Signature Generation -- ML-DSA-65
message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
deterministic: true
sk: 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
rho: D26EE59A89F67C98B20F890B03422C8027B776FC305BEF422CDED403AA705DA5
k: DC380AD909E3C13A76F7F59BDD27A843F5F9A1B8E5B7B524EC445A916B7A44A1
tr: 5167716BC609B3EC0C653B210C6569BA2F8233E7F6E404B92EB21F39729FEBC06A644087C75FA7DA3DDC5B85A89F55C9F87A15014E27AB325EBEE0FE472B2F56
mu: FF253A11B6FB8185B2DD5713A30839ED8873037BD15F87FD4245F35C2602ED0062EDFF95E13CAFE61688DD4E3BC421904BC64F6F6CB0B0ACB706891C5AB1E749
rnd: 0000000000000000000000000000000000000000000000000000000000000000
aHat: [[[7070134, 1577377, 714885, 1093856, 3397558, 4823510, 416386, 2677182, 7683695, 4668145, 6900630, 2283364, 8186656, 2610993, 1791271, 4932385, 7777769, 7324490, 3763859, 4967778, 6252771, 5338587, 6369292, 6119713, 6927608, 5381550, 5204823, 5161654, 3364233, 6116458, 1093263, 7050711, 3072891, 754596, 6240735, 7976285, 7643032, 7677715, 5293315, 2705353, 157961, 2258470, 4131420, 7412157, 6010274, 2475260, 1247368, 4132148, 4425701, 1540943, 6581395, 6344713, 1635346, 1321960, 4017656, 720947, 5034045, 7076039, 6642482, 7345401, 4167553, 3924386, 2785696, 2280678, 6156209, 5174009, 8206167, 4544999, 6089892, 6114584, 7929603, 4787978, 3718623, 5961932, 7617187, 8334252, 1370275, 1201882, 5406198, 6585656, 7158507, 5499382, 4823835, 5949947, 684288, 4364299, 3229100, 6006999, 5487612, 4751791, 7820482, 7526494, 5941348, 6467601, 7071296, 5637739, 7831005, 7086466, 4396619, 955011, 7220606, 2368761, 4106716, 5252040, 7228202, 4432070, 2968966, 49471, 590903, 3285939, 281189, 7796736, 4141657, 5809408, 5847018, 568073, 2340243, 5192244, 4035953, 7165659, 2931115, 6169975, 5362495, 7918998, 5551360, 7306991, 1130479, 6520478, 1351430, 3661016, 5421526, 6653420, 1667517, 1576391, 4922551, 2112917, 5936905, 6156332, 6211337, 4631507, 3448511, 1580616, 5395030, 2097399, 5840546, 4846106, 7002268, 3392589, 7288967, 6920293, 6918964, 8202945, 2039960, 2555344, 476217, 5578231, 5557118, 3225898, 5104752, 775860, 3066826, 4131891, 7817361, 6358154, 3560607, 7559476, 4697643, 964817, 278186, 3789239, 2700828, 704179, 4735330, 4249857, 6391167, 7146078, 1900987, 2889062, 7922178, 5639842, 7781413, 258423, 4570650, 5372710, 6419056, 667146, 7043726, 4002367, 3929153, 2817541, 1116994, 7528299, 4579621, 3845190, 1340471, 6911382, 3893913, 4115090, 1848100, 4504340, 2088719, 8266421, 1051011, 469824, 5732015, 5353865, 5653453, 3856040, 5537923, 6728347, 3558197, 3446316, 7224753, 794316, 8046514, 5970859, 1414508, 5193651, 7534889, 139698, 2042677, 5956781, 8377287, 934274, 418688, 5939563, 6451912, 3662414, 5509430, 2412997, 5367001, 2811603, 7462125, 1396765, 6898485, 943966, 733426, 118871, 264329, 1758982, 6206336, 302489, 975495, 3287914, 4597453, 4120568, 1707565, 6067201, 4498297, 8182557, 2437779, 1715287, 7428063, 1044776, 7816011, 3165829],
[4600394, 5576201, 8016384, 4754202, 6787727, 592189, 4612121, 3394665, 7038485, 7473009, 6692465, 2051536, 6601222, 5197463, 4672049, 2025038, 1667946, 6052692, 7774795, 5688604, 7247763, 1428635, 5894966, 2914513, 5839959, 5734553, 7987834, 4799326, 2181784, 6550378, 4408623, 2258770, 8257748, 6166677, 142717, 6376651, 7744502, 5077355, 6520509, 75739, 1104942, 126571, 851844, 4102336, 3474371, 5027025, 2831056, 1366990, 289071, 3615416, 5434462, 5230839, 3292325, 6850488, 1257315, 999277, 4313023, 644692, 398461, 6615602, 1155298, 2696723, 2214961, 4945053, 6549262, 3714122, 5466750, 555748, 2274370, 1495559, 1805069, 1070000, 898692, 5133909, 6644258, 2345553, 3619006, 2122416, 3941136, 421279, 481001, 6853366, 4103202, 4978981, 4869144, 957457, 6743727, 5347573, 6414133, 2337889, 2326507, 8140605, 1035708, 7150185, 8339688, 5888756, 7466030, 5742694, 7887802, 2881573, 3225573, 6555422, 2383886, 105590, 301105, 2063062, 6488306, 7497115, 1254033, 2950238, 1736235, 24507, 7528756, 3912071, 5943519, 5057415, 3411750, 6030677, 5478015, 4981357, 5773280, 4666014, 47353, 2559833, 7917687, 6247301, 2978601, 4542059, 1142989, 3048192, 1745363, 1285088, 3637252, 197293, 6672651, 5870503, 2766404, 1188833, 587821, 7472671, 6203360, 7884389, 2546006, 5641590, 3377197, 5284348, 7247894, 4104048, 2718786, 5436886, 8102324, 1940845, 3771197, 7861884, 458464, 7801351, 5333681, 2598325, 870342, 3714639, 3234684, 5287739, 3012712, 3588566, 114530, 4169227, 1711214, 7681620, 5963941, 6222200, 2692964, 7118922, 971100, 4272009, 2156224, 1924359, 1050377, 971584, 2702083, 2355646, 3568399, 5737001, 3231290, 4899957, 5260201, 1488835, 5212057, 7268836, 7505957, 4191343, 6342250, 4487820, 3950755, 4353290, 2052974, 3253587, 4647627, 5519799, 2603523, 8349708, 8140359, 5702291, 6561273, 5125649, 2869237, 1904717, 2780151, 7997958, 4535572, 885804, 3658629, 2850997, 1018603, 3007571, 6521179, 1955586, 5331638, 971437, 6384475, 8205407, 4213799, 7957788, 8216007, 3679583, 5158657, 280069, 3822385, 5709964, 1538812, 5487960, 3720142, 1835618, 4655936, 58286, 5753407, 2542709, 290268, 5858428, 5458318, 852718, 5131948, 7555432, 8301049, 206141, 5130126, 7020904, 6707586, 5810176, 2445485, 6336048, 1032164, 1942014, 338743, 1029077, 6934368, 6468588],
[972540, 2699299, 6992252, 7518599, 1768119, 6369335, 4945635, 3994220, 7122543, 5589687, 909577, 6363532, 5980765, 39013, 7035863, 3743860, 5069334, 1839988, 3370968, 666144, 5511617, 7247538, 6108702, 5585177, 4071779, 1323965, 6689080, 8282554, 4778273, 1434908, 7977692, 510312, 2869585, 3776894, 6963287, 3762680, 4776150, 3713918, 3104329, 6672515, 3858734, 3131698, 11023, 5482889, 895810, 1326966, 5857099, 6776288, 1952598, 3324104, 3662162, 3611927, 6558610, 2167449, 4414099, 7901313, 3060391, 7021464, 7786345, 2691755, 3299926, 574058, 1697320, 3118193, 7221249, 7837166, 8379668, 2020127, 898776, 5960914, 7817860, 4495562, 6040508, 3382501, 3511900, 6405114, 26972, 7216770, 6173849, 4978644, 5320165, 7246859, 4216018, 4363277, 1138023, 3079114, 5248423, 5991608, 3932860, 2942558, 628487, 2413652, 4366476, 4673681, 2108140, 1057253, 2796924, 5112625, 7111647, 5093079, 3099365, 277612, 4311450, 2252487, 7864524, 3458, 1992314, 7582634, 994063, 5791621, 6399375, 7550203, 6336015, 8066386, 2745678, 6258621, 59068, 6258315, 4091618, 8048424, 8115559, 3539115, 2594410, 7626762, 2646855, 7750777, 2675159, 6518092, 7235079, 7980835, 3105870, 6887931, 3758908, 1235908, 2803632, 5491370, 384493, 6614281, 5069201, 7798449, 488482, 6647091, 4010539, 7971097, 6156655, 7108425, 2999824, 6879384, 1412221, 5925375, 6601723, 2670373, 5096232, 6033913, 1612790, 3671140, 5796874, 1395395, 6211142, 3787161, 2845271, 4479026, 8331376, 933790, 2768055, 532980, 6795975, 1422505, 2251528, 3955130, 3980811, 6000004, 654701, 2113823, 5309851, 1513651, 7654387, 1785155, 391208, 123272, 6765587, 3388981, 3520682, 5350176, 7739840, 5455245, 5380840, 4902637, 7910214, 7264112, 5808181, 2940726, 8024631, 6836332, 1858963, 4510273, 543016, 1372456, 7764804, 4273830, 6477514, 2082118, 1926085, 1609241, 4102493, 5181582, 5524896, 7564320, 6383955, 3488872, 1246262, 3428532, 3086341, 3294851, 7434087, 5494033, 4238181, 4119946, 7419729, 5732801, 3231033, 1626418, 8235140, 3737584, 7920005, 8137782, 521475, 2661358, 529050, 6854728, 2470389, 1974704, 34401, 8040544, 2967343, 2884554, 6051195, 8129410, 956705, 1322481, 5753314, 5814463, 6305566, 7043432, 5496717, 8097945, 2275989, 623632, 1271572, 7623544, 3977927, 1776856, 5375710, 4823342, 3075045, 1698896],
[5972107, 6909829, 3379538, 2413367, 1416819, 3881522, 4977221, 8163627, 8339231, 5841330, 3164909, 3818264, 699509, 5511477, 7897434, 6683877, 2033144, 6516310, 6501137, 1254724, 1179888, 3518485, 8047610, 7600957, 760188, 4137871, 5521751, 4476208, 8252960, 3932053, 2701612, 7545290, 7685184, 699340, 7071309, 1231863, 1098042, 2840983, 2362385, 398264, 6639042, 4124261, 6225453, 4327735, 6589835, 7294301, 993524, 8043353, 1248813, 1351244, 6606855, 5806755, 4162670, 6964316, 6283991, 3653272, 7316880, 1297541, 6687278, 7342668, 5390711, 1401619, 4597994, 1304472, 632345, 6993215, 3874486, 1754586, 7513700, 3224999, 608932, 5547340, 2747808, 8221735, 5502647, 5429395, 1736984, 3342902, 2240155, 505124, 1302903, 8248493, 6639528, 1835605, 7595258, 8169316, 2761999, 5195289, 3109234, 5596197, 2174190, 1946475, 900022, 6630572, 2209807, 1631072, 3632200, 6940815, 3444295, 6438226, 5845475, 6749119, 8102302, 7276799, 3071894, 5896879, 4437197, 7501455, 314375, 2423700, 6357442, 5877061, 5123980, 434290, 4045474, 1958302, 5628855, 8328222, 6732673, 6638496, 2082097, 6570351, 4526383, 5335945, 6813750, 7230688, 7455062, 2496154, 6270656, 3397844, 1511847, 5873485, 2949318, 3713761, 4709614, 1390335, 8322655, 25743, 7547783, 1259460, 4797995, 2993411, 8177022, 4129870, 792213, 7787284, 7838862, 2044096, 327915, 1884285, 6897191, 1550108, 3233028, 1723004, 4015377, 6814205, 5660776, 4038870, 2581711, 4282120, 6468791, 4542684, 7873460, 6647012, 3729263, 2907561, 8254443, 3508149, 8109887, 1152510, 4166692, 2435502, 262525, 4551375, 3725404, 3017465, 1097588, 1996871, 7389719, 2656686, 5442968, 3383783, 2176426, 5391279, 357399, 4044777, 4180211, 7839123, 1743844, 1279514, 2805428, 4538935, 750725, 3775534, 2915480, 3980704, 7562812, 4896244, 5586323, 2307723, 2544668, 476916, 8372877, 2996417, 5419712, 3528821, 3783845, 6019238, 5662568, 68720, 1247622, 3664839, 3472102, 4410524, 920010, 5253309, 2993530, 4744286, 7729440, 1339673, 1299214, 4549516, 5646506, 4126299, 2476700, 2386859, 1729965, 6897592, 2326252, 2707976, 7576752, 3554161, 4430940, 1366487, 5031951, 7046344, 5313068, 4511100, 1058298, 2945648, 5723150, 4867027, 5851263, 6624668, 3082492, 6658073, 252986, 2194080, 6240219, 2388749, 2457475, 2089692, 8030147, 3710718, 4418705, 7953275],
[5540048, 6431928, 4520140, 3607688, 7260986, 1555656, 1420144, 4740689, 7805648, 1053681, 6928727, 7387257, 7640489, 6578385, 2695980, 1776648, 5453283, 974087, 1164288, 305868, 7071233, 3675766, 6567652, 2789594, 5569208, 3228753, 1300411, 8333345, 2200068, 2329529, 958591, 2041262, 1973720, 4804504, 1915416, 3204916, 5510016, 5227687, 6433749, 6428626, 3877348, 2583885, 8102628, 992619, 3664149, 3092480, 1619666, 7792408, 2406676, 3896333, 7417072, 1205393, 1310661, 3436947, 2034307, 5059359, 3168707, 2913575, 6819048, 5073492, 4945171, 3479865, 2731087, 2678979, 6534408, 6373038, 2568611, 811564, 4881793, 152098, 7208050, 8227260, 6909975, 1976562, 768020, 2622494, 314269, 6253519, 7430809, 7266905, 2780613, 8313386, 2137963, 5439099, 1979073, 3109773, 2347208, 6970792, 3322457, 6471883, 6254123, 1759988, 3966716, 3262914, 6532485, 6534469, 2739252, 2127976, 6512270, 8314243, 2476408, 5881110, 6580132, 3293943, 5610536, 7378443, 12628, 3273903, 2263840, 6212143, 3949279, 1722468, 6389743, 3856924, 5759351, 5982056, 1747094, 8273559, 680513, 8019696, 2188548, 4893553, 1815112, 79638, 1929058, 5853563, 6390713, 7253270, 1196522, 4202311, 6334634, 3077922, 6681668, 6576554, 4206801, 629913, 7561973, 6362547, 7296816, 6101986, 8236614, 3356536, 6994571, 929090, 7964160, 7973755, 5424610, 6433301, 8007614, 3950770, 749601, 7759101, 5471056, 4387926, 2698040, 8232396, 3905290, 3344668, 918898, 5432028, 631641, 5565334, 5345041, 1622467, 4826500, 2324025, 1322489, 981037, 7690071, 1692104, 3619263, 5680974, 4288873, 3412683, 6846496, 4610307, 2041768, 151633, 2903726, 7425339, 3365295, 856787, 6160756, 7801828, 6932746, 510465, 3630964, 6803192, 4515031, 1968691, 1058129, 5282979, 6408800, 6173469, 2131889, 7679147, 5546028, 2355640, 5095342, 6146034, 2756280, 454153, 4517755, 4844354, 4623589, 6859868, 4225446, 7507287, 659357, 2542537, 6957926, 5921372, 8145409, 5369426, 3848963, 7479403, 13807, 4290493, 4820978, 3154197, 5886875, 3937350, 7541699, 790295, 2139682, 3865273, 6864811, 1625381, 6308908, 770500, 3590623, 3469918, 2289088, 725804, 7626622, 1334992, 4652194, 7116728, 7155231, 1364062, 2123876, 872174, 1285717, 7679430, 5516989, 6092067, 1148254, 6560247, 3228256, 6660234, 7692679, 6062510, 6462493, 8252954, 1158600, 5929690]],
[[7693815, 1882484, 167998, 7297973, 6736964, 4929570, 6173364, 3586617, 5884687, 1748356, 3958478, 585800, 8272285, 7394928, 4253234, 8081619, 8001842, 4862556, 2452673, 8219333, 1600163, 359825, 7082101, 5796579, 1825863, 4610247, 4508878, 2799529, 2082327, 2627255, 5184417, 2071591, 8173573, 26307, 6560694, 8257511, 2205991, 3633725, 195183, 7544409, 3636038, 488902, 5677811, 3494617, 2226346, 2631124, 2860900, 7541544, 5369562, 6077539, 7099136, 5837822, 1812140, 6457498, 5005971, 7289942, 8242991, 2004849, 299815, 1928652, 7809896, 2023930, 4304933, 3206119, 2046977, 7160694, 1666931, 6829733, 665196, 5688120, 7796254, 4728752, 3500865, 3953888, 7135376, 5060938, 7640093, 1189947, 5318512, 3986017, 549805, 1541556, 5801279, 8033885, 3854316, 5428577, 6405091, 1680009, 186189, 7488252, 3225890, 2000284, 1937243, 6629532, 1870652, 1293543, 7471158, 365231, 3283680, 896598, 1289920, 7599035, 3466017, 7568415, 2312291, 5605697, 6734233, 2982547, 2239497, 7374565, 7293493, 6010640, 4126370, 3171305, 1787695, 7907523, 7088243, 6066451, 219035, 485205, 4812440, 4425528, 4754285, 1459621, 4847568, 45111, 7219282, 5766748, 6780103, 817056, 1204877, 5091332, 2114728, 6073904, 6360684, 2099669, 8139714, 4000574, 5446966, 2673438, 2875704, 2989869, 7749150, 6399027, 5325314, 2120088, 2408395, 6286621, 5208901, 6476228, 660533, 5599865, 6734800, 4361538, 7039821, 5520358, 7188623, 5341164, 7191702, 3411656, 4351247, 4923980, 966671, 4747179, 561961, 1000559, 4382588, 7315692, 5100494, 4153344, 832702, 6291469, 2167824, 6794097, 2735430, 5163643, 1458049, 7933491, 6416720, 2780890, 1844064, 4606962, 4739506, 3642544, 6776759, 240495, 4435920, 1502123, 5998081, 6140373, 6545443, 2764530, 2950920, 1762135, 6356507, 7524461, 1651034, 3907084, 4327558, 4750211, 2007666, 4073125, 197162, 1726879, 6090561, 5473656, 6659062, 176763, 588658, 2642573, 1369347, 3752909, 4922845, 2973784, 3700489, 5370132, 1633652, 7736880, 4551565, 6852385, 5027866, 3670823, 7228556, 1743029, 1996195, 6144078, 6617034, 5700657, 5522881, 4933902, 2311223, 1405833, 2485769, 4596471, 1660051, 179276, 4415913, 7422425, 7832333, 6675773, 153330, 7674919, 6408569, 6567276, 4468493, 564681, 5337224, 5481650, 7889117, 5871641, 4584925, 643903, 2905210, 4384661, 1795662, 2959446],
[6322209, 3641383, 4061442, 4222050, 7955807, 6955885, 7866524, 6921045, 6540249, 2599322, 1359674, 779263, 520439, 1298739, 2483885, 406247, 3920846, 4870383, 7326149, 6104691, 6847808, 684952, 6955550, 3490063, 7218064, 8174201, 940272, 6862253, 128026, 4697463, 6802409, 116586, 4282723, 5284544, 7006832, 7832897, 4513465, 1816085, 41318, 92329, 1958176, 647713, 7696556, 4460996, 3869482, 6131656, 7036177, 3882551, 4251946, 6494439, 7340950, 260910, 5617524, 5011928, 4663769, 568818, 3858984, 4746144, 5040757, 2546151, 821229, 4999014, 2753041, 1231045, 4843429, 6701924, 7163628, 662706, 1357579, 4693787, 3858070, 6823788, 5927383, 5141298, 4048818, 1293972, 1254295, 4458189, 5381838, 6148908, 4038380, 3788600, 1170743, 1297459, 2373572, 6096908, 193087, 3420598, 4090697, 8174988, 1632445, 7600867, 4692251, 7568828, 4609312, 4535614, 2938424, 390705, 7244184, 2303642, 2018130, 1455422, 2150911, 6037543, 5098665, 955929, 6876240, 4048623, 2370806, 66087, 3903081, 4687271, 8085662, 1067769, 7574807, 2976993, 3744389, 4347833, 2387972, 4592672, 2152791, 247113, 6586150, 2120348, 7007578, 7756302, 7840423, 6376820, 1933533, 3775630, 4245076, 5515219, 1520554, 3566619, 1508089, 531643, 6350022, 5067717, 2676135, 6997572, 7207946, 864374, 7104084, 1623619, 3619163, 2120277, 938296, 5620579, 2991261, 2202835, 6361727, 4911816, 7873258, 5904408, 3619574, 2151546, 7047743, 5559566, 7990319, 2773318, 5317338, 5585690, 3899005, 7148722, 5273289, 6712889, 1870740, 1683743, 2936021, 5882527, 851580, 152857, 2646147, 934611, 2911380, 7068350, 3535600, 5032133, 5357603, 2412716, 2150167, 3740630, 4877645, 595288, 6652777, 7381927, 6565684, 713365, 1231386, 5419868, 6761803, 1782060, 5427622, 4107038, 2402049, 625204, 7349870, 4314120, 8114372, 4774291, 2084084, 2593208, 5576343, 5471719, 159188, 5881562, 5895398, 1676480, 2962096, 3071171, 3125356, 2190975, 3837693, 6701217, 317334, 5534985, 4107636, 7672832, 192002, 3681401, 1186509, 3932293, 3263250, 8106241, 4229724, 5596370, 3343337, 4595443, 457224, 1317477, 8366823, 3015643, 6133711, 4430180, 1681046, 412290, 6679244, 4091999, 3569755, 1288557, 7562480, 3644450, 3798596, 5572772, 3213447, 4622547, 6798378, 1333303, 2144264, 3555217, 3219746, 30188, 6053984, 3166014, 7723531, 5124311],
[3756672, 7736103, 2825780, 2943756, 2727290, 2561738, 1484911, 561739, 3096000, 7207241, 8069616, 2741085, 1636416, 4637829, 3443392, 3478709, 1819290, 4719933, 3770168, 7092075, 1019321, 5180817, 5455123, 4622116, 719498, 1736653, 2936988, 9387, 6455606, 5256153, 195582, 6320087, 5030526, 3989229, 4165343, 2017455, 761018, 6897417, 8363952, 2761283, 1782585, 5262849, 3497566, 7731736, 6835996, 2062971, 3495079, 1774629, 780273, 1215276, 7911639, 310156, 2001586, 5364660, 5821516, 6499960, 8366932, 1373905, 6073141, 4450215, 1056303, 207754, 8021044, 2598291, 461653, 2428221, 6629739, 3644919, 524949, 1745299, 4648795, 2160481, 3092495, 3595379, 6280876, 4619932, 26747, 1122340, 1272013, 6691410, 3877943, 6518188, 3679354, 5324912, 2421265, 7278907, 4777431, 479393, 6748856, 3380229, 5087260, 1166559, 5211690, 4239131, 4661653, 1563707, 3940838, 445288, 3416981, 4767077, 2218621, 3804273, 3736829, 2018266, 1569575, 7361787, 780888, 4876754, 4703319, 6124290, 7340628, 3649094, 6590588, 7720530, 6238131, 4136708, 2816946, 1983424, 4412260, 4194338, 1110737, 4061073, 7565434, 3100356, 4426980, 390680, 1190121, 7980855, 6514996, 7523964, 3699173, 748578, 4124545, 4875977, 2835927, 2702043, 7114400, 4742082, 2460943, 3448368, 2352829, 7519293, 6260861, 5490490, 1104243, 1510509, 7193332, 6203351, 3705552, 3704991, 7648980, 5791073, 621125, 3072467, 3588489, 5223225, 960313, 6319739, 5958466, 3784189, 8043021, 1622929, 1899237, 3702089, 6476633, 1167024, 6793044, 3679107, 2587333, 5698562, 5415190, 5682952, 1305364, 7304625, 8245036, 6455824, 3767514, 2021300, 7714850, 5276933, 1744660, 6046758, 2254730, 2283801, 2308265, 7790653, 8320823, 3354773, 6863690, 4564693, 5178961, 4822319, 6318902, 1506412, 3190632, 5259097, 3853857, 5530324, 7723450, 530507, 4369102, 7220371, 6368518, 5759618, 7341620, 1740302, 4523473, 3977819, 6526553, 4162646, 6961077, 3502207, 5360855, 5945530, 5363357, 7195389, 3586887, 2597499, 1878458, 3360362, 1736137, 3139438, 1172375, 1996672, 8136034, 2568680, 1065260, 392823, 5774940, 3668862, 2166047, 2447344, 7238524, 5568342, 7377980, 3528786, 5382220, 8068273, 782950, 339002, 2302524, 7875602, 2849279, 4714021, 5168868, 2521974, 3176807, 5656280, 2276804, 6779758, 494143, 6538752, 8172021, 5389904, 3071338, 229213],
[2358292, 7885884, 2619080, 6346122, 6834595, 3600178, 5974397, 3369626, 78273, 2728173, 149354, 1700462, 3882482, 5793306, 5220481, 5999073, 6077871, 6408969, 2313920, 706918, 1997558, 3595359, 5040032, 4145802, 1002088, 3662841, 1044884, 7240852, 7627909, 8335737, 5271511, 2809065, 4615252, 5491072, 7348200, 7134316, 892056, 4315106, 2095030, 116453, 2839605, 8168939, 1267469, 6080844, 614486, 4676441, 4895193, 1353833, 5420760, 5663510, 7565030, 7890505, 4793806, 7085374, 8035075, 2285947, 6850412, 1478307, 6806441, 1618642, 3675249, 1451767, 6723492, 4674510, 6366901, 7276568, 8321434, 422434, 3001747, 2161632, 6413809, 1403104, 1490244, 4289684, 7132551, 5008327, 6726388, 887250, 2540975, 1533585, 5649064, 2218456, 6103991, 1277866, 3015715, 533086, 2250567, 5948382, 990238, 481535, 6209169, 3550878, 3704493, 3182391, 3081558, 251514, 1771009, 6663074, 635375, 5710734, 1719980, 7112636, 7635906, 3235044, 890243, 3767858, 3871471, 848957, 6783749, 6393788, 3780983, 2983612, 1398257, 379364, 6304952, 1816175, 7890478, 3206007, 4102895, 3152700, 5729135, 2380559, 4607316, 7201524, 7000430, 3737477, 1898272, 461163, 2853736, 4034706, 6536824, 5938428, 6717627, 7345531, 7727663, 2455232, 683189, 1493814, 2325099, 5761267, 3620763, 2797755, 4905629, 6190654, 104046, 3729698, 5663825, 7476279, 4578690, 2770512, 5443005, 5074678, 6784027, 5158665, 4078965, 228749, 2694194, 5036274, 6313353, 7130628, 7462409, 6386713, 1700581, 4225626, 5598787, 5487370, 649719, 6927919, 7180844, 1793853, 3910772, 6448610, 2097613, 6162784, 448266, 4606395, 7819312, 5120210, 5811342, 7741218, 5602768, 8202048, 4836554, 4287499, 6761865, 5783623, 3799589, 856169, 5486457, 86375, 6377651, 5114007, 5307960, 201225, 8216304, 822361, 8270022, 3526704, 1761244, 138335, 5699744, 3913726, 5205161, 4234110, 8260224, 1376922, 5688707, 1512298, 6496912, 2995942, 1129037, 5094785, 2625858, 6891134, 5730945, 7664399, 1212625, 3731224, 6881542, 1595079, 7812953, 6600900, 6827071, 3541951, 4501427, 1036484, 4836218, 6226888, 233745, 3899899, 6504428, 6755630, 7058058, 2272315, 5686767, 649087, 7723701, 551380, 6742764, 7447128, 1200591, 6421714, 3944399, 1954637, 5505146, 6007249, 2932714, 4364963, 4077051, 4021706, 5064969, 6455512, 1822156, 2259294, 828607, 406191],
