455
      ├── Some((3, 5)): 17/36 ≈ 0.472
      ├── Some((3, 6)): 37/60 ≈ 0.617
      ├── Some((3, 7)): 51/76 ≈ 0.671
      └── Some((3, 8)): 26/47 ≈ 0.553
    ├── Some((7, 4)): 256/449 ≈ 0.570
      ├── Some((4, 0)): 19/39 ≈ 0.487
      ├── Some((4, 1)): 24/45 ≈ 0.533
      ├── Some((4, 2)): 50/75 ≈ 0.667
      ├── Some((4, 3)): 12/30 ≈ 0.400
      ├── Some((4, 4)): 32/54 ≈ 0.593
      ├── Some((4, 5)): 26/47 ≈ 0.553
      ├── Some((4, 6)): 17/36 ≈ 0.472
      ├── Some((4, 7)): 27/48 ≈ 0.562
      └── Some((4, 8)): 49/74 ≈ 0.662
    ├── Some((7, 5)): 107/221 ≈ 0.484
      ├── Some((5, 0)): 12/25 ≈ 0.480
      ├── Some((5, 1)): 16/29 ≈ 0.552
      ├── Some((5, 2)): 16/29 ≈ 0.552
      ├── Some((5, 3)): 16/30 ≈ 0.533
      ├── Some((5, 4)): 9/21 ≈ 0.429
      ├── Some((5, 5)): 4/15 ≈ 0.267
      ├── Some((5, 6)): 21/35 ≈ 0.600
      ├── Some((5, 7)): 5/16 ≈ 0.312
      └── Some((5, 8)): 8/20 ≈ 0.400
    ├── Some((7, 6)): 174/326 ≈ 0.534
      ├── Some((6, 0)): 8/22 ≈ 0.364
      ├── Some((6, 1)): 20/37 ≈ 0.541
      ├── Some((6, 2)): 19/36 ≈ 0.528
      ├── Some((6, 3)): 25/43 ≈ 0.581
      ├── Some((6, 4)): 12/27 ≈ 0.444
      ├── Some((6, 5)): 34/53 ≈ 0.642
      ├── Some((6, 6)): 9/24 ≈ 0.375
      ├── Some((6, 7)): 18/35 ≈ 0.514
      └── Some((6, 8)): 29/48 ≈ 0.604
    ├── Some((7, 7)): 136/267 ≈ 0.509
      ├── Some((7, 0)): 25/43 ≈ 0.581
      ├── Some((7, 1)): 22/40 ≈ 0.550
      ├── Some((7, 2)): 3/15 ≈ 0.200
      ├── Some((7, 3)): 19/36 ≈ 0.528
      ├── Some((7, 4)): 26/45 ≈ 0.578
      ├── Some((7, 5)): 4/17 ≈ 0.235
      ├── Some((7, 6)): 22/40 ≈ 0.550
      └── Some((7, 8)): 14/30 ≈ 0.467
    └── Some((7, 8)): 211/382 ≈ 0.552
      ├── Some((8, 1)): 23/44 ≈ 0.523
      ├── Some((8, 2)): 21/41 ≈ 0.512
      ├── Some((8, 3)): 16/35 ≈ 0.457
      ├── Some((8, 4)): 28/50 ≈ 0.560
      ├── Some((8, 5)): 31/53 ≈ 0.585
      ├── Some((8, 6)): 14/32 ≈ 0.438
      ├── Some((8, 7)): 49/75 ≈ 0.653
      └── Some((8, 8)): 29/51 ≈ 0.569
  └── Some((0, 8)): 897/1735 ≈ 0.517
    ├── Some((8, 1)): 99/197 ≈ 0.503
      ├── Some((1, 0)): 19/31 ≈ 0.613
      ├── Some((1, 1)): 10/21 ≈ 0.476
      ├── Some((1, 2)): 11/22 ≈ 0.500
      ├── Some((1, 3)): 2/11 ≈ 0.182
      ├── Some((1, 4)): 7/18 ≈ 0.389
      ├── Some((1, 5)): 11/22 ≈ 0.500
      ├── Some((1, 6)): 13/24 ≈ 0.542
      ├── Some((1, 7)): 21/33 ≈ 0.636
      └── Some((1, 8)): 4/14 ≈ 0.286
    ├── Some((8, 2)): 69/150 ≈ 0.460
      ├── Some((2, 0)): 8/17 ≈ 0.471
      ├── Some((2, 1)): 3/11 ≈ 0.273
      ├── Some((2, 2)): 15/25 ≈ 0.600
      ├── Some((2, 3)): 10/19 ≈ 0.526
      ├── Some((2, 4)): 13/23 ≈ 0.565
      ├── Some((2, 5)): 12/22 ≈ 0.545
      ├── Some((2, 6)): 4/12 ≈ 0.333
      ├── Some((2, 7)): 3/11 ≈ 0.273
      └── Some((2, 8)): 1/9 ≈ 0.111
    ├── Some((8, 3)): 77/163 ≈ 0.472
      ├── Some((3, 0)): 10/20 ≈ 0.500
      ├── Some((3, 1)): 11/21 ≈ 0.524
      ├── Some((3, 2)): 6/15 ≈ 0.400
      ├── Some((3, 3)): 9/19 ≈ 0.474
      ├── Some((3, 4)): 18/28 ≈ 0.643
      ├── Some((3, 5)): 4/13 ≈ 0.308
      ├── Some((3, 6)): 3/11 ≈ 0.273
      ├── Some((3, 7)): 7/16 ≈ 0.438
      └── Some((3, 8)): 9/19 ≈ 0.474
    ├── Some((8, 4)): 185/326 ≈ 0.567
      ├── Some((4, 0)): 10/24 ≈ 0.417
      ├── Some((4, 1)): 18/33 ≈ 0.545
      ├── Some((4, 2)): 32/49 ≈ 0.653
      ├── Some((4, 3)): 22/38 ≈ 0.579
      ├── Some((4, 4)): 28/45 ≈ 0.622
      ├── Some((4, 5)): 5/17 ≈ 0.294
      ├── Some((4, 6)): 27/44 ≈ 0.614
      ├── Some((4, 7)): 30/47 ≈ 0.638
      └── Some((4, 8)): 13/28 ≈ 0.464
    ├── Some((8, 5)): 114/220 ≈ 0.518
      ├── Some((5, 0)): 10/21 ≈ 0.476
      ├── Some((5, 1)): 29/42 ≈ 0.690
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 3)): 16/28 ≈ 0.571
      ├── Some((5, 4)): 9/20 ≈ 0.450
      ├── Some((5, 5)): 11/23 ≈ 0.478
      ├── Some((5, 6)): 9/20 ≈ 0.450
      ├── Some((5, 7)): 10/22 ≈ 0.455
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((8, 6)): 123/234 ≈ 0.526
      ├── Some((6, 0)): 14/27 ≈ 0.519
      ├── Some((6, 1)): 15/28 ≈ 0.536
      ├── Some((6, 2)): 20/33 ≈ 0.606
      ├── Some((6, 3)): 12/24 ≈ 0.500
      ├── Some((6, 4)): 12/24 ≈ 0.500
      ├── Some((6, 5)): 17/30 ≈ 0.567
      ├── Some((6, 6)): 1/10 ≈ 0.100
      ├── Some((6, 7)): 26/40 ≈ 0.650
      └── Some((6, 8)): 6/17 ≈ 0.353
    ├── Some((8, 7)): 96/193 ≈ 0.497
      ├── Some((7, 0)): 16/27 ≈ 0.593
      ├── Some((7, 1)): 11/22 ≈ 0.500
      ├── Some((7, 2)): 12/23 ≈ 0.522
      ├── Some((7, 3)): 13/24 ≈ 0.542
      ├── Some((7, 4)): 11/22 ≈ 0.500
      ├── Some((7, 5)): 8/18 ≈ 0.444
      ├── Some((7, 6)): 8/19 ≈ 0.421
      ├── Some((7, 7)): 11/22 ≈ 0.500
      └── Some((7, 8)): 5/15 ≈ 0.333
    └── Some((8, 8)): 134/251 ≈ 0.534
      ├── Some((8, 1)): 10/25 ≈ 0.400
      ├── Some((8, 2)): 7/21 ≈ 0.333
      ├── Some((8, 3)): 19/36 ≈ 0.528
      ├── Some((8, 4)): 26/44 ≈ 0.591
      ├── Some((8, 5)): 29/47 ≈ 0.617
      ├── Some((8, 6)): 23/41 ≈ 0.561
      └── Some((8, 7)): 19/36 ≈ 0.528
├── Some((8, 1)): 8042/15318 ≈ 0.525
  ├── Some((1, 0)): 1041/1955 ≈ 0.532
    ├── Some((0, 0)): 140/253 ≈ 0.553
      ├── Some((0, 1)): 20/35 ≈ 0.571
      ├── Some((0, 2)): 4/15 ≈ 0.267
      ├── Some((0, 3)): 21/36 ≈ 0.583
      ├── Some((0, 4)): 29/45 ≈ 0.644
      ├── Some((0, 5)): 14/28 ≈ 0.500
      ├── Some((0, 6)): 12/25 ≈ 0.480
      ├── Some((0, 7)): 23/38 ≈ 0.605
      └── Some((0, 8)): 16/30 ≈ 0.533
    ├── Some((0, 1)): 67/144 ≈ 0.465
      ├── Some((1, 1)): 12/22 ≈ 0.545
      ├── Some((1, 2)): 0/8 ≈ 0.000
      ├── Some((1, 3)): 3/12 ≈ 0.250
      ├── Some((1, 4)): 6/16 ≈ 0.375
      ├── Some((1, 5)): 16/27 ≈ 0.593
      ├── Some((1, 6)): 11/21 ≈ 0.524
      ├── Some((1, 7)): 13/23 ≈ 0.565
      └── Some((1, 8)): 5/14 ≈ 0.357
    ├── Some((0, 2)): 120/224 ≈ 0.536
      ├── Some((2, 0)): 17/29 ≈ 0.586
      ├── Some((2, 1)): 21/33 ≈ 0.636
      ├── Some((2, 2)): 11/22 ≈ 0.500
      ├── Some((2, 3)): 9/20 ≈ 0.450
      ├── Some((2, 4)): 9/20 ≈ 0.450
      ├── Some((2, 5)): 15/27 ≈ 0.556
      ├── Some((2, 6)): 14/26 ≈ 0.538
      ├── Some((2, 7)): 9/20 ≈ 0.450
      └── Some((2, 8)): 14/26 ≈ 0.538
    ├── Some((0, 3)): 151/270 ≈ 0.559
      ├── Some((3, 0)): 26/40 ≈ 0.650
      ├── Some((3, 1)): 14/27 ≈ 0.519
      ├── Some((3, 2)): 15/28 ≈ 0.536
      ├── Some((3, 3)): 17/30 ≈ 0.567
      ├── Some((3, 4)): 15/28 ≈ 0.536
      ├── Some((3, 5)): 9/21 ≈ 0.429
      ├── Some((3, 6)): 18/31 ≈ 0.581
      ├── Some((3, 7)): 18/32 ≈ 0.562
      └── Some((3, 8)): 18/32 ≈ 0.562
    ├── Some((0, 4)): 94/185 ≈ 0.508
      ├── Some((4, 0)): 11/21 ≈ 0.524
      ├── Some((4, 1)): 13/23 ≈ 0.565
      ├── Some((4, 2)): 6/15 ≈ 0.400
      ├── Some((4, 3)): 7/17 ≈ 0.412
      ├── Some((4, 4)): 14/24 ≈ 0.583
      ├── Some((4, 5)): 8/18 ≈ 0.444
      ├── Some((4, 6)): 11/21 ≈ 0.524
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 16/27 ≈ 0.593
    ├── Some((0, 5)): 123/228 ≈ 0.539
      ├── Some((5, 0)): 16/28 ≈ 0.571
      ├── Some((5, 1)): 11/22 ≈ 0.500
      ├── Some((5, 2)): 9/20 ≈ 0.450
      ├── Some((5, 3)): 12/24 ≈ 0.500
      ├── Some((5, 4)): 6/17 ≈ 0.353
      ├── Some((5, 5)): 9/20 ≈ 0.450
      ├── Some((5, 6)): 20/32 ≈ 0.625
      ├── Some((5, 7)): 16/28 ≈ 0.571
      └── Some((5, 8)): 23/36 ≈ 0.639
    ├── Some((0, 6)): 110/209 ≈ 0.526
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 5/15 ≈ 0.333
      ├── Some((6, 2)): 20/32 ≈ 0.625
      ├── Some((6, 3)): 10/21 ≈ 0.476
      ├── Some((6, 4)): 8/18 ≈ 0.444
      ├── Some((6, 5)): 13/24 ≈ 0.542
      ├── Some((6, 6)): 25/37 ≈ 0.676
      ├── Some((6, 7)): 13/24 ≈ 0.542
      └── Some((6, 8)): 9/20 ≈ 0.450
    ├── Some((0, 7)): 120/224 ≈ 0.536
      ├── Some((7, 0)): 17/29 ≈ 0.586
      ├── Some((7, 1)): 6/17 ≈ 0.353
      ├── Some((7, 2)): 20/32 ≈ 0.625
      ├── Some((7, 3)): 14/26 ≈ 0.538
      ├── Some((7, 4)): 9/20 ≈ 0.450
      ├── Some((7, 5)): 18/30 ≈ 0.600
      ├── Some((7, 6)): 19/31 ≈ 0.613
      ├── Some((7, 7)): 7/18 ≈ 0.389
      └── Some((7, 8)): 9/20 ≈ 0.450
    └── Some((0, 8)): 115/217 ≈ 0.530
      ├── Some((8, 0)): 6/17 ≈ 0.353
      ├── Some((8, 2)): 19/32 ≈ 0.594
      ├── Some((8, 3)): 15/28 ≈ 0.536
      ├── Some((8, 4)): 13/26 ≈ 0.500
      ├── Some((8, 5)): 12/24 ≈ 0.500
      ├── Some((8, 6)): 12/25 ≈ 0.480
      ├── Some((8, 7)): 19/32 ≈ 0.594
      └── Some((8, 8)): 19/32 ≈ 0.594
  ├── Some((1, 1)): 844/1617 ≈ 0.522
    ├── Some((1, 0)): 96/188 ≈ 0.511
      ├── Some((0, 0)): 11/21 ≈ 0.524
      ├── Some((0, 1)): 7/17 ≈ 0.412
      ├── Some((0, 2)): 15/26 ≈ 0.577
      ├── Some((0, 3)): 2/11 ≈ 0.182
      ├── Some((0, 4)): 6/16 ≈ 0.375
      ├── Some((0, 5)): 13/23 ≈ 0.565
      ├── Some((0, 6)): 12/22 ≈ 0.545
      ├── Some((0, 7)): 7/17 ≈ 0.412
      └── Some((0, 8)): 23/34 ≈ 0.676
    ├── Some((1, 2)): 83/168 ≈ 0.494
      ├── Some((2, 0)): 8/17 ≈ 0.471
      ├── Some((2, 1)): 15/25 ≈ 0.600
      ├── Some((2, 2)): 4/13 ≈ 0.308
      ├── Some((2, 3)): 9/18 ≈ 0.500
      ├── Some((2, 4)): 16/26 ≈ 0.615
      ├── Some((2, 5)): 1/9 ≈ 0.111
      ├── Some((2, 6)): 6/15 ≈ 0.400
      ├── Some((2, 7)): 12/22 ≈ 0.545
      └── Some((2, 8)): 12/22 ≈ 0.545
    ├── Some((1, 3)): 75/156 ≈ 0.481
      ├── Some((3, 0)): 12/22 ≈ 0.545
      ├── Some((3, 1)): 8/17 ≈ 0.471
      ├── Some((3, 2)): 4/12 ≈ 0.333
      ├── Some((3, 3)): 6/15 ≈ 0.400
      ├── Some((3, 4)): 14/24 ≈ 0.583
      ├── Some((3, 5)): 11/20 ≈ 0.550
      ├── Some((3, 6)): 5/14 ≈ 0.357
      ├── Some((3, 7)): 0/7 ≈ 0.000
      └── Some((3, 8)): 14/24 ≈ 0.583
    ├── Some((1, 4)): 68/145 ≈ 0.469
      ├── Some((4, 0)): 5/13 ≈ 0.385
      ├── Some((4, 1)): 4/12 ≈ 0.333
      ├── Some((4, 2)): 11/20 ≈ 0.550
      ├── Some((4, 3)): 8/17 ≈ 0.471
      ├── Some((4, 4)): 16/25 ≈ 0.640
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 5/13 ≈ 0.385
      └── Some((4, 8)): 5/14 ≈ 0.357
    ├── Some((1, 5)): 115/217 ≈ 0.530
      ├── Some((5, 0)): 7/18 ≈ 0.389
      ├── Some((5, 1)): 17/29 ≈ 0.586
      ├── Some((5, 2)): 21/33 ≈ 0.636
      ├── Some((5, 3)): 13/24 ≈ 0.542
      ├── Some((5, 4)): 9/20 ≈ 0.450
      ├── Some((5, 5)): 15/27 ≈ 0.556
      ├── Some((5, 6)): 12/23 ≈ 0.522
      ├── Some((5, 7)): 1/10 ≈ 0.100
      └── Some((5, 8)): 20/32 ≈ 0.625
    ├── Some((1, 6)): 155/276 ≈ 0.562
      ├── Some((6, 0)): 9/21 ≈ 0.429
      ├── Some((6, 1)): 28/43 ≈ 0.651
      ├── Some((6, 2)): 16/29 ≈ 0.552
      ├── Some((6, 3)): 29/44 ≈ 0.659
      ├── Some((6, 4)): 14/27 ≈ 0.519
      ├── Some((6, 5)): 26/41 ≈ 0.634
      ├── Some((6, 6)): 5/16 ≈ 0.312
      ├── Some((6, 7)): 8/20 ≈ 0.400
      └── Some((6, 8)): 20/34 ≈ 0.588
    ├── Some((1, 7)): 149/267 ≈ 0.558
      ├── Some((7, 0)): 6/17 ≈ 0.353
      ├── Some((7, 1)): 15/28 ≈ 0.536
      ├── Some((7, 2)): 12/25 ≈ 0.480
      ├── Some((7, 3)): 9/21 ≈ 0.429
      ├── Some((7, 4)): 25/39 ≈ 0.641
      ├── Some((7, 5)): 29/43 ≈ 0.674
      ├── Some((7, 6)): 13/26 ≈ 0.500
      ├── Some((7, 7)): 24/38 ≈ 0.632
      └── Some((7, 8)): 16/29 ≈ 0.552
    └── Some((1, 8)): 103/199 ≈ 0.518
      ├── Some((8, 0)): 17/30 ≈ 0.567
      ├── Some((8, 2)): 17/30 ≈ 0.567
      ├── Some((8, 3)): 15/27 ≈ 0.556
      ├── Some((8, 4)): 16/29 ≈ 0.552
      ├── Some((8, 5)): 9/20 ≈ 0.450
      ├── Some((8, 6)): 10/22 ≈ 0.455
      ├── Some((8, 7)): 2/11 ≈ 0.182
      └── Some((8, 8)): 16/29 ≈ 0.552
  ├── Some((1, 2)): 929/1764 ≈ 0.527
    ├── Some((2, 0)): 122/224 ≈ 0.545
      ├── Some((0, 0)): 10/21 ≈ 0.476
      ├── Some((0, 1)): 21/33 ≈ 0.636
      ├── Some((0, 2)): 11/22 ≈ 0.500
      ├── Some((0, 3)): 9/20 ≈ 0.450
      ├── Some((0, 4)): 11/22 ≈ 0.500
      ├── Some((0, 5)): 8/19 ≈ 0.421
      ├── Some((0, 6)): 16/28 ≈ 0.571
      ├── Some((0, 7)): 13/24 ≈ 0.542
      └── Some((0, 8)): 22/34 ≈ 0.647
    ├── Some((2, 1)): 108/203 ≈ 0.532
      ├── Some((1, 0)): 14/26 ≈ 0.538
      ├── Some((1, 1)): 7/18 ≈ 0.389
      ├── Some((1, 3)): 6/17 ≈ 0.353
      ├── Some((1, 4)): 14/26 ≈ 0.538
      ├── Some((1, 5)): 14/26 ≈ 0.538
      ├── Some((1, 6)): 15/27 ≈ 0.556
      ├── Some((1, 7)): 12/24 ≈ 0.500
      └── Some((1, 8)): 25/38 ≈ 0.658
    ├── Some((2, 2)): 75/154 ≈ 0.487
      ├── Some((2, 0)): 15/26 ≈ 0.577
      ├── Some((2, 1)): 2/10 ≈ 0.200
      ├── Some((2, 3)): 16/27 ≈ 0.593
      ├── Some((2, 4)): 8/18 ≈ 0.444
      ├── Some((2, 5)): 13/24 ≈ 0.542
      ├── Some((2, 6)): 16/27 ≈ 0.593
      ├── Some((2, 7)): 1/9 ≈ 0.111
      └── Some((2, 8)): 3/12 ≈ 0.250
    ├── Some((2, 3)): 116/215 ≈ 0.540
      ├── Some((3, 0)): 16/28 ≈ 0.571
      ├── Some((3, 1)): 5/15 ≈ 0.333
      ├── Some((3, 2)): 7/17 ≈ 0.412
      ├── Some((3, 3)): 16/28 ≈ 0.571
      ├── Some((3, 4)): 20/32 ≈ 0.625
      ├── Some((3, 5)): 7/17 ≈ 0.412
      ├── Some((3, 6)): 4/14 ≈ 0.286
      ├── Some((3, 7)): 13/24 ≈ 0.542
      └── Some((3, 8)): 27/39 ≈ 0.692
    ├── Some((2, 4)): 143/255 ≈ 0.561
      ├── Some((4, 0)): 9/21 ≈ 0.429
      ├── Some((4, 1)): 14/26 ≈ 0.538
      ├── Some((4, 2)): 14/26 ≈ 0.538
      ├── Some((4, 3)): 10/22 ≈ 0.455
      ├── Some((4, 4)): 16/28 ≈ 0.571
      ├── Some((4, 5)): 22/35 ≈ 0.629
      ├── Some((4, 6)): 24/37 ≈ 0.649
      ├── Some((4, 7)): 15/27 ≈ 0.556
      └── Some((4, 8)): 19/32 ≈ 0.594
    ├── Some((2, 5)): 83/166 ≈ 0.500
      ├── Some((5, 0)): 3/11 ≈ 0.273
      ├── Some((5, 1)): 9/18 ≈ 0.500
      ├── Some((5, 2)): 12/22 ≈ 0.545
      ├── Some((5, 3)): 11/21 ≈ 0.524
      ├── Some((5, 4)): 20/30 ≈ 0.667
      ├── Some((5, 5)): 10/20 ≈ 0.500
      ├── Some((5, 6)): 8/17 ≈ 0.471
      ├── Some((5, 7)): 3/11 ≈ 0.273
      └── Some((5, 8)): 6/15 ≈ 0.400
    ├── Some((2, 6)): 108/203 ≈ 0.532
      ├── Some((6, 0)): 17/28 ≈ 0.607
      ├── Some((6, 1)): 12/23 ≈ 0.522
      ├── Some((6, 2)): 15/26 ≈ 0.577
      ├── Some((6, 3)): 24/36 ≈ 0.667
      ├── Some((6, 4)): 8/18 ≈ 0.444
      ├── Some((6, 5)): 10/21 ≈ 0.476
      ├── Some((6, 6)): 1/9 ≈ 0.111
      ├── Some((6, 7)): 7/17 ≈ 0.412
      └── Some((6, 8)): 13/24 ≈ 0.542
    ├── Some((2, 7)): 80/162 ≈ 0.494
      ├── Some((7, 0)): 2/10 ≈ 0.200
      ├── Some((7, 1)): 9/18 ≈ 0.500
      ├── Some((7, 2)): 7/16 ≈ 0.438
      ├── Some((7, 3)): 6/15 ≈ 0.400
      ├── Some((7, 4)): 9/18 ≈ 0.500
      ├── Some((7, 5)): 10/20 ≈ 0.500
      ├── Some((7, 6)): 9/18 ≈ 0.500
      ├── Some((7, 7)): 18/28 ≈ 0.643
      └── Some((7, 8)): 9/18 ≈ 0.500
    └── Some((2, 8)): 93/181 ≈ 0.514
      ├── Some((8, 0)): 13/24 ≈ 0.542
      ├── Some((8, 2)): 13/24 ≈ 0.542
      ├── Some((8, 3)): 11/22 ≈ 0.500
      ├── Some((8, 4)): 10/21 ≈ 0.476
      ├── Some((8, 5)): 18/30 ≈ 0.600
      ├── Some((8, 6)): 2/11 ≈ 0.182
      ├── Some((8, 7)): 11/22 ≈ 0.500
      └── Some((8, 8)): 15/26 ≈ 0.577
  ├── Some((1, 3)): 671/1317 ≈ 0.509
    ├── Some((3, 0)): 84/160 ≈ 0.525
      ├── Some((0, 0)): 3/11 ≈ 0.273
      ├── Some((0, 1)): 10/19 ≈ 0.526
      ├── Some((0, 2)): 5/13 ≈ 0.385
      ├── Some((0, 3)): 12/21 ≈ 0.571
      ├── Some((0, 4)): 23/32 ≈ 0.719
      ├── Some((0, 5)): 6/14 ≈ 0.429
      ├── Some((0, 6)): 7/15 ≈ 0.467
      ├── Some((0, 7)): 5/13 ≈ 0.385
      └── Some((0, 8)): 12/21 ≈ 0.571
    ├── Some((3, 1)): 93/173 ≈ 0.538
      ├── Some((1, 0)): 10/20 ≈ 0.500
      ├── Some((1, 1)): 12/22 ≈ 0.545
      ├── Some((1, 2)): 19/29 ≈ 0.655
      ├── Some((1, 4)): 6/15 ≈ 0.400
      ├── Some((1, 5)): 8/18 ≈ 0.444
      ├── Some((1, 6)): 14/24 ≈ 0.583
      ├── Some((1, 7)): 15/25 ≈ 0.600
      └── Some((1, 8)): 9/19 ≈ 0.474
    ├── Some((3, 2)): 58/122 ≈ 0.475
      ├── Some((2, 0)): 9/16 ≈ 0.562
      ├── Some((2, 1)): 12/20 ≈ 0.600
      ├── Some((2, 2)): 9/17 ≈ 0.529
      ├── Some((2, 3)): 3/10 ≈ 0.300
      ├── Some((2, 4)): 8/15 ≈ 0.533
      ├── Some((2, 5)): 0/6 ≈ 0.000
      ├── Some((2, 6)): 4/11 ≈ 0.364
      ├── Some((2, 7)): 4/11 ≈ 0.364
      └── Some((2, 8)): 8/15 ≈ 0.533
    ├── Some((3, 3)): 78/152 ≈ 0.513
      ├── Some((3, 0)): 12/21 ≈ 0.571
      ├── Some((3, 1)): 2/10 ≈ 0.200
      ├── Some((3, 2)): 7/16 ≈ 0.438
      ├── Some((3, 4)): 12/21 ≈ 0.571
      ├── Some((3, 5)): 14/24 ≈ 0.583
      ├── Some((3, 6)): 9/18 ≈ 0.500
      ├── Some((3, 7)): 16/26 ≈ 0.615
      └── Some((3, 8)): 6/15 ≈ 0.400
    ├── Some((3, 4)): 80/154 ≈ 0.519
      ├── Some((4, 0)): 7/15 ≈ 0.467
      ├── Some((4, 1)): 15/24 ≈ 0.625
      ├── Some((4, 2)): 9/17 ≈ 0.529
      ├── Some((4, 3)): 2/9 ≈ 0.222
      ├── Some((4, 4)): 8/16 ≈ 0.500
      ├── Some((4, 5)): 9/18 ≈ 0.500
      ├── Some((4, 6)): 7/15 ≈ 0.467
      ├── Some((4, 7)): 16/25 ≈ 0.640
      └── Some((4, 8)): 6/14 ≈ 0.429
    ├── Some((3, 5)): 68/137 ≈ 0.496
      ├── Some((5, 0)): 8/16 ≈ 0.500
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 5/12 ≈ 0.417
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 10/18 ≈ 0.556
      ├── Some((5, 5)): 12/20 ≈ 0.600
      ├── Some((5, 6)): 4/11 ≈ 0.364
      ├── Some((5, 7)): 9/17 ≈ 0.529
      └── Some((5, 8)): 9/17 ≈ 0.529
    ├── Some((3, 6)): 99/182 ≈ 0.544
      ├── Some((6, 0)): 14/23 ≈ 0.609
      ├── Some((6, 1)): 8/17 ≈ 0.471
      ├── Some((6, 2)): 5/14 ≈ 0.357
      ├── Some((6, 3)): 13/22 ≈ 0.591
      ├── Some((6, 4)): 15/24 ≈ 0.625
      ├── Some((6, 5)): 2/10 ≈ 0.200
      ├── Some((6, 6)): 15/25 ≈ 0.600
      ├── Some((6, 7)): 6/15 ≈ 0.400
      └── Some((6, 8)): 21/31 ≈ 0.677
    ├── Some((3, 7)): 60/125 ≈ 0.480
      ├── Some((7, 0)): 9/16 ≈ 0.562
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 9/16 ≈ 0.562
      ├── Some((7, 3)): 5/12 ≈ 0.417
      ├── Some((7, 4)): 5/12 ≈ 0.417
      ├── Some((7, 5)): 1/8 ≈ 0.125
      ├── Some((7, 6)): 15/22 ≈ 0.682
      ├── Some((7, 7)): 10/18 ≈ 0.556
      └── Some((7, 8)): 3/10 ≈ 0.300
    └── Some((3, 8)): 51/111 ≈ 0.459
      ├── Some((8, 0)): 6/14 ≈ 0.429
      ├── Some((8, 2)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 3/10 ≈ 0.300
      ├── Some((8, 4)): 5/12 ≈ 0.417
      ├── Some((8, 5)): 3/10 ≈ 0.300
      ├── Some((8, 6)): 16/24 ≈ 0.667
      ├── Some((8, 7)): 9/17 ≈ 0.529
      └── Some((8, 8)): 5/13 ≈ 0.385
  ├── Some((1, 4)): 913/1736 ≈ 0.526
    ├── Some((4, 0)): 162/282 ≈ 0.574
      ├── Some((0, 0)): 9/21 ≈ 0.429
      ├── Some((0, 1)): 22/36 ≈ 0.611
      ├── Some((0, 2)): 12/25 ≈ 0.480
      ├── Some((0, 3)): 20/33 ≈ 0.606
      ├── Some((0, 4)): 22/36 ≈ 0.611
      ├── Some((0, 5)): 24/38 ≈ 0.632
      ├── Some((0, 6)): 4/15 ≈ 0.267
      ├── Some((0, 7)): 26/40 ≈ 0.650
      └── Some((0, 8)): 23/37 ≈ 0.622
    ├── Some((4, 1)): 71/147 ≈ 0.483
      ├── Some((1, 0)): 14/24 ≈ 0.583
      ├── Some((1, 1)): 11/21 ≈ 0.524
      ├── Some((1, 2)): 9/18 ≈ 0.500
      ├── Some((1, 3)): 4/13 ≈ 0.308
      ├── Some((1, 5)): 4/13 ≈ 0.308
      ├── Some((1, 6)): 9/18 ≈ 0.500
      ├── Some((1, 7)): 14/24 ≈ 0.583
      └── Some((1, 8)): 6/15 ≈ 0.400
    ├── Some((4, 2)): 55/123 ≈ 0.447
      ├── Some((2, 0)): 11/19 ≈ 0.579
      ├── Some((2, 1)): 4/11 ≈ 0.364
      ├── Some((2, 2)): 14/22 ≈ 0.636
      ├── Some((2, 3)): 1/8 ≈ 0.125
      ├── Some((2, 4)): 0/6 ≈ 0.000
      ├── Some((2, 5)): 9/17 ≈ 0.529
      ├── Some((2, 6)): 4/12 ≈ 0.333
      ├── Some((2, 7)): 1/8 ≈ 0.125
      └── Some((2, 8)): 11/19 ≈ 0.579
    ├── Some((4, 3)): 96/185 ≈ 0.519
      ├── Some((3, 0)): 10/20 ≈ 0.500
      ├── Some((3, 1)): 10/20 ≈ 0.500
      ├── Some((3, 2)): 9/19 ≈ 0.474
      ├── Some((3, 3)): 10/20 ≈ 0.500
      ├── Some((3, 4)): 17/27 ≈ 0.630
      ├── Some((3, 5)): 12/22 ≈ 0.545
      ├── Some((3, 6)): 8/18 ≈ 0.444
      ├── Some((3, 7)): 14/24 ≈ 0.583
      └── Some((3, 8)): 5/14 ≈ 0.357
    ├── Some((4, 4)): 105/199 ≈ 0.528
      ├── Some((4, 0)): 6/17 ≈ 0.353
      ├── Some((4, 1)): 10/21 ≈ 0.476
      ├── Some((4, 2)): 12/24 ≈ 0.500
      ├── Some((4, 3)): 15/27 ≈ 0.556
      ├── Some((4, 5)): 10/21 ≈ 0.476
      ├── Some((4, 6)): 10/21 ≈ 0.476
      ├── Some((4, 7)): 15/27 ≈ 0.556
      └── Some((4, 8)): 27/40 ≈ 0.675
    ├── Some((4, 5)): 111/208 ≈ 0.534
      ├── Some((5, 0)): 12/23 ≈ 0.522
      ├── Some((5, 1)): 8/18 ≈ 0.444
      ├── Some((5, 2)): 21/33 ≈ 0.636
      ├── Some((5, 3)): 5/15 ≈ 0.333
      ├── Some((5, 4)): 19/30 ≈ 0.633
      ├── Some((5, 5)): 15/26 ≈ 0.577
      ├── Some((5, 6)): 12/23 ≈ 0.522
      ├── Some((5, 7)): 4/14 ≈ 0.286
      └── Some((5, 8)): 14/25 ≈ 0.560
    ├── Some((4, 6)): 103/196 ≈ 0.526
      ├── Some((6, 0)): 15/26 ≈ 0.577
      ├── Some((6, 1)): 8/18 ≈ 0.444
      ├── Some((6, 2)): 11/21 ≈ 0.524
      ├── Some((6, 3)): 2/11 ≈ 0.182
      ├── Some((6, 4)): 6/16 ≈ 0.375
      ├── Some((6, 5)): 16/27 ≈ 0.593
      ├── Some((6, 6)): 24/35 ≈ 0.686
      ├── Some((6, 7)): 11/21 ≈ 0.524
      └── Some((6, 8)): 10/20 ≈ 0.500
    ├── Some((4, 7)): 123/225 ≈ 0.547
      ├── Some((7, 0)): 18/30 ≈ 0.600
      ├── Some((7, 1)): 22/34 ≈ 0.647
      ├── Some((7, 2)): 4/14 ≈ 0.286
      ├── Some((7, 3)): 22/34 ≈ 0.647
      ├── Some((7, 4)): 7/18 ≈ 0.389
      ├── Some((7, 5)): 8/19 ≈ 0.421
      ├── Some((7, 6)): 14/25 ≈ 0.560
      ├── Some((7, 7)): 8/19 ≈ 0.421
      └── Some((7, 8)): 19/31 ≈ 0.613
    └── Some((4, 8)): 86/170 ≈ 0.506
      ├── Some((8, 0)): 8/18 ≈ 0.444
      ├── Some((8, 2)): 22/34 ≈ 0.647
      ├── Some((8, 3)): 1/9 ≈ 0.111
      ├── Some((8, 4)): 15/26 ≈ 0.577
      ├── Some((8, 5)): 17/28 ≈ 0.607
      ├── Some((8, 6)): 5/15 ≈ 0.333
      ├── Some((8, 7)): 8/18 ≈ 0.444
      └── Some((8, 8)): 10/21 ≈ 0.476
  ├── Some((1, 5)): 1123/2095 ≈ 0.536
    ├── Some((5, 0)): 56/128 ≈ 0.438
      ├── Some((0, 0)): 1/8 ≈ 0.125
      ├── Some((0, 1)): 9/17 ≈ 0.529
      ├── Some((0, 2)): 11/20 ≈ 0.550
      ├── Some((0, 3)): 2/9 ≈ 0.222
      ├── Some((0, 4)): 6/14 ≈ 0.429
      ├── Some((0, 5)): 2/9 ≈ 0.222
      ├── Some((0, 6)): 3/11 ≈ 0.273
      ├── Some((0, 7)): 9/17 ≈ 0.529
      └── Some((0, 8)): 13/22 ≈ 0.591
    ├── Some((5, 1)): 119/225 ≈ 0.529
      ├── Some((1, 0)): 12/25 ≈ 0.480
      ├── Some((1, 1)): 18/32 ≈ 0.562
      ├── Some((1, 2)): 12/25 ≈ 0.480
      ├── Some((1, 3)): 13/26 ≈ 0.500
      ├── Some((1, 4)): 5/16 ≈ 0.312
      ├── Some((1, 6)): 19/33 ≈ 0.576
      ├── Some((1, 7)): 20/34 ≈ 0.588
      └── Some((1, 8)): 19/33 ≈ 0.576
    ├── Some((5, 2)): 213/362 ≈ 0.588
      ├── Some((2, 0)): 17/33 ≈ 0.515
      ├── Some((2, 1)): 28/45 ≈ 0.622
      ├── Some((2, 2)): 30/47 ≈ 0.638
      ├── Some((2, 3)): 33/51 ≈ 0.647
      ├── Some((2, 4)): 14/29 ≈ 0.483
      ├── Some((2, 5)): 33/51 ≈ 0.647
      ├── Some((2, 6)): 31/48 ≈ 0.646
      ├── Some((2, 7)): 15/30 ≈ 0.500
      └── Some((2, 8)): 12/27 ≈ 0.444
    ├── Some((5, 3)): 102/199 ≈ 0.513
      ├── Some((3, 0)): 8/19 ≈ 0.421
      ├── Some((3, 1)): 7/17 ≈ 0.412
      ├── Some((3, 2)): 16/27 ≈ 0.593
      ├── Some((3, 3)): 13/24 ≈ 0.542
      ├── Some((3, 4)): 13/24 ≈ 0.542
      ├── Some((3, 5)): 13/24 ≈ 0.542
      ├── Some((3, 6)): 7/17 ≈ 0.412
      ├── Some((3, 7)): 13/24 ≈ 0.542
      └── Some((3, 8)): 11/22 ≈ 0.500
    ├── Some((5, 4)): 92/184 ≈ 0.500
      ├── Some((4, 0)): 11/21 ≈ 0.524
      ├── Some((4, 1)): 10/20 ≈ 0.500
      ├── Some((4, 2)): 5/15 ≈ 0.333
      ├── Some((4, 3)): 4/13 ≈ 0.308
      ├── Some((4, 4)): 10/20 ≈ 0.500
      ├── Some((4, 5)): 15/26 ≈ 0.577
      ├── Some((4, 6)): 14/25 ≈ 0.560
      ├── Some((4, 7)): 11/21 ≈ 0.524
      └── Some((4, 8)): 11/22 ≈ 0.500
    ├── Some((5, 5)): 133/246 ≈ 0.541
      ├── Some((5, 0)): 15/29 ≈ 0.517
      ├── Some((5, 1)): 26/41 ≈ 0.634
      ├── Some((5, 2)): 16/30 ≈ 0.533
      ├── Some((5, 3)): 13/27 ≈ 0.481
      ├── Some((5, 4)): 20/35 ≈ 0.571
      ├── Some((5, 6)): 23/38 ≈ 0.605
      ├── Some((5, 7)): 12/26 ≈ 0.462
      └── Some((5, 8)): 7/19 ≈ 0.368
    ├── Some((5, 6)): 186/324 ≈ 0.574
      ├── Some((6, 0)): 18/33 ≈ 0.545
      ├── Some((6, 1)): 20/35 ≈ 0.571
      ├── Some((6, 2)): 41/58 ≈ 0.707
      ├── Some((6, 3)): 15/30 ≈ 0.500
      ├── Some((6, 4)): 27/43 ≈ 0.628
      ├── Some((6, 5)): 19/34 ≈ 0.559
      ├── Some((6, 6)): 22/38 ≈ 0.579
      ├── Some((6, 7)): 18/33 ≈ 0.545
      └── Some((6, 8)): 6/19 ≈ 0.316
    ├── Some((5, 7)): 131/243 ≈ 0.539
      ├── Some((7, 0)): 6/17 ≈ 0.353
      ├── Some((7, 1)): 17/30 ≈ 0.567
      ├── Some((7, 2)): 19/32 ≈ 0.594
      ├── Some((7, 3)): 19/32 ≈ 0.594
      ├── Some((7, 4)): 19/32 ≈ 0.594
      ├── Some((7, 5)): 8/19 ≈ 0.421
      ├── Some((7, 6)): 15/28 ≈ 0.536
      ├── Some((7, 7)): 18/31 ≈ 0.581
      └── Some((7, 8)): 9/21 ≈ 0.429
    └── Some((5, 8)): 91/183 ≈ 0.497
      ├── Some((8, 0)): 11/22 ≈ 0.500
      ├── Some((8, 2)): 22/35 ≈ 0.629
      ├── Some((8, 3)): 6/17 ≈ 0.353
      ├── Some((8, 4)): 2/11 ≈ 0.182
      ├── Some((8, 5)): 13/25 ≈ 0.520
      ├── Some((8, 6)): 8/19 ≈ 0.421
      ├── Some((8, 7)): 22/35 ≈ 0.629
      └── Some((8, 8)): 7/18 ≈ 0.389
  ├── Some((1, 6)): 766/1483 ≈ 0.517
    ├── Some((6, 0)): 77/153 ≈ 0.503
      ├── Some((0, 0)): 9/18 ≈ 0.500
      ├── Some((0, 1)): 15/24 ≈ 0.625
      ├── Some((0, 2)): 6/14 ≈ 0.429
      ├── Some((0, 3)): 12/21 ≈ 0.571
      ├── Some((0, 4)): 6/14 ≈ 0.429
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 7/15 ≈ 0.467
      └── Some((0, 8)): 9/18 ≈ 0.500
    ├── Some((6, 1)): 73/147 ≈ 0.497
      ├── Some((1, 0)): 12/21 ≈ 0.571
      ├── Some((1, 1)): 5/14 ≈ 0.357
      ├── Some((1, 2)): 18/28 ≈ 0.643
      ├── Some((1, 3)): 7/16 ≈ 0.438
      ├── Some((1, 4)): 10/19 ≈ 0.526
      ├── Some((1, 5)): 5/14 ≈ 0.357
      ├── Some((1, 7)): 15/25 ≈ 0.600
      └── Some((1, 8)): 1/9 ≈ 0.111
    ├── Some((6, 2)): 149/258 ≈ 0.578
      ├── Some((2, 0)): 19/32 ≈ 0.594
      ├── Some((2, 1)): 30/43 ≈ 0.698
      ├── Some((2, 2)): 10/22 ≈ 0.455
      ├── Some((2, 3)): 13/25 ≈ 0.520
      ├── Some((2, 4)): 18/30 ≈ 0.600
      ├── Some((2, 5)): 17/29 ≈ 0.586
      ├── Some((2, 6)): 4/14 ≈ 0.286
      ├── Some((2, 7)): 16/28 ≈ 0.571
      └── Some((2, 8)): 21/34 ≈ 0.618
    ├── Some((6, 3)): 100/188 ≈ 0.532
      ├── Some((3, 0)): 11/21 ≈ 0.524
      ├── Some((3, 1)): 7/16 ≈ 0.438
      ├── Some((3, 2)): 6/15 ≈ 0.400
      ├── Some((3, 3)): 10/20 ≈ 0.500
      ├── Some((3, 4)): 6/15 ≈ 0.400
      ├── Some((3, 5)): 8/18 ≈ 0.444
      ├── Some((3, 6)): 24/34 ≈ 0.706
      ├── Some((3, 7)): 9/19 ≈ 0.474
      └── Some((3, 8)): 19/29 ≈ 0.655
    ├── Some((6, 4)): 119/215 ≈ 0.553
      ├── Some((4, 0)): 15/26 ≈ 0.577
      ├── Some((4, 1)): 11/22 ≈ 0.500
      ├── Some((4, 2)): 10/20 ≈ 0.500
      ├── Some((4, 3)): 18/29 ≈ 0.621
      ├── Some((4, 4)): 16/27 ≈ 0.593
      ├── Some((4, 5)): 5/15 ≈ 0.333
      ├── Some((4, 6)): 12/23 ≈ 0.522
      ├── Some((4, 7)): 23/34 ≈ 0.676
      └── Some((4, 8)): 8/18 ≈ 0.444
    ├── Some((6, 5)): 77/154 ≈ 0.500
      ├── Some((5, 0)): 9/18 ≈ 0.500
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 14/23 ≈ 0.609
      ├── Some((5, 3)): 17/26 ≈ 0.654
      ├── Some((5, 4)): 8/16 ≈ 0.500
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 11/20 ≈ 0.550
      ├── Some((5, 7)): 3/11 ≈ 0.273
      └── Some((5, 8)): 4/12 ≈ 0.333
    ├── Some((6, 6)): 43/101 ≈ 0.426
      ├── Some((6, 0)): 2/9 ≈ 0.222
      ├── Some((6, 1)): 7/14 ≈ 0.500
      ├── Some((6, 2)): 4/11 ≈ 0.364
      ├── Some((6, 3)): 8/15 ≈ 0.533
      ├── Some((6, 4)): 11/19 ≈ 0.579
      ├── Some((6, 5)): 2/9 ≈ 0.222
      ├── Some((6, 7)): 5/12 ≈ 0.417
      └── Some((6, 8)): 4/11 ≈ 0.364
    ├── Some((6, 7)): 60/128 ≈ 0.469
      ├── Some((7, 0)): 2/9 ≈ 0.222
      ├── Some((7, 1)): 10/18 ≈ 0.556
      ├── Some((7, 2)): 7/14 ≈ 0.500
      ├── Some((7, 3)): 10/18 ≈ 0.556
      ├── Some((7, 4)): 7/15 ≈ 0.467
      ├── Some((7, 5)): 4/11 ≈ 0.364
      ├── Some((7, 6)): 6/13 ≈ 0.462
      ├── Some((7, 7)): 4/11 ≈ 0.364
      └── Some((7, 8)): 10/18 ≈ 0.556
    └── Some((6, 8)): 67/138 ≈ 0.486
      ├── Some((8, 0)): 7/16 ≈ 0.438
      ├── Some((8, 2)): 15/25 ≈ 0.600
      ├── Some((8, 3)): 4/12 ≈ 0.333
      ├── Some((8, 4)): 12/21 ≈ 0.571
      ├── Some((8, 5)): 9/18 ≈ 0.500
      ├── Some((8, 6)): 6/15 ≈ 0.400
      ├── Some((8, 7)): 10/19 ≈ 0.526
      └── Some((8, 8)): 3/11 ≈ 0.273
  ├── Some((1, 7)): 893/1702 ≈ 0.525
    ├── Some((7, 0)): 82/164 ≈ 0.500
      ├── Some((0, 0)): 10/19 ≈ 0.526
      ├── Some((0, 1)): 7/16 ≈ 0.438
      ├── Some((0, 2)): 19/29 ≈ 0.655
      ├── Some((0, 3)): 11/20 ≈ 0.550
      ├── Some((0, 4)): 7/16 ≈ 0.438
      ├── Some((0, 5)): 10/19 ≈ 0.526
      ├── Some((0, 6)): 9/18 ≈ 0.500
      ├── Some((0, 7)): 6/15 ≈ 0.400
      └── Some((0, 8)): 3/11 ≈ 0.273
    ├── Some((7, 1)): 129/233 ≈ 0.554
      ├── Some((1, 0)): 21/34 ≈ 0.618
      ├── Some((1, 1)): 19/32 ≈ 0.594
      ├── Some((1, 2)): 13/26 ≈ 0.500
      ├── Some((1, 3)): 16/29 ≈ 0.552
      ├── Some((1, 4)): 21/35 ≈ 0.600
      ├── Some((1, 5)): 16/29 ≈ 0.552
      ├── Some((1, 6)): 5/16 ≈ 0.312
      └── Some((1, 8)): 18/31 ≈ 0.581
    ├── Some((7, 2)): 60/130 ≈ 0.462
      ├── Some((2, 0)): 1/8 ≈ 0.125
      ├── Some((2, 1)): 0/6 ≈ 0.000
      ├── Some((2, 2)): 8/16 ≈ 0.500
      ├── Some((2, 3)): 8/16 ≈ 0.500
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 7/15 ≈ 0.467
      ├── Some((2, 6)): 8/16 ≈ 0.500
      ├── Some((2, 7)): 13/21 ≈ 0.619
      └── Some((2, 8)): 5/13 ≈ 0.385
    ├── Some((7, 3)): 105/198 ≈ 0.530
      ├── Some((3, 0)): 16/27 ≈ 0.593
      ├── Some((3, 1)): 16/27 ≈ 0.593
      ├── Some((3, 2)): 4/13 ≈ 0.308
      ├── Some((3, 3)): 9/19 ≈ 0.474
      ├── Some((3, 4)): 7/17 ≈ 0.412
      ├── Some((3, 5)): 13/23 ≈ 0.565
      ├── Some((3, 6)): 9/19 ≈ 0.474
      ├── Some((3, 7)): 14/25 ≈ 0.560
      └── Some((3, 8)): 16/27 ≈ 0.593
    ├── Some((7, 4)): 73/150 ≈ 0.487
      ├── Some((4, 0)): 5/13 ≈ 0.385
      ├── Some((4, 1)): 13/22 ≈ 0.591
      ├── Some((4, 2)): 6/14 ≈ 0.429
      ├── Some((4, 3)): 8/17 ≈ 0.471
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 15/24 ≈ 0.625
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 3/11 ≈ 0.273