[4035469, 2801957, 171288, 4726722, 3288158, 8059965, 7103846, 983085, 3664218, 6895647, 4725799, 933159, 7665089, 7873980, 7188661, 1754032, 6765385, 2744063, 6473697, 6603300, 4019825, 7049088, 27735, 2603903, 5007594, 6698919, 4749724, 2970941, 764834, 1090298, 5632050, 2934895, 2154901, 8237956, 5297025, 8318516, 3302349, 4600209, 919622, 577203, 5388082, 1468723, 2752849, 1658076, 2430310, 1150554, 582769, 4226013, 1452138, 7856144, 4866856, 5268123, 7085876, 2650151, 7597544, 1238691, 6581657, 8144596, 1427984, 1989195, 8162508, 1142916, 8284421, 1858024, 3554196, 7142255, 7299230, 7425229, 3997055, 859566, 4709804, 7513118, 1747877, 709700, 4349065, 4002938, 7083359, 3562856, 6460455, 7208699, 7558680, 3769811, 6454770, 8229541, 6137983, 4047144, 7804011, 6284572, 1301356, 7100947, 1283269, 4390448, 8258350, 2366803, 249945, 5228757, 4821903, 4689548, 4972443, 1682084, 4970859, 24328, 161901, 1949687, 806110, 7608261, 6864235, 8360641, 1711159, 3806282, 2346341, 1749729, 7469462, 4661825, 271775, 1384486, 2063630, 3243088, 2272574, 7343921, 7167659, 4060211, 3915126, 6781780, 2329066, 4796015, 2610612, 3022006, 749208, 7094228, 5747174, 1260351, 8272435, 916440, 558066, 1327994, 2783898, 4064862, 2421588, 3470645, 1987582, 648294, 1406680, 6585273, 1854876, 7543310, 2879653, 7901754, 3848674, 7039494, 470087, 5480039, 8018121, 6424366, 8094720, 1473130, 4459546, 4007847, 412662, 8061230, 1132637, 1643113, 2118756, 4422556, 2981527, 4186777, 961917, 1161367, 6138904, 2507834, 5230225, 3343960, 4586757, 6485721, 3011705, 6364321, 6320810, 5702120, 3929687, 2592402, 3215581, 5788247, 3583302, 6787465, 7098911, 2405636, 1870338, 3287625, 5154229, 4985532, 7403400, 1468403, 8280488, 6963349, 7562028, 936845, 1326398, 8099005, 2254121, 2716850, 2186346, 4123578, 7115115, 7814420, 549474, 1974772, 5649664, 4536299, 6247305, 7893691, 2955440, 698400, 1436850, 2885211, 3126869, 6771994, 8320740, 4437202, 4006735, 5721579, 6944843, 8346331, 5532188, 6527433, 811661, 7401089, 1861972, 2202096, 7849519, 246527, 4568089, 436208, 8219038, 2756585, 206974, 445236, 3841676, 1957571, 3808239, 5188818, 2020073, 4497323, 6775618, 2840919, 1314046, 6936276, 3540045, 2390515, 4452041, 1490301, 667947, 2896248, 1053604, 6052970, 2458066, 2596887]],
[[3910367, 2228457, 6884424, 3462238, 1063668, 3561936, 5476453, 2654213, 2909876, 7106050, 957368, 6179922, 7084838, 7718859, 4539874, 603612, 2971058, 3232649, 3882157, 242143, 5966074, 2539005, 5131158, 223274, 4975229, 1619020, 5604115, 3884179, 8261362, 6165885, 8072385, 8146835, 5160565, 3102719, 7533302, 6729761, 3722903, 6858607, 2503266, 2382025, 8073865, 8168522, 1432024, 6407140, 7233118, 1705485, 6228732, 3090297, 3560107, 3583390, 6931711, 2844972, 3767623, 3067011, 4433148, 5497539, 3723625, 7081532, 7527914, 3461095, 7825067, 4532647, 4274854, 7163005, 3683963, 3003250, 7500148, 2146357, 6047390, 2064036, 5356383, 4795924, 2817643, 1935428, 7879908, 2101294, 3086759, 7718228, 167413, 1053616, 3315442, 1996249, 8256765, 3991153, 4735369, 6398679, 1026625, 2015589, 3683442, 486537, 5253956, 7459072, 1934341, 4411978, 637811, 1439557, 8156704, 5359234, 91909, 1557739, 3704089, 3789081, 4119816, 3860121, 575308, 7685137, 2564828, 1516816, 2532876, 7368096, 2227404, 5367387, 3853872, 7732649, 4195742, 2967018, 6582053, 4511117, 1792550, 4755844, 3445894, 4754027, 1866524, 346768, 6981533, 1016621, 6298342, 806420, 6968086, 306544, 2656678, 201127, 648044, 3115900, 6826525, 55627, 8191798, 893032, 596016, 6363503, 6779602, 6289454, 733550, 3318134, 356577, 2177969, 1107500, 4873590, 3733588, 5084957, 438461, 6513759, 3539737, 4989516, 1254692, 2238854, 5487899, 6805766, 1958863, 6677839, 106418, 7083910, 3790469, 6396790, 7451796, 1950029, 1103797, 1609133, 2052066, 7701577, 2159490, 3265741, 4844327, 1672224, 4132356, 6460005, 2716063, 3768134, 2393795, 5863915, 1583049, 1908150, 1031469, 2054794, 1838255, 3434711, 3432765, 6558554, 4308405, 1803407, 5309833, 6250761, 2296040, 4949718, 3201439, 4744356, 1072930, 7731718, 5348914, 6067356, 2648243, 6083542, 8140313, 3712827, 4493962, 7778298, 4998847, 36742, 5417447, 4244218, 7211730, 6586563, 6831326, 763957, 3627303, 6524902, 1152088, 2808044, 7096088, 4799186, 5349583, 7213968, 3753195, 1563369, 7616695, 633486, 7215467, 8301978, 4774382, 2001320, 1516480, 1004405, 2950346, 5647137, 5453897, 5628666, 4315157, 4376363, 600417, 6940487, 4730649, 5151519, 652210, 732903, 4250606, 6892214, 4303095, 5921039, 3746161, 3353434, 5721771, 4065668, 6478833, 6660046, 7936996, 4261083],
[5378232, 5519568, 2355810, 3621403, 5539526, 6187133, 2653144, 6109264, 1730233, 8189627, 499940, 7783460, 833940, 4477684, 2045325, 5885297, 6984345, 4388026, 1079881, 5874265, 122313, 1943074, 7594897, 1305742, 1862534, 6248389, 2691285, 4923809, 8130997, 7008875, 5698602, 7086629, 6178518, 6579692, 4606344, 2901588, 5303340, 6761970, 2984821, 4702431, 1728972, 7714698, 4341053, 2995356, 6957019, 4958529, 3863814, 977827, 5297520, 4642633, 549572, 5420178, 2908131, 6762098, 7215334, 3869182, 4217291, 8220278, 3463118, 2765199, 600163, 6813710, 1173334, 5683258, 381988, 7820562, 6506503, 7166247, 3342831, 3698129, 4310784, 2284071, 186716, 6566115, 6278221, 6856302, 5881026, 7406499, 3288717, 1050314, 6507863, 2287516, 3204019, 7633001, 7754103, 1463830, 7771401, 6410495, 891372, 4782273, 7479723, 2006984, 4929558, 388890, 4134533, 5335354, 954387, 7928970, 4459966, 5177744, 6408930, 3022173, 7553307, 7866347, 6207115, 3832721, 4238462, 6641491, 6067244, 6160973, 2899785, 6131915, 2781095, 4308389, 2977666, 7350224, 4806890, 635528, 2824939, 6976672, 1158457, 7259189, 3845871, 3083866, 785129, 8176387, 5636564, 2395814, 7344953, 3593714, 8358884, 2601000, 540222, 2639816, 3742184, 636046, 142634, 898643, 2537432, 5072039, 5986331, 6541054, 7837094, 4558652, 3250767, 7584036, 6294681, 6189173, 1582821, 2780369, 6062455, 4522430, 3841559, 2638465, 5228066, 3730307, 6638190, 6311935, 4636091, 2138840, 7866730, 7748280, 439873, 6098115, 7033343, 8266676, 3387673, 7843800, 5801100, 4818283, 7661043, 338985, 5618912, 5790698, 7332316, 4988265, 7270926, 1366668, 2972283, 6567252, 5181152, 7926761, 2122551, 8071258, 4143213, 2878259, 1309688, 914364, 5467523, 2912492, 200102, 2531388, 1235659, 2519176, 1477947, 4606921, 7296170, 8076122, 742207, 3818833, 5051033, 588625, 547456, 8258174, 7944609, 4277846, 5896672, 1771745, 6627981, 1767923, 8099791, 3091208, 7095235, 1772442, 2528699, 8303486, 4964405, 3916502, 5768158, 5575577, 2709084, 5233488, 4461827, 5341935, 1552101, 4093582, 3202478, 7261692, 7417357, 3549472, 7975921, 1546998, 4412096, 4174489, 3784283, 1949058, 1690762, 5073231, 7162061, 846725, 2034908, 8052784, 2453721, 5602524, 2245985, 6412959, 5795220, 4250156, 4940466, 3055634, 6639046, 5186132, 1434572, 37074, 614382, 3802312],
[5436353, 5274401, 4212034, 936401, 3815775, 5644067, 1365496, 7212505, 7623262, 7348927, 4429029, 6758201, 4210369, 1383162, 49214, 4227716, 6344440, 5701425, 733605, 6793090, 3206873, 6655299, 3234008, 2989593, 6230709, 7978148, 8291411, 6342949, 2040880, 4519697, 464252, 6067351, 221790, 4964161, 740625, 4177070, 168342, 898238, 4371996, 677710, 6635182, 7908077, 7615091, 6780788, 5873272, 7246868, 2207487, 1651751, 8326726, 4668667, 3230869, 4164443, 4774338, 4338492, 4876751, 1098402, 1078522, 5119349, 3057530, 8066207, 5095839, 528216, 8276836, 4360736, 4156767, 5986862, 8255635, 3780563, 2069353, 17919, 7120858, 6195475, 597983, 215615, 2665097, 7600860, 5851044, 3237114, 3349394, 3786690, 6622086, 3145294, 2788299, 7494984, 5527854, 1053149, 3487085, 939407, 8331201, 1807550, 2886683, 2972286, 2529737, 2557773, 5989245, 3172412, 1767779, 1563470, 5057859, 937549, 6585369, 7362223, 5853469, 1469596, 5050573, 36104, 3701261, 330682, 3116096, 4630492, 813079, 2130234, 3205887, 3596534, 7598404, 7629766, 3653200, 4274662, 4262627, 436270, 7684970, 1699282, 8263952, 1733120, 6364734, 2624342, 7422938, 4282363, 8270185, 2817614, 54422, 8125817, 17461, 6388071, 4506669, 2887562, 4916951, 4395622, 7244707, 3272383, 7348019, 985071, 5091114, 7225084, 6583593, 7400179, 727486, 6564146, 308586, 1048188, 8250425, 4735141, 4398457, 6775980, 5762240, 6935921, 1625074, 1507334, 3326439, 2174796, 3800220, 6354817, 3469442, 4740236, 7134547, 2600800, 3036585, 3332703, 2378565, 3025430, 1226150, 4584968, 1584386, 4183116, 552722, 1121406, 8039922, 6987828, 8324164, 6382626, 3027994, 7453037, 3769251, 1739495, 69340, 4751084, 7306130, 7014399, 4700566, 8062945, 7826860, 7394745, 591395, 2592720, 6421885, 6808176, 4661651, 7187771, 5441974, 164194, 309966, 425154, 3794776, 3854098, 8312524, 6630102, 6172682, 3364239, 6413624, 1067524, 4404191, 4274687, 1646184, 1274730, 7477107, 6946766, 7880989, 1961387, 8215781, 7546117, 4620949, 8057551, 655965, 7274095, 4283198, 2222040, 5407101, 4925800, 3906733, 1951352, 1867810, 2643711, 6675346, 7018179, 5682890, 7515128, 4953882, 5879585, 1772086, 3864228, 7407145, 8258523, 6131764, 5330660, 2475741, 6790557, 5268386, 6966218, 285605, 7352203, 3935001, 3690979, 239344, 5714330, 7402683, 3635018],
[4868571, 2112075, 3888661, 2844204, 7580130, 1181296, 3470083, 700792, 6026967, 5505833, 5544653, 1434462, 432836, 4320907, 4843976, 59541, 5586428, 3183362, 6455239, 5366173, 1084079, 7848185, 3896816, 2557875, 6198548, 4590575, 7060133, 162686, 2615161, 1918971, 7205994, 5178573, 5520375, 3978845, 5884665, 4162504, 745613, 501213, 4878715, 3242085, 8056748, 620794, 2320079, 8151017, 8197215, 3666991, 2050124, 7868455, 6526057, 4445020, 1609241, 6110839, 8085596, 4549261, 5621436, 7857957, 4187534, 6031927, 5702355, 1192339, 1959694, 6887757, 6855844, 294554, 938996, 7762509, 2020608, 596913, 3758436, 3991460, 577373, 5271042, 2194983, 7528222, 4153479, 6092217, 1598135, 2735556, 21180, 6224817, 7920225, 1959518, 3296883, 4548943, 578306, 3895072, 1921527, 6462541, 671817, 6803640, 1200407, 4174657, 7377920, 1786222, 2060466, 1760498, 5274434, 2551822, 8156246, 4718344, 7014539, 864132, 2413743, 832648, 5971725, 4692096, 203643, 414796, 1059343, 3344095, 8113893, 3739307, 6160714, 420883, 5661995, 5822678, 7262718, 4280344, 7384945, 6489499, 2087483, 2375128, 2195168, 3861342, 7840279, 5428816, 3612009, 8210268, 3847915, 2246453, 1486951, 2543940, 7988280, 4654624, 2710480, 8146317, 1277963, 3875790, 6469274, 2323723, 4371796, 6725450, 2775285, 1726688, 6173723, 4014490, 2250509, 4567166, 5015390, 4328935, 2307669, 7892718, 4503923, 4141122, 2379652, 6265269, 2495940, 2701991, 4424169, 5053846, 3255440, 7512386, 5392875, 5246897, 5926299, 7959528, 8228585, 2699079, 3295782, 2630977, 2502580, 2440697, 7480612, 6001043, 7083205, 4323683, 1934558, 4111227, 6769488, 3130183, 6197469, 2282524, 650130, 6039456, 813118, 1042901, 2239326, 713988, 5511280, 769356, 6447023, 2338001, 1940520, 3615476, 7780851, 6895020, 3730210, 7276099, 5465437, 3416882, 4158471, 8013608, 5154275, 2371114, 6451181, 7621580, 1170278, 7056972, 7990183, 2952654, 4133994, 7876696, 6311839, 864745, 6454862, 168047, 2306325, 1912511, 6632572, 4069327, 5873730, 804704, 8249667, 3945970, 2007521, 6114710, 1922092, 3094844, 6316281, 3785849, 461318, 2005180, 3984409, 6315913, 4719925, 5908530, 970374, 2711592, 158663, 3251054, 2233548, 1200644, 2493559, 5973230, 8369965, 1587871, 8117328, 7767154, 5252999, 2119863, 5178068, 3797695, 292757, 1385933, 2815883, 3820572],
[1455975, 7617044, 6476902, 6055551, 1343603, 4515127, 3948099, 4839790, 5385735, 2746859, 3925963, 98578, 7421098, 817772, 2516427, 1652567, 8218176, 1758473, 625106, 6937317, 6905812, 6869640, 1443970, 1467285, 1346589, 2014111, 7805292, 6259857, 7246507, 4564981, 7045751, 5796313, 7656873, 539995, 5378074, 1931521, 2106800, 3555888, 2466776, 4882888, 3865168, 829888, 6598063, 139406, 2316106, 8345094, 314666, 5545676, 8050720, 2101, 8277504, 4867492, 4273751, 5098854, 5692628, 3051206, 7441864, 8159258, 5869938, 6253981, 5650668, 4807537, 2830829, 2383669, 3968995, 745577, 5492235, 6095574, 121392, 6781178, 3309785, 2738250, 7590504, 4196881, 1027472, 2615057, 243908, 624530, 3598563, 7079612, 5947285, 526998, 4472426, 282327, 4050210, 4764226, 6172677, 6576325, 1010130, 6708952, 451403, 1421242, 7881636, 6171108, 7314482, 809506, 6463549, 489448, 672619, 2858380, 4321538, 2954945, 2806419, 7684200, 2676223, 6914942, 7814081, 6566590, 5012038, 8112003, 7025175, 4890020, 7833243, 4634271, 431983, 6524294, 5091213, 6709805, 2421300, 2321144, 7049893, 2086597, 3656856, 3380998, 967639, 175204, 1607906, 4186122, 6804190, 6617915, 379354, 4661933, 5327410, 3198556, 8279090, 3238863, 228733, 2057470, 4478494, 6260126, 5680331, 4958456, 1913878, 1683389, 2618488, 1650427, 5335236, 7914171, 2086005, 319422, 4201269, 8203991, 4322050, 5943000, 3895173, 4146035, 1653430, 2996318, 3774196, 5327031, 7024970, 2706738, 4345649, 488193, 222406, 4502510, 8112207, 491368, 5171991, 6565230, 4208345, 3270968, 2514842, 597645, 1589217, 332312, 4184298, 3271587, 4112324, 3156618, 5609699, 2697281, 4511068, 127519, 3190572, 2363768, 3398631, 8030276, 5261264, 7701974, 3084902, 1534471, 4564576, 2827373, 3296043, 2407668, 7851695, 5815286, 6705916, 2463877, 7007480, 7230111, 2942615, 5998681, 7854906, 5338053, 2399716, 7694259, 984730, 3847526, 5401956, 4651057, 5465961, 2569872, 5785033, 8209083, 7272007, 101195, 5958569, 1339422, 3916462, 421926, 4700976, 4482072, 4759531, 3501830, 4581476, 3672715, 3592595, 6254976, 574072, 242336, 4970725, 1045214, 6972040, 3659484, 6727442, 1999563, 5713105, 5979935, 3471699, 647430, 7824348, 8317082, 6249166, 216838, 5533718, 1333364, 2144559, 8075253, 3592196, 8184470, 3699292, 146503, 6489090, 7968488]],
[[211455, 5110739, 4010153, 1816649, 8238857, 64, 290833, 2776837, 1384620, 1232467, 2532554, 7695847, 1084507, 4063883, 5429493, 7859004, 6434758, 3592383, 109901, 4007253, 5323915, 5151790, 1840389, 202415, 157989, 7585285, 6592821, 3705493, 2585464, 1520219, 3816927, 8053479, 6806044, 903742, 4986828, 7463859, 4985825, 2452049, 2033248, 92232, 8220226, 2566188, 7492261, 7433593, 2303502, 3762015, 6691216, 3678125, 3947320, 2073553, 154768, 1583379, 2445923, 3888124, 1888684, 5149761, 2170266, 6943702, 3731815, 7227612, 965427, 5877129, 2189291, 3807866, 5010281, 779179, 5864549, 7045922, 1108785, 6438704, 130268, 3626884, 6501514, 1253173, 4376520, 934191, 8368094, 1206714, 1816947, 1412891, 7329113, 6062172, 4197377, 5931821, 4568950, 347147, 6788905, 3820907, 6571254, 1501583, 91246, 6426659, 6607828, 5787161, 7895756, 7487909, 4787802, 8343736, 2517461, 7795424, 5102461, 3213526, 143098, 2510703, 4067150, 5984942, 8359640, 6181802, 4135644, 2379441, 4640385, 8075595, 166923, 2223553, 2382291, 3265566, 2567207, 3408633, 1727100, 154784, 3723481, 1114749, 3038482, 2410835, 4401472, 1590922, 124248, 4258784, 6861877, 7655957, 3143406, 2441884, 5353512, 1889851, 4680168, 7408350, 7535522, 6694286, 4408842, 2228309, 5642791, 2244144, 3209022, 5852834, 4663288, 3224664, 6966917, 2307867, 1519912, 5431268, 2932763, 6333388, 6166831, 5842485, 2829454, 4052657, 1486725, 5377268, 677989, 1774381, 4011353, 4105984, 587010, 1584571, 1959905, 1020061, 3611119, 4638622, 7810086, 7539039, 4489990, 7344330, 1757066, 1024612, 5945592, 2562876, 7714648, 4047999, 723100, 5244614, 2633572, 6502064, 3934460, 3143179, 1696079, 3131920, 7506584, 6399455, 4223208, 1769592, 7381558, 1282280, 4284521, 2209873, 7622483, 2002686, 3451416, 2430236, 4778443, 8268653, 1250343, 514343, 1896423, 2261542, 6017733, 6971890, 337147, 8051217, 8136682, 1760774, 7958861, 1717732, 6303548, 7082373, 3863359, 6561436, 7613045, 2630273, 3239782, 7406239, 3547589, 2812086, 3940837, 4194550, 4916477, 5179760, 4131967, 7392612, 8353290, 4478699, 957910, 7592263, 8146789, 4684695, 5646212, 6281157, 3130395, 8075967, 6043183, 423745, 4535138, 1658381, 4443719, 2204637, 1548109, 1430750, 32905, 6364664, 7646520, 2919121, 3181257, 635085, 1071546, 5099860, 2534083, 2304975],
[2247242, 4979366, 1683095, 8098528, 4971454, 6741551, 2121295, 7003273, 8331843, 5522362, 2035899, 2167623, 549411, 3728812, 6480582, 8337303, 7874247, 200635, 6451686, 977534, 2503681, 2019608, 1938821, 5522510, 3558508, 5087213, 5715405, 630911, 1863937, 5839077, 1744417, 2815452, 2472926, 4601112, 4577894, 7662551, 4452700, 1397541, 5686523, 3782405, 3391582, 3330770, 3820268, 8313216, 7288365, 2810699, 7580267, 2272426, 5591991, 286930, 6431173, 1757181, 7602624, 7897941, 6936488, 7686464, 3989362, 4317259, 8004431, 383821, 1743192, 713246, 5936887, 4414066, 7139384, 4322596, 7266041, 1087730, 7262206, 1531610, 1783481, 1934616, 315536, 3316192, 332329, 7839907, 3874876, 2101050, 5453877, 7243570, 3387996, 5285306, 1715391, 2596433, 1242317, 7235138, 7534674, 8077609, 5566433, 6491416, 5628451, 6138334, 3347187, 3459850, 1815251, 174698, 6339315, 3575735, 6547746, 2634118, 3993082, 2543690, 7612339, 1487842, 1556105, 1188637, 337706, 2535754, 5210747, 5320900, 5395651, 488266, 4507838, 1220843, 2728288, 5370929, 5035483, 1851390, 3465354, 1546559, 2212736, 327060, 4392314, 5440996, 5335943, 2715353, 1068813, 2991090, 3752829, 2302112, 4206799, 8377732, 3541425, 5967333, 2024171, 423385, 6388068, 4570083, 1076313, 1042826, 76293, 251354, 2273277, 1036606, 3562410, 2996125, 8378846, 4450004, 7733315, 3123971, 7246223, 7673089, 2115748, 2853166, 8329895, 175729, 2236466, 2434050, 1368508, 1975084, 4393336, 4967847, 1137861, 3990219, 5484252, 3444076, 4311716, 5862762, 2486904, 554649, 3601440, 2314300, 7260555, 8368707, 1354939, 1335747, 3285744, 8043060, 6231519, 8192534, 8272985, 5165903, 3510357, 3704761, 1538679, 1903391, 3410398, 3314999, 1839507, 7673733, 1820058, 7237445, 2896179, 2668167, 6462756, 612124, 2345465, 6703244, 4487818, 5908110, 5817089, 16790, 3503689, 7344990, 8325039, 4804471, 3244319, 4123956, 2617552, 2550107, 8000910, 7714723, 6876053, 2325545, 4551463, 6754130, 7653668, 6254934, 1821010, 2735524, 1176303, 827506, 5354927, 4677520, 3565402, 2776524, 7288687, 4323423, 841826, 7411216, 4499836, 1314582, 6685565, 4813622, 4352880, 6777043, 7710397, 8174566, 2368505, 3959920, 1744817, 98403, 5372429, 4925764, 2181956, 337196, 133122, 1730692, 3985860, 2607309, 5432592, 1617941, 1946597, 1854545, 1789039, 1953223],
[813421, 1050099, 8332070, 3981790, 3797141, 2562948, 1862474, 4785049, 564305, 1425435, 4948651, 5186467, 54722, 4398015, 2889240, 3211316, 3594218, 2199024, 5814016, 3765930, 8089282, 5517716, 3090636, 3829674, 7778905, 1063267, 2960003, 8334303, 1059815, 2027010, 508643, 5665691, 65144, 1975858, 1878080, 5375826, 1105246, 2223170, 6934419, 6058819, 7058454, 4090997, 7641318, 5552662, 7542809, 3631663, 1758192, 2535846, 4549505, 2861784, 3924769, 5711664, 2052230, 7131330, 3558287, 1786119, 7111727, 7897869, 1894174, 4058832, 4819720, 6019633, 2791457, 6238083, 3124589, 4551405, 7144655, 6369695, 4723819, 4154603, 7798666, 4772806, 7205103, 904634, 3657439, 2142679, 3971677, 2537418, 5401822, 6304800, 5591858, 8307472, 1430067, 5283681, 3631874, 7965752, 5043976, 7957851, 3947426, 7059741, 4893851, 2846403, 1715617, 6866801, 2296048, 137729, 4389323, 2115288, 3703417, 8053325, 29744, 6703982, 4961918, 6284349, 1637714, 3488355, 7891208, 7450271, 3986982, 5586093, 2059196, 6519785, 2611506, 7897290, 3698472, 6007278, 4284393, 5274503, 5589053, 7599888, 2837675, 3131731, 5825031, 4663097, 2773722, 3758681, 145245, 4610108, 4043821, 4676720, 7934300, 7738816, 7355133, 400234, 502909, 6513530, 6073998, 1447953, 6018153, 3955103, 4157034, 7812563, 2345639, 1463144, 6244457, 2764801, 4458453, 7083288, 4133864, 3938357, 7197908, 6126720, 7312909, 5252537, 496253, 1252332, 615691, 8303558, 6193924, 5696773, 7341664, 7706105, 5849752, 7889195, 4027783, 1712369, 3790686, 3330592, 6363685, 4700691, 7545492, 2019756, 6780531, 7017426, 3619119, 2320334, 5966321, 8311298, 7687022, 2603392, 5316484, 2125259, 7695319, 4789840, 3294378, 1947272, 8044406, 1620276, 6993427, 5996335, 2285412, 733047, 8173669, 2752853, 6188289, 4501539, 4075745, 6407696, 6561051, 7745742, 5325351, 5365375, 2058100, 8089646, 6516059, 229377, 2581954, 569291, 6431279, 6590668, 5386247, 4910571, 6288046, 746989, 7680993, 3471913, 8229825, 2881113, 763817, 7721775, 6536664, 7887304, 6509682, 5517202, 4978401, 7462736, 6134, 5105597, 2516386, 3300946, 6416677, 492932, 1989438, 6178016, 7430928, 4697786, 6620976, 1757057, 535288, 1996103, 3700533, 4754028, 5354745, 8226008, 5497326, 1688654, 2511330, 8347714, 3381556, 2378793, 6611153, 7090836, 4569739, 8162115, 3982805, 2211832],