      └── Some((4, 8)): 11/20 ≈ 0.550
    ├── Some((7, 5)): 134/240 ≈ 0.558
      ├── Some((5, 0)): 6/17 ≈ 0.353
      ├── Some((5, 1)): 13/25 ≈ 0.520
      ├── Some((5, 2)): 19/31 ≈ 0.613
      ├── Some((5, 3)): 16/28 ≈ 0.571
      ├── Some((5, 4)): 12/24 ≈ 0.500
      ├── Some((5, 5)): 7/18 ≈ 0.389
      ├── Some((5, 6)): 9/20 ≈ 0.450
      ├── Some((5, 7)): 33/46 ≈ 0.717
      └── Some((5, 8)): 18/30 ≈ 0.600
    ├── Some((7, 6)): 91/177 ≈ 0.514
      ├── Some((6, 0)): 10/20 ≈ 0.500
      ├── Some((6, 1)): 12/22 ≈ 0.545
      ├── Some((6, 2)): 8/17 ≈ 0.471
      ├── Some((6, 3)): 15/25 ≈ 0.600
      ├── Some((6, 4)): 8/17 ≈ 0.471
      ├── Some((6, 5)): 9/18 ≈ 0.500
      ├── Some((6, 6)): 8/17 ≈ 0.471
      ├── Some((6, 7)): 7/16 ≈ 0.438
      └── Some((6, 8)): 14/24 ≈ 0.583
    ├── Some((7, 7)): 133/239 ≈ 0.556
      ├── Some((7, 0)): 12/25 ≈ 0.480
      ├── Some((7, 1)): 11/23 ≈ 0.478
      ├── Some((7, 2)): 11/23 ≈ 0.478
      ├── Some((7, 3)): 16/29 ≈ 0.552
      ├── Some((7, 4)): 22/36 ≈ 0.611
      ├── Some((7, 5)): 18/32 ≈ 0.562
      ├── Some((7, 6)): 27/41 ≈ 0.659
      └── Some((7, 8)): 16/29 ≈ 0.552
    └── Some((7, 8)): 86/170 ≈ 0.506
      ├── Some((8, 0)): 9/19 ≈ 0.474
      ├── Some((8, 2)): 13/24 ≈ 0.542
      ├── Some((8, 3)): 17/28 ≈ 0.607
      ├── Some((8, 4)): 14/25 ≈ 0.560
      ├── Some((8, 5)): 10/20 ≈ 0.500
      ├── Some((8, 6)): 8/18 ≈ 0.444
      ├── Some((8, 7)): 4/13 ≈ 0.308
      └── Some((8, 8)): 11/22 ≈ 0.500
  └── Some((1, 8)): 862/1648 ≈ 0.523
    ├── Some((8, 0)): 135/247 ≈ 0.547
      ├── Some((0, 0)): 10/22 ≈ 0.455
      ├── Some((0, 1)): 20/33 ≈ 0.606
      ├── Some((0, 2)): 13/25 ≈ 0.520
      ├── Some((0, 3)): 11/23 ≈ 0.478
      ├── Some((0, 4)): 14/26 ≈ 0.538
      ├── Some((0, 5)): 14/27 ≈ 0.519
      ├── Some((0, 6)): 19/32 ≈ 0.594
      ├── Some((0, 7)): 23/36 ≈ 0.639
      └── Some((0, 8)): 10/22 ≈ 0.455
    ├── Some((8, 2)): 43/106 ≈ 0.406
      ├── Some((2, 0)): 2/9 ≈ 0.222
      ├── Some((2, 1)): 8/15 ≈ 0.533
      ├── Some((2, 2)): 5/12 ≈ 0.417
      ├── Some((2, 3)): 7/14 ≈ 0.500
      ├── Some((2, 4)): 10/18 ≈ 0.556
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 5/12 ≈ 0.417
      ├── Some((2, 7)): 1/7 ≈ 0.143
      └── Some((2, 8)): 0/6 ≈ 0.000
    ├── Some((8, 3)): 156/278 ≈ 0.561
      ├── Some((3, 0)): 23/37 ≈ 0.622
      ├── Some((3, 1)): 33/48 ≈ 0.688
      ├── Some((3, 2)): 13/26 ≈ 0.500
      ├── Some((3, 3)): 23/37 ≈ 0.622
      ├── Some((3, 4)): 11/24 ≈ 0.458
      ├── Some((3, 5)): 17/31 ≈ 0.548
      ├── Some((3, 6)): 10/23 ≈ 0.435
      ├── Some((3, 7)): 11/24 ≈ 0.458
      └── Some((3, 8)): 14/27 ≈ 0.519
    ├── Some((8, 4)): 93/185 ≈ 0.503
      ├── Some((4, 0)): 12/23 ≈ 0.522
      ├── Some((4, 1)): 14/25 ≈ 0.560
      ├── Some((4, 2)): 1/9 ≈ 0.111
      ├── Some((4, 3)): 12/23 ≈ 0.522
      ├── Some((4, 4)): 5/14 ≈ 0.357
      ├── Some((4, 5)): 17/28 ≈ 0.607
      ├── Some((4, 6)): 9/19 ≈ 0.474
      ├── Some((4, 7)): 17/28 ≈ 0.607
      └── Some((4, 8)): 5/15 ≈ 0.333
    ├── Some((8, 5)): 102/198 ≈ 0.515
      ├── Some((5, 0)): 6/16 ≈ 0.375
      ├── Some((5, 1)): 11/22 ≈ 0.500
      ├── Some((5, 2)): 16/27 ≈ 0.593
      ├── Some((5, 3)): 11/22 ≈ 0.500
      ├── Some((5, 4)): 18/29 ≈ 0.621
      ├── Some((5, 5)): 11/22 ≈ 0.500
      ├── Some((5, 6)): 8/18 ≈ 0.444
      ├── Some((5, 7)): 5/15 ≈ 0.333
      └── Some((5, 8)): 15/26 ≈ 0.577
    ├── Some((8, 6)): 100/195 ≈ 0.513
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 13/24 ≈ 0.542
      ├── Some((6, 2)): 15/26 ≈ 0.577
      ├── Some((6, 3)): 4/13 ≈ 0.308
      ├── Some((6, 4)): 10/21 ≈ 0.476
      ├── Some((6, 5)): 12/23 ≈ 0.522
      ├── Some((6, 6)): 17/28 ≈ 0.607
      ├── Some((6, 7)): 6/16 ≈ 0.375
      └── Some((6, 8)): 15/26 ≈ 0.577
    ├── Some((8, 7)): 134/246 ≈ 0.545
      ├── Some((7, 0)): 13/25 ≈ 0.520
      ├── Some((7, 1)): 13/25 ≈ 0.520
      ├── Some((7, 2)): 15/28 ≈ 0.536
      ├── Some((7, 3)): 16/29 ≈ 0.552
      ├── Some((7, 4)): 11/23 ≈ 0.478
      ├── Some((7, 5)): 7/18 ≈ 0.389
      ├── Some((7, 6)): 29/43 ≈ 0.674
      ├── Some((7, 7)): 19/32 ≈ 0.594
      └── Some((7, 8)): 10/22 ≈ 0.455
    └── Some((8, 8)): 98/192 ≈ 0.510
      ├── Some((8, 0)): 7/19 ≈ 0.368
      ├── Some((8, 2)): 19/33 ≈ 0.576
      ├── Some((8, 3)): 11/24 ≈ 0.458
      ├── Some((8, 4)): 15/29 ≈ 0.517
      ├── Some((8, 5)): 8/20 ≈ 0.400
      ├── Some((8, 6)): 19/33 ≈ 0.576
      └── Some((8, 7)): 19/33 ≈ 0.576
├── Some((8, 2)): 10296/19419 ≈ 0.530
  ├── Some((2, 0)): 1480/2735 ≈ 0.541
    ├── Some((0, 0)): 144/273 ≈ 0.527
      ├── Some((0, 1)): 16/32 ≈ 0.500
      ├── Some((0, 2)): 14/29 ≈ 0.483
      ├── Some((0, 3)): 31/49 ≈ 0.633
      ├── Some((0, 4)): 11/26 ≈ 0.423
      ├── Some((0, 5)): 12/27 ≈ 0.444
      ├── Some((0, 6)): 16/32 ≈ 0.500
      ├── Some((0, 7)): 25/43 ≈ 0.581
      └── Some((0, 8)): 18/34 ≈ 0.529
    ├── Some((0, 1)): 124/243 ≈ 0.510
      ├── Some((1, 0)): 12/25 ≈ 0.480
      ├── Some((1, 1)): 4/15 ≈ 0.267
      ├── Some((1, 2)): 8/20 ≈ 0.400
      ├── Some((1, 3)): 9/22 ≈ 0.409
      ├── Some((1, 4)): 11/24 ≈ 0.458
      ├── Some((1, 5)): 28/44 ≈ 0.636
      ├── Some((1, 6)): 8/20 ≈ 0.400
      ├── Some((1, 7)): 17/31 ≈ 0.548
      └── Some((1, 8)): 26/41 ≈ 0.634
    ├── Some((0, 2)): 214/379 ≈ 0.565
      ├── Some((2, 1)): 20/39 ≈ 0.513
      ├── Some((2, 2)): 17/36 ≈ 0.472
      ├── Some((2, 3)): 19/38 ≈ 0.500
      ├── Some((2, 4)): 28/49 ≈ 0.571
      ├── Some((2, 5)): 42/65 ≈ 0.646
      ├── Some((2, 6)): 41/64 ≈ 0.641
      ├── Some((2, 7)): 33/55 ≈ 0.600
      └── Some((2, 8)): 14/32 ≈ 0.438
    ├── Some((0, 3)): 167/308 ≈ 0.542
      ├── Some((3, 0)): 14/29 ≈ 0.483
      ├── Some((3, 1)): 21/37 ≈ 0.568
      ├── Some((3, 2)): 20/36 ≈ 0.556
      ├── Some((3, 3)): 30/47 ≈ 0.638
      ├── Some((3, 4)): 20/36 ≈ 0.556
      ├── Some((3, 5)): 16/31 ≈ 0.516
      ├── Some((3, 6)): 17/32 ≈ 0.531
      ├── Some((3, 7)): 9/23 ≈ 0.391
      └── Some((3, 8)): 20/36 ≈ 0.556
    ├── Some((0, 4)): 154/289 ≈ 0.533
      ├── Some((4, 0)): 13/27 ≈ 0.481
      ├── Some((4, 1)): 17/32 ≈ 0.531
      ├── Some((4, 2)): 12/26 ≈ 0.462
      ├── Some((4, 3)): 21/37 ≈ 0.568
      ├── Some((4, 4)): 18/33 ≈ 0.545
      ├── Some((4, 5)): 18/33 ≈ 0.545
      ├── Some((4, 6)): 17/32 ≈ 0.531
      ├── Some((4, 7)): 14/29 ≈ 0.483
      └── Some((4, 8)): 23/39 ≈ 0.590
    ├── Some((0, 5)): 185/335 ≈ 0.552
      ├── Some((5, 0)): 39/59 ≈ 0.661
      ├── Some((5, 1)): 12/27 ≈ 0.444
      ├── Some((5, 2)): 20/37 ≈ 0.541
      ├── Some((5, 3)): 22/39 ≈ 0.564
      ├── Some((5, 4)): 7/21 ≈ 0.333
      ├── Some((5, 5)): 12/27 ≈ 0.444
      ├── Some((5, 6)): 29/47 ≈ 0.617
      ├── Some((5, 7)): 20/37 ≈ 0.541
      └── Some((5, 8)): 23/40 ≈ 0.575
    ├── Some((0, 6)): 225/395 ≈ 0.570
      ├── Some((6, 0)): 41/63 ≈ 0.651
      ├── Some((6, 1)): 25/44 ≈ 0.568
      ├── Some((6, 2)): 14/31 ≈ 0.452
      ├── Some((6, 3)): 15/32 ≈ 0.469
      ├── Some((6, 4)): 19/37 ≈ 0.514
      ├── Some((6, 5)): 33/53 ≈ 0.623
      ├── Some((6, 6)): 9/24 ≈ 0.375
      ├── Some((6, 7)): 45/67 ≈ 0.672
      └── Some((6, 8)): 24/43 ≈ 0.558
    ├── Some((0, 7)): 157/293 ≈ 0.536
      ├── Some((7, 0)): 4/16 ≈ 0.250
      ├── Some((7, 1)): 20/36 ≈ 0.556
      ├── Some((7, 2)): 7/20 ≈ 0.350
      ├── Some((7, 3)): 30/47 ≈ 0.638
      ├── Some((7, 4)): 23/40 ≈ 0.575
      ├── Some((7, 5)): 46/65 ≈ 0.708
      ├── Some((7, 6)): 7/20 ≈ 0.350
      ├── Some((7, 7)): 15/30 ≈ 0.500
      └── Some((7, 8)): 5/18 ≈ 0.278
    └── Some((0, 8)): 109/219 ≈ 0.498
      ├── Some((8, 0)): 30/46 ≈ 0.652
      ├── Some((8, 1)): 8/21 ≈ 0.381
      ├── Some((8, 3)): 9/22 ≈ 0.409
      ├── Some((8, 4)): 15/29 ≈ 0.517
      ├── Some((8, 5)): 20/35 ≈ 0.571
      ├── Some((8, 6)): 7/20 ≈ 0.350
      ├── Some((8, 7)): 9/22 ≈ 0.409
      └── Some((8, 8)): 10/23 ≈ 0.435
  ├── Some((2, 1)): 906/1747 ≈ 0.519
    ├── Some((1, 0)): 81/165 ≈ 0.491
      ├── Some((0, 0)): 6/15 ≈ 0.400
      ├── Some((0, 1)): 9/18 ≈ 0.500
      ├── Some((0, 2)): 14/24 ≈ 0.583
      ├── Some((0, 3)): 8/17 ≈ 0.471
      ├── Some((0, 4)): 16/26 ≈ 0.615
      ├── Some((0, 5)): 6/15 ≈ 0.400
      ├── Some((0, 6)): 10/20 ≈ 0.500
      ├── Some((0, 7)): 7/16 ≈ 0.438
      └── Some((0, 8)): 4/13 ≈ 0.308
    ├── Some((1, 1)): 130/238 ≈ 0.546
      ├── Some((1, 0)): 22/36 ≈ 0.611
      ├── Some((1, 2)): 12/25 ≈ 0.480
      ├── Some((1, 3)): 14/27 ≈ 0.519
      ├── Some((1, 4)): 24/39 ≈ 0.615
      ├── Some((1, 5)): 17/31 ≈ 0.548
      ├── Some((1, 6)): 14/27 ≈ 0.519
      ├── Some((1, 7)): 8/20 ≈ 0.400
      └── Some((1, 8)): 18/32 ≈ 0.562
    ├── Some((1, 2)): 70/148 ≈ 0.473
      ├── Some((2, 0)): 12/22 ≈ 0.545
      ├── Some((2, 2)): 10/20 ≈ 0.500
      ├── Some((2, 3)): 10/20 ≈ 0.500
      ├── Some((2, 4)): 8/17 ≈ 0.471
      ├── Some((2, 5)): 7/16 ≈ 0.438
      ├── Some((2, 6)): 8/18 ≈ 0.444
      ├── Some((2, 7)): 8/18 ≈ 0.444
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((1, 3)): 87/174 ≈ 0.500
      ├── Some((3, 0)): 18/28 ≈ 0.643
      ├── Some((3, 1)): 8/18 ≈ 0.444
      ├── Some((3, 2)): 3/12 ≈ 0.250
      ├── Some((3, 3)): 12/22 ≈ 0.545
      ├── Some((3, 4)): 10/20 ≈ 0.500
      ├── Some((3, 5)): 2/10 ≈ 0.200
      ├── Some((3, 6)): 9/19 ≈ 0.474
      ├── Some((3, 7)): 12/22 ≈ 0.545
      └── Some((3, 8)): 12/22 ≈ 0.545
    ├── Some((1, 4)): 72/151 ≈ 0.477
      ├── Some((4, 0)): 8/17 ≈ 0.471
      ├── Some((4, 1)): 5/13 ≈ 0.385
      ├── Some((4, 2)): 10/19 ≈ 0.526
      ├── Some((4, 3)): 14/23 ≈ 0.609
      ├── Some((4, 4)): 5/14 ≈ 0.357
      ├── Some((4, 5)): 8/17 ≈ 0.471
      ├── Some((4, 6)): 4/12 ≈ 0.333
      ├── Some((4, 7)): 14/23 ≈ 0.609
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((1, 5)): 90/178 ≈ 0.506
      ├── Some((5, 0)): 9/19 ≈ 0.474
      ├── Some((5, 1)): 5/14 ≈ 0.357
      ├── Some((5, 2)): 14/24 ≈ 0.583
      ├── Some((5, 3)): 14/24 ≈ 0.583
      ├── Some((5, 4)): 12/22 ≈ 0.545
      ├── Some((5, 5)): 14/24 ≈ 0.583
      ├── Some((5, 6)): 10/20 ≈ 0.500
      ├── Some((5, 7)): 7/16 ≈ 0.438
      └── Some((5, 8)): 5/14 ≈ 0.357
    ├── Some((1, 6)): 116/217 ≈ 0.535
      ├── Some((6, 0)): 22/34 ≈ 0.647
      ├── Some((6, 1)): 21/33 ≈ 0.636
      ├── Some((6, 2)): 18/30 ≈ 0.600
      ├── Some((6, 3)): 4/14 ≈ 0.286
      ├── Some((6, 4)): 18/30 ≈ 0.600
      ├── Some((6, 5)): 6/16 ≈ 0.375
      ├── Some((6, 6)): 15/27 ≈ 0.556
      ├── Some((6, 7)): 3/13 ≈ 0.231
      └── Some((6, 8)): 8/19 ≈ 0.421
    ├── Some((1, 7)): 123/228 ≈ 0.539
      ├── Some((7, 0)): 11/22 ≈ 0.500
      ├── Some((7, 1)): 9/20 ≈ 0.450
      ├── Some((7, 2)): 28/41 ≈ 0.683
      ├── Some((7, 3)): 11/23 ≈ 0.478
      ├── Some((7, 4)): 14/26 ≈ 0.538
      ├── Some((7, 5)): 20/32 ≈ 0.625
      ├── Some((7, 6)): 16/28 ≈ 0.571
      ├── Some((7, 7)): 4/14 ≈ 0.286
      └── Some((7, 8)): 10/21 ≈ 0.476
    └── Some((1, 8)): 136/247 ≈ 0.551
      ├── Some((8, 0)): 5/17 ≈ 0.294
      ├── Some((8, 1)): 10/23 ≈ 0.435
      ├── Some((8, 3)): 10/23 ≈ 0.435
      ├── Some((8, 4)): 23/38 ≈ 0.605
      ├── Some((8, 5)): 12/25 ≈ 0.480
      ├── Some((8, 6)): 20/35 ≈ 0.571
      ├── Some((8, 7)): 18/32 ≈ 0.562
      └── Some((8, 8)): 37/53 ≈ 0.698
  ├── Some((2, 2)): 1057/2009 ≈ 0.526
    ├── Some((2, 0)): 112/221 ≈ 0.507
      ├── Some((0, 0)): 16/29 ≈ 0.552
      ├── Some((0, 1)): 7/18 ≈ 0.389
      ├── Some((0, 2)): 21/34 ≈ 0.618
      ├── Some((0, 3)): 12/24 ≈ 0.500
      ├── Some((0, 4)): 6/17 ≈ 0.353
      ├── Some((0, 5)): 25/39 ≈ 0.641
      ├── Some((0, 6)): 12/24 ≈ 0.500
      ├── Some((0, 7)): 2/12 ≈ 0.167
      └── Some((0, 8)): 11/23 ≈ 0.478
    ├── Some((2, 1)): 135/256 ≈ 0.527
      ├── Some((1, 0)): 11/24 ≈ 0.458
      ├── Some((1, 1)): 15/29 ≈ 0.517
      ├── Some((1, 2)): 5/16 ≈ 0.312
      ├── Some((1, 3)): 15/29 ≈ 0.517
      ├── Some((1, 4)): 23/37 ≈ 0.622
      ├── Some((1, 5)): 16/30 ≈ 0.533
      ├── Some((1, 6)): 17/31 ≈ 0.548
      ├── Some((1, 7)): 14/27 ≈ 0.519
      └── Some((1, 8)): 18/32 ≈ 0.562
    ├── Some((2, 3)): 160/294 ≈ 0.544
      ├── Some((3, 0)): 17/32 ≈ 0.531
      ├── Some((3, 1)): 12/26 ≈ 0.462
      ├── Some((3, 2)): 18/33 ≈ 0.545
      ├── Some((3, 3)): 12/26 ≈ 0.462
      ├── Some((3, 4)): 13/27 ≈ 0.481
      ├── Some((3, 5)): 36/53 ≈ 0.679
      ├── Some((3, 6)): 17/32 ≈ 0.531
      ├── Some((3, 7)): 13/27 ≈ 0.481
      └── Some((3, 8)): 21/37 ≈ 0.568
    ├── Some((2, 4)): 135/256 ≈ 0.527
      ├── Some((4, 0)): 5/16 ≈ 0.312
      ├── Some((4, 1)): 13/26 ≈ 0.500
      ├── Some((4, 2)): 23/38 ≈ 0.605
      ├── Some((4, 3)): 17/31 ≈ 0.548
      ├── Some((4, 4)): 15/29 ≈ 0.517
      ├── Some((4, 5)): 17/31 ≈ 0.548
      ├── Some((4, 6)): 21/35 ≈ 0.600
      ├── Some((4, 7)): 6/18 ≈ 0.333
      └── Some((4, 8)): 17/31 ≈ 0.548
    ├── Some((2, 5)): 150/279 ≈ 0.538
      ├── Some((5, 0)): 16/30 ≈ 0.533
      ├── Some((5, 1)): 11/24 ≈ 0.458
      ├── Some((5, 2)): 28/44 ≈ 0.636
      ├── Some((5, 3)): 11/24 ≈ 0.458
      ├── Some((5, 4)): 7/20 ≈ 0.350
      ├── Some((5, 5)): 21/36 ≈ 0.583
      ├── Some((5, 6)): 23/38 ≈ 0.605
      ├── Some((5, 7)): 18/33 ≈ 0.545
      └── Some((5, 8)): 15/29 ≈ 0.517
    ├── Some((2, 6)): 183/328 ≈ 0.558
      ├── Some((6, 0)): 17/33 ≈ 0.515
      ├── Some((6, 1)): 30/48 ≈ 0.625
      ├── Some((6, 2)): 28/45 ≈ 0.622
      ├── Some((6, 3)): 38/56 ≈ 0.679
      ├── Some((6, 4)): 10/24 ≈ 0.417
      ├── Some((6, 5)): 9/23 ≈ 0.391
      ├── Some((6, 6)): 24/41 ≈ 0.585
      ├── Some((6, 7)): 17/33 ≈ 0.515
      └── Some((6, 8)): 10/24 ≈ 0.417
    ├── Some((2, 7)): 66/148 ≈ 0.446
      ├── Some((7, 0)): 10/20 ≈ 0.500
      ├── Some((7, 1)): 6/15 ≈ 0.400
      ├── Some((7, 2)): 4/13 ≈ 0.308
      ├── Some((7, 3)): 7/16 ≈ 0.438
      ├── Some((7, 4)): 2/10 ≈ 0.200
      ├── Some((7, 5)): 11/21 ≈ 0.524
      ├── Some((7, 6)): 9/18 ≈ 0.500
      ├── Some((7, 7)): 14/24 ≈ 0.583
      └── Some((7, 8)): 2/10 ≈ 0.200
    └── Some((2, 8)): 115/226 ≈ 0.509
      ├── Some((8, 0)): 14/28 ≈ 0.500
      ├── Some((8, 1)): 12/25 ≈ 0.480
      ├── Some((8, 3)): 7/19 ≈ 0.368
      ├── Some((8, 4)): 16/30 ≈ 0.533
      ├── Some((8, 5)): 24/39 ≈ 0.615
      ├── Some((8, 6)): 19/34 ≈ 0.559
      ├── Some((8, 7)): 14/28 ≈ 0.500
      └── Some((8, 8)): 9/22 ≈ 0.409
  ├── Some((2, 3)): 889/1718 ≈ 0.517
    ├── Some((3, 0)): 60/132 ≈ 0.455
      ├── Some((0, 0)): 4/12 ≈ 0.333
      ├── Some((0, 1)): 10/18 ≈ 0.556
      ├── Some((0, 2)): 12/20 ≈ 0.600
      ├── Some((0, 3)): 3/11 ≈ 0.273
      ├── Some((0, 4)): 5/13 ≈ 0.385
      ├── Some((0, 5)): 5/13 ≈ 0.385
      ├── Some((0, 6)): 3/11 ≈ 0.273
      ├── Some((0, 7)): 8/16 ≈ 0.500
      └── Some((0, 8)): 9/17 ≈ 0.529
    ├── Some((3, 1)): 85/171 ≈ 0.497
      ├── Some((1, 0)): 6/15 ≈ 0.400
      ├── Some((1, 1)): 6/15 ≈ 0.400
      ├── Some((1, 2)): 6/15 ≈ 0.400
      ├── Some((1, 3)): 11/21 ≈ 0.524
      ├── Some((1, 4)): 9/19 ≈ 0.474
      ├── Some((1, 5)): 7/16 ≈ 0.438
      ├── Some((1, 6)): 22/33 ≈ 0.667
      ├── Some((1, 7)): 6/15 ≈ 0.400
      └── Some((1, 8)): 11/21 ≈ 0.524
    ├── Some((3, 2)): 74/154 ≈ 0.481
      ├── Some((2, 0)): 8/18 ≈ 0.444
      ├── Some((2, 1)): 21/32 ≈ 0.656
      ├── Some((2, 2)): 12/23 ≈ 0.522
      ├── Some((2, 4)): 4/13 ≈ 0.308
      ├── Some((2, 5)): 5/14 ≈ 0.357
      ├── Some((2, 6)): 10/20 ≈ 0.500
      ├── Some((2, 7)): 5/15 ≈ 0.333
      └── Some((2, 8)): 8/18 ≈ 0.444
    ├── Some((3, 3)): 98/190 ≈ 0.516
      ├── Some((3, 0)): 14/26 ≈ 0.538
      ├── Some((3, 1)): 10/21 ≈ 0.476
      ├── Some((3, 2)): 9/20 ≈ 0.450
      ├── Some((3, 4)): 12/24 ≈ 0.500
      ├── Some((3, 5)): 10/21 ≈ 0.476
      ├── Some((3, 6)): 22/34 ≈ 0.647
      ├── Some((3, 7)): 15/27 ≈ 0.556
      └── Some((3, 8)): 6/16 ≈ 0.375
    ├── Some((3, 4)): 100/193 ≈ 0.518
      ├── Some((4, 0)): 9/20 ≈ 0.450
      ├── Some((4, 1)): 10/21 ≈ 0.476
      ├── Some((4, 2)): 8/18 ≈ 0.444
      ├── Some((4, 3)): 18/29 ≈ 0.621
      ├── Some((4, 4)): 4/13 ≈ 0.308
      ├── Some((4, 5)): 8/18 ≈ 0.444
      ├── Some((4, 6)): 18/29 ≈ 0.621
      ├── Some((4, 7)): 1/9 ≈ 0.111
      └── Some((4, 8)): 23/35 ≈ 0.657
    ├── Some((3, 5)): 95/186 ≈ 0.511
      ├── Some((5, 0)): 24/35 ≈ 0.686
      ├── Some((5, 1)): 19/30 ≈ 0.633
      ├── Some((5, 2)): 8/18 ≈ 0.444
      ├── Some((5, 3)): 5/14 ≈ 0.357
      ├── Some((5, 4)): 7/17 ≈ 0.412
      ├── Some((5, 5)): 9/19 ≈ 0.474
      ├── Some((5, 6)): 5/14 ≈ 0.357
      ├── Some((5, 7)): 4/13 ≈ 0.308
      └── Some((5, 8)): 14/25 ≈ 0.560
    ├── Some((3, 6)): 75/155 ≈ 0.484
      ├── Some((6, 0)): 13/22 ≈ 0.591
      ├── Some((6, 1)): 8/17 ≈ 0.471
      ├── Some((6, 2)): 8/17 ≈ 0.471
      ├── Some((6, 3)): 7/16 ≈ 0.438
      ├── Some((6, 4)): 13/22 ≈ 0.591
      ├── Some((6, 5)): 4/12 ≈ 0.333
      ├── Some((6, 6)): 10/19 ≈ 0.526
      ├── Some((6, 7)): 5/13 ≈ 0.385
      └── Some((6, 8)): 7/16 ≈ 0.438
    ├── Some((3, 7)): 149/266 ≈ 0.560
      ├── Some((7, 0)): 31/46 ≈ 0.674
      ├── Some((7, 1)): 11/23 ≈ 0.478
      ├── Some((7, 2)): 20/34 ≈ 0.588
      ├── Some((7, 3)): 15/28 ≈ 0.536
      ├── Some((7, 4)): 20/34 ≈ 0.588
      ├── Some((7, 5)): 20/34 ≈ 0.588
      ├── Some((7, 6)): 18/31 ≈ 0.581
      ├── Some((7, 7)): 11/23 ≈ 0.478
      └── Some((7, 8)): 2/12 ≈ 0.167
    └── Some((3, 8)): 152/270 ≈ 0.563
      ├── Some((8, 0)): 26/42 ≈ 0.619
      ├── Some((8, 1)): 11/25 ≈ 0.440
      ├── Some((8, 3)): 15/30 ≈ 0.500
      ├── Some((8, 4)): 7/20 ≈ 0.350
      ├── Some((8, 5)): 19/34 ≈ 0.559
      ├── Some((8, 6)): 6/18 ≈ 0.333
      ├── Some((8, 7)): 26/42 ≈ 0.619
      └── Some((8, 8)): 41/58 ≈ 0.707
  ├── Some((2, 4)): 1338/2492 ≈ 0.537
    ├── Some((4, 0)): 82/175 ≈ 0.469
      ├── Some((0, 0)): 11/22 ≈ 0.500
      ├── Some((0, 1)): 6/16 ≈ 0.375
      ├── Some((0, 2)): 13/24 ≈ 0.542
      ├── Some((0, 3)): 15/26 ≈ 0.577
      ├── Some((0, 4)): 4/13 ≈ 0.308
      ├── Some((0, 5)): 6/16 ≈ 0.375
      ├── Some((0, 6)): 7/17 ≈ 0.412
      ├── Some((0, 7)): 10/21 ≈ 0.476
      └── Some((0, 8)): 9/19 ≈ 0.474
    ├── Some((4, 1)): 139/264 ≈ 0.527
      ├── Some((1, 0)): 13/27 ≈ 0.481
      ├── Some((1, 1)): 16/30 ≈ 0.533
      ├── Some((1, 2)): 12/25 ≈ 0.480
      ├── Some((1, 3)): 12/25 ≈ 0.480
      ├── Some((1, 4)): 27/42 ≈ 0.643
      ├── Some((1, 5)): 20/35 ≈ 0.571
      ├── Some((1, 6)): 8/21 ≈ 0.381
      ├── Some((1, 7)): 17/31 ≈ 0.548
      └── Some((1, 8)): 13/27 ≈ 0.481
    ├── Some((4, 2)): 261/444 ≈ 0.588
      ├── Some((2, 0)): 21/41 ≈ 0.512
      ├── Some((2, 1)): 50/76 ≈ 0.658
      ├── Some((2, 2)): 37/61 ≈ 0.607
      ├── Some((2, 3)): 29/51 ≈ 0.569
      ├── Some((2, 5)): 45/70 ≈ 0.643
      ├── Some((2, 6)): 19/39 ≈ 0.487
      ├── Some((2, 7)): 22/43 ≈ 0.512
      └── Some((2, 8)): 38/62 ≈ 0.613
    ├── Some((4, 3)): 223/389 ≈ 0.573
      ├── Some((3, 0)): 13/29 ≈ 0.448
      ├── Some((3, 1)): 24/43 ≈ 0.558
      ├── Some((3, 2)): 35/55 ≈ 0.636
      ├── Some((3, 3)): 23/41 ≈ 0.561
      ├── Some((3, 4)): 17/34 ≈ 0.500
      ├── Some((3, 5)): 38/59 ≈ 0.644
      ├── Some((3, 6)): 18/35 ≈ 0.514
      ├── Some((3, 7)): 33/53 ≈ 0.623
      └── Some((3, 8)): 21/39 ≈ 0.538
    ├── Some((4, 4)): 158/292 ≈ 0.541
      ├── Some((4, 0)): 24/42 ≈ 0.571
      ├── Some((4, 1)): 13/28 ≈ 0.464
      ├── Some((4, 2)): 13/28 ≈ 0.464
      ├── Some((4, 3)): 11/26 ≈ 0.423
      ├── Some((4, 5)): 18/35 ≈ 0.514
      ├── Some((4, 6)): 17/33 ≈ 0.515
      ├── Some((4, 7)): 27/45 ≈ 0.600
      └── Some((4, 8)): 35/54 ≈ 0.648
    ├── Some((4, 5)): 86/182 ≈ 0.473
      ├── Some((5, 0)): 9/20 ≈ 0.450
      ├── Some((5, 1)): 2/11 ≈ 0.182
      ├── Some((5, 2)): 9/20 ≈ 0.450
      ├── Some((5, 3)): 13/24 ≈ 0.542
      ├── Some((5, 4)): 4/14 ≈ 0.286
      ├── Some((5, 5)): 4/14 ≈ 0.286
      ├── Some((5, 6)): 25/37 ≈ 0.676
      ├── Some((5, 7)): 8/19 ≈ 0.421
      └── Some((5, 8)): 11/22 ≈ 0.500
    ├── Some((4, 6)): 138/262 ≈ 0.527
      ├── Some((6, 0)): 23/38 ≈ 0.605
      ├── Some((6, 1)): 19/33 ≈ 0.576
      ├── Some((6, 2)): 11/24 ≈ 0.458
      ├── Some((6, 3)): 12/25 ≈ 0.480
      ├── Some((6, 4)): 11/24 ≈ 0.458
      ├── Some((6, 5)): 16/30 ≈ 0.533
      ├── Some((6, 6)): 22/37 ≈ 0.595
      ├── Some((6, 7)): 12/25 ≈ 0.480
      └── Some((6, 8)): 12/25 ≈ 0.480
    ├── Some((4, 7)): 74/162 ≈ 0.457
      ├── Some((7, 0)): 8/18 ≈ 0.444
      ├── Some((7, 1)): 6/16 ≈ 0.375
      ├── Some((7, 2)): 6/16 ≈ 0.375
      ├── Some((7, 3)): 2/10 ≈ 0.200
      ├── Some((7, 4)): 14/25 ≈ 0.560
      ├── Some((7, 5)): 12/22 ≈ 0.545
      ├── Some((7, 6)): 10/20 ≈ 0.500
      ├── Some((7, 7)): 10/20 ≈ 0.500
      └── Some((7, 8)): 5/14 ≈ 0.357
    └── Some((4, 8)): 177/321 ≈ 0.551
      ├── Some((8, 0)): 18/35 ≈ 0.514
      ├── Some((8, 1)): 26/45 ≈ 0.578
      ├── Some((8, 3)): 25/43 ≈ 0.581
      ├── Some((8, 4)): 32/52 ≈ 0.615
      ├── Some((8, 5)): 27/46 ≈ 0.587
      ├── Some((8, 6)): 11/26 ≈ 0.423
      ├── Some((8, 7)): 16/33 ≈ 0.485
      └── Some((8, 8)): 22/40 ≈ 0.550
  ├── Some((2, 5)): 1321/2463 ≈ 0.536
    ├── Some((5, 0)): 162/298 ≈ 0.544
      ├── Some((0, 0)): 23/39 ≈ 0.590
      ├── Some((0, 1)): 21/37 ≈ 0.568
      ├── Some((0, 2)): 6/19 ≈ 0.316
      ├── Some((0, 3)): 21/37 ≈ 0.568
      ├── Some((0, 4)): 27/43 ≈ 0.628
      ├── Some((0, 5)): 17/32 ≈ 0.531
      ├── Some((0, 6)): 23/39 ≈ 0.590
      ├── Some((0, 7)): 8/21 ≈ 0.381
      └── Some((0, 8)): 15/30 ≈ 0.500
    ├── Some((5, 1)): 174/316 ≈ 0.551
      ├── Some((1, 0)): 38/56 ≈ 0.679
      ├── Some((1, 1)): 20/36 ≈ 0.556
      ├── Some((1, 2)): 18/34 ≈ 0.529
      ├── Some((1, 3)): 12/27 ≈ 0.444
      ├── Some((1, 4)): 17/33 ≈ 0.515
      ├── Some((1, 5)): 23/39 ≈ 0.590
      ├── Some((1, 6)): 10/24 ≈ 0.417
      ├── Some((1, 7)): 20/36 ≈ 0.556
      └── Some((1, 8)): 15/30 ≈ 0.500
    ├── Some((5, 2)): 86/181 ≈ 0.475
      ├── Some((2, 0)): 17/30 ≈ 0.567
      ├── Some((2, 1)): 3/13 ≈ 0.231
      ├── Some((2, 2)): 4/15 ≈ 0.267
      ├── Some((2, 3)): 9/21 ≈ 0.429
      ├── Some((2, 4)): 25/39 ≈ 0.641
      ├── Some((2, 6)): 3/13 ≈ 0.231
      ├── Some((2, 7)): 10/22 ≈ 0.455
      └── Some((2, 8)): 14/27 ≈ 0.519
    ├── Some((5, 3)): 47/118 ≈ 0.398
      ├── Some((3, 0)): 6/14 ≈ 0.429
      ├── Some((3, 1)): 11/19 ≈ 0.579
      ├── Some((3, 2)): 8/16 ≈ 0.500
      ├── Some((3, 3)): 1/8 ≈ 0.125
      ├── Some((3, 4)): 1/8 ≈ 0.125
      ├── Some((3, 5)): 3/11 ≈ 0.273
      ├── Some((3, 6)): 5/13 ≈ 0.385
      ├── Some((3, 7)): 4/12 ≈ 0.333
      └── Some((3, 8)): 8/16 ≈ 0.500
    ├── Some((5, 4)): 173/314 ≈ 0.551
      ├── Some((4, 0)): 20/36 ≈ 0.556
      ├── Some((4, 1)): 18/33 ≈ 0.545
      ├── Some((4, 2)): 12/26 ≈ 0.462
      ├── Some((4, 3)): 17/32 ≈ 0.531
      ├── Some((4, 4)): 26/43 ≈ 0.605
      ├── Some((4, 5)): 22/38 ≈ 0.579
      ├── Some((4, 6)): 16/31 ≈ 0.516
      ├── Some((4, 7)): 16/31 ≈ 0.516
      └── Some((4, 8)): 26/43 ≈ 0.605
    ├── Some((5, 5)): 156/289 ≈ 0.540
      ├── Some((5, 0)): 23/40 ≈ 0.575
      ├── Some((5, 1)): 8/22 ≈ 0.364
      ├── Some((5, 2)): 21/38 ≈ 0.553
      ├── Some((5, 3)): 14/30 ≈ 0.467
      ├── Some((5, 4)): 28/46 ≈ 0.609
      ├── Some((5, 6)): 17/33 ≈ 0.515
      ├── Some((5, 7)): 14/30 ≈ 0.467
      └── Some((5, 8)): 30/49 ≈ 0.612
    ├── Some((5, 6)): 200/354 ≈ 0.565
      ├── Some((6, 0)): 15/31 ≈ 0.484
      ├── Some((6, 1)): 16/32 ≈ 0.500
      ├── Some((6, 2)): 10/25 ≈ 0.400
      ├── Some((6, 3)): 16/32 ≈ 0.500
      ├── Some((6, 4)): 36/56 ≈ 0.643
      ├── Some((6, 5)): 46/66 ≈ 0.697
      ├── Some((6, 6)): 20/37 ≈ 0.541
      ├── Some((6, 7)): 25/43 ≈ 0.581
      └── Some((6, 8)): 15/31 ≈ 0.484
    ├── Some((5, 7)): 181/326 ≈ 0.555
      ├── Some((7, 0)): 29/47 ≈ 0.617
      ├── Some((7, 1)): 21/38 ≈ 0.553
      ├── Some((7, 2)): 20/36 ≈ 0.556
      ├── Some((7, 3)): 7/20 ≈ 0.350
      ├── Some((7, 4)): 25/42 ≈ 0.595
      ├── Some((7, 5)): 9/23 ≈ 0.391
      ├── Some((7, 6)): 31/49 ≈ 0.633
      ├── Some((7, 7)): 23/40 ≈ 0.575
      └── Some((7, 8)): 15/30 ≈ 0.500
    └── Some((5, 8)): 141/266 ≈ 0.530
      ├── Some((8, 0)): 9/23 ≈ 0.391
      ├── Some((8, 1)): 11/25 ≈ 0.440
      ├── Some((8, 3)): 9/23 ≈ 0.391
      ├── Some((8, 4)): 12/27 ≈ 0.444
      ├── Some((8, 5)): 23/40 ≈ 0.575
      ├── Some((8, 6)): 20/36 ≈ 0.556
      ├── Some((8, 7)): 30/48 ≈ 0.625
      └── Some((8, 8)): 26/43 ≈ 0.605
  ├── Some((2, 6)): 900/1737 ≈ 0.518
    ├── Some((6, 0)): 128/235 ≈ 0.545
      ├── Some((0, 0)): 18/30 ≈ 0.600
      ├── Some((0, 1)): 20/33 ≈ 0.606
      ├── Some((0, 2)): 15/27 ≈ 0.556
      ├── Some((0, 3)): 10/22 ≈ 0.455
      ├── Some((0, 4)): 2/11 ≈ 0.182
      ├── Some((0, 5)): 7/18 ≈ 0.389
      ├── Some((0, 6)): 24/37 ≈ 0.649
      ├── Some((0, 7)): 21/34 ≈ 0.618
      └── Some((0, 8)): 10/22 ≈ 0.455
    ├── Some((6, 1)): 80/163 ≈ 0.491
      ├── Some((1, 0)): 11/21 ≈ 0.524
      ├── Some((1, 1)): 4/13 ≈ 0.308
      ├── Some((1, 2)): 7/16 ≈ 0.438
      ├── Some((1, 3)): 9/18 ≈ 0.500
      ├── Some((1, 4)): 8/17 ≈ 0.471
      ├── Some((1, 5)): 3/11 ≈ 0.273
      ├── Some((1, 6)): 9/19 ≈ 0.474
      ├── Some((1, 7)): 7/16 ≈ 0.438
      └── Some((1, 8)): 21/31 ≈ 0.677
    ├── Some((6, 2)): 98/190 ≈ 0.516
      ├── Some((2, 0)): 2/11 ≈ 0.182
      ├── Some((2, 1)): 21/34 ≈ 0.618
      ├── Some((2, 2)): 12/24 ≈ 0.500
      ├── Some((2, 3)): 11/23 ≈ 0.478
      ├── Some((2, 4)): 10/21 ≈ 0.476
      ├── Some((2, 5)): 15/27 ≈ 0.556
      ├── Some((2, 7)): 10/21 ≈ 0.476
      └── Some((2, 8)): 16/28 ≈ 0.571
    ├── Some((6, 3)): 124/229 ≈ 0.541
      ├── Some((3, 0)): 19/31 ≈ 0.613
      ├── Some((3, 1)): 12/24 ≈ 0.500
      ├── Some((3, 2)): 9/20 ≈ 0.450
      ├── Some((3, 3)): 8/19 ≈ 0.421
      ├── Some((3, 4)): 23/35 ≈ 0.657
      ├── Some((3, 5)): 6/17 ≈ 0.353
      ├── Some((3, 6)): 11/22 ≈ 0.500
      ├── Some((3, 7)): 21/33 ≈ 0.636
      └── Some((3, 8)): 15/27 ≈ 0.556
    ├── Some((6, 4)): 109/207 ≈ 0.527
      ├── Some((4, 0)): 13/24 ≈ 0.542
      ├── Some((4, 1)): 6/16 ≈ 0.375
      ├── Some((4, 2)): 17/28 ≈ 0.607
      ├── Some((4, 3)): 17/28 ≈ 0.607
      ├── Some((4, 4)): 12/23 ≈ 0.522
      ├── Some((4, 5)): 13/24 ≈ 0.542
      ├── Some((4, 6)): 4/14 ≈ 0.286
      ├── Some((4, 7)): 15/26 ≈ 0.577
      └── Some((4, 8)): 12/23 ≈ 0.522
    ├── Some((6, 5)): 107/204 ≈ 0.525
      ├── Some((5, 0)): 21/33 ≈ 0.636
      ├── Some((5, 1)): 8/19 ≈ 0.421
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 4/14 ≈ 0.286
      ├── Some((5, 4)): 25/37 ≈ 0.676
      ├── Some((5, 5)): 1/10 ≈ 0.100
      ├── Some((5, 6)): 14/25 ≈ 0.560
      ├── Some((5, 7)): 7/17 ≈ 0.412
      └── Some((5, 8)): 15/26 ≈ 0.577
    ├── Some((6, 6)): 99/192 ≈ 0.516
      ├── Some((6, 0)): 17/29 ≈ 0.586
      ├── Some((6, 1)): 11/22 ≈ 0.500
      ├── Some((6, 2)): 15/27 ≈ 0.556
      ├── Some((6, 3)): 8/19 ≈ 0.421
      ├── Some((6, 4)): 10/21 ≈ 0.476
      ├── Some((6, 5)): 17/29 ≈ 0.586
      ├── Some((6, 7)): 9/20 ≈ 0.450
      └── Some((6, 8)): 12/24 ≈ 0.500
    ├── Some((6, 7)): 67/143 ≈ 0.469
      ├── Some((7, 0)): 3/11 ≈ 0.273
      ├── Some((7, 1)): 7/15 ≈ 0.467
      ├── Some((7, 2)): 8/17 ≈ 0.471
      ├── Some((7, 3)): 13/22 ≈ 0.591
      ├── Some((7, 4)): 6/14 ≈ 0.429
      ├── Some((7, 5)): 7/16 ≈ 0.438
      ├── Some((7, 6)): 5/13 ≈ 0.385
      ├── Some((7, 7)): 4/12 ≈ 0.333
      └── Some((7, 8)): 13/22 ≈ 0.591
    └── Some((6, 8)): 87/173 ≈ 0.503
      ├── Some((8, 0)): 13/24 ≈ 0.542
      ├── Some((8, 1)): 9/19 ≈ 0.474
      ├── Some((8, 3)): 11/22 ≈ 0.500
      ├── Some((8, 4)): 18/29 ≈ 0.621
      ├── Some((8, 5)): 10/21 ≈ 0.476
      ├── Some((8, 6)): 4/13 ≈ 0.308
      ├── Some((8, 7)): 11/22 ≈ 0.500
      └── Some((8, 8)): 11/22 ≈ 0.500
  ├── Some((2, 7)): 1322/2465 ≈ 0.536
    ├── Some((7, 0)): 181/326 ≈ 0.555
      ├── Some((0, 0)): 29/47 ≈ 0.617
      ├── Some((0, 1)): 21/37 ≈ 0.568
      ├── Some((0, 2)): 19/35 ≈ 0.543
      ├── Some((0, 3)): 13/28 ≈ 0.464
      ├── Some((0, 4)): 27/44 ≈ 0.614
      ├── Some((0, 5)): 18/34 ≈ 0.529
      ├── Some((0, 6)): 28/45 ≈ 0.622
      ├── Some((0, 7)): 12/27 ≈ 0.444
      └── Some((0, 8)): 13/28 ≈ 0.464
    ├── Some((7, 1)): 133/254 ≈ 0.524
      ├── Some((1, 0)): 7/19 ≈ 0.368
      ├── Some((1, 1)): 9/22 ≈ 0.409
      ├── Some((1, 2)): 1/11 ≈ 0.091
      ├── Some((1, 3)): 21/36 ≈ 0.583
      ├── Some((1, 4)): 19/33 ≈ 0.576
      ├── Some((1, 5)): 29/45 ≈ 0.644
      ├── Some((1, 6)): 21/36 ≈ 0.583
      ├── Some((1, 7)): 18/32 ≈ 0.562
      └── Some((1, 8)): 7/19 ≈ 0.368
    ├── Some((7, 2)): 94/194 ≈ 0.485
      ├── Some((2, 0)): 15/28 ≈ 0.536
      ├── Some((2, 1)): 9/21 ≈ 0.429
      ├── Some((2, 2)): 19/33 ≈ 0.576
      ├── Some((2, 3)): 7/18 ≈ 0.389
      ├── Some((2, 4)): 10/22 ≈ 0.455
      ├── Some((2, 5)): 15/28 ≈ 0.536
      ├── Some((2, 6)): 12/25 ≈ 0.480
      └── Some((2, 8)): 7/18 ≈ 0.389
    ├── Some((7, 3)): 186/333 ≈ 0.559
      ├── Some((3, 0)): 33/51 ≈ 0.647
      ├── Some((3, 1)): 16/32 ≈ 0.500
      ├── Some((3, 2)): 21/38 ≈ 0.553
      ├── Some((3, 3)): 9/23 ≈ 0.391
      ├── Some((3, 4)): 29/47 ≈ 0.617
      ├── Some((3, 5)): 7/21 ≈ 0.333
      ├── Some((3, 6)): 18/34 ≈ 0.529
      ├── Some((3, 7)): 12/27 ≈ 0.444
      └── Some((3, 8)): 40/59 ≈ 0.678
    ├── Some((7, 4)): 148/277 ≈ 0.534
      ├── Some((4, 0)): 25/41 ≈ 0.610
      ├── Some((4, 1)): 19/34 ≈ 0.559
      ├── Some((4, 2)): 15/29 ≈ 0.517
      ├── Some((4, 3)): 13/27 ≈ 0.481
      ├── Some((4, 4)): 16/30 ≈ 0.533
      ├── Some((4, 5)): 24/39 ≈ 0.615
      ├── Some((4, 6)): 9/22 ≈ 0.409
      ├── Some((4, 7)): 13/27 ≈ 0.481
      └── Some((4, 8)): 13/27 ≈ 0.481
    ├── Some((7, 5)): 194/345 ≈ 0.562
      ├── Some((5, 0)): 21/38 ≈ 0.553
      ├── Some((5, 1)): 24/42 ≈ 0.571
      ├── Some((5, 2)): 10/25 ≈ 0.400
      ├── Some((5, 3)): 5/18 ≈ 0.278
      ├── Some((5, 4)): 40/59 ≈ 0.678