[4860380, 6528639, 7841259, 7146628, 2792115, 446910, 7578172, 7175575, 3954830, 3894110, 2538321, 1234155, 441437, 1625348, 5895167, 5025129, 6767204, 292851, 4154032, 5640025, 1197172, 1220708, 2529639, 1749550, 7122346, 4340406, 6360461, 6948095, 7130215, 4652884, 4966301, 6164386, 5803146, 7416270, 1200349, 7559267, 63180, 2484041, 2700910, 7844998, 4187182, 7382001, 3154531, 6370920, 2770036, 1195194, 6425620, 2289257, 7275828, 856739, 5125879, 723268, 8025344, 4184323, 5456825, 8201820, 4534009, 1686863, 3677307, 3128625, 4409319, 2897470, 798982, 7026121, 6443475, 105885, 7431729, 2643066, 79440, 2190167, 6960535, 5520082, 4127142, 6818715, 6277520, 7725658, 430115, 3678170, 2952319, 1065923, 398401, 7574999, 3501483, 3146897, 1173248, 7587193, 5547248, 545979, 2066924, 2388741, 3719816, 7640190, 2152915, 1115996, 3229074, 2358973, 5988169, 291122, 6969157, 3121707, 2714845, 2069024, 66472, 5135719, 3336192, 784746, 7320753, 7163246, 1276303, 3604612, 2669830, 4157783, 4273250, 4106187, 2744547, 4999139, 3804474, 3596899, 7538407, 1163874, 972183, 1319115, 8028051, 6010427, 7312919, 98785, 2168988, 3326354, 7790343, 5745705, 3085073, 5439533, 3521301, 8315006, 5511878, 7638633, 7169504, 5386075, 4620508, 5035583, 2153517, 4280216, 1807595, 4756436, 4908047, 8128617, 3958237, 4307172, 5162909, 5874223, 3841434, 4220729, 4495472, 1526808, 6344713, 2338014, 1770484, 369736, 4576203, 257422, 4283075, 6223474, 7230653, 3653112, 996583, 1463780, 7584491, 4271801, 2370222, 3926308, 3903696, 2076095, 1605055, 1290747, 7880434, 1280914, 1083462, 3973146, 5947907, 5856846, 7833157, 7976157, 7328159, 961861, 28357, 5787846, 6008929, 2526438, 2039903, 6146445, 1204339, 3350286, 3126006, 2520150, 4668957, 3643269, 8098116, 6365506, 2353184, 670351, 2486008, 3294858, 4991574, 8169349, 7878560, 8024566, 6059201, 1151958, 1798919, 6079075, 1203593, 2576546, 5553451, 4669787, 28031, 2303524, 130575, 7906165, 3176770, 2507171, 7183703, 3073924, 3420227, 1287440, 5681570, 7414411, 8339990, 103808, 5015564, 5251854, 3505679, 5271535, 6181121, 5535987, 3754380, 1317900, 2395383, 2708748, 3700589, 3444775, 5853171, 4338276, 7133605, 2409621, 3554000, 4795815, 5229021, 4612874, 5419447, 7641882, 6924517, 2383938, 3772614, 5981729, 7917706, 4961400],
[7269680, 247417, 4929082, 4703750, 4319874, 6022760, 7373390, 4352006, 4629384, 7301321, 6061868, 2272287, 995548, 8359395, 8029510, 159928, 5748511, 4800278, 5259862, 7630098, 8305185, 3222119, 7547448, 3620201, 5255968, 8245500, 1326024, 5976386, 61302, 6452906, 3769651, 1877396, 2588689, 7733319, 76155, 6939691, 7431806, 4430637, 6247037, 6142920, 661801, 3574349, 7963097, 338885, 1037896, 6901675, 7131345, 6389870, 700232, 373055, 8046235, 5970302, 7201278, 7076866, 2826110, 5091047, 7490100, 2860682, 52391, 7176464, 4171403, 2364082, 6834659, 1062875, 1473283, 5580683, 7466334, 6231786, 4516166, 7326354, 4385973, 3398233, 3418379, 6040177, 4383401, 7503783, 5040815, 7085882, 1223084, 4154483, 989671, 2416830, 3582649, 8049895, 6395684, 2350423, 2704187, 6380161, 1879394, 7407921, 7238859, 5016287, 87627, 1067356, 6814027, 4814818, 578014, 780327, 7077669, 2200180, 127318, 4541885, 378543, 1116298, 3420887, 8014537, 1721503, 2095828, 2381094, 2167113, 5911586, 6592880, 3689476, 1969777, 4445823, 4222844, 447652, 823265, 2988116, 102522, 1052431, 2788107, 4494377, 4973998, 8359119, 349931, 6867376, 8049072, 7388266, 1871559, 4608857, 7066415, 7887125, 3756424, 7063252, 6349679, 7506873, 7977509, 3249874, 4276752, 8020506, 3951026, 2025372, 1795489, 2930945, 6629604, 7074915, 2466133, 7543170, 7488653, 1318215, 4325519, 6564118, 5768732, 4778567, 2815070, 3742021, 1850809, 7625962, 4328407, 1190848, 225055, 3254216, 8141182, 5949499, 4115428, 2433771, 982126, 1798560, 6308044, 1658372, 6039434, 3901871, 4067067, 7504486, 6024995, 812274, 554802, 1248268, 3899937, 6908773, 4292449, 3709863, 2521645, 3602871, 1354587, 4128366, 4356734, 6388022, 5144742, 1392062, 4297363, 5160654, 7801466, 1331170, 5283162, 5869237, 6560708, 3425315, 3141984, 1603869, 6746917, 2348495, 1031109, 7479190, 6171523, 1087428, 7767256, 3884072, 2881270, 831831, 1622429, 6916271, 2754036, 7017604, 4132668, 8134368, 4628378, 1366821, 7888456, 1054264, 4419625, 4611609, 5213163, 483726, 916162, 735794, 183887, 2981611, 1200655, 1300642, 3997767, 5690112, 4196021, 6264999, 4205103, 2031842, 3236938, 1102795, 3721712, 7497206, 4510625, 6979898, 1037866, 2351170, 5075971, 5389091, 443033, 241708, 287793, 2564548, 2410503, 8254433, 1474945, 4297208, 1488956]],
[[2106789, 541302, 6506183, 4859176, 2110201, 6324623, 2431823, 4690463, 571522, 7280423, 951381, 1144531, 1314344, 4398443, 451207, 8106292, 7401324, 3972323, 11817, 8249077, 1511506, 4011918, 6785183, 8359245, 5352277, 7675231, 2446039, 3866758, 4036466, 2800613, 55354, 4980237, 7294364, 5915405, 6601106, 6789890, 2215404, 4009122, 370919, 7605395, 3321924, 3928533, 7240817, 6226172, 2542573, 2051529, 6184775, 8280198, 7853107, 7123206, 3869096, 5432064, 8374824, 6098701, 2749540, 7766372, 921541, 1925371, 5242034, 3059149, 8005775, 109578, 4472059, 4735543, 796485, 377484, 2977513, 8179994, 2550962, 2929097, 333351, 6892610, 7513912, 3538391, 963412, 6658944, 6388016, 3857242, 4060093, 6344507, 6087151, 733469, 1516250, 7577153, 7269303, 2663174, 6487629, 6132007, 1751555, 1932295, 4748508, 8219387, 3171557, 4442084, 5034898, 80015, 1941736, 3246713, 1596603, 7814663, 2874289, 1960519, 4088777, 2958403, 4208325, 3497358, 4406477, 7610650, 3693144, 242924, 3663905, 3820612, 2332435, 6625583, 8279182, 7344620, 7398313, 4558970, 765535, 6467962, 2158811, 4348748, 4178254, 4478928, 5509843, 4232792, 8088070, 3344778, 1099222, 7956912, 6724195, 6276453, 961347, 5685449, 6920970, 5182264, 2087883, 6950004, 4022256, 4836594, 5955756, 1638453, 5219858, 8082820, 4374352, 5680622, 2706476, 5874140, 6428834, 5835992, 4783247, 1139712, 3736002, 7697399, 7643540, 350976, 1633567, 3355863, 1131156, 109225, 2774053, 6894011, 2121580, 3210401, 4527713, 7035112, 759440, 2734141, 1736060, 7344472, 4044675, 7540230, 1521530, 8244467, 2072575, 2553724, 587371, 2073304, 4696332, 5473706, 6771601, 1734979, 6087167, 8194771, 7896554, 2628525, 6602843, 4808297, 1822775, 4311762, 7937262, 6132101, 3689858, 7585762, 1158245, 4164486, 1937767, 2566854, 3373100, 2127573, 158137, 2189317, 6389847, 3135445, 4433727, 5513298, 3266567, 7465438, 1202417, 1900029, 2260502, 6390157, 6433418, 7425334, 7726858, 4519798, 4921389, 3075201, 7225189, 3478080, 3456930, 1722789, 1164554, 6821480, 5547422, 3197972, 2115659, 6844335, 1961639, 7440813, 7963044, 1339878, 5331249, 2097517, 7276165, 4532010, 4499541, 5539143, 3611974, 3967476, 7666860, 7851423, 2925931, 7223037, 6301919, 5514525, 4551398, 5291117, 7524184, 7266223, 4975729, 6115672, 52755, 8144658, 643673, 7184751],
[1072825, 2185568, 6392306, 5265996, 8366217, 6120648, 2612265, 6945041, 2817725, 1117102, 5329626, 4190083, 429888, 387801, 3292810, 6945115, 1640401, 4495324, 4417586, 4712585, 7602615, 3462181, 4476951, 7447163, 4451691, 144285, 1987394, 1571724, 7521890, 7714151, 42423, 985708, 3932234, 5471747, 2116201, 5399709, 6188828, 2480136, 786315, 3414741, 3086884, 3008249, 7850025, 2809512, 7890347, 4328378, 7694704, 79364, 6010132, 4388099, 7794717, 6487720, 1395306, 7539365, 5988480, 5013934, 2066479, 900734, 1517696, 2580085, 7199347, 8361087, 311819, 4352404, 6155541, 1425215, 8161787, 7216107, 1116464, 932958, 4307574, 7956833, 1240884, 5504732, 4612051, 7693793, 4022002, 3112515, 4711500, 5930953, 3747057, 2275191, 2879701, 8293857, 6106871, 2572267, 4218754, 6802311, 315439, 2302677, 3294502, 6778447, 156698, 4291348, 1951377, 2592507, 4718846, 1468657, 2175634, 476128, 1887365, 6452413, 1688363, 302829, 6053470, 3599191, 2162390, 4037953, 3921530, 4353623, 6378645, 1628651, 2919517, 791848, 1772985, 3601029, 5093593, 8277068, 8131818, 3118364, 801723, 2834606, 3649396, 5804364, 5124791, 6487635, 4124870, 5265731, 305398, 7790818, 618430, 7397046, 695117, 2202755, 1453858, 4706111, 2850852, 6028033, 8232726, 7110078, 3889748, 8200561, 6064313, 5177596, 8331267, 2589241, 625866, 4439443, 389852, 3742845, 655862, 1341458, 7187689, 2918896, 8236363, 4724550, 5844329, 3530837, 1381176, 2203672, 6478995, 2358848, 4130720, 5294419, 6737635, 7468665, 7864301, 4974842, 5326688, 4378389, 5801750, 2588421, 6128624, 1761858, 6598969, 1889401, 3355253, 5989526, 2071384, 6036699, 1153712, 9679, 651367, 8017534, 7663959, 5412294, 7342116, 6384818, 6246131, 2065391, 1492396, 6703932, 3613240, 4712717, 7492491, 88145, 7591277, 1108840, 3862966, 2472869, 2500542, 2436392, 6157203, 5044955, 4404562, 2179770, 6483146, 2514842, 5469125, 6709762, 3180932, 4182367, 5937515, 1580713, 1100045, 113578, 1241056, 6407697, 4100952, 7219481, 5675287, 1522494, 664245, 5119892, 7840559, 4389436, 4882657, 4992049, 1769515, 3489560, 4526318, 7882646, 3352375, 6186495, 3824282, 4064712, 3362059, 3126551, 1564641, 7960916, 5074099, 7613161, 8194708, 3439511, 542154, 6583634, 2429101, 5738196, 5388586, 4857903, 5998402, 1366375, 2729841, 2021571, 6222365, 6619093],
[5796085, 5196732, 3553791, 3086621, 688862, 1478847, 98300, 5851938, 6404694, 7475276, 851592, 4458081, 3011638, 3879232, 120785, 2324718, 7935961, 2082185, 7942477, 911446, 1945689, 2381043, 5413220, 5157344, 4658679, 138732, 2458783, 7327808, 6386977, 4261653, 2028380, 7638758, 5329384, 1194987, 1020898, 6447312, 905871, 747470, 3337264, 2140625, 2336862, 3506937, 2845061, 1621936, 4153181, 1830916, 771504, 7355028, 3935553, 2403256, 2619796, 6692604, 2893124, 6563316, 1126208, 2373738, 7146679, 6406320, 4869563, 4548218, 5258986, 8313847, 6674292, 2990606, 1288533, 5285848, 5195654, 1823229, 483634, 766163, 810261, 7636418, 6338329, 7263549, 2736679, 5069429, 4733641, 1684760, 1667457, 7485615, 5431328, 7356629, 1530556, 2663945, 6940201, 6848050, 4646221, 56183, 1962036, 1318037, 6008568, 7447711, 1459203, 2705069, 3901025, 4291348, 1066941, 5716142, 3372573, 645825, 4619556, 3347172, 1004521, 6320980, 3527317, 4034194, 5425278, 1442777, 6054999, 6176377, 3108384, 1304530, 1361832, 5133243, 1652692, 1020866, 2786006, 7249364, 3781394, 1433587, 8349440, 2284581, 2715735, 240977, 296867, 6874433, 2527851, 3983255, 1815360, 6210203, 4357376, 5259594, 419193, 949806, 7553387, 3149622, 3008528, 1176044, 748508, 409708, 6528627, 6046615, 1252029, 1966745, 3028458, 1036604, 7232997, 1036064, 6409157, 1092054, 863024, 3418679, 5030402, 4342587, 106165, 2173632, 2673150, 165466, 6632859, 3821640, 3224460, 2544776, 5216632, 3448448, 3811914, 6981733, 828589, 8047373, 4853892, 3474037, 4295930, 502659, 6984976, 3768545, 439721, 507973, 263005, 3077483, 5889353, 7879839, 927337, 1385853, 3591502, 6627504, 7662900, 3370230, 4772300, 3124671, 1961633, 4024473, 5623175, 3889884, 5329214, 7559838, 7188984, 7092361, 6578873, 4452662, 2660290, 953405, 3756264, 2011766, 6195229, 903108, 3419366, 302008, 3687537, 6101837, 1207053, 1312575, 797960, 1400735, 4142579, 1931881, 1008564, 4587634, 4742131, 5813350, 5941320, 7582442, 2656529, 4102263, 6525500, 4263699, 758355, 6489233, 4182777, 6624923, 7546454, 2836965, 947600, 3907377, 333108, 4330459, 7948826, 7094838, 6428002, 6502794, 6568640, 1838174, 2129731, 6048020, 4037828, 4580987, 7911145, 7720137, 4677001, 2184294, 2359243, 7992275, 4870996, 7169241, 4731873, 6385417, 4925021, 7112804],
[5580830, 6593831, 6708724, 4246361, 5193168, 3971457, 7977360, 6997450, 1471475, 3710267, 5213820, 1104636, 709871, 1995369, 4848445, 6517980, 5261396, 1220887, 7941445, 4067179, 4484441, 208854, 6112432, 5062241, 5601054, 2748725, 6801198, 3519204, 1897507, 450193, 2971968, 2578914, 7807194, 4124986, 5981690, 5143700, 3372534, 3344946, 3356302, 4785714, 2713036, 6242376, 1619257, 3693297, 4202465, 4099685, 788629, 1747035, 1130576, 4864594, 8210937, 5750444, 4169753, 4447389, 506691, 5682718, 8118172, 1283387, 7365541, 3283191, 2199925, 5916461, 2879232, 3163038, 6535718, 3585851, 6137305, 1331361, 4489860, 6400385, 837122, 541458, 2945114, 4778836, 4785272, 1433751, 2156728, 8209047, 8355485, 1071056, 3454583, 1758281, 17092, 3335030, 5665435, 5201289, 3871351, 5182, 7547974, 6444960, 6001912, 4578951, 3346611, 843903, 4486425, 7649838, 2228948, 2288995, 5847232, 2954286, 2404146, 825471, 3501817, 6021855, 1822258, 3103793, 8117183, 930227, 998397, 6338944, 2116555, 2336713, 3348185, 1926884, 7610514, 4875543, 5966713, 2772765, 3191058, 5129090, 1007406, 3089031, 3763165, 5868776, 3507982, 3770478, 5245456, 146092, 7759745, 3965277, 7256470, 7237319, 4869243, 5293916, 1236049, 1040323, 2332870, 7053412, 2337104, 5909179, 1834768, 5299009, 3196456, 6463755, 5442246, 1553087, 7180081, 1901752, 3771539, 2276024, 2773288, 5065890, 5494597, 982233, 2663835, 1123650, 5992210, 4623727, 6153609, 5091795, 6546630, 2476035, 7872318, 1671050, 1661479, 6827363, 6502531, 2776756, 3955373, 2226073, 1457875, 6104034, 2867894, 138885, 2685853, 7206269, 1021439, 1764317, 8341230, 7258632, 2722199, 2443588, 5573436, 3311945, 2991961, 2390167, 5345970, 6463156, 420278, 5582951, 2661741, 7629580, 3269115, 5611463, 5293972, 682928, 7715981, 7616107, 4224309, 6053464, 3498882, 4859058, 6116457, 7598242, 4058132, 5248529, 8058947, 3100949, 6163812, 1070381, 6577374, 7327242, 7669032, 4001446, 4797739, 5805213, 7603669, 3200594, 4365493, 5607944, 6880757, 6615151, 2295418, 2500229, 4713825, 4537098, 157486, 971636, 20892, 7821409, 1390120, 1166426, 5738743, 5970753, 5045936, 6961792, 7338757, 2673340, 5607643, 3386331, 4267658, 7795004, 645395, 3543160, 6479384, 1890138, 2195171, 7067951, 3676274, 5242555, 6262342, 4672033, 1627809, 7545177, 617741, 5235341],
[1915730, 333195, 4073768, 1498602, 5468671, 979416, 7084808, 4741565, 5591581, 4769214, 6087932, 4847641, 8209736, 3131512, 4055782, 1668154, 4243336, 7129589, 6671773, 695251, 240270, 5148320, 2665048, 7229436, 3232022, 2688833, 8145814, 1476256, 3424206, 4277726, 3987817, 6630944, 5026080, 3101450, 4257662, 1110369, 977866, 6374346, 5525143, 1514789, 3828035, 5916702, 1907561, 6512026, 3837267, 5438338, 4777946, 7591612, 8086497, 875551, 2808449, 370353, 4272757, 4485057, 6803168, 1862133, 7831663, 6729411, 6806573, 8220846, 3806368, 6405154, 6006303, 1604828, 6362775, 7794975, 2416527, 5764266, 6720865, 7075456, 1140974, 1174731, 4308420, 4121550, 7347076, 198931, 3908163, 5041271, 1722121, 6801252, 3971623, 7681206, 2711039, 6060600, 6924609, 6492632, 786746, 4688854, 1386460, 3965926, 7264463, 5730035, 808705, 5408326, 5182188, 1548651, 5772603, 623014, 4678391, 2530847, 4800099, 6679649, 7313425, 2160474, 584417, 3342298, 3042912, 349820, 5146538, 1120439, 2624303, 83274, 3635364, 8290404, 7493296, 5536412, 2241071, 726486, 6642249, 1810047, 6460157, 2219494, 1193399, 8173054, 4819662, 6144152, 2804522, 2090285, 4449822, 2314221, 1085945, 8164908, 7972411, 252911, 2509679, 7904788, 1396504, 4534596, 1817773, 7130296, 953681, 5160085, 5708464, 9234, 2285536, 6596751, 6140245, 6374052, 7884619, 2156770, 4238557, 903126, 1193110, 6817505, 1351105, 7708801, 7135592, 4963558, 2544565, 2980261, 655882, 1328011, 3713801, 5555447, 6261019, 2274001, 2762465, 7214038, 4915228, 1058161, 7654861, 2549948, 6707301, 5157385, 3011314, 3522174, 5856095, 7263357, 5174442, 6689299, 6906020, 1826047, 212026, 7892293, 2741670, 4844882, 10179, 6428001, 4032630, 560575, 7420663, 3412518, 6416819, 6644072, 3885637, 4176132, 3777549, 1017880, 556078, 4281329, 8044808, 8036499, 981370, 4297713, 4511946, 3550342, 920613, 2315223, 6574932, 5211512, 1249973, 3949490, 800545, 7537526, 8117825, 5372524, 4473195, 6653625, 4904300, 4081150, 332691, 6866330, 5380797, 4323948, 2849402, 5738016, 3978837, 6705177, 1086631, 2959454, 3806017, 2390823, 7939129, 7366800, 73678, 2823467, 2219578, 556975, 1455561, 6129142, 6369091, 1535192, 5950588, 1475849, 5334305, 3766570, 3414397, 6054381, 2039782, 5964731, 926337, 2832036, 8365121, 1689074, 285733, 2926636]],
[[3738138, 763645, 7645767, 1997766, 7585129, 5796037, 2787182, 4058367, 8015229, 5565595, 3882391, 7084366, 3775399, 3504647, 66712, 6851599, 5770108, 3980154, 2191635, 4954880, 1214666, 8109610, 2835374, 5961451, 3567275, 1814192, 2004227, 6988545, 7246857, 4951513, 6550317, 3535726, 4350934, 5923044, 6256492, 6494779, 3826120, 6364355, 4357307, 6671945, 5522084, 6207890, 8139211, 5569595, 2508322, 6505650, 2512711, 284668, 7584709, 3304142, 7906955, 5652234, 4259472, 1801236, 495947, 5260134, 6061380, 433147, 4323715, 6917953, 5403232, 5069612, 7421292, 7251318, 2167729, 3668353, 7111019, 6275326, 57163, 6072358, 2939741, 1440392, 6893193, 5757369, 7074276, 6323089, 47789, 6118259, 7361266, 3414795, 8181884, 2460980, 7437212, 1393360, 3947641, 7289315, 5072326, 7266074, 4015977, 6820304, 4516817, 7656483, 3131696, 7222432, 1418720, 1213791, 292009, 4534999, 3540859, 6529441, 668558, 5738483, 4274511, 4608042, 7398542, 6750212, 4891138, 5515885, 2003502, 4241925, 1712409, 1166863, 4345740, 559747, 644229, 5278384, 6030062, 6994255, 7483260, 7668519, 739067, 516687, 7234734, 7843628, 6474112, 5089913, 6896416, 5163628, 2530151, 250255, 3439663, 2646847, 6396016, 6588941, 7418043, 5808705, 4233457, 7489792, 4184431, 5957390, 5709115, 5195522, 1518704, 4984691, 8310991, 6552070, 548811, 2863269, 6039370, 4120544, 7973473, 8058295, 7149611, 1565150, 1189897, 2781605, 2812832, 3104812, 4211668, 3407249, 7479001, 4274701, 3407414, 601245, 2533767, 1541431, 7792808, 4389664, 5406924, 1626965, 4089549, 1711279, 4449867, 4661788, 5141243, 2820020, 2662337, 3210595, 1822991, 1803113, 8119575, 2360211, 6115400, 123549, 5314945, 5430250, 7737803, 243246, 6833208, 8345919, 5677766, 1947154, 2923400, 7028148, 8233170, 6829912, 1732460, 1310162, 4813822, 1953103, 343586, 5269932, 5615860, 4401625, 7377116, 7706580, 8207628, 2291283, 6237818, 403976, 6454316, 7748902, 6473630, 3035645, 3946174, 6534803, 423599, 5933188, 2807168, 5812921, 2717109, 348061, 2589160, 5914090, 5932696, 550652, 4437666, 505977, 3447475, 880430, 2148810, 7319890, 4336472, 32618, 6996365, 762065, 644040, 6342019, 3121916, 8003553, 3096151, 3791855, 3003766, 8020176, 2944703, 8060735, 745653, 4129274, 7741709, 2389009, 5771322, 5829258, 6808603, 3641885, 7202891, 4791571],
[114065, 6246542, 2886221, 3670967, 5280732, 6632102, 1196119, 1032280, 4551989, 4149476, 1968925, 3348514, 7014795, 986849, 6237572, 4324883, 4073710, 6273104, 1074136, 866145, 3569676, 7357687, 3895925, 3803014, 2877118, 7916681, 321891, 3300885, 6082113, 1696059, 3592106, 6708192, 2469151, 4380593, 2500293, 2135876, 7702633, 4802352, 2798711, 7887244, 393736, 7732939, 3463248, 6321323, 6527941, 2124554, 5570464, 1602665, 1575471, 1650022, 4829838, 4054534, 4863757, 289752, 6610370, 2970512, 2959757, 6607289, 8237086, 1625913, 8239705, 1473831, 5171338, 3361000, 5114471, 4497351, 5815756, 7788498, 7517516, 413572, 4205074, 4960129, 2143884, 753828, 7198193, 1612757, 4925114, 472564, 6820282, 2783707, 3029089, 826781, 6873793, 1442383, 8101320, 5416551, 6441481, 2843356, 8364515, 8066042, 4594990, 1490274, 7793694, 4671455, 7357126, 8322324, 4041580, 1453251, 3376934, 903667, 1416013, 4074084, 7797876, 2321151, 7486968, 1940916, 1787527, 8375134, 4007395, 7505576, 1190255, 7816391, 1191893, 7784808, 4911339, 4106761, 6846508, 7842873, 7768217, 3942795, 3281766, 4873784, 4327222, 5263924, 7266856, 5421894, 5252575, 3669447, 5233253, 7617365, 3974678, 5539819, 7593323, 4677242, 4584643, 4334284, 4823444, 2592903, 7918368, 962735, 291018, 1969632, 7124828, 8095930, 6376147, 3164915, 5051597, 4238930, 7603519, 528437, 4960611, 4799375, 5278206, 2596389, 788558, 6098640, 2287251, 266024, 6359624, 3491156, 5067559, 1744306, 3373330, 5760485, 4198627, 3023406, 2774448, 3489338, 4258818, 1825699, 4393870, 6344312, 4022357, 6505584, 6038267, 1986641, 6074865, 4381131, 7794437, 7214049, 7525340, 5899746, 6195921, 4106463, 5111883, 2734273, 1933500, 568268, 132917, 3398585, 3305882, 5414699, 38219, 5526774, 3442953, 7261371, 7622444, 361498, 6267039, 5922660, 7728632, 1337556, 5973126, 2369856, 7649717, 7963924, 4380624, 7329875, 8233857, 6671906, 3747317, 6949035, 3244650, 3741505, 7703038, 6140513, 7789494, 723805, 3823695, 1218477, 853145, 6815464, 1951662, 1633168, 2000875, 5602631, 1821676, 4159657, 2753056, 4645782, 2692374, 3588104, 3624145, 4549284, 6131873, 6241172, 7720329, 6260051, 7643964, 4926049, 5187032, 944728, 971906, 5485429, 7968202, 3594155, 4278368, 2045923, 5298324, 218171, 5445922, 4135741, 7337105, 1918378, 8074571, 3303054],
[8051140, 3063488, 1777148, 3074988, 600192, 2998849, 7574065, 2536382, 8261201, 7458049, 7622427, 7309785, 6615147, 2191608, 1933387, 4452574, 131770, 6236847, 7699593, 5183216, 400620, 6194811, 5277337, 4549230, 4358084, 421975, 4572030, 3314740, 2927130, 6783471, 2722614, 1705449, 3436661, 4692686, 4740453, 4256132, 6692398, 1138780, 7016969, 6154818, 4498493, 3139481, 4131806, 3585792, 4319033, 6258215, 793309, 1223526, 744962, 5735472, 7223573, 2227068, 2635144, 11547, 4073333, 7179416, 6882911, 2288061, 2648146, 3396909, 2072397, 7467102, 3247621, 5404842, 3826496, 581510, 2721551, 762537, 3223624, 6487973, 8376293, 5767273, 1046934, 1835264, 6991913, 2998906, 7140297, 5843023, 4434623, 3744291, 4377514, 8200841, 3810344, 343873, 3241798, 4170273, 7725037, 7378396, 2748616, 4887019, 5729921, 97063, 4504987, 7607515, 4125379, 4256304, 6602017, 7703296, 7017309, 8274706, 649693, 3243364, 2793602, 2266427, 5110955, 5038697, 6451321, 2474210, 3360624, 1778141, 1069370, 2173120, 3258187, 8264498, 5943250, 7269428, 5575079, 7607203, 4998587, 4599935, 2862564, 7721940, 3774273, 4148699, 6498182, 5255214, 5319792, 6970847, 6527934, 7892497, 718511, 7071694, 7652356, 7212992, 6979264, 2073366, 2446321, 3638166, 4521535, 4194212, 7603856, 2641963, 6479831, 2271266, 4926918, 1300411, 4931715, 2938798, 5288392, 7742280, 6379382, 476754, 3669283, 3634978, 4463157, 7568660, 1245988, 4120907, 2334708, 5523996, 3430583, 4748919, 5520426, 5586466, 3310254, 6037035, 6980580, 5648396, 3412475, 7553569, 1134746, 3194278, 4008235, 7005529, 4382648, 2229702, 4832345, 6965645, 7151063, 3715372, 5398122, 4129271, 8294187, 5759952, 5985685, 2898302, 3432791, 6894701, 7793793, 2937963, 2748184, 6955670, 616472, 7628592, 3022213, 2103610, 4100573, 2261354, 4161746, 3893109, 6112480, 6491302, 3268934, 3245150, 609699, 5170802, 6168376, 7115404, 296407, 3050398, 6357168, 212949, 7642885, 2105316, 8102278, 8237237, 4481859, 6320713, 5293278, 4072925, 4091680, 2313799, 6123181, 3153477, 8217599, 3690532, 1129087, 1063209, 4182484, 2576150, 1524725, 4352432, 3438812, 7765782, 2249896, 4432984, 633967, 5402405, 8003867, 2382422, 6372362, 1933380, 4310167, 4480609, 3245177, 2860030, 4926348, 2366948, 7916974, 1562421, 1841930, 6673944, 401315, 6418994, 290594, 8070741],
[6567201, 4801411, 6261153, 4839058, 6079347, 8060730, 4944077, 7741807, 1125460, 6839567, 8100720, 8152952, 6283324, 3521255, 5623660, 1004288, 7749396, 6097191, 2725133, 2643395, 4238523, 3012124, 3844422, 5701859, 58458, 2661932, 5831016, 6372070, 2723433, 1324729, 5419547, 7935907, 3422202, 3943536, 4183506, 3867510, 8007046, 556719, 2699749, 1820463, 4687964, 5036446, 1672014, 7376223, 2007377, 5345035, 3192683, 2491702, 3904182, 7130809, 4106560, 4878309, 5885089, 545484, 8168079, 2903833, 361772, 173154, 7860145, 1907567, 554571, 6564193, 6384805, 3588490, 7703455, 688935, 748668, 4854187, 4174192, 4954209, 7618948, 3831502, 4760106, 1535370, 4764863, 4070847, 2175391, 1455070, 5772591, 5748897, 4677710, 2508333, 6857323, 6080141, 274956, 3345677, 4179601, 8195736, 2217472, 68896, 7720014, 2785883, 7259099, 7394889, 5356197, 8083127, 3484776, 2317639, 3921048, 3950923, 1139050, 8093164, 2872947, 5208059, 7821873, 3410006, 7379602, 1767702, 8364750, 2273399, 7503140, 6996265, 4002549, 1883981, 1389455, 5404804, 4779958, 1880326, 6157684, 4732061, 2245500, 2898135, 4120150, 1834833, 7349790, 6287947, 984464, 6043170, 2589276, 7180968, 170526, 666011, 935163, 4188400, 2741774, 1459371, 1855913, 4775333, 5037771, 7851195, 8032073, 2820517, 7451737, 1352211, 1287881, 7692642, 5092425, 7170805, 4024478, 3817283, 3317659, 7276484, 2519427, 5240595, 20400, 5432969, 1498021, 205081, 7806521, 4046612, 2884425, 4415502, 3304429, 8334797, 6023207, 1966858, 7882905, 2385647, 7105759, 4339091, 747894, 8247688, 3875369, 6926614, 474903, 5012736, 4887648, 7703360, 6409889, 3611214, 733355, 1268647, 5145501, 5741137, 3508795, 5428402, 7983428, 3165354, 3115466, 179817, 4097204, 3869460, 5316436, 3813784, 2735262, 5374011, 987500, 6593252, 7908823, 2505242, 2455123, 7746216, 5046493, 6347076, 5744157, 4002028, 7228607, 3561325, 523644, 3574645, 3027315, 552063, 5199505, 6779222, 6007256, 2184898, 3314796, 3149110, 3620194, 3711226, 5992850, 3799939, 4841803, 1328515, 4490254, 6470526, 1141096, 2596280, 6294285, 6503127, 4632979, 6337868, 5985080, 6762032, 6195504, 7231176, 4284860, 1998855, 1624470, 691712, 7543441, 1174363, 6136357, 5045021, 2713997, 8316761, 7292452, 4158814, 3020972, 3089997, 520082, 828659, 6370759, 8056821, 558210, 3557361],
[3346451, 2733440, 2513636, 5934841, 530835, 5040354, 6075253, 7765896, 1084896, 3674313, 5142814, 8369461, 7404264, 4702357, 7770367, 8133137, 2969050, 7387720, 143289, 2006448, 5137146, 7838645, 3968795, 5682810, 4250081, 4992163, 5933619, 8128534, 2379825, 4163649, 6050981, 5793528, 704545, 263011, 2960625, 7447161, 5424304, 5053717, 338422, 3126684, 6630993, 6958919, 2821662, 2135812, 6386798, 526619, 45393, 417005, 8261214, 2616572, 7150773, 119778, 2950618, 3831915, 5241111, 7274643, 898952, 6457563, 3699096, 1324304, 3776067, 8304973, 3545004, 3691388, 4712345, 6102559, 4100002, 6943502, 1362733, 8148730, 1165336, 2402399, 4437949, 5310832, 5195131, 7185250, 3625627, 5085497, 3579991, 2102547, 6828769, 8321889, 7388420, 4263820, 1543847, 2678869, 5642032, 68448, 5662032, 1393570, 7747763, 5015146, 8007064, 4355820, 4215729, 6657476, 5463456, 8107195, 850073, 3844932, 7947378, 2381686, 1796318, 5381348, 72063, 2469408, 3655645, 5640337, 306803, 1773691, 2197481, 2436365, 340894, 4503663, 6975548, 7359288, 6491799, 6628785, 7418281, 1530720, 3831786, 1724780, 3153222, 5645483, 7315731, 2210079, 2836882, 2480926, 4892474, 6789374, 1570926, 2247975, 2008501, 1046819, 7578597, 5813907, 994139, 7373314, 202298, 3921049, 7435793, 6613992, 3772486, 2729992, 3711359, 7828309, 1303379, 6780255, 3903279, 3298256, 4503440, 6764755, 4939607, 6317822, 6857604, 2553301, 7582281, 3568855, 7379506, 3912786, 2545263, 1779329, 5967901, 6227022, 5779265, 7534498, 3354517, 4681031, 6015976, 916540, 5767059, 7229460, 5525125, 6831440, 4986302, 2141869, 5920195, 3423325, 7067616, 8339472, 2484779, 3457826, 3618920, 8331028, 3569103, 7258085, 1163999, 6478726, 3719181, 871024, 7710644, 7625131, 3411550, 7046028, 6900129, 4999115, 1555891, 138753, 2027583, 1586058, 3083301, 1137769, 6516740, 5184777, 7808076, 5816845, 2358726, 7303180, 6328150, 576299, 6860216, 7887588, 7414874, 6019409, 1934235, 4690682, 5630582, 3686713, 7870315, 4219014, 4462127, 2962036, 3894867, 6100835, 6997508, 2237891, 2228672, 8378529, 4359467, 8029496, 7027042, 8151875, 7695969, 6661854, 41191, 2018282, 8182243, 7390051, 2804348, 2779065, 751047, 7532507, 2555291, 5126788, 3548454, 6238161, 6201602, 2442666, 7856417, 1812876, 5854465, 2779579, 5132733, 2763704, 501283, 4605035]]]
s1Hat: [[2499317, 1795259, 4800980, 869430, 521202, 2485579, 6071362, 6893228, 5482588, 4624568, 7180362, 1042863, 4704703, 5961819, 3878803, 1464267, 5349558, 125687, 1911866, 4959252, 6586021, 2789240, 5672943, 2562685, 3301923, 5245791, 3281478, 4876663, 7560914, 6846013, 5814281, 2873811, 2836529, 5104012, 4153621, 7766640, 2329649, 4447214, 7186740, 5909473, 3012478, 5201314, 2536809, 5094038, 4886166, 255364, 5813136, 6513945, 5249622, 6832201, 3852181, 1337700, 56921, 7405816, 4004806, 4503705, 3961845, 2970737, 3208991, 5161320, 6039814, 4982733, 8068997, 3110511, 4696081, 7546144, 8058120, 2376964, 18807, 3353850, 5647725, 6125614, 3829972, 1707112, 5566655, 4606649, 7610912, 3624329, 3666151, 1816760, 7365954, 3138467, 3627495, 1904802, 4077804, 1246870, 4707885, 7050957, 2348360, 892896, 6692625, 6593299, 5890947, 3690999, 439172, 1903112, 2112324, 437167, 5841490, 6341646, 250122, 2479284, 1532667, 1513791, 5697986, 6795323, 2466295, 2173840, 2881886, 5268264, 996653, 7376568, 6236322, 979786, 216770, 8087598, 3023587, 6248177, 450772, 7155218, 1700825, 2771430, 7382363, 7601624, 7601532, 5079850, 8241489, 6406334, 5909888, 4755139, 3588220, 8061308, 256344, 1158999, 8016107, 4478765, 733955, 5800847, 3285, 5491638, 3013839, 5944015, 5115729, 1121305, 4239374, 7936183, 5748161, 5758104, 7874012, 532783, 4668698, 533622, 3018336, 996369, 7873561, 2755532, 3594125, 6351864, 2831338, 6673409, 2337032, 3842692, 166620, 3066927, 5276706, 5492054, 6344323, 1289575, 8171484, 7093920, 3682812, 1822905, 3039183, 3855049, 1770740, 1493816, 2923344, 6157697, 4020314, 3806934, 8031275, 2873980, 5715708, 6292382, 4659042, 794757, 480131, 7247601, 7018713, 1064798, 3596127, 4530816, 3631153, 1020033, 2279949, 6404559, 5739349, 4203650, 6642603, 4429043, 5903089, 592672, 4357901, 3020178, 687323, 5127407, 625770, 5062114, 1351148, 7301194, 7559720, 2629945, 4502206, 3307209, 2112358, 6727192, 774171, 7566672, 859795, 2196300, 2059420, 100532, 763073, 6458377, 6368686, 3388729, 504051, 5473018, 7588962, 4976083, 7102547, 2159122, 807104, 1650415, 747698, 4936520, 4128700, 778229, 316121, 8159159, 2493094, 4404023, 184401, 2703402, 6234733, 3911324, 1134659, 4517577, 3561981, 1173750, 842181, 3548586, 6603552, 3224308, 1014501, 8362727],
[2379854, 6041593, 4102404, 3336186, 748390, 2744743, 5663207, 2128166, 8271852, 4550614, 6234160, 1847437, 5654729, 1744925, 1611310, 2002109, 6706628, 7877036, 8099159, 5595873, 1458176, 3763567, 5257320, 4613025, 1620503, 4045832, 4654547, 5843988, 161498, 1383498, 22784, 894335, 6691247, 8018554, 4030574, 1580416, 877654, 414157, 2268099, 5111387, 7999790, 3115400, 3173574, 861109, 4296754, 4206607, 7357709, 1318292, 1818823, 8237739, 533254, 6464491, 457166, 4669446, 68488, 6094033, 2023251, 4473214, 2920903, 433313, 1192534, 1678030, 4030753, 6983974, 1252438, 8165669, 478596, 3141768, 3037197, 6511582, 3864498, 3549256, 3773317, 3378469, 3928915, 6965296, 8379232, 1250335, 5477073, 1779140, 450628, 6359178, 5966209, 4033813, 1862142, 4610037, 4965188, 4199603, 8044885, 171528, 6424235, 5415578, 2091309, 1663691, 2342520, 3543799, 5818336, 7320640, 2638950, 1066189, 4778634, 8327997, 6594521, 2892385, 6569448, 8070309, 2100392, 220559, 6741328, 233657, 1376902, 2322014, 6204011, 6245602, 7398943, 3266657, 7421220, 6884863, 7093511, 2193024, 1948774, 3900796, 949272, 7172278, 2565999, 577217, 2747172, 3968106, 5554287, 6200681, 1222560, 5474201, 3289023, 6710851, 3690610, 2815315, 678846, 2313075, 1002268, 3098223, 6055798, 4784288, 3382091, 4766285, 1151589, 3940849, 2798410, 523666, 1306475, 3601697, 3619357, 5278495, 909354, 7780751, 2213132, 563341, 7288574, 2669395, 7986885, 1779475, 1465021, 4796946, 8265051, 6012186, 5092355, 5776451, 2819681, 3184873, 3829422, 1160989, 1861002, 16005, 6253324, 5279702, 2523364, 2047878, 1850929, 3438433, 3582509, 8007045, 7302057, 3441471, 5555231, 6528229, 6848948, 7877425, 3137167, 2243845, 548859, 5450611, 3641746, 3540469, 6025558, 6078671, 5186874, 4073755, 5740501, 4221206, 3801206, 940870, 3933451, 94306, 8002498, 2685670, 4993584, 5601642, 8350466, 3434558, 5222137, 6301215, 6144389, 927490, 304221, 2705345, 2764164, 5461827, 4961806, 509923, 3372141, 7135750, 2861840, 6222640, 6690758, 2610562, 479212, 1187011, 7304848, 4201165, 3332027, 4736157, 7688755, 6502048, 2708108, 2868784, 87571, 491298, 6348483, 5397539, 3290008, 3556374, 3512850, 5110262, 5809579, 4807149, 4670533, 7904502, 5460412, 8213669, 6507408, 4762901, 473103, 2392156, 5447729, 2667316, 7154735, 3000842],
[6349296, 6112582, 1734815, 1227186, 2003385, 1242596, 1101137, 6399070, 6957717, 1642627, 4892050, 3630307, 395737, 4027591, 4190884, 6310909, 5003944, 3949568, 1390219, 6128796, 4035941, 6561136, 2815808, 4290631, 6788139, 5305542, 2815103, 1425933, 1886367, 4249111, 5334874, 3003057, 6531276, 710563, 7871775, 3100442, 4413052, 8260360, 6468435, 1263959, 3796215, 923752, 7848772, 394311, 2719155, 3495480, 815819, 609250, 105839, 3426950, 4031928, 7282093, 1705440, 6762835, 2343609, 7684277, 636745, 3956282, 309989, 432980, 5587366, 7146766, 7096228, 6315222, 5369645, 7949523, 7958654, 4481475, 7135461, 5880522, 4458049, 2049329, 2398744, 1460667, 1651251, 7684145, 5411052, 627727, 2151041, 3365857, 4111095, 7613985, 6667212, 2687444, 3502968, 1310438, 2522894, 2337, 6032782, 7388343, 3437508, 5301387, 3020918, 6772298, 4405529, 1037684, 5355194, 5005615, 1393473, 7931028, 5981268, 6547137, 2013445, 6252648, 5997165, 6157891, 4104953, 4383323, 2627753, 744767, 1249514, 535699, 4926652, 7455887, 4132403, 2192215, 4174967, 4984539, 7204947, 7418832, 5630263, 178157, 206165, 5508309, 8276270, 2745384, 4411396, 8118446, 2649468, 7403526, 5491388, 3986329, 3521700, 2246803, 85393, 1279136, 2264366, 8064206, 6954323, 8063214, 1951292, 798097, 6826957, 6859012, 7433372, 1852525, 1391138, 1836879, 5106524, 5996580, 922887, 5436351, 3042958, 3656972, 367136, 1586846, 4377641, 4653933, 5604283, 2354514, 8110366, 6340960, 6174554, 8175794, 818650, 1791133, 5994765, 6542070, 3606413, 1038552, 3561934, 2030477, 3686271, 3797402, 3950179, 5367692, 1112158, 154784, 4496927, 973559, 733650, 7393293, 572839, 7156975, 4760671, 5418515, 7556806, 2007007, 2361174, 5367750, 4164617, 6845557, 3970145, 4364613, 5353011, 2567547, 333373, 3703862, 3915924, 6701381, 5159674, 3003079, 1799843, 7867899, 7752817, 1068394, 2278186, 3235867, 1787870, 8110699, 7762857, 5168041, 5119677, 2626959, 4847331, 7706462, 3444540, 951173, 2936445, 8069792, 2803161, 1850337, 2581475, 7157282, 6375649, 6042017, 4189124, 1924550, 6256620, 6367826, 408931, 2595224, 2876562, 3930579, 3671458, 1747034, 3784099, 5967342, 64864, 1123174, 1695110, 659263, 1294710, 6665312, 625600, 3478455, 687206, 5082876, 3016379, 7445229, 245409, 2523419, 5476789, 5527240, 4947175, 5024727],
[4363745, 2812325, 885232, 7413585, 5145924, 5080865, 3694601, 2091302, 2004338, 275662, 7876289, 7552250, 2477475, 5486858, 8281007, 6775861, 2220956, 5103349, 1729575, 7975334, 4912182, 3346608, 7373639, 8069830, 1218723, 3832441, 923853, 7954358, 8253476, 589791, 774392, 3085997, 3116048, 5233360, 5991045, 1818325, 2436869, 7600424, 4771187, 3950081, 1405748, 3236847, 4984153, 4964243, 7391651, 1505919, 7002442, 8201629, 5150794, 1416392, 5150808, 6013752, 6272945, 216440, 3789560, 8244012, 3208123, 7433430, 2286147, 4502390, 713133, 7883178, 6041397, 5176469, 1621345, 5398173, 3576345, 3253701, 3654581, 7719452, 1010073, 41073, 8145824, 7649499, 1475422, 651793, 539302, 3742700, 7956860, 6659589, 2244802, 5583808, 6098953, 1477195, 4837767, 600774, 3714844, 7926694, 2440096, 7012447, 4679197, 7776053, 3569290, 6745582, 4382797, 826852, 102251, 3731865, 1203922, 678789, 6615793, 6849042, 4821152, 5377986, 2917182, 3239138, 2603740, 6596065, 687874, 7823763, 5304649, 1769099, 491395, 4344863, 3548508, 371936, 2901391, 5842450, 4414012, 2635472, 6652924, 2641414, 5619641, 2321021, 7881947, 4374201, 540069, 1739359, 3297365, 7855301, 108419, 5718129, 7236556, 7879256, 1184308, 8095084, 4284900, 4412881, 4300555, 1628161, 5509820, 4591570, 1146897, 3663040, 7134371, 2321936, 1404024, 6757781, 125647, 5002556, 808542, 1765828, 1357222, 7192593, 222326, 2864273, 2809217, 6689014, 7361713, 1799029, 3686605, 3991337, 6236483, 6141671, 7356092, 1376879, 6924660, 250626, 2414768, 557940, 939073, 5982631, 1380139, 3064350, 658880, 5993262, 6257166, 4281291, 2596369, 5912859, 7311869, 4810822, 5615576, 7790050, 7415807, 1183696, 712907, 1029368, 2512402, 3914639, 5105102, 3497479, 2823791, 6332647, 3260691, 4051304, 6720525, 6445152, 1622534, 7680286, 1669072, 2719574, 2118864, 3939195, 4204579, 7184988, 1615037, 2880554, 1763729, 6982042, 154953, 4451744, 4840785, 3407982, 2124241, 3259613, 4100353, 6704846, 2413235, 501098, 1437064, 7185139, 2508065, 3829647, 2341997, 4147450, 6763225, 2054152, 1648756, 8357070, 3307066, 8290442, 7205153, 3121433, 1004756, 3124824, 1405794, 790057, 5523720, 5706831, 6274551, 3399650, 919808, 4125582, 1576794, 523616, 4445073, 3251671, 4300421, 967284, 2795083, 5372831, 2808743, 3005894, 2827701, 312189],
[7119500, 2742251, 7078689, 976113, 3930636, 5568082, 5778734, 403706, 1742113, 7211512, 2759301, 4499632, 6309005, 3830906, 8370273, 3428549, 1890009, 1171349, 7433909, 7500574, 302820, 2133009, 2744969, 401362, 6107026, 6751658, 3446390, 839841, 6179705, 6568193, 3677904, 3318013, 6205786, 2656937, 5887087, 4532708, 2049682, 29554, 2522821, 6900390, 8312884, 6254921, 989832, 7561197, 5475415, 2341362, 1170009, 1907051, 3272725, 1447039, 1756087, 3447206, 3702536, 2612978, 1690556, 3589999, 6346907, 6088517, 8012514, 7380338, 2287515, 2660501, 3937897, 7574327, 7062533, 5014845, 7424821, 3430314, 521210, 4843683, 5796707, 2610629, 6226510, 3034953, 7338881, 3833258, 2808696, 7017033, 1284099, 2763491, 6163967, 7316035, 5558332, 4563277, 2333607, 4615181, 2654409, 1551302, 30435, 50113, 1653402, 3755880, 5680755, 1364247, 6635458, 7272699, 8118201, 5128680, 802285, 2553088, 5802496, 292556, 1752086, 1094660, 2102089, 8242599, 592916, 5987322, 7070021, 2477434, 3762045, 7392504, 3636095, 3669967, 4766046, 558651, 5553927, 2972317, 3076390, 2613508, 2305945, 1894319, 7454248, 8099551, 2104808, 5020743, 2719096, 2889834, 713936, 7280006, 3602017, 6611346, 7772343, 2911062, 2518367, 618420, 2058499, 7471680, 1829360, 3787086, 7463442, 911726, 2614372, 3537329, 5781867, 378349, 7295132, 8347424, 2519795, 1265686, 870445, 1908375, 5443483, 6005773, 1634803, 5044468, 1671756, 701916, 3651794, 6303419, 5453441, 1861448, 7488088, 7883969, 5772066, 4941255, 7057661, 3984537, 1061386, 8177099, 6538435, 4372562, 2327837, 8069079, 7043438, 2103745, 6271736, 2696943, 4401612, 4455441, 1390731, 3135085, 6189984, 7707856, 8068411, 6486531, 776396, 1800534, 3502402, 7776165, 6505561, 5802205, 4315704, 6138960, 816478, 91615, 4828128, 3947881, 1716179, 2063571, 5962040, 207414, 3212494, 5376152, 6970096, 5855420, 1302778, 6642105, 4210127, 317575, 19513, 6854289, 6629966, 7486098, 6618456, 3298944, 5140371, 1934097, 1601962, 1701286, 4415776, 4896563, 4254020, 1989172, 7557889, 2643847, 4290545, 5161561, 7078367, 1365991, 6988264, 196704, 7252599, 427388, 3562626, 5533061, 4782814, 5305054, 6775289, 3189679, 6206080, 2568655, 2465859, 4005346, 6772850, 3628739, 3579737, 465398, 7937103, 532301, 3025586, 2540198, 4244935, 2985680, 682263, 3816404]]
s2Hat: [[5227188, 8196134, 7938228, 6128519, 7544880, 7734355, 4170169, 4191494, 6104760, 482583, 1223376, 7248944, 5636976, 3691739, 5815638, 380889, 7273457, 8249072, 1258447, 4480737, 3653833, 6607083, 3443966, 2075348, 1856333, 2468622, 7766355, 5824412, 7368459, 4619943, 161873, 3311293, 163775, 8296254, 7146990, 7052922, 2175191, 5767795, 6779110, 831316, 921939, 6041190, 3003390, 6214487, 6903694, 465811, 7630692, 1741209, 6699540, 7904398, 4073420, 5848868, 7522564, 5839311, 4401204, 7246313, 3737833, 7136519, 1379124, 5180393, 7459433, 5651301, 4597959, 5374880, 6761033, 236004, 1738855, 6864262, 1694822, 7677673, 3140568, 7952764, 4224527, 5496877, 2991606, 7314342, 3542706, 2368815, 1333084, 1602396, 3554924, 6991914, 6084398, 6886286, 6069039, 1780279, 7218380, 3250398, 5738770, 5508111, 6043049, 4272298, 6560204, 635797, 2775732, 3495714, 1348969, 4096311, 6411991, 1340585, 5031581, 701039, 6559698, 111270, 4613027, 5687602, 134838, 6250259, 5432759, 7739732, 8042972, 11590, 7075711, 3849565, 4858749, 1750994, 3966822, 2102418, 7308345, 4065141, 7191003, 5427509, 6840080, 3714051, 5705671, 5604789, 3013296, 1236799, 4309865, 4608643, 2244801, 666212, 2438467, 1262588, 3081714, 4094335, 3225383, 4504229, 623584, 1570371, 8215625, 7269790, 8301280, 5453909, 1913553, 370792, 435450, 1333180, 5118797, 7957299, 2094316, 6026008, 1705131, 5221128, 7370631, 2401088, 2077041, 866206, 835709, 6070217, 6818305, 792353, 4058830, 2488828, 7896329, 5759153, 902282, 8147719, 7614535, 5988831, 3579356, 129131, 8035615, 7005292, 7637878, 3340771, 5152929, 6050962, 4368555, 6512013, 4654063, 7571535, 3655776, 6076476, 6291776, 4649690, 3908453, 108921, 2766413, 2184279, 3223231, 3610498, 524549, 2536569, 5728394, 3121267, 8186775, 4835327, 4249365, 3165422, 7273748, 4781304, 615959, 48211, 6475075, 2827769, 6722026, 4281555, 295403, 4463816, 7352198, 7495023, 3783090, 5435406, 3887699, 7507451, 7176804, 3090244, 7272515, 1067798, 3872792, 2996101, 1811524, 8144880, 902149, 3986864, 5380212, 8251180, 8033495, 837815, 2153576, 516780, 7278307, 2677169, 3345689, 8099446, 6146772, 8375824, 7786353, 8253829, 1995661, 7489899, 2171448, 7747413, 7314206, 4571643, 4094113, 6814720, 6482851, 4588681, 6611959, 3244484, 1374742, 3890160, 136213, 7914735],
[1529957, 8373383, 8180333, 3335667, 7490716, 52263, 4946305, 1691137, 67053, 3629948, 2869925, 4697872, 1492533, 4592677, 7883419, 994710, 890373, 112535, 7710890, 4780442, 5907679, 2018475, 1873631, 5530463, 4526777, 7311615, 3875146, 6770369, 2226435, 6659813, 4390884, 2890707, 6782545, 7294514, 8123914, 4695585, 4792386, 604529, 1138486, 2034072, 6493553, 1375247, 4367210, 3666796, 2091346, 5093443, 4214980, 851877, 7301345, 1792589, 7129682, 7268402, 4464707, 5753532, 1310146, 6508591, 1102826, 4880633, 1264523, 2779131, 7226807, 1194588, 4315547, 4125905, 1658049, 3102336, 5135414, 2882912, 3069271, 4384176, 6070558, 8318144, 5071405, 8243061, 3921405, 3837170, 4911430, 1370612, 1706562, 316586, 1141008, 3502884, 1418366, 7702757, 934008, 3270281, 333936, 534618, 7832624, 8032689, 7884647, 3299111, 3153481, 5661661, 5836919, 573287, 5786014, 2418939, 2150812, 6235841, 7563159, 5593619, 1441954, 2869971, 7600741, 3881376, 4125588, 5926050, 7753333, 864485, 1939479, 5336733, 5419245, 2025151, 5490938, 6536126, 7611735, 6552739, 6799682, 4575867, 3315017, 5947900, 7183670, 92968, 6650295, 1932206, 825991, 3766248, 448374, 2661264, 1715067, 414227, 6152404, 1201665, 3387060, 1912259, 6539237, 5290564, 6644062, 708779, 5868967, 7462311, 5493221, 5817903, 1894527, 471991, 4810117, 280710, 7134504, 2400923, 7151878, 3631554, 6164195, 2941806, 6025183, 3521182, 5512130, 6586179, 3810193, 6813840, 1939341, 1243207, 2765604, 1546921, 4754431, 193795, 6507691, 5148358, 259209, 5027096, 5531337, 6540592, 3632852, 6616107, 3120896, 1236907, 5912495, 4888627, 29803, 172620, 5890409, 3594265, 5527886, 3195423, 1120151, 3929580, 781085, 2101727, 3398777, 876186, 7391904, 5185215, 7609414, 2151825, 4465093, 8244245, 2528651, 7746829, 3391816, 5880565, 7104812, 271312, 1816020, 7141340, 4345785, 6461571, 5365421, 7746669, 7945276, 2305358, 634268, 3695920, 7483847, 315699, 4278743, 946056, 2893639, 6062691, 4400568, 5813468, 5934629, 6542883, 4017733, 6845198, 1434184, 7679362, 2493729, 6846302, 268259, 7225745, 1125435, 6471581, 7866643, 3581550, 3534194, 7324725, 2045420, 3385094, 5589430, 7846244, 3209660, 1781774, 7342534, 272495, 517747, 8078721, 2707399, 4403644, 96947, 5898630, 2423779, 8189234, 5700649, 5384131, 1265898, 6337918],