      ├── Some((5, 5)): 21/38 ≈ 0.553
      ├── Some((5, 6)): 27/45 ≈ 0.600
      ├── Some((5, 7)): 23/40 ≈ 0.575
      └── Some((5, 8)): 22/39 ≈ 0.564
    ├── Some((7, 6)): 128/246 ≈ 0.520
      ├── Some((6, 0)): 21/35 ≈ 0.600
      ├── Some((6, 1)): 10/22 ≈ 0.455
      ├── Some((6, 2)): 17/31 ≈ 0.548
      ├── Some((6, 3)): 6/18 ≈ 0.333
      ├── Some((6, 4)): 21/35 ≈ 0.600
      ├── Some((6, 5)): 11/24 ≈ 0.458
      ├── Some((6, 6)): 21/35 ≈ 0.600
      ├── Some((6, 7)): 16/29 ≈ 0.552
      └── Some((6, 8)): 5/16 ≈ 0.312
    ├── Some((7, 7)): 198/351 ≈ 0.564
      ├── Some((7, 0)): 26/46 ≈ 0.565
      ├── Some((7, 1)): 13/30 ≈ 0.433
      ├── Some((7, 2)): 50/73 ≈ 0.685
      ├── Some((7, 3)): 32/52 ≈ 0.615
      ├── Some((7, 4)): 24/43 ≈ 0.558
      ├── Some((7, 5)): 23/42 ≈ 0.548
      ├── Some((7, 6)): 12/28 ≈ 0.429
      └── Some((7, 8)): 18/36 ≈ 0.500
    └── Some((7, 8)): 59/138 ≈ 0.428
      ├── Some((8, 0)): 6/16 ≈ 0.375
      ├── Some((8, 1)): 15/26 ≈ 0.577
      ├── Some((8, 3)): 11/21 ≈ 0.524
      ├── Some((8, 4)): 16/27 ≈ 0.593
      ├── Some((8, 5)): 6/16 ≈ 0.375
      ├── Some((8, 6)): 2/11 ≈ 0.182
      ├── Some((8, 7)): 1/9 ≈ 0.111
      └── Some((8, 8)): 2/11 ≈ 0.182
  └── Some((2, 8)): 1082/2052 ≈ 0.527
    ├── Some((8, 0)): 109/217 ≈ 0.502
      ├── Some((0, 0)): 4/14 ≈ 0.286
      ├── Some((0, 1)): 13/25 ≈ 0.520
      ├── Some((0, 2)): 3/13 ≈ 0.231
      ├── Some((0, 3)): 11/23 ≈ 0.478
      ├── Some((0, 4)): 14/26 ≈ 0.538
      ├── Some((0, 5)): 14/27 ≈ 0.519
      ├── Some((0, 6)): 13/25 ≈ 0.520
      ├── Some((0, 7)): 9/21 ≈ 0.429
      └── Some((0, 8)): 28/42 ≈ 0.667
    ├── Some((8, 1)): 93/192 ≈ 0.484
      ├── Some((1, 0)): 6/16 ≈ 0.375
      ├── Some((1, 1)): 1/10 ≈ 0.100
      ├── Some((1, 2)): 20/32 ≈ 0.625
      ├── Some((1, 3)): 14/26 ≈ 0.538
      ├── Some((1, 4)): 13/25 ≈ 0.520
      ├── Some((1, 5)): 3/12 ≈ 0.250
      ├── Some((1, 6)): 7/18 ≈ 0.389
      ├── Some((1, 7)): 13/25 ≈ 0.520
      └── Some((1, 8)): 15/27 ≈ 0.556
    ├── Some((8, 3)): 94/194 ≈ 0.485
      ├── Some((3, 0)): 10/21 ≈ 0.476
      ├── Some((3, 1)): 4/14 ≈ 0.286
      ├── Some((3, 2)): 12/24 ≈ 0.500
      ├── Some((3, 3)): 11/22 ≈ 0.500
      ├── Some((3, 4)): 10/21 ≈ 0.476
      ├── Some((3, 5)): 13/25 ≈ 0.520
      ├── Some((3, 6)): 6/16 ≈ 0.375
      ├── Some((3, 7)): 17/29 ≈ 0.586
      └── Some((3, 8)): 10/21 ≈ 0.476
    ├── Some((8, 4)): 193/345 ≈ 0.559
      ├── Some((4, 0)): 23/40 ≈ 0.575
      ├── Some((4, 1)): 16/32 ≈ 0.500
      ├── Some((4, 2)): 24/41 ≈ 0.585
      ├── Some((4, 3)): 17/33 ≈ 0.515
      ├── Some((4, 4)): 22/39 ≈ 0.564
      ├── Some((4, 5)): 25/42 ≈ 0.595
      ├── Some((4, 6)): 28/46 ≈ 0.609
      ├── Some((4, 7)): 18/34 ≈ 0.529
      └── Some((4, 8)): 20/37 ≈ 0.541
    ├── Some((8, 5)): 222/387 ≈ 0.574
      ├── Some((5, 0)): 27/46 ≈ 0.587
      ├── Some((5, 1)): 22/40 ≈ 0.550
      ├── Some((5, 2)): 16/33 ≈ 0.485
      ├── Some((5, 3)): 36/56 ≈ 0.643
      ├── Some((5, 4)): 26/45 ≈ 0.578
      ├── Some((5, 5)): 31/51 ≈ 0.608
      ├── Some((5, 6)): 34/54 ≈ 0.630
      ├── Some((5, 7)): 24/42 ≈ 0.571
      └── Some((5, 8)): 5/19 ≈ 0.263
    ├── Some((8, 6)): 88/184 ≈ 0.478
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 8/18 ≈ 0.444
      ├── Some((6, 2)): 15/26 ≈ 0.577
      ├── Some((6, 3)): 8/19 ≈ 0.421
      ├── Some((6, 4)): 11/22 ≈ 0.500
      ├── Some((6, 5)): 14/25 ≈ 0.560
      ├── Some((6, 6)): 10/21 ≈ 0.476
      ├── Some((6, 7)): 5/15 ≈ 0.333
      └── Some((6, 8)): 9/20 ≈ 0.450
    ├── Some((8, 7)): 160/295 ≈ 0.542
      ├── Some((7, 0)): 9/22 ≈ 0.409
      ├── Some((7, 1)): 27/43 ≈ 0.628
      ├── Some((7, 2)): 18/33 ≈ 0.545
      ├── Some((7, 3)): 18/33 ≈ 0.545
      ├── Some((7, 4)): 20/35 ≈ 0.571
      ├── Some((7, 5)): 21/37 ≈ 0.568
      ├── Some((7, 6)): 15/30 ≈ 0.500
      ├── Some((7, 7)): 14/28 ≈ 0.500
      └── Some((7, 8)): 18/33 ≈ 0.545
    └── Some((8, 8)): 122/237 ≈ 0.515
      ├── Some((8, 0)): 26/44 ≈ 0.591
      ├── Some((8, 1)): 13/28 ≈ 0.464
      ├── Some((8, 3)): 17/33 ≈ 0.515
      ├── Some((8, 4)): 14/30 ≈ 0.467
      ├── Some((8, 5)): 10/25 ≈ 0.400
      ├── Some((8, 6)): 16/32 ≈ 0.500
      └── Some((8, 7)): 26/44 ≈ 0.591
├── Some((8, 3)): 9397/17786 ≈ 0.528
  ├── Some((3, 0)): 1155/2168 ≈ 0.533
    ├── Some((0, 0)): 98/195 ≈ 0.503
      ├── Some((0, 1)): 15/28 ≈ 0.536
      ├── Some((0, 2)): 14/26 ≈ 0.538
      ├── Some((0, 3)): 3/13 ≈ 0.231
      ├── Some((0, 4)): 17/30 ≈ 0.567
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 17/30 ≈ 0.567
      ├── Some((0, 7)): 8/19 ≈ 0.421
      └── Some((0, 8)): 12/24 ≈ 0.500
    ├── Some((0, 1)): 155/281 ≈ 0.552
      ├── Some((1, 0)): 24/39 ≈ 0.615
      ├── Some((1, 1)): 15/29 ≈ 0.517
      ├── Some((1, 2)): 13/26 ≈ 0.500
      ├── Some((1, 3)): 9/22 ≈ 0.409
      ├── Some((1, 4)): 29/44 ≈ 0.659
      ├── Some((1, 5)): 20/34 ≈ 0.588
      ├── Some((1, 6)): 17/31 ≈ 0.548
      ├── Some((1, 7)): 6/18 ≈ 0.333
      └── Some((1, 8)): 22/37 ≈ 0.595
    ├── Some((0, 2)): 127/239 ≈ 0.531
      ├── Some((2, 0)): 12/24 ≈ 0.500
      ├── Some((2, 1)): 10/22 ≈ 0.455
      ├── Some((2, 2)): 13/25 ≈ 0.520
      ├── Some((2, 3)): 7/18 ≈ 0.389
      ├── Some((2, 4)): 16/29 ≈ 0.552
      ├── Some((2, 5)): 15/28 ≈ 0.536
      ├── Some((2, 6)): 13/26 ≈ 0.500
      ├── Some((2, 7)): 21/34 ≈ 0.618
      └── Some((2, 8)): 19/32 ≈ 0.594
    ├── Some((0, 3)): 144/265 ≈ 0.543
      ├── Some((3, 1)): 5/17 ≈ 0.294
      ├── Some((3, 2)): 14/29 ≈ 0.483
      ├── Some((3, 3)): 14/29 ≈ 0.483
      ├── Some((3, 4)): 31/48 ≈ 0.646
      ├── Some((3, 5)): 20/36 ≈ 0.556
      ├── Some((3, 6)): 18/33 ≈ 0.545
      ├── Some((3, 7)): 24/40 ≈ 0.600
      └── Some((3, 8)): 17/32 ≈ 0.531
    ├── Some((0, 4)): 166/297 ≈ 0.559
      ├── Some((4, 0)): 9/22 ≈ 0.409
      ├── Some((4, 1)): 3/14 ≈ 0.214
      ├── Some((4, 2)): 13/27 ≈ 0.481
      ├── Some((4, 3)): 13/27 ≈ 0.481
      ├── Some((4, 4)): 18/33 ≈ 0.545
      ├── Some((4, 5)): 28/44 ≈ 0.636
      ├── Some((4, 6)): 24/40 ≈ 0.600
      ├── Some((4, 7)): 31/47 ≈ 0.660
      └── Some((4, 8)): 26/42 ≈ 0.619
    ├── Some((0, 5)): 115/221 ≈ 0.520
      ├── Some((5, 0)): 18/30 ≈ 0.600
      ├── Some((5, 1)): 8/19 ≈ 0.421
      ├── Some((5, 2)): 8/19 ≈ 0.421
      ├── Some((5, 3)): 15/27 ≈ 0.556
      ├── Some((5, 4)): 14/26 ≈ 0.538
      ├── Some((5, 5)): 12/24 ≈ 0.500
      ├── Some((5, 6)): 15/27 ≈ 0.556
      ├── Some((5, 7)): 8/19 ≈ 0.421
      └── Some((5, 8)): 17/29 ≈ 0.586
    ├── Some((0, 6)): 150/273 ≈ 0.549
      ├── Some((6, 0)): 4/15 ≈ 0.267
      ├── Some((6, 1)): 5/17 ≈ 0.294
      ├── Some((6, 2)): 17/31 ≈ 0.548
      ├── Some((6, 3)): 41/57 ≈ 0.719
      ├── Some((6, 4)): 11/24 ≈ 0.458
      ├── Some((6, 5)): 23/38 ≈ 0.605
      ├── Some((6, 6)): 11/24 ≈ 0.458
      ├── Some((6, 7)): 24/39 ≈ 0.615
      └── Some((6, 8)): 13/27 ≈ 0.481
    ├── Some((0, 7)): 83/172 ≈ 0.483
      ├── Some((7, 0)): 12/22 ≈ 0.545
      ├── Some((7, 1)): 19/30 ≈ 0.633
      ├── Some((7, 2)): 8/18 ≈ 0.444
      ├── Some((7, 3)): 11/21 ≈ 0.524
      ├── Some((7, 4)): 8/18 ≈ 0.444
      ├── Some((7, 5)): 0/8 ≈ 0.000
      ├── Some((7, 6)): 5/14 ≈ 0.357
      ├── Some((7, 7)): 11/21 ≈ 0.524
      └── Some((7, 8)): 9/19 ≈ 0.474
    └── Some((0, 8)): 117/224 ≈ 0.522
      ├── Some((8, 0)): 4/15 ≈ 0.267
      ├── Some((8, 1)): 8/20 ≈ 0.400
      ├── Some((8, 2)): 23/38 ≈ 0.605
      ├── Some((8, 4)): 18/32 ≈ 0.562
      ├── Some((8, 5)): 17/31 ≈ 0.548
      ├── Some((8, 6)): 28/44 ≈ 0.636
      ├── Some((8, 7)): 10/23 ≈ 0.435
      └── Some((8, 8)): 8/20 ≈ 0.400
  ├── Some((3, 1)): 952/1819 ≈ 0.523
    ├── Some((1, 0)): 110/209 ≈ 0.526
      ├── Some((0, 0)): 11/22 ≈ 0.500
      ├── Some((0, 1)): 12/23 ≈ 0.522
      ├── Some((0, 2)): 12/23 ≈ 0.522
      ├── Some((0, 3)): 11/22 ≈ 0.500
      ├── Some((0, 4)): 13/24 ≈ 0.542
      ├── Some((0, 5)): 6/16 ≈ 0.375
      ├── Some((0, 6)): 8/19 ≈ 0.421
      ├── Some((0, 7)): 16/27 ≈ 0.593
      └── Some((0, 8)): 20/32 ≈ 0.625
    ├── Some((1, 1)): 104/200 ≈ 0.520
      ├── Some((1, 0)): 15/27 ≈ 0.556
      ├── Some((1, 2)): 12/24 ≈ 0.500
      ├── Some((1, 3)): 18/30 ≈ 0.600
      ├── Some((1, 4)): 19/32 ≈ 0.594
      ├── Some((1, 5)): 14/26 ≈ 0.538
      ├── Some((1, 6)): 6/17 ≈ 0.353
      ├── Some((1, 7)): 11/23 ≈ 0.478
      └── Some((1, 8)): 9/20 ≈ 0.450
    ├── Some((1, 2)): 105/201 ≈ 0.522
      ├── Some((2, 0)): 8/18 ≈ 0.444
      ├── Some((2, 1)): 18/29 ≈ 0.621
      ├── Some((2, 2)): 12/23 ≈ 0.522
      ├── Some((2, 3)): 10/20 ≈ 0.500
      ├── Some((2, 4)): 15/26 ≈ 0.577
      ├── Some((2, 5)): 16/27 ≈ 0.593
      ├── Some((2, 6)): 2/11 ≈ 0.182
      ├── Some((2, 7)): 13/24 ≈ 0.542
      └── Some((2, 8)): 11/22 ≈ 0.500
    ├── Some((1, 3)): 79/162 ≈ 0.488
      ├── Some((3, 0)): 2/11 ≈ 0.182
      ├── Some((3, 2)): 13/24 ≈ 0.542
      ├── Some((3, 3)): 8/18 ≈ 0.444
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 5/15 ≈ 0.333
      ├── Some((3, 6)): 16/27 ≈ 0.593
      ├── Some((3, 7)): 9/20 ≈ 0.450
      └── Some((3, 8)): 17/28 ≈ 0.607
    ├── Some((1, 4)): 124/230 ≈ 0.539
      ├── Some((4, 0)): 14/26 ≈ 0.538
      ├── Some((4, 1)): 11/22 ≈ 0.500
      ├── Some((4, 2)): 27/40 ≈ 0.675
      ├── Some((4, 3)): 14/26 ≈ 0.538
      ├── Some((4, 4)): 11/22 ≈ 0.500
      ├── Some((4, 5)): 14/26 ≈ 0.538
      ├── Some((4, 6)): 16/28 ≈ 0.571
      ├── Some((4, 7)): 10/21 ≈ 0.476
      └── Some((4, 8)): 7/18 ≈ 0.389
    ├── Some((1, 5)): 119/222 ≈ 0.536
      ├── Some((5, 0)): 13/24 ≈ 0.542
      ├── Some((5, 1)): 15/27 ≈ 0.556
      ├── Some((5, 2)): 15/27 ≈ 0.556
      ├── Some((5, 3)): 15/27 ≈ 0.556
      ├── Some((5, 4)): 12/23 ≈ 0.522
      ├── Some((5, 5)): 17/29 ≈ 0.586
      ├── Some((5, 6)): 7/17 ≈ 0.412
      ├── Some((5, 7)): 13/24 ≈ 0.542
      └── Some((5, 8)): 12/23 ≈ 0.522
    ├── Some((1, 6)): 66/142 ≈ 0.465
      ├── Some((6, 0)): 3/11 ≈ 0.273
      ├── Some((6, 1)): 3/11 ≈ 0.273
      ├── Some((6, 2)): 6/14 ≈ 0.429
      ├── Some((6, 3)): 15/24 ≈ 0.625
      ├── Some((6, 4)): 6/14 ≈ 0.429
      ├── Some((6, 5)): 11/20 ≈ 0.550
      ├── Some((6, 6)): 4/12 ≈ 0.333
      ├── Some((6, 7)): 6/15 ≈ 0.400
      └── Some((6, 8)): 11/20 ≈ 0.550
    ├── Some((1, 7)): 171/298 ≈ 0.574
      ├── Some((7, 0)): 31/47 ≈ 0.660
      ├── Some((7, 1)): 16/30 ≈ 0.533
      ├── Some((7, 2)): 29/45 ≈ 0.644
      ├── Some((7, 3)): 18/32 ≈ 0.562
      ├── Some((7, 4)): 10/23 ≈ 0.435
      ├── Some((7, 5)): 26/41 ≈ 0.634
      ├── Some((7, 6)): 27/42 ≈ 0.643
      ├── Some((7, 7)): 7/19 ≈ 0.368
      └── Some((7, 8)): 6/18 ≈ 0.333
    └── Some((1, 8)): 74/154 ≈ 0.481
      ├── Some((8, 0)): 13/24 ≈ 0.542
      ├── Some((8, 1)): 3/12 ≈ 0.250
      ├── Some((8, 2)): 3/12 ≈ 0.250
      ├── Some((8, 4)): 19/30 ≈ 0.633
      ├── Some((8, 5)): 13/24 ≈ 0.542
      ├── Some((8, 6)): 10/20 ≈ 0.500
      ├── Some((8, 7)): 8/18 ≈ 0.444
      └── Some((8, 8)): 4/13 ≈ 0.308
  ├── Some((3, 2)): 921/1765 ≈ 0.522
    ├── Some((2, 0)): 105/201 ≈ 0.522
      ├── Some((0, 0)): 10/20 ≈ 0.500
      ├── Some((0, 1)): 16/27 ≈ 0.593
      ├── Some((0, 2)): 9/19 ≈ 0.474
      ├── Some((0, 3)): 9/19 ≈ 0.474
      ├── Some((0, 4)): 14/25 ≈ 0.560
      ├── Some((0, 5)): 10/21 ≈ 0.476
      ├── Some((0, 6)): 20/31 ≈ 0.645
      ├── Some((0, 7)): 10/21 ≈ 0.476
      └── Some((0, 8)): 7/17 ≈ 0.412
    ├── Some((2, 1)): 134/244 ≈ 0.549
      ├── Some((1, 0)): 12/24 ≈ 0.500
      ├── Some((1, 1)): 16/29 ≈ 0.552
      ├── Some((1, 2)): 4/15 ≈ 0.267
      ├── Some((1, 3)): 9/21 ≈ 0.429
      ├── Some((1, 4)): 5/16 ≈ 0.312
      ├── Some((1, 5)): 19/32 ≈ 0.594
      ├── Some((1, 6)): 1/10 ≈ 0.100
      ├── Some((1, 7)): 32/46 ≈ 0.696
      └── Some((1, 8)): 36/50 ≈ 0.720
    ├── Some((2, 2)): 121/224 ≈ 0.540
      ├── Some((2, 0)): 10/22 ≈ 0.455
      ├── Some((2, 1)): 17/30 ≈ 0.567
      ├── Some((2, 3)): 16/29 ≈ 0.552
      ├── Some((2, 4)): 14/27 ≈ 0.519
      ├── Some((2, 5)): 19/33 ≈ 0.576
      ├── Some((2, 6)): 10/22 ≈ 0.455
      ├── Some((2, 7)): 24/38 ≈ 0.632
      └── Some((2, 8)): 10/22 ≈ 0.455
    ├── Some((2, 3)): 80/163 ≈ 0.491
      ├── Some((3, 0)): 8/18 ≈ 0.444
      ├── Some((3, 1)): 17/28 ≈ 0.607
      ├── Some((3, 3)): 20/31 ≈ 0.645
      ├── Some((3, 4)): 7/17 ≈ 0.412
      ├── Some((3, 5)): 3/12 ≈ 0.250
      ├── Some((3, 6)): 7/17 ≈ 0.412
      ├── Some((3, 7)): 7/17 ≈ 0.412
      └── Some((3, 8)): 11/22 ≈ 0.500
    ├── Some((2, 4)): 45/108 ≈ 0.417
      ├── Some((4, 0)): 8/15 ≈ 0.533
      ├── Some((4, 1)): 2/9 ≈ 0.222
      ├── Some((4, 2)): 3/10 ≈ 0.300
      ├── Some((4, 3)): 6/13 ≈ 0.462
      ├── Some((4, 4)): 9/16 ≈ 0.562
      ├── Some((4, 5)): 5/12 ≈ 0.417
      ├── Some((4, 6)): 1/7 ≈ 0.143
      ├── Some((4, 7)): 5/12 ≈ 0.417
      └── Some((4, 8)): 6/13 ≈ 0.462
    ├── Some((2, 5)): 70/147 ≈ 0.476
      ├── Some((5, 0)): 13/22 ≈ 0.591
      ├── Some((5, 1)): 4/12 ≈ 0.333
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 7/15 ≈ 0.467
      ├── Some((5, 4)): 10/19 ≈ 0.526
      ├── Some((5, 5)): 10/19 ≈ 0.526
      ├── Some((5, 6)): 10/19 ≈ 0.526
      ├── Some((5, 7)): 2/10 ≈ 0.200
      └── Some((5, 8)): 7/15 ≈ 0.467
    ├── Some((2, 6)): 165/289 ≈ 0.571
      ├── Some((6, 0)): 30/45 ≈ 0.667
      ├── Some((6, 1)): 16/30 ≈ 0.533
      ├── Some((6, 2)): 24/38 ≈ 0.632
      ├── Some((6, 3)): 11/24 ≈ 0.458
      ├── Some((6, 4)): 15/28 ≈ 0.536
      ├── Some((6, 5)): 13/26 ≈ 0.500
      ├── Some((6, 6)): 18/32 ≈ 0.562
      ├── Some((6, 7)): 11/24 ≈ 0.458
      └── Some((6, 8)): 26/41 ≈ 0.634
    ├── Some((2, 7)): 108/205 ≈ 0.527
      ├── Some((7, 0)): 13/24 ≈ 0.542
      ├── Some((7, 1)): 11/21 ≈ 0.524
      ├── Some((7, 2)): 14/25 ≈ 0.560
      ├── Some((7, 3)): 18/29 ≈ 0.621
      ├── Some((7, 4)): 13/24 ≈ 0.542
      ├── Some((7, 5)): 12/23 ≈ 0.522
      ├── Some((7, 6)): 5/15 ≈ 0.333
      ├── Some((7, 7)): 8/18 ≈ 0.444
      └── Some((7, 8)): 14/25 ≈ 0.560
    └── Some((2, 8)): 93/183 ≈ 0.508
      ├── Some((8, 0)): 8/19 ≈ 0.421
      ├── Some((8, 1)): 12/23 ≈ 0.522
      ├── Some((8, 2)): 17/29 ≈ 0.586
      ├── Some((8, 4)): 16/28 ≈ 0.571
      ├── Some((8, 5)): 3/12 ≈ 0.250
      ├── Some((8, 6)): 11/22 ≈ 0.500
      ├── Some((8, 7)): 19/31 ≈ 0.613
      └── Some((8, 8)): 7/18 ≈ 0.389
  ├── Some((3, 3)): 903/1734 ≈ 0.521
    ├── Some((3, 0)): 163/292 ≈ 0.558
      ├── Some((0, 0)): 14/28 ≈ 0.500
      ├── Some((0, 1)): 16/30 ≈ 0.533
      ├── Some((0, 2)): 10/23 ≈ 0.435
      ├── Some((0, 3)): 29/45 ≈ 0.644
      ├── Some((0, 4)): 23/38 ≈ 0.605
      ├── Some((0, 5)): 16/30 ≈ 0.533
      ├── Some((0, 6)): 8/21 ≈ 0.381
      ├── Some((0, 7)): 27/42 ≈ 0.643
      └── Some((0, 8)): 19/34 ≈ 0.559
    ├── Some((3, 1)): 81/168 ≈ 0.482
      ├── Some((1, 0)): 14/24 ≈ 0.583
      ├── Some((1, 1)): 10/20 ≈ 0.500
      ├── Some((1, 2)): 7/16 ≈ 0.438
      ├── Some((1, 3)): 10/20 ≈ 0.500
      ├── Some((1, 4)): 4/13 ≈ 0.308
      ├── Some((1, 5)): 19/29 ≈ 0.655
      ├── Some((1, 6)): 5/14 ≈ 0.357
      ├── Some((1, 7)): 3/12 ≈ 0.250
      └── Some((1, 8)): 9/19 ≈ 0.474
    ├── Some((3, 2)): 74/157 ≈ 0.471
      ├── Some((2, 0)): 3/11 ≈ 0.273
      ├── Some((2, 1)): 3/11 ≈ 0.273
      ├── Some((2, 2)): 13/23 ≈ 0.565
      ├── Some((2, 3)): 2/10 ≈ 0.200
      ├── Some((2, 4)): 12/22 ≈ 0.545
      ├── Some((2, 5)): 9/18 ≈ 0.500
      ├── Some((2, 6)): 9/18 ≈ 0.500
      ├── Some((2, 7)): 12/22 ≈ 0.545
      └── Some((2, 8)): 11/21 ≈ 0.524
    ├── Some((3, 4)): 127/239 ≈ 0.531
      ├── Some((4, 0)): 21/34 ≈ 0.618
      ├── Some((4, 1)): 9/21 ≈ 0.429
      ├── Some((4, 2)): 24/37 ≈ 0.649
      ├── Some((4, 3)): 11/23 ≈ 0.478
      ├── Some((4, 4)): 17/30 ≈ 0.567
      ├── Some((4, 5)): 14/27 ≈ 0.519
      ├── Some((4, 6)): 7/18 ≈ 0.389
      ├── Some((4, 7)): 18/31 ≈ 0.581
      └── Some((4, 8)): 6/17 ≈ 0.353
    ├── Some((3, 5)): 92/186 ≈ 0.495
      ├── Some((5, 0)): 9/19 ≈ 0.474
      ├── Some((5, 1)): 15/26 ≈ 0.577
      ├── Some((5, 2)): 9/19 ≈ 0.474
      ├── Some((5, 3)): 4/13 ≈ 0.308
      ├── Some((5, 4)): 11/21 ≈ 0.524
      ├── Some((5, 5)): 13/24 ≈ 0.542
      ├── Some((5, 6)): 12/23 ≈ 0.522
      ├── Some((5, 7)): 8/18 ≈ 0.444
      └── Some((5, 8)): 11/22 ≈ 0.500
    ├── Some((3, 6)): 150/273 ≈ 0.549
      ├── Some((6, 0)): 8/20 ≈ 0.400
      ├── Some((6, 1)): 7/19 ≈ 0.368
      ├── Some((6, 2)): 11/24 ≈ 0.458
      ├── Some((6, 3)): 25/40 ≈ 0.625
      ├── Some((6, 4)): 9/22 ≈ 0.409
      ├── Some((6, 5)): 20/34 ≈ 0.588
      ├── Some((6, 6)): 32/47 ≈ 0.681
      ├── Some((6, 7)): 22/37 ≈ 0.595
      └── Some((6, 8)): 15/29 ≈ 0.517
    ├── Some((3, 7)): 105/205 ≈ 0.512
      ├── Some((7, 0)): 12/23 ≈ 0.522
      ├── Some((7, 1)): 11/22 ≈ 0.500
      ├── Some((7, 2)): 6/16 ≈ 0.375
      ├── Some((7, 3)): 12/23 ≈ 0.522
      ├── Some((7, 4)): 9/20 ≈ 0.450
      ├── Some((7, 5)): 16/27 ≈ 0.593
      ├── Some((7, 6)): 9/20 ≈ 0.450
      ├── Some((7, 7)): 19/31 ≈ 0.613
      └── Some((7, 8)): 11/22 ≈ 0.500
    └── Some((3, 8)): 110/213 ≈ 0.516
      ├── Some((8, 0)): 13/26 ≈ 0.500
      ├── Some((8, 1)): 18/31 ≈ 0.581
      ├── Some((8, 2)): 5/16 ≈ 0.312
      ├── Some((8, 4)): 17/30 ≈ 0.567
      ├── Some((8, 5)): 11/23 ≈ 0.478
      ├── Some((8, 6)): 14/27 ≈ 0.519
      ├── Some((8, 7)): 13/26 ≈ 0.500
      └── Some((8, 8)): 19/33 ≈ 0.576
  ├── Some((3, 4)): 1439/2653 ≈ 0.542
    ├── Some((4, 0)): 135/258 ≈ 0.523
      ├── Some((0, 0)): 18/33 ≈ 0.545
      ├── Some((0, 1)): 6/18 ≈ 0.333
      ├── Some((0, 2)): 12/25 ≈ 0.480
      ├── Some((0, 3)): 10/23 ≈ 0.435
      ├── Some((0, 4)): 19/34 ≈ 0.559
      ├── Some((0, 5)): 2/12 ≈ 0.167
      ├── Some((0, 6)): 19/34 ≈ 0.559
      ├── Some((0, 7)): 17/31 ≈ 0.548
      └── Some((0, 8)): 31/47 ≈ 0.660
    ├── Some((4, 1)): 210/370 ≈ 0.568
      ├── Some((1, 0)): 30/49 ≈ 0.612
      ├── Some((1, 1)): 19/36 ≈ 0.528
      ├── Some((1, 2)): 21/38 ≈ 0.553
      ├── Some((1, 3)): 17/34 ≈ 0.500
      ├── Some((1, 4)): 37/57 ≈ 0.649
      ├── Some((1, 5)): 21/38 ≈ 0.553
      ├── Some((1, 6)): 14/30 ≈ 0.467
      ├── Some((1, 7)): 32/51 ≈ 0.627
      └── Some((1, 8)): 19/36 ≈ 0.528
    ├── Some((4, 2)): 258/441 ≈ 0.585
      ├── Some((2, 0)): 28/48 ≈ 0.583
      ├── Some((2, 1)): 34/55 ≈ 0.618
      ├── Some((2, 2)): 35/57 ≈ 0.614
      ├── Some((2, 3)): 37/59 ≈ 0.627
      ├── Some((2, 4)): 13/30 ≈ 0.433
      ├── Some((2, 5)): 13/30 ≈ 0.433
      ├── Some((2, 6)): 31/52 ≈ 0.596
      ├── Some((2, 7)): 46/69 ≈ 0.667
      └── Some((2, 8)): 21/40 ≈ 0.525
    ├── Some((4, 3)): 202/358 ≈ 0.564
      ├── Some((3, 0)): 18/36 ≈ 0.500
      ├── Some((3, 1)): 27/47 ≈ 0.574
      ├── Some((3, 2)): 21/40 ≈ 0.525
      ├── Some((3, 3)): 19/37 ≈ 0.514
      ├── Some((3, 5)): 39/61 ≈ 0.639
      ├── Some((3, 6)): 15/33 ≈ 0.455
      ├── Some((3, 7)): 33/54 ≈ 0.611
      └── Some((3, 8)): 29/49 ≈ 0.592
    ├── Some((4, 4)): 109/218 ≈ 0.500
      ├── Some((4, 0)): 7/19 ≈ 0.368
      ├── Some((4, 1)): 14/28 ≈ 0.500
      ├── Some((4, 2)): 13/27 ≈ 0.481
      ├── Some((4, 3)): 18/32 ≈ 0.562
      ├── Some((4, 5)): 22/37 ≈ 0.595
      ├── Some((4, 6)): 8/20 ≈ 0.400
      ├── Some((4, 7)): 10/23 ≈ 0.435
      └── Some((4, 8)): 17/31 ≈ 0.548
    ├── Some((4, 5)): 120/235 ≈ 0.511
      ├── Some((5, 0)): 6/18 ≈ 0.333
      ├── Some((5, 1)): 10/22 ≈ 0.455
      ├── Some((5, 2)): 13/26 ≈ 0.500
      ├── Some((5, 3)): 15/28 ≈ 0.536
      ├── Some((5, 4)): 12/25 ≈ 0.480
      ├── Some((5, 5)): 30/45 ≈ 0.667
      ├── Some((5, 6)): 15/28 ≈ 0.536
      ├── Some((5, 7)): 3/13 ≈ 0.231
      └── Some((5, 8)): 16/29 ≈ 0.552
    ├── Some((4, 6)): 133/255 ≈ 0.522
      ├── Some((6, 0)): 11/24 ≈ 0.458
      ├── Some((6, 1)): 14/28 ≈ 0.500
      ├── Some((6, 2)): 18/32 ≈ 0.562
      ├── Some((6, 3)): 8/21 ≈ 0.381
      ├── Some((6, 4)): 2/12 ≈ 0.167
      ├── Some((6, 5)): 18/32 ≈ 0.562
      ├── Some((6, 6)): 31/47 ≈ 0.660
      ├── Some((6, 7)): 14/28 ≈ 0.500
      └── Some((6, 8)): 16/30 ≈ 0.533
    ├── Some((4, 7)): 105/212 ≈ 0.495
      ├── Some((7, 0)): 5/15 ≈ 0.333
      ├── Some((7, 1)): 12/24 ≈ 0.500
      ├── Some((7, 2)): 14/26 ≈ 0.538
      ├── Some((7, 3)): 14/26 ≈ 0.538
      ├── Some((7, 4)): 20/33 ≈ 0.606
      ├── Some((7, 5)): 8/19 ≈ 0.421
      ├── Some((7, 6)): 11/23 ≈ 0.478
      ├── Some((7, 7)): 11/23 ≈ 0.478
      └── Some((7, 8)): 10/22 ≈ 0.455
    └── Some((4, 8)): 166/305 ≈ 0.544
      ├── Some((8, 0)): 23/41 ≈ 0.561
      ├── Some((8, 1)): 10/25 ≈ 0.400
      ├── Some((8, 2)): 7/21 ≈ 0.333
      ├── Some((8, 4)): 11/27 ≈ 0.407
      ├── Some((8, 5)): 30/49 ≈ 0.612
      ├── Some((8, 6)): 19/37 ≈ 0.514
      ├── Some((8, 7)): 29/48 ≈ 0.604
      └── Some((8, 8)): 36/56 ≈ 0.643
  ├── Some((3, 5)): 717/1410 ≈ 0.509
    ├── Some((5, 0)): 85/165 ≈ 0.515
      ├── Some((0, 0)): 12/21 ≈ 0.571
      ├── Some((0, 1)): 10/19 ≈ 0.526
      ├── Some((0, 2)): 7/16 ≈ 0.438
      ├── Some((0, 3)): 9/18 ≈ 0.500
      ├── Some((0, 4)): 16/25 ≈ 0.640
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 12/21 ≈ 0.571
      ├── Some((0, 7)): 1/8 ≈ 0.125
      └── Some((0, 8)): 9/18 ≈ 0.500
    ├── Some((5, 1)): 55/119 ≈ 0.462
      ├── Some((1, 0)): 6/13 ≈ 0.462
      ├── Some((1, 1)): 3/10 ≈ 0.300
      ├── Some((1, 2)): 5/12 ≈ 0.417
      ├── Some((1, 3)): 9/16 ≈ 0.562
      ├── Some((1, 4)): 12/19 ≈ 0.632
      ├── Some((1, 5)): 7/14 ≈ 0.500
      ├── Some((1, 6)): 4/11 ≈ 0.364
      ├── Some((1, 7)): 7/14 ≈ 0.500
      └── Some((1, 8)): 2/9 ≈ 0.222
    ├── Some((5, 2)): 89/170 ≈ 0.524
      ├── Some((2, 0)): 15/24 ≈ 0.625
      ├── Some((2, 1)): 9/18 ≈ 0.500
      ├── Some((2, 2)): 6/14 ≈ 0.429
      ├── Some((2, 3)): 9/18 ≈ 0.500
      ├── Some((2, 4)): 9/18 ≈ 0.500
      ├── Some((2, 5)): 13/22 ≈ 0.591
      ├── Some((2, 6)): 9/18 ≈ 0.500
      ├── Some((2, 7)): 12/21 ≈ 0.571
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((5, 3)): 88/169 ≈ 0.521
      ├── Some((3, 0)): 16/27 ≈ 0.593
      ├── Some((3, 1)): 6/16 ≈ 0.375
      ├── Some((3, 2)): 11/21 ≈ 0.524
      ├── Some((3, 3)): 12/22 ≈ 0.545
      ├── Some((3, 4)): 14/24 ≈ 0.583
      ├── Some((3, 6)): 3/12 ≈ 0.250
      ├── Some((3, 7)): 7/17 ≈ 0.412
      └── Some((3, 8)): 18/29 ≈ 0.621
    ├── Some((5, 4)): 81/159 ≈ 0.509
      ├── Some((4, 0)): 12/21 ≈ 0.571
      ├── Some((4, 1)): 6/14 ≈ 0.429
      ├── Some((4, 2)): 13/22 ≈ 0.591
      ├── Some((4, 3)): 6/14 ≈ 0.429
      ├── Some((4, 4)): 8/17 ≈ 0.471
      ├── Some((4, 5)): 10/19 ≈ 0.526
      ├── Some((4, 6)): 11/20 ≈ 0.550
      ├── Some((4, 7)): 6/14 ≈ 0.429
      └── Some((4, 8)): 8/17 ≈ 0.471
    ├── Some((5, 5)): 64/133 ≈ 0.481
      ├── Some((5, 0)): 11/20 ≈ 0.550
      ├── Some((5, 1)): 6/15 ≈ 0.400
      ├── Some((5, 2)): 9/18 ≈ 0.500
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 4/12 ≈ 0.333
      ├── Some((5, 6)): 3/11 ≈ 0.273
      ├── Some((5, 7)): 15/24 ≈ 0.625
      └── Some((5, 8)): 10/19 ≈ 0.526
    ├── Some((5, 6)): 107/197 ≈ 0.543
      ├── Some((6, 0)): 9/19 ≈ 0.474
      ├── Some((6, 1)): 16/26 ≈ 0.615
      ├── Some((6, 2)): 6/15 ≈ 0.400
      ├── Some((6, 3)): 8/18 ≈ 0.444
      ├── Some((6, 4)): 17/27 ≈ 0.630
      ├── Some((6, 5)): 20/31 ≈ 0.645
      ├── Some((6, 6)): 7/17 ≈ 0.412
      ├── Some((6, 7)): 11/21 ≈ 0.524
      └── Some((6, 8)): 12/22 ≈ 0.545
    ├── Some((5, 7)): 65/135 ≈ 0.481
      ├── Some((7, 0)): 8/16 ≈ 0.500
      ├── Some((7, 1)): 3/10 ≈ 0.300
      ├── Some((7, 2)): 7/15 ≈ 0.467
      ├── Some((7, 3)): 9/17 ≈ 0.529
      ├── Some((7, 4)): 5/13 ≈ 0.385
      ├── Some((7, 5)): 12/20 ≈ 0.600
      ├── Some((7, 6)): 8/16 ≈ 0.500
      ├── Some((7, 7)): 2/9 ≈ 0.222
      └── Some((7, 8)): 10/18 ≈ 0.556
    └── Some((5, 8)): 83/162 ≈ 0.512
      ├── Some((8, 0)): 9/19 ≈ 0.474
      ├── Some((8, 1)): 15/25 ≈ 0.600
      ├── Some((8, 2)): 7/16 ≈ 0.438
      ├── Some((8, 4)): 8/17 ≈ 0.471
      ├── Some((8, 5)): 8/18 ≈ 0.444
      ├── Some((8, 6)): 10/20 ≈ 0.500
      ├── Some((8, 7)): 11/21 ≈ 0.524
      └── Some((8, 8)): 15/25 ≈ 0.600
  ├── Some((3, 6)): 911/1748 ≈ 0.521
    ├── Some((6, 0)): 192/327 ≈ 0.587
      ├── Some((0, 0)): 8/21 ≈ 0.381
      ├── Some((0, 1)): 22/37 ≈ 0.595
      ├── Some((0, 2)): 16/30 ≈ 0.533
      ├── Some((0, 3)): 25/41 ≈ 0.610
      ├── Some((0, 4)): 27/43 ≈ 0.628
      ├── Some((0, 5)): 18/33 ≈ 0.545
      ├── Some((0, 6)): 36/52 ≈ 0.692
      ├── Some((0, 7)): 20/35 ≈ 0.571
      └── Some((0, 8)): 19/34 ≈ 0.559
    ├── Some((6, 1)): 89/177 ≈ 0.503
      ├── Some((1, 0)): 14/24 ≈ 0.583
      ├── Some((1, 1)): 16/26 ≈ 0.615
      ├── Some((1, 2)): 8/18 ≈ 0.444
      ├── Some((1, 3)): 8/18 ≈ 0.444
      ├── Some((1, 4)): 7/16 ≈ 0.438
      ├── Some((1, 5)): 9/19 ≈ 0.474
      ├── Some((1, 6)): 10/20 ≈ 0.500
      ├── Some((1, 7)): 9/19 ≈ 0.474
      └── Some((1, 8)): 7/16 ≈ 0.438
    ├── Some((6, 2)): 86/172 ≈ 0.500
      ├── Some((2, 0)): 4/13 ≈ 0.308
      ├── Some((2, 1)): 12/22 ≈ 0.545
      ├── Some((2, 2)): 12/22 ≈ 0.545
      ├── Some((2, 3)): 17/27 ≈ 0.630
      ├── Some((2, 4)): 7/16 ≈ 0.438
      ├── Some((2, 5)): 6/15 ≈ 0.400
      ├── Some((2, 6)): 8/18 ≈ 0.444
      ├── Some((2, 7)): 18/28 ≈ 0.643
      └── Some((2, 8)): 2/10 ≈ 0.200
    ├── Some((6, 3)): 79/161 ≈ 0.491
      ├── Some((3, 0)): 9/19 ≈ 0.474
      ├── Some((3, 1)): 13/24 ≈ 0.542
      ├── Some((3, 2)): 12/22 ≈ 0.545
      ├── Some((3, 3)): 7/17 ≈ 0.412
      ├── Some((3, 4)): 9/19 ≈ 0.474
      ├── Some((3, 5)): 11/21 ≈ 0.524
      ├── Some((3, 7)): 8/18 ≈ 0.444
      └── Some((3, 8)): 10/20 ≈ 0.500
    ├── Some((6, 4)): 90/178 ≈ 0.506
      ├── Some((4, 0)): 11/21 ≈ 0.524
      ├── Some((4, 1)): 14/24 ≈ 0.583
      ├── Some((4, 2)): 15/25 ≈ 0.600
      ├── Some((4, 3)): 10/20 ≈ 0.500
      ├── Some((4, 4)): 3/12 ≈ 0.250
      ├── Some((4, 5)): 17/27 ≈ 0.630
      ├── Some((4, 6)): 12/22 ≈ 0.545
      ├── Some((4, 7)): 4/13 ≈ 0.308
      └── Some((4, 8)): 4/13 ≈ 0.308
    ├── Some((6, 5)): 48/113 ≈ 0.425
      ├── Some((5, 0)): 4/11 ≈ 0.364
      ├── Some((5, 1)): 4/11 ≈ 0.364
      ├── Some((5, 2)): 9/17 ≈ 0.529
      ├── Some((5, 3)): 3/10 ≈ 0.300
      ├── Some((5, 4)): 7/14 ≈ 0.500
      ├── Some((5, 5)): 5/12 ≈ 0.417
      ├── Some((5, 6)): 5/12 ≈ 0.417
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 7/14 ≈ 0.500
    ├── Some((6, 6)): 120/223 ≈ 0.538
      ├── Some((6, 0)): 17/31 ≈ 0.548
      ├── Some((6, 1)): 21/35 ≈ 0.600
      ├── Some((6, 2)): 10/22 ≈ 0.455
      ├── Some((6, 3)): 3/13 ≈ 0.231
      ├── Some((6, 4)): 12/25 ≈ 0.480
      ├── Some((6, 5)): 10/22 ≈ 0.455
      ├── Some((6, 7)): 27/41 ≈ 0.659
      └── Some((6, 8)): 19/33 ≈ 0.576
    ├── Some((6, 7)): 83/168 ≈ 0.494
      ├── Some((7, 0)): 10/20 ≈ 0.500
      ├── Some((7, 1)): 12/22 ≈ 0.545
      ├── Some((7, 2)): 3/11 ≈ 0.273
      ├── Some((7, 3)): 9/18 ≈ 0.500
      ├── Some((7, 4)): 6/15 ≈ 0.400
      ├── Some((7, 5)): 9/19 ≈ 0.474
      ├── Some((7, 6)): 20/30 ≈ 0.667
      ├── Some((7, 7)): 3/11 ≈ 0.273
      └── Some((7, 8)): 11/21 ≈ 0.524
    └── Some((6, 8)): 123/228 ≈ 0.539
      ├── Some((8, 0)): 17/30 ≈ 0.567
      ├── Some((8, 1)): 20/34 ≈ 0.588
      ├── Some((8, 2)): 14/27 ≈ 0.519
      ├── Some((8, 4)): 5/16 ≈ 0.312
      ├── Some((8, 5)): 24/38 ≈ 0.632
      ├── Some((8, 6)): 18/32 ≈ 0.562
      ├── Some((8, 7)): 9/21 ≈ 0.429
      └── Some((8, 8)): 16/29 ≈ 0.552
  ├── Some((3, 7)): 1230/2297 ≈ 0.535
    ├── Some((7, 0)): 81/171 ≈ 0.474
      ├── Some((0, 0)): 7/17 ≈ 0.412
      ├── Some((0, 1)): 11/21 ≈ 0.524
      ├── Some((0, 2)): 16/27 ≈ 0.593
      ├── Some((0, 3)): 9/19 ≈ 0.474
      ├── Some((0, 4)): 2/11 ≈ 0.182
      ├── Some((0, 5)): 17/28 ≈ 0.607
      ├── Some((0, 6)): 7/17 ≈ 0.412
      ├── Some((0, 7)): 3/12 ≈ 0.250
      └── Some((0, 8)): 8/18 ≈ 0.444
    ├── Some((7, 1)): 161/293 ≈ 0.549
      ├── Some((1, 0)): 11/24 ≈ 0.458
      ├── Some((1, 1)): 25/41 ≈ 0.610
      ├── Some((1, 2)): 26/42 ≈ 0.619
      ├── Some((1, 3)): 21/36 ≈ 0.583
      ├── Some((1, 4)): 8/21 ≈ 0.381
      ├── Some((1, 5)): 25/41 ≈ 0.610
      ├── Some((1, 6)): 10/23 ≈ 0.435
      ├── Some((1, 7)): 21/36 ≈ 0.583
      └── Some((1, 8)): 14/28 ≈ 0.500
    ├── Some((7, 2)): 80/169 ≈ 0.473
      ├── Some((2, 0)): 4/13 ≈ 0.308
      ├── Some((2, 1)): 6/16 ≈ 0.375
      ├── Some((2, 2)): 7/17 ≈ 0.412
      ├── Some((2, 3)): 3/12 ≈ 0.250
      ├── Some((2, 4)): 7/17 ≈ 0.412
      ├── Some((2, 5)): 11/21 ≈ 0.524
      ├── Some((2, 6)): 4/13 ≈ 0.308
      ├── Some((2, 7)): 23/34 ≈ 0.676
      └── Some((2, 8)): 14/25 ≈ 0.560
    ├── Some((7, 3)): 192/338 ≈ 0.568
      ├── Some((3, 0)): 16/33 ≈ 0.485
      ├── Some((3, 1)): 23/41 ≈ 0.561
      ├── Some((3, 2)): 38/59 ≈ 0.644
      ├── Some((3, 3)): 31/51 ≈ 0.608
      ├── Some((3, 4)): 16/33 ≈ 0.485
      ├── Some((3, 5)): 25/44 ≈ 0.568
      ├── Some((3, 6)): 36/56 ≈ 0.643
      └── Some((3, 8)): 6/20 ≈ 0.300
    ├── Some((7, 4)): 100/200 ≈ 0.500
      ├── Some((4, 0)): 4/14 ≈ 0.286
      ├── Some((4, 1)): 1/10 ≈ 0.100
      ├── Some((4, 2)): 12/23 ≈ 0.522
      ├── Some((4, 3)): 12/24 ≈ 0.500
      ├── Some((4, 4)): 26/39 ≈ 0.667
      ├── Some((4, 5)): 15/27 ≈ 0.556
      ├── Some((4, 6)): 6/16 ≈ 0.375
      ├── Some((4, 7)): 12/24 ≈ 0.500
      └── Some((4, 8)): 11/22 ≈ 0.500
    ├── Some((7, 5)): 167/301 ≈ 0.555
      ├── Some((5, 0)): 13/27 ≈ 0.481
      ├── Some((5, 1)): 22/38 ≈ 0.579
      ├── Some((5, 2)): 8/21 ≈ 0.381
      ├── Some((5, 3)): 17/32 ≈ 0.531
      ├── Some((5, 4)): 21/36 ≈ 0.583
      ├── Some((5, 5)): 27/43 ≈ 0.628
      ├── Some((5, 6)): 21/37 ≈ 0.568
      ├── Some((5, 7)): 9/22 ≈ 0.409
      └── Some((5, 8)): 28/44 ≈ 0.636
    ├── Some((7, 6)): 104/207 ≈ 0.502
      ├── Some((6, 0)): 5/16 ≈ 0.312
      ├── Some((6, 1)): 16/28 ≈ 0.571
      ├── Some((6, 2)): 7/18 ≈ 0.389
      ├── Some((6, 3)): 11/23 ≈ 0.478
      ├── Some((6, 4)): 24/37 ≈ 0.649
      ├── Some((6, 5)): 14/26 ≈ 0.538
      ├── Some((6, 6)): 16/28 ≈ 0.571
      ├── Some((6, 7)): 8/19 ≈ 0.421
      └── Some((6, 8)): 2/11 ≈ 0.182
    ├── Some((7, 7)): 137/257 ≈ 0.533
      ├── Some((7, 0)): 19/35 ≈ 0.543
      ├── Some((7, 1)): 22/38 ≈ 0.579
      ├── Some((7, 2)): 3/15 ≈ 0.200
      ├── Some((7, 3)): 10/24 ≈ 0.417
      ├── Some((7, 4)): 37/55 ≈ 0.673
      ├── Some((7, 5)): 7/20 ≈ 0.350
      ├── Some((7, 6)): 8/21 ≈ 0.381
      └── Some((7, 8)): 30/48 ≈ 0.625
    └── Some((7, 8)): 207/360 ≈ 0.575
      ├── Some((8, 0)): 40/62 ≈ 0.645
      ├── Some((8, 1)): 17/35 ≈ 0.486
      ├── Some((8, 2)): 20/38 ≈ 0.526
      ├── Some((8, 4)): 30/50 ≈ 0.600
      ├── Some((8, 5)): 36/57 ≈ 0.632
      ├── Some((8, 6)): 35/56 ≈ 0.625
      ├── Some((8, 7)): 9/24 ≈ 0.375
      └── Some((8, 8)): 19/37 ≈ 0.514
  └── Some((3, 8)): 1168/2191 ≈ 0.533
    ├── Some((8, 0)): 240/415 ≈ 0.578
      ├── Some((0, 0)): 24/43 ≈ 0.558
      ├── Some((0, 1)): 37/58 ≈ 0.638
      ├── Some((0, 2)): 26/45 ≈ 0.578
      ├── Some((0, 3)): 20/38 ≈ 0.526
      ├── Some((0, 4)): 45/67 ≈ 0.672
      ├── Some((0, 5)): 27/47 ≈ 0.574
      ├── Some((0, 6)): 18/36 ≈ 0.500
      ├── Some((0, 7)): 15/32 ≈ 0.469
      └── Some((0, 8)): 28/48 ≈ 0.583
    ├── Some((8, 1)): 89/187 ≈ 0.476
      ├── Some((1, 0)): 11/22 ≈ 0.500
      ├── Some((1, 1)): 7/18 ≈ 0.389
      ├── Some((1, 2)): 10/21 ≈ 0.476
      ├── Some((1, 3)): 11/22 ≈ 0.500
      ├── Some((1, 4)): 6/16 ≈ 0.375
      ├── Some((1, 5)): 8/19 ≈ 0.421
      ├── Some((1, 6)): 6/16 ≈ 0.375
      ├── Some((1, 7)): 19/31 ≈ 0.613
      └── Some((1, 8)): 10/21 ≈ 0.476
    ├── Some((8, 2)): 136/260 ≈ 0.523
      ├── Some((2, 0)): 10/23 ≈ 0.435
      ├── Some((2, 1)): 37/53 ≈ 0.698
      ├── Some((2, 2)): 18/33 ≈ 0.545
      ├── Some((2, 3)): 13/27 ≈ 0.481
      ├── Some((2, 4)): 17/31 ≈ 0.548
      ├── Some((2, 5)): 9/22 ≈ 0.409
      ├── Some((2, 6)): 12/25 ≈ 0.480
      ├── Some((2, 7)): 4/15 ≈ 0.267
      └── Some((2, 8)): 16/30 ≈ 0.533
    ├── Some((8, 4)): 230/400 ≈ 0.575
      ├── Some((4, 0)): 15/32 ≈ 0.469
      ├── Some((4, 1)): 32/52 ≈ 0.615
      ├── Some((4, 2)): 33/53 ≈ 0.623
      ├── Some((4, 3)): 20/38 ≈ 0.526
      ├── Some((4, 4)): 11/27 ≈ 0.407
      ├── Some((4, 5)): 34/54 ≈ 0.630
      ├── Some((4, 6)): 22/40 ≈ 0.550
      ├── Some((4, 7)): 22/41 ≈ 0.537
      └── Some((4, 8)): 41/62 ≈ 0.661
    ├── Some((8, 5)): 86/182 ≈ 0.473
      ├── Some((5, 0)): 8/18 ≈ 0.444
      ├── Some((5, 1)): 10/21 ≈ 0.476
      ├── Some((5, 2)): 3/12 ≈ 0.250
      ├── Some((5, 3)): 7/17 ≈ 0.412
      ├── Some((5, 4)): 3/12 ≈ 0.250
      ├── Some((5, 5)): 16/28 ≈ 0.571
      ├── Some((5, 6)): 8/19 ≈ 0.421
      ├── Some((5, 7)): 18/30 ≈ 0.600
      └── Some((5, 8)): 13/24 ≈ 0.542
    ├── Some((8, 6)): 132/254 ≈ 0.520
      ├── Some((6, 0)): 10/23 ≈ 0.435
      ├── Some((6, 1)): 19/34 ≈ 0.559
      ├── Some((6, 2)): 6/18 ≈ 0.333
      ├── Some((6, 3)): 12/25 ≈ 0.480
      ├── Some((6, 4)): 8/20 ≈ 0.400
      ├── Some((6, 5)): 10/23 ≈ 0.435
      ├── Some((6, 6)): 22/37 ≈ 0.595
      ├── Some((6, 7)): 12/25 ≈ 0.480
      └── Some((6, 8)): 32/48 ≈ 0.667
    ├── Some((8, 7)): 166/305 ≈ 0.544
      ├── Some((7, 0)): 12/26 ≈ 0.462
      ├── Some((7, 1)): 19/35 ≈ 0.543
      ├── Some((7, 2)): 17/32 ≈ 0.531
      ├── Some((7, 3)): 12/26 ≈ 0.462
      ├── Some((7, 4)): 16/31 ≈ 0.516
      ├── Some((7, 5)): 27/44 ≈ 0.614
      ├── Some((7, 6)): 13/27 ≈ 0.481
      ├── Some((7, 7)): 14/29 ≈ 0.483
      └── Some((7, 8)): 36/54 ≈ 0.667
    └── Some((8, 8)): 89/187 ≈ 0.476
      ├── Some((8, 0)): 16/31 ≈ 0.516
      ├── Some((8, 1)): 11/25 ≈ 0.440
      ├── Some((8, 2)): 4/16 ≈ 0.250
      ├── Some((8, 4)): 14/28 ≈ 0.500
      ├── Some((8, 5)): 16/31 ≈ 0.516
      ├── Some((8, 6)): 20/35 ≈ 0.571
      └── Some((8, 7)): 7/20 ≈ 0.350
├── Some((8, 4)): 13103/24505 ≈ 0.535
  ├── Some((4, 0)): 1219/2314 ≈ 0.527
    ├── Some((0, 0)): 96/197 ≈ 0.487
      ├── Some((0, 1)): 14/27 ≈ 0.519
      ├── Some((0, 2)): 6/17 ≈ 0.353
      ├── Some((0, 3)): 10/22 ≈ 0.455
      ├── Some((0, 4)): 20/34 ≈ 0.588
      ├── Some((0, 5)): 17/30 ≈ 0.567
      ├── Some((0, 6)): 8/20 ≈ 0.400
      ├── Some((0, 7)): 10/22 ≈ 0.455
      └── Some((0, 8)): 11/24 ≈ 0.458
    ├── Some((0, 1)): 163/299 ≈ 0.545
      ├── Some((1, 0)): 9/22 ≈ 0.409
      ├── Some((1, 1)): 25/41 ≈ 0.610
      ├── Some((1, 2)): 13/27 ≈ 0.481
      ├── Some((1, 3)): 11/25 ≈ 0.440
      ├── Some((1, 4)): 23/39 ≈ 0.590
      ├── Some((1, 5)): 13/27 ≈ 0.481
      ├── Some((1, 6)): 29/46 ≈ 0.630
      ├── Some((1, 7)): 15/30 ≈ 0.500
      └── Some((1, 8)): 25/41 ≈ 0.610
    ├── Some((0, 2)): 101/205 ≈ 0.493
      ├── Some((2, 0)): 14/26 ≈ 0.538
      ├── Some((2, 1)): 10/21 ≈ 0.476
      ├── Some((2, 2)): 18/31 ≈ 0.581
      ├── Some((2, 3)): 7/18 ≈ 0.389
      ├── Some((2, 4)): 13/25 ≈ 0.520
      ├── Some((2, 5)): 10/21 ≈ 0.476
      ├── Some((2, 6)): 7/18 ≈ 0.389
      ├── Some((2, 7)): 9/20 ≈ 0.450
      └── Some((2, 8)): 12/24 ≈ 0.500
    ├── Some((0, 3)): 177/320 ≈ 0.553
      ├── Some((3, 0)): 23/39 ≈ 0.590
      ├── Some((3, 1)): 18/34 ≈ 0.529
      ├── Some((3, 2)): 13/28 ≈ 0.464
      ├── Some((3, 3)): 29/46 ≈ 0.630
      ├── Some((3, 4)): 23/40 ≈ 0.575
      ├── Some((3, 5)): 20/36 ≈ 0.556
      ├── Some((3, 6)): 15/30 ≈ 0.500
      ├── Some((3, 7)): 14/29 ≈ 0.483
      └── Some((3, 8)): 21/37 ≈ 0.568
    ├── Some((0, 4)): 133/254 ≈ 0.524
      ├── Some((4, 1)): 22/38 ≈ 0.579
      ├── Some((4, 2)): 16/31 ≈ 0.516
      ├── Some((4, 3)): 11/25 ≈ 0.440
      ├── Some((4, 4)): 14/29 ≈ 0.483
      ├── Some((4, 5)): 14/29 ≈ 0.483
      ├── Some((4, 6)): 8/21 ≈ 0.381
      ├── Some((4, 7)): 29/46 ≈ 0.630
      └── Some((4, 8)): 19/34 ≈ 0.559
    ├── Some((0, 5)): 102/206 ≈ 0.495
      ├── Some((5, 0)): 17/29 ≈ 0.586
      ├── Some((5, 1)): 14/26 ≈ 0.538
      ├── Some((5, 2)): 18/31 ≈ 0.581
      ├── Some((5, 3)): 4/14 ≈ 0.286
      ├── Some((5, 4)): 14/26 ≈ 0.538
      ├── Some((5, 5)): 10/22 ≈ 0.455
      ├── Some((5, 6)): 4/14 ≈ 0.286
      ├── Some((5, 7)): 8/19 ≈ 0.421
      └── Some((5, 8)): 12/24 ≈ 0.500
    ├── Some((0, 6)): 106/212 ≈ 0.500
      ├── Some((6, 0)): 12/24 ≈ 0.500
      ├── Some((6, 1)): 4/14 ≈ 0.286
      ├── Some((6, 2)): 19/32 ≈ 0.594
      ├── Some((6, 3)): 20/33 ≈ 0.606
      ├── Some((6, 4)): 5/15 ≈ 0.333
      ├── Some((6, 5)): 17/30 ≈ 0.567
      ├── Some((6, 6)): 13/25 ≈ 0.520
      ├── Some((6, 7)): 7/18 ≈ 0.389
      └── Some((6, 8)): 9/20 ≈ 0.450
    ├── Some((0, 7)): 119/233 ≈ 0.511
      ├── Some((7, 0)): 9/21 ≈ 0.429
      ├── Some((7, 1)): 16/29 ≈ 0.552
      ├── Some((7, 2)): 8/20 ≈ 0.400
      ├── Some((7, 3)): 17/30 ≈ 0.567
      ├── Some((7, 4)): 14/27 ≈ 0.519
      ├── Some((7, 5)): 16/29 ≈ 0.552
      ├── Some((7, 6)): 11/23 ≈ 0.478
      ├── Some((7, 7)): 16/29 ≈ 0.552
      └── Some((7, 8)): 11/24 ≈ 0.458
    └── Some((0, 8)): 222/387 ≈ 0.574
      ├── Some((8, 0)): 19/38 ≈ 0.500
      ├── Some((8, 1)): 16/34 ≈ 0.471
      ├── Some((8, 2)): 31/52 ≈ 0.596
      ├── Some((8, 3)): 26/46 ≈ 0.565
      ├── Some((8, 5)): 25/45 ≈ 0.556
      ├── Some((8, 6)): 32/54 ≈ 0.593
      ├── Some((8, 7)): 26/46 ≈ 0.565
      └── Some((8, 8)): 47/71 ≈ 0.662
  ├── Some((4, 1)): 1341/2525 ≈ 0.531
    ├── Some((1, 0)): 204/364 ≈ 0.560
      ├── Some((0, 0)): 16/33 ≈ 0.485
      ├── Some((0, 1)): 13/29 ≈ 0.448
      ├── Some((0, 2)): 21/38 ≈ 0.553
      ├── Some((0, 3)): 31/50 ≈ 0.620
      ├── Some((0, 4)): 17/34 ≈ 0.500
      ├── Some((0, 5)): 23/41 ≈ 0.561
      ├── Some((0, 6)): 16/33 ≈ 0.485
      ├── Some((0, 7)): 31/50 ≈ 0.620
      └── Some((0, 8)): 35/55 ≈ 0.636
    ├── Some((1, 1)): 163/302 ≈ 0.540
      ├── Some((1, 0)): 21/39 ≈ 0.538
      ├── Some((1, 2)): 29/48 ≈ 0.604
      ├── Some((1, 3)): 18/35 ≈ 0.514
      ├── Some((1, 4)): 29/48 ≈ 0.604
      ├── Some((1, 5)): 18/35 ≈ 0.514
      ├── Some((1, 6)): 10/25 ≈ 0.400
      ├── Some((1, 7)): 13/29 ≈ 0.448
      └── Some((1, 8)): 24/42 ≈ 0.571
    ├── Some((1, 2)): 163/302 ≈ 0.540
      ├── Some((2, 0)): 14/29 ≈ 0.483
      ├── Some((2, 1)): 18/33 ≈ 0.545
      ├── Some((2, 2)): 18/33 ≈ 0.545
      ├── Some((2, 3)): 14/29 ≈ 0.483
      ├── Some((2, 4)): 22/38 ≈ 0.579
      ├── Some((2, 5)): 21/37 ≈ 0.568
      ├── Some((2, 6)): 24/40 ≈ 0.600
      ├── Some((2, 7)): 14/29 ≈ 0.483
      └── Some((2, 8)): 18/33 ≈ 0.545
    ├── Some((1, 3)): 179/326 ≈ 0.549
      ├── Some((3, 0)): 27/45 ≈ 0.600
      ├── Some((3, 1)): 13/28 ≈ 0.464
      ├── Some((3, 2)): 19/35 ≈ 0.543
      ├── Some((3, 3)): 20/37 ≈ 0.541
      ├── Some((3, 4)): 2/14 ≈ 0.143
      ├── Some((3, 5)): 34/53 ≈ 0.642
      ├── Some((3, 6)): 17/33 ≈ 0.515
      ├── Some((3, 7)): 30/48 ≈ 0.625
      └── Some((3, 8)): 16/32 ≈ 0.500
    ├── Some((1, 4)): 79/172 ≈ 0.459
      ├── Some((4, 0)): 11/23 ≈ 0.478
      ├── Some((4, 2)): 16/28 ≈ 0.571
      ├── Some((4, 3)): 10/22 ≈ 0.455
      ├── Some((4, 4)): 7/18 ≈ 0.389
      ├── Some((4, 5)): 4/14 ≈ 0.286
      ├── Some((4, 6)): 8/19 ≈ 0.421
      ├── Some((4, 7)): 16/29 ≈ 0.552
      └── Some((4, 8)): 7/18 ≈ 0.389
    ├── Some((1, 5)): 127/247 ≈ 0.514
      ├── Some((5, 0)): 12/25 ≈ 0.480
      ├── Some((5, 1)): 11/24 ≈ 0.458
      ├── Some((5, 2)): 14/27 ≈ 0.519
      ├── Some((5, 3)): 20/34 ≈ 0.588
      ├── Some((5, 4)): 9/22 ≈ 0.409
      ├── Some((5, 5)): 14/27 ≈ 0.519
      ├── Some((5, 6)): 20/34 ≈ 0.588
      ├── Some((5, 7)): 10/23 ≈ 0.435
      └── Some((5, 8)): 16/30 ≈ 0.533
    ├── Some((1, 6)): 122/240 ≈ 0.508
      ├── Some((6, 0)): 18/32 ≈ 0.562
      ├── Some((6, 1)): 10/22 ≈ 0.455
      ├── Some((6, 2)): 9/21 ≈ 0.429
      ├── Some((6, 3)): 11/24 ≈ 0.458
      ├── Some((6, 4)): 18/32 ≈ 0.562
      ├── Some((6, 5)): 10/22 ≈ 0.455
      ├── Some((6, 6)): 23/37 ≈ 0.622
      ├── Some((6, 7)): 10/23 ≈ 0.435
      └── Some((6, 8)): 13/26 ≈ 0.500
    ├── Some((1, 7)): 170/313 ≈ 0.543
      ├── Some((7, 0)): 31/49 ≈ 0.633
      ├── Some((7, 1)): 11/25 ≈ 0.440
      ├── Some((7, 2)): 10/24 ≈ 0.417
      ├── Some((7, 3)): 20/36 ≈ 0.556
      ├── Some((7, 4)): 22/39 ≈ 0.564
      ├── Some((7, 5)): 18/34 ≈ 0.529
      ├── Some((7, 6)): 25/42 ≈ 0.595
      ├── Some((7, 7)): 20/36 ≈ 0.556
      └── Some((7, 8)): 12/27 ≈ 0.444
    └── Some((1, 8)): 134/258 ≈ 0.519
      ├── Some((8, 0)): 21/37 ≈ 0.568
      ├── Some((8, 1)): 7/20 ≈ 0.350
      ├── Some((8, 2)): 21/38 ≈ 0.553
      ├── Some((8, 3)): 23/40 ≈ 0.575
      ├── Some((8, 5)): 22/39 ≈ 0.564
      ├── Some((8, 6)): 21/38 ≈ 0.553
      ├── Some((8, 7)): 16/32 ≈ 0.500
      └── Some((8, 8)): 2/13 ≈ 0.154
  ├── Some((4, 2)): 1187/2259 ≈ 0.525
    ├── Some((2, 0)): 194/345 ≈ 0.562
      ├── Some((0, 0)): 17/33 ≈ 0.515
      ├── Some((0, 1)): 38/57 ≈ 0.667
      ├── Some((0, 2)): 13/28 ≈ 0.464
      ├── Some((0, 3)): 15/31 ≈ 0.484
      ├── Some((0, 4)): 14/30 ≈ 0.467
      ├── Some((0, 5)): 19/35 ≈ 0.543
      ├── Some((0, 6)): 24/41 ≈ 0.585
      ├── Some((0, 7)): 31/49 ≈ 0.633
      └── Some((0, 8)): 23/40 ≈ 0.575
    ├── Some((2, 1)): 222/387 ≈ 0.574
      ├── Some((1, 0)): 20/38 ≈ 0.526
      ├── Some((1, 1)): 19/37 ≈ 0.514
      ├── Some((1, 2)): 33/53 ≈ 0.623
      ├── Some((1, 3)): 17/34 ≈ 0.500
      ├── Some((1, 4)): 13/29 ≈ 0.448
      ├── Some((1, 5)): 31/50 ≈ 0.620
      ├── Some((1, 6)): 31/50 ≈ 0.620
      ├── Some((1, 7)): 27/46 ≈ 0.587
      └── Some((1, 8)): 30/49 ≈ 0.612
    ├── Some((2, 2)): 87/182 ≈ 0.478
      ├── Some((2, 0)): 4/14 ≈ 0.286
      ├── Some((2, 1)): 15/28 ≈ 0.536
      ├── Some((2, 3)): 12/24 ≈ 0.500
      ├── Some((2, 4)): 15/28 ≈ 0.536
      ├── Some((2, 5)): 7/18 ≈ 0.389
      ├── Some((2, 6)): 8/20 ≈ 0.400
      ├── Some((2, 7)): 6/17 ≈ 0.353
      └── Some((2, 8)): 19/32 ≈ 0.594
    ├── Some((2, 3)): 80/171 ≈ 0.468
      ├── Some((3, 0)): 10/20 ≈ 0.500
      ├── Some((3, 1)): 10/20 ≈ 0.500
      ├── Some((3, 2)): 17/28 ≈ 0.607
      ├── Some((3, 3)): 5/14 ≈ 0.357
      ├── Some((3, 4)): 7/17 ≈ 0.412
      ├── Some((3, 5)): 6/16 ≈ 0.375
      ├── Some((3, 6)): 6/16 ≈ 0.375
      ├── Some((3, 7)): 11/21 ≈ 0.524
      └── Some((3, 8)): 8/18 ≈ 0.444
    ├── Some((2, 4)): 155/287 ≈ 0.540
      ├── Some((4, 0)): 15/31 ≈ 0.484
      ├── Some((4, 1)): 14/29 ≈ 0.483
      ├── Some((4, 3)): 35/54 ≈ 0.648
      ├── Some((4, 4)): 14/30 ≈ 0.467
      ├── Some((4, 5)): 27/45 ≈ 0.600
      ├── Some((4, 6)): 8/22 ≈ 0.364
      ├── Some((4, 7)): 20/37 ≈ 0.541
      └── Some((4, 8)): 21/38 ≈ 0.553
    ├── Some((2, 5)): 101/204 ≈ 0.495
      ├── Some((5, 0)): 12/24 ≈ 0.500
      ├── Some((5, 1)): 11/22 ≈ 0.500
      ├── Some((5, 2)): 11/22 ≈ 0.500
      ├── Some((5, 3)): 13/25 ≈ 0.520
      ├── Some((5, 4)): 11/22 ≈ 0.500
      ├── Some((5, 5)): 20/32 ≈ 0.625
      ├── Some((5, 6)): 9/20 ≈ 0.450
      ├── Some((5, 7)): 6/17 ≈ 0.353
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((2, 6)): 125/241 ≈ 0.519
      ├── Some((6, 0)): 25/40 ≈ 0.625
      ├── Some((6, 1)): 10/22 ≈ 0.455
      ├── Some((6, 2)): 22/36 ≈ 0.611
      ├── Some((6, 3)): 12/25 ≈ 0.480
      ├── Some((6, 4)): 7/19 ≈ 0.368
      ├── Some((6, 5)): 9/21 ≈ 0.429
      ├── Some((6, 6)): 10/22 ≈ 0.455
      ├── Some((6, 7)): 9/21 ≈ 0.429
      └── Some((6, 8)): 20/34 ≈ 0.588
    ├── Some((2, 7)): 89/186 ≈ 0.478
      ├── Some((7, 0)): 3/12 ≈ 0.250
      ├── Some((7, 1)): 16/28 ≈ 0.571
      ├── Some((7, 2)): 3/12 ≈ 0.250
      ├── Some((7, 3)): 15/27 ≈ 0.556
      ├── Some((7, 4)): 20/32 ≈ 0.625
      ├── Some((7, 5)): 9/20 ≈ 0.450
      ├── Some((7, 6)): 9/20 ≈ 0.450
      ├── Some((7, 7)): 12/23 ≈ 0.522
      └── Some((7, 8)): 2/11 ≈ 0.182
    └── Some((2, 8)): 134/255 ≈ 0.525
      ├── Some((8, 0)): 27/44 ≈ 0.614
      ├── Some((8, 1)): 4/16 ≈ 0.250
      ├── Some((8, 2)): 12/26 ≈ 0.462
      ├── Some((8, 3)): 16/31 ≈ 0.516
      ├── Some((8, 5)): 29/46 ≈ 0.630
      ├── Some((8, 6)): 14/29 ≈ 0.483
      ├── Some((8, 7)): 21/37 ≈ 0.568
      └── Some((8, 8)): 11/25 ≈ 0.440
  ├── Some((4, 3)): 1743/3217 ≈ 0.542
    ├── Some((3, 0)): 180/337 ≈ 0.534
      ├── Some((0, 0)): 21/39 ≈ 0.538
      ├── Some((0, 1)): 11/27 ≈ 0.407
      ├── Some((0, 2)): 29/48 ≈ 0.604
      ├── Some((0, 3)): 34/54 ≈ 0.630
      ├── Some((0, 4)): 17/34 ≈ 0.500
      ├── Some((0, 5)): 21/39 ≈ 0.538
      ├── Some((0, 6)): 23/41 ≈ 0.561
      ├── Some((0, 7)): 17/34 ≈ 0.500
      └── Some((0, 8)): 6/20 ≈ 0.300
    ├── Some((3, 1)): 126/253 ≈ 0.498
      ├── Some((1, 0)): 10/23 ≈ 0.435
      ├── Some((1, 1)): 18/33 ≈ 0.545
      ├── Some((1, 2)): 16/31 ≈ 0.516
      ├── Some((1, 3)): 19/34 ≈ 0.559
      ├── Some((1, 4)): 15/30 ≈ 0.500
      ├── Some((1, 5)): 20/35 ≈ 0.571
      ├── Some((1, 6)): 2/13 ≈ 0.154
      ├── Some((1, 7)): 12/26 ≈ 0.462
      └── Some((1, 8)): 13/27 ≈ 0.481
    ├── Some((3, 2)): 160/306 ≈ 0.523
      ├── Some((2, 0)): 24/41 ≈ 0.585
      ├── Some((2, 1)): 6/19 ≈ 0.316
      ├── Some((2, 2)): 12/27 ≈ 0.444
      ├── Some((2, 3)): 24/42 ≈ 0.571
      ├── Some((2, 4)): 11/26 ≈ 0.423
      ├── Some((2, 5)): 15/31 ≈ 0.484
      ├── Some((2, 6)): 35/54 ≈ 0.648
      ├── Some((2, 7)): 15/31 ≈ 0.484
      └── Some((2, 8)): 18/34 ≈ 0.529
    ├── Some((3, 3)): 242/431 ≈ 0.561
      ├── Some((3, 0)): 31/55 ≈ 0.564
      ├── Some((3, 1)): 44/70 ≈ 0.629
      ├── Some((3, 2)): 32/56 ≈ 0.571
      ├── Some((3, 4)): 18/39 ≈ 0.462
      ├── Some((3, 5)): 14/33 ≈ 0.424
      ├── Some((3, 6)): 50/78 ≈ 0.641
      ├── Some((3, 7)): 22/44 ≈ 0.500
      └── Some((3, 8)): 31/55 ≈ 0.564
    ├── Some((3, 4)): 144/281 ≈ 0.512
      ├── Some((4, 0)): 12/28 ≈ 0.429
      ├── Some((4, 1)): 10/25 ≈ 0.400
      ├── Some((4, 2)): 6/20 ≈ 0.300
      ├── Some((4, 4)): 35/55 ≈ 0.636
      ├── Some((4, 5)): 23/42 ≈ 0.548
      ├── Some((4, 6)): 18/35 ≈ 0.514
      ├── Some((4, 7)): 19/37 ≈ 0.514
      └── Some((4, 8)): 20/38 ≈ 0.526
    ├── Some((3, 5)): 221/400 ≈ 0.553
      ├── Some((5, 0)): 22/42 ≈ 0.524
      ├── Some((5, 1)): 39/62 ≈ 0.629
      ├── Some((5, 2)): 13/30 ≈ 0.433
      ├── Some((5, 3)): 37/59 ≈ 0.627
      ├── Some((5, 4)): 31/53 ≈ 0.585
      ├── Some((5, 5)): 10/26 ≈ 0.385
      ├── Some((5, 6)): 9/25 ≈ 0.360
      ├── Some((5, 7)): 30/51 ≈ 0.588
      └── Some((5, 8)): 30/51 ≈ 0.588
    ├── Some((3, 6)): 248/440 ≈ 0.564
      ├── Some((6, 0)): 19/38 ≈ 0.500
      ├── Some((6, 1)): 31/53 ≈ 0.585
      ├── Some((6, 2)): 22/42 ≈ 0.524
      ├── Some((6, 3)): 39/62 ≈ 0.629
      ├── Some((6, 4)): 33/55 ≈ 0.600
      ├── Some((6, 5)): 25/46 ≈ 0.543
      ├── Some((6, 6)): 19/39 ≈ 0.487
      ├── Some((6, 7)): 24/45 ≈ 0.533
      └── Some((6, 8)): 36/59 ≈ 0.610
    ├── Some((3, 7)): 214/389 ≈ 0.550
      ├── Some((7, 0)): 27/47 ≈ 0.574
      ├── Some((7, 1)): 20/39 ≈ 0.513
      ├── Some((7, 2)): 27/47 ≈ 0.574
      ├── Some((7, 3)): 29/49 ≈ 0.592
      ├── Some((7, 4)): 19/38 ≈ 0.500
      ├── Some((7, 5)): 22/41 ≈ 0.537
      ├── Some((7, 6)): 25/45 ≈ 0.556
      ├── Some((7, 7)): 18/36 ≈ 0.500
      └── Some((7, 8)): 26/46 ≈ 0.565
    └── Some((3, 8)): 207/379 ≈ 0.546
      ├── Some((8, 0)): 25/47 ≈ 0.532
      ├── Some((8, 1)): 26/48 ≈ 0.542
      ├── Some((8, 2)): 38/62 ≈ 0.613
      ├── Some((8, 3)): 19/39 ≈ 0.487
      ├── Some((8, 5)): 40/65 ≈ 0.615
      ├── Some((8, 6)): 17/36 ≈ 0.472
      ├── Some((8, 7)): 10/27 ≈ 0.370
      └── Some((8, 8)): 31/54 ≈ 0.574
  ├── Some((4, 4)): 1156/2205 ≈ 0.524
    ├── Some((4, 0)): 145/277 ≈ 0.523
      ├── Some((0, 0)): 24/40 ≈ 0.600
      ├── Some((0, 1)): 11/25 ≈ 0.440
      ├── Some((0, 2)): 22/38 ≈ 0.579
      ├── Some((0, 3)): 27/43 ≈ 0.628
      ├── Some((0, 4)): 5/17 ≈ 0.294
      ├── Some((0, 5)): 15/30 ≈ 0.500
      ├── Some((0, 6)): 16/31 ≈ 0.516
      ├── Some((0, 7)): 22/38 ≈ 0.579
      └── Some((0, 8)): 3/14 ≈ 0.214
    ├── Some((4, 1)): 229/405 ≈ 0.565
      ├── Some((1, 0)): 10/26 ≈ 0.385
      ├── Some((1, 1)): 19/38 ≈ 0.500
      ├── Some((1, 2)): 31/52 ≈ 0.596
      ├── Some((1, 3)): 40/62 ≈ 0.645
      ├── Some((1, 4)): 35/56 ≈ 0.625
      ├── Some((1, 5)): 22/41 ≈ 0.537
      ├── Some((1, 6)): 21/40 ≈ 0.525
      ├── Some((1, 7)): 23/42 ≈ 0.548
      └── Some((1, 8)): 27/47 ≈ 0.574
    ├── Some((4, 2)): 118/235 ≈ 0.502
      ├── Some((2, 0)): 2/12 ≈ 0.167
      ├── Some((2, 1)): 9/22 ≈ 0.409
      ├── Some((2, 2)): 18/32 ≈ 0.562
      ├── Some((2, 3)): 5/16 ≈ 0.312
      ├── Some((2, 4)): 8/20 ≈ 0.400
      ├── Some((2, 5)): 23/38 ≈ 0.605
      ├── Some((2, 6)): 21/35 ≈ 0.600
      ├── Some((2, 7)): 14/27 ≈ 0.519
      └── Some((2, 8)): 18/32 ≈ 0.562
    ├── Some((4, 3)): 143/274 ≈ 0.522
      ├── Some((3, 0)): 22/38 ≈ 0.579
      ├── Some((3, 1)): 14/28 ≈ 0.500
      ├── Some((3, 2)): 20/35 ≈ 0.571
      ├── Some((3, 3)): 10/23 ≈ 0.435
      ├── Some((3, 4)): 13/27 ≈ 0.481
      ├── Some((3, 5)): 14/28 ≈ 0.500
      ├── Some((3, 6)): 15/29 ≈ 0.517
      ├── Some((3, 7)): 12/26 ≈ 0.462
      └── Some((3, 8)): 23/39 ≈ 0.590
    ├── Some((4, 5)): 80/175 ≈ 0.457
      ├── Some((5, 0)): 7/17 ≈ 0.412
      ├── Some((5, 1)): 16/28 ≈ 0.571
      ├── Some((5, 2)): 6/16 ≈ 0.375
      ├── Some((5, 3)): 8/19 ≈ 0.421
      ├── Some((5, 4)): 6/16 ≈ 0.375
      ├── Some((5, 5)): 6/16 ≈ 0.375
      ├── Some((5, 6)): 11/22 ≈ 0.500
      ├── Some((5, 7)): 5/15 ≈ 0.333
      └── Some((5, 8)): 14/25 ≈ 0.560
    ├── Some((4, 6)): 132/257 ≈ 0.514
      ├── Some((6, 0)): 10/23 ≈ 0.435
      ├── Some((6, 1)): 18/33 ≈ 0.545
      ├── Some((6, 2)): 12/26 ≈ 0.462
      ├── Some((6, 3)): 24/39 ≈ 0.615
      ├── Some((6, 4)): 21/36 ≈ 0.583
      ├── Some((6, 5)): 3/14 ≈ 0.214
      ├── Some((6, 6)): 17/31 ≈ 0.548
      ├── Some((6, 7)): 7/19 ≈ 0.368
      └── Some((6, 8)): 20/35 ≈ 0.571
    ├── Some((4, 7)): 121/240 ≈ 0.504
      ├── Some((7, 0)): 25/40 ≈ 0.625
      ├── Some((7, 1)): 21/35 ≈ 0.600
      ├── Some((7, 2)): 4/15 ≈ 0.267
      ├── Some((7, 3)): 6/18 ≈ 0.333
      ├── Some((7, 4)): 22/37 ≈ 0.595
      ├── Some((7, 5)): 10/23 ≈ 0.435
      ├── Some((7, 6)): 13/26 ≈ 0.500
      ├── Some((7, 7)): 10/23 ≈ 0.435
      └── Some((7, 8)): 9/22 ≈ 0.409
    └── Some((4, 8)): 187/341 ≈ 0.548
      ├── Some((8, 0)): 23/42 ≈ 0.548
      ├── Some((8, 1)): 24/44 ≈ 0.545
      ├── Some((8, 2)): 27/47 ≈ 0.574
      ├── Some((8, 3)): 11/27 ≈ 0.407
      ├── Some((8, 5)): 22/41 ≈ 0.537
      ├── Some((8, 6)): 25/45 ≈ 0.556
      ├── Some((8, 7)): 36/58 ≈ 0.621
      └── Some((8, 8)): 18/36 ≈ 0.500
  ├── Some((4, 5)): 1441/2698 ≈ 0.534
    ├── Some((5, 0)): 198/357 ≈ 0.555
      ├── Some((0, 0)): 6/20 ≈ 0.300
      ├── Some((0, 1)): 24/42 ≈ 0.571
      ├── Some((0, 2)): 21/39 ≈ 0.538
      ├── Some((0, 3)): 37/57 ≈ 0.649
      ├── Some((0, 4)): 29/48 ≈ 0.604
      ├── Some((0, 5)): 20/38 ≈ 0.526
      ├── Some((0, 6)): 29/48 ≈ 0.604
      ├── Some((0, 7)): 19/36 ≈ 0.528
      └── Some((0, 8)): 12/28 ≈ 0.429
    ├── Some((5, 1)): 119/237 ≈ 0.502
      ├── Some((1, 0)): 14/27 ≈ 0.519
      ├── Some((1, 1)): 12/25 ≈ 0.480
      ├── Some((1, 2)): 24/39 ≈ 0.615
      ├── Some((1, 3)): 21/35 ≈ 0.600
      ├── Some((1, 4)): 5/16 ≈ 0.312
      ├── Some((1, 5)): 3/14 ≈ 0.214
      ├── Some((1, 6)): 17/31 ≈ 0.548
      ├── Some((1, 7)): 12/25 ≈ 0.480
      └── Some((1, 8)): 11/24 ≈ 0.458
    ├── Some((5, 2)): 162/303 ≈ 0.535
      ├── Some((2, 0)): 15/30 ≈ 0.500
      ├── Some((2, 1)): 33/51 ≈ 0.647
      ├── Some((2, 2)): 15/30 ≈ 0.500
      ├── Some((2, 3)): 20/36 ≈ 0.556
      ├── Some((2, 4)): 23/40 ≈ 0.575
      ├── Some((2, 5)): 9/23 ≈ 0.391
      ├── Some((2, 6)): 19/35 ≈ 0.543
      ├── Some((2, 7)): 13/28 ≈ 0.464
      └── Some((2, 8)): 14/29 ≈ 0.483
    ├── Some((5, 3)): 149/283 ≈ 0.527
      ├── Some((3, 0)): 19/35 ≈ 0.543
      ├── Some((3, 1)): 17/32 ≈ 0.531
      ├── Some((3, 2)): 31/48 ≈ 0.646
      ├── Some((3, 3)): 10/24 ≈ 0.417
      ├── Some((3, 4)): 27/44 ≈ 0.614
      ├── Some((3, 5)): 6/19 ≈ 0.316
      ├── Some((3, 6)): 16/31 ≈ 0.516
      ├── Some((3, 7)): 9/22 ≈ 0.409
      └── Some((3, 8)): 13/27 ≈ 0.481
    ├── Some((5, 4)): 153/289 ≈ 0.529
      ├── Some((4, 0)): 14/30 ≈ 0.467
      ├── Some((4, 1)): 26/44 ≈ 0.591
      ├── Some((4, 2)): 17/34 ≈ 0.500
      ├── Some((4, 3)): 22/40 ≈ 0.550
      ├── Some((4, 4)): 29/48 ≈ 0.604
      ├── Some((4, 6)): 15/31 ≈ 0.484
      ├── Some((4, 7)): 14/30 ≈ 0.467
      └── Some((4, 8)): 15/31 ≈ 0.484
    ├── Some((5, 5)): 129/252 ≈ 0.512
      ├── Some((5, 0)): 16/31 ≈ 0.516
      ├── Some((5, 1)): 12/27 ≈ 0.444
      ├── Some((5, 2)): 18/34 ≈ 0.529
      ├── Some((5, 3)): 14/29 ≈ 0.483
      ├── Some((5, 4)): 15/30 ≈ 0.500
      ├── Some((5, 6)): 17/33 ≈ 0.515
      ├── Some((5, 7)): 25/42 ≈ 0.595
      └── Some((5, 8)): 11/25 ≈ 0.440
    ├── Some((5, 6)): 128/251 ≈ 0.510
      ├── Some((6, 0)): 7/19 ≈ 0.368
      ├── Some((6, 1)): 24/39 ≈ 0.615
      ├── Some((6, 2)): 7/19 ≈ 0.368
      ├── Some((6, 3)): 5/17 ≈ 0.294
      ├── Some((6, 4)): 25/40 ≈ 0.625
      ├── Some((6, 5)): 5/17 ≈ 0.294
      ├── Some((6, 6)): 22/37 ≈ 0.595
      ├── Some((6, 7)): 14/28 ≈ 0.500
      └── Some((6, 8)): 19/34 ≈ 0.559
    ├── Some((5, 7)): 214/381 ≈ 0.562
      ├── Some((7, 0)): 26/45 ≈ 0.578
      ├── Some((7, 1)): 27/46 ≈ 0.587
      ├── Some((7, 2)): 14/30 ≈ 0.467
      ├── Some((7, 3)): 15/32 ≈ 0.469
      ├── Some((7, 4)): 30/50 ≈ 0.600
      ├── Some((7, 5)): 24/43 ≈ 0.558
      ├── Some((7, 6)): 24/43 ≈ 0.558
      ├── Some((7, 7)): 23/41 ≈ 0.561
      └── Some((7, 8)): 30/50 ≈ 0.600
    └── Some((5, 8)): 189/344 ≈ 0.549
      ├── Some((8, 0)): 16/34 ≈ 0.471
      ├── Some((8, 1)): 18/36 ≈ 0.500
      ├── Some((8, 2)): 27/47 ≈ 0.574
      ├── Some((8, 3)): 36/58 ≈ 0.621
      ├── Some((8, 5)): 26/46 ≈ 0.565
      ├── Some((8, 6)): 9/25 ≈ 0.360
      ├── Some((8, 7)): 34/55 ≈ 0.618
      └── Some((8, 8)): 23/42 ≈ 0.548
  ├── Some((4, 6)): 1646/3051 ≈ 0.539
    ├── Some((6, 0)): 123/247 ≈ 0.498
      ├── Some((0, 0)): 13/27 ≈ 0.481
      ├── Some((0, 1)): 11/24 ≈ 0.458
      ├── Some((0, 2)): 23/38 ≈ 0.605
      ├── Some((0, 3)): 14/28 ≈ 0.500
      ├── Some((0, 4)): 13/27 ≈ 0.481
      ├── Some((0, 5)): 12/26 ≈ 0.462
      ├── Some((0, 6)): 2/12 ≈ 0.167
      ├── Some((0, 7)): 15/29 ≈ 0.517
      └── Some((0, 8)): 20/35 ≈ 0.571
    ├── Some((6, 1)): 242/429 ≈ 0.564
      ├── Some((1, 0)): 20/39 ≈ 0.513
      ├── Some((1, 1)): 30/51 ≈ 0.588
      ├── Some((1, 2)): 32/54 ≈ 0.593
      ├── Some((1, 3)): 17/36 ≈ 0.472
      ├── Some((1, 4)): 24/44 ≈ 0.545
      ├── Some((1, 5)): 18/37 ≈ 0.486
      ├── Some((1, 6)): 24/44 ≈ 0.545
      ├── Some((1, 7)): 45/69 ≈ 0.652
      └── Some((1, 8)): 32/54 ≈ 0.593
    ├── Some((6, 2)): 254/447 ≈ 0.568
      ├── Some((2, 0)): 34/57 ≈ 0.596
      ├── Some((2, 1)): 30/52 ≈ 0.577
      ├── Some((2, 2)): 11/28 ≈ 0.393
      ├── Some((2, 3)): 30/52 ≈ 0.577
      ├── Some((2, 4)): 23/43 ≈ 0.535
      ├── Some((2, 5)): 25/46 ≈ 0.543
      ├── Some((2, 6)): 30/52 ≈ 0.577
      ├── Some((2, 7)): 47/71 ≈ 0.662
      └── Some((2, 8)): 24/45 ≈ 0.533
    ├── Some((6, 3)): 145/281 ≈ 0.516
      ├── Some((3, 0)): 11/25 ≈ 0.440
      ├── Some((3, 1)): 24/41 ≈ 0.585
      ├── Some((3, 2)): 10/24 ≈ 0.417
      ├── Some((3, 3)): 28/45 ≈ 0.622
      ├── Some((3, 4)): 25/42 ≈ 0.595
      ├── Some((3, 5)): 22/38 ≈ 0.579
      ├── Some((3, 6)): 9/23 ≈ 0.391
      ├── Some((3, 7)): 11/25 ≈ 0.440
      └── Some((3, 8)): 5/17 ≈ 0.294
    ├── Some((6, 4)): 155/297 ≈ 0.522
      ├── Some((4, 0)): 9/24 ≈ 0.375
      ├── Some((4, 1)): 38/59 ≈ 0.644
      ├── Some((4, 2)): 28/48 ≈ 0.583
      ├── Some((4, 3)): 7/22 ≈ 0.318
      ├── Some((4, 4)): 17/35 ≈ 0.486
      ├── Some((4, 5)): 19/37 ≈ 0.514
      ├── Some((4, 7)): 21/39 ≈ 0.538
      └── Some((4, 8)): 15/32 ≈ 0.469
    ├── Some((6, 5)): 220/396 ≈ 0.556
      ├── Some((5, 0)): 33/54 ≈ 0.611
      ├── Some((5, 1)): 21/40 ≈ 0.525
      ├── Some((5, 2)): 25/45 ≈ 0.556
      ├── Some((5, 3)): 17/35 ≈ 0.486
      ├── Some((5, 4)): 22/41 ≈ 0.537
      ├── Some((5, 5)): 17/35 ≈ 0.486
      ├── Some((5, 6)): 28/48 ≈ 0.583
      ├── Some((5, 7)): 34/56 ≈ 0.607
      └── Some((5, 8)): 22/41 ≈ 0.537
    ├── Some((6, 6)): 186/345 ≈ 0.539
      ├── Some((6, 0)): 24/44 ≈ 0.545
      ├── Some((6, 1)): 18/37 ≈ 0.486
      ├── Some((6, 2)): 25/45 ≈ 0.556
      ├── Some((6, 3)): 31/53 ≈ 0.585
      ├── Some((6, 4)): 20/39 ≈ 0.513
      ├── Some((6, 5)): 23/43 ≈ 0.535
      ├── Some((6, 7)): 19/38 ≈ 0.500
      └── Some((6, 8)): 25/45 ≈ 0.556
    ├── Some((6, 7)): 200/366 ≈ 0.546
      ├── Some((7, 0)): 39/60 ≈ 0.650
      ├── Some((7, 1)): 20/38 ≈ 0.526
      ├── Some((7, 2)): 22/40 ≈ 0.550
      ├── Some((7, 3)): 29/49 ≈ 0.592
      ├── Some((7, 4)): 12/28 ≈ 0.429
      ├── Some((7, 5)): 17/34 ≈ 0.500
      ├── Some((7, 6)): 18/36 ≈ 0.500
      ├── Some((7, 7)): 25/44 ≈ 0.568
      └── Some((7, 8)): 18/36 ≈ 0.500
    └── Some((6, 8)): 120/242 ≈ 0.496
      ├── Some((8, 0)): 12/27 ≈ 0.444
      ├── Some((8, 1)): 19/35 ≈ 0.543
      ├── Some((8, 2)): 20/36 ≈ 0.556
      ├── Some((8, 3)): 11/25 ≈ 0.440
      ├── Some((8, 5)): 21/37 ≈ 0.568
      ├── Some((8, 6)): 12/27 ≈ 0.444
      ├── Some((8, 7)): 11/25 ≈ 0.440
      └── Some((8, 8)): 14/29 ≈ 0.483
  ├── Some((4, 7)): 1798/3311 ≈ 0.543
    ├── Some((7, 0)): 166/316 ≈ 0.525
      ├── Some((0, 0)): 18/35 ≈ 0.514
      ├── Some((0, 1)): 22/40 ≈ 0.550
      ├── Some((0, 2)): 15/31 ≈ 0.484
      ├── Some((0, 3)): 16/33 ≈ 0.485
      ├── Some((0, 4)): 24/42 ≈ 0.571
      ├── Some((0, 5)): 15/31 ≈ 0.484
      ├── Some((0, 6)): 39/59 ≈ 0.661
      ├── Some((0, 7)): 5/18 ≈ 0.278
      └── Some((0, 8)): 11/26 ≈ 0.423
    ├── Some((7, 1)): 189/352 ≈ 0.537
      ├── Some((1, 0)): 20/38 ≈ 0.526
      ├── Some((1, 1)): 23/42 ≈ 0.548
      ├── Some((1, 2)): 16/33 ≈ 0.485
      ├── Some((1, 3)): 12/28 ≈ 0.429
      ├── Some((1, 4)): 31/51 ≈ 0.608
      ├── Some((1, 5)): 26/45 ≈ 0.578
      ├── Some((1, 6)): 12/28 ≈ 0.429
      ├── Some((1, 7)): 33/54 ≈ 0.611
      └── Some((1, 8)): 15/32 ≈ 0.469
    ├── Some((7, 2)): 214/390 ≈ 0.549
      ├── Some((2, 0)): 7/22 ≈ 0.318
      ├── Some((2, 1)): 32/54 ≈ 0.593
      ├── Some((2, 2)): 9/25 ≈ 0.360
      ├── Some((2, 3)): 10/26 ≈ 0.385
      ├── Some((2, 4)): 42/65 ≈ 0.646
      ├── Some((2, 5)): 30/51 ≈ 0.588
      ├── Some((2, 6)): 20/39 ≈ 0.513
      ├── Some((2, 7)): 40/63 ≈ 0.635
      └── Some((2, 8)): 24/44 ≈ 0.545
    ├── Some((7, 3)): 181/339 ≈ 0.534
      ├── Some((3, 0)): 29/48 ≈ 0.604
      ├── Some((3, 1)): 23/41 ≈ 0.561
      ├── Some((3, 2)): 17/34 ≈ 0.500
      ├── Some((3, 3)): 18/35 ≈ 0.514
      ├── Some((3, 4)): 14/30 ≈ 0.467
      ├── Some((3, 5)): 25/44 ≈ 0.568
      ├── Some((3, 6)): 24/43 ≈ 0.558
      ├── Some((3, 7)): 16/33 ≈ 0.485
      └── Some((3, 8)): 14/30 ≈ 0.467
    ├── Some((7, 4)): 181/339 ≈ 0.534
      ├── Some((4, 0)): 21/41 ≈ 0.512
      ├── Some((4, 1)): 19/38 ≈ 0.500
      ├── Some((4, 2)): 29/50 ≈ 0.580
      ├── Some((4, 3)): 42/65 ≈ 0.646
      ├── Some((4, 4)): 7/22 ≈ 0.318
      ├── Some((4, 5)): 22/42 ≈ 0.524
      ├── Some((4, 6)): 24/44 ≈ 0.545
      └── Some((4, 8)): 17/36 ≈ 0.472
    ├── Some((7, 5)): 150/291 ≈ 0.515
      ├── Some((5, 0)): 16/31 ≈ 0.516
      ├── Some((5, 1)): 10/24 ≈ 0.417
      ├── Some((5, 2)): 16/31 ≈ 0.516
      ├── Some((5, 3)): 26/43 ≈ 0.605
      ├── Some((5, 4)): 16/32 ≈ 0.500
      ├── Some((5, 5)): 13/28 ≈ 0.464
      ├── Some((5, 6)): 17/33 ≈ 0.515
      ├── Some((5, 7)): 16/32 ≈ 0.500
      └── Some((5, 8)): 20/36 ≈ 0.556
    ├── Some((7, 6)): 220/399 ≈ 0.551
      ├── Some((6, 0)): 39/61 ≈ 0.639
      ├── Some((6, 1)): 15/33 ≈ 0.455
      ├── Some((6, 2)): 15/33 ≈ 0.455
      ├── Some((6, 3)): 39/61 ≈ 0.639
      ├── Some((6, 4)): 24/44 ≈ 0.545
      ├── Some((6, 5)): 32/53 ≈ 0.604
      ├── Some((6, 6)): 18/37 ≈ 0.486