[7845161, 3683011, 4412858, 7596066, 7056705, 2257634, 7398448, 1769649, 3335523, 3939644, 1702266, 2828940, 2208856, 2540533, 6462873, 4306577, 6744592, 5612676, 5314342, 891272, 7587812, 7766337, 7841571, 7008970, 5722716, 745319, 656165, 4403989, 4684511, 304332, 5404659, 745210, 7439433, 7028359, 792631, 4052830, 1175058, 856302, 3804213, 745416, 1563371, 6543465, 3444996, 1057012, 7349463, 1301886, 4302850, 3762058, 5127988, 7358615, 1834852, 3028198, 2364079, 7127446, 5337599, 7820725, 6511933, 8010162, 7858510, 1156518, 906916, 4411576, 1843817, 2723111, 1822036, 654967, 3594533, 1563219, 5701267, 5023689, 4794855, 6019881, 1643795, 4847856, 4442373, 2397980, 4107651, 1792148, 5224051, 4912364, 6660005, 4468636, 5958072, 2525112, 5868716, 5162223, 7244730, 8005230, 7593425, 5138644, 5652431, 8139449, 6940282, 1831607, 4687521, 1721912, 2606570, 2025878, 4191047, 328815, 634661, 3132976, 522137, 8149439, 4804957, 4968832, 5750216, 4521371, 1366526, 7588797, 5689049, 1544126, 1181152, 4314145, 7254689, 7478066, 8092288, 4315289, 5713790, 7587935, 2144640, 693295, 4533299, 4692905, 5292461, 6546365, 5869177, 4011492, 4718399, 1480039, 361680, 350194, 8219746, 2340277, 884062, 3278515, 30292, 7785152, 7010475, 2748868, 3669018, 8064865, 3669436, 5572519, 3792697, 4985402, 6858056, 6907648, 3729425, 224783, 2587977, 4387544, 7938651, 1875811, 1706706, 4292359, 2377559, 7354499, 5272727, 7046177, 3474161, 6726072, 5491120, 3026776, 1276594, 5596322, 89861, 3929654, 7835789, 2323801, 2878959, 5932909, 592918, 5716860, 8103710, 2518618, 4350761, 2807545, 5130168, 1387893, 4401331, 5086658, 3237998, 4044078, 3165456, 1202896, 7363313, 6481111, 6343381, 7002900, 4418330, 7795216, 4886251, 557561, 7473909, 1984748, 7976018, 3459861, 3036546, 5426269, 951899, 5138772, 1916580, 4038166, 861134, 7427872, 5834267, 1194869, 4219517, 1808688, 383359, 474010, 347458, 7863538, 3831810, 7627416, 6807161, 2434727, 7435935, 3038848, 3078250, 1184650, 4551213, 4608976, 6540176, 6206960, 3362462, 4942649, 2733538, 2582344, 121509, 6784762, 7635025, 3621450, 4143848, 3851794, 2763566, 1000144, 6810175, 5096725, 2106281, 2187550, 2507358, 2015740, 5330928, 6107150, 7911260, 4273814, 6819951, 1656491, 7032809, 1527183, 4922038, 1498872, 18571, 2357864],
[3175675, 1571759, 4112062, 2895282, 172355, 7715225, 4530213, 6243862, 29078, 1797132, 6654058, 4657907, 686772, 8287004, 3918555, 3480944, 7862445, 833601, 7662734, 953416, 3433751, 2838576, 4863191, 1274524, 2141465, 1576248, 4373154, 713207, 516442, 616883, 3260766, 114520, 5411773, 3903425, 7371374, 1892975, 6695912, 931270, 4670924, 1510851, 7040102, 3825988, 5369586, 727299, 1777934, 7978741, 4768800, 5815863, 3009603, 5225932, 7490589, 147819, 5664546, 3709020, 7783574, 4439345, 7764912, 6082760, 1046651, 4871319, 7891425, 2226598, 8000738, 4617248, 8305258, 898679, 1686328, 614756, 3981369, 6708331, 4637844, 8333019, 4758255, 6938403, 5467889, 778310, 3888758, 2505372, 3247711, 7747062, 6718652, 3664084, 366339, 3311489, 7015665, 4330464, 6962852, 7800854, 1490169, 2008195, 757553, 4303224, 8310028, 4872378, 4761621, 5340573, 708075, 3671199, 1193976, 1734284, 4903885, 2977634, 5141484, 4041834, 4356331, 7841181, 1351779, 572868, 6348829, 7906999, 2577736, 4420482, 3798607, 7258256, 935204, 3727640, 1977413, 2285432, 5136641, 5050287, 131507, 597593, 4956981, 5043568, 6447701, 210324, 5032854, 1072655, 2500995, 4645090, 1818728, 2298654, 5768773, 4080664, 1229340, 7516764, 5165910, 339895, 6836727, 1387070, 5011731, 8101350, 5006494, 2825372, 4320835, 6385878, 2441802, 7722176, 2846764, 2810130, 1074076, 2164669, 5931055, 7008336, 1157032, 8304552, 216227, 2874981, 6431699, 2737820, 4868746, 1498582, 2014000, 6302622, 3375215, 4920245, 8219340, 7184402, 7340564, 7993595, 6277808, 3815441, 4028574, 6410493, 534909, 2671323, 1133120, 3099408, 7403109, 4328346, 6871701, 1886032, 1743033, 3855183, 4929829, 7470280, 2890327, 1783059, 7470269, 8352204, 254715, 845149, 4186768, 1197392, 8109095, 764969, 6172208, 2526576, 1752136, 7081757, 5240613, 6028746, 2158962, 8043362, 7045484, 7447612, 164476, 6302282, 6922088, 2747495, 2482847, 7862924, 7484793, 3400534, 5030939, 3253748, 7768498, 7588851, 6511080, 8289929, 5782709, 4416241, 7331102, 8341457, 197572, 2764787, 2659314, 5787471, 7601864, 7818168, 7490768, 2010550, 887567, 5123940, 5310659, 4665240, 4899865, 1431857, 3003777, 1872387, 2301589, 416522, 4074528, 8320635, 7773473, 5792858, 804749, 5780622, 1258777, 2009950, 7123275, 4491497, 1072556, 3807313, 1548927, 3868497],
[3099830, 6814088, 588739, 5605532, 2409666, 5731691, 1212247, 4523953, 295554, 6455530, 6507052, 2789259, 8227335, 3680685, 6330435, 3330023, 3765960, 5424381, 5260527, 5549291, 6148041, 7834238, 6864361, 6581748, 6318225, 2186329, 7969809, 2864864, 7696792, 5186985, 5740470, 89938, 1505555, 6270466, 2751594, 656053, 3746873, 1368558, 4334890, 2796081, 8033063, 1414938, 1922892, 1097935, 4347860, 6753500, 6128804, 906232, 1502613, 2430439, 192950, 8306370, 4562165, 8270979, 2674762, 3453157, 3693896, 1831998, 2850248, 406345, 723085, 2778004, 4885213, 7251867, 5763810, 1452703, 8336580, 3342177, 7038939, 661077, 5700477, 2291981, 5082835, 8074557, 3426942, 3071158, 1884756, 3239267, 1521295, 1632494, 2443766, 5565329, 1407425, 3840759, 4555714, 5742910, 3614497, 6404821, 4130027, 4807350, 3280383, 3456080, 2650220, 185317, 1600021, 6613782, 5418821, 2137343, 5384418, 5769396, 5929483, 6903185, 2765344, 996773, 5150927, 819638, 8153019, 6421602, 6716716, 4697850, 346635, 6638824, 4754810, 5542591, 5971936, 354824, 1330503, 3650358, 2831480, 2402995, 5797860, 4813866, 5555322, 6061211, 126130, 2956079, 5225741, 1184639, 6048214, 2515291, 2987416, 7962073, 8242756, 8028289, 3849965, 1913529, 1959976, 7459363, 6958282, 7052325, 5346443, 5954952, 4662122, 7132608, 5414260, 6100279, 4032183, 3397105, 8031618, 1472435, 2509355, 4311848, 4522811, 2023000, 3864119, 7922002, 3758782, 7328567, 5094173, 2902215, 8051360, 7804174, 4711360, 164288, 50830, 7969449, 942867, 5481979, 1700655, 7918672, 3457599, 4085968, 858520, 3057606, 1963953, 5650270, 7355829, 3632843, 5962375, 2417197, 5829999, 3454025, 3903318, 7128875, 7471715, 8258241, 8275054, 3263819, 230724, 4829934, 6182329, 3558532, 2868920, 5390144, 4901467, 6866, 2399183, 3698355, 3386870, 1210399, 5488249, 2818256, 1532791, 6166909, 1743844, 314071, 800666, 4502995, 1872554, 5555334, 4551729, 922692, 1095984, 3579595, 6968999, 4455790, 2832277, 6887810, 1445066, 625105, 1315267, 5993266, 3407820, 651819, 4961247, 5875811, 6417613, 3047501, 8019168, 2337348, 8104900, 4282416, 2067885, 3346873, 1392716, 5225410, 4755348, 7732449, 2426609, 429539, 5347663, 3265495, 5927670, 4515565, 6766405, 2684384, 8124794, 4134012, 4227375, 4129525, 2437864, 99425, 908250, 3842192, 6899851, 6244142],
[5461891, 2165040, 2772851, 8358963, 4454998, 4414892, 1894519, 3049575, 5138620, 5376063, 7807073, 2917980, 1229493, 1246057, 1898158, 741979, 3093340, 3057411, 1266245, 4075299, 5882333, 3508108, 2943050, 8224154, 4290209, 978042, 3028140, 7266497, 1846773, 8321238, 6778775, 5956513, 6860021, 3189414, 7943188, 7770105, 40936, 4715774, 7206195, 5954336, 1963157, 6170248, 7734574, 559076, 6297933, 7747057, 321123, 2798709, 4410958, 7163709, 3151308, 5338961, 6824930, 1722960, 5611226, 5903724, 7970328, 8218772, 1080973, 4410490, 3776853, 2843198, 7958918, 5150323, 7954160, 7623593, 7506859, 7588978, 1812082, 7118595, 6195256, 5789254, 2067044, 2090755, 2948568, 2459255, 3539608, 5634265, 6770154, 3751556, 804126, 511098, 8158251, 5770010, 1079790, 6285424, 2571179, 2345450, 1038341, 7866538, 6511057, 262783, 8036279, 4970092, 697017, 6741974, 6426124, 4188494, 4405547, 7577942, 1124971, 291194, 1509928, 7851076, 3792736, 1096334, 7969303, 5232203, 2894535, 8377802, 3592317, 8254590, 7920781, 920393, 5449847, 40046, 1864654, 4842214, 5323568, 7367614, 7172323, 7143889, 6551924, 8178743, 771242, 7515990, 7526797, 7034325, 1580375, 3182843, 6420773, 4559057, 7303755, 2119440, 2697801, 8091913, 624201, 6975828, 6709697, 2916127, 4109331, 2381316, 4514526, 1532624, 7054672, 7297936, 3064607, 6760638, 1505555, 6608880, 1377293, 1244792, 2495709, 4388789, 3785253, 5676680, 1102651, 6443526, 5041913, 3792647, 7299277, 1294248, 6569763, 2679119, 1312518, 1541749, 5569723, 2566782, 2465795, 1289377, 3820379, 6916779, 5582339, 6355462, 1290517, 475460, 4594379, 2222916, 1766351, 1512525, 1216227, 6619972, 6237491, 6608884, 3538227, 6976397, 7969915, 1665385, 1670505, 3164717, 3637712, 7511352, 1350901, 6460174, 1407286, 2970903, 399941, 682826, 2161217, 3470482, 4073122, 2247201, 7560186, 476456, 768918, 498216, 7289255, 6386660, 3611874, 4650222, 4851550, 274320, 961515, 2847617, 2056524, 8301315, 7735624, 2293322, 2496367, 6707192, 7248300, 2686339, 7263377, 5282958, 1920660, 7161801, 321685, 3742937, 2385259, 5480811, 5943665, 380510, 2135050, 4358217, 1481295, 6751629, 7481820, 5961980, 7694274, 2216073, 837031, 3383190, 5991354, 7539125, 1066883, 8353084, 2409046, 7716285, 3428994, 6302885, 6383632, 3631782, 1343150, 6090903, 2129890, 6452513]]
t0Hat: [[144788, 8221339, 3635367, 6392957, 8097917, 58500, 1015198, 6109618, 3428568, 2306691, 2202273, 3726539, 3534818, 7177558, 7198145, 1437441, 8348522, 5803442, 1891479, 3154328, 4488877, 7070851, 7032272, 4554528, 912833, 4586437, 3065337, 5304808, 3034444, 5902813, 4463609, 2315636, 8162873, 4252834, 2277030, 1560408, 2204225, 2237446, 2376229, 267480, 5769547, 2778585, 5282982, 532912, 1760516, 6580330, 5979389, 4980838, 3779358, 5707355, 1363253, 4635541, 5229771, 2673700, 6418282, 2194351, 8346956, 6637313, 6365030, 3008305, 1363924, 777406, 5421138, 7590173, 644655, 7972466, 2003972, 7215300, 6768904, 2911400, 280140, 6580674, 4085738, 1627581, 3385996, 1728944, 6203652, 2111243, 4610117, 3223729, 3413566, 4674752, 3580959, 4680630, 7009729, 2645299, 5296138, 6216787, 6429026, 7077595, 85303, 8142746, 531777, 4102533, 5597415, 5030522, 466975, 1166425, 1687943, 5011902, 2025343, 4012320, 2419499, 4954401, 5802188, 1935869, 1998030, 2038253, 1333831, 2882727, 6806832, 1365918, 1830820, 2917905, 2144953, 4406583, 1851668, 7661001, 302765, 2862027, 3219835, 5065735, 2742327, 6507653, 6469275, 425567, 4225033, 5610893, 755132, 3129088, 6515113, 3473976, 1266233, 7680948, 2709453, 748540, 2961127, 3136866, 441771, 5389930, 2301871, 1678360, 93881, 2357064, 5386406, 288283, 2153501, 5528664, 6183013, 633388, 266700, 1180185, 4489959, 3621512, 3434583, 336176, 5741174, 6344563, 108352, 6050513, 3598246, 7580682, 820224, 6757350, 3819433, 156523, 8306011, 2996579, 4165062, 829632, 4764402, 704831, 5061867, 459202, 1042690, 7770621, 1653492, 4570532, 213354, 351615, 6953854, 4067030, 4927708, 857271, 8335740, 8053464, 7015414, 288282, 8202687, 4103038, 6880844, 2685231, 4767851, 1707745, 7107822, 6942373, 4892738, 7414765, 587872, 343431, 3607272, 7131629, 6692132, 1527766, 6268252, 6633174, 2198844, 363590, 5539035, 5512194, 701612, 1552477, 5831048, 159615, 1836031, 6586578, 5076740, 2709328, 3016449, 6206603, 3384898, 7775233, 7476523, 5757766, 6778743, 2059617, 1083708, 5569785, 6295999, 6668136, 6121158, 4249024, 7408070, 6347583, 3630563, 6628430, 6927604, 3963283, 7070639, 713350, 1715496, 5201935, 942064, 6170332, 1415480, 85292, 7383698, 5031683, 6080567, 4275012, 7578780, 8063256, 5911122, 8120525, 7050665, 7590449],
[4059942, 3950847, 6162127, 7515512, 7338337, 2854549, 3291766, 3909857, 3291400, 4976426, 5833013, 5471045, 3304570, 4820910, 2125034, 3595928, 6877900, 4685977, 7132438, 6086142, 8318247, 1980335, 2862991, 1375838, 7825946, 1699491, 5421183, 2061015, 131195, 2467589, 2401427, 2438235, 7274277, 2283868, 630870, 1115653, 1754991, 3617819, 486854, 3607658, 1348564, 5792475, 3634882, 3490537, 7115267, 2733861, 4194691, 1438526, 3959966, 2425357, 5828770, 7426165, 326004, 7250749, 1453533, 3919302, 595878, 4997191, 7659298, 5514096, 2755591, 4018786, 5477513, 8138878, 8371060, 1209630, 6549511, 5718084, 985851, 5182995, 8304778, 5058982, 5015224, 2467957, 1199585, 8182715, 3359627, 920478, 1869264, 2865121, 4558061, 601178, 4845680, 5792581, 905306, 4608963, 3314171, 1163806, 8115005, 1754524, 1547528, 2562450, 6811052, 793817, 464749, 8228330, 833292, 8301930, 3196919, 7603973, 569916, 6453979, 7703274, 5731199, 5049608, 2024583, 3302260, 7457108, 2088418, 2838176, 7834322, 3773420, 2747332, 179209, 3947078, 4857233, 1319207, 8213869, 1387417, 361140, 6674967, 5539964, 6325827, 959123, 367444, 4051216, 6665072, 498660, 7013214, 7758201, 6882027, 4407909, 5041344, 1421058, 3160325, 572842, 6748975, 3118787, 2760656, 1592498, 6621196, 7959017, 6105311, 1831029, 5362524, 3338455, 196112, 2427818, 4254964, 2109670, 3399467, 4330510, 551432, 3555154, 125669, 8376905, 4642351, 6907683, 6311551, 5144004, 6545639, 3128982, 2517863, 5477364, 1164406, 4088323, 2588493, 7227667, 5785230, 5800120, 6084928, 1184363, 3461606, 150710, 688626, 7152141, 3763413, 2697791, 3610593, 6496675, 6395850, 2917431, 1396728, 4233930, 7231195, 5047136, 7863516, 7851479, 3914555, 7863681, 4221473, 2372575, 737811, 3515881, 4569288, 500859, 3915882, 2325753, 189064, 7061470, 6014684, 1367216, 6811939, 5606008, 6970295, 452070, 6028626, 1022464, 8333135, 2580494, 2695227, 115365, 1558770, 6641895, 2959869, 1458862, 7348647, 1462335, 6990944, 5347935, 1263265, 198647, 6832993, 5694220, 3932951, 7635539, 2321375, 3119071, 1146818, 1271796, 7453657, 1552548, 4979482, 6879313, 8299313, 1698625, 2549009, 4944908, 5298919, 909675, 1844161, 934055, 7047637, 280216, 2637037, 5552340, 1708430, 3508873, 3414500, 603389, 377268, 7441647, 1834147, 6010895, 1246801, 505161],
[6334957, 7219104, 4183977, 5357028, 2775572, 6613045, 5995856, 727098, 5899235, 7309716, 5657994, 105394, 6763807, 5169981, 2266768, 818511, 813323, 7449575, 4949544, 2526679, 717587, 7725244, 6642750, 6843059, 7051109, 8376491, 2176880, 1402457, 7833907, 4275860, 1969775, 2719521, 3739151, 4563498, 8214421, 5539720, 908678, 1609537, 1211222, 2726927, 6995881, 3971268, 7130512, 7839671, 4258476, 7153669, 1753101, 2055394, 5195730, 7446830, 2945677, 8000719, 7888567, 87415, 1655980, 4921588, 663953, 5473602, 2999935, 2747701, 8204466, 3150194, 7942905, 6384145, 8237061, 443637, 964917, 3986799, 1142016, 3790195, 2769947, 8078434, 7379762, 4653343, 8192792, 2006650, 6388717, 2954313, 3050532, 3654643, 2884747, 5077756, 4972605, 4632366, 5827590, 8202506, 6349771, 3704421, 2534287, 1243178, 7210560, 2840642, 4555673, 7077559, 198273, 2345885, 910172, 469454, 7104165, 1090759, 3455757, 2686352, 3359937, 3770021, 2748066, 4285067, 8098068, 2464351, 7874524, 1100432, 4759256, 6558012, 7562524, 4184839, 7317856, 1630381, 3406918, 2708585, 1667934, 396911, 4515547, 5418029, 4231722, 7667456, 6397061, 287016, 2967894, 1632214, 7425981, 3540777, 2305497, 110318, 6936238, 2443175, 7420172, 2229503, 7370948, 8358202, 459764, 4033137, 7468211, 5759849, 647329, 2158719, 1548604, 3486701, 4240045, 1452530, 5465334, 6220700, 6949201, 8089880, 6784411, 2774812, 2581050, 4497113, 696274, 6805746, 593410, 6616569, 251563, 3976625, 7932341, 7805846, 4067521, 745823, 1186734, 225634, 7436721, 3729038, 3808013, 7294606, 5708952, 1232113, 7140685, 2283451, 7082953, 6778182, 240455, 1881448, 249353, 6246273, 2424902, 6370889, 3110529, 1878450, 715981, 835035, 1486712, 3656617, 2142266, 1274053, 7297572, 3299074, 3228942, 4564360, 488653, 3702914, 1386499, 834836, 6053879, 2633268, 2169257, 3768168, 7676540, 2569456, 5875939, 8005791, 4003507, 813984, 3727570, 2622322, 173733, 4710636, 7520013, 6806416, 2799431, 6123368, 3755091, 4945418, 3729225, 6779583, 3519373, 2807123, 1048091, 6090994, 544485, 3358218, 6365703, 439375, 8069688, 4783879, 832376, 6049947, 8051380, 1611544, 7274069, 1132136, 4265542, 6022512, 5970163, 7732672, 2766222, 7942423, 3588554, 7114007, 537724, 1519759, 6987047, 403964, 8090920, 6589492, 2015695, 6794086, 4867618, 5163768],
[4943662, 2075083, 4328044, 4778930, 1567165, 7377916, 674011, 6078949, 4360103, 6645200, 7186689, 251935, 1470885, 1755247, 7234625, 2131833, 8241176, 6935658, 5589259, 923283, 8232353, 3396697, 1281836, 3377654, 1401117, 7720604, 69554, 6800091, 221630, 2095525, 7990484, 7115256, 2062416, 2509807, 8376939, 3138137, 8105883, 1126016, 126407, 6026585, 5038087, 1083643, 5511979, 5105691, 555036, 5458127, 7737726, 7003597, 5665697, 976337, 4772860, 27710, 791450, 4134745, 6409940, 6739383, 6176144, 1933093, 7564879, 4506230, 1442504, 3715522, 5180031, 4523771, 8047664, 1149005, 395344, 4372633, 1303755, 4886859, 5182447, 8342151, 3109557, 3698646, 7814095, 588948, 1614266, 3701749, 5346388, 415076, 1355180, 8265382, 1519627, 1131909, 4533228, 2986263, 3462201, 4335590, 2627208, 6735851, 8096210, 4570933, 6975828, 2921506, 1419126, 1569601, 2035044, 7483741, 1422990, 7101943, 5671902, 650053, 7523327, 2989818, 8085977, 1072866, 828869, 5349124, 7199677, 5610840, 7382470, 8274305, 5739300, 4831205, 6674946, 3172221, 6941721, 4090819, 7085995, 6788789, 6959676, 1266514, 4880610, 6519284, 2497064, 4069039, 57506, 424120, 2034627, 4721508, 3276253, 3333602, 1295970, 5326519, 5383215, 7844622, 2648763, 6123135, 7171575, 4333651, 5757909, 1695896, 4631190, 5323298, 1089598, 4444641, 1648454, 582379, 2187024, 5982511, 8081838, 5692872, 4155401, 1153155, 1891999, 2479480, 2447434, 6984201, 7020569, 5040173, 3498307, 4668123, 7955317, 1858422, 2242877, 4330036, 5598451, 619134, 4194558, 3457163, 7049150, 4126446, 2596861, 6739035, 6275499, 2246045, 5434687, 5082014, 1753108, 6662440, 3466016, 4046906, 8146228, 2381127, 3623159, 7294889, 3781551, 1131898, 1610141, 2451591, 8331127, 6830276, 5333359, 2912569, 1230990, 8211398, 7876720, 7989320, 7958421, 1217440, 6432883, 3610760, 3204817, 3543539, 2578529, 191116, 64162, 6819133, 4472850, 6456173, 5513519, 2607742, 1282957, 4270727, 5256677, 6925350, 190895, 8285930, 3443522, 4536021, 3176666, 5187269, 6461517, 2800942, 72766, 3340213, 3139813, 8315942, 4430567, 3773230, 642236, 7745444, 7771796, 4768529, 4077431, 4828125, 4407086, 6640068, 6794814, 2866283, 5088592, 6638268, 3019323, 7428823, 6818844, 3319139, 5112533, 7681728, 6167691, 2755139, 980196, 5025564, 912377, 469314, 4863994, 5149739],
[3492587, 3434810, 5096509, 1590334, 3517835, 355808, 1116128, 7788352, 6606156, 2528461, 1068520, 4221610, 1123249, 1677736, 5237078, 5139998, 3005667, 3045252, 2466892, 5083666, 6877238, 6432592, 3747700, 4339077, 236033, 3892287, 3451079, 978072, 3735139, 1926212, 7376597, 4888305, 6535037, 7722734, 5365667, 2879236, 4492930, 5591887, 3455302, 5876222, 5388001, 7269463, 3623475, 8266599, 4757887, 1426159, 5760484, 2668807, 8357905, 2609862, 4476220, 392667, 1223367, 3246401, 4461290, 174539, 4444834, 1938957, 1676196, 739664, 1422086, 1060154, 3290663, 1610786, 716341, 4798154, 5782520, 4636996, 1287807, 5798376, 1107742, 7389726, 2533621, 3675871, 1209088, 2928601, 1209488, 8267215, 6774659, 1870572, 7440298, 5417360, 6444943, 8054302, 1811037, 6976067, 8107107, 4185268, 7236733, 4159763, 4901497, 3450727, 5259935, 2251815, 2769807, 1249726, 3592364, 5293425, 142743, 3268866, 7954621, 890564, 7719278, 5449748, 4453862, 6355695, 8023023, 4724279, 4602066, 2662088, 3913877, 2647997, 3375067, 8286636, 327925, 3541517, 6410166, 1310960, 1414438, 3946606, 2233366, 6451924, 2281764, 3112229, 6771541, 6682234, 1852451, 5051240, 2507331, 4832135, 185259, 1011391, 6108667, 7220979, 5309646, 1893298, 23575, 2431644, 4225630, 7975982, 5831263, 3390478, 4291858, 1970821, 6705703, 1470020, 1271442, 3077013, 2923557, 6554078, 1524224, 5907516, 2757583, 7687937, 1731402, 2475920, 6836218, 5028399, 598519, 2464010, 7024629, 1231523, 727324, 3237579, 7650488, 308034, 4013088, 489219, 1002104, 6657016, 331289, 1007860, 6944278, 1068362, 71503, 1163413, 2415383, 178345, 5252245, 870744, 7593142, 2548158, 1781397, 4647937, 6873620, 3839623, 2990355, 996025, 5598024, 4689691, 3437572, 570736, 744469, 3234271, 4130001, 7764000, 3000672, 7414480, 1830553, 6279749, 6641042, 3839894, 4871149, 4665947, 5221856, 3126192, 8317005, 4481011, 5126373, 7203116, 5289698, 8149367, 205394, 7225484, 7277121, 1941395, 7146290, 981406, 4533184, 6396231, 159141, 7867938, 6433659, 5056865, 2425350, 8118428, 5038407, 2510313, 7578144, 929563, 7179666, 289833, 255980, 1957272, 5451452, 8136206, 4858880, 6375154, 533336, 4366274, 2035809, 5527408, 2324594, 1262669, 7779552, 5989519, 3332743, 6517535, 1622396, 2150680, 481132, 7683911, 1413725, 8339128, 877864, 7489539],
[5304873, 4632900, 2299246, 3405659, 7320134, 6805607, 466102, 3416434, 637094, 4925133, 1792465, 4583252, 3576770, 6090238, 6039997, 6820178, 5244509, 2569427, 6855268, 4675498, 2869787, 3405120, 8069147, 2988548, 2292857, 341277, 3480605, 7057299, 2297402, 2600184, 1965412, 3221495, 1592844, 6018160, 4573560, 7568869, 8269147, 7588831, 2123918, 7845098, 2552619, 4083901, 3807141, 5479612, 5819874, 7635398, 1088659, 526719, 1808886, 7186299, 3174161, 6919114, 1805044, 3798000, 6102057, 6785483, 6834855, 7318267, 2620122, 7932309, 5489847, 1153618, 2228819, 1172324, 3217243, 2379154, 922109, 954867, 6684237, 2349774, 3564187, 2109242, 2708038, 5219681, 7285586, 6272451, 2142888, 1742923, 4530044, 6734652, 5654207, 5328747, 788112, 5060062, 6137433, 448114, 1691492, 7854578, 4066717, 2244499, 6051572, 4197248, 390761, 4958463, 1086206, 5351554, 3262351, 6675036, 2090202, 4864040, 5867914, 4557962, 4376621, 7587079, 5411109, 2181817, 3397771, 7847432, 4223933, 3789154, 7323366, 7519365, 5941166, 744704, 956953, 4691335, 4098343, 4453794, 7104156, 4005597, 7182128, 2322251, 3477547, 3862896, 2688330, 24065, 2353014, 675525, 5199110, 5535515, 4878658, 437597, 1716118, 3281681, 5582870, 4090382, 6753597, 2923839, 5973502, 5159054, 4197937, 5119801, 1984329, 7236853, 1012436, 4228339, 8025256, 4502354, 2517673, 3219636, 5886237, 5916180, 6029970, 1813508, 4554602, 5419717, 4165194, 4300945, 4679217, 4028006, 5963979, 1376037, 8212231, 6424160, 2836729, 1113678, 4065422, 7814388, 944827, 5602718, 2547118, 5772901, 7533755, 323036, 4442824, 2301597, 7644398, 6417045, 2132060, 5321551, 4234937, 6906554, 1635864, 7388064, 5097572, 7094150, 538568, 7347475, 1729328, 5868808, 6543302, 8010900, 6496537, 5603516, 8306973, 3486371, 5658120, 4091052, 5925283, 2766596, 1753098, 4010597, 5897730, 2271632, 5065704, 2410695, 180491, 2402833, 665806, 282295, 1835801, 8030085, 2551766, 5686863, 4693637, 1652731, 3208836, 2625650, 5325690, 8047746, 131943, 34086, 1657802, 7730283, 5576227, 6118126, 5474507, 4975484, 3338047, 5784070, 7632751, 7291807, 6106427, 7340785, 7029574, 1284002, 5298303, 2334085, 6693735, 6989442, 3565156, 4399390, 6335593, 7937856, 1097849, 828829, 847313, 2297582, 4329111, 7664653, 4207787, 5962989, 541268, 2586556, 878354, 1916402]]

rhoPrime: 426BF2D193968547C76767C38B01FF4C7425BCE393D3AB9837C6EA5DBB0EBECFF4240FBBF3445DB2B1100B7544944E96C6DE50B91D6D9275EFE585A3EFF12B04
y: [[143810, 123640, 293464, -417597, 162667, 130587, -125858, 454704, 117407, -351414, -443185, 24595, 281098, 332541, -422883, -320096, 55485, -394129, -420057, 405393, 400218, 387810, -356510, 310112, -54216, 151872, 519707, -273847, 441489, -388012, 29308, 398280, 380783, -69999, 243004, -349780, 12511, -49301, -255749, -79257, 259685, -104213, 162456, -133635, 11592, 182695, 470519, -379762, -499828, 110141, -363359, -405216, -134250, -324885, -414281, 59403, 38551, -430782, -447035, -190705, 159859, 284510, -8624, 286443, -309660, -375181, 284292, -492795, -10870, -353905, -161234, -375798, 517815, -428872, -445997, 109504, -464489, 482694, -199832, 22890, -169909, 23524, -22352, 69427, 389005, 249419, -40417, 147070, 107700, -498596, 136439, 518192, 92206, -453039, 74777, -108669, 445936, -425518, 113190, 309537, -424768, -191671, -344710, 296007, 441413, 103021, -28866, -296167, 412061, -377633, -2072, -37188, 516366, -381799, 150128, 439378, -455409, 500944, -369023, -208198, 18835, -454365, -134092, -109582, 198239, 383054, -111120, -352085, -133036, -384325, 433850, -411801, -365017, 456365, -513773, 268731, 6919, -98040, -486131, -52041, -152612, -410880, -350203, -225771, -37508, 60347, -126602, -1666, -219581, 189523, -112078, 451542, -522420, 15694, -28827, 297114, -508305, -374711, -43552, 169605, -19913, 473773, -229303, -55733, 306800, 418163, -114474, 136791, -181826, -524250, 205472, -513161, -478307, -190169, -225067, -473284, 169104, -193794, 228607, 63966, -278999, -126863, -209669, -326841, -350715, -329880, -505037, 519013, -187178, 390980, -391985, 406169, -423722, -218317, -33201, 443323, 393362, -265971, -293940, 363255, 210517, 303156, 441749, 396335, 215232, 164832, 72878, 363567, -336681, 402839, 148222, -316753, 306618, -466559, -27255, -496864, -45660, -197394, 260735, -205247, -349115, 40451, 443221, 64869, 469314, 441143, -481048, 291788, -343808, 226726, -477791, -106488, 440071, 122128, -428444, 20947, -358820, -409323, 344582, -349917, -268674, -168138, 51167, -121857, 196568, 293196, 448319, 379849, -517222, 491399, -239937, -418099, 150908, -168912, 518926, -427774],
[-321069, -326077, 478479, 190613, 96855, 440687, 411255, -242139, 306728, 161830, -172463, 277448, -842, -251970, -74016, -334819, 293700, -141163, -328948, -259848, 40022, 91633, -216281, -260190, 355601, -70258, 14066, 280732, -454074, -36617, 399189, -466513, -99537, 200252, 458878, 30003, 162644, -65978, -6116, -149861, 460376, -303281, 441363, 292260, 122053, 488687, -423874, 96799, -321218, 300364, -251995, 277775, 324181, 426098, 448921, -463641, -475041, 147033, 303280, -391735, 97575, 66749, -338124, -160967, -523476, 264042, 198035, 419624, -161134, -359179, 234477, -231429, 488098, 28132, 21724, -285108, -317166, 299509, -284572, -45758, -381871, 245167, -178956, 44509, -28034, -450511, 55717, -77158, -369056, -438860, -166468, 171030, -312474, -489965, -102294, -240830, 163401, -461713, 230586, 358213, -189741, -297554, -501264, 515308, -291624, 499136, 2347, -94354, -438759, 191369, -167424, -511444, -381544, -150296, 271669, -226781, -385963, -212481, -501533, -384457, -64755, 360360, -513289, 124833, 275888, -224637, 333863, -260164, 336857, 476698, -134172, 120736, 122309, 314256, -75328, 437461, -520253, -354996, -346086, 7324, -94229, 22319, 33716, -295518, -342321, 65876, 225034, 52701, 316982, -463212, 241497, -353454, 258279, -89827, 262195, 259575, -476200, -253947, -337824, 309613, -238157, 154308, -391172, -359271, -280217, 459488, 44344, -347845, 209884, -388816, -143552, -249604, 250020, -243883, 490756, 201421, -34895, -495058, -54803, 428106, 126976, 189035, -457855, 344735, -146993, 173358, -231139, -22864, 126559, 331842, -361319, 505916, 25849, 268425, -179748, 226301, -281133, -470550, -363151, -343, 6683, 107972, -282603, -455304, 124563, 148798, -341013, 484596, 398464, 446631, -185960, 53877, 465116, -78342, -164484, -418888, 127084, -371631, -52543, 63399, -299334, 227884, 373350, 79887, -43217, 109771, -307561, 287312, -129800, 237107, -149052, 482157, -416605, -901, -9833, 496811, -488452, 307745, 204193, -220602, -264008, 210733, -256666, 278582, -203321, 244972, -350578, -406711, -230555, 90675, -309502, 112450, 148360, 301540, -89544, 513847],
[134788, -275508, 229083, -466357, -491032, -258321, 306775, 85980, -225820, -289652, -312231, 155232, -394790, 481788, -140402, -26739, -321845, -15373, -343480, 268410, 477062, -405004, 514116, 475127, -517492, 332270, -49406, 11071, -109119, 167134, 291280, 93826, -486666, 197906, -140700, 427961, 278502, -256988, -81090, 237088, 30729, 122237, 366724, 433505, 269468, -429723, 101561, -462275, 473736, 308548, 448190, 219677, 14298, 338350, -256577, -53290, 403749, 222115, 451086, 65255, 443139, 65674, -416411, -444340, -366054, 53436, 104662, -320389, -211819, -303082, 499378, -456011, 476675, -205606, -65142, 375678, 349200, 368886, 398465, -458993, -317167, 343682, -469030, -386367, -147869, -482699, 309247, -4985, 366158, 271775, -355814, 429361, 183619, 482793, -15201, -505283, -411391, -437173, 43301, -252206, 344485, -354241, 246488, -375010, 291073, -120083, -352485, -54658, -165575, -248976, 342733, 82348, -274728, 162823, 111170, -54661, 345851, -52094, 293405, 163501, 85436, 170219, 429436, -387899, -524238, 233115, 346506, 212499, -372709, 499346, -248402, -51589, -413024, -246921, 50536, -238952, 381720, 297839, 389042, 267192, -443827, 230698, -43783, 266560, -442247, -283300, 133754, 241312, -269951, -512641, 410361, 221444, 76159, -107723, 155413, -85212, 237217, -50319, -146039, 459262, 287839, -151958, -218590, -142232, -483620, 306494, 165912, -224166, -308655, -1892, 132350, 130889, 105729, -120327, -154361, 257847, -317335, -516068, 405679, -449629, -71025, 122966, 195731, 18297, -441019, -321710, 310958, 329700, -265278, -132146, 44462, -314637, -65864, -87739, 73407, -389958, -504070, 131810, 426753, 252529, -302441, -235213, -455901, 103576, -43339, 284913, -220938, 367938, -409704, 57083, -111410, -499998, -299214, -38809, 6054, -53691, 258606, -288381, -207975, 96086, -288646, 359434, 314544, -208342, -236322, -490289, -389749, -214252, 356320, -209439, -140098, -138648, -263509, -227043, -71246, -63514, -180773, 146430, -179542, 125443, -398713, -508150, -20647, 521367, 66222, 342208, 176500, -176229, 475076, 342261, -76540, -174769, -99106, 335606, -70531, 263830],
[105084, 443910, -336307, -363732, -472944, -413077, 232065, -387908, 372505, -217659, 13520, 147668, -376021, 96113, 10472, -111190, -77391, -403916, 464756, -391804, -428088, -52129, -487538, -54461, -142409, -477947, -103250, 29780, -261761, 260422, -474460, 112110, -51646, -360415, -67528, -115982, -211417, -377299, -434437, -93567, 485446, 288996, -199408, 291721, 353085, 211524, -404090, 55955, 267451, 205655, -520588, -461635, 504153, 358621, 308647, 291091, -227961, 327213, -393861, 116378, -114786, -156053, -6142, -64473, -136391, -229682, 485891, 459333, -494684, -274463, -307968, 313289, 427917, -189491, 514829, 181537, -502782, 22630, 286244, -292396, -10147, -64843, 322460, 196891, -117696, 33494, -521687, 473803, 189571, -295414, 477702, 509578, -461783, -499182, -162313, -415614, -509561, -404225, 458575, -4831, -108704, 31092, -224901, 318087, -295845, 339693, 43355, -2618, 79988, -284270, 208881, -334301, 145468, -125660, 238740, 479006, -86896, -400290, 453187, -461181, 518998, 104073, -24457, -357716, -219049, -323717, 454387, -183088, -307935, 219622, 269073, -260548, -77685, -282207, 246924, -110172, 522510, -197, 300763, 33173, 358678, -255370, -409624, -321530, 80369, -98740, 267746, 115501, -294561, -127980, 420656, -53451, -197870, -273082, -264622, -64264, -139017, 136862, -301632, -346671, -212888, 14262, 193116, 9038, -389026, 349718, -88651, -202534, -279131, -45240, -95338, 142317, -325928, 389720, 19304, 379373, -258832, -318029, 270362, 159718, 202231, 385894, -444708, -477632, -436371, 318761, -27107, -78403, -352766, 326168, 162148, 508200, 103548, -156814, -463063, -421262, -326927, 138404, 465619, 185879, -70918, 162097, 252094, -473888, -66987, -509214, -300271, -248813, 307501, 268696, -74995, 32474, -346580, 185234, -21214, 513138, -144302, 190049, 47161, 217268, -35099, -388394, -220280, -505047, 277155, -221030, -57612, 269809, -246395, 222871, 124446, 303441, -17771, -249463, -495460, 356159, -360569, -262655, -483658, 110536, -33061, -17952, 318637, 300939, -342440, 95187, -371739, 283533, 249856, -277106, -500881, 11514, -467857, 182535, 343425, 509671],
[-100251, -197048, -399141, 140584, -248501, -43489, 169335, -120893, 6955, -6051, 396766, 323459, -145488, 140925, 1551, -353587, -23247, 381443, 211085, -215691, -313120, -223490, 251987, -341621, -252565, -271672, -516881, 213142, -293221, -146078, -259820, 476934, 469656, -260532, -128137, 242776, 455397, -53182, 315527, 500149, 238257, 362223, -236380, 397360, -259955, 361804, 215359, 117248, 326190, 121256, 329876, 422701, -282104, 349670, -172473, 521470, -462763, -158516, -362021, 329237, 418901, 273613, 222834, -434929, -394672, 500306, 341198, -375099, -338394, -175618, 4351, 251494, -330727, -47920, -171615, 80168, -267427, 336584, 486696, -107528, -421011, 275434, -243605, 122938, -34152, 209218, 325984, -198607, -473439, -488311, -184770, -70349, 401496, -403389, -370601, 352675, 484916, -261158, 9217, -193874, -323167, -45230, -497252, -45823, -380585, 471688, 67207, -100629, -441866, 264934, 346766, -339249, 273484, 445513, -499769, 232598, -443116, 122407, 206317, 497544, -308985, 254605, -297628, -78685, -391184, 173417, -395495, -362769, -200729, -181987, 2366, 138913, 22800, 382462, -226570, 74160, 373818, 429910, -41392, -341573, -132017, -116121, 306699, -192072, -378108, -311366, -523057, 476847, 184572, 120352, -410325, 316222, 101432, -135207, 52416, 39598, 478117, -310861, -465229, -216909, -37757, -108528, -267949, 25116, 489480, -156932, -518450, -132963, -520558, 113283, 103869, 483631, 103631, -376488, 201831, 442783, 470327, -285160, -284154, -447858, -12588, -119755, -102407, -251841, 338071, 370260, -377812, 202988, -274138, -516916, -30222, -25404, 329319, -239747, 374507, -122349, -337765, -172116, -33635, 389537, 75301, -122609, -189681, -439233, 323037, -295011, 101573, -117467, 126072, -184995, -498740, -95770, 124093, -352595, 382400, -369537, 170048, -154608, 144009, 224040, 515413, 213456, -336154, -127874, -1103, -478824, -28133, 300400, -254614, 139978, -465591, 348758, -66486, -95479, 151571, 17574, 128718, -218274, 283251, -153338, 234094, -391161, 256039, 91777, -393708, 505136, 433880, 363672, 236662, 266960, -511178, 464056, -87257, -430688, 122916, 351204]]
NTT(y): [[6647644, 3736536, 335764, 2137570, 2150431, 1873619, 5642660, 6512628, 6274882, 6704330, 1276914, 2654339, 5909824, 2882865, 3444360, 4761229, 7644160, 5673490, 4958112, 8163347, 6087001, 4455475, 2067215, 2988452, 1421840, 950378, 8288363, 4083514, 3632303, 2342387, 871251, 6101202, 5514150, 5568514, 3434462, 3339661, 6109743, 196298, 249549, 2116065, 8348724, 2322536, 1031772, 5060403, 2258042, 6532900, 5707188, 8199104, 7418648, 3032440, 681377, 7243063, 2268159, 7361912, 1703976, 7013230, 5370613, 1642650, 4770815, 7699101, 5405424, 4627585, 2292508, 4730763, 7967688, 7953819, 2477572, 5489843, 2113968, 2907325, 1144712, 4250388, 2318976, 3400101, 7098749, 2677751, 7734096, 482301, 4841160, 2716998, 6076729, 3235390, 2462679, 7769991, 2955221, 6956126, 3361302, 6782000, 8293161, 1971873, 6431832, 1291943, 6266730, 4390792, 1672228, 2142732, 3767782, 6090002, 7059823, 1113119, 3597009, 495379, 7457818, 143025, 2685266, 5999258, 594597, 853424, 3106543, 1973316, 2884557, 6458706, 7198978, 1160916, 6666186, 1353041, 3687675, 6642418, 319220, 1882809, 3740165, 4390773, 6881805, 6209002, 7446148, 3024387, 2368483, 2064656, 2859966, 5138226, 580742, 4061336, 3543054, 2901161, 1656665, 8327452, 5665897, 4417713, 2641378, 7186625, 4294509, 765361, 2552041, 2438431, 5399693, 3378497, 1638900, 1498735, 5675658, 339779, 6685023, 6024451, 4650832, 2645334, 1428536, 1600118, 1865804, 254589, 4615875, 4220444, 5648860, 3930921, 2055773, 7025359, 3161027, 6898753, 76084, 1046966, 1497015, 8282104, 945879, 930095, 6558266, 4975311, 2774339, 27147, 7981224, 3025792, 1762031, 6619717, 2144690, 6377124, 722206, 7635418, 7824359, 4419755, 7137018, 5251118, 230764, 1616670, 1108975, 6993432, 1218961, 5580547, 6565558, 1055682, 299272, 6657807, 6283095, 7918535, 950800, 6802273, 857245, 4841984, 1726801, 7496980, 2539323, 6596945, 3565352, 7027386, 2190004, 7372490, 7468674, 1692266, 3134102, 3853672, 7014636, 1728704, 4179764, 372338, 6577308, 3115736, 5163700, 8311905, 1425820, 7408293, 124144, 3995855, 1817358, 6780405, 6739484, 1927581, 7865613, 2347131, 1747023, 4409445, 1451139, 6277596, 1532860, 6540080, 3603924, 998824, 5476998, 2746594, 8248063, 2055457, 2641432, 3708760, 3884622, 4596541, 3089267, 3961020, 5325775, 7644350, 860713, 6178032],
[4542528, 8160725, 3765878, 2286588, 4474350, 8253963, 4169791, 2737175, 6209736, 5941507, 4776690, 3740617, 1897694, 6000633, 100469, 1705025, 2151690, 3146984, 2965526, 900959, 7868566, 2586654, 1998007, 8345369, 1599371, 2919031, 2651818, 2252244, 3415109, 572479, 7260274, 6648506, 661629, 7514366, 6572509, 7680820, 2245879, 4851576, 6136099, 5265523, 6893611, 637768, 3046882, 4041692, 7003973, 33364, 1053635, 1895353, 1497549, 2001037, 4543964, 2194666, 7890026, 7930137, 3706801, 6190015, 4202659, 3430133, 5271182, 7226543, 7980186, 1124815, 2216412, 2868667, 1091659, 5316493, 7632496, 1301403, 6888953, 8197884, 4890659, 2579775, 523780, 5328176, 3205255, 6925944, 2118068, 7285816, 7414385, 1657846, 7397485, 1773008, 4344052, 2229636, 5832615, 2324852, 5987191, 6653059, 2616796, 3836776, 1632306, 6404722, 2346042, 2839332, 2570860, 5881570, 8296043, 7131423, 5116890, 4681899, 5017151, 3279137, 7864539, 8088722, 3922814, 7509611, 4592404, 3548843, 353249, 1548926, 3537184, 1027643, 1002965, 4334978, 6527500, 6813212, 7128567, 8129338, 1100517, 6422873, 909690, 5452581, 5977891, 1638506, 7743850, 901172, 7751199, 4498272, 822792, 3179953, 5061479, 3490262, 3096015, 2664310, 2172062, 4725284, 1185888, 3774879, 1278333, 6303642, 3637886, 6981372, 4840557, 149496, 5755037, 654215, 7829263, 2850106, 2538855, 3401286, 3467638, 1366955, 2984858, 5260930, 7944596, 7642552, 7790668, 2388996, 4369273, 3707093, 7916184, 4187905, 192789, 971160, 1203935, 3043795, 4903920, 6404874, 1532994, 2899849, 7282738, 6468051, 3865020, 847164, 698133, 3436366, 7666393, 135771, 1776030, 1059700, 7302786, 118126, 5181349, 3603005, 5539933, 324544, 684881, 7743179, 7295883, 6912702, 409471, 3245105, 6113066, 91850, 6106742, 3599814, 1119575, 8145408, 7492085, 6730203, 1152035, 2666243, 2285435, 2574812, 3747282, 2129432, 2825793, 5244407, 3644502, 2943560, 997154, 7637690, 8082476, 4091675, 7931259, 2338196, 5282976, 5479386, 5723000, 2179939, 6552437, 5816947, 7939486, 6034277, 2791567, 1748964, 7957120, 505518, 6542313, 666523, 3139262, 7647295, 3074677, 1281636, 5347387, 7628596, 3606520, 2111698, 3786747, 7552849, 438711, 180128, 7064223, 4809077, 1982406, 2701510, 7005882, 4881982, 6636159, 5746176, 4221220, 809520, 6644759, 8133026, 2970399, 2706297],
[1983762, 3468525, 4074895, 2623883, 501889, 1526860, 3676148, 8075100, 1026694, 4037145, 6151506, 4189919, 4958148, 4200951, 3285564, 2103979, 7654297, 7855638, 4530778, 7741169, 2139143, 8320971, 3246931, 749652, 3988601, 487285, 403451, 7562654, 1437392, 3617613, 689148, 3134085, 4865320, 4162608, 1237304, 1535573, 6759847, 589844, 5439681, 6569535, 2505997, 3614415, 1593272, 5458736, 3284031, 2542034, 7067564, 6443098, 6678661, 3406216, 4169417, 8320858, 4639882, 262447, 6267757, 5271968, 8291063, 2879878, 5017783, 4716315, 2842308, 7789692, 5665891, 1368569, 5974573, 1050176, 1971699, 291689, 6528686, 676244, 624454, 6016026, 3287294, 1778348, 156058, 6813041, 5968930, 4475468, 3871853, 8284688, 414759, 5336928, 4544972, 2942199, 5989404, 2720298, 5734200, 3703472, 7171039, 5213756, 8067463, 3333312, 8152085, 6612425, 7371696, 1358317, 8264023, 2727283, 3868649, 6425905, 424920, 3952841, 695862, 7027741, 6565451, 7117760, 7065280, 1036136, 8161346, 6350133, 6127616, 5366036, 3228937, 474542, 700758, 3462845, 2603516, 6103555, 2067439, 6767028, 746112, 6622087, 7737338, 4124924, 958741, 6618648, 2077795, 3977224, 4188396, 4739722, 4268727, 5879584, 7749935, 2648738, 7892146, 4260421, 1807258, 6689826, 3375585, 660411, 3183625, 6281524, 7136127, 3190605, 5091751, 2427928, 381451, 3233175, 5459922, 3793609, 6569024, 5889130, 4190037, 1130915, 7852795, 3425508, 6861033, 1655096, 2598951, 3109887, 2235413, 3900478, 4405155, 6692971, 1677396, 285624, 5227561, 7349422, 7056235, 1040706, 6502638, 234303, 380383, 8176405, 3542711, 8005432, 4712424, 6462678, 7579477, 4014973, 4154059, 966496, 2142475, 6925836, 3424030, 1465169, 488381, 3677635, 696485, 2540915, 4670389, 7067093, 6727648, 5486985, 5697518, 7605710, 3598366, 2924764, 1730035, 2686113, 6541076, 6184164, 4391611, 1805135, 313705, 6161372, 1122576, 8193154, 1006871, 4993559, 7853212, 8233864, 3375358, 7330317, 4289960, 5757814, 8271863, 2035361, 4501928, 2989040, 747486, 5931390, 1310260, 6358297, 4729112, 6307753, 5484609, 1024159, 5661796, 3053583, 2375404, 826233, 5339435, 361749, 83179, 589614, 6827108, 189089, 3851646, 7393238, 2072648, 5284568, 4375003, 3689298, 3848129, 3302209, 2914409, 826678, 4321060, 2185568, 3571433, 1100697, 260778, 3525419, 7909026, 5565907],
[8048190, 68021, 5370941, 5846834, 5841984, 2365888, 6445319, 5052494, 1771742, 1276962, 3195414, 7458010, 4851066, 1470042, 6402258, 563278, 6391186, 1962130, 4396625, 2093018, 5569984, 1364861, 546743, 4467413, 4749534, 1987558, 7138435, 6721397, 8349878, 144379, 6552624, 6685207, 1269148, 5440603, 5242593, 188996, 7053941, 6884352, 2869260, 6429968, 2828836, 3909188, 7490475, 7050197, 6713074, 2384795, 3098938, 7080621, 5350016, 2073237, 5822440, 4833581, 3538733, 2384197, 6436895, 5753898, 5603397, 7193553, 1323402, 4434899, 6910958, 7349875, 8286653, 2264136, 2159551, 7049833, 563491, 5322833, 8276525, 7964494, 5626836, 3781339, 2870873, 6102346, 2325583, 8049873, 2737294, 6320917, 4505967, 2819524, 4805474, 2104945, 8258263, 6346063, 5949021, 7570263, 2904307, 241645, 2593019, 6841124, 5835090, 5861241, 5189521, 2339646, 151778, 7153875, 3814324, 7512499, 1492021, 8073055, 1940487, 2358618, 6470779, 6680092, 541041, 4838726, 8008313, 4888375, 6160089, 5042068, 176059, 6575678, 1439877, 4170782, 5575449, 7276733, 6598030, 6165923, 2422153, 3908602, 8271847, 6282428, 8117471, 1704849, 4259787, 7887122, 8014906, 2354487, 2854000, 930303, 5088064, 7576112, 3486561, 6223909, 3269611, 7800997, 3164579, 7845214, 4249481, 114871, 1374511, 7952475, 4921128, 3526690, 8306779, 3136965, 5921336, 3235145, 701593, 2534676, 5859745, 5001261, 1873122, 3930617, 7349568, 72871, 2443080, 727198, 8214213, 360561, 4280959, 4233957, 4252803, 3988864, 5406669, 6099986, 4555504, 8073746, 3377281, 8052522, 3047912, 5283352, 6323350, 3496080, 7010447, 7773357, 7308321, 1844496, 294506, 3055804, 4162153, 7711148, 4470366, 5048033, 3366332, 5966133, 294985, 2632573, 1831722, 499008, 1192035, 6660934, 6927290, 3723759, 7994598, 7446102, 3201296, 3308584, 5169902, 7518646, 3852198, 4622163, 5348834, 2276024, 3307425, 6218651, 6764656, 5844797, 3868605, 45020, 947985, 552028, 1491435, 5132855, 3212176, 6035816, 5919751, 1343185, 3188354, 4603233, 2585764, 2865343, 7122668, 6270933, 1059199, 8306104, 2926550, 7103625, 1793279, 7372984, 5665330, 5785405, 6104513, 4235884, 2361352, 1522858, 3800481, 3730149, 700382, 212339, 7906900, 6096411, 509082, 2503278, 1579323, 475525, 7478535, 5891178, 2691536, 5053434, 1123314, 3859810, 4634897, 4811317, 432282, 4747148],