      ├── Some((6, 7)): 22/42 ≈ 0.524
      └── Some((6, 8)): 16/34 ≈ 0.471
    ├── Some((7, 7)): 204/375 ≈ 0.544
      ├── Some((7, 0)): 39/63 ≈ 0.619
      ├── Some((7, 1)): 28/50 ≈ 0.560
      ├── Some((7, 2)): 19/39 ≈ 0.487
      ├── Some((7, 3)): 21/41 ≈ 0.512
      ├── Some((7, 4)): 21/41 ≈ 0.512
      ├── Some((7, 5)): 26/48 ≈ 0.542
      ├── Some((7, 6)): 17/36 ≈ 0.472
      └── Some((7, 8)): 33/56 ≈ 0.589
    └── Some((7, 8)): 293/509 ≈ 0.576
      ├── Some((8, 0)): 19/42 ≈ 0.452
      ├── Some((8, 1)): 28/54 ≈ 0.519
      ├── Some((8, 2)): 18/40 ≈ 0.450
      ├── Some((8, 3)): 53/84 ≈ 0.631
      ├── Some((8, 5)): 44/73 ≈ 0.603
      ├── Some((8, 6)): 39/67 ≈ 0.582
      ├── Some((8, 7)): 18/40 ≈ 0.450
      └── Some((8, 8)): 73/108 ≈ 0.676
  └── Some((4, 8)): 1572/2924 ≈ 0.538
    ├── Some((8, 0)): 136/271 ≈ 0.502
      ├── Some((0, 0)): 12/26 ≈ 0.462
      ├── Some((0, 1)): 24/40 ≈ 0.600
      ├── Some((0, 2)): 5/17 ≈ 0.294
      ├── Some((0, 3)): 18/34 ≈ 0.529
      ├── Some((0, 4)): 19/35 ≈ 0.543
      ├── Some((0, 5)): 14/29 ≈ 0.483
      ├── Some((0, 6)): 17/32 ≈ 0.531
      ├── Some((0, 7)): 13/28 ≈ 0.464
      └── Some((0, 8)): 14/29 ≈ 0.483
    ├── Some((8, 1)): 163/314 ≈ 0.519
      ├── Some((1, 0)): 7/21 ≈ 0.333
      ├── Some((1, 1)): 18/35 ≈ 0.514
      ├── Some((1, 2)): 16/33 ≈ 0.485
      ├── Some((1, 3)): 24/42 ≈ 0.571
      ├── Some((1, 4)): 23/41 ≈ 0.561
      ├── Some((1, 5)): 30/49 ≈ 0.612
      ├── Some((1, 6)): 19/36 ≈ 0.528
      ├── Some((1, 7)): 20/38 ≈ 0.526
      └── Some((1, 8)): 5/18 ≈ 0.278
    ├── Some((8, 2)): 242/436 ≈ 0.555
      ├── Some((2, 0)): 36/60 ≈ 0.600
      ├── Some((2, 1)): 12/30 ≈ 0.400
      ├── Some((2, 2)): 39/64 ≈ 0.609
      ├── Some((2, 3)): 20/40 ≈ 0.500
      ├── Some((2, 4)): 14/33 ≈ 0.424
      ├── Some((2, 5)): 55/82 ≈ 0.671
      ├── Some((2, 6)): 32/55 ≈ 0.582
      ├── Some((2, 7)): 10/27 ≈ 0.370
      └── Some((2, 8)): 23/44 ≈ 0.523
    ├── Some((8, 3)): 261/464 ≈ 0.562
      ├── Some((3, 0)): 30/53 ≈ 0.566
      ├── Some((3, 1)): 27/49 ≈ 0.551
      ├── Some((3, 2)): 27/49 ≈ 0.551
      ├── Some((3, 3)): 38/62 ≈ 0.613
      ├── Some((3, 4)): 33/56 ≈ 0.589
      ├── Some((3, 5)): 23/44 ≈ 0.523
      ├── Some((3, 6)): 29/52 ≈ 0.558
      ├── Some((3, 7)): 40/65 ≈ 0.615
      └── Some((3, 8)): 14/33 ≈ 0.424
    ├── Some((8, 5)): 211/388 ≈ 0.544
      ├── Some((5, 0)): 25/45 ≈ 0.556
      ├── Some((5, 1)): 30/51 ≈ 0.588
      ├── Some((5, 2)): 8/24 ≈ 0.333
      ├── Some((5, 3)): 31/53 ≈ 0.585
      ├── Some((5, 4)): 28/49 ≈ 0.571
      ├── Some((5, 5)): 30/51 ≈ 0.588
      ├── Some((5, 6)): 13/30 ≈ 0.433
      ├── Some((5, 7)): 35/57 ≈ 0.614
      └── Some((5, 8)): 10/27 ≈ 0.370
    ├── Some((8, 6)): 186/350 ≈ 0.531
      ├── Some((6, 0)): 12/28 ≈ 0.429
      ├── Some((6, 1)): 23/42 ≈ 0.548
      ├── Some((6, 2)): 22/41 ≈ 0.537
      ├── Some((6, 3)): 29/49 ≈ 0.592
      ├── Some((6, 4)): 28/48 ≈ 0.583
      ├── Some((6, 5)): 22/41 ≈ 0.537
      ├── Some((6, 6)): 31/52 ≈ 0.596
      ├── Some((6, 7)): 12/28 ≈ 0.429
      └── Some((6, 8)): 6/20 ≈ 0.300
    ├── Some((8, 7)): 162/312 ≈ 0.519
      ├── Some((7, 0)): 27/45 ≈ 0.600
      ├── Some((7, 1)): 14/30 ≈ 0.467
      ├── Some((7, 2)): 18/35 ≈ 0.514
      ├── Some((7, 3)): 23/41 ≈ 0.561
      ├── Some((7, 4)): 14/30 ≈ 0.467
      ├── Some((7, 5)): 7/21 ≈ 0.333
      ├── Some((7, 6)): 13/29 ≈ 0.448
      ├── Some((7, 7)): 18/35 ≈ 0.514
      └── Some((7, 8)): 27/45 ≈ 0.600
    └── Some((8, 8)): 211/388 ≈ 0.544
      ├── Some((8, 0)): 22/45 ≈ 0.489
      ├── Some((8, 1)): 27/52 ≈ 0.519
      ├── Some((8, 2)): 12/32 ≈ 0.375
      ├── Some((8, 3)): 39/67 ≈ 0.582
      ├── Some((8, 5)): 38/66 ≈ 0.576
      ├── Some((8, 6)): 22/45 ≈ 0.489
      └── Some((8, 7)): 50/80 ≈ 0.625
├── Some((8, 5)): 9153/17342 ≈ 0.528
  ├── Some((5, 0)): 1427/2630 ≈ 0.543
    ├── Some((0, 0)): 151/281 ≈ 0.537
      ├── Some((0, 1)): 6/19 ≈ 0.316
      ├── Some((0, 2)): 19/35 ≈ 0.543
      ├── Some((0, 3)): 22/39 ≈ 0.564
      ├── Some((0, 4)): 27/45 ≈ 0.600
      ├── Some((0, 5)): 24/41 ≈ 0.585
      ├── Some((0, 6)): 12/27 ≈ 0.444
      ├── Some((0, 7)): 25/42 ≈ 0.595
      └── Some((0, 8)): 16/32 ≈ 0.500
    ├── Some((0, 1)): 126/243 ≈ 0.519
      ├── Some((1, 0)): 17/31 ≈ 0.548
      ├── Some((1, 1)): 16/30 ≈ 0.533
      ├── Some((1, 2)): 13/26 ≈ 0.500
      ├── Some((1, 3)): 10/22 ≈ 0.455
      ├── Some((1, 4)): 10/22 ≈ 0.455
      ├── Some((1, 5)): 4/15 ≈ 0.267
      ├── Some((1, 6)): 10/23 ≈ 0.435
      ├── Some((1, 7)): 21/35 ≈ 0.600
      └── Some((1, 8)): 24/38 ≈ 0.632
    ├── Some((0, 2)): 218/381 ≈ 0.572
      ├── Some((2, 0)): 26/45 ≈ 0.578
      ├── Some((2, 1)): 20/37 ≈ 0.541
      ├── Some((2, 2)): 21/39 ≈ 0.538
      ├── Some((2, 3)): 20/37 ≈ 0.541
      ├── Some((2, 4)): 36/56 ≈ 0.643
      ├── Some((2, 5)): 9/24 ≈ 0.375
      ├── Some((2, 6)): 25/43 ≈ 0.581
      ├── Some((2, 7)): 28/47 ≈ 0.596
      └── Some((2, 8)): 33/52 ≈ 0.635
    ├── Some((0, 3)): 169/308 ≈ 0.549
      ├── Some((3, 0)): 19/35 ≈ 0.543
      ├── Some((3, 1)): 19/35 ≈ 0.543
      ├── Some((3, 2)): 4/16 ≈ 0.250
      ├── Some((3, 3)): 10/24 ≈ 0.417
      ├── Some((3, 4)): 22/38 ≈ 0.579
      ├── Some((3, 5)): 20/36 ≈ 0.556
      ├── Some((3, 6)): 24/40 ≈ 0.600
      ├── Some((3, 7)): 16/31 ≈ 0.516
      └── Some((3, 8)): 34/52 ≈ 0.654
    ├── Some((0, 4)): 172/313 ≈ 0.550
      ├── Some((4, 0)): 10/24 ≈ 0.417
      ├── Some((4, 1)): 26/43 ≈ 0.605
      ├── Some((4, 2)): 20/36 ≈ 0.556
      ├── Some((4, 3)): 20/36 ≈ 0.556
      ├── Some((4, 4)): 16/31 ≈ 0.516
      ├── Some((4, 5)): 28/45 ≈ 0.622
      ├── Some((4, 6)): 12/27 ≈ 0.444
      ├── Some((4, 7)): 35/53 ≈ 0.660
      └── Some((4, 8)): 5/17 ≈ 0.294
    ├── Some((0, 5)): 214/375 ≈ 0.571
      ├── Some((5, 1)): 31/52 ≈ 0.596
      ├── Some((5, 2)): 32/53 ≈ 0.604
      ├── Some((5, 3)): 25/45 ≈ 0.556
      ├── Some((5, 4)): 39/62 ≈ 0.629
      ├── Some((5, 5)): 7/22 ≈ 0.318
      ├── Some((5, 6)): 18/37 ≈ 0.486
      ├── Some((5, 7)): 36/58 ≈ 0.621
      └── Some((5, 8)): 25/45 ≈ 0.556
    ├── Some((0, 6)): 95/196 ≈ 0.485
      ├── Some((6, 0)): 13/24 ≈ 0.542
      ├── Some((6, 1)): 16/28 ≈ 0.571
      ├── Some((6, 2)): 13/24 ≈ 0.542
      ├── Some((6, 3)): 5/15 ≈ 0.333
      ├── Some((6, 4)): 14/26 ≈ 0.538
      ├── Some((6, 5)): 13/25 ≈ 0.520
      ├── Some((6, 6)): 8/19 ≈ 0.421
      ├── Some((6, 7)): 8/19 ≈ 0.421
      └── Some((6, 8)): 5/15 ≈ 0.333
    ├── Some((0, 7)): 147/275 ≈ 0.535
      ├── Some((7, 0)): 14/28 ≈ 0.500
      ├── Some((7, 1)): 11/24 ≈ 0.458
      ├── Some((7, 2)): 22/37 ≈ 0.595
      ├── Some((7, 3)): 10/23 ≈ 0.435
      ├── Some((7, 4)): 9/22 ≈ 0.409
      ├── Some((7, 5)): 17/31 ≈ 0.548
      ├── Some((7, 6)): 26/42 ≈ 0.619
      ├── Some((7, 7)): 18/33 ≈ 0.545
      └── Some((7, 8)): 19/34 ≈ 0.559
    └── Some((0, 8)): 135/257 ≈ 0.525
      ├── Some((8, 0)): 18/34 ≈ 0.529
      ├── Some((8, 1)): 13/28 ≈ 0.464
      ├── Some((8, 2)): 11/25 ≈ 0.440
      ├── Some((8, 3)): 5/17 ≈ 0.294
      ├── Some((8, 4)): 23/39 ≈ 0.590
      ├── Some((8, 6)): 23/39 ≈ 0.590
      ├── Some((8, 7)): 31/49 ≈ 0.633
      └── Some((8, 8)): 11/25 ≈ 0.440
  ├── Some((5, 1)): 632/1259 ≈ 0.502
    ├── Some((1, 0)): 68/137 ≈ 0.496
      ├── Some((0, 0)): 10/18 ≈ 0.556
      ├── Some((0, 1)): 8/16 ≈ 0.500
      ├── Some((0, 2)): 9/17 ≈ 0.529
      ├── Some((0, 3)): 5/12 ≈ 0.417
      ├── Some((0, 4)): 8/16 ≈ 0.500
      ├── Some((0, 5)): 12/20 ≈ 0.600
      ├── Some((0, 6)): 5/12 ≈ 0.417
      ├── Some((0, 7)): 7/14 ≈ 0.500
      └── Some((0, 8)): 4/11 ≈ 0.364
    ├── Some((1, 1)): 79/153 ≈ 0.516
      ├── Some((1, 0)): 13/23 ≈ 0.565
      ├── Some((1, 2)): 12/22 ≈ 0.545
      ├── Some((1, 3)): 6/15 ≈ 0.400
      ├── Some((1, 4)): 3/11 ≈ 0.273
      ├── Some((1, 5)): 9/18 ≈ 0.500
      ├── Some((1, 6)): 8/17 ≈ 0.471
      ├── Some((1, 7)): 26/36 ≈ 0.722
      └── Some((1, 8)): 2/10 ≈ 0.200
    ├── Some((1, 2)): 60/125 ≈ 0.480
      ├── Some((2, 0)): 9/16 ≈ 0.562
      ├── Some((2, 1)): 8/15 ≈ 0.533
      ├── Some((2, 2)): 4/11 ≈ 0.364
      ├── Some((2, 3)): 4/11 ≈ 0.364
      ├── Some((2, 4)): 11/19 ≈ 0.579
      ├── Some((2, 5)): 6/13 ≈ 0.462
      ├── Some((2, 6)): 3/10 ≈ 0.300
      ├── Some((2, 7)): 3/10 ≈ 0.300
      └── Some((2, 8)): 12/19 ≈ 0.632
    ├── Some((1, 3)): 30/78 ≈ 0.385
      ├── Some((3, 0)): 8/14 ≈ 0.571
      ├── Some((3, 1)): 1/6 ≈ 0.167
      ├── Some((3, 2)): 3/8 ≈ 0.375
      ├── Some((3, 3)): 0/5 ≈ 0.000
      ├── Some((3, 4)): 5/11 ≈ 0.455
      ├── Some((3, 5)): 6/12 ≈ 0.500
      ├── Some((3, 6)): 2/7 ≈ 0.286
      ├── Some((3, 7)): 3/8 ≈ 0.375
      └── Some((3, 8)): 1/6 ≈ 0.167
    ├── Some((1, 4)): 86/164 ≈ 0.524
      ├── Some((4, 0)): 5/13 ≈ 0.385
      ├── Some((4, 1)): 12/21 ≈ 0.571
      ├── Some((4, 2)): 8/17 ≈ 0.471
      ├── Some((4, 3)): 17/26 ≈ 0.654
      ├── Some((4, 4)): 6/14 ≈ 0.429
      ├── Some((4, 5)): 15/24 ≈ 0.625
      ├── Some((4, 6)): 9/18 ≈ 0.500
      ├── Some((4, 7)): 7/16 ≈ 0.438
      └── Some((4, 8)): 6/14 ≈ 0.429
    ├── Some((1, 5)): 62/128 ≈ 0.484
      ├── Some((5, 0)): 8/16 ≈ 0.500
      ├── Some((5, 2)): 4/12 ≈ 0.333
      ├── Some((5, 3)): 6/14 ≈ 0.429
      ├── Some((5, 4)): 5/13 ≈ 0.385
      ├── Some((5, 5)): 10/18 ≈ 0.556
      ├── Some((5, 6)): 6/14 ≈ 0.429
      ├── Some((5, 7)): 11/19 ≈ 0.579
      └── Some((5, 8)): 12/21 ≈ 0.571
    ├── Some((1, 6)): 78/152 ≈ 0.513
      ├── Some((6, 0)): 7/15 ≈ 0.467
      ├── Some((6, 1)): 8/16 ≈ 0.500
      ├── Some((6, 2)): 6/14 ≈ 0.429
      ├── Some((6, 3)): 21/30 ≈ 0.700
      ├── Some((6, 4)): 13/22 ≈ 0.591
      ├── Some((6, 5)): 8/16 ≈ 0.500
      ├── Some((6, 6)): 2/10 ≈ 0.200
      ├── Some((6, 7)): 5/13 ≈ 0.385
      └── Some((6, 8)): 7/15 ≈ 0.467
    ├── Some((1, 7)): 85/162 ≈ 0.525
      ├── Some((7, 0)): 4/12 ≈ 0.333
      ├── Some((7, 1)): 10/19 ≈ 0.526
      ├── Some((7, 2)): 8/16 ≈ 0.500
      ├── Some((7, 3)): 4/12 ≈ 0.333
      ├── Some((7, 4)): 14/23 ≈ 0.609
      ├── Some((7, 5)): 7/15 ≈ 0.467
      ├── Some((7, 6)): 13/22 ≈ 0.591
      ├── Some((7, 7)): 19/28 ≈ 0.679
      └── Some((7, 8)): 6/14 ≈ 0.429
    └── Some((1, 8)): 83/159 ≈ 0.522
      ├── Some((8, 0)): 19/29 ≈ 0.655
      ├── Some((8, 1)): 6/15 ≈ 0.400
      ├── Some((8, 2)): 6/15 ≈ 0.400
      ├── Some((8, 3)): 11/20 ≈ 0.550
      ├── Some((8, 4)): 5/14 ≈ 0.357
      ├── Some((8, 6)): 13/23 ≈ 0.565
      ├── Some((8, 7)): 18/28 ≈ 0.643
      └── Some((8, 8)): 5/14 ≈ 0.357
  ├── Some((5, 2)): 1123/2111 ≈ 0.532
    ├── Some((2, 0)): 175/310 ≈ 0.565
      ├── Some((0, 0)): 13/27 ≈ 0.481
      ├── Some((0, 1)): 29/45 ≈ 0.644
      ├── Some((0, 2)): 21/37 ≈ 0.568
      ├── Some((0, 3)): 24/40 ≈ 0.600
      ├── Some((0, 4)): 6/18 ≈ 0.333
      ├── Some((0, 5)): 33/50 ≈ 0.660
      ├── Some((0, 6)): 18/33 ≈ 0.545
      ├── Some((0, 7)): 13/27 ≈ 0.481
      └── Some((0, 8)): 17/32 ≈ 0.531
    ├── Some((2, 1)): 93/187 ≈ 0.497
      ├── Some((1, 0)): 11/22 ≈ 0.500
      ├── Some((1, 1)): 1/9 ≈ 0.111
      ├── Some((1, 2)): 3/12 ≈ 0.250
      ├── Some((1, 3)): 12/23 ≈ 0.522
      ├── Some((1, 4)): 14/25 ≈ 0.560
      ├── Some((1, 5)): 16/27 ≈ 0.593
      ├── Some((1, 6)): 12/23 ≈ 0.522
      ├── Some((1, 7)): 14/25 ≈ 0.560
      └── Some((1, 8)): 10/20 ≈ 0.500
    ├── Some((2, 2)): 114/219 ≈ 0.521
      ├── Some((2, 0)): 4/15 ≈ 0.267
      ├── Some((2, 1)): 34/50 ≈ 0.680
      ├── Some((2, 3)): 9/21 ≈ 0.429
      ├── Some((2, 4)): 19/33 ≈ 0.576
      ├── Some((2, 5)): 8/20 ≈ 0.400
      ├── Some((2, 6)): 16/30 ≈ 0.533
      ├── Some((2, 7)): 14/28 ≈ 0.500
      └── Some((2, 8)): 9/21 ≈ 0.429
    ├── Some((2, 3)): 157/283 ≈ 0.555
      ├── Some((3, 0)): 14/28 ≈ 0.500
      ├── Some((3, 1)): 24/39 ≈ 0.615
      ├── Some((3, 2)): 6/18 ≈ 0.333
      ├── Some((3, 3)): 33/49 ≈ 0.673
      ├── Some((3, 4)): 8/20 ≈ 0.400
      ├── Some((3, 5)): 11/24 ≈ 0.458
      ├── Some((3, 6)): 24/39 ≈ 0.615
      ├── Some((3, 7)): 29/44 ≈ 0.659
      └── Some((3, 8)): 8/21 ≈ 0.381
    ├── Some((2, 4)): 72/155 ≈ 0.465
      ├── Some((4, 0)): 2/10 ≈ 0.200
      ├── Some((4, 1)): 10/20 ≈ 0.500
      ├── Some((4, 2)): 7/16 ≈ 0.438
      ├── Some((4, 3)): 5/14 ≈ 0.357
      ├── Some((4, 4)): 9/18 ≈ 0.500
      ├── Some((4, 5)): 14/24 ≈ 0.583
      ├── Some((4, 6)): 4/13 ≈ 0.308
      ├── Some((4, 7)): 7/16 ≈ 0.438
      └── Some((4, 8)): 13/23 ≈ 0.565
    ├── Some((2, 5)): 59/134 ≈ 0.440
      ├── Some((5, 0)): 6/15 ≈ 0.400
      ├── Some((5, 1)): 7/16 ≈ 0.438
      ├── Some((5, 3)): 6/15 ≈ 0.400
      ├── Some((5, 4)): 4/13 ≈ 0.308
      ├── Some((5, 5)): 11/21 ≈ 0.524
      ├── Some((5, 6)): 11/21 ≈ 0.524
      ├── Some((5, 7)): 8/17 ≈ 0.471
      └── Some((5, 8)): 6/15 ≈ 0.400
    ├── Some((2, 6)): 114/219 ≈ 0.521
      ├── Some((6, 0)): 11/23 ≈ 0.478
      ├── Some((6, 1)): 27/40 ≈ 0.675
      ├── Some((6, 2)): 7/18 ≈ 0.389
      ├── Some((6, 3)): 8/19 ≈ 0.421
      ├── Some((6, 4)): 13/25 ≈ 0.520
      ├── Some((6, 5)): 10/21 ≈ 0.476
      ├── Some((6, 6)): 18/30 ≈ 0.600
      ├── Some((6, 7)): 16/28 ≈ 0.571
      └── Some((6, 8)): 4/14 ≈ 0.286
    ├── Some((2, 7)): 156/282 ≈ 0.553
      ├── Some((7, 0)): 19/33 ≈ 0.576
      ├── Some((7, 1)): 7/19 ≈ 0.368
      ├── Some((7, 2)): 23/38 ≈ 0.605
      ├── Some((7, 3)): 10/23 ≈ 0.435
      ├── Some((7, 4)): 7/19 ≈ 0.368
      ├── Some((7, 5)): 16/30 ≈ 0.533
      ├── Some((7, 6)): 19/34 ≈ 0.559
      ├── Some((7, 7)): 30/46 ≈ 0.652
      └── Some((7, 8)): 24/39 ≈ 0.615
    └── Some((2, 8)): 183/321 ≈ 0.570
      ├── Some((8, 0)): 24/42 ≈ 0.571
      ├── Some((8, 1)): 17/33 ≈ 0.515
      ├── Some((8, 2)): 22/39 ≈ 0.564
      ├── Some((8, 3)): 30/49 ≈ 0.612
      ├── Some((8, 4)): 26/44 ≈ 0.591
      ├── Some((8, 6)): 7/21 ≈ 0.333
      ├── Some((8, 7)): 27/45 ≈ 0.600
      └── Some((8, 8)): 29/47 ≈ 0.617
  ├── Some((5, 3)): 845/1632 ≈ 0.518
    ├── Some((3, 0)): 107/201 ≈ 0.532
      ├── Some((0, 0)): 5/15 ≈ 0.333
      ├── Some((0, 1)): 17/28 ≈ 0.607
      ├── Some((0, 2)): 9/19 ≈ 0.474
      ├── Some((0, 3)): 18/29 ≈ 0.621
      ├── Some((0, 4)): 7/17 ≈ 0.412
      ├── Some((0, 5)): 10/20 ≈ 0.500
      ├── Some((0, 6)): 11/21 ≈ 0.524
      ├── Some((0, 7)): 15/26 ≈ 0.577
      └── Some((0, 8)): 14/25 ≈ 0.560
    ├── Some((3, 1)): 69/144 ≈ 0.479
      ├── Some((1, 0)): 3/11 ≈ 0.273
      ├── Some((1, 1)): 5/13 ≈ 0.385
      ├── Some((1, 2)): 12/21 ≈ 0.571
      ├── Some((1, 3)): 10/18 ≈ 0.556
      ├── Some((1, 4)): 3/11 ≈ 0.273
      ├── Some((1, 5)): 0/7 ≈ 0.000
      ├── Some((1, 6)): 15/24 ≈ 0.625
      ├── Some((1, 7)): 10/19 ≈ 0.526
      └── Some((1, 8)): 10/19 ≈ 0.526
    ├── Some((3, 2)): 100/191 ≈ 0.524
      ├── Some((2, 0)): 5/14 ≈ 0.357
      ├── Some((2, 1)): 7/17 ≈ 0.412
      ├── Some((2, 2)): 10/20 ≈ 0.500
      ├── Some((2, 3)): 7/17 ≈ 0.412
      ├── Some((2, 4)): 15/26 ≈ 0.577
      ├── Some((2, 5)): 22/33 ≈ 0.667
      ├── Some((2, 6)): 11/21 ≈ 0.524
      ├── Some((2, 7)): 18/29 ≈ 0.621
      └── Some((2, 8)): 4/13 ≈ 0.308
    ├── Some((3, 3)): 97/186 ≈ 0.522
      ├── Some((3, 0)): 14/25 ≈ 0.560
      ├── Some((3, 1)): 7/17 ≈ 0.412
      ├── Some((3, 2)): 16/28 ≈ 0.571
      ├── Some((3, 4)): 21/33 ≈ 0.636
      ├── Some((3, 5)): 15/26 ≈ 0.577
      ├── Some((3, 6)): 6/16 ≈ 0.375
      ├── Some((3, 7)): 9/20 ≈ 0.450
      └── Some((3, 8)): 9/20 ≈ 0.450
    ├── Some((3, 4)): 88/173 ≈ 0.509
      ├── Some((4, 0)): 21/31 ≈ 0.677
      ├── Some((4, 1)): 5/14 ≈ 0.357
      ├── Some((4, 2)): 12/22 ≈ 0.545
      ├── Some((4, 3)): 7/16 ≈ 0.438
      ├── Some((4, 4)): 3/12 ≈ 0.250
      ├── Some((4, 5)): 13/23 ≈ 0.565
      ├── Some((4, 6)): 7/16 ≈ 0.438
      ├── Some((4, 7)): 11/21 ≈ 0.524
      └── Some((4, 8)): 8/17 ≈ 0.471
    ├── Some((3, 5)): 118/217 ≈ 0.544
      ├── Some((5, 0)): 5/16 ≈ 0.312
      ├── Some((5, 1)): 16/29 ≈ 0.552
      ├── Some((5, 2)): 8/19 ≈ 0.421
      ├── Some((5, 4)): 20/33 ≈ 0.606
      ├── Some((5, 5)): 16/29 ≈ 0.552
      ├── Some((5, 6)): 7/18 ≈ 0.389
      ├── Some((5, 7)): 23/36 ≈ 0.639
      └── Some((5, 8)): 23/36 ≈ 0.639
    ├── Some((3, 6)): 90/176 ≈ 0.511
      ├── Some((6, 0)): 8/17 ≈ 0.471
      ├── Some((6, 1)): 4/13 ≈ 0.308
      ├── Some((6, 2)): 7/16 ≈ 0.438
      ├── Some((6, 3)): 11/21 ≈ 0.524
      ├── Some((6, 4)): 5/14 ≈ 0.357
      ├── Some((6, 5)): 8/17 ≈ 0.471
      ├── Some((6, 6)): 15/25 ≈ 0.600
      ├── Some((6, 7)): 12/22 ≈ 0.545
      └── Some((6, 8)): 20/30 ≈ 0.667
    ├── Some((3, 7)): 102/193 ≈ 0.528
      ├── Some((7, 0)): 8/18 ≈ 0.444
      ├── Some((7, 1)): 19/30 ≈ 0.633
      ├── Some((7, 2)): 10/20 ≈ 0.500
      ├── Some((7, 3)): 11/21 ≈ 0.524
      ├── Some((7, 4)): 11/21 ≈ 0.524
      ├── Some((7, 5)): 12/22 ≈ 0.545
      ├── Some((7, 6)): 1/9 ≈ 0.111
      ├── Some((7, 7)): 15/25 ≈ 0.600
      └── Some((7, 8)): 15/26 ≈ 0.577
    └── Some((3, 8)): 73/150 ≈ 0.487
      ├── Some((8, 0)): 6/15 ≈ 0.400
      ├── Some((8, 1)): 15/25 ≈ 0.600
      ├── Some((8, 2)): 9/19 ≈ 0.474
      ├── Some((8, 3)): 12/22 ≈ 0.545
      ├── Some((8, 4)): 9/19 ≈ 0.474
      ├── Some((8, 6)): 4/13 ≈ 0.308
      ├── Some((8, 7)): 10/20 ≈ 0.500
      └── Some((8, 8)): 7/16 ≈ 0.438
  ├── Some((5, 4)): 950/1813 ≈ 0.524
    ├── Some((4, 0)): 78/160 ≈ 0.488
      ├── Some((0, 0)): 2/10 ≈ 0.200
      ├── Some((0, 1)): 4/12 ≈ 0.333
      ├── Some((0, 2)): 8/17 ≈ 0.471
      ├── Some((0, 3)): 3/11 ≈ 0.273
      ├── Some((0, 4)): 11/20 ≈ 0.550
      ├── Some((0, 5)): 15/25 ≈ 0.600
      ├── Some((0, 6)): 9/18 ≈ 0.500
      ├── Some((0, 7)): 12/22 ≈ 0.545
      └── Some((0, 8)): 14/24 ≈ 0.583
    ├── Some((4, 1)): 145/260 ≈ 0.558
      ├── Some((1, 0)): 11/23 ≈ 0.478
      ├── Some((1, 1)): 18/31 ≈ 0.581
      ├── Some((1, 2)): 29/43 ≈ 0.674
      ├── Some((1, 3)): 8/20 ≈ 0.400
      ├── Some((1, 4)): 16/29 ≈ 0.552
      ├── Some((1, 5)): 22/36 ≈ 0.611
      ├── Some((1, 6)): 16/29 ≈ 0.552
      ├── Some((1, 7)): 25/39 ≈ 0.641
      └── Some((1, 8)): 0/9 ≈ 0.000
    ├── Some((4, 2)): 58/129 ≈ 0.450
      ├── Some((2, 0)): 8/16 ≈ 0.500
      ├── Some((2, 1)): 5/13 ≈ 0.385
      ├── Some((2, 2)): 9/17 ≈ 0.529
      ├── Some((2, 3)): 3/10 ≈ 0.300
      ├── Some((2, 4)): 5/13 ≈ 0.385
      ├── Some((2, 5)): 7/15 ≈ 0.467
      ├── Some((2, 6)): 11/19 ≈ 0.579
      ├── Some((2, 7)): 6/14 ≈ 0.429
      └── Some((2, 8)): 4/11 ≈ 0.364
    ├── Some((4, 3)): 96/188 ≈ 0.511
      ├── Some((3, 0)): 9/19 ≈ 0.474
      ├── Some((3, 1)): 4/13 ≈ 0.308
      ├── Some((3, 2)): 19/30 ≈ 0.633
      ├── Some((3, 3)): 10/20 ≈ 0.500
      ├── Some((3, 4)): 2/11 ≈ 0.182
      ├── Some((3, 5)): 7/17 ≈ 0.412
      ├── Some((3, 6)): 12/23 ≈ 0.522
      ├── Some((3, 7)): 18/29 ≈ 0.621
      └── Some((3, 8)): 14/25 ≈ 0.560
    ├── Some((4, 4)): 104/200 ≈ 0.520
      ├── Some((4, 0)): 14/26 ≈ 0.538
      ├── Some((4, 1)): 16/28 ≈ 0.571
      ├── Some((4, 2)): 7/18 ≈ 0.389
      ├── Some((4, 3)): 16/28 ≈ 0.571
      ├── Some((4, 5)): 6/17 ≈ 0.353
      ├── Some((4, 6)): 17/30 ≈ 0.567
      ├── Some((4, 7)): 20/33 ≈ 0.606
      └── Some((4, 8)): 8/19 ≈ 0.421
    ├── Some((4, 5)): 85/171 ≈ 0.497
      ├── Some((5, 0)): 2/11 ≈ 0.182
      ├── Some((5, 1)): 15/27 ≈ 0.556
      ├── Some((5, 2)): 3/12 ≈ 0.250
      ├── Some((5, 3)): 4/14 ≈ 0.286
      ├── Some((5, 5)): 18/30 ≈ 0.600
      ├── Some((5, 6)): 18/30 ≈ 0.600
      ├── Some((5, 7)): 12/23 ≈ 0.522
      └── Some((5, 8)): 12/23 ≈ 0.522
    ├── Some((4, 6)): 102/197 ≈ 0.518
      ├── Some((6, 0)): 15/26 ≈ 0.577
      ├── Some((6, 1)): 3/12 ≈ 0.250
      ├── Some((6, 2)): 1/9 ≈ 0.111
      ├── Some((6, 3)): 7/17 ≈ 0.412
      ├── Some((6, 4)): 26/38 ≈ 0.684
      ├── Some((6, 5)): 10/21 ≈ 0.476
      ├── Some((6, 6)): 18/30 ≈ 0.600
      ├── Some((6, 7)): 10/21 ≈ 0.476
      └── Some((6, 8)): 11/22 ≈ 0.500
    ├── Some((4, 7)): 193/330 ≈ 0.585
      ├── Some((7, 0)): 24/40 ≈ 0.600
      ├── Some((7, 1)): 22/37 ≈ 0.595
      ├── Some((7, 2)): 24/40 ≈ 0.600
      ├── Some((7, 3)): 20/35 ≈ 0.571
      ├── Some((7, 4)): 30/46 ≈ 0.652
      ├── Some((7, 5)): 11/25 ≈ 0.440
      ├── Some((7, 6)): 33/49 ≈ 0.673
      ├── Some((7, 7)): 13/27 ≈ 0.481
      └── Some((7, 8)): 16/30 ≈ 0.533
    └── Some((4, 8)): 89/177 ≈ 0.503
      ├── Some((8, 0)): 2/11 ≈ 0.182
      ├── Some((8, 1)): 6/16 ≈ 0.375
      ├── Some((8, 2)): 20/32 ≈ 0.625
      ├── Some((8, 3)): 8/19 ≈ 0.421
      ├── Some((8, 4)): 27/40 ≈ 0.675
      ├── Some((8, 6)): 8/19 ≈ 0.421
      ├── Some((8, 7)): 5/15 ≈ 0.333
      └── Some((8, 8)): 12/24 ≈ 0.500
  ├── Some((5, 5)): 1309/2429 ≈ 0.539
    ├── Some((5, 0)): 97/201 ≈ 0.483
      ├── Some((0, 0)): 12/24 ≈ 0.500
      ├── Some((0, 1)): 3/13 ≈ 0.231
      ├── Some((0, 2)): 13/25 ≈ 0.520
      ├── Some((0, 3)): 11/23 ≈ 0.478
      ├── Some((0, 4)): 14/26 ≈ 0.538
      ├── Some((0, 5)): 7/18 ≈ 0.389
      ├── Some((0, 6)): 12/24 ≈ 0.500
      ├── Some((0, 7)): 9/20 ≈ 0.450
      └── Some((0, 8)): 15/27 ≈ 0.556
    ├── Some((5, 1)): 214/380 ≈ 0.563
      ├── Some((1, 0)): 28/47 ≈ 0.596
      ├── Some((1, 1)): 29/48 ≈ 0.604
      ├── Some((1, 2)): 36/56 ≈ 0.643
      ├── Some((1, 3)): 22/40 ≈ 0.550
      ├── Some((1, 4)): 23/42 ≈ 0.548
      ├── Some((1, 5)): 22/40 ≈ 0.550
      ├── Some((1, 6)): 22/40 ≈ 0.550
      ├── Some((1, 7)): 16/33 ≈ 0.485
      └── Some((1, 8)): 16/33 ≈ 0.485
    ├── Some((5, 2)): 202/362 ≈ 0.558
      ├── Some((2, 0)): 10/25 ≈ 0.400
      ├── Some((2, 1)): 17/34 ≈ 0.500
      ├── Some((2, 2)): 27/46 ≈ 0.587
      ├── Some((2, 3)): 14/30 ≈ 0.467
      ├── Some((2, 4)): 28/47 ≈ 0.596
      ├── Some((2, 5)): 17/34 ≈ 0.500
      ├── Some((2, 6)): 23/41 ≈ 0.561
      ├── Some((2, 7)): 30/49 ≈ 0.612
      └── Some((2, 8)): 35/55 ≈ 0.636
    ├── Some((5, 3)): 131/254 ≈ 0.516
      ├── Some((3, 0)): 11/24 ≈ 0.458
      ├── Some((3, 1)): 17/31 ≈ 0.548
      ├── Some((3, 2)): 13/27 ≈ 0.481
      ├── Some((3, 3)): 20/35 ≈ 0.571
      ├── Some((3, 4)): 4/15 ≈ 0.267
      ├── Some((3, 5)): 25/40 ≈ 0.625
      ├── Some((3, 6)): 11/24 ≈ 0.458
      ├── Some((3, 7)): 11/24 ≈ 0.458
      └── Some((3, 8)): 19/33 ≈ 0.576
    ├── Some((5, 4)): 197/355 ≈ 0.555
      ├── Some((4, 0)): 10/25 ≈ 0.400
      ├── Some((4, 1)): 33/52 ≈ 0.635
      ├── Some((4, 2)): 20/37 ≈ 0.541
      ├── Some((4, 3)): 21/39 ≈ 0.538
      ├── Some((4, 4)): 9/24 ≈ 0.375
      ├── Some((4, 5)): 15/31 ≈ 0.484
      ├── Some((4, 6)): 36/56 ≈ 0.643
      ├── Some((4, 7)): 35/55 ≈ 0.636
      └── Some((4, 8)): 18/35 ≈ 0.514
    ├── Some((5, 6)): 148/281 ≈ 0.527
      ├── Some((6, 0)): 24/40 ≈ 0.600
      ├── Some((6, 1)): 17/32 ≈ 0.531
      ├── Some((6, 2)): 8/21 ≈ 0.381
      ├── Some((6, 3)): 12/26 ≈ 0.462
      ├── Some((6, 4)): 8/21 ≈ 0.381
      ├── Some((6, 5)): 13/27 ≈ 0.481
      ├── Some((6, 6)): 25/41 ≈ 0.610
      ├── Some((6, 7)): 26/42 ≈ 0.619
      └── Some((6, 8)): 15/30 ≈ 0.500
    ├── Some((5, 7)): 190/344 ≈ 0.552
      ├── Some((7, 0)): 10/25 ≈ 0.400
      ├── Some((7, 1)): 23/41 ≈ 0.561
      ├── Some((7, 2)): 5/18 ≈ 0.278
      ├── Some((7, 3)): 17/34 ≈ 0.500
      ├── Some((7, 4)): 33/52 ≈ 0.635
      ├── Some((7, 5)): 11/26 ≈ 0.423
      ├── Some((7, 6)): 37/57 ≈ 0.649
      ├── Some((7, 7)): 33/53 ≈ 0.623
      └── Some((7, 8)): 20/37 ≈ 0.541
    └── Some((5, 8)): 129/251 ≈ 0.514
      ├── Some((8, 0)): 18/34 ≈ 0.529
      ├── Some((8, 1)): 16/31 ≈ 0.516
      ├── Some((8, 2)): 7/20 ≈ 0.350
      ├── Some((8, 3)): 16/31 ≈ 0.516
      ├── Some((8, 4)): 17/33 ≈ 0.515
      ├── Some((8, 6)): 16/31 ≈ 0.516
      ├── Some((8, 7)): 15/30 ≈ 0.500
      └── Some((8, 8)): 23/40 ≈ 0.575
  ├── Some((5, 6)): 1058/1999 ≈ 0.529
    ├── Some((6, 0)): 148/268 ≈ 0.552
      ├── Some((0, 0)): 16/29 ≈ 0.552
      ├── Some((0, 1)): 17/31 ≈ 0.548
      ├── Some((0, 2)): 14/27 ≈ 0.519
      ├── Some((0, 3)): 14/27 ≈ 0.519
      ├── Some((0, 4)): 19/33 ≈ 0.576
      ├── Some((0, 5)): 15/28 ≈ 0.536
      ├── Some((0, 6)): 23/37 ≈ 0.622
      ├── Some((0, 7)): 9/21 ≈ 0.429
      └── Some((0, 8)): 20/34 ≈ 0.588
    ├── Some((6, 1)): 109/210 ≈ 0.519
      ├── Some((1, 0)): 5/15 ≈ 0.333
      ├── Some((1, 1)): 13/24 ≈ 0.542
      ├── Some((1, 2)): 4/14 ≈ 0.286
      ├── Some((1, 3)): 15/27 ≈ 0.556
      ├── Some((1, 4)): 17/29 ≈ 0.586
      ├── Some((1, 5)): 20/32 ≈ 0.625
      ├── Some((1, 6)): 19/31 ≈ 0.613
      ├── Some((1, 7)): 10/21 ≈ 0.476
      └── Some((1, 8)): 6/16 ≈ 0.375
    ├── Some((6, 2)): 135/248 ≈ 0.544
      ├── Some((2, 0)): 16/29 ≈ 0.552
      ├── Some((2, 1)): 18/31 ≈ 0.581
      ├── Some((2, 2)): 16/29 ≈ 0.552
      ├── Some((2, 3)): 7/18 ≈ 0.389
      ├── Some((2, 4)): 13/25 ≈ 0.520
      ├── Some((2, 5)): 24/37 ≈ 0.649
      ├── Some((2, 6)): 18/31 ≈ 0.581
      ├── Some((2, 7)): 10/22 ≈ 0.455
      └── Some((2, 8)): 13/25 ≈ 0.520
    ├── Some((6, 3)): 98/193 ≈ 0.508
      ├── Some((3, 0)): 14/25 ≈ 0.560
      ├── Some((3, 1)): 11/21 ≈ 0.524
      ├── Some((3, 2)): 8/18 ≈ 0.444
      ├── Some((3, 3)): 19/30 ≈ 0.633
      ├── Some((3, 4)): 14/25 ≈ 0.560
      ├── Some((3, 5)): 7/17 ≈ 0.412
      ├── Some((3, 6)): 7/17 ≈ 0.412
      ├── Some((3, 7)): 6/16 ≈ 0.375
      └── Some((3, 8)): 12/23 ≈ 0.522
    ├── Some((6, 4)): 141/257 ≈ 0.549
      ├── Some((4, 0)): 16/29 ≈ 0.552
      ├── Some((4, 1)): 20/34 ≈ 0.588
      ├── Some((4, 2)): 10/22 ≈ 0.455
      ├── Some((4, 3)): 35/50 ≈ 0.700
      ├── Some((4, 4)): 5/16 ≈ 0.312
      ├── Some((4, 5)): 16/29 ≈ 0.552
      ├── Some((4, 6)): 10/22 ≈ 0.455
      ├── Some((4, 7)): 14/27 ≈ 0.519
      └── Some((4, 8)): 14/27 ≈ 0.519
    ├── Some((6, 5)): 135/249 ≈ 0.542
      ├── Some((5, 0)): 24/39 ≈ 0.615
      ├── Some((5, 1)): 14/28 ≈ 0.500
      ├── Some((5, 2)): 19/33 ≈ 0.576
      ├── Some((5, 3)): 16/30 ≈ 0.533
      ├── Some((5, 4)): 14/28 ≈ 0.500
      ├── Some((5, 5)): 17/31 ≈ 0.548
      ├── Some((5, 7)): 15/29 ≈ 0.517
      └── Some((5, 8)): 16/30 ≈ 0.533
    ├── Some((6, 6)): 133/246 ≈ 0.541
      ├── Some((6, 0)): 26/41 ≈ 0.634
      ├── Some((6, 1)): 9/22 ≈ 0.409
      ├── Some((6, 2)): 16/30 ≈ 0.533
      ├── Some((6, 3)): 20/34 ≈ 0.588
      ├── Some((6, 4)): 11/24 ≈ 0.458
      ├── Some((6, 5)): 14/28 ≈ 0.500
      ├── Some((6, 7)): 17/31 ≈ 0.548
      └── Some((6, 8)): 20/35 ≈ 0.571
    ├── Some((6, 7)): 98/193 ≈ 0.508
      ├── Some((7, 0)): 15/26 ≈ 0.577
      ├── Some((7, 1)): 15/26 ≈ 0.577
      ├── Some((7, 2)): 13/24 ≈ 0.542
      ├── Some((7, 3)): 5/15 ≈ 0.333
      ├── Some((7, 4)): 7/17 ≈ 0.412
      ├── Some((7, 5)): 17/28 ≈ 0.607
      ├── Some((7, 6)): 18/30 ≈ 0.600
      ├── Some((7, 7)): 7/17 ≈ 0.412
      └── Some((7, 8)): 1/9 ≈ 0.111
    └── Some((6, 8)): 60/134 ≈ 0.448
      ├── Some((8, 0)): 17/27 ≈ 0.630
      ├── Some((8, 1)): 4/13 ≈ 0.308
      ├── Some((8, 2)): 7/16 ≈ 0.438
      ├── Some((8, 3)): 7/16 ≈ 0.438
      ├── Some((8, 4)): 5/14 ≈ 0.357
      ├── Some((8, 6)): 4/13 ≈ 0.308
      ├── Some((8, 7)): 5/14 ≈ 0.357
      └── Some((8, 8)): 10/20 ≈ 0.500
  ├── Some((5, 7)): 841/1625 ≈ 0.518
    ├── Some((7, 0)): 68/143 ≈ 0.476
      ├── Some((0, 0)): 4/12 ≈ 0.333
      ├── Some((0, 1)): 5/13 ≈ 0.385
      ├── Some((0, 2)): 7/15 ≈ 0.467
      ├── Some((0, 3)): 7/15 ≈ 0.467
      ├── Some((0, 4)): 10/19 ≈ 0.526
      ├── Some((0, 5)): 8/16 ≈ 0.500
      ├── Some((0, 6)): 6/14 ≈ 0.429
      ├── Some((0, 7)): 8/17 ≈ 0.471
      └── Some((0, 8)): 12/21 ≈ 0.571
    ├── Some((7, 1)): 93/180 ≈ 0.517
      ├── Some((1, 0)): 6/15 ≈ 0.400
      ├── Some((1, 1)): 7/17 ≈ 0.412
      ├── Some((1, 2)): 17/27 ≈ 0.630
      ├── Some((1, 3)): 6/15 ≈ 0.400
      ├── Some((1, 4)): 12/22 ≈ 0.545
      ├── Some((1, 5)): 10/20 ≈ 0.500
      ├── Some((1, 6)): 2/10 ≈ 0.200
      ├── Some((1, 7)): 21/32 ≈ 0.656
      └── Some((1, 8)): 11/21 ≈ 0.524
    ├── Some((7, 2)): 113/210 ≈ 0.538
      ├── Some((2, 0)): 20/31 ≈ 0.645
      ├── Some((2, 1)): 11/22 ≈ 0.500
      ├── Some((2, 2)): 16/27 ≈ 0.593
      ├── Some((2, 3)): 4/13 ≈ 0.308
      ├── Some((2, 4)): 7/17 ≈ 0.412
      ├── Some((2, 5)): 10/21 ≈ 0.476
      ├── Some((2, 6)): 14/25 ≈ 0.560
      ├── Some((2, 7)): 22/34 ≈ 0.647
      └── Some((2, 8)): 9/19 ≈ 0.474
    ├── Some((7, 3)): 62/133 ≈ 0.466
      ├── Some((3, 0)): 13/21 ≈ 0.619
      ├── Some((3, 1)): 5/13 ≈ 0.385
      ├── Some((3, 2)): 7/15 ≈ 0.467
      ├── Some((3, 3)): 4/12 ≈ 0.333
      ├── Some((3, 4)): 11/19 ≈ 0.579
      ├── Some((3, 5)): 3/10 ≈ 0.300
      ├── Some((3, 6)): 4/12 ≈ 0.333
      ├── Some((3, 7)): 9/17 ≈ 0.529
      └── Some((3, 8)): 5/13 ≈ 0.385
    ├── Some((7, 4)): 100/191 ≈ 0.524
      ├── Some((4, 0)): 15/26 ≈ 0.577
      ├── Some((4, 1)): 11/21 ≈ 0.524
      ├── Some((4, 2)): 7/17 ≈ 0.412
      ├── Some((4, 3)): 10/20 ≈ 0.500
      ├── Some((4, 4)): 12/22 ≈ 0.545
      ├── Some((4, 5)): 13/24 ≈ 0.542
      ├── Some((4, 6)): 10/20 ≈ 0.500
      ├── Some((4, 7)): 21/32 ≈ 0.656
      └── Some((4, 8)): 0/8 ≈ 0.000
    ├── Some((7, 5)): 156/272 ≈ 0.574
      ├── Some((5, 0)): 22/37 ≈ 0.595
      ├── Some((5, 1)): 19/34 ≈ 0.559
      ├── Some((5, 2)): 25/40 ≈ 0.625
      ├── Some((5, 3)): 18/32 ≈ 0.562
      ├── Some((5, 4)): 15/29 ≈ 0.517
      ├── Some((5, 5)): 26/41 ≈ 0.634
      ├── Some((5, 6)): 20/35 ≈ 0.571
      └── Some((5, 8)): 10/23 ≈ 0.435
    ├── Some((7, 6)): 99/189 ≈ 0.524
      ├── Some((6, 0)): 8/18 ≈ 0.444
      ├── Some((6, 1)): 14/25 ≈ 0.560
      ├── Some((6, 2)): 3/12 ≈ 0.250
      ├── Some((6, 3)): 13/23 ≈ 0.565
      ├── Some((6, 4)): 6/16 ≈ 0.375
      ├── Some((6, 5)): 3/12 ≈ 0.250
      ├── Some((6, 6)): 15/26 ≈ 0.577
      ├── Some((6, 7)): 3/12 ≈ 0.250
      └── Some((6, 8)): 33/44 ≈ 0.750
    ├── Some((7, 7)): 71/147 ≈ 0.483
      ├── Some((7, 0)): 5/14 ≈ 0.357
      ├── Some((7, 1)): 15/25 ≈ 0.600
      ├── Some((7, 2)): 7/16 ≈ 0.438
      ├── Some((7, 3)): 5/14 ≈ 0.357
      ├── Some((7, 4)): 6/15 ≈ 0.400
      ├── Some((7, 5)): 6/15 ≈ 0.400
      ├── Some((7, 6)): 11/21 ≈ 0.524
      └── Some((7, 8)): 16/26 ≈ 0.615
    └── Some((7, 8)): 79/159 ≈ 0.497
      ├── Some((8, 0)): 16/27 ≈ 0.593
      ├── Some((8, 1)): 6/16 ≈ 0.375
      ├── Some((8, 2)): 13/23 ≈ 0.565
      ├── Some((8, 3)): 4/13 ≈ 0.308
      ├── Some((8, 4)): 8/18 ≈ 0.444
      ├── Some((8, 6)): 12/22 ≈ 0.545
      ├── Some((8, 7)): 15/26 ≈ 0.577
      └── Some((8, 8)): 4/13 ≈ 0.308
  └── Some((5, 8)): 967/1843 ≈ 0.525
    ├── Some((8, 0)): 157/285 ≈ 0.551
      ├── Some((0, 0)): 15/29 ≈ 0.517
      ├── Some((0, 1)): 20/35 ≈ 0.571
      ├── Some((0, 2)): 14/28 ≈ 0.500
      ├── Some((0, 3)): 11/24 ≈ 0.458
      ├── Some((0, 4)): 7/19 ≈ 0.368
      ├── Some((0, 5)): 24/39 ≈ 0.615
      ├── Some((0, 6)): 25/40 ≈ 0.625
      ├── Some((0, 7)): 23/38 ≈ 0.605
      └── Some((0, 8)): 17/32 ≈ 0.531
    ├── Some((8, 1)): 124/235 ≈ 0.528
      ├── Some((1, 0)): 13/25 ≈ 0.520
      ├── Some((1, 1)): 21/34 ≈ 0.618
      ├── Some((1, 2)): 7/18 ≈ 0.389
      ├── Some((1, 3)): 3/13 ≈ 0.231
      ├── Some((1, 4)): 14/27 ≈ 0.519
      ├── Some((1, 5)): 22/36 ≈ 0.611
      ├── Some((1, 6)): 10/22 ≈ 0.455
      ├── Some((1, 7)): 21/34 ≈ 0.618
      └── Some((1, 8)): 13/25 ≈ 0.520
    ├── Some((8, 2)): 147/270 ≈ 0.544
      ├── Some((2, 0)): 13/26 ≈ 0.500
      ├── Some((2, 1)): 13/26 ≈ 0.500
      ├── Some((2, 2)): 22/37 ≈ 0.595
      ├── Some((2, 3)): 2/12 ≈ 0.167
      ├── Some((2, 4)): 21/35 ≈ 0.600
      ├── Some((2, 5)): 17/31 ≈ 0.548
      ├── Some((2, 6)): 18/32 ≈ 0.562
      ├── Some((2, 7)): 23/38 ≈ 0.605
      └── Some((2, 8)): 18/32 ≈ 0.562
    ├── Some((8, 3)): 79/166 ≈ 0.476
      ├── Some((3, 0)): 11/21 ≈ 0.524
      ├── Some((3, 1)): 8/18 ≈ 0.444
      ├── Some((3, 2)): 5/14 ≈ 0.357
      ├── Some((3, 3)): 13/23 ≈ 0.565
      ├── Some((3, 4)): 11/21 ≈ 0.524
      ├── Some((3, 5)): 11/21 ≈ 0.524
      ├── Some((3, 6)): 14/24 ≈ 0.583
      ├── Some((3, 7)): 0/8 ≈ 0.000
      └── Some((3, 8)): 6/15 ≈ 0.400
    ├── Some((8, 4)): 117/225 ≈ 0.520
      ├── Some((4, 0)): 11/23 ≈ 0.478
      ├── Some((4, 1)): 19/32 ≈ 0.594
      ├── Some((4, 2)): 2/12 ≈ 0.167
      ├── Some((4, 3)): 15/27 ≈ 0.556
      ├── Some((4, 4)): 19/32 ≈ 0.594
      ├── Some((4, 5)): 11/23 ≈ 0.478
      ├── Some((4, 6)): 16/28 ≈ 0.571
      ├── Some((4, 7)): 20/33 ≈ 0.606
      └── Some((4, 8)): 4/14 ≈ 0.286
    ├── Some((8, 6)): 98/196 ≈ 0.500
      ├── Some((6, 0)): 8/19 ≈ 0.421
      ├── Some((6, 1)): 13/24 ≈ 0.542
      ├── Some((6, 2)): 7/18 ≈ 0.389
      ├── Some((6, 3)): 6/16 ≈ 0.375
      ├── Some((6, 4)): 12/23 ≈ 0.522
      ├── Some((6, 5)): 3/12 ≈ 0.250
      ├── Some((6, 6)): 16/28 ≈ 0.571
      ├── Some((6, 7)): 19/31 ≈ 0.613
      └── Some((6, 8)): 13/24 ≈ 0.542
    ├── Some((8, 7)): 126/239 ≈ 0.527
      ├── Some((7, 0)): 20/33 ≈ 0.606
      ├── Some((7, 1)): 18/31 ≈ 0.581
      ├── Some((7, 2)): 11/23 ≈ 0.478
      ├── Some((7, 3)): 14/27 ≈ 0.519
      ├── Some((7, 4)): 10/22 ≈ 0.455
      ├── Some((7, 5)): 10/22 ≈ 0.455
      ├── Some((7, 6)): 17/30 ≈ 0.567
      ├── Some((7, 7)): 18/31 ≈ 0.581
      └── Some((7, 8)): 8/19 ≈ 0.421
    └── Some((8, 8)): 118/226 ≈ 0.522
      ├── Some((8, 0)): 23/40 ≈ 0.575
      ├── Some((8, 1)): 11/25 ≈ 0.440
      ├── Some((8, 2)): 11/25 ≈ 0.440
      ├── Some((8, 3)): 13/28 ≈ 0.464
      ├── Some((8, 4)): 26/43 ≈ 0.605
      ├── Some((8, 6)): 19/35 ≈ 0.543
      └── Some((8, 7)): 14/29 ≈ 0.483
├── Some((8, 6)): 8685/16490 ≈ 0.527
  ├── Some((6, 0)): 1254/2328 ≈ 0.539
    ├── Some((0, 0)): 157/285 ≈ 0.551
      ├── Some((0, 1)): 12/26 ≈ 0.462
      ├── Some((0, 2)): 24/41 ≈ 0.585
      ├── Some((0, 3)): 13/28 ≈ 0.464
      ├── Some((0, 4)): 12/27 ≈ 0.444
      ├── Some((0, 5)): 18/34 ≈ 0.529
      ├── Some((0, 6)): 18/34 ≈ 0.529
      ├── Some((0, 7)): 38/56 ≈ 0.679
      └── Some((0, 8)): 22/38 ≈ 0.579
    ├── Some((0, 1)): 146/269 ≈ 0.543
      ├── Some((1, 0)): 20/34 ≈ 0.588
      ├── Some((1, 1)): 13/26 ≈ 0.500
      ├── Some((1, 2)): 28/43 ≈ 0.651
      ├── Some((1, 3)): 12/25 ≈ 0.480
      ├── Some((1, 4)): 25/40 ≈ 0.625
      ├── Some((1, 5)): 11/24 ≈ 0.458
      ├── Some((1, 6)): 14/28 ≈ 0.500
      ├── Some((1, 7)): 18/32 ≈ 0.562
      └── Some((1, 8)): 5/16 ≈ 0.312
    ├── Some((0, 2)): 187/330 ≈ 0.567
      ├── Some((2, 0)): 21/37 ≈ 0.568
      ├── Some((2, 1)): 16/31 ≈ 0.516
      ├── Some((2, 2)): 15/30 ≈ 0.500
      ├── Some((2, 3)): 25/42 ≈ 0.595
      ├── Some((2, 4)): 17/32 ≈ 0.531
      ├── Some((2, 5)): 29/46 ≈ 0.630
      ├── Some((2, 6)): 15/30 ≈ 0.500
      ├── Some((2, 7)): 31/48 ≈ 0.646
      └── Some((2, 8)): 17/33 ≈ 0.515
    ├── Some((0, 3)): 172/308 ≈ 0.558
      ├── Some((3, 0)): 9/23 ≈ 0.391
      ├── Some((3, 1)): 12/26 ≈ 0.462
      ├── Some((3, 2)): 19/35 ≈ 0.543
      ├── Some((3, 3)): 12/26 ≈ 0.462
      ├── Some((3, 4)): 36/53 ≈ 0.679
      ├── Some((3, 5)): 24/40 ≈ 0.600
      ├── Some((3, 6)): 10/24 ≈ 0.417
      ├── Some((3, 7)): 13/27 ≈ 0.481
      └── Some((3, 8)): 36/53 ≈ 0.679
    ├── Some((0, 4)): 95/192 ≈ 0.495
      ├── Some((4, 0)): 6/16 ≈ 0.375
      ├── Some((4, 1)): 10/21 ≈ 0.476
      ├── Some((4, 2)): 17/29 ≈ 0.586
      ├── Some((4, 3)): 12/23 ≈ 0.522
      ├── Some((4, 4)): 1/10 ≈ 0.100
      ├── Some((4, 5)): 16/27 ≈ 0.593
      ├── Some((4, 6)): 16/27 ≈ 0.593
      ├── Some((4, 7)): 9/20 ≈ 0.450
      └── Some((4, 8)): 8/18 ≈ 0.444
    ├── Some((0, 5)): 174/310 ≈ 0.561
      ├── Some((5, 0)): 15/29 ≈ 0.517
      ├── Some((5, 1)): 16/31 ≈ 0.516
      ├── Some((5, 2)): 16/31 ≈ 0.516
      ├── Some((5, 3)): 29/45 ≈ 0.644
      ├── Some((5, 4)): 23/39 ≈ 0.590
      ├── Some((5, 5)): 18/33 ≈ 0.545
      ├── Some((5, 6)): 14/28 ≈ 0.500
      ├── Some((5, 7)): 29/45 ≈ 0.644
      └── Some((5, 8)): 14/28 ≈ 0.500
    ├── Some((0, 6)): 103/204 ≈ 0.505
      ├── Some((6, 1)): 8/20 ≈ 0.400
      ├── Some((6, 2)): 17/30 ≈ 0.567
      ├── Some((6, 3)): 17/30 ≈ 0.567
      ├── Some((6, 4)): 14/27 ≈ 0.519
      ├── Some((6, 5)): 17/31 ≈ 0.548
      ├── Some((6, 6)): 19/33 ≈ 0.576
      ├── Some((6, 7)): 6/17 ≈ 0.353
      └── Some((6, 8)): 4/15 ≈ 0.267
    ├── Some((0, 7)): 138/257 ≈ 0.537
      ├── Some((7, 0)): 16/29 ≈ 0.552
      ├── Some((7, 1)): 9/21 ≈ 0.429
      ├── Some((7, 2)): 17/30 ≈ 0.567
      ├── Some((7, 3)): 21/35 ≈ 0.600
      ├── Some((7, 4)): 11/24 ≈ 0.458
      ├── Some((7, 5)): 31/46 ≈ 0.674
      ├── Some((7, 6)): 7/19 ≈ 0.368
      ├── Some((7, 7)): 17/31 ≈ 0.548
      └── Some((7, 8)): 9/21 ≈ 0.429
    └── Some((0, 8)): 82/172 ≈ 0.477
      ├── Some((8, 0)): 11/22 ≈ 0.500
      ├── Some((8, 1)): 12/24 ≈ 0.500
      ├── Some((8, 2)): 10/21 ≈ 0.476
      ├── Some((8, 3)): 4/14 ≈ 0.286
      ├── Some((8, 4)): 1/10 ≈ 0.100
      ├── Some((8, 5)): 21/34 ≈ 0.618
      ├── Some((8, 7)): 15/27 ≈ 0.556
      └── Some((8, 8)): 8/19 ≈ 0.421
  ├── Some((6, 1)): 709/1390 ≈ 0.510
    ├── Some((1, 0)): 83/161 ≈ 0.516
      ├── Some((0, 0)): 11/20 ≈ 0.550
      ├── Some((0, 1)): 7/16 ≈ 0.438
      ├── Some((0, 2)): 6/14 ≈ 0.429
      ├── Some((0, 3)): 15/24 ≈ 0.625
      ├── Some((0, 4)): 8/17 ≈ 0.471
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 4/12 ≈ 0.333
      ├── Some((0, 7)): 4/12 ≈ 0.333
      └── Some((0, 8)): 18/27 ≈ 0.667
    ├── Some((1, 1)): 113/205 ≈ 0.551
      ├── Some((1, 0)): 9/20 ≈ 0.450
      ├── Some((1, 2)): 11/22 ≈ 0.500
      ├── Some((1, 3)): 9/20 ≈ 0.450
      ├── Some((1, 4)): 21/33 ≈ 0.636
      ├── Some((1, 5)): 12/23 ≈ 0.522
      ├── Some((1, 6)): 26/38 ≈ 0.684
      ├── Some((1, 7)): 10/21 ≈ 0.476
      └── Some((1, 8)): 15/27 ≈ 0.556
    ├── Some((1, 2)): 65/134 ≈ 0.485
      ├── Some((2, 0)): 6/13 ≈ 0.462
      ├── Some((2, 1)): 2/9 ≈ 0.222
      ├── Some((2, 2)): 9/17 ≈ 0.529
      ├── Some((2, 3)): 6/14 ≈ 0.429
      ├── Some((2, 4)): 7/15 ≈ 0.467
      ├── Some((2, 5)): 9/17 ≈ 0.529
      ├── Some((2, 6)): 12/20 ≈ 0.600
      ├── Some((2, 7)): 4/11 ≈ 0.364
      └── Some((2, 8)): 9/17 ≈ 0.529
    ├── Some((1, 3)): 84/162 ≈ 0.519
      ├── Some((3, 0)): 5/13 ≈ 0.385
      ├── Some((3, 1)): 8/16 ≈ 0.500
      ├── Some((3, 2)): 2/10 ≈ 0.200
      ├── Some((3, 3)): 16/25 ≈ 0.640
      ├── Some((3, 4)): 12/21 ≈ 0.571
      ├── Some((3, 5)): 8/17 ≈ 0.471
      ├── Some((3, 6)): 13/22 ≈ 0.591
      ├── Some((3, 7)): 4/12 ≈ 0.333
      └── Some((3, 8)): 16/25 ≈ 0.640
    ├── Some((1, 4)): 60/126 ≈ 0.476
      ├── Some((4, 0)): 7/14 ≈ 0.500
      ├── Some((4, 1)): 6/13 ≈ 0.462
      ├── Some((4, 2)): 4/11 ≈ 0.364
      ├── Some((4, 3)): 7/15 ≈ 0.467
      ├── Some((4, 4)): 1/8 ≈ 0.125
      ├── Some((4, 5)): 6/13 ≈ 0.462
      ├── Some((4, 6)): 12/20 ≈ 0.600
      ├── Some((4, 7)): 4/11 ≈ 0.364
      └── Some((4, 8)): 12/20 ≈ 0.600
    ├── Some((1, 5)): 65/134 ≈ 0.485
      ├── Some((5, 0)): 2/9 ≈ 0.222
      ├── Some((5, 1)): 3/10 ≈ 0.300
      ├── Some((5, 2)): 10/18 ≈ 0.556
      ├── Some((5, 3)): 8/16 ≈ 0.500
      ├── Some((5, 4)): 19/27 ≈ 0.704
      ├── Some((5, 5)): 1/8 ≈ 0.125
      ├── Some((5, 6)): 7/15 ≈ 0.467
      ├── Some((5, 7)): 4/12 ≈ 0.333
      └── Some((5, 8)): 10/18 ≈ 0.556
    ├── Some((1, 6)): 77/152 ≈ 0.507
      ├── Some((6, 0)): 7/16 ≈ 0.438
      ├── Some((6, 2)): 18/28 ≈ 0.643
      ├── Some((6, 3)): 11/21 ≈ 0.524
      ├── Some((6, 4)): 1/9 ≈ 0.111
      ├── Some((6, 5)): 14/24 ≈ 0.583
      ├── Some((6, 6)): 6/15 ≈ 0.400
      ├── Some((6, 7)): 10/20 ≈ 0.500
      └── Some((6, 8)): 9/18 ≈ 0.500
    ├── Some((1, 7)): 95/179 ≈ 0.531
      ├── Some((7, 0)): 10/19 ≈ 0.526
      ├── Some((7, 1)): 24/34 ≈ 0.706
      ├── Some((7, 2)): 10/19 ≈ 0.526
      ├── Some((7, 3)): 11/20 ≈ 0.550
      ├── Some((7, 4)): 7/16 ≈ 0.438
      ├── Some((7, 5)): 16/26 ≈ 0.615
      ├── Some((7, 6)): 7/16 ≈ 0.438
      ├── Some((7, 7)): 4/13 ≈ 0.308
      └── Some((7, 8)): 6/15 ≈ 0.400
    └── Some((1, 8)): 66/136 ≈ 0.485
      ├── Some((8, 0)): 13/22 ≈ 0.591
      ├── Some((8, 1)): 10/19 ≈ 0.526
      ├── Some((8, 2)): 14/24 ≈ 0.583
      ├── Some((8, 3)): 1/8 ≈ 0.125
      ├── Some((8, 4)): 12/21 ≈ 0.571
      ├── Some((8, 5)): 6/15 ≈ 0.400
      ├── Some((8, 7)): 10/19 ≈ 0.526
      └── Some((8, 8)): 0/7 ≈ 0.000
  ├── Some((6, 2)): 1073/2019 ≈ 0.531
    ├── Some((2, 0)): 117/222 ≈ 0.527
      ├── Some((0, 0)): 5/15 ≈ 0.333
      ├── Some((0, 1)): 10/21 ≈ 0.476
      ├── Some((0, 2)): 19/31 ≈ 0.613
      ├── Some((0, 3)): 7/18 ≈ 0.389
      ├── Some((0, 4)): 7/18 ≈ 0.389
      ├── Some((0, 5)): 16/28 ≈ 0.571
      ├── Some((0, 6)): 17/29 ≈ 0.586
      ├── Some((0, 7)): 22/35 ≈ 0.629
      └── Some((0, 8)): 14/26 ≈ 0.538
    ├── Some((2, 1)): 65/142 ≈ 0.458
      ├── Some((1, 0)): 17/26 ≈ 0.654
      ├── Some((1, 1)): 10/19 ≈ 0.526
      ├── Some((1, 2)): 5/13 ≈ 0.385
      ├── Some((1, 3)): 1/8 ≈ 0.125
      ├── Some((1, 4)): 9/18 ≈ 0.500
      ├── Some((1, 5)): 2/10 ≈ 0.200
      ├── Some((1, 6)): 11/20 ≈ 0.550
      ├── Some((1, 7)): 5/13 ≈ 0.385
      └── Some((1, 8)): 5/14 ≈ 0.357
    ├── Some((2, 2)): 69/148 ≈ 0.466
      ├── Some((2, 0)): 8/18 ≈ 0.444
      ├── Some((2, 1)): 16/27 ≈ 0.593
      ├── Some((2, 3)): 2/10 ≈ 0.200
      ├── Some((2, 4)): 5/14 ≈ 0.357
      ├── Some((2, 5)): 4/13 ≈ 0.308
      ├── Some((2, 6)): 14/25 ≈ 0.560
      ├── Some((2, 7)): 4/13 ≈ 0.308
      └── Some((2, 8)): 16/27 ≈ 0.593
    ├── Some((2, 3)): 134/247 ≈ 0.543
      ├── Some((3, 0)): 22/35 ≈ 0.629
      ├── Some((3, 1)): 19/32 ≈ 0.594
      ├── Some((3, 2)): 7/18 ≈ 0.389
      ├── Some((3, 3)): 17/30 ≈ 0.567
      ├── Some((3, 4)): 11/23 ≈ 0.478
      ├── Some((3, 5)): 18/31 ≈ 0.581
      ├── Some((3, 6)): 17/30 ≈ 0.567
      ├── Some((3, 7)): 14/27 ≈ 0.519
      └── Some((3, 8)): 8/20 ≈ 0.400
    ├── Some((2, 4)): 137/251 ≈ 0.546
      ├── Some((4, 0)): 17/30 ≈ 0.567
      ├── Some((4, 1)): 16/29 ≈ 0.552
      ├── Some((4, 2)): 15/28 ≈ 0.536
      ├── Some((4, 3)): 5/16 ≈ 0.312
      ├── Some((4, 4)): 13/25 ≈ 0.520
      ├── Some((4, 5)): 32/46 ≈ 0.696
      ├── Some((4, 6)): 13/26 ≈ 0.500
      ├── Some((4, 7)): 10/22 ≈ 0.455
      └── Some((4, 8)): 15/28 ≈ 0.536
    ├── Some((2, 5)): 128/238 ≈ 0.538
      ├── Some((5, 0)): 18/31 ≈ 0.581
      ├── Some((5, 1)): 10/22 ≈ 0.455
      ├── Some((5, 2)): 22/35 ≈ 0.629
      ├── Some((5, 3)): 13/25 ≈ 0.520
      ├── Some((5, 4)): 11/23 ≈ 0.478
      ├── Some((5, 5)): 12/24 ≈ 0.500
      ├── Some((5, 6)): 14/26 ≈ 0.538
      ├── Some((5, 7)): 11/23 ≈ 0.478
      └── Some((5, 8)): 16/28 ≈ 0.571
    ├── Some((2, 6)): 170/300 ≈ 0.567
      ├── Some((6, 0)): 41/60 ≈ 0.683
      ├── Some((6, 1)): 14/29 ≈ 0.483
      ├── Some((6, 3)): 19/35 ≈ 0.543
      ├── Some((6, 4)): 33/51 ≈ 0.647
      ├── Some((6, 5)): 13/28 ≈ 0.464
      ├── Some((6, 6)): 16/31 ≈ 0.516
      ├── Some((6, 7)): 23/40 ≈ 0.575
      └── Some((6, 8)): 11/25 ≈ 0.440
    ├── Some((2, 7)): 126/235 ≈ 0.536
      ├── Some((7, 0)): 10/22 ≈ 0.455
      ├── Some((7, 1)): 14/26 ≈ 0.538
      ├── Some((7, 2)): 20/33 ≈ 0.606
      ├── Some((7, 3)): 18/30 ≈ 0.600
      ├── Some((7, 4)): 14/26 ≈ 0.538
      ├── Some((7, 5)): 15/27 ≈ 0.556
      ├── Some((7, 6)): 3/13 ≈ 0.231
      ├── Some((7, 7)): 14/26 ≈ 0.538
      └── Some((7, 8)): 18/31 ≈ 0.581
    └── Some((2, 8)): 126/235 ≈ 0.536
      ├── Some((8, 0)): 8/20 ≈ 0.400
      ├── Some((8, 1)): 14/27 ≈ 0.519
      ├── Some((8, 2)): 24/39 ≈ 0.615
      ├── Some((8, 3)): 6/18 ≈ 0.333
      ├── Some((8, 4)): 25/40 ≈ 0.625
      ├── Some((8, 5)): 18/32 ≈ 0.562
      ├── Some((8, 7)): 11/24 ≈ 0.458
      └── Some((8, 8)): 20/34 ≈ 0.588
  ├── Some((6, 3)): 877/1682 ≈ 0.521
    ├── Some((3, 0)): 99/189 ≈ 0.524
      ├── Some((0, 0)): 11/21 ≈ 0.524
      ├── Some((0, 1)): 10/20 ≈ 0.500
      ├── Some((0, 2)): 11/21 ≈ 0.524
      ├── Some((0, 3)): 12/22 ≈ 0.545
      ├── Some((0, 4)): 17/28 ≈ 0.607
      ├── Some((0, 5)): 11/21 ≈ 0.524
      ├── Some((0, 6)): 8/18 ≈ 0.444
      ├── Some((0, 7)): 17/28 ≈ 0.607
      └── Some((0, 8)): 1/9 ≈ 0.111
    ├── Some((3, 1)): 102/194 ≈ 0.526
      ├── Some((1, 0)): 15/26 ≈ 0.577
      ├── Some((1, 1)): 12/22 ≈ 0.545
      ├── Some((1, 2)): 8/18 ≈ 0.444
      ├── Some((1, 3)): 13/23 ≈ 0.565
      ├── Some((1, 4)): 14/24 ≈ 0.583
      ├── Some((1, 5)): 16/27 ≈ 0.593
      ├── Some((1, 6)): 5/14 ≈ 0.357
      ├── Some((1, 7)): 11/21 ≈ 0.524
      └── Some((1, 8)): 8/18 ≈ 0.444
    ├── Some((3, 2)): 104/197 ≈ 0.528
      ├── Some((2, 0)): 15/25 ≈ 0.600
      ├── Some((2, 1)): 9/19 ≈ 0.474
      ├── Some((2, 2)): 6/16 ≈ 0.375
      ├── Some((2, 3)): 23/34 ≈ 0.676
      ├── Some((2, 4)): 8/18 ≈ 0.444
      ├── Some((2, 5)): 8/18 ≈ 0.444
      ├── Some((2, 6)): 9/19 ≈ 0.474
      ├── Some((2, 7)): 10/20 ≈ 0.500
      └── Some((2, 8)): 16/27 ≈ 0.593
    ├── Some((3, 3)): 109/204 ≈ 0.534
      ├── Some((3, 0)): 11/22 ≈ 0.500
      ├── Some((3, 1)): 11/22 ≈ 0.500
      ├── Some((3, 2)): 9/20 ≈ 0.450
      ├── Some((3, 4)): 25/38 ≈ 0.658
      ├── Some((3, 5)): 7/18 ≈ 0.389
      ├── Some((3, 6)): 11/23 ≈ 0.478
      ├── Some((3, 7)): 24/37 ≈ 0.649
      └── Some((3, 8)): 11/23 ≈ 0.478
    ├── Some((3, 4)): 72/148 ≈ 0.486
      ├── Some((4, 0)): 11/20 ≈ 0.550
      ├── Some((4, 1)): 8/16 ≈ 0.500
      ├── Some((4, 2)): 6/14 ≈ 0.429
      ├── Some((4, 3)): 7/15 ≈ 0.467
      ├── Some((4, 4)): 7/15 ≈ 0.467
      ├── Some((4, 5)): 9/18 ≈ 0.500
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 13/22 ≈ 0.591
      └── Some((4, 8)): 6/14 ≈ 0.429
    ├── Some((3, 5)): 109/204 ≈ 0.534
      ├── Some((5, 0)): 7/17 ≈ 0.412
      ├── Some((5, 1)): 8/18 ≈ 0.444
      ├── Some((5, 2)): 16/27 ≈ 0.593
      ├── Some((5, 3)): 8/18 ≈ 0.444
      ├── Some((5, 4)): 15/26 ≈ 0.577
      ├── Some((5, 5)): 17/28 ≈ 0.607
      ├── Some((5, 6)): 8/18 ≈ 0.444
      ├── Some((5, 7)): 19/30 ≈ 0.633
      └── Some((5, 8)): 11/21 ≈ 0.524
    ├── Some((3, 6)): 91/177 ≈ 0.514
      ├── Some((6, 0)): 11/22 ≈ 0.500
      ├── Some((6, 1)): 5/15 ≈ 0.333
      ├── Some((6, 2)): 17/28 ≈ 0.607
      ├── Some((6, 4)): 15/26 ≈ 0.577
      ├── Some((6, 5)): 6/16 ≈ 0.375
      ├── Some((6, 6)): 10/21 ≈ 0.476
      ├── Some((6, 7)): 16/27 ≈ 0.593
      └── Some((6, 8)): 10/21 ≈ 0.476
    ├── Some((3, 7)): 119/219 ≈ 0.543
      ├── Some((7, 0)): 8/18 ≈ 0.444
      ├── Some((7, 1)): 21/33 ≈ 0.636
      ├── Some((7, 2)): 20/32 ≈ 0.625
      ├── Some((7, 3)): 13/24 ≈ 0.542
      ├── Some((7, 4)): 12/23 ≈ 0.522
      ├── Some((7, 5)): 12/23 ≈ 0.522
      ├── Some((7, 6)): 8/19 ≈ 0.421
      ├── Some((7, 7)): 15/26 ≈ 0.577
      └── Some((7, 8)): 9/20 ≈ 0.450
    └── Some((3, 8)): 72/149 ≈ 0.483
      ├── Some((8, 0)): 13/23 ≈ 0.565
      ├── Some((8, 1)): 13/23 ≈ 0.565
      ├── Some((8, 2)): 10/20 ≈ 0.500
      ├── Some((8, 3)): 4/13 ≈ 0.308
      ├── Some((8, 4)): 4/13 ≈ 0.308
      ├── Some((8, 5)): 20/30 ≈ 0.667
      ├── Some((8, 7)): 5/14 ≈ 0.357
      └── Some((8, 8)): 3/12 ≈ 0.250
  ├── Some((6, 4)): 777/1509 ≈ 0.515
    ├── Some((4, 0)): 111/205 ≈ 0.541
      ├── Some((0, 0)): 8/18 ≈ 0.444
      ├── Some((0, 1)): 8/18 ≈ 0.444
      ├── Some((0, 2)): 10/20 ≈ 0.500
      ├── Some((0, 3)): 24/35 ≈ 0.686
      ├── Some((0, 4)): 10/20 ≈ 0.500
      ├── Some((0, 5)): 14/25 ≈ 0.560
      ├── Some((0, 6)): 4/13 ≈ 0.308
      ├── Some((0, 7)): 23/34 ≈ 0.676
      └── Some((0, 8)): 10/21 ≈ 0.476
    ├── Some((4, 1)): 103/193 ≈ 0.534
      ├── Some((1, 0)): 22/33 ≈ 0.667
      ├── Some((1, 1)): 8/18 ≈ 0.444
      ├── Some((1, 2)): 1/9 ≈ 0.111
      ├── Some((1, 3)): 17/27 ≈ 0.630
      ├── Some((1, 4)): 9/19 ≈ 0.474
      ├── Some((1, 5)): 6/15 ≈ 0.400
      ├── Some((1, 6)): 14/24 ≈ 0.583
      ├── Some((1, 7)): 9/19 ≈ 0.474
      └── Some((1, 8)): 17/28 ≈ 0.607
    ├── Some((4, 2)): 97/184 ≈ 0.527
      ├── Some((2, 0)): 7/16 ≈ 0.438
      ├── Some((2, 1)): 19/29 ≈ 0.655
      ├── Some((2, 2)): 14/24 ≈ 0.583
      ├── Some((2, 3)): 2/10 ≈ 0.200
      ├── Some((2, 4)): 9/19 ≈ 0.474
      ├── Some((2, 5)): 10/20 ≈ 0.500
      ├── Some((2, 6)): 14/24 ≈ 0.583
      ├── Some((2, 7)): 10/20 ≈ 0.500
      └── Some((2, 8)): 11/21 ≈ 0.524
    ├── Some((4, 3)): 42/100 ≈ 0.420
      ├── Some((3, 0)): 3/9 ≈ 0.333
      ├── Some((3, 1)): 4/10 ≈ 0.400
      ├── Some((3, 2)): 4/10 ≈ 0.400
      ├── Some((3, 3)): 2/8 ≈ 0.250
      ├── Some((3, 4)): 5/12 ≈ 0.417
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 1/7 ≈ 0.143
      ├── Some((3, 7)): 8/15 ≈ 0.533
      └── Some((3, 8)): 8/15 ≈ 0.533
    ├── Some((4, 4)): 102/191 ≈ 0.534
      ├── Some((4, 0)): 11/22 ≈ 0.500
      ├── Some((4, 1)): 10/21 ≈ 0.476
      ├── Some((4, 2)): 6/16 ≈ 0.375
      ├── Some((4, 3)): 9/20 ≈ 0.450
      ├── Some((4, 5)): 15/26 ≈ 0.577
      ├── Some((4, 6)): 15/26 ≈ 0.577
      ├── Some((4, 7)): 14/25 ≈ 0.560
      └── Some((4, 8)): 22/34 ≈ 0.647
    ├── Some((4, 5)): 51/114 ≈ 0.447
      ├── Some((5, 0)): 3/10 ≈ 0.300
      ├── Some((5, 1)): 5/12 ≈ 0.417
      ├── Some((5, 2)): 8/15 ≈ 0.533
      ├── Some((5, 3)): 9/16 ≈ 0.562
      ├── Some((5, 4)): 4/11 ≈ 0.364
      ├── Some((5, 5)): 9/16 ≈ 0.562
      ├── Some((5, 6)): 5/12 ≈ 0.417
      ├── Some((5, 7)): 2/8 ≈ 0.250
      └── Some((5, 8)): 6/13 ≈ 0.462
    ├── Some((4, 6)): 99/187 ≈ 0.529
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 20/32 ≈ 0.625
      ├── Some((6, 2)): 13/24 ≈ 0.542
      ├── Some((6, 3)): 13/24 ≈ 0.542
      ├── Some((6, 5)): 13/24 ≈ 0.542
      ├── Some((6, 6)): 16/28 ≈ 0.571
      ├── Some((6, 7)): 14/25 ≈ 0.560
      └── Some((6, 8)): 3/12 ≈ 0.250
    ├── Some((4, 7)): 115/210 ≈ 0.548
      ├── Some((7, 0)): 5/14 ≈ 0.357
      ├── Some((7, 1)): 9/19 ≈ 0.474
      ├── Some((7, 2)): 18/29 ≈ 0.621
      ├── Some((7, 3)): 22/33 ≈ 0.667
      ├── Some((7, 4)): 12/22 ≈ 0.545
      ├── Some((7, 5)): 16/27 ≈ 0.593
      ├── Some((7, 6)): 13/24 ≈ 0.542
      ├── Some((7, 7)): 7/17 ≈ 0.412
      └── Some((7, 8)): 13/24 ≈ 0.542
    └── Some((4, 8)): 57/124 ≈ 0.460
      ├── Some((8, 0)): 4/12 ≈ 0.333
      ├── Some((8, 1)): 9/18 ≈ 0.500
      ├── Some((8, 2)): 8/16 ≈ 0.500
      ├── Some((8, 3)): 8/16 ≈ 0.500
      ├── Some((8, 4)): 14/23 ≈ 0.609
      ├── Some((8, 5)): 0/7 ≈ 0.000
      ├── Some((8, 7)): 8/17 ≈ 0.471
      └── Some((8, 8)): 6/14 ≈ 0.429
  ├── Some((6, 5)): 912/1742 ≈ 0.524
    ├── Some((5, 0)): 59/130 ≈ 0.454
      ├── Some((0, 0)): 6/14 ≈ 0.429
      ├── Some((0, 1)): 9/17 ≈ 0.529
      ├── Some((0, 2)): 10/18 ≈ 0.556
      ├── Some((0, 3)): 4/12 ≈ 0.333
      ├── Some((0, 4)): 4/12 ≈ 0.333
      ├── Some((0, 5)): 10/18 ≈ 0.556
      ├── Some((0, 6)): 1/8 ≈ 0.125
      ├── Some((0, 7)): 4/12 ≈ 0.333
      └── Some((0, 8)): 10/18 ≈ 0.556
    ├── Some((5, 1)): 103/197 ≈ 0.523
      ├── Some((1, 0)): 6/16 ≈ 0.375
      ├── Some((1, 1)): 17/28 ≈ 0.607
      ├── Some((1, 2)): 14/25 ≈ 0.560
      ├── Some((1, 3)): 8/18 ≈ 0.444
      ├── Some((1, 4)): 19/30 ≈ 0.633
      ├── Some((1, 5)): 11/21 ≈ 0.524
      ├── Some((1, 6)): 10/20 ≈ 0.500
      ├── Some((1, 7)): 9/19 ≈ 0.474
      └── Some((1, 8)): 9/19 ≈ 0.474
    ├── Some((5, 2)): 48/112 ≈ 0.429
      ├── Some((2, 0)): 7/14 ≈ 0.500
      ├── Some((2, 1)): 9/17 ≈ 0.529
      ├── Some((2, 2)): 2/9 ≈ 0.222
      ├── Some((2, 3)): 4/11 ≈ 0.364
      ├── Some((2, 4)): 1/7 ≈ 0.143
      ├── Some((2, 5)): 5/12 ≈ 0.417
      ├── Some((2, 6)): 8/15 ≈ 0.533
      ├── Some((2, 7)): 1/7 ≈ 0.143
      └── Some((2, 8)): 11/19 ≈ 0.579
    ├── Some((5, 3)): 105/200 ≈ 0.525
      ├── Some((3, 0)): 6/16 ≈ 0.375
      ├── Some((3, 1)): 19/30 ≈ 0.633
      ├── Some((3, 2)): 16/27 ≈ 0.593
      ├── Some((3, 3)): 10/21 ≈ 0.476
      ├── Some((3, 4)): 6/16 ≈ 0.375
      ├── Some((3, 5)): 12/23 ≈ 0.522
      ├── Some((3, 6)): 3/12 ≈ 0.250
      ├── Some((3, 7)): 23/35 ≈ 0.657
      └── Some((3, 8)): 9/19 ≈ 0.474
    ├── Some((5, 4)): 131/238 ≈ 0.550
      ├── Some((4, 0)): 19/31 ≈ 0.613
      ├── Some((4, 1)): 16/28 ≈ 0.571
      ├── Some((4, 2)): 11/22 ≈ 0.500
      ├── Some((4, 3)): 18/30 ≈ 0.600
      ├── Some((4, 4)): 12/24 ≈ 0.500
      ├── Some((4, 5)): 17/29 ≈ 0.586
      ├── Some((4, 6)): 8/19 ≈ 0.421
      ├── Some((4, 7)): 7/18 ≈ 0.389
      └── Some((4, 8)): 23/36 ≈ 0.639
    ├── Some((5, 5)): 88/174 ≈ 0.506
      ├── Some((5, 0)): 8/18 ≈ 0.444
      ├── Some((5, 1)): 7/17 ≈ 0.412
      ├── Some((5, 2)): 15/26 ≈ 0.577
      ├── Some((5, 3)): 9/20 ≈ 0.450
      ├── Some((5, 4)): 17/29 ≈ 0.586
      ├── Some((5, 6)): 5/15 ≈ 0.333
      ├── Some((5, 7)): 12/23 ≈ 0.522
      └── Some((5, 8)): 14/25 ≈ 0.560
    ├── Some((5, 6)): 85/170 ≈ 0.500
      ├── Some((6, 0)): 7/17 ≈ 0.412
      ├── Some((6, 1)): 16/27 ≈ 0.593
      ├── Some((6, 2)): 18/30 ≈ 0.600
      ├── Some((6, 3)): 4/13 ≈ 0.308
      ├── Some((6, 4)): 10/21 ≈ 0.476
      ├── Some((6, 6)): 4/14 ≈ 0.286
      ├── Some((6, 7)): 13/24 ≈ 0.542
      └── Some((6, 8)): 12/23 ≈ 0.522
    ├── Some((5, 7)): 181/311 ≈ 0.582
      ├── Some((7, 0)): 21/36 ≈ 0.583
      ├── Some((7, 1)): 13/26 ≈ 0.500
      ├── Some((7, 2)): 23/38 ≈ 0.605
      ├── Some((7, 3)): 19/33 ≈ 0.576
      ├── Some((7, 4)): 15/29 ≈ 0.517
      ├── Some((7, 5)): 24/39 ≈ 0.615
      ├── Some((7, 6)): 32/47 ≈ 0.681
      ├── Some((7, 7)): 17/31 ≈ 0.548
      └── Some((7, 8)): 17/31 ≈ 0.548
    └── Some((5, 8)): 111/209 ≈ 0.531
      ├── Some((8, 0)): 19/32 ≈ 0.594
      ├── Some((8, 1)): 16/29 ≈ 0.552
      ├── Some((8, 2)): 8/19 ≈ 0.421
      ├── Some((8, 3)): 18/31 ≈ 0.581
      ├── Some((8, 4)): 25/38 ≈ 0.658
      ├── Some((8, 5)): 6/17 ≈ 0.353
      ├── Some((8, 7)): 6/17 ≈ 0.353
      └── Some((8, 8)): 13/25 ≈ 0.520
  ├── Some((6, 6)): 1364/2516 ≈ 0.542
    ├── Some((6, 0)): 76/168 ≈ 0.452
      ├── Some((0, 0)): 4/13 ≈ 0.308
      ├── Some((0, 1)): 18/30 ≈ 0.600
      ├── Some((0, 2)): 14/25 ≈ 0.560
      ├── Some((0, 3)): 6/16 ≈ 0.375
      ├── Some((0, 4)): 11/22 ≈ 0.500
      ├── Some((0, 5)): 4/13 ≈ 0.308
      ├── Some((0, 6)): 5/15 ≈ 0.333
      ├── Some((0, 7)): 7/17 ≈ 0.412
      └── Some((0, 8)): 6/16 ≈ 0.375
    ├── Some((6, 1)): 199/358 ≈ 0.556
      ├── Some((1, 0)): 48/69 ≈ 0.696
      ├── Some((1, 1)): 17/34 ≈ 0.500
      ├── Some((1, 2)): 11/27 ≈ 0.407
      ├── Some((1, 3)): 14/30 ≈ 0.467
      ├── Some((1, 4)): 7/21 ≈ 0.333
      ├── Some((1, 5)): 18/35 ≈ 0.514
      ├── Some((1, 6)): 36/56 ≈ 0.643
      ├── Some((1, 7)): 20/38 ≈ 0.526
      └── Some((1, 8)): 28/47 ≈ 0.596
    ├── Some((6, 2)): 128/250 ≈ 0.512
      ├── Some((2, 0)): 15/29 ≈ 0.517
      ├── Some((2, 1)): 24/39 ≈ 0.615
      ├── Some((2, 2)): 11/24 ≈ 0.458
      ├── Some((2, 3)): 14/28 ≈ 0.500
      ├── Some((2, 4)): 15/29 ≈ 0.517
      ├── Some((2, 5)): 21/36 ≈ 0.583
      ├── Some((2, 6)): 12/25 ≈ 0.480
      ├── Some((2, 7)): 4/15 ≈ 0.267
      └── Some((2, 8)): 11/24 ≈ 0.458
    ├── Some((6, 3)): 184/336 ≈ 0.548
      ├── Some((3, 0)): 26/44 ≈ 0.591
      ├── Some((3, 1)): 8/22 ≈ 0.364
      ├── Some((3, 2)): 27/45 ≈ 0.600
      ├── Some((3, 3)): 18/35 ≈ 0.514
      ├── Some((3, 4)): 17/33 ≈ 0.515
      ├── Some((3, 5)): 12/27 ≈ 0.444
      ├── Some((3, 6)): 26/44 ≈ 0.591
      ├── Some((3, 7)): 23/41 ≈ 0.561
      └── Some((3, 8)): 26/44 ≈ 0.591
    ├── Some((6, 4)): 217/385 ≈ 0.564
      ├── Some((4, 0)): 12/28 ≈ 0.429
      ├── Some((4, 1)): 15/32 ≈ 0.469
      ├── Some((4, 2)): 12/28 ≈ 0.429
      ├── Some((4, 3)): 7/22 ≈ 0.318
      ├── Some((4, 4)): 44/66 ≈ 0.667
      ├── Some((4, 5)): 33/54 ≈ 0.611
      ├── Some((4, 6)): 31/52 ≈ 0.596
      ├── Some((4, 7)): 47/70 ≈ 0.671
      └── Some((4, 8)): 15/32 ≈ 0.469
    ├── Some((6, 5)): 230/404 ≈ 0.569
      ├── Some((5, 0)): 42/64 ≈ 0.656
      ├── Some((5, 1)): 28/48 ≈ 0.583
      ├── Some((5, 2)): 16/34 ≈ 0.471
      ├── Some((5, 3)): 36/57 ≈ 0.632
      ├── Some((5, 4)): 11/27 ≈ 0.407
      ├── Some((5, 5)): 22/41 ≈ 0.537
      ├── Some((5, 6)): 31/52 ≈ 0.596
      ├── Some((5, 7)): 24/43 ≈ 0.558
      └── Some((5, 8)): 19/37 ≈ 0.514
    ├── Some((6, 7)): 175/322 ≈ 0.543
      ├── Some((7, 0)): 11/26 ≈ 0.423
      ├── Some((7, 1)): 16/32 ≈ 0.500
      ├── Some((7, 2)): 29/47 ≈ 0.617
      ├── Some((7, 3)): 15/30 ≈ 0.500
      ├── Some((7, 4)): 16/32 ≈ 0.500
      ├── Some((7, 5)): 19/35 ≈ 0.543
      ├── Some((7, 6)): 12/27 ≈ 0.444
      ├── Some((7, 7)): 42/61 ≈ 0.689
      └── Some((7, 8)): 15/31 ≈ 0.484
    └── Some((6, 8)): 155/292 ≈ 0.531
      ├── Some((8, 0)): 14/30 ≈ 0.467
      ├── Some((8, 1)): 13/29 ≈ 0.448
      ├── Some((8, 2)): 14/30 ≈ 0.467
      ├── Some((8, 3)): 37/57 ≈ 0.649
      ├── Some((8, 4)): 11/26 ≈ 0.423
      ├── Some((8, 5)): 15/32 ≈ 0.469
      ├── Some((8, 7)): 31/51 ≈ 0.608
      └── Some((8, 8)): 19/36 ≈ 0.528
  ├── Some((6, 7)): 750/1462 ≈ 0.513
    ├── Some((7, 0)): 88/170 ≈ 0.518
      ├── Some((0, 0)): 9/18 ≈ 0.500
      ├── Some((0, 1)): 12/21 ≈ 0.571
      ├── Some((0, 2)): 12/21 ≈ 0.571
      ├── Some((0, 3)): 11/20 ≈ 0.550
      ├── Some((0, 4)): 4/13 ≈ 0.308
      ├── Some((0, 5)): 9/18 ≈ 0.500
      ├── Some((0, 6)): 14/24 ≈ 0.583
      ├── Some((0, 7)): 8/17 ≈ 0.471
      └── Some((0, 8)): 8/17 ≈ 0.471
    ├── Some((7, 1)): 69/141 ≈ 0.489
      ├── Some((1, 0)): 15/23 ≈ 0.652
      ├── Some((1, 1)): 4/12 ≈ 0.333
      ├── Some((1, 2)): 6/14 ≈ 0.429
      ├── Some((1, 3)): 5/13 ≈ 0.385
      ├── Some((1, 4)): 9/17 ≈ 0.529
      ├── Some((1, 5)): 12/20 ≈ 0.600
      ├── Some((1, 6)): 5/13 ≈ 0.385
      ├── Some((1, 7)): 10/18 ≈ 0.556
      └── Some((1, 8)): 3/10 ≈ 0.300
    ├── Some((7, 2)): 104/193 ≈ 0.539
      ├── Some((2, 0)): 9/19 ≈ 0.474
      ├── Some((2, 1)): 12/22 ≈ 0.545
      ├── Some((2, 2)): 9/19 ≈ 0.474
      ├── Some((2, 3)): 9/19 ≈ 0.474
      ├── Some((2, 4)): 6/15 ≈ 0.400
      ├── Some((2, 5)): 11/21 ≈ 0.524
      ├── Some((2, 6)): 19/29 ≈ 0.655
      ├── Some((2, 7)): 22/32 ≈ 0.688
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((7, 3)): 104/193 ≈ 0.539
      ├── Some((3, 0)): 14/24 ≈ 0.583
      ├── Some((3, 1)): 6/15 ≈ 0.400
      ├── Some((3, 2)): 13/23 ≈ 0.565
      ├── Some((3, 3)): 9/19 ≈ 0.474
      ├── Some((3, 4)): 15/25 ≈ 0.600
      ├── Some((3, 5)): 16/26 ≈ 0.615
      ├── Some((3, 6)): 13/23 ≈ 0.565
      ├── Some((3, 7)): 9/19 ≈ 0.474
      └── Some((3, 8)): 8/18 ≈ 0.444
    ├── Some((7, 4)): 62/130 ≈ 0.477
      ├── Some((4, 0)): 9/17 ≈ 0.529
      ├── Some((4, 1)): 5/12 ≈ 0.417
      ├── Some((4, 2)): 1/8 ≈ 0.125
      ├── Some((4, 3)): 5/13 ≈ 0.385
      ├── Some((4, 4)): 11/19 ≈ 0.579
      ├── Some((4, 5)): 4/11 ≈ 0.364
      ├── Some((4, 6)): 2/9 ≈ 0.222
      ├── Some((4, 7)): 11/19 ≈ 0.579
      └── Some((4, 8)): 13/21 ≈ 0.619
    ├── Some((7, 5)): 72/146 ≈ 0.493
      ├── Some((5, 0)): 4/12 ≈ 0.333
      ├── Some((5, 1)): 8/16 ≈ 0.500
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 12/21 ≈ 0.571
      ├── Some((5, 4)): 9/17 ≈ 0.529
      ├── Some((5, 5)): 8/16 ≈ 0.500
      ├── Some((5, 6)): 11/19 ≈ 0.579
      ├── Some((5, 7)): 12/21 ≈ 0.571
      └── Some((5, 8)): 0/7 ≈ 0.000
    ├── Some((7, 6)): 60/127 ≈ 0.472
      ├── Some((6, 0)): 5/13 ≈ 0.385
      ├── Some((6, 1)): 10/19 ≈ 0.526
      ├── Some((6, 2)): 16/25 ≈ 0.640
      ├── Some((6, 3)): 9/17 ≈ 0.529
      ├── Some((6, 4)): 1/8 ≈ 0.125
      ├── Some((6, 5)): 5/13 ≈ 0.385
      ├── Some((6, 6)): 9/18 ≈ 0.500
      └── Some((6, 8)): 5/13 ≈ 0.385
    ├── Some((7, 7)): 96/181 ≈ 0.530
      ├── Some((7, 0)): 12/23 ≈ 0.522
      ├── Some((7, 1)): 18/29 ≈ 0.621
      ├── Some((7, 2)): 5/15 ≈ 0.333
      ├── Some((7, 3)): 6/16 ≈ 0.375
      ├── Some((7, 4)): 15/26 ≈ 0.577
      ├── Some((7, 5)): 23/35 ≈ 0.657
      ├── Some((7, 6)): 8/18 ≈ 0.444
      └── Some((7, 8)): 8/18 ≈ 0.444
    └── Some((7, 8)): 95/180 ≈ 0.528
      ├── Some((8, 0)): 13/24 ≈ 0.542
      ├── Some((8, 1)): 17/28 ≈ 0.607
      ├── Some((8, 2)): 4/13 ≈ 0.308
      ├── Some((8, 3)): 10/21 ≈ 0.476
      ├── Some((8, 4)): 11/22 ≈ 0.500