[658397, 6875506, 192705, 6382226, 7722261, 8282313, 4607845, 3500461, 2531245, 2097569, 4335520, 4797631, 5455576, 8250533, 7102917, 1965533, 594004, 6656324, 5635228, 7381175, 4404732, 7310491, 1811496, 1956396, 4603034, 32226, 4773985, 7054348, 5319598, 810452, 5454530, 5057900, 6482017, 2495714, 5010033, 3755837, 4053231, 242949, 4156322, 983049, 2203988, 3660789, 2052964, 3988402, 5259861, 5933290, 2696710, 638651, 7631942, 2067046, 4702453, 2582864, 656735, 8339013, 3011483, 2734553, 4197057, 1496888, 1681443, 4997174, 1679313, 3205814, 7839642, 2847130, 3722522, 391223, 2859220, 3973303, 3907740, 6967824, 1519505, 594647, 7607559, 5401449, 4706574, 6704546, 6352874, 7190426, 2479233, 2719985, 4824234, 5112891, 5968983, 2585888, 5565965, 4977616, 8217851, 8377647, 3837027, 2550127, 8172942, 1161637, 7064868, 6557734, 5198356, 1551174, 2908101, 7052291, 489672, 5305025, 6992308, 369889, 4421323, 1573266, 7491644, 36599, 5499931, 5887550, 4325155, 3951169, 486464, 2359017, 5502082, 7471623, 771288, 7652279, 5770370, 5170016, 3956394, 4629286, 5661638, 5436771, 8192301, 7754195, 2577364, 632217, 2980661, 6518584, 5824295, 785873, 5123691, 3649848, 2078006, 7923119, 7790733, 2178278, 8223447, 6113891, 837389, 7948699, 8121968, 6737134, 5326341, 4916884, 49119, 1974068, 6029451, 770353, 5239484, 2737375, 93418, 766801, 2130942, 5079976, 1862557, 4350723, 1614932, 8236270, 5394401, 5680707, 7946919, 1086013, 1561597, 2950282, 3476870, 460136, 3839514, 2263795, 4516599, 2340804, 6093115, 4725345, 7438269, 313510, 4161280, 4227325, 5950029, 2830910, 7964857, 7130316, 3946871, 2194079, 2720004, 3559006, 5671148, 2334942, 7175689, 1612249, 3559015, 124304, 4594610, 3752837, 8142756, 138382, 5869190, 3237136, 7030705, 7906004, 7880232, 2414110, 836606, 4112530, 3291079, 759493, 6402483, 5323344, 5446099, 3219357, 4916824, 8238366, 411227, 7150123, 6721039, 4366983, 1095844, 5426516, 1533465, 4857477, 451193, 5230177, 7850733, 2952537, 645393, 4766513, 4116616, 2838455, 8143626, 3698772, 4649491, 7783759, 1038895, 3072, 8156282, 2965986, 7404197, 7904615, 5618961, 1973433, 7191053, 7327233, 3890208, 7825997, 6224119, 993940, 7460564, 2187662, 43902, 7790633, 3379652, 5456179, 6347256, 8133601, 598532, 3739093, 1493550, 266986]]
aHat * NTT(y): [[3030962, 8163160, 7615388, 8261104, 7974524, 2409962, 3629073, 6437734, 7307917, 3213063, 2293346, 70396, 3137848, 5209543, 5325091, 7138614, 4939934, 3670474, 4202986, 4662214, 4721740, 4445580, 7864969, 1076743, 7686369, 4501100, 5799899, 293292, 1053624, 3103024, 1519801, 3898029, 7699386, 7663597, 4275215, 2777998, 6140433, 6105163, 4925372, 6572594, 1171262, 8092114, 7661899, 7707877, 7726869, 1333347, 1420525, 7368945, 1176052, 3218251, 6099701, 2864543, 5954696, 5251601, 6659643, 2847757, 3303038, 7200575, 7801771, 1346663, 6016570, 2675096, 8344045, 95790, 5374594, 3898271, 6672564, 2135665, 5168766, 46261, 1464361, 6019049, 4844021, 1431199, 115585, 7286950, 4924150, 3601252, 1537190, 14109, 7308161, 2996320, 324302, 8370075, 7475094, 7007850, 843492, 553125, 4840607, 6043487, 3862902, 7328126, 6500889, 5157829, 5447907, 4424908, 7091305, 5745548, 1721312, 403708, 5954378, 7107480, 3111264, 153283, 3560733, 3239737, 5138969, 2586553, 6120107, 5223098, 6493454, 1946788, 7462675, 1668162, 1343275, 1266822, 2607493, 2408477, 1971912, 4269453, 6059056, 4054487, 4037053, 8076535, 6829055, 1958033, 1438537, 1575748, 97535, 7619686, 5977397, 6523685, 4285621, 4151438, 5383397, 4661993, 1210540, 800115, 5344539, 6065637, 545398, 4132071, 270952, 6863740, 7939381, 6112945, 71128, 6133789, 7777995, 5044893, 964387, 3693579, 1465636, 1426737, 834189, 6281488, 995728, 6017032, 4533737, 2076225, 264512, 2082531, 2942921, 621766, 6260115, 3772835, 4403858, 8134407, 304345, 6818090, 4527925, 625552, 5990065, 7190845, 1272898, 82753, 7454674, 6536513, 4526862, 4919559, 4764103, 3237803, 1812896, 7151103, 461700, 8031408, 3867252, 4110719, 7070780, 7525441, 1498561, 4610857, 5707009, 7654727, 2359121, 3844323, 645428, 1959214, 6002443, 2722841, 7557877, 6155879, 3498826, 1491714, 5198278, 5412084, 1910113, 4021798, 277796, 3809033, 4456542, 5093347, 2434636, 6802808, 5587053, 1078506, 2306715, 3588354, 2520850, 7198826, 6155522, 4981982, 1786696, 527385, 8246570, 3678366, 3591608, 1351781, 6812123, 5218997, 5900160, 7101052, 2474073, 1927984, 5141014, 5929704, 6892206, 2086828, 2734038, 931257, 5620262, 3542791, 5061767, 7220507, 3257745, 2784415, 5464079, 7273449, 5258527, 8237054, 7243169, 2655642, 8060812, 7438108, 6524376, 5487731],
[2283115, 2242425, 7717285, 1739848, 7631041, 1255290, 6551101, 6606948, 1222761, 7355026, 3906252, 7517176, 2262854, 3070470, 4517247, 392023, 23334, 6654188, 6997159, 2412888, 6152372, 6346775, 5526210, 8146769, 3212430, 6075101, 4402551, 7092918, 2881113, 6713862, 2415568, 2479780, 2039773, 1079634, 1827815, 111623, 2728106, 3266834, 5338865, 3052624, 7126541, 4154709, 8165321, 1911126, 2124864, 359287, 953281, 3599221, 1547224, 2005633, 925473, 5790045, 6768232, 2073172, 2138083, 7748239, 1203389, 3677135, 1338126, 5502778, 3992231, 7352771, 7724192, 7613048, 3977688, 7743138, 4280930, 4344774, 3501967, 4138846, 6588358, 1088062, 5402613, 4942348, 3348838, 1035803, 6294089, 5030750, 556568, 6004995, 3299244, 7135256, 2112285, 6820293, 8292545, 5874770, 6828581, 2096171, 527515, 1569079, 1743184, 7428129, 275538, 4493114, 1231703, 631658, 460846, 5151438, 8236504, 3257412, 5087941, 4528498, 1768057, 5098065, 7049578, 6846941, 7756584, 6329001, 3584897, 5123111, 6711221, 4817965, 443700, 1402960, 153110, 5582268, 5105838, 2810925, 7930654, 3245224, 4033440, 2692211, 4837942, 5902983, 5834802, 3815181, 3942413, 998936, 7089893, 1724397, 7307588, 1465588, 2204951, 5659262, 4732040, 8065579, 6496795, 7128070, 5871199, 7964831, 6500212, 900136, 4852965, 869934, 6837036, 4902021, 5489717, 6075177, 469366, 5774769, 611437, 2010937, 6198207, 4858872, 7613258, 4823001, 7483359, 7572830, 4931521, 2632040, 5415839, 4531590, 5402586, 4378224, 5417345, 4948355, 7946674, 4086802, 3972333, 1002874, 3950127, 2261108, 1283152, 2742628, 4977451, 1989561, 7434286, 1031567, 5110542, 5341270, 8046931, 7417845, 1163381, 444576, 1921903, 3685436, 4393622, 6857008, 5336355, 4475807, 5234626, 8169715, 6065054, 3756516, 6380649, 1062519, 5293422, 8037003, 4234448, 5257707, 3817669, 2204217, 3966050, 7342516, 2669286, 7541465, 1750968, 105914, 3507487, 4144134, 8296572, 1005515, 3521582, 98842, 6665436, 5919734, 6122568, 7470943, 7960274, 5398434, 6128852, 387833, 5648740, 6588328, 7458310, 577489, 5473254, 111864, 1796143, 6308161, 6303952, 3807229, 476372, 2177983, 2946120, 6537697, 3266146, 7953254, 1249328, 3757003, 2439580, 3311980, 3889910, 2811318, 4041100, 3883550, 4905475, 5432031, 3951425, 3547143, 5726106, 8363061, 2363045, 401235, 4490175, 2815662],
[6038520, 6549261, 7274156, 663731, 8329793, 5983116, 5175477, 7660958, 4708220, 3624908, 8299198, 7618214, 2805475, 6011274, 5072841, 7593957, 6353852, 2342824, 3882638, 6338748, 3266859, 2219384, 5989675, 5552964, 969863, 213522, 4688543, 301382, 7884137, 2239714, 6539163, 7965048, 1569881, 3828853, 4471499, 354644, 8091253, 1473475, 545987, 2129136, 3072245, 1794811, 3206483, 656616, 4809443, 1832682, 1165041, 5307903, 7530955, 8003082, 2530098, 6499550, 577959, 250880, 5914505, 3699777, 4066642, 2504623, 5390222, 4284947, 2101270, 2021702, 7322621, 1913924, 4613745, 868774, 380590, 9642, 8012710, 6048020, 2336229, 3953477, 2699748, 539956, 7813996, 3519677, 5651965, 2213153, 7672692, 3248266, 8115624, 1662674, 7872227, 2490906, 7801722, 5137464, 5275851, 7524375, 7290659, 927065, 1753407, 1596912, 5433332, 1618723, 7403553, 2143183, 169142, 7127496, 1228856, 3407087, 2543716, 5582550, 6859547, 522315, 1439284, 3345620, 6894248, 3952220, 715740, 1259, 8167061, 3110708, 1641560, 8151396, 3783414, 7233114, 7023962, 4429087, 3736045, 4118876, 6267967, 3731681, 3264627, 5271397, 1771122, 5670915, 3721598, 234072, 5522185, 565542, 233780, 7405065, 3305330, 3093775, 314617, 5993008, 3911238, 7611626, 4920649, 7629631, 4294498, 711449, 2171707, 1331618, 5968957, 4643167, 7184308, 5301969, 6011939, 2978012, 1989340, 2612444, 3512674, 5504276, 7530859, 2371685, 3106934, 7206819, 4117724, 6474355, 7442576, 4697391, 1070627, 2321212, 712359, 6251932, 4027985, 3704496, 7729905, 4411514, 6272478, 467794, 5671377, 8244588, 4326979, 2974618, 6748479, 8056830, 5483421, 6283614, 842955, 7088187, 2119738, 2682123, 5505226, 2767573, 3696751, 2569995, 79034, 3396438, 1416979, 6442508, 6110568, 165520, 3621268, 763770, 4943122, 3809936, 632685, 6243151, 3979092, 2716172, 3111816, 1588436, 3949294, 7637536, 1013743, 3114598, 3426140, 6554634, 8198013, 1427735, 734953, 1747495, 1146283, 2453244, 5225233, 2405080, 219070, 5500844, 4974549, 6843424, 5898186, 7547882, 8262076, 3556353, 6656424, 6315649, 8146509, 5903564, 6757747, 2740238, 6934013, 4547277, 7793994, 4857209, 7840482, 5302703, 6388141, 5674142, 6183398, 2094785, 4908307, 7460408, 2699770, 7758191, 5030519, 5530444, 3729840, 4377291, 4869679, 4391888, 6381782, 8303425, 2180012, 6931496],
[5578188, 3555640, 6998607, 530305, 4289043, 965980, 5701026, 4696390, 5655315, 6253867, 646017, 5890928, 3440616, 6235954, 4894939, 960093, 3802923, 670783, 2307471, 4322870, 4937296, 593064, 3585771, 8189482, 3164500, 675361, 5953791, 957055, 6821369, 1651646, 753178, 77625, 1852149, 2895876, 7624815, 8126568, 8315427, 5522307, 7236443, 7509982, 317607, 1179043, 7052382, 4917032, 7562400, 6711575, 5104127, 1057663, 5624003, 610261, 6761773, 2112370, 4953457, 4670379, 5654974, 7402890, 4226249, 7152637, 7145453, 3309509, 22056, 3801037, 497536, 4398191, 400931, 8293825, 1209921, 5559725, 6724770, 7950747, 5185053, 1449691, 7862351, 3620825, 4997682, 529079, 3209284, 2052005, 6867464, 2345305, 7750265, 229142, 4242384, 6645649, 6801237, 6465520, 1543887, 3813449, 3820033, 878553, 713698, 367440, 5062885, 7588117, 2757979, 4305588, 7517144, 6282771, 2346313, 3931595, 7588644, 5340542, 6151651, 774379, 4673031, 266579, 6156103, 5380007, 7535674, 872186, 3957088, 6677601, 6444240, 863416, 2130308, 5282025, 7442743, 1441448, 5363710, 5869382, 5000550, 3890682, 982448, 6793663, 8020652, 780526, 5697478, 8351754, 2202741, 3397087, 7255701, 3804458, 1667277, 5693210, 7732000, 4492357, 2814870, 6148178, 7457253, 2687217, 1918273, 8028129, 7777402, 1362653, 5822564, 7657187, 721265, 8101858, 5423782, 2201209, 8038368, 112986, 8230088, 4698491, 3474424, 2429818, 661572, 2590144, 7038448, 7581403, 1116510, 8042810, 160994, 4042710, 1629497, 2933680, 4667054, 1335598, 481500, 3093087, 4774430, 3057726, 1106953, 23746, 7283301, 1687855, 5496906, 6679959, 2302148, 2134316, 3744554, 2973159, 5015560, 6848965, 806823, 5846573, 3367159, 8013469, 304667, 3352768, 3370357, 3262752, 6035170, 6216021, 6374477, 1428962, 4570768, 832949, 5248054, 1270148, 7025838, 525047, 5623466, 1355616, 3686171, 2803396, 5147057, 2560275, 7011366, 5568697, 1628537, 6851434, 2338434, 2837799, 3331499, 4389380, 1986071, 7061550, 444426, 3941774, 2445480, 5816892, 7768894, 5668695, 4198240, 3307273, 4446357, 1458809, 2973741, 679809, 4213425, 6121419, 6994884, 3542131, 448659, 7510036, 3375262, 1754605, 5144744, 7787543, 4091440, 1577251, 6154408, 3475063, 6880374, 6589009, 4122509, 2803850, 1858227, 2592776, 874127, 2601120, 3754534, 4413971, 3577524, 5838008],
[6758145, 5922560, 2048600, 7571929, 3261726, 3044315, 7782520, 3651866, 1744036, 3922529, 835135, 7478696, 3024280, 7427146, 1711790, 1875610, 268315, 7894585, 1126935, 5958887, 2195252, 6069918, 7697858, 6618605, 3737868, 3476589, 5095915, 710859, 1177224, 6571115, 7824583, 3518847, 1767527, 2582854, 6841285, 7907162, 4707658, 6251580, 1952456, 2004724, 5598384, 3786963, 3134407, 5974879, 1683357, 7378244, 7720711, 2852021, 394392, 6656972, 6931090, 4342998, 6002128, 5948366, 553549, 6380641, 6530598, 2095902, 7787444, 6583736, 1403127, 2578087, 6500521, 1100987, 2558206, 7836377, 7768318, 8275435, 4844309, 219877, 8250893, 6533248, 3319737, 3015897, 310872, 4508045, 474136, 5363047, 6701232, 1461617, 4740239, 3697607, 1429953, 5500961, 5514545, 5386011, 7353319, 2179171, 6033060, 8019796, 3272599, 6995700, 6273262, 6512899, 2427604, 8292690, 3763758, 6097906, 5932976, 5294265, 781982, 7621206, 8299564, 5234238, 1175538, 4553761, 6995258, 5033115, 6623689, 1613989, 8103229, 1595831, 4392675, 5501327, 5739269, 2916783, 8239916, 2558459, 2325386, 1788006, 6116327, 1747451, 7875616, 7401527, 3955211, 449606, 5158104, 3520960, 7785684, 2547328, 5881470, 248889, 8256233, 5474898, 477526, 8210713, 7331926, 767443, 6181754, 7614880, 4025941, 4465288, 3108505, 7606480, 3995817, 4860131, 5655800, 3613499, 3453982, 1359577, 3404574, 1111617, 7853579, 2997156, 398181, 4361720, 8148580, 7233032, 4815786, 5462271, 6309879, 589910, 2382160, 1189322, 5619663, 7452693, 1995360, 2213823, 870698, 2099002, 7559846, 2059713, 8003742, 2348113, 287963, 6651794, 1205923, 4215059, 790071, 4579742, 3012418, 8094284, 6861422, 1372357, 655027, 3853052, 6701464, 433831, 3756371, 1027923, 4379552, 745074, 781506, 3381493, 5792387, 491947, 8262485, 7065658, 175997, 2566791, 4826104, 3507857, 4322769, 3885084, 508461, 6466889, 6571989, 7804531, 6007038, 7032582, 342039, 8215371, 2118152, 3404932, 6030803, 1593492, 152296, 3828787, 5944129, 1235534, 7137582, 1261219, 8260098, 3589276, 2915823, 6587619, 1358783, 4151648, 873194, 2677994, 6142149, 3864, 875369, 2874234, 394800, 5959067, 1245216, 1147201, 7624684, 3535448, 2016766, 6616128, 2013931, 2045121, 6913794, 1802232, 3864737, 4602785, 2471337, 5438200, 1400612, 8217320, 2670614, 8061685, 7598350, 6761546],
[4888731, 810472, 5895608, 3680701, 6133197, 2833490, 6754027, 4464140, 5704350, 7728508, 8357456, 7712443, 7295341, 659194, 4449085, 3870874, 3643523, 7327077, 7140369, 3434712, 4553581, 5573554, 1639043, 712979, 6250321, 3165607, 4475886, 5806768, 7674070, 602962, 839570, 1390748, 2372040, 3833492, 8061795, 3618772, 7055406, 687554, 7580845, 5171459, 2969319, 4533779, 4682951, 3122800, 1910969, 6310945, 5918757, 7356487, 1435969, 4768211, 6328588, 7217697, 767299, 2148911, 4199002, 3207214, 4190743, 1544358, 3849531, 2038747, 4344367, 2108713, 2350930, 1106857, 345784, 90248, 5954006, 98034, 3650481, 7232181, 723651, 5351799, 4766199, 7870087, 4267522, 1712965, 1536814, 1080872, 1419116, 5017850, 5628454, 6033331, 2319907, 5757390, 4886243, 7797718, 482795, 5587362, 1197686, 2026402, 5201533, 2166011, 4384874, 4472222, 6455470, 2371383, 8042944, 5319003, 4920931, 7883548, 6467778, 2309628, 983099, 7766063, 4683456, 3685612, 5202154, 7723734, 3695381, 7987601, 6818635, 6403168, 7593095, 2120483, 1944382, 6218629, 4931018, 1899402, 838461, 8131354, 6324225, 1865637, 2300287, 3656444, 4838607, 2656646, 4795961, 5226735, 5610745, 3581967, 8225771, 7553342, 2202496, 3948581, 5585489, 755660, 3073984, 1177524, 2330310, 2021395, 3387606, 2070192, 4915323, 2354287, 7891168, 2493128, 2520502, 3264126, 1601408, 4687615, 2950665, 5134626, 6087898, 1267492, 6683789, 8208395, 5138952, 2279538, 5532182, 6829204, 4751857, 7904465, 638734, 2196264, 1548798, 6150416, 5562831, 1111581, 7238043, 4911114, 7075957, 8287660, 7942807, 4735890, 8252586, 1120994, 3069873, 3303289, 7960406, 1958484, 3296983, 1237829, 8371690, 1811514, 1309629, 4503582, 8325469, 2464880, 2971885, 8072530, 7308458, 7880149, 2737073, 1079697, 2232407, 8205077, 7247408, 538191, 4429783, 6194127, 8357272, 1075210, 5635120, 2058478, 7516867, 6734978, 6665286, 4092516, 766396, 5947060, 2814049, 64961, 5768210, 7961527, 2821939, 6177222, 1483809, 3992047, 3914519, 3985173, 5890344, 8144479, 6216926, 5818061, 7334512, 948381, 1782388, 260024, 1489974, 2698786, 2041539, 20700, 489920, 5643562, 2907311, 7083022, 1382614, 5100647, 6409034, 6132724, 2002985, 8168005, 5489639, 3342669, 4729422, 5105581, 6202407, 2080249, 7489315, 7323518, 6256079, 3404167, 6372233, 7327484, 4606710, 5946574]]
w = NTTInverse(aHat * NTT(y)): [[1398502, 2912460, 1321383, 4677021, 5037058, 770457, 1975114, 1929754, 7527149, 6975674, 7408973, 3608183, 7516655, 2019037, 2575360, 1872448, 7669162, 752181, 5764812, 6035002, 2277848, 7687903, 5737979, 6804860, 1238237, 5565, 5784306, 8332228, 268170, 2868211, 3452699, 5632804, 3994348, 3863645, 6025339, 2672916, 876342, 4737290, 707832, 1806450, 1259726, 4014079, 4910408, 6085648, 6339010, 6307471, 7058887, 6518711, 415698, 3513779, 3277027, 3932836, 5788579, 4542047, 5141400, 2890456, 4742223, 7784002, 4903903, 1361795, 3030918, 5409401, 5294076, 7190464, 893437, 8306029, 8314424, 4908347, 1559527, 7347799, 19753, 7300999, 7872955, 1402006, 3591098, 945510, 6640529, 83131, 1394419, 856988, 6889187, 4414911, 5432132, 4716266, 1555042, 5752847, 7990724, 7019160, 6124647, 573749, 6351585, 2847186, 5603594, 7413897, 6382408, 7260047, 2707020, 4068074, 4108924, 511946, 7882619, 1973529, 7034447, 6347735, 3968544, 6148313, 4153262, 3697959, 7861276, 7300841, 7628281, 2396581, 6360633, 4462568, 3524058, 4375369, 2300928, 3723128, 2847051, 3045693, 7480174, 6960467, 6436219, 6058765, 4490192, 7219978, 4918766, 473314, 4009340, 3181010, 5228911, 4508560, 625940, 5331929, 7016399, 6756661, 1695450, 3561478, 2788678, 8319759, 1510251, 2337707, 528800, 3685714, 3879827, 1200795, 1104858, 5053594, 3931505, 4914525, 2717995, 2529614, 315125, 5641426, 6028516, 570013, 1696373, 4484677, 1285991, 1637224, 4500393, 3762399, 1410197, 3001875, 7307829, 3347405, 6823890, 5826209, 3000752, 2089494, 1896508, 1401788, 7960903, 5556290, 2020378, 5635088, 3432287, 5595321, 5577518, 2944611, 1623173, 1793647, 3498838, 7469718, 4045380, 4629346, 2683517, 790724, 4659817, 5778432, 4661588, 2254904, 6462906, 5233226, 3337730, 6527731, 2781262, 5731186, 6350654, 2485933, 5376945, 4419057, 846702, 6533115, 3579420, 2342898, 587953, 8138041, 8032078, 3078068, 1067586, 4406355, 6949698, 6967603, 308195, 5177076, 3933068, 5077730, 7685517, 3714665, 2986435, 1315337, 2699819, 5310962, 189758, 6744849, 6773281, 1115597, 3819264, 3077323, 7354116, 2283575, 1170076, 3869631, 5677829, 4399059, 2031922, 1218108, 5821288, 3926416, 4764401, 7018327, 5785718, 7819319, 6777266, 4102382, 5242905, 2055587, 8136576, 2720927, 2926958, 4395652, 4549232, 888111, 5671653, 257320],
[7491859, 8088505, 1665651, 3891088, 4063580, 4132058, 6543527, 2638803, 1773535, 1148810, 699174, 1076699, 709915, 6277404, 36639, 7449039, 2273951, 1929814, 6213553, 4332948, 3506625, 6810896, 326774, 6265881, 7116137, 3892893, 7474035, 1538437, 7450570, 1523099, 2455904, 3502584, 6394681, 7377197, 3012741, 6434932, 7725116, 3253611, 4736759, 6173971, 3349133, 1025992, 7224926, 5806128, 2376108, 8301402, 3920784, 6436236, 3304777, 3688454, 3250348, 3356623, 3822065, 1126519, 7309887, 1359258, 6496710, 7909561, 19274, 1556592, 7112048, 3215440, 7275370, 8129218, 6664220, 4701960, 2075196, 1046788, 6544078, 2995295, 5090244, 2634948, 4370079, 1148536, 1389915, 3021780, 7196594, 2179952, 6861706, 4028513, 7485354, 4266242, 5791389, 697462, 1951250, 4237964, 6410808, 5455525, 6717162, 2192273, 1836977, 5130763, 6717728, 5049768, 5942723, 1306317, 4544924, 5030292, 5345258, 7121075, 4721625, 1565965, 4117014, 2830749, 7107187, 4848216, 6918495, 3751237, 5091367, 4698270, 2254704, 6292895, 7583140, 4004953, 2481785, 3379541, 2433271, 6865801, 3105539, 2221740, 1999730, 4322106, 7399281, 2641175, 1639393, 1516896, 3729957, 1943686, 1540973, 2831577, 2001623, 2612206, 2939829, 7976849, 3358274, 303588, 3941997, 5836041, 6210767, 3142928, 1080540, 2486699, 7163866, 411210, 3826143, 3146979, 5194887, 7557465, 864196, 80923, 3195099, 4006305, 1113924, 1590136, 4393074, 7093319, 3611143, 2794130, 2586998, 7416999, 3936166, 2619601, 2740687, 1139634, 4634100, 7161687, 614731, 7057330, 4670493, 3583923, 233790, 329505, 5482756, 2169254, 4895047, 7761774, 7526046, 5921397, 6229959, 1526016, 5452387, 2940702, 551851, 3611522, 1800813, 2670204, 883166, 1222575, 800075, 2481457, 311472, 4177981, 7225104, 3776588, 2453912, 885446, 1032344, 184908, 8241345, 8220674, 3474149, 1505366, 7653176, 1049546, 6340670, 443723, 6026904, 268467, 6885125, 6578472, 2853006, 1906590, 1252177, 2478651, 8242234, 5532950, 7538236, 4926338, 1058326, 4791909, 4500516, 1731481, 4130254, 1589872, 5725072, 6659309, 4260306, 5650064, 6885632, 1752696, 5341951, 5701597, 5049760, 2798248, 6884609, 5795927, 2400998, 2509239, 7532867, 2006346, 2018049, 6193174, 5385053, 2620480, 1338235, 446838, 2128030, 4510721, 4134538, 4947976, 43716, 3104359, 5991899, 3931231, 3897220, 6338002],