      ├── Some((8, 5)): 12/23 ≈ 0.522
      ├── Some((8, 7)): 27/39 ≈ 0.692
      └── Some((8, 8)): 1/9 ≈ 0.111
  └── Some((6, 8)): 969/1841 ≈ 0.526
    ├── Some((8, 0)): 89/182 ≈ 0.489
      ├── Some((0, 0)): 6/16 ≈ 0.375
      ├── Some((0, 1)): 8/18 ≈ 0.444
      ├── Some((0, 2)): 18/29 ≈ 0.621
      ├── Some((0, 3)): 2/11 ≈ 0.182
      ├── Some((0, 4)): 4/13 ≈ 0.308
      ├── Some((0, 5)): 21/33 ≈ 0.636
      ├── Some((0, 6)): 8/18 ≈ 0.444
      ├── Some((0, 7)): 8/18 ≈ 0.444
      └── Some((0, 8)): 14/25 ≈ 0.560
    ├── Some((8, 1)): 177/314 ≈ 0.564
      ├── Some((1, 0)): 26/42 ≈ 0.619
      ├── Some((1, 1)): 22/38 ≈ 0.579
      ├── Some((1, 2)): 9/22 ≈ 0.409
      ├── Some((1, 3)): 16/31 ≈ 0.516
      ├── Some((1, 4)): 11/25 ≈ 0.440
      ├── Some((1, 5)): 13/27 ≈ 0.481
      ├── Some((1, 6)): 33/50 ≈ 0.660
      ├── Some((1, 7)): 19/34 ≈ 0.559
      └── Some((1, 8)): 28/44 ≈ 0.636
    ├── Some((8, 2)): 171/306 ≈ 0.559
      ├── Some((2, 0)): 22/38 ≈ 0.579
      ├── Some((2, 1)): 27/43 ≈ 0.628
      ├── Some((2, 2)): 12/26 ≈ 0.462
      ├── Some((2, 3)): 9/22 ≈ 0.409
      ├── Some((2, 4)): 24/40 ≈ 0.600
      ├── Some((2, 5)): 18/33 ≈ 0.545
      ├── Some((2, 6)): 13/27 ≈ 0.481
      ├── Some((2, 7)): 16/31 ≈ 0.516
      └── Some((2, 8)): 29/45 ≈ 0.644
    ├── Some((8, 3)): 99/197 ≈ 0.503
      ├── Some((3, 0)): 9/20 ≈ 0.450
      ├── Some((3, 1)): 12/23 ≈ 0.522
      ├── Some((3, 2)): 12/23 ≈ 0.522
      ├── Some((3, 3)): 12/23 ≈ 0.522
      ├── Some((3, 4)): 12/23 ≈ 0.522
      ├── Some((3, 5)): 15/26 ≈ 0.577
      ├── Some((3, 6)): 8/18 ≈ 0.444
      ├── Some((3, 7)): 7/17 ≈ 0.412
      └── Some((3, 8)): 12/23 ≈ 0.522
    ├── Some((8, 4)): 61/138 ≈ 0.442
      ├── Some((4, 0)): 11/20 ≈ 0.550
      ├── Some((4, 1)): 6/15 ≈ 0.400
      ├── Some((4, 2)): 12/21 ≈ 0.571
      ├── Some((4, 3)): 7/16 ≈ 0.438
      ├── Some((4, 4)): 4/12 ≈ 0.333
      ├── Some((4, 5)): 7/16 ≈ 0.438
      ├── Some((4, 6)): 5/13 ≈ 0.385
      ├── Some((4, 7)): 4/12 ≈ 0.333
      └── Some((4, 8)): 4/12 ≈ 0.333
    ├── Some((8, 5)): 80/168 ≈ 0.476
      ├── Some((5, 0)): 5/14 ≈ 0.357
      ├── Some((5, 1)): 5/14 ≈ 0.357
      ├── Some((5, 2)): 8/18 ≈ 0.444
      ├── Some((5, 3)): 13/23 ≈ 0.565
      ├── Some((5, 4)): 10/20 ≈ 0.500
      ├── Some((5, 5)): 11/21 ≈ 0.524
      ├── Some((5, 6)): 13/23 ≈ 0.565
      ├── Some((5, 7)): 8/18 ≈ 0.444
      └── Some((5, 8)): 6/16 ≈ 0.375
    ├── Some((8, 7)): 148/271 ≈ 0.546
      ├── Some((7, 0)): 21/36 ≈ 0.583
      ├── Some((7, 1)): 18/32 ≈ 0.562
      ├── Some((7, 2)): 20/34 ≈ 0.588
      ├── Some((7, 3)): 11/24 ≈ 0.458
      ├── Some((7, 4)): 18/32 ≈ 0.562
      ├── Some((7, 5)): 24/39 ≈ 0.615
      ├── Some((7, 6)): 4/15 ≈ 0.267
      ├── Some((7, 7)): 5/17 ≈ 0.294
      └── Some((7, 8)): 26/41 ≈ 0.634
    └── Some((8, 8)): 143/264 ≈ 0.542
      ├── Some((8, 0)): 35/55 ≈ 0.636
      ├── Some((8, 1)): 17/34 ≈ 0.500
      ├── Some((8, 2)): 26/45 ≈ 0.578
      ├── Some((8, 3)): 3/15 ≈ 0.200
      ├── Some((8, 4)): 18/35 ≈ 0.514
      ├── Some((8, 5)): 16/33 ≈ 0.485
      └── Some((8, 7)): 27/46 ≈ 0.587
├── Some((8, 7)): 11410/21440 ≈ 0.532
  ├── Some((7, 0)): 1284/2412 ≈ 0.532
    ├── Some((0, 0)): 114/225 ≈ 0.507
      ├── Some((0, 1)): 4/15 ≈ 0.267
      ├── Some((0, 2)): 18/33 ≈ 0.545
      ├── Some((0, 3)): 12/26 ≈ 0.462
      ├── Some((0, 4)): 14/28 ≈ 0.500
      ├── Some((0, 5)): 24/40 ≈ 0.600
      ├── Some((0, 6)): 16/30 ≈ 0.533
      ├── Some((0, 7)): 15/29 ≈ 0.517
      └── Some((0, 8)): 10/23 ≈ 0.435
    ├── Some((0, 1)): 183/329 ≈ 0.556
      ├── Some((1, 0)): 21/38 ≈ 0.553
      ├── Some((1, 1)): 22/39 ≈ 0.564
      ├── Some((1, 2)): 26/43 ≈ 0.605
      ├── Some((1, 3)): 19/35 ≈ 0.543
      ├── Some((1, 4)): 24/41 ≈ 0.585
      ├── Some((1, 5)): 6/19 ≈ 0.316
      ├── Some((1, 6)): 21/38 ≈ 0.553
      ├── Some((1, 7)): 15/30 ≈ 0.500
      └── Some((1, 8)): 28/45 ≈ 0.622
    ├── Some((0, 2)): 150/279 ≈ 0.538
      ├── Some((2, 0)): 18/33 ≈ 0.545
      ├── Some((2, 1)): 11/24 ≈ 0.458
      ├── Some((2, 2)): 12/26 ≈ 0.462
      ├── Some((2, 3)): 8/21 ≈ 0.381
      ├── Some((2, 4)): 13/27 ≈ 0.481
      ├── Some((2, 5)): 27/43 ≈ 0.628
      ├── Some((2, 6)): 26/42 ≈ 0.619
      ├── Some((2, 7)): 23/38 ≈ 0.605
      └── Some((2, 8)): 11/24 ≈ 0.458
    ├── Some((0, 3)): 103/207 ≈ 0.498
      ├── Some((3, 0)): 12/24 ≈ 0.500
      ├── Some((3, 1)): 14/26 ≈ 0.538
      ├── Some((3, 2)): 11/22 ≈ 0.500
      ├── Some((3, 3)): 14/26 ≈ 0.538
      ├── Some((3, 4)): 14/26 ≈ 0.538
      ├── Some((3, 5)): 9/20 ≈ 0.450
      ├── Some((3, 6)): 6/16 ≈ 0.375
      ├── Some((3, 7)): 15/27 ≈ 0.556
      └── Some((3, 8)): 8/19 ≈ 0.421
    ├── Some((0, 4)): 150/279 ≈ 0.538
      ├── Some((4, 0)): 30/46 ≈ 0.652
      ├── Some((4, 1)): 19/34 ≈ 0.559
      ├── Some((4, 2)): 19/34 ≈ 0.559
      ├── Some((4, 3)): 18/33 ≈ 0.545
      ├── Some((4, 4)): 4/16 ≈ 0.250
      ├── Some((4, 5)): 16/30 ≈ 0.533
      ├── Some((4, 6)): 6/18 ≈ 0.333
      ├── Some((4, 7)): 24/39 ≈ 0.615
      └── Some((4, 8)): 14/28 ≈ 0.500
    ├── Some((0, 5)): 109/217 ≈ 0.502
      ├── Some((5, 0)): 14/26 ≈ 0.538
      ├── Some((5, 1)): 13/25 ≈ 0.520
      ├── Some((5, 2)): 12/24 ≈ 0.500
      ├── Some((5, 3)): 18/31 ≈ 0.581
      ├── Some((5, 4)): 14/27 ≈ 0.519
      ├── Some((5, 5)): 14/27 ≈ 0.519
      ├── Some((5, 6)): 8/19 ≈ 0.421
      ├── Some((5, 7)): 7/18 ≈ 0.389
      └── Some((5, 8)): 8/19 ≈ 0.421
    ├── Some((0, 6)): 184/330 ≈ 0.558
      ├── Some((6, 0)): 18/34 ≈ 0.529
      ├── Some((6, 1)): 16/31 ≈ 0.516
      ├── Some((6, 2)): 21/37 ≈ 0.568
      ├── Some((6, 3)): 14/29 ≈ 0.483
      ├── Some((6, 4)): 23/40 ≈ 0.575
      ├── Some((6, 5)): 29/46 ≈ 0.630
      ├── Some((6, 6)): 14/29 ≈ 0.483
      ├── Some((6, 7)): 26/43 ≈ 0.605
      └── Some((6, 8)): 23/40 ≈ 0.575
    ├── Some((0, 7)): 150/279 ≈ 0.538
      ├── Some((7, 1)): 12/27 ≈ 0.444
      ├── Some((7, 2)): 28/46 ≈ 0.609
      ├── Some((7, 3)): 10/24 ≈ 0.417
      ├── Some((7, 4)): 34/53 ≈ 0.642
      ├── Some((7, 5)): 10/24 ≈ 0.417
      ├── Some((7, 6)): 28/46 ≈ 0.609
      ├── Some((7, 7)): 17/33 ≈ 0.515
      └── Some((7, 8)): 10/25 ≈ 0.400
    └── Some((0, 8)): 141/266 ≈ 0.530
      ├── Some((8, 0)): 15/30 ≈ 0.500
      ├── Some((8, 1)): 23/40 ≈ 0.575
      ├── Some((8, 2)): 4/16 ≈ 0.250
      ├── Some((8, 3)): 14/29 ≈ 0.483
      ├── Some((8, 4)): 20/36 ≈ 0.556
      ├── Some((8, 5)): 24/41 ≈ 0.585
      ├── Some((8, 6)): 19/35 ≈ 0.543
      └── Some((8, 8)): 21/38 ≈ 0.553
  ├── Some((7, 1)): 1019/1954 ≈ 0.521
    ├── Some((1, 0)): 115/220 ≈ 0.523
      ├── Some((0, 0)): 13/25 ≈ 0.520
      ├── Some((0, 1)): 11/22 ≈ 0.500
      ├── Some((0, 2)): 14/26 ≈ 0.538
      ├── Some((0, 3)): 8/19 ≈ 0.421
      ├── Some((0, 4)): 7/18 ≈ 0.389
      ├── Some((0, 5)): 20/32 ≈ 0.625
      ├── Some((0, 6)): 20/32 ≈ 0.625
      ├── Some((0, 7)): 14/26 ≈ 0.538
      └── Some((0, 8)): 8/19 ≈ 0.421
    ├── Some((1, 1)): 127/238 ≈ 0.534
      ├── Some((1, 0)): 11/24 ≈ 0.458
      ├── Some((1, 2)): 14/28 ≈ 0.500
      ├── Some((1, 3)): 18/32 ≈ 0.562
      ├── Some((1, 4)): 22/37 ≈ 0.595
      ├── Some((1, 5)): 6/18 ≈ 0.333
      ├── Some((1, 6)): 16/30 ≈ 0.533
      ├── Some((1, 7)): 21/35 ≈ 0.600
      └── Some((1, 8)): 19/33 ≈ 0.576
    ├── Some((1, 2)): 98/194 ≈ 0.505
      ├── Some((2, 0)): 4/13 ≈ 0.308
      ├── Some((2, 1)): 8/18 ≈ 0.444
      ├── Some((2, 2)): 12/23 ≈ 0.522
      ├── Some((2, 3)): 5/15 ≈ 0.333
      ├── Some((2, 4)): 6/16 ≈ 0.375
      ├── Some((2, 5)): 23/35 ≈ 0.657
      ├── Some((2, 6)): 12/23 ≈ 0.522
      ├── Some((2, 7)): 16/27 ≈ 0.593
      └── Some((2, 8)): 12/23 ≈ 0.522
    ├── Some((1, 3)): 129/241 ≈ 0.535
      ├── Some((3, 0)): 10/22 ≈ 0.455
      ├── Some((3, 1)): 13/25 ≈ 0.520
      ├── Some((3, 2)): 13/25 ≈ 0.520
      ├── Some((3, 3)): 8/19 ≈ 0.421
      ├── Some((3, 4)): 25/39 ≈ 0.641
      ├── Some((3, 5)): 18/31 ≈ 0.581
      ├── Some((3, 6)): 14/26 ≈ 0.538
      ├── Some((3, 7)): 18/31 ≈ 0.581
      └── Some((3, 8)): 10/22 ≈ 0.455
    ├── Some((1, 4)): 122/231 ≈ 0.528
      ├── Some((4, 0)): 10/22 ≈ 0.455
      ├── Some((4, 1)): 13/25 ≈ 0.520
      ├── Some((4, 2)): 20/33 ≈ 0.606
      ├── Some((4, 3)): 12/24 ≈ 0.500
      ├── Some((4, 4)): 11/23 ≈ 0.478
      ├── Some((4, 5)): 16/28 ≈ 0.571
      ├── Some((4, 6)): 4/14 ≈ 0.286
      ├── Some((4, 7)): 18/31 ≈ 0.581
      └── Some((4, 8)): 17/30 ≈ 0.567
    ├── Some((1, 5)): 91/184 ≈ 0.495
      ├── Some((5, 0)): 7/17 ≈ 0.412
      ├── Some((5, 1)): 3/12 ≈ 0.250
      ├── Some((5, 2)): 4/14 ≈ 0.286
      ├── Some((5, 3)): 10/21 ≈ 0.476
      ├── Some((5, 4)): 7/17 ≈ 0.412
      ├── Some((5, 5)): 27/39 ≈ 0.692
      ├── Some((5, 6)): 18/29 ≈ 0.621
      ├── Some((5, 7)): 12/23 ≈ 0.522
      └── Some((5, 8)): 2/11 ≈ 0.182
    ├── Some((1, 6)): 94/188 ≈ 0.500
      ├── Some((6, 0)): 8/18 ≈ 0.444
      ├── Some((6, 1)): 6/16 ≈ 0.375
      ├── Some((6, 2)): 13/24 ≈ 0.542
      ├── Some((6, 3)): 12/23 ≈ 0.522
      ├── Some((6, 4)): 10/20 ≈ 0.500
      ├── Some((6, 5)): 6/16 ≈ 0.375
      ├── Some((6, 6)): 4/13 ≈ 0.308
      ├── Some((6, 7)): 24/35 ≈ 0.686
      └── Some((6, 8)): 11/22 ≈ 0.500
    ├── Some((1, 7)): 106/206 ≈ 0.515
      ├── Some((7, 0)): 12/24 ≈ 0.500
      ├── Some((7, 2)): 19/32 ≈ 0.594
      ├── Some((7, 3)): 18/31 ≈ 0.581
      ├── Some((7, 4)): 9/21 ≈ 0.429
      ├── Some((7, 5)): 4/15 ≈ 0.267
      ├── Some((7, 6)): 14/27 ≈ 0.519
      ├── Some((7, 7)): 20/34 ≈ 0.588
      └── Some((7, 8)): 9/21 ≈ 0.429
    └── Some((1, 8)): 136/251 ≈ 0.542
      ├── Some((8, 0)): 15/29 ≈ 0.517
      ├── Some((8, 1)): 9/22 ≈ 0.409
      ├── Some((8, 2)): 19/34 ≈ 0.559
      ├── Some((8, 3)): 14/28 ≈ 0.500
      ├── Some((8, 4)): 7/19 ≈ 0.368
      ├── Some((8, 5)): 18/33 ≈ 0.545
      ├── Some((8, 6)): 16/30 ≈ 0.533
      └── Some((8, 8)): 38/55 ≈ 0.691
  ├── Some((7, 2)): 1737/3187 ≈ 0.545
    ├── Some((2, 0)): 182/338 ≈ 0.538
      ├── Some((0, 0)): 15/31 ≈ 0.484
      ├── Some((0, 1)): 12/28 ≈ 0.429
      ├── Some((0, 2)): 18/35 ≈ 0.514
      ├── Some((0, 3)): 22/40 ≈ 0.550
      ├── Some((0, 4)): 25/43 ≈ 0.581
      ├── Some((0, 5)): 8/22 ≈ 0.364
      ├── Some((0, 6)): 26/45 ≈ 0.578
      ├── Some((0, 7)): 12/28 ≈ 0.429
      └── Some((0, 8)): 44/65 ≈ 0.677
    ├── Some((2, 1)): 180/335 ≈ 0.537
      ├── Some((1, 0)): 13/29 ≈ 0.448
      ├── Some((1, 1)): 22/40 ≈ 0.550
      ├── Some((1, 2)): 26/44 ≈ 0.591
      ├── Some((1, 3)): 27/45 ≈ 0.600
      ├── Some((1, 4)): 10/25 ≈ 0.400
      ├── Some((1, 5)): 26/44 ≈ 0.591
      ├── Some((1, 6)): 11/26 ≈ 0.423
      ├── Some((1, 7)): 16/33 ≈ 0.485
      └── Some((1, 8)): 29/48 ≈ 0.604
    ├── Some((2, 2)): 237/421 ≈ 0.563
      ├── Some((2, 0)): 20/41 ≈ 0.488
      ├── Some((2, 1)): 29/52 ≈ 0.558
      ├── Some((2, 3)): 24/46 ≈ 0.522
      ├── Some((2, 4)): 32/55 ≈ 0.582
      ├── Some((2, 5)): 30/53 ≈ 0.566
      ├── Some((2, 6)): 36/60 ≈ 0.600
      ├── Some((2, 7)): 38/62 ≈ 0.613
      └── Some((2, 8)): 28/51 ≈ 0.549
    ├── Some((2, 3)): 109/225 ≈ 0.484
      ├── Some((3, 0)): 3/14 ≈ 0.214
      ├── Some((3, 1)): 23/38 ≈ 0.605
      ├── Some((3, 2)): 13/26 ≈ 0.500
      ├── Some((3, 3)): 11/24 ≈ 0.458
      ├── Some((3, 4)): 14/27 ≈ 0.519
      ├── Some((3, 5)): 12/25 ≈ 0.480
      ├── Some((3, 6)): 15/28 ≈ 0.536
      ├── Some((3, 7)): 9/21 ≈ 0.429
      └── Some((3, 8)): 9/21 ≈ 0.429
    ├── Some((2, 4)): 236/420 ≈ 0.562
      ├── Some((4, 0)): 28/49 ≈ 0.571
      ├── Some((4, 1)): 17/36 ≈ 0.472
      ├── Some((4, 2)): 51/76 ≈ 0.671
      ├── Some((4, 3)): 30/52 ≈ 0.577
      ├── Some((4, 4)): 7/22 ≈ 0.318
      ├── Some((4, 5)): 24/44 ≈ 0.545
      ├── Some((4, 6)): 29/50 ≈ 0.580
      ├── Some((4, 7)): 12/29 ≈ 0.414
      └── Some((4, 8)): 38/61 ≈ 0.623
    ├── Some((2, 5)): 162/307 ≈ 0.528
      ├── Some((5, 0)): 28/46 ≈ 0.609
      ├── Some((5, 1)): 21/38 ≈ 0.553
      ├── Some((5, 2)): 10/24 ≈ 0.417
      ├── Some((5, 3)): 7/20 ≈ 0.350
      ├── Some((5, 4)): 25/42 ≈ 0.595
      ├── Some((5, 5)): 20/37 ≈ 0.541
      ├── Some((5, 6)): 19/35 ≈ 0.543
      ├── Some((5, 7)): 16/32 ≈ 0.500
      └── Some((5, 8)): 16/32 ≈ 0.500
    ├── Some((2, 6)): 161/306 ≈ 0.526
      ├── Some((6, 0)): 25/42 ≈ 0.595
      ├── Some((6, 1)): 14/29 ≈ 0.483
      ├── Some((6, 2)): 29/47 ≈ 0.617
      ├── Some((6, 3)): 20/37 ≈ 0.541
      ├── Some((6, 4)): 13/28 ≈ 0.464
      ├── Some((6, 5)): 16/32 ≈ 0.500
      ├── Some((6, 6)): 10/24 ≈ 0.417
      ├── Some((6, 7)): 13/28 ≈ 0.464
      └── Some((6, 8)): 21/38 ≈ 0.553
    ├── Some((2, 7)): 162/307 ≈ 0.528
      ├── Some((7, 0)): 21/39 ≈ 0.538
      ├── Some((7, 1)): 8/23 ≈ 0.348
      ├── Some((7, 3)): 24/43 ≈ 0.558
      ├── Some((7, 4)): 30/50 ≈ 0.600
      ├── Some((7, 5)): 29/49 ≈ 0.592
      ├── Some((7, 6)): 10/26 ≈ 0.385
      ├── Some((7, 7)): 21/40 ≈ 0.525
      └── Some((7, 8)): 18/36 ≈ 0.500
    └── Some((2, 8)): 308/527 ≈ 0.584
      ├── Some((8, 0)): 44/73 ≈ 0.603
      ├── Some((8, 1)): 56/87 ≈ 0.644
      ├── Some((8, 2)): 25/49 ≈ 0.510
      ├── Some((8, 3)): 26/50 ≈ 0.520
      ├── Some((8, 4)): 48/77 ≈ 0.623
      ├── Some((8, 5)): 30/56 ≈ 0.536
      ├── Some((8, 6)): 42/70 ≈ 0.600
      └── Some((8, 8)): 37/64 ≈ 0.578
  ├── Some((7, 3)): 972/1872 ≈ 0.519
    ├── Some((3, 0)): 118/224 ≈ 0.527
      ├── Some((0, 0)): 20/33 ≈ 0.606
      ├── Some((0, 1)): 18/30 ≈ 0.600
      ├── Some((0, 2)): 5/15 ≈ 0.333
      ├── Some((0, 3)): 8/19 ≈ 0.421
      ├── Some((0, 4)): 18/30 ≈ 0.600
      ├── Some((0, 5)): 8/19 ≈ 0.421
      ├── Some((0, 6)): 8/19 ≈ 0.421
      ├── Some((0, 7)): 14/26 ≈ 0.538
      └── Some((0, 8)): 19/32 ≈ 0.594
    ├── Some((3, 1)): 168/297 ≈ 0.566
      ├── Some((1, 0)): 9/22 ≈ 0.409
      ├── Some((1, 1)): 29/45 ≈ 0.644
      ├── Some((1, 2)): 22/37 ≈ 0.595
      ├── Some((1, 3)): 26/41 ≈ 0.634
      ├── Some((1, 4)): 10/23 ≈ 0.435
      ├── Some((1, 5)): 11/24 ≈ 0.458
      ├── Some((1, 6)): 16/30 ≈ 0.533
      ├── Some((1, 7)): 28/44 ≈ 0.636
      └── Some((1, 8)): 16/30 ≈ 0.533
    ├── Some((3, 2)): 80/166 ≈ 0.482
      ├── Some((2, 0)): 7/16 ≈ 0.438
      ├── Some((2, 1)): 3/12 ≈ 0.250
      ├── Some((2, 2)): 11/21 ≈ 0.524
      ├── Some((2, 3)): 14/24 ≈ 0.583
      ├── Some((2, 4)): 8/18 ≈ 0.444
      ├── Some((2, 5)): 16/26 ≈ 0.615
      ├── Some((2, 6)): 12/22 ≈ 0.545
      ├── Some((2, 7)): 2/10 ≈ 0.200
      └── Some((2, 8)): 7/16 ≈ 0.438
    ├── Some((3, 3)): 96/190 ≈ 0.505
      ├── Some((3, 0)): 10/22 ≈ 0.455
      ├── Some((3, 1)): 12/24 ≈ 0.500
      ├── Some((3, 2)): 24/37 ≈ 0.649
      ├── Some((3, 4)): 12/24 ≈ 0.500
      ├── Some((3, 5)): 9/20 ≈ 0.450
      ├── Some((3, 6)): 14/26 ≈ 0.538
      ├── Some((3, 7)): 9/20 ≈ 0.450
      └── Some((3, 8)): 5/16 ≈ 0.312
    ├── Some((3, 4)): 100/196 ≈ 0.510
      ├── Some((4, 0)): 14/25 ≈ 0.560
      ├── Some((4, 1)): 9/19 ≈ 0.474
      ├── Some((4, 2)): 13/24 ≈ 0.542
      ├── Some((4, 3)): 14/25 ≈ 0.560
      ├── Some((4, 4)): 13/24 ≈ 0.542
      ├── Some((4, 5)): 18/29 ≈ 0.621
      ├── Some((4, 6)): 4/13 ≈ 0.308
      ├── Some((4, 7)): 9/20 ≈ 0.450
      └── Some((4, 8)): 6/16 ≈ 0.375
    ├── Some((3, 5)): 65/142 ≈ 0.458
      ├── Some((5, 0)): 14/23 ≈ 0.609
      ├── Some((5, 1)): 5/13 ≈ 0.385
      ├── Some((5, 2)): 2/10 ≈ 0.200
      ├── Some((5, 3)): 6/15 ≈ 0.400
      ├── Some((5, 4)): 12/21 ≈ 0.571
      ├── Some((5, 5)): 4/12 ≈ 0.333
      ├── Some((5, 6)): 10/19 ≈ 0.526
      ├── Some((5, 7)): 7/16 ≈ 0.438
      └── Some((5, 8)): 4/12 ≈ 0.333
    ├── Some((3, 6)): 95/189 ≈ 0.503
      ├── Some((6, 0)): 9/20 ≈ 0.450
      ├── Some((6, 1)): 15/26 ≈ 0.577
      ├── Some((6, 2)): 15/26 ≈ 0.577
      ├── Some((6, 3)): 4/13 ≈ 0.308
      ├── Some((6, 4)): 18/29 ≈ 0.621
      ├── Some((6, 5)): 4/13 ≈ 0.308
      ├── Some((6, 6)): 13/24 ≈ 0.542
      ├── Some((6, 7)): 12/23 ≈ 0.522
      └── Some((6, 8)): 4/14 ≈ 0.286
    ├── Some((3, 7)): 142/259 ≈ 0.548
      ├── Some((7, 0)): 17/32 ≈ 0.531
      ├── Some((7, 1)): 10/23 ≈ 0.435
      ├── Some((7, 2)): 5/17 ≈ 0.294
      ├── Some((7, 4)): 11/25 ≈ 0.440
      ├── Some((7, 5)): 13/27 ≈ 0.481
      ├── Some((7, 6)): 36/53 ≈ 0.679
      ├── Some((7, 7)): 30/46 ≈ 0.652
      └── Some((7, 8)): 20/35 ≈ 0.571
    └── Some((3, 8)): 108/208 ≈ 0.519
      ├── Some((8, 0)): 6/17 ≈ 0.353
      ├── Some((8, 1)): 18/31 ≈ 0.581
      ├── Some((8, 2)): 3/13 ≈ 0.231
      ├── Some((8, 3)): 15/28 ≈ 0.536
      ├── Some((8, 4)): 24/38 ≈ 0.632
      ├── Some((8, 5)): 12/25 ≈ 0.480
      ├── Some((8, 6)): 10/22 ≈ 0.455
      └── Some((8, 8)): 19/33 ≈ 0.576
  ├── Some((7, 4)): 1213/2289 ≈ 0.530
    ├── Some((4, 0)): 133/252 ≈ 0.528
      ├── Some((0, 0)): 13/26 ≈ 0.500
      ├── Some((0, 1)): 24/38 ≈ 0.632
      ├── Some((0, 2)): 12/25 ≈ 0.480
      ├── Some((0, 3)): 10/23 ≈ 0.435
      ├── Some((0, 4)): 4/15 ≈ 0.267
      ├── Some((0, 5)): 11/24 ≈ 0.458
      ├── Some((0, 6)): 20/34 ≈ 0.588
      ├── Some((0, 7)): 12/25 ≈ 0.480
      └── Some((0, 8)): 26/41 ≈ 0.634
    ├── Some((4, 1)): 57/133 ≈ 0.429
      ├── Some((1, 0)): 6/14 ≈ 0.429
      ├── Some((1, 1)): 11/20 ≈ 0.550
      ├── Some((1, 2)): 3/11 ≈ 0.273
      ├── Some((1, 3)): 8/17 ≈ 0.471
      ├── Some((1, 4)): 4/12 ≈ 0.333
      ├── Some((1, 5)): 12/21 ≈ 0.571
      ├── Some((1, 6)): 7/15 ≈ 0.467
      ├── Some((1, 7)): 2/10 ≈ 0.200
      └── Some((1, 8)): 4/12 ≈ 0.333
    ├── Some((4, 2)): 115/225 ≈ 0.511
      ├── Some((2, 0)): 23/36 ≈ 0.639
      ├── Some((2, 1)): 23/37 ≈ 0.622
      ├── Some((2, 2)): 15/28 ≈ 0.536
      ├── Some((2, 3)): 6/17 ≈ 0.353
      ├── Some((2, 4)): 4/14 ≈ 0.286
      ├── Some((2, 5)): 15/28 ≈ 0.536
      ├── Some((2, 6)): 9/21 ≈ 0.429
      ├── Some((2, 7)): 2/12 ≈ 0.167
      └── Some((2, 8)): 18/31 ≈ 0.581
    ├── Some((4, 3)): 165/301 ≈ 0.548
      ├── Some((3, 0)): 16/31 ≈ 0.516
      ├── Some((3, 1)): 23/39 ≈ 0.590
      ├── Some((3, 2)): 11/25 ≈ 0.440
      ├── Some((3, 3)): 13/27 ≈ 0.481
      ├── Some((3, 4)): 9/22 ≈ 0.409
      ├── Some((3, 5)): 16/31 ≈ 0.516
      ├── Some((3, 6)): 20/36 ≈ 0.556
      ├── Some((3, 7)): 23/39 ≈ 0.590
      └── Some((3, 8)): 33/50 ≈ 0.660
    ├── Some((4, 4)): 135/255 ≈ 0.529
      ├── Some((4, 0)): 25/41 ≈ 0.610
      ├── Some((4, 1)): 11/25 ≈ 0.440
      ├── Some((4, 2)): 11/25 ≈ 0.440
      ├── Some((4, 3)): 10/24 ≈ 0.417
      ├── Some((4, 5)): 26/42 ≈ 0.619
      ├── Some((4, 6)): 24/40 ≈ 0.600
      ├── Some((4, 7)): 7/20 ≈ 0.350
      └── Some((4, 8)): 21/37 ≈ 0.568
    ├── Some((4, 5)): 201/354 ≈ 0.568
      ├── Some((5, 0)): 10/25 ≈ 0.400
      ├── Some((5, 1)): 33/52 ≈ 0.635
      ├── Some((5, 2)): 28/46 ≈ 0.609
      ├── Some((5, 3)): 21/38 ≈ 0.553
      ├── Some((5, 4)): 9/23 ≈ 0.391
      ├── Some((5, 5)): 15/31 ≈ 0.484
      ├── Some((5, 6)): 16/32 ≈ 0.500
      ├── Some((5, 7)): 39/58 ≈ 0.672
      └── Some((5, 8)): 30/48 ≈ 0.625
    ├── Some((4, 6)): 121/234 ≈ 0.517
      ├── Some((6, 0)): 13/26 ≈ 0.500
      ├── Some((6, 1)): 14/27 ≈ 0.519
      ├── Some((6, 2)): 23/37 ≈ 0.622
      ├── Some((6, 3)): 20/34 ≈ 0.588
      ├── Some((6, 4)): 7/18 ≈ 0.389
      ├── Some((6, 5)): 8/20 ≈ 0.400
      ├── Some((6, 6)): 18/31 ≈ 0.581
      ├── Some((6, 7)): 10/22 ≈ 0.455
      └── Some((6, 8)): 7/18 ≈ 0.389
    ├── Some((4, 7)): 119/231 ≈ 0.515
      ├── Some((7, 0)): 10/23 ≈ 0.435
      ├── Some((7, 1)): 2/13 ≈ 0.154
      ├── Some((7, 2)): 18/33 ≈ 0.545
      ├── Some((7, 3)): 19/34 ≈ 0.559
      ├── Some((7, 5)): 15/29 ≈ 0.517
      ├── Some((7, 6)): 31/48 ≈ 0.646
      ├── Some((7, 7)): 10/23 ≈ 0.435
      └── Some((7, 8)): 13/27 ≈ 0.481
    └── Some((4, 8)): 167/303 ≈ 0.551
      ├── Some((8, 0)): 16/32 ≈ 0.500
      ├── Some((8, 1)): 12/27 ≈ 0.444
      ├── Some((8, 2)): 9/24 ≈ 0.375
      ├── Some((8, 3)): 14/30 ≈ 0.467
      ├── Some((8, 4)): 16/32 ≈ 0.500
      ├── Some((8, 5)): 44/64 ≈ 0.688
      ├── Some((8, 6)): 32/51 ≈ 0.627
      └── Some((8, 8)): 24/42 ≈ 0.571
  ├── Some((7, 5)): 971/1870 ≈ 0.519
    ├── Some((5, 0)): 120/226 ≈ 0.531
      ├── Some((0, 0)): 16/28 ≈ 0.571
      ├── Some((0, 1)): 13/25 ≈ 0.520
      ├── Some((0, 2)): 19/31 ≈ 0.613
      ├── Some((0, 3)): 10/21 ≈ 0.476
      ├── Some((0, 4)): 22/35 ≈ 0.629
      ├── Some((0, 5)): 8/19 ≈ 0.421
      ├── Some((0, 6)): 6/17 ≈ 0.353
      ├── Some((0, 7)): 16/28 ≈ 0.571
      └── Some((0, 8)): 10/21 ≈ 0.476
    ├── Some((5, 1)): 127/237 ≈ 0.536
      ├── Some((1, 0)): 14/27 ≈ 0.519
      ├── Some((1, 1)): 8/19 ≈ 0.421
      ├── Some((1, 2)): 22/35 ≈ 0.629
      ├── Some((1, 3)): 14/27 ≈ 0.519
      ├── Some((1, 4)): 15/28 ≈ 0.536
      ├── Some((1, 5)): 31/45 ≈ 0.689
      ├── Some((1, 6)): 3/13 ≈ 0.231
      ├── Some((1, 7)): 11/23 ≈ 0.478
      └── Some((1, 8)): 8/19 ≈ 0.421
    ├── Some((5, 2)): 104/202 ≈ 0.515
      ├── Some((2, 0)): 21/33 ≈ 0.636
      ├── Some((2, 1)): 5/15 ≈ 0.333
      ├── Some((2, 2)): 12/23 ≈ 0.522
      ├── Some((2, 3)): 3/12 ≈ 0.250
      ├── Some((2, 4)): 15/27 ≈ 0.556
      ├── Some((2, 5)): 4/14 ≈ 0.286
      ├── Some((2, 6)): 22/34 ≈ 0.647
      ├── Some((2, 7)): 12/23 ≈ 0.522
      └── Some((2, 8)): 9/20 ≈ 0.450
    ├── Some((5, 3)): 92/184 ≈ 0.500
      ├── Some((3, 0)): 7/17 ≈ 0.412
      ├── Some((3, 1)): 3/12 ≈ 0.250
      ├── Some((3, 2)): 5/14 ≈ 0.357
      ├── Some((3, 3)): 7/17 ≈ 0.412
      ├── Some((3, 4)): 8/18 ≈ 0.444
      ├── Some((3, 5)): 23/34 ≈ 0.676
      ├── Some((3, 6)): 19/30 ≈ 0.633
      ├── Some((3, 7)): 14/25 ≈ 0.560
      └── Some((3, 8)): 6/16 ≈ 0.375
    ├── Some((5, 4)): 107/207 ≈ 0.517
      ├── Some((4, 0)): 11/22 ≈ 0.500
      ├── Some((4, 1)): 10/21 ≈ 0.476
      ├── Some((4, 2)): 11/22 ≈ 0.500
      ├── Some((4, 3)): 15/26 ≈ 0.577
      ├── Some((4, 4)): 15/26 ≈ 0.577
      ├── Some((4, 5)): 19/31 ≈ 0.613
      ├── Some((4, 6)): 13/24 ≈ 0.542
      ├── Some((4, 7)): 8/19 ≈ 0.421
      └── Some((4, 8)): 5/15 ≈ 0.333
    ├── Some((5, 5)): 81/167 ≈ 0.485
      ├── Some((5, 0)): 10/21 ≈ 0.476
      ├── Some((5, 1)): 12/23 ≈ 0.522
      ├── Some((5, 2)): 3/12 ≈ 0.250
      ├── Some((5, 3)): 11/22 ≈ 0.500
      ├── Some((5, 4)): 4/14 ≈ 0.286
      ├── Some((5, 6)): 12/23 ≈ 0.522
      ├── Some((5, 7)): 13/24 ≈ 0.542
      └── Some((5, 8)): 16/27 ≈ 0.593
    ├── Some((5, 6)): 91/183 ≈ 0.497
      ├── Some((6, 0)): 4/13 ≈ 0.308
      ├── Some((6, 1)): 16/27 ≈ 0.593
      ├── Some((6, 2)): 6/16 ≈ 0.375
      ├── Some((6, 3)): 3/12 ≈ 0.250
      ├── Some((6, 4)): 20/31 ≈ 0.645
      ├── Some((6, 5)): 8/18 ≈ 0.444
      ├── Some((6, 6)): 13/24 ≈ 0.542
      ├── Some((6, 7)): 10/20 ≈ 0.500
      └── Some((6, 8)): 10/21 ≈ 0.476
    ├── Some((5, 7)): 171/302 ≈ 0.566
      ├── Some((7, 0)): 7/20 ≈ 0.350
      ├── Some((7, 1)): 19/35 ≈ 0.543
      ├── Some((7, 2)): 29/46 ≈ 0.630
      ├── Some((7, 3)): 20/36 ≈ 0.556
      ├── Some((7, 4)): 24/41 ≈ 0.585
      ├── Some((7, 6)): 31/49 ≈ 0.633
      ├── Some((7, 7)): 17/33 ≈ 0.515
      └── Some((7, 8)): 24/41 ≈ 0.585
    └── Some((5, 8)): 77/161 ≈ 0.478
      ├── Some((8, 0)): 4/14 ≈ 0.286
      ├── Some((8, 1)): 8/18 ≈ 0.444
      ├── Some((8, 2)): 7/17 ≈ 0.412
      ├── Some((8, 3)): 13/24 ≈ 0.542
      ├── Some((8, 4)): 19/31 ≈ 0.613
      ├── Some((8, 5)): 11/22 ≈ 0.500
      ├── Some((8, 6)): 2/11 ≈ 0.182
      └── Some((8, 8)): 12/23 ≈ 0.522
  ├── Some((7, 6)): 1306/2450 ≈ 0.533
    ├── Some((6, 0)): 137/261 ≈ 0.525
      ├── Some((0, 0)): 16/30 ≈ 0.533
      ├── Some((0, 1)): 9/22 ≈ 0.409
      ├── Some((0, 2)): 15/29 ≈ 0.517
      ├── Some((0, 3)): 3/14 ≈ 0.214
      ├── Some((0, 4)): 13/26 ≈ 0.500
      ├── Some((0, 5)): 25/40 ≈ 0.625
      ├── Some((0, 6)): 20/35 ≈ 0.571
      ├── Some((0, 7)): 19/33 ≈ 0.576
      └── Some((0, 8)): 17/31 ≈ 0.548
    ├── Some((6, 1)): 88/185 ≈ 0.476
      ├── Some((1, 0)): 11/22 ≈ 0.500
      ├── Some((1, 1)): 11/22 ≈ 0.500
      ├── Some((1, 2)): 11/22 ≈ 0.500
      ├── Some((1, 3)): 6/16 ≈ 0.375
      ├── Some((1, 4)): 8/18 ≈ 0.444
      ├── Some((1, 5)): 7/17 ≈ 0.412
      ├── Some((1, 6)): 14/25 ≈ 0.560
      ├── Some((1, 7)): 9/20 ≈ 0.450
      └── Some((1, 8)): 11/22 ≈ 0.500
    ├── Some((6, 2)): 226/394 ≈ 0.574
      ├── Some((2, 0)): 18/35 ≈ 0.514
      ├── Some((2, 1)): 16/33 ≈ 0.485
      ├── Some((2, 2)): 19/37 ≈ 0.514
      ├── Some((2, 3)): 37/58 ≈ 0.638
      ├── Some((2, 4)): 35/55 ≈ 0.636
      ├── Some((2, 5)): 35/55 ≈ 0.636
      ├── Some((2, 6)): 23/41 ≈ 0.561
      ├── Some((2, 7)): 18/36 ≈ 0.500
      └── Some((2, 8)): 24/43 ≈ 0.558
    ├── Some((6, 3)): 134/256 ≈ 0.523
      ├── Some((3, 0)): 10/23 ≈ 0.435
      ├── Some((3, 1)): 13/26 ≈ 0.500
      ├── Some((3, 2)): 17/31 ≈ 0.548
      ├── Some((3, 3)): 21/35 ≈ 0.600
      ├── Some((3, 4)): 16/30 ≈ 0.533
      ├── Some((3, 5)): 7/19 ≈ 0.368
      ├── Some((3, 6)): 8/20 ≈ 0.400
      ├── Some((3, 7)): 21/35 ≈ 0.600
      └── Some((3, 8)): 21/36 ≈ 0.583
    ├── Some((6, 4)): 89/186 ≈ 0.478
      ├── Some((4, 0)): 21/33 ≈ 0.636
      ├── Some((4, 1)): 6/16 ≈ 0.375
      ├── Some((4, 2)): 14/25 ≈ 0.560
      ├── Some((4, 3)): 6/16 ≈ 0.375
      ├── Some((4, 4)): 6/16 ≈ 0.375
      ├── Some((4, 5)): 14/25 ≈ 0.560
      ├── Some((4, 6)): 4/14 ≈ 0.286
      ├── Some((4, 7)): 9/20 ≈ 0.450
      └── Some((4, 8)): 9/20 ≈ 0.450
    ├── Some((6, 5)): 151/282 ≈ 0.535
      ├── Some((5, 0)): 21/36 ≈ 0.583
      ├── Some((5, 1)): 10/23 ≈ 0.435
      ├── Some((5, 2)): 34/51 ≈ 0.667
      ├── Some((5, 3)): 15/29 ≈ 0.517
      ├── Some((5, 4)): 16/31 ≈ 0.516
      ├── Some((5, 5)): 16/31 ≈ 0.516
      ├── Some((5, 6)): 10/23 ≈ 0.435
      ├── Some((5, 7)): 16/31 ≈ 0.516
      └── Some((5, 8)): 12/26 ≈ 0.462
    ├── Some((6, 6)): 195/348 ≈ 0.560
      ├── Some((6, 0)): 29/49 ≈ 0.592
      ├── Some((6, 1)): 32/52 ≈ 0.615
      ├── Some((6, 2)): 30/50 ≈ 0.600
      ├── Some((6, 3)): 32/53 ≈ 0.604
      ├── Some((6, 4)): 20/38 ≈ 0.526
      ├── Some((6, 5)): 19/37 ≈ 0.514
      ├── Some((6, 7)): 14/31 ≈ 0.452
      └── Some((6, 8)): 19/37 ≈ 0.514
    ├── Some((6, 7)): 111/221 ≈ 0.502
      ├── Some((7, 0)): 12/26 ≈ 0.462
      ├── Some((7, 1)): 14/28 ≈ 0.500
      ├── Some((7, 2)): 15/29 ≈ 0.517
      ├── Some((7, 3)): 1/11 ≈ 0.091
      ├── Some((7, 4)): 6/18 ≈ 0.333
      ├── Some((7, 5)): 15/29 ≈ 0.517
      ├── Some((7, 7)): 19/34 ≈ 0.559
      └── Some((7, 8)): 29/45 ≈ 0.644
    └── Some((6, 8)): 174/316 ≈ 0.551
      ├── Some((8, 0)): 28/47 ≈ 0.596
      ├── Some((8, 1)): 28/47 ≈ 0.596
      ├── Some((8, 2)): 18/35 ≈ 0.514
      ├── Some((8, 3)): 18/35 ≈ 0.514
      ├── Some((8, 4)): 25/44 ≈ 0.568
      ├── Some((8, 5)): 23/41 ≈ 0.561
      ├── Some((8, 6)): 6/20 ≈ 0.300
      └── Some((8, 8)): 27/46 ≈ 0.587
  ├── Some((7, 7)): 1325/2482 ≈ 0.534
    ├── Some((7, 0)): 151/288 ≈ 0.524
      ├── Some((0, 0)): 14/29 ≈ 0.483
      ├── Some((0, 1)): 15/30 ≈ 0.500
      ├── Some((0, 2)): 25/42 ≈ 0.595
      ├── Some((0, 3)): 20/36 ≈ 0.556
      ├── Some((0, 4)): 20/36 ≈ 0.556
      ├── Some((0, 5)): 18/33 ≈ 0.545
      ├── Some((0, 6)): 11/25 ≈ 0.440
      ├── Some((0, 7)): 16/31 ≈ 0.516
      └── Some((0, 8)): 11/25 ≈ 0.440
    ├── Some((7, 1)): 204/369 ≈ 0.553
      ├── Some((1, 0)): 24/43 ≈ 0.558
      ├── Some((1, 1)): 20/38 ≈ 0.526
      ├── Some((1, 2)): 36/56 ≈ 0.643
      ├── Some((1, 3)): 28/47 ≈ 0.596
      ├── Some((1, 4)): 16/33 ≈ 0.485
      ├── Some((1, 5)): 16/33 ≈ 0.485
      ├── Some((1, 6)): 31/51 ≈ 0.608
      ├── Some((1, 7)): 12/28 ≈ 0.429
      └── Some((1, 8)): 21/39 ≈ 0.538
    ├── Some((7, 2)): 142/274 ≈ 0.518
      ├── Some((2, 0)): 10/24 ≈ 0.417
      ├── Some((2, 1)): 17/32 ≈ 0.531
      ├── Some((2, 2)): 19/34 ≈ 0.559
      ├── Some((2, 3)): 24/40 ≈ 0.600
      ├── Some((2, 4)): 24/40 ≈ 0.600
      ├── Some((2, 5)): 11/25 ≈ 0.440
      ├── Some((2, 6)): 5/17 ≈ 0.294
      ├── Some((2, 7)): 17/32 ≈ 0.531
      └── Some((2, 8)): 14/29 ≈ 0.483
    ├── Some((7, 3)): 228/405 ≈ 0.563
      ├── Some((3, 0)): 26/46 ≈ 0.565
      ├── Some((3, 1)): 32/53 ≈ 0.604
      ├── Some((3, 2)): 19/37 ≈ 0.514
      ├── Some((3, 3)): 23/42 ≈ 0.548
      ├── Some((3, 4)): 14/31 ≈ 0.452
      ├── Some((3, 5)): 38/60 ≈ 0.633
      ├── Some((3, 6)): 16/34 ≈ 0.471
      ├── Some((3, 7)): 20/39 ≈ 0.513
      └── Some((3, 8)): 40/62 ≈ 0.645
    ├── Some((7, 4)): 153/291 ≈ 0.526
      ├── Some((4, 0)): 16/31 ≈ 0.516
      ├── Some((4, 1)): 24/41 ≈ 0.585
      ├── Some((4, 2)): 16/31 ≈ 0.516
      ├── Some((4, 3)): 19/35 ≈ 0.543
      ├── Some((4, 4)): 5/17 ≈ 0.294
      ├── Some((4, 5)): 17/33 ≈ 0.515
      ├── Some((4, 6)): 16/31 ≈ 0.516
      ├── Some((4, 7)): 21/37 ≈ 0.568
      └── Some((4, 8)): 18/34 ≈ 0.529
    ├── Some((7, 5)): 150/287 ≈ 0.523
      ├── Some((5, 0)): 15/30 ≈ 0.500
      ├── Some((5, 1)): 20/36 ≈ 0.556
      ├── Some((5, 2)): 29/46 ≈ 0.630
      ├── Some((5, 3)): 13/28 ≈ 0.464
      ├── Some((5, 4)): 18/34 ≈ 0.529
      ├── Some((5, 5)): 5/17 ≈ 0.294
      ├── Some((5, 6)): 17/33 ≈ 0.515
      ├── Some((5, 7)): 20/36 ≈ 0.556
      └── Some((5, 8)): 12/26 ≈ 0.462
    ├── Some((7, 6)): 197/359 ≈ 0.549
      ├── Some((6, 0)): 5/19 ≈ 0.263
      ├── Some((6, 1)): 26/45 ≈ 0.578
      ├── Some((6, 2)): 26/45 ≈ 0.578
      ├── Some((6, 3)): 35/55 ≈ 0.636
      ├── Some((6, 4)): 22/40 ≈ 0.550
      ├── Some((6, 5)): 25/44 ≈ 0.568
      ├── Some((6, 6)): 22/40 ≈ 0.550
      ├── Some((6, 7)): 11/27 ≈ 0.407
      └── Some((6, 8)): 24/43 ≈ 0.558
    └── Some((7, 8)): 100/208 ≈ 0.481
      ├── Some((8, 0)): 11/24 ≈ 0.458
      ├── Some((8, 1)): 3/14 ≈ 0.214
      ├── Some((8, 2)): 5/17 ≈ 0.294
      ├── Some((8, 3)): 16/30 ≈ 0.533
      ├── Some((8, 4)): 17/31 ≈ 0.548
      ├── Some((8, 5)): 21/36 ≈ 0.583
      ├── Some((8, 6)): 9/22 ≈ 0.409
      └── Some((8, 8)): 18/33 ≈ 0.545
  └── Some((7, 8)): 1582/2923 ≈ 0.541
    ├── Some((8, 0)): 166/317 ≈ 0.524
      ├── Some((0, 0)): 19/36 ≈ 0.528
      ├── Some((0, 1)): 11/26 ≈ 0.423
      ├── Some((0, 2)): 19/36 ≈ 0.528
      ├── Some((0, 3)): 11/26 ≈ 0.423
      ├── Some((0, 4)): 18/35 ≈ 0.514
      ├── Some((0, 5)): 32/51 ≈ 0.627
      ├── Some((0, 6)): 22/40 ≈ 0.550
      ├── Some((0, 7)): 15/31 ≈ 0.484
      └── Some((0, 8)): 18/35 ≈ 0.514
    ├── Some((8, 1)): 169/322 ≈ 0.525
      ├── Some((1, 0)): 15/32 ≈ 0.469
      ├── Some((1, 1)): 12/28 ≈ 0.429
      ├── Some((1, 2)): 18/35 ≈ 0.514
      ├── Some((1, 3)): 22/40 ≈ 0.550
      ├── Some((1, 4)): 18/35 ≈ 0.514
      ├── Some((1, 5)): 50/72 ≈ 0.694
      ├── Some((1, 6)): 17/34 ≈ 0.500
      ├── Some((1, 7)): 1/12 ≈ 0.083
      └── Some((1, 8)): 16/33 ≈ 0.485
    ├── Some((8, 2)): 215/392 ≈ 0.548
      ├── Some((2, 0)): 25/45 ≈ 0.556
      ├── Some((2, 1)): 14/31 ≈ 0.452
      ├── Some((2, 2)): 29/50 ≈ 0.580
      ├── Some((2, 3)): 19/38 ≈ 0.500
      ├── Some((2, 4)): 42/65 ≈ 0.646
      ├── Some((2, 5)): 14/31 ≈ 0.452
      ├── Some((2, 6)): 28/49 ≈ 0.571
      ├── Some((2, 7)): 32/53 ≈ 0.604
      └── Some((2, 8)): 12/29 ≈ 0.414
    ├── Some((8, 3)): 245/438 ≈ 0.559
      ├── Some((3, 0)): 25/46 ≈ 0.543
      ├── Some((3, 1)): 10/27 ≈ 0.370
      ├── Some((3, 2)): 25/46 ≈ 0.543
      ├── Some((3, 3)): 30/52 ≈ 0.577
      ├── Some((3, 4)): 37/61 ≈ 0.607
      ├── Some((3, 5)): 21/41 ≈ 0.512
      ├── Some((3, 6)): 25/46 ≈ 0.543
      ├── Some((3, 7)): 29/51 ≈ 0.569
      └── Some((3, 8)): 42/67 ≈ 0.627
    ├── Some((8, 4)): 280/491 ≈ 0.570
      ├── Some((4, 0)): 15/35 ≈ 0.429
      ├── Some((4, 1)): 38/63 ≈ 0.603
      ├── Some((4, 2)): 22/44 ≈ 0.500
      ├── Some((4, 3)): 45/71 ≈ 0.634
      ├── Some((4, 4)): 21/42 ≈ 0.500
      ├── Some((4, 5)): 38/63 ≈ 0.603
      ├── Some((4, 6)): 36/61 ≈ 0.590
      ├── Some((4, 7)): 45/71 ≈ 0.634
      └── Some((4, 8)): 19/40 ≈ 0.475
    ├── Some((8, 5)): 142/279 ≈ 0.509
      ├── Some((5, 0)): 20/36 ≈ 0.556
      ├── Some((5, 1)): 8/21 ≈ 0.381
      ├── Some((5, 2)): 28/45 ≈ 0.622
      ├── Some((5, 3)): 12/26 ≈ 0.462
      ├── Some((5, 4)): 18/34 ≈ 0.529
      ├── Some((5, 5)): 16/31 ≈ 0.516
      ├── Some((5, 6)): 17/33 ≈ 0.515
      ├── Some((5, 7)): 9/23 ≈ 0.391
      └── Some((5, 8)): 14/29 ≈ 0.483
    ├── Some((8, 6)): 158/304 ≈ 0.520
      ├── Some((6, 0)): 13/29 ≈ 0.448
      ├── Some((6, 1)): 14/30 ≈ 0.467
      ├── Some((6, 2)): 19/36 ≈ 0.528
      ├── Some((6, 3)): 21/38 ≈ 0.553
      ├── Some((6, 4)): 12/27 ≈ 0.444
      ├── Some((6, 5)): 6/19 ≈ 0.316
      ├── Some((6, 6)): 13/29 ≈ 0.448
      ├── Some((6, 7)): 45/65 ≈ 0.692
      └── Some((6, 8)): 14/30 ≈ 0.467
    └── Some((8, 8)): 206/379 ≈ 0.544
      ├── Some((8, 0)): 26/50 ≈ 0.520
      ├── Some((8, 1)): 11/30 ≈ 0.367
      ├── Some((8, 2)): 24/48 ≈ 0.500
      ├── Some((8, 3)): 48/77 ≈ 0.623
      ├── Some((8, 4)): 31/56 ≈ 0.554
      ├── Some((8, 5)): 31/56 ≈ 0.554
      └── Some((8, 6)): 35/61 ≈ 0.574
└── Some((8, 8)): 9631/18211 ≈ 0.529
  ├── Some((8, 0)): 1370/2567 ≈ 0.534
    ├── Some((0, 0)): 163/302 ≈ 0.540
      ├── Some((0, 1)): 9/24 ≈ 0.375
      ├── Some((0, 2)): 14/30 ≈ 0.467
      ├── Some((0, 3)): 19/36 ≈ 0.528
      ├── Some((0, 4)): 16/33 ≈ 0.485
      ├── Some((0, 5)): 42/63 ≈ 0.667
      ├── Some((0, 6)): 28/47 ≈ 0.596
      ├── Some((0, 7)): 11/27 ≈ 0.407
      └── Some((0, 8)): 23/41 ≈ 0.561
    ├── Some((0, 1)): 148/279 ≈ 0.530
      ├── Some((1, 0)): 7/20 ≈ 0.350
      ├── Some((1, 1)): 2/13 ≈ 0.154
      ├── Some((1, 2)): 21/37 ≈ 0.568
      ├── Some((1, 3)): 18/33 ≈ 0.545
      ├── Some((1, 4)): 32/49 ≈ 0.653
      ├── Some((1, 5)): 20/36 ≈ 0.556
      ├── Some((1, 6)): 27/43 ≈ 0.628
      ├── Some((1, 7)): 5/17 ≈ 0.294
      └── Some((1, 8)): 15/30 ≈ 0.500
    ├── Some((0, 2)): 124/242 ≈ 0.512
      ├── Some((2, 0)): 19/33 ≈ 0.576
      ├── Some((2, 1)): 13/26 ≈ 0.500
      ├── Some((2, 2)): 15/28 ≈ 0.536
      ├── Some((2, 3)): 17/31 ≈ 0.548
      ├── Some((2, 4)): 15/28 ≈ 0.536
      ├── Some((2, 5)): 8/20 ≈ 0.400
      ├── Some((2, 6)): 17/31 ≈ 0.548
      ├── Some((2, 7)): 7/19 ≈ 0.368
      └── Some((2, 8)): 12/25 ≈ 0.480
    ├── Some((0, 3)): 191/344 ≈ 0.555
      ├── Some((3, 0)): 24/42 ≈ 0.571
      ├── Some((3, 1)): 11/26 ≈ 0.423
      ├── Some((3, 2)): 15/31 ≈ 0.484
      ├── Some((3, 3)): 34/53 ≈ 0.642
      ├── Some((3, 4)): 30/49 ≈ 0.612
      ├── Some((3, 5)): 8/22 ≈ 0.364
      ├── Some((3, 6)): 16/32 ≈ 0.500
      ├── Some((3, 7)): 28/46 ≈ 0.609
      └── Some((3, 8)): 24/42 ≈ 0.571
    ├── Some((0, 4)): 209/371 ≈ 0.563
      ├── Some((4, 0)): 17/34 ≈ 0.500
      ├── Some((4, 1)): 26/45 ≈ 0.578
      ├── Some((4, 2)): 18/35 ≈ 0.514
      ├── Some((4, 3)): 16/33 ≈ 0.485
      ├── Some((4, 4)): 36/56 ≈ 0.643
      ├── Some((4, 5)): 41/61 ≈ 0.672
      ├── Some((4, 6)): 15/31 ≈ 0.484
      ├── Some((4, 7)): 21/39 ≈ 0.538
      └── Some((4, 8)): 19/36 ≈ 0.528
    ├── Some((0, 5)): 117/232 ≈ 0.504
      ├── Some((5, 0)): 1/11 ≈ 0.091
      ├── Some((5, 1)): 16/30 ≈ 0.533
      ├── Some((5, 2)): 9/21 ≈ 0.429
      ├── Some((5, 3)): 2/12 ≈ 0.167
      ├── Some((5, 4)): 17/31 ≈ 0.548
      ├── Some((5, 5)): 12/25 ≈ 0.480
      ├── Some((5, 6)): 11/24 ≈ 0.458
      ├── Some((5, 7)): 23/37 ≈ 0.622
      └── Some((5, 8)): 25/40 ≈ 0.625
    ├── Some((0, 6)): 105/213 ≈ 0.493
      ├── Some((6, 0)): 8/19 ≈ 0.421
      ├── Some((6, 1)): 15/28 ≈ 0.536
      ├── Some((6, 2)): 8/19 ≈ 0.421
      ├── Some((6, 3)): 17/30 ≈ 0.567
      ├── Some((6, 4)): 10/22 ≈ 0.455
      ├── Some((6, 5)): 12/24 ≈ 0.500
      ├── Some((6, 6)): 11/23 ≈ 0.478
      ├── Some((6, 7)): 14/26 ≈ 0.538
      └── Some((6, 8)): 9/21 ≈ 0.429
    ├── Some((0, 7)): 143/271 ≈ 0.528
      ├── Some((7, 0)): 15/29 ≈ 0.517
      ├── Some((7, 1)): 20/35 ≈ 0.571
      ├── Some((7, 2)): 20/35 ≈ 0.571
      ├── Some((7, 3)): 10/23 ≈ 0.435
      ├── Some((7, 4)): 21/36 ≈ 0.583
      ├── Some((7, 5)): 17/32 ≈ 0.531
      ├── Some((7, 6)): 7/20 ≈ 0.350
      ├── Some((7, 7)): 10/23 ≈ 0.435
      └── Some((7, 8)): 22/37 ≈ 0.595
    └── Some((0, 8)): 170/312 ≈ 0.545
      ├── Some((8, 1)): 28/49 ≈ 0.571
      ├── Some((8, 2)): 32/54 ≈ 0.593
      ├── Some((8, 3)): 6/21 ≈ 0.286
      ├── Some((8, 4)): 25/46 ≈ 0.543
      ├── Some((8, 5)): 30/52 ≈ 0.577
      ├── Some((8, 6)): 32/54 ≈ 0.593
      └── Some((8, 7)): 16/35 ≈ 0.457
  ├── Some((8, 1)): 1054/2020 ≈ 0.522
    ├── Some((1, 0)): 99/198 ≈ 0.500
      ├── Some((0, 0)): 8/19 ≈ 0.421
      ├── Some((0, 1)): 10/21 ≈ 0.476
      ├── Some((0, 2)): 12/23 ≈ 0.522
      ├── Some((0, 3)): 8/19 ≈ 0.421
      ├── Some((0, 4)): 17/29 ≈ 0.586
      ├── Some((0, 5)): 4/14 ≈ 0.286
      ├── Some((0, 6)): 12/23 ≈ 0.522
      ├── Some((0, 7)): 16/27 ≈ 0.593
      └── Some((0, 8)): 11/22 ≈ 0.500
    ├── Some((1, 1)): 143/264 ≈ 0.542
      ├── Some((1, 0)): 19/34 ≈ 0.559
      ├── Some((1, 2)): 13/27 ≈ 0.481
      ├── Some((1, 3)): 12/26 ≈ 0.462
      ├── Some((1, 4)): 29/46 ≈ 0.630
      ├── Some((1, 5)): 11/25 ≈ 0.440
      ├── Some((1, 6)): 25/41 ≈ 0.610
      ├── Some((1, 7)): 17/32 ≈ 0.531
      └── Some((1, 8)): 17/32 ≈ 0.531
    ├── Some((1, 2)): 134/251 ≈ 0.534
      ├── Some((2, 0)): 16/29 ≈ 0.552
      ├── Some((2, 1)): 18/32 ≈ 0.562
      ├── Some((2, 2)): 8/20 ≈ 0.400
      ├── Some((2, 3)): 29/44 ≈ 0.659
      ├── Some((2, 4)): 14/27 ≈ 0.519
      ├── Some((2, 5)): 15/28 ≈ 0.536
      ├── Some((2, 6)): 13/26 ≈ 0.500
      ├── Some((2, 7)): 10/22 ≈ 0.455
      └── Some((2, 8)): 10/22 ≈ 0.455
    ├── Some((1, 3)): 86/177 ≈ 0.486
      ├── Some((3, 0)): 24/36 ≈ 0.667
      ├── Some((3, 1)): 6/16 ≈ 0.375
      ├── Some((3, 2)): 1/9 ≈ 0.111
      ├── Some((3, 3)): 6/16 ≈ 0.375
      ├── Some((3, 4)): 17/28 ≈ 0.607
      ├── Some((3, 5)): 6/16 ≈ 0.375
      ├── Some((3, 6)): 15/26 ≈ 0.577
      ├── Some((3, 7)): 3/12 ≈ 0.250
      └── Some((3, 8)): 7/17 ≈ 0.412
    ├── Some((1, 4)): 110/214 ≈ 0.514
      ├── Some((4, 0)): 10/21 ≈ 0.476
      ├── Some((4, 1)): 14/26 ≈ 0.538
      ├── Some((4, 2)): 17/29 ≈ 0.586
      ├── Some((4, 3)): 8/19 ≈ 0.421
      ├── Some((4, 4)): 14/26 ≈ 0.538
      ├── Some((4, 5)): 14/26 ≈ 0.538
      ├── Some((4, 6)): 12/23 ≈ 0.522
      ├── Some((4, 7)): 10/21 ≈ 0.476
      └── Some((4, 8)): 11/22 ≈ 0.500
    ├── Some((1, 5)): 143/264 ≈ 0.542
      ├── Some((5, 0)): 12/25 ≈ 0.480
      ├── Some((5, 1)): 10/22 ≈ 0.455
      ├── Some((5, 2)): 13/26 ≈ 0.500
      ├── Some((5, 3)): 19/33 ≈ 0.576
      ├── Some((5, 4)): 22/36 ≈ 0.611
      ├── Some((5, 5)): 18/32 ≈ 0.562
      ├── Some((5, 6)): 10/23 ≈ 0.435
      ├── Some((5, 7)): 26/41 ≈ 0.634
      └── Some((5, 8)): 12/25 ≈ 0.480
    ├── Some((1, 6)): 41/105 ≈ 0.390
      ├── Some((6, 0)): 5/12 ≈ 0.417
      ├── Some((6, 1)): 3/10 ≈ 0.300
      ├── Some((6, 2)): 8/16 ≈ 0.500
      ├── Some((6, 3)): 1/8 ≈ 0.125
      ├── Some((6, 4)): 5/12 ≈ 0.417
      ├── Some((6, 5)): 4/11 ≈ 0.364
      ├── Some((6, 6)): 3/10 ≈ 0.300
      ├── Some((6, 7)): 6/13 ≈ 0.462
      └── Some((6, 8)): 5/12 ≈ 0.417
    ├── Some((1, 7)): 158/286 ≈ 0.552
      ├── Some((7, 0)): 17/31 ≈ 0.548
      ├── Some((7, 1)): 8/20 ≈ 0.400
      ├── Some((7, 2)): 31/47 ≈ 0.660
      ├── Some((7, 3)): 22/37 ≈ 0.595
      ├── Some((7, 4)): 19/33 ≈ 0.576
      ├── Some((7, 5)): 15/29 ≈ 0.517
      ├── Some((7, 6)): 15/29 ≈ 0.517
      ├── Some((7, 7)): 10/23 ≈ 0.435
      └── Some((7, 8)): 21/36 ≈ 0.583
    └── Some((1, 8)): 140/260 ≈ 0.538
      ├── Some((8, 0)): 6/19 ≈ 0.316
      ├── Some((8, 2)): 23/41 ≈ 0.561
      ├── Some((8, 3)): 27/45 ≈ 0.600
      ├── Some((8, 4)): 20/37 ≈ 0.541
      ├── Some((8, 5)): 22/40 ≈ 0.550
      ├── Some((8, 6)): 24/42 ≈ 0.571
      └── Some((8, 7)): 18/35 ≈ 0.514
  ├── Some((8, 2)): 768/1519 ≈ 0.506
    ├── Some((2, 0)): 97/187 ≈ 0.519
      ├── Some((0, 0)): 14/24 ≈ 0.583
      ├── Some((0, 1)): 11/21 ≈ 0.524
      ├── Some((0, 2)): 8/18 ≈ 0.444
      ├── Some((0, 3)): 9/19 ≈ 0.474
      ├── Some((0, 4)): 13/23 ≈ 0.565
      ├── Some((0, 5)): 4/13 ≈ 0.308
      ├── Some((0, 6)): 24/35 ≈ 0.686
      ├── Some((0, 7)): 6/15 ≈ 0.400
      └── Some((0, 8)): 8/18 ≈ 0.444
    ├── Some((2, 1)): 106/201 ≈ 0.527
      ├── Some((1, 0)): 6/16 ≈ 0.375
      ├── Some((1, 1)): 7/17 ≈ 0.412
      ├── Some((1, 2)): 23/34 ≈ 0.676
      ├── Some((1, 3)): 8/18 ≈ 0.444
      ├── Some((1, 4)): 14/25 ≈ 0.560
      ├── Some((1, 5)): 13/24 ≈ 0.542
      ├── Some((1, 6)): 8/18 ≈ 0.444
      ├── Some((1, 7)): 14/25 ≈ 0.560
      └── Some((1, 8)): 12/23 ≈ 0.522
    ├── Some((2, 2)): 74/153 ≈ 0.484
      ├── Some((2, 0)): 4/13 ≈ 0.308
      ├── Some((2, 1)): 12/22 ≈ 0.545
      ├── Some((2, 3)): 14/24 ≈ 0.583
      ├── Some((2, 4)): 15/26 ≈ 0.577
      ├── Some((2, 5)): 5/14 ≈ 0.357
      ├── Some((2, 6)): 10/20 ≈ 0.500
      ├── Some((2, 7)): 4/13 ≈ 0.308
      └── Some((2, 8)): 10/20 ≈ 0.500
    ├── Some((2, 3)): 73/151 ≈ 0.483
      ├── Some((3, 0)): 11/20 ≈ 0.550
      ├── Some((3, 1)): 11/20 ≈ 0.550
      ├── Some((3, 2)): 6/14 ≈ 0.429
      ├── Some((3, 3)): 13/22 ≈ 0.591
      ├── Some((3, 4)): 7/16 ≈ 0.438
      ├── Some((3, 5)): 6/14 ≈ 0.429
      ├── Some((3, 6)): 8/17 ≈ 0.471
      ├── Some((3, 7)): 5/13 ≈ 0.385
      └── Some((3, 8)): 6/14 ≈ 0.429
    ├── Some((2, 4)): 102/195 ≈ 0.523
      ├── Some((4, 0)): 5/14 ≈ 0.357
      ├── Some((4, 1)): 10/20 ≈ 0.500
      ├── Some((4, 2)): 15/26 ≈ 0.577
      ├── Some((4, 3)): 13/23 ≈ 0.565
      ├── Some((4, 4)): 18/29 ≈ 0.621
      ├── Some((4, 5)): 13/24 ≈ 0.542
      ├── Some((4, 6)): 5/14 ≈ 0.357
      ├── Some((4, 7)): 8/18 ≈ 0.444
      └── Some((4, 8)): 15/26 ≈ 0.577
    ├── Some((2, 5)): 52/118 ≈ 0.441
      ├── Some((5, 0)): 0/6 ≈ 0.000
      ├── Some((5, 1)): 6/13 ≈ 0.462
      ├── Some((5, 2)): 8/16 ≈ 0.500
      ├── Some((5, 3)): 9/17 ≈ 0.529
      ├── Some((5, 4)): 11/19 ≈ 0.579
      ├── Some((5, 5)): 7/15 ≈ 0.467
      ├── Some((5, 6)): 1/8 ≈ 0.125
      ├── Some((5, 7)): 6/13 ≈ 0.462
      └── Some((5, 8)): 3/10 ≈ 0.300
    ├── Some((2, 6)): 124/227 ≈ 0.546
      ├── Some((6, 0)): 9/20 ≈ 0.450
      ├── Some((6, 1)): 18/30 ≈ 0.600
      ├── Some((6, 2)): 14/25 ≈ 0.560
      ├── Some((6, 3)): 6/16 ≈ 0.375
      ├── Some((6, 4)): 7/18 ≈ 0.389
      ├── Some((6, 5)): 21/33 ≈ 0.636
      ├── Some((6, 6)): 19/31 ≈ 0.613
      ├── Some((6, 7)): 15/27 ≈ 0.556
      └── Some((6, 8)): 14/26 ≈ 0.538
    ├── Some((2, 7)): 117/217 ≈ 0.539
      ├── Some((7, 0)): 16/27 ≈ 0.593
      ├── Some((7, 1)): 16/27 ≈ 0.593
      ├── Some((7, 2)): 12/23 ≈ 0.522
      ├── Some((7, 3)): 10/21 ≈ 0.476
      ├── Some((7, 4)): 13/24 ≈ 0.542
      ├── Some((7, 5)): 9/20 ≈ 0.450
      ├── Some((7, 6)): 12/23 ≈ 0.522
      ├── Some((7, 7)): 14/25 ≈ 0.560
      └── Some((7, 8)): 15/26 ≈ 0.577
    └── Some((2, 8)): 22/69 ≈ 0.319
      ├── Some((8, 0)): 1/7 ≈ 0.143
      ├── Some((8, 1)): 3/10 ≈ 0.300
      ├── Some((8, 3)): 4/11 ≈ 0.364
      ├── Some((8, 4)): 4/11 ≈ 0.364
      ├── Some((8, 5)): 0/6 ≈ 0.000
      ├── Some((8, 6)): 1/7 ≈ 0.143
      └── Some((8, 7)): 8/16 ≈ 0.500
  ├── Some((8, 3)): 1029/1976 ≈ 0.521
    ├── Some((3, 0)): 120/228 ≈ 0.526
      ├── Some((0, 0)): 5/16 ≈ 0.312
      ├── Some((0, 1)): 9/21 ≈ 0.429
      ├── Some((0, 2)): 23/36 ≈ 0.639
      ├── Some((0, 3)): 6/17 ≈ 0.353
      ├── Some((0, 4)): 4/14 ≈ 0.286
      ├── Some((0, 5)): 12/24 ≈ 0.500
      ├── Some((0, 6)): 34/48 ≈ 0.708
      ├── Some((0, 7)): 14/27 ≈ 0.519
      └── Some((0, 8)): 12/24 ≈ 0.500
    ├── Some((3, 1)): 139/257 ≈ 0.541
      ├── Some((1, 0)): 15/28 ≈ 0.536
      ├── Some((1, 1)): 8/20 ≈ 0.400
      ├── Some((1, 2)): 11/24 ≈ 0.458
      ├── Some((1, 3)): 9/21 ≈ 0.429
      ├── Some((1, 4)): 21/35 ≈ 0.600
      ├── Some((1, 5)): 21/35 ≈ 0.600
      ├── Some((1, 6)): 15/28 ≈ 0.536
      ├── Some((1, 7)): 16/29 ≈ 0.552
      └── Some((1, 8)): 22/36 ≈ 0.611
    ├── Some((3, 2)): 105/206 ≈ 0.510
      ├── Some((2, 0)): 4/14 ≈ 0.286
      ├── Some((2, 1)): 4/14 ≈ 0.286
      ├── Some((2, 2)): 26/39 ≈ 0.667
      ├── Some((2, 3)): 11/23 ≈ 0.478
      ├── Some((2, 4)): 18/30 ≈ 0.600
      ├── Some((2, 5)): 9/20 ≈ 0.450
      ├── Some((2, 6)): 19/31 ≈ 0.613
      ├── Some((2, 7)): 10/21 ≈ 0.476
      └── Some((2, 8)): 3/13 ≈ 0.231
    ├── Some((3, 3)): 115/221 ≈ 0.520
      ├── Some((3, 0)): 8/20 ≈ 0.400
      ├── Some((3, 1)): 6/18 ≈ 0.333
      ├── Some((3, 2)): 14/27 ≈ 0.519
      ├── Some((3, 4)): 21/35 ≈ 0.600
      ├── Some((3, 5)): 15/28 ≈ 0.536
      ├── Some((3, 6)): 16/30 ≈ 0.533
      ├── Some((3, 7)): 7/19 ≈ 0.368
      └── Some((3, 8)): 28/43 ≈ 0.651
    ├── Some((3, 4)): 122/231 ≈ 0.528
      ├── Some((4, 0)): 22/35 ≈ 0.629
      ├── Some((4, 1)): 9/20 ≈ 0.450
      ├── Some((4, 2)): 17/30 ≈ 0.567
      ├── Some((4, 3)): 9/20 ≈ 0.450
      ├── Some((4, 4)): 15/27 ≈ 0.556
      ├── Some((4, 5)): 19/32 ≈ 0.594
      ├── Some((4, 6)): 14/26 ≈ 0.538
      ├── Some((4, 7)): 7/18 ≈ 0.389
      └── Some((4, 8)): 10/22 ≈ 0.455
    ├── Some((3, 5)): 65/144 ≈ 0.451
      ├── Some((5, 0)): 3/11 ≈ 0.273
      ├── Some((5, 1)): 7/16 ≈ 0.438
      ├── Some((5, 2)): 5/14 ≈ 0.357
      ├── Some((5, 3)): 4/12 ≈ 0.333
      ├── Some((5, 4)): 4/12 ≈ 0.333
      ├── Some((5, 5)): 8/17 ≈ 0.471
      ├── Some((5, 6)): 12/21 ≈ 0.571
      ├── Some((5, 7)): 4/12 ≈ 0.333
      └── Some((5, 8)): 18/28 ≈ 0.643
    ├── Some((3, 6)): 93/187 ≈ 0.497
      ├── Some((6, 0)): 13/24 ≈ 0.542
      ├── Some((6, 1)): 22/33 ≈ 0.667
      ├── Some((6, 2)): 6/16 ≈ 0.375
      ├── Some((6, 3)): 11/22 ≈ 0.500
      ├── Some((6, 4)): 6/16 ≈ 0.375
      ├── Some((6, 5)): 2/11 ≈ 0.182
      ├── Some((6, 6)): 8/18 ≈ 0.444
      ├── Some((6, 7)): 16/27 ≈ 0.593
      └── Some((6, 8)): 9/19 ≈ 0.474
    ├── Some((3, 7)): 166/297 ≈ 0.559
      ├── Some((7, 0)): 16/31 ≈ 0.516
      ├── Some((7, 1)): 18/33 ≈ 0.545
      ├── Some((7, 2)): 27/43 ≈ 0.628
      ├── Some((7, 3)): 9/22 ≈ 0.409
      ├── Some((7, 4)): 33/49 ≈ 0.673
      ├── Some((7, 5)): 29/45 ≈ 0.644
      ├── Some((7, 6)): 14/28 ≈ 0.500
      ├── Some((7, 7)): 14/28 ≈ 0.500
      └── Some((7, 8)): 5/17 ≈ 0.294
    └── Some((3, 8)): 104/204 ≈ 0.510
      ├── Some((8, 0)): 12/26 ≈ 0.462
      ├── Some((8, 1)): 14/28 ≈ 0.500
      ├── Some((8, 2)): 10/23 ≈ 0.435
      ├── Some((8, 4)): 21/36 ≈ 0.583
      ├── Some((8, 5)): 8/21 ≈ 0.381
      ├── Some((8, 6)): 26/42 ≈ 0.619
      └── Some((8, 7)): 13/27 ≈ 0.481
  ├── Some((8, 4)): 766/1515 ≈ 0.506
    ├── Some((4, 0)): 148/262 ≈ 0.565
      ├── Some((0, 0)): 19/32 ≈ 0.594
      ├── Some((0, 1)): 11/23 ≈ 0.478
      ├── Some((0, 2)): 24/38 ≈ 0.632
      ├── Some((0, 3)): 6/17 ≈ 0.353
      ├── Some((0, 4)): 5/16 ≈ 0.312
      ├── Some((0, 5)): 27/41 ≈ 0.659
      ├── Some((0, 6)): 13/25 ≈ 0.520
      ├── Some((0, 7)): 25/39 ≈ 0.641
      └── Some((0, 8)): 17/30 ≈ 0.567
    ├── Some((4, 1)): 91/178 ≈ 0.511
      ├── Some((1, 0)): 17/27 ≈ 0.630
      ├── Some((1, 1)): 11/21 ≈ 0.524
      ├── Some((1, 2)): 10/20 ≈ 0.500
      ├── Some((1, 3)): 7/16 ≈ 0.438
      ├── Some((1, 4)): 12/22 ≈ 0.545
      ├── Some((1, 5)): 12/22 ≈ 0.545
      ├── Some((1, 6)): 4/13 ≈ 0.308
      ├── Some((1, 7)): 9/19 ≈ 0.474
      └── Some((1, 8)): 8/17 ≈ 0.471
    ├── Some((4, 2)): 81/163 ≈ 0.497
      ├── Some((2, 0)): 7/16 ≈ 0.438
      ├── Some((2, 1)): 3/11 ≈ 0.273
      ├── Some((2, 2)): 13/23 ≈ 0.565
      ├── Some((2, 3)): 8/17 ≈ 0.471
      ├── Some((2, 4)): 11/20 ≈ 0.550
      ├── Some((2, 5)): 20/30 ≈ 0.667
      ├── Some((2, 6)): 7/16 ≈ 0.438
      ├── Some((2, 7)): 4/12 ≈ 0.333
      └── Some((2, 8)): 8/17 ≈ 0.471
    ├── Some((4, 3)): 48/112 ≈ 0.429
      ├── Some((3, 0)): 13/21 ≈ 0.619
      ├── Some((3, 1)): 7/14 ≈ 0.500
      ├── Some((3, 2)): 1/8 ≈ 0.125
      ├── Some((3, 3)): 5/12 ≈ 0.417
      ├── Some((3, 4)): 2/9 ≈ 0.222
      ├── Some((3, 5)): 6/13 ≈ 0.462
      ├── Some((3, 6)): 5/12 ≈ 0.417
      ├── Some((3, 7)): 7/14 ≈ 0.500
      └── Some((3, 8)): 1/8 ≈ 0.125
    ├── Some((4, 4)): 122/224 ≈ 0.545
      ├── Some((4, 0)): 19/32 ≈ 0.594
      ├── Some((4, 1)): 17/30 ≈ 0.567
      ├── Some((4, 2)): 8/20 ≈ 0.400
      ├── Some((4, 3)): 13/26 ≈ 0.500
      ├── Some((4, 5)): 7/18 ≈ 0.389
      ├── Some((4, 6)): 16/29 ≈ 0.552
      ├── Some((4, 7)): 23/37 ≈ 0.622
      └── Some((4, 8)): 18/31 ≈ 0.581
    ├── Some((4, 5)): 53/120 ≈ 0.442
      ├── Some((5, 0)): 5/12 ≈ 0.417
      ├── Some((5, 1)): 3/10 ≈ 0.300
      ├── Some((5, 2)): 7/15 ≈ 0.467
      ├── Some((5, 3)): 5/13 ≈ 0.385
      ├── Some((5, 4)): 3/10 ≈ 0.300
      ├── Some((5, 5)): 1/8 ≈ 0.125
      ├── Some((5, 6)): 11/19 ≈ 0.579
      ├── Some((5, 7)): 4/11 ≈ 0.364
      └── Some((5, 8)): 13/21 ≈ 0.619
    ├── Some((4, 6)): 99/190 ≈ 0.521
      ├── Some((6, 0)): 15/26 ≈ 0.577
      ├── Some((6, 1)): 14/24 ≈ 0.583
      ├── Some((6, 2)): 5/14 ≈ 0.357
      ├── Some((6, 3)): 6/16 ≈ 0.375
      ├── Some((6, 4)): 12/22 ≈ 0.545
      ├── Some((6, 5)): 19/30 ≈ 0.633
      ├── Some((6, 6)): 11/21 ≈ 0.524
      ├── Some((6, 7)): 12/22 ≈ 0.545
      └── Some((6, 8)): 5/14 ≈ 0.357
    ├── Some((4, 7)): 74/152 ≈ 0.487
      ├── Some((7, 0)): 18/27 ≈ 0.667
      ├── Some((7, 1)): 10/19 ≈ 0.526
      ├── Some((7, 2)): 0/7 ≈ 0.000
      ├── Some((7, 3)): 3/11 ≈ 0.273
      ├── Some((7, 4)): 9/18 ≈ 0.500
      ├── Some((7, 5)): 11/20 ≈ 0.550
      ├── Some((7, 6)): 12/21 ≈ 0.571
      ├── Some((7, 7)): 3/11 ≈ 0.273
      └── Some((7, 8)): 8/17 ≈ 0.471
    └── Some((4, 8)): 49/113 ≈ 0.434
      ├── Some((8, 0)): 7/16 ≈ 0.438
      ├── Some((8, 1)): 5/14 ≈ 0.357
      ├── Some((8, 2)): 9/19 ≈ 0.474
      ├── Some((8, 3)): 13/23 ≈ 0.565
      ├── Some((8, 5)): 7/16 ≈ 0.438
      ├── Some((8, 6)): 3/11 ≈ 0.273
      └── Some((8, 7)): 4/13 ≈ 0.308
  ├── Some((8, 5)): 1842/3376 ≈ 0.546
    ├── Some((5, 0)): 217/395 ≈ 0.549
      ├── Some((0, 0)): 20/39 ≈ 0.513
      ├── Some((0, 1)): 22/41 ≈ 0.537
      ├── Some((0, 2)): 16/34 ≈ 0.471
      ├── Some((0, 3)): 33/54 ≈ 0.611
      ├── Some((0, 4)): 9/25 ≈ 0.360
      ├── Some((0, 5)): 19/38 ≈ 0.500
      ├── Some((0, 6)): 32/53 ≈ 0.604
      ├── Some((0, 7)): 33/55 ≈ 0.600
      └── Some((0, 8)): 33/55 ≈ 0.600
    ├── Some((5, 1)): 231/416 ≈ 0.555
      ├── Some((1, 0)): 27/48 ≈ 0.562
      ├── Some((1, 1)): 9/25 ≈ 0.360
      ├── Some((1, 2)): 31/53 ≈ 0.585
      ├── Some((1, 3)): 32/54 ≈ 0.593
      ├── Some((1, 4)): 26/47 ≈ 0.553
      ├── Some((1, 5)): 25/45 ≈ 0.556
      ├── Some((1, 6)): 31/53 ≈ 0.585
      ├── Some((1, 7)): 35/57 ≈ 0.614
      └── Some((1, 8)): 15/33 ≈ 0.455
    ├── Some((5, 2)): 259/459 ≈ 0.564
      ├── Some((2, 0)): 21/42 ≈ 0.500
      ├── Some((2, 1)): 37/61 ≈ 0.607
      ├── Some((2, 2)): 26/48 ≈ 0.542
      ├── Some((2, 3)): 29/52 ≈ 0.558
      ├── Some((2, 4)): 27/49 ≈ 0.551
      ├── Some((2, 5)): 45/70 ≈ 0.643
      ├── Some((2, 6)): 19/39 ≈ 0.487
      ├── Some((2, 7)): 12/30 ≈ 0.400
      └── Some((2, 8)): 42/67 ≈ 0.627
    ├── Some((5, 3)): 78/177 ≈ 0.441
      ├── Some((3, 0)): 6/16 ≈ 0.375
      ├── Some((3, 1)): 9/20 ≈ 0.450
      ├── Some((3, 2)): 8/19 ≈ 0.421
      ├── Some((3, 3)): 15/27 ≈ 0.556
      ├── Some((3, 4)): 11/22 ≈ 0.500
      ├── Some((3, 5)): 12/24 ≈ 0.500
      ├── Some((3, 6)): 7/18 ≈ 0.389
      ├── Some((3, 7)): 6/17 ≈ 0.353
      └── Some((3, 8)): 3/13 ≈ 0.231
    ├── Some((5, 4)): 211/386 ≈ 0.547
      ├── Some((4, 0)): 9/25 ≈ 0.360
      ├── Some((4, 1)): 13/30 ≈ 0.433
      ├── Some((4, 2)): 46/70 ≈ 0.657
      ├── Some((4, 3)): 18/37 ≈ 0.486
      ├── Some((4, 4)): 26/47 ≈ 0.553
      ├── Some((4, 5)): 20/39 ≈ 0.513
      ├── Some((4, 6)): 4/18 ≈ 0.222
      ├── Some((4, 7)): 32/54 ≈ 0.593
      └── Some((4, 8)): 42/65 ≈ 0.646
    ├── Some((5, 5)): 210/385 ≈ 0.545
      ├── Some((5, 0)): 42/67 ≈ 0.627
      ├── Some((5, 1)): 15/34 ≈ 0.441
      ├── Some((5, 2)): 18/38 ≈ 0.474
      ├── Some((5, 3)): 26/48 ≈ 0.542
      ├── Some((5, 4)): 30/53 ≈ 0.566
      ├── Some((5, 6)): 37/62 ≈ 0.597
      ├── Some((5, 7)): 15/34 ≈ 0.441
      └── Some((5, 8)): 26/48 ≈ 0.542
    ├── Some((5, 6)): 317/545 ≈ 0.582
      ├── Some((6, 0)): 32/57 ≈ 0.561
      ├── Some((6, 1)): 12/31 ≈ 0.387
      ├── Some((6, 2)): 40/67 ≈ 0.597
      ├── Some((6, 3)): 69/101 ≈ 0.683
      ├── Some((6, 4)): 23/46 ≈ 0.500
      ├── Some((6, 5)): 23/46 ≈ 0.500
      ├── Some((6, 6)): 50/79 ≈ 0.633
      ├── Some((6, 7)): 24/47 ≈ 0.511
      └── Some((6, 8)): 43/70 ≈ 0.614
    ├── Some((5, 7)): 138/273 ≈ 0.505
      ├── Some((7, 0)): 12/26 ≈ 0.462
      ├── Some((7, 1)): 26/43 ≈ 0.605
      ├── Some((7, 2)): 13/28 ≈ 0.464
      ├── Some((7, 3)): 21/37 ≈ 0.568
      ├── Some((7, 4)): 12/27 ≈ 0.444
      ├── Some((7, 5)): 8/21 ≈ 0.381
      ├── Some((7, 6)): 16/31 ≈ 0.516
      ├── Some((7, 7)): 11/25 ≈ 0.440
      └── Some((7, 8)): 18/34 ≈ 0.529
    └── Some((5, 8)): 180/339 ≈ 0.531
      ├── Some((8, 0)): 23/45 ≈ 0.511
      ├── Some((8, 1)): 28/52 ≈ 0.538
      ├── Some((8, 2)): 27/50 ≈ 0.540
      ├── Some((8, 3)): 19/40 ≈ 0.475
      ├── Some((8, 4)): 10/28 ≈ 0.357
      ├── Some((8, 6)): 46/74 ≈ 0.622
      └── Some((8, 7)): 26/49 ≈ 0.531
  ├── Some((8, 6)): 1630/3014 ≈ 0.541
    ├── Some((6, 0)): 164/309 ≈ 0.531
      ├── Some((0, 0)): 14/29 ≈ 0.483
      ├── Some((0, 1)): 20/36 ≈ 0.556
      ├── Some((0, 2)): 22/39 ≈ 0.564
      ├── Some((0, 3)): 12/27 ≈ 0.444
      ├── Some((0, 4)): 17/33 ≈ 0.515
      ├── Some((0, 5)): 10/24 ≈ 0.417
      ├── Some((0, 6)): 20/37 ≈ 0.541
      ├── Some((0, 7)): 17/33 ≈ 0.515
      └── Some((0, 8)): 32/50 ≈ 0.640
    ├── Some((6, 1)): 153/292 ≈ 0.524
      ├── Some((1, 0)): 20/36 ≈ 0.556
      ├── Some((1, 1)): 19/35 ≈ 0.543
      ├── Some((1, 2)): 7/20 ≈ 0.350
      ├── Some((1, 3)): 25/42 ≈ 0.595
      ├── Some((1, 4)): 20/36 ≈ 0.556
      ├── Some((1, 5)): 21/37 ≈ 0.568
      ├── Some((1, 6)): 10/24 ≈ 0.417
      ├── Some((1, 7)): 17/33 ≈ 0.515
      └── Some((1, 8)): 13/28 ≈ 0.464
    ├── Some((6, 2)): 221/396 ≈ 0.558
      ├── Some((2, 0)): 14/32 ≈ 0.438
      ├── Some((2, 1)): 8/24 ≈ 0.333
      ├── Some((2, 2)): 24/44 ≈ 0.545
      ├── Some((2, 3)): 20/39 ≈ 0.513
      ├── Some((2, 4)): 54/78 ≈ 0.692
      ├── Some((2, 5)): 7/22 ≈ 0.318
      ├── Some((2, 6)): 19/38 ≈ 0.500
      ├── Some((2, 7)): 42/65 ≈ 0.646
      └── Some((2, 8)): 32/53 ≈ 0.604
    ├── Some((6, 3)): 120/241 ≈ 0.498
      ├── Some((3, 0)): 12/25 ≈ 0.480
      ├── Some((3, 1)): 29/45 ≈ 0.644
      ├── Some((3, 2)): 11/24 ≈ 0.458
      ├── Some((3, 3)): 18/32 ≈ 0.562
      ├── Some((3, 4)): 15/29 ≈ 0.517
      ├── Some((3, 5)): 7/19 ≈ 0.368
      ├── Some((3, 6)): 16/30 ≈ 0.533
      ├── Some((3, 7)): 3/14 ≈ 0.214
      └── Some((3, 8)): 9/22 ≈ 0.409
    ├── Some((6, 4)): 210/379 ≈ 0.554
      ├── Some((4, 0)): 20/38 ≈ 0.526
      ├── Some((4, 1)): 46/69 ≈ 0.667
      ├── Some((4, 2)): 29/49 ≈ 0.592
      ├── Some((4, 3)): 20/38 ≈ 0.526
      ├── Some((4, 4)): 11/27 ≈ 0.407
      ├── Some((4, 5)): 13/30 ≈ 0.433
      ├── Some((4, 6)): 15/32 ≈ 0.469
      ├── Some((4, 7)): 28/48 ≈ 0.583
      └── Some((4, 8)): 27/47 ≈ 0.574
    ├── Some((6, 5)): 267/465 ≈ 0.574
      ├── Some((5, 0)): 24/45 ≈ 0.533
      ├── Some((5, 1)): 54/80 ≈ 0.675
      ├── Some((5, 2)): 40/64 ≈ 0.625
      ├── Some((5, 3)): 24/45 ≈ 0.533
      ├── Some((5, 4)): 23/44 ≈ 0.523
      ├── Some((5, 5)): 26/47 ≈ 0.553
      ├── Some((5, 6)): 31/53 ≈ 0.585
      ├── Some((5, 7)): 33/56 ≈ 0.589
      └── Some((5, 8)): 12/30 ≈ 0.400
    ├── Some((6, 6)): 167/314 ≈ 0.532
      ├── Some((6, 0)): 33/54 ≈ 0.611
      ├── Some((6, 1)): 15/33 ≈ 0.455
      ├── Some((6, 2)): 2/14 ≈ 0.143
      ├── Some((6, 3)): 23/42 ≈ 0.548
      ├── Some((6, 4)): 27/47 ≈ 0.574
      ├── Some((6, 5)): 34/55 ≈ 0.618
      ├── Some((6, 7)): 15/33 ≈ 0.455
      └── Some((6, 8)): 17/35 ≈ 0.486
    ├── Some((6, 7)): 137/268 ≈ 0.511
      ├── Some((7, 0)): 17/32 ≈ 0.531
      ├── Some((7, 1)): 11/25 ≈ 0.440
      ├── Some((7, 2)): 9/22 ≈ 0.409
      ├── Some((7, 3)): 12/26 ≈ 0.462
      ├── Some((7, 4)): 19/34 ≈ 0.559
      ├── Some((7, 5)): 26/42 ≈ 0.619
      ├── Some((7, 6)): 23/39 ≈ 0.590
      ├── Some((7, 7)): 6/18 ≈ 0.333
      └── Some((7, 8)): 14/29 ≈ 0.483
    └── Some((6, 8)): 190/349 ≈ 0.544
      ├── Some((8, 0)): 21/42 ≈ 0.500
      ├── Some((8, 1)): 35/60 ≈ 0.583
      ├── Some((8, 2)): 14/33 ≈ 0.424
      ├── Some((8, 3)): 25/47 ≈ 0.532
      ├── Some((8, 4)): 25/48 ≈ 0.521
      ├── Some((8, 5)): 38/63 ≈ 0.603
      └── Some((8, 7)): 31/55 ≈ 0.564
  └── Some((8, 7)): 1171/2223 ≈ 0.527
    ├── Some((7, 0)): 135/255 ≈ 0.529
      ├── Some((0, 0)): 7/19 ≈ 0.368
      ├── Some((0, 1)): 12/25 ≈ 0.480
      ├── Some((0, 2)): 13/26 ≈ 0.500
      ├── Some((0, 3)): 14/27 ≈ 0.519
      ├── Some((0, 4)): 15/28 ≈ 0.536
      ├── Some((0, 5)): 26/41 ≈ 0.634
      ├── Some((0, 6)): 18/32 ≈ 0.562
      ├── Some((0, 7)): 15/28 ≈ 0.536
      └── Some((0, 8)): 15/28 ≈ 0.536
    ├── Some((7, 1)): 183/327 ≈ 0.560
      ├── Some((1, 0)): 26/43 ≈ 0.605
      ├── Some((1, 1)): 20/36 ≈ 0.556
      ├── Some((1, 2)): 17/33 ≈ 0.515
      ├── Some((1, 3)): 26/43 ≈ 0.605
      ├── Some((1, 4)): 11/25 ≈ 0.440
      ├── Some((1, 5)): 15/30 ≈ 0.500
      ├── Some((1, 6)): 19/35 ≈ 0.543
      ├── Some((1, 7)): 31/48 ≈ 0.646
      └── Some((1, 8)): 17/33 ≈ 0.515
    ├── Some((7, 2)): 125/240 ≈ 0.521
      ├── Some((2, 0)): 17/30 ≈ 0.567
      ├── Some((2, 1)): 10/22 ≈ 0.455
      ├── Some((2, 2)): 20/34 ≈ 0.588
      ├── Some((2, 3)): 14/27 ≈ 0.519
      ├── Some((2, 4)): 21/35 ≈ 0.600
      ├── Some((2, 5)): 11/23 ≈ 0.478
      ├── Some((2, 6)): 13/26 ≈ 0.500
      ├── Some((2, 7)): 8/20 ≈ 0.400
      └── Some((2, 8)): 10/22 ≈ 0.455
    ├── Some((7, 3)): 162/296 ≈ 0.547
      ├── Some((3, 0)): 21/36 ≈ 0.583
      ├── Some((3, 1)): 11/25 ≈ 0.440
      ├── Some((3, 2)): 14/28 ≈ 0.500
      ├── Some((3, 3)): 11/25 ≈ 0.440
      ├── Some((3, 4)): 28/44 ≈ 0.636
      ├── Some((3, 5)): 16/31 ≈ 0.516
      ├── Some((3, 6)): 22/38 ≈ 0.579
      ├── Some((3, 7)): 26/42 ≈ 0.619
      └── Some((3, 8)): 12/26 ≈ 0.462
    ├── Some((7, 4)): 64/145 ≈ 0.441
      ├── Some((4, 0)): 14/24 ≈ 0.583
      ├── Some((4, 1)): 3/11 ≈ 0.273
      ├── Some((4, 2)): 2/10 ≈ 0.200
      ├── Some((4, 3)): 5/14 ≈ 0.357
      ├── Some((4, 4)): 3/12 ≈ 0.250
      ├── Some((4, 5)): 0/7 ≈ 0.000
      ├── Some((4, 6)): 9/19 ≈ 0.474
      ├── Some((4, 7)): 12/22 ≈ 0.545
      └── Some((4, 8)): 15/25 ≈ 0.600
    ├── Some((7, 5)): 150/278 ≈ 0.540
      ├── Some((5, 0)): 21/36 ≈ 0.583
      ├── Some((5, 1)): 15/29 ≈ 0.517
      ├── Some((5, 2)): 11/24 ≈ 0.458
      ├── Some((5, 3)): 18/32 ≈ 0.562
      ├── Some((5, 4)): 24/39 ≈ 0.615
      ├── Some((5, 5)): 16/30 ≈ 0.533
      ├── Some((5, 6)): 14/28 ≈ 0.500
      ├── Some((5, 7)): 15/29 ≈ 0.517
      └── Some((5, 8)): 16/30 ≈ 0.533
    ├── Some((7, 6)): 87/181 ≈ 0.481
      ├── Some((6, 0)): 6/16 ≈ 0.375
      ├── Some((6, 1)): 8/18 ≈ 0.444
      ├── Some((6, 2)): 11/22 ≈ 0.500
      ├── Some((6, 3)): 8/18 ≈ 0.444
      ├── Some((6, 4)): 5/15 ≈ 0.333
      ├── Some((6, 5)): 20/32 ≈ 0.625
      ├── Some((6, 6)): 8/18 ≈ 0.444
      ├── Some((6, 7)): 14/25 ≈ 0.560
      └── Some((6, 8)): 6/16 ≈ 0.375
    ├── Some((7, 7)): 187/333 ≈ 0.562
      ├── Some((7, 0)): 18/35 ≈ 0.514
      ├── Some((7, 1)): 11/27 ≈ 0.407
      ├── Some((7, 2)): 14/31 ≈ 0.452
      ├── Some((7, 3)): 25/44 ≈ 0.568
      ├── Some((7, 4)): 18/35 ≈ 0.514
      ├── Some((7, 5)): 39/60 ≈ 0.650
      ├── Some((7, 6)): 20/38 ≈ 0.526
      └── Some((7, 8)): 41/62 ≈ 0.661
    └── Some((7, 8)): 78/167 ≈ 0.467
      ├── Some((8, 0)): 14/27 ≈ 0.519
      ├── Some((8, 1)): 10/22 ≈ 0.455
      ├── Some((8, 2)): 11/24 ≈ 0.458
      ├── Some((8, 3)): 9/21 ≈ 0.429
      ├── Some((8, 4)): 10/22 ≈ 0.455
      ├── Some((8, 5)): 13/26 ≈ 0.500
      └── Some((8, 6)): 11/24 ≈ 0.458