[6216886, 2405060, 3403288, 8161322, 4098055, 917281, 2735971, 7054374, 627751, 8086504, 5581260, 631281, 1546330, 8146555, 4331626, 2747973, 2956509, 255375, 952974, 950284, 3308606, 666252, 1538727, 3839996, 356688, 5199160, 2855363, 4501670, 6809875, 5820687, 3432443, 1931376, 3270153, 40897, 8264005, 3324511, 7487743, 6567200, 3407654, 7382051, 7281015, 6490602, 2096442, 4738540, 263919, 373226, 739345, 1141887, 1690499, 5239053, 2929435, 981145, 7384833, 63523, 6921288, 6819043, 8240992, 5329917, 4310078, 2252434, 4892231, 6309731, 1770582, 3647778, 7618314, 7967251, 5044061, 2697238, 5595495, 5111358, 7683864, 6877814, 394790, 7224055, 3877093, 1417556, 5707694, 2959097, 808178, 3111775, 1767872, 4147781, 7451209, 4137490, 5297085, 6472378, 260958, 6353923, 4664515, 5588480, 6780489, 5952138, 554320, 2065970, 3611974, 5341100, 4927619, 6395411, 6343293, 2888666, 3511757, 1706305, 2920293, 5626485, 851558, 1650525, 7664558, 3569024, 2403856, 1984553, 143758, 1834270, 101220, 5021450, 116692, 5705920, 6931456, 5708000, 5047495, 2600641, 8272944, 4941936, 1479127, 7781944, 4743936, 3619484, 7077123, 5002063, 7474362, 5910614, 6740512, 2447311, 5093217, 2965187, 6895676, 1497105, 4456170, 160222, 3465211, 7751382, 6708867, 7024336, 7386154, 6033897, 2441325, 3005181, 1266164, 801797, 3293259, 2632243, 2068250, 6749229, 3570484, 7078932, 3675227, 7848328, 1951637, 4916159, 698185, 14792, 2234800, 4951038, 5888981, 634394, 5369336, 7205485, 7208516, 4398094, 315549, 5704115, 6293437, 1506657, 919383, 3715574, 7828323, 625261, 7717275, 2878366, 3230016, 562150, 1135564, 6871077, 420001, 6464379, 5472866, 7344337, 7347705, 6852384, 2606061, 6778269, 4306415, 2768960, 4223981, 2641863, 1108574, 3376710, 6493425, 8177430, 6112303, 6271170, 6829167, 1064530, 3246044, 1672185, 5868703, 4844165, 5090898, 8309740, 6836468, 2844247, 8378903, 4357096, 7630425, 5318459, 2371386, 5891188, 7240927, 2970862, 6701416, 426792, 3556170, 4997684, 4718174, 2289876, 146122, 2919148, 1506694, 5886202, 6414814, 5705196, 5632004, 7661726, 406106, 5966867, 1726047, 1478895, 7970822, 4160507, 3262281, 62706, 836973, 1330813, 710347, 4605368, 2844889, 1016221, 1932543, 6596460, 446484, 6078550, 7653721, 4072152, 3677183, 243049, 3223499, 5197311],
[6269526, 8057920, 5786623, 2493366, 548545, 8304627, 7127876, 6076101, 4425259, 2552036, 7516157, 5957264, 8251829, 2587065, 601141, 3261735, 4861825, 3552203, 6776872, 4460376, 7148219, 4676869, 5963663, 449276, 113158, 8268909, 5414068, 6004263, 130218, 71136, 1569921, 1967970, 3357208, 926224, 5704413, 5404187, 350783, 8065613, 4595441, 4227610, 1964413, 6235882, 5259539, 4620135, 5718800, 6097934, 2646342, 5526429, 6351173, 2121552, 407958, 7045206, 1311448, 7119674, 1485370, 8196225, 5630666, 4880780, 7775827, 2174636, 7722471, 4782481, 6568445, 5993144, 90000, 2266106, 3297701, 2876647, 3398479, 8070401, 2646103, 1329937, 2036019, 2029452, 7614420, 6021323, 488671, 2935075, 8264371, 6449573, 6838862, 1097062, 4871385, 7861921, 6585189, 87675, 7690677, 391684, 1012071, 4643995, 3834147, 4716172, 2120970, 1345976, 4894499, 169279, 7945921, 3936360, 5045247, 3908256, 7436570, 4443121, 7803787, 2471444, 3965338, 3758546, 1549270, 528494, 4222452, 1513227, 8365822, 4448104, 7834879, 6328623, 7202213, 109166, 1403598, 7691254, 6666294, 517392, 6260255, 7552206, 7607830, 3483251, 5451265, 1847388, 5542268, 2703943, 2896114, 1416565, 2531075, 6005139, 2647318, 363965, 3244583, 729433, 6038514, 3745866, 2137177, 8082086, 4675045, 3059706, 7152838, 5052067, 4054544, 2227679, 2167726, 6543090, 3886645, 2529097, 2189737, 4413902, 2702970, 5385810, 921969, 3020916, 6656460, 3738753, 6690408, 113526, 3299888, 982656, 3306363, 6841889, 3422719, 1824469, 856298, 3583562, 4466135, 1105878, 4153378, 5805380, 881284, 7124752, 1546339, 4253648, 2571147, 1173174, 4598963, 8341517, 4156159, 1026146, 5833095, 2103501, 982329, 1204193, 6347094, 2554560, 1582809, 5416617, 2687340, 5571444, 6120480, 6682352, 699160, 5486787, 6327175, 6432833, 3034600, 5935394, 3886622, 6733964, 813956, 2822441, 3229144, 6939406, 5308497, 3877092, 4474784, 5302205, 8309034, 3806299, 2080168, 7791564, 5869887, 266961, 1801378, 5942700, 5513187, 4060683, 4969341, 2775197, 7768188, 4937000, 1392562, 4993304, 7840416, 6802924, 146389, 1213093, 6155095, 6195530, 4922817, 8299183, 3334645, 4952149, 1069038, 2370588, 3256058, 6599755, 6942030, 74733, 1170868, 4593152, 3710091, 8145951, 701253, 698090, 6518555, 4729617, 4656656, 7932868, 5100815, 739066, 4940511, 1423593],
[6314287, 3841955, 4102893, 5821702, 3799001, 3674829, 7100631, 689339, 505173, 6775021, 1425053, 6867604, 8046729, 3317650, 1510462, 5218978, 5680810, 2061345, 1675624, 5278206, 215174, 4606925, 2203207, 3226035, 2467730, 1593062, 204839, 7863754, 5070198, 3054846, 1793988, 3378866, 2844145, 1094007, 3758107, 3155169, 924828, 8075598, 1773896, 929549, 1679324, 612338, 3780972, 3860253, 5505689, 7136419, 4929172, 841778, 5518366, 3805596, 8092731, 5169669, 6566867, 6449998, 6892744, 4547184, 2295004, 3483812, 171722, 3676128, 4893598, 3101880, 5856315, 4110195, 4493837, 4475529, 5311845, 6562685, 5726126, 2900517, 4481003, 6925068, 500005, 3009299, 1892731, 5437822, 6381495, 36580, 1423067, 7269813, 5465176, 6113280, 6089313, 4604890, 2240224, 6250063, 6846960, 1643923, 2176837, 1110858, 6555038, 1910395, 5638029, 2790732, 5455550, 7619386, 7499475, 1977925, 4316647, 2936273, 7743936, 6401909, 2826670, 4415503, 4189398, 4451701, 6295100, 4591718, 6996702, 3869546, 7825290, 6338387, 3217992, 3990904, 4255212, 3783358, 3931445, 4763593, 3517987, 3462722, 3857288, 2418742, 8024390, 628340, 1387100, 5757946, 4883838, 7079907, 4438949, 4379095, 1897461, 1914349, 7170333, 2259893, 1011705, 656999, 7214264, 3011852, 3201616, 5011651, 6115934, 6784933, 6010770, 314194, 1679979, 1312000, 7322972, 4234380, 870070, 4078977, 2485820, 4369716, 5566593, 5308917, 3237015, 7034399, 5838560, 3299714, 5710835, 4981705, 3026384, 7258302, 6261156, 1707229, 2966021, 8236532, 752990, 4462980, 4426856, 6067850, 4473994, 4086147, 3788809, 7118454, 7452765, 2778045, 252265, 5903488, 6965884, 5416466, 2638527, 5827343, 3458086, 1454216, 2751283, 2562038, 3712350, 3610472, 6065020, 4643890, 6165431, 3664724, 867243, 3308507, 3093833, 53242, 2880667, 3127687, 1370437, 3587554, 553964, 2972771, 6134809, 3737362, 8073405, 4383860, 3988139, 8185052, 3319285, 83478, 5077822, 1199785, 2179322, 4043456, 6160350, 5220915, 3826891, 2145632, 6121010, 1417933, 1571153, 6757924, 2975544, 3206630, 520072, 355744, 5835031, 5613524, 4770650, 5054086, 2595791, 2226896, 2212099, 4735366, 3417204, 6156485, 7881255, 5271940, 1589593, 5900149, 2511519, 8340583, 3678092, 7220426, 4583947, 8377720, 6730428, 3471863, 4247049, 8335553, 405145, 5179220, 6420846, 2802060, 7733815, 752622],
[2158890, 3906430, 4560810, 2532163, 8255397, 940635, 5450255, 4222428, 8306388, 516275, 2439887, 5598621, 7434351, 2953931, 7666484, 1791634, 2046337, 5397626, 5809988, 1115784, 4715891, 3020655, 7119158, 1914008, 4850218, 3424580, 1649813, 3800900, 6149572, 7295344, 2038866, 7228073, 8278933, 283807, 418024, 763921, 1901720, 15545, 3853288, 1245376, 52641, 3360248, 3431269, 2579689, 8039825, 5203766, 2551547, 4626119, 4686654, 5139942, 2890940, 3896588, 6039751, 6714698, 4097540, 2885195, 2114873, 728045, 5268965, 4385543, 1149574, 1887609, 5669685, 7533183, 2159858, 3741115, 5997454, 7032585, 7100032, 3197835, 2004060, 52420, 6400200, 4884930, 3101496, 6299012, 330766, 780038, 242503, 8296008, 8341381, 6787038, 5823993, 496014, 6338310, 5017516, 4104677, 6152969, 4645602, 6482986, 5027856, 6510252, 3064093, 5292560, 4913587, 1666974, 7684462, 7272151, 171699, 145186, 5569024, 7157817, 355412, 1617166, 158170, 5297423, 5649104, 349745, 3820939, 2310697, 3257777, 6796548, 5481732, 6346081, 350866, 4176191, 130824, 6480210, 7043701, 6942140, 7972996, 7576396, 1969887, 2192495, 2257476, 4102319, 4135970, 859439, 6146991, 2398496, 3923173, 457578, 7795525, 8182119, 6423270, 52570, 5590315, 6316566, 351218, 1696691, 5683987, 139461, 2880332, 8117175, 5444730, 3754643, 3520906, 2385541, 1128974, 2129195, 4033619, 2183503, 5286422, 5948611, 4536111, 8049146, 3480453, 3753440, 4084792, 1530235, 5166916, 3210201, 5301482, 4770470, 5877448, 509329, 1903416, 5549442, 6264411, 6476580, 6414661, 809266, 2108102, 2070477, 7029147, 5641472, 6057109, 932436, 839408, 1435622, 2658311, 4592974, 5604019, 3317839, 8220375, 6913903, 2281646, 6315005, 3488809, 8380077, 5758692, 2683089, 3043125, 2710173, 6197364, 590857, 4243376, 2713454, 8165514, 2592653, 3464149, 1931517, 1302033, 8038188, 3612111, 5783089, 3080353, 7565420, 1206069, 129611, 262305, 1686993, 3890910, 4568917, 7838469, 7925989, 4699117, 1535742, 8202194, 7444390, 1336009, 3074702, 2564883, 883678, 2648394, 1631900, 7002464, 4093586, 4977640, 5061051, 8235391, 1708016, 4445472, 1198984, 5418024, 998737, 6691385, 1584140, 4575229, 3418445, 6639511, 5325450, 490270, 4395632, 5797171, 5399003, 988824, 770592, 7427422, 7101561, 5986873, 7627960, 485417, 7763432, 106250, 3988890]]

w1: [[3, 6, 3, 9, 10, 1, 4, 4, 14, 13, 14, 7, 14, 4, 5, 4, 15, 1, 11, 12, 4, 15, 11, 13, 2, 0, 11, 0, 1, 5, 7, 11, 8, 7, 12, 5, 2, 9, 1, 3, 2, 8, 9, 12, 12, 12, 13, 12, 1, 7, 6, 8, 11, 9, 10, 6, 9, 15, 9, 3, 6, 10, 10, 14, 2, 0, 0, 9, 3, 14, 0, 14, 15, 3, 7, 2, 13, 0, 3, 2, 13, 8, 10, 9, 3, 11, 15, 13, 12, 1, 12, 5, 11, 14, 12, 14, 5, 8, 8, 1, 15, 4, 13, 12, 8, 12, 8, 7, 15, 14, 15, 5, 12, 9, 7, 8, 4, 7, 5, 6, 14, 13, 12, 12, 9, 14, 9, 1, 8, 6, 10, 9, 1, 10, 13, 13, 3, 7, 5, 0, 3, 4, 1, 7, 7, 2, 2, 10, 8, 9, 5, 5, 1, 11, 12, 1, 3, 9, 2, 3, 9, 7, 3, 6, 14, 6, 13, 11, 6, 4, 4, 3, 15, 11, 4, 11, 7, 11, 11, 6, 3, 3, 7, 14, 8, 9, 5, 2, 9, 11, 9, 4, 12, 10, 6, 12, 5, 11, 12, 5, 10, 8, 2, 12, 7, 4, 1, 0, 15, 6, 2, 8, 13, 13, 1, 10, 8, 10, 15, 7, 6, 3, 5, 10, 0, 13, 13, 2, 7, 6, 14, 4, 2, 7, 11, 8, 4, 2, 11, 7, 9, 13, 11, 15, 13, 8, 10, 4, 0, 5, 6, 8, 9, 2, 11, 0],
[14, 15, 3, 7, 8, 8, 12, 5, 3, 2, 1, 2, 1, 12, 0, 14, 4, 4, 12, 8, 7, 13, 1, 12, 14, 7, 14, 3, 14, 3, 5, 7, 12, 14, 6, 12, 15, 6, 9, 12, 6, 2, 14, 11, 5, 0, 7, 12, 6, 7, 6, 6, 7, 2, 14, 3, 12, 15, 0, 3, 14, 6, 14, 0, 13, 9, 4, 2, 12, 6, 10, 5, 8, 2, 3, 6, 14, 4, 13, 8, 14, 8, 11, 1, 4, 8, 12, 10, 13, 4, 4, 10, 13, 10, 11, 2, 9, 10, 10, 14, 9, 3, 8, 5, 14, 9, 13, 7, 10, 9, 4, 12, 14, 8, 5, 6, 5, 13, 6, 4, 4, 8, 14, 5, 3, 3, 7, 4, 3, 5, 4, 5, 6, 15, 6, 1, 8, 11, 12, 6, 2, 5, 14, 1, 7, 6, 10, 14, 2, 0, 6, 8, 2, 3, 8, 14, 7, 5, 5, 14, 8, 5, 5, 2, 9, 14, 1, 13, 9, 7, 0, 1, 10, 4, 9, 15, 14, 11, 12, 3, 10, 6, 1, 7, 3, 5, 2, 2, 2, 5, 1, 8, 14, 7, 5, 2, 2, 0, 0, 0, 7, 3, 15, 2, 12, 1, 12, 1, 13, 13, 5, 4, 2, 5, 0, 11, 14, 9, 2, 9, 9, 3, 8, 3, 11, 13, 8, 11, 13, 3, 10, 11, 10, 5, 13, 11, 5, 5, 14, 4, 4, 12, 10, 5, 3, 1, 4, 9, 8, 9, 0, 6, 11, 8, 7, 12],
[12, 5, 6, 0, 8, 2, 5, 13, 1, 15, 11, 1, 3, 0, 8, 5, 6, 0, 2, 2, 6, 1, 3, 7, 1, 10, 5, 9, 13, 11, 7, 4, 6, 0, 0, 6, 14, 13, 7, 14, 14, 12, 4, 9, 1, 1, 1, 2, 3, 10, 6, 2, 14, 0, 13, 13, 0, 10, 8, 4, 9, 12, 3, 7, 15, 15, 10, 5, 11, 10, 15, 13, 1, 14, 7, 3, 11, 6, 2, 6, 3, 8, 14, 8, 10, 12, 0, 12, 9, 11, 13, 11, 1, 4, 7, 10, 9, 12, 12, 6, 7, 3, 6, 11, 2, 3, 15, 7, 5, 4, 0, 4, 0, 10, 0, 11, 13, 11, 10, 5, 0, 9, 3, 15, 9, 7, 14, 10, 14, 11, 13, 5, 10, 6, 13, 3, 9, 0, 7, 15, 13, 13, 14, 12, 5, 6, 2, 2, 6, 5, 4, 13, 7, 14, 7, 15, 4, 9, 1, 0, 4, 9, 11, 1, 10, 14, 14, 8, 1, 11, 12, 3, 2, 7, 15, 1, 15, 5, 6, 1, 2, 13, 1, 12, 10, 14, 14, 13, 5, 13, 8, 5, 8, 5, 2, 6, 12, 0, 12, 12, 13, 2, 6, 3, 11, 9, 10, 0, 13, 5, 0, 8, 15, 10, 5, 11, 14, 6, 13, 1, 7, 10, 9, 4, 0, 6, 3, 11, 12, 11, 11, 15, 1, 11, 3, 3, 15, 8, 6, 0, 2, 3, 1, 9, 5, 2, 4, 13, 1, 12, 15, 8, 7, 0, 6, 10],
[12, 15, 11, 5, 1, 0, 14, 12, 8, 5, 14, 11, 0, 5, 1, 6, 9, 7, 13, 9, 14, 9, 11, 1, 0, 0, 10, 11, 0, 0, 3, 4, 6, 2, 11, 10, 1, 15, 9, 8, 4, 12, 10, 9, 11, 12, 5, 11, 12, 4, 1, 13, 3, 14, 3, 0, 11, 9, 15, 4, 15, 9, 13, 11, 0, 4, 6, 5, 6, 15, 5, 3, 4, 4, 15, 11, 1, 6, 0, 12, 13, 2, 9, 15, 13, 0, 15, 1, 2, 9, 7, 9, 4, 3, 9, 0, 15, 8, 10, 7, 14, 8, 15, 5, 8, 7, 3, 1, 8, 3, 0, 8, 15, 12, 14, 0, 3, 15, 13, 1, 12, 14, 15, 7, 10, 4, 11, 5, 6, 3, 5, 11, 5, 1, 6, 1, 12, 7, 4, 15, 9, 6, 14, 10, 8, 4, 4, 12, 7, 5, 4, 8, 5, 10, 2, 6, 13, 7, 13, 0, 6, 2, 6, 13, 7, 3, 2, 7, 9, 2, 8, 11, 2, 14, 3, 8, 5, 2, 9, 0, 8, 2, 11, 4, 2, 2, 12, 5, 3, 10, 5, 11, 12, 13, 1, 10, 12, 12, 6, 11, 7, 13, 2, 5, 6, 13, 10, 7, 9, 10, 0, 7, 4, 15, 11, 1, 3, 11, 11, 8, 9, 5, 15, 9, 3, 10, 15, 13, 0, 2, 12, 12, 9, 0, 6, 9, 2, 5, 6, 13, 13, 0, 2, 9, 7, 0, 1, 1, 12, 9, 9, 15, 10, 1, 9, 3],
[12, 7, 8, 11, 7, 7, 14, 1, 1, 13, 3, 13, 15, 6, 3, 10, 11, 4, 3, 10, 0, 9, 4, 6, 5, 3, 0, 15, 10, 6, 3, 6, 5, 2, 7, 6, 2, 15, 3, 2, 3, 1, 7, 7, 11, 14, 9, 2, 11, 7, 15, 10, 13, 12, 13, 9, 4, 7, 0, 7, 9, 6, 11, 8, 9, 9, 10, 13, 11, 6, 9, 13, 1, 6, 4, 10, 12, 0, 3, 14, 10, 12, 12, 9, 4, 12, 13, 3, 4, 2, 13, 4, 11, 5, 10, 15, 14, 4, 8, 6, 15, 12, 5, 8, 8, 8, 12, 9, 13, 7, 15, 12, 6, 8, 8, 7, 8, 9, 7, 7, 7, 5, 15, 1, 3, 11, 9, 14, 8, 8, 4, 4, 14, 4, 2, 1, 14, 6, 6, 10, 12, 13, 11, 1, 3, 3, 14, 8, 2, 8, 5, 8, 11, 10, 6, 13, 11, 6, 11, 10, 6, 14, 12, 3, 6, 0, 1, 9, 8, 12, 9, 8, 7, 14, 14, 5, 0, 11, 13, 10, 5, 11, 7, 3, 5, 5, 7, 7, 12, 9, 12, 7, 2, 6, 6, 0, 5, 6, 3, 7, 1, 6, 12, 7, 15, 8, 8, 0, 6, 0, 10, 2, 4, 8, 12, 10, 7, 4, 12, 3, 3, 13, 6, 6, 1, 1, 11, 11, 9, 10, 5, 4, 4, 9, 7, 12, 15, 10, 3, 11, 5, 0, 7, 14, 9, 0, 13, 7, 8, 0, 1, 10, 12, 5, 15, 1],
[4, 7, 9, 5, 0, 2, 10, 8, 0, 1, 5, 11, 14, 6, 15, 3, 4, 10, 11, 2, 9, 6, 14, 4, 9, 7, 3, 7, 12, 14, 4, 14, 0, 1, 1, 1, 4, 0, 7, 2, 0, 6, 7, 5, 15, 10, 5, 9, 9, 10, 6, 7, 12, 13, 8, 6, 4, 1, 10, 8, 2, 4, 11, 14, 4, 7, 11, 13, 14, 6, 4, 0, 12, 9, 6, 12, 1, 1, 0, 0, 0, 13, 11, 1, 12, 10, 8, 12, 9, 12, 10, 12, 6, 10, 9, 3, 15, 14, 0, 0, 11, 14, 1, 3, 0, 10, 11, 1, 7, 4, 6, 13, 10, 12, 1, 8, 0, 12, 13, 13, 15, 14, 4, 4, 4, 8, 8, 2, 12, 5, 7, 1, 15, 0, 12, 0, 11, 12, 1, 3, 11, 0, 5, 15, 10, 7, 7, 5, 2, 4, 8, 4, 10, 11, 9, 15, 7, 7, 8, 3, 10, 6, 10, 9, 11, 1, 4, 11, 12, 12, 12, 2, 4, 4, 13, 11, 12, 2, 2, 3, 5, 9, 11, 6, 0, 13, 4, 12, 7, 0, 11, 5, 6, 5, 12, 1, 8, 5, 0, 5, 7, 4, 2, 15, 7, 11, 6, 14, 2, 0, 1, 3, 7, 9, 15, 15, 9, 3, 0, 14, 3, 6, 5, 2, 5, 3, 13, 8, 10, 10, 0, 3, 8, 2, 10, 2, 13, 3, 9, 7, 13, 10, 1, 8, 11, 10, 2, 1, 14, 14, 11, 15, 1, 15, 0, 8]]
w1Encode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

cTilde: 4C5CB1C3B116E450C025233F1B6BE3BB79385FBF9626D6F27958FC529590ADC03C1B9F58675DCE1F24CBFC85443F31DE
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
c: [-1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, -1, 0, 0]
cHat: [5998204, 1033172, 4358473, 231018, 7119592, 4447599, 4459583, 3619279, 2165424, 6960342, 3508718, 4945897, 3751115, 556163, 3118658, 167655, 1690162, 5421749, 6704858, 4505899, 5648135, 6100757, 7158964, 6449354, 7456006, 6276301, 5592689, 8124092, 7473854, 5928963, 6428402, 3416474, 3586758, 2906690, 2563163, 4908248, 6508015, 7274901, 5033057, 887041, 7502267, 3833384, 4017436, 4173610, 635289, 5579380, 7267277, 3297587, 4607311, 295869, 3450093, 4154344, 3595004, 3183328, 4095403, 5356675, 4342996, 1701231, 2992268, 1410821, 298057, 2247920, 1433694, 4160860, 1227715, 1322180, 5546585, 18493, 2808790, 2799639, 5434285, 5710032, 4454142, 7567190, 8010268, 5843171, 1592022, 1699734, 3237332, 3862337, 4982052, 2121501, 538464, 1333840, 7502060, 6213805, 3386337, 3471433, 3723987, 3854106, 4649157, 7902552, 4692979, 3476667, 8271805, 4506795, 1503777, 3059605, 2096843, 7514191, 3377083, 7746890, 2988833, 7907207, 7449115, 3822676, 2348932, 1766084, 3817239, 6257654, 5936999, 3494379, 4052208, 48111, 2580456, 8323362, 5327957, 1532194, 1980559, 1353151, 409062, 2984494, 3675856, 4259398, 6524755, 751008, 6116518, 2378538, 6607598, 5696424, 1933202, 8176839, 5452864, 8283513, 3675093, 4232403, 1541223, 6333345, 5232171, 5323950, 5895466, 5261828, 5162143, 2579982, 7626622, 519163, 5505938, 6432582, 4951035, 1710770, 6735491, 2701184, 8255361, 102117, 2123535, 213845, 1040804, 151410, 5134042, 1688874, 5646642, 4874510, 5316025, 3618141, 2867587, 1428371, 1571326, 656545, 6734720, 242064, 4528668, 791863, 1245688, 6719045, 6715944, 1035643, 6530456, 6811242, 6182126, 2726193, 960793, 6387292, 7868790, 1306410, 8375319, 3880501, 452780, 2856450, 1737896, 3557991, 2597973, 3290893, 4206444, 1628906, 5011895, 2282119, 1943375, 5972552, 324958, 7571617, 6267101, 8346624, 1325184, 3583804, 5535809, 834705, 691330, 4629156, 4656748, 7525698, 5642234, 8378672, 1434589, 3399999, 2369752, 165304, 969968, 4815075, 219511, 5537548, 1647845, 2960053, 3471556, 4136606, 1958105, 816707, 730074, 8032673, 2772018, 4895806, 41885, 1685487, 2165109, 7418246, 8240552, 7885508, 7761781, 2216858, 5651524, 120286, 5702522, 7365345, 7279963, 2847086, 2835528, 825200, 7190002, 4847480, 2860462, 26486, 1936002, 2345379, 363091, 7930352, 7572394, 1543149]
cs1: [[8380379, 16, 8380416, 8380412, 8380388, 28, 8380406, 8380405, 11, 13, 8380398, 47, 3, 8380415, 8380406, 8380409, 8380403, 8380398, 8380385, 8380415, 7, 5, 9, 8380401, 8380397, 8380407, 8380412, 8380399, 2, 30, 8380406, 8380410, 17, 8380399, 8380396, 0, 4, 44, 8380405, 21, 8380404, 8380411, 8380396, 10, 8380408, 11, 32, 8380415, 8380407, 8380395, 8380414, 9, 8380406, 15, 14, 8380394, 29, 8380394, 16, 8380410, 11, 0, 8380400, 8380412, 8380416, 8380410, 4, 7, 8380410, 5, 25, 8380403, 8380406, 10, 8, 8380386, 24, 28, 8380412, 6, 18, 3, 22, 5, 12, 8380397, 2, 2, 8380412, 8380413, 8380398, 8380410, 19, 8, 3, 9, 24, 8380413, 6, 8380380, 12, 8380415, 18, 8380393, 42, 31, 8380416, 8380394, 8380414, 8380385, 19, 8380414, 8380403, 11, 5, 8380415, 8380415, 27, 1, 8380409, 8380402, 8380410, 13, 9, 8380406, 8380414, 8380384, 2, 21, 8380412, 8380406, 8380414, 6, 8380393, 8380405, 8380412, 8380411, 8380414, 8380412, 2, 42, 2, 8380395, 8380395, 17, 36, 8380402, 8380406, 8380414, 5, 8380415, 18, 8380409, 8380390, 8380396, 7, 8380403, 23, 8380383, 16, 17, 5, 7, 8, 8380409, 8380411, 8380398, 19, 5, 16, 8380415, 3, 8380416, 12, 8380396, 8380416, 8380408, 8380377, 8380392, 17, 4, 8, 4, 12, 29, 8380411, 8380396, 8380415, 8380392, 10, 8380412, 8380411, 3, 8380388, 2, 28, 9, 42, 8380410, 2, 8380379, 8380376, 8380403, 5, 8380383, 21, 19, 13, 35, 8380409, 8380416, 3, 31, 8380391, 8380414, 2, 8380402, 8380395, 5, 8380372, 8380414, 34, 5, 6, 26, 3, 7, 8380394, 8380387, 14, 4, 20, 2, 8380409, 3, 12, 12, 12, 8380397, 8380404, 8380412, 8380396, 8380411, 8380402, 6, 8380413, 4, 10, 24, 16, 8380400, 8380411, 8380402, 40, 11, 8380408],
[8380407, 8380402, 6, 3, 8380403, 29, 9, 3, 8380395, 16, 2, 21, 12, 8380381, 5, 9, 1, 8380406, 2, 8380407, 8380412, 1, 1, 8380411, 8380416, 8380407, 15, 28, 2, 3, 16, 0, 2, 26, 4, 8380411, 3, 14, 13, 19, 47, 8380388, 0, 16, 20, 8380409, 8380413, 8380405, 17, 8380400, 8380411, 8380412, 8380409, 8380401, 16, 8380400, 11, 8380401, 8380413, 8380394, 8380408, 12, 8380407, 2, 6, 8380392, 29, 2, 8380399, 8380402, 8380411, 7, 8380403, 21, 10, 6, 0, 8380407, 8380411, 18, 8380412, 27, 1, 13, 14, 16, 35, 11, 22, 14, 8380400, 18, 3, 8380405, 15, 15, 8380407, 9, 20, 21, 8380410, 8380385, 1, 8380387, 8380407, 8380409, 8380384, 13, 2, 8380392, 8, 1, 8380386, 16, 8380369, 12, 8380372, 8380382, 32, 3, 8380412, 3, 8380409, 8380416, 7, 8380410, 32, 8380394, 10, 5, 33, 38, 8380406, 7, 38, 7, 23, 17, 8380405, 35, 8380399, 12, 23, 8380412, 8380387, 31, 5, 9, 8380402, 14, 8380411, 8380399, 8380405, 1, 13, 17, 8380414, 8380405, 2, 8380412, 8380405, 9, 8380402, 8380406, 1, 8380410, 8380406, 8380397, 8380381, 8380414, 4, 8380391, 21, 33, 8380401, 9, 6, 8380407, 3, 8380396, 8, 8380413, 8380416, 27, 27, 13, 6, 20, 23, 22, 8380390, 8380410, 8380408, 8380414, 21, 8380413, 11, 11, 8380406, 30, 20, 8380416, 6, 8380393, 8380403, 11, 14, 3, 8380406, 8380397, 9, 8380398, 7, 8380415, 8380387, 8380402, 8380411, 24, 20, 4, 8380381, 26, 8380414, 8380405, 8380409, 8380402, 8380404, 3, 8380410, 22, 8380416, 8380401, 18, 2, 8, 8380393, 8380388, 4, 1, 8380399, 39, 8380386, 4, 4, 1, 27, 11, 8380395, 18, 8380411, 15, 12, 8380405, 2, 10, 8380399],
[36, 8380401, 10, 8380395, 8380415, 9, 15, 8380397, 4, 13, 8380411, 16, 38, 8380415, 21, 21, 8380414, 18, 8380385, 15, 8380403, 21, 11, 30, 8380409, 8380414, 8380395, 11, 8380381, 8380380, 8380404, 8380393, 3, 12, 8380399, 9, 8380410, 8380408, 23, 8380412, 15, 8380375, 10, 33, 8380391, 8380400, 8380393, 8380404, 8380402, 8380411, 8380397, 8380412, 8380397, 9, 8380416, 8380401, 5, 22, 14, 25, 23, 11, 10, 38, 49, 35, 12, 7, 26, 34, 8380395, 1, 5, 8380407, 24, 8380404, 8380408, 14, 8380374, 5, 8380387, 9, 36, 8380394, 15, 8380411, 8380383, 2, 8380409, 8380399, 46, 8380400, 8380388, 8380410, 8380354, 8380403, 8380403, 8380410, 11, 8380398, 8380407, 24, 8, 8, 1, 8380411, 8, 27, 32, 17, 8380408, 9, 8380413, 15, 28, 8380413, 6, 8380389, 8380415, 8380415, 1, 8380409, 8380409, 8380397, 18, 8380415, 45, 8380410, 27, 28, 34, 26, 19, 14, 2, 8380408, 8380399, 8380386, 8380390, 8380402, 8380389, 11, 8380416, 8380409, 8380412, 8380410, 8380413, 8380405, 8380411, 8380383, 8380411, 8380410, 25, 11, 8380416, 10, 30, 8380404, 18, 8380405, 8380382, 0, 0, 8380400, 8380402, 8380408, 15, 3, 8380403, 4, 4, 42, 15, 1, 36, 6, 15, 37, 1, 8380406, 0, 8380404, 6, 43, 8380391, 8380412, 8380377, 13, 8380414, 12, 7, 8380401, 8380415, 14, 8380413, 11, 8380409, 8380387, 30, 8, 13, 8380411, 8380392, 5, 8380391, 8380384, 8380412, 8380406, 8380412, 8380404, 8380410, 11, 8380398, 8380416, 8380391, 16, 11, 32, 8380414, 12, 8380403, 8, 9, 8380395, 3, 8380413, 6, 17, 11, 15, 8380376, 8380388, 8380411, 14, 8380410, 20, 8380415, 17, 3, 8380413, 34, 28, 33, 7, 8380411, 2, 21, 8380410, 11, 0, 3, 8380410, 8380406, 8380399, 8380408, 1],
[8380409, 9, 8380402, 8380414, 21, 4, 8380365, 23, 8380409, 7, 8380400, 0, 8380396, 8380409, 8380416, 17, 8380407, 8380403, 8380406, 8380400, 8380408, 8380413, 1, 31, 8380409, 14, 8, 10, 8380401, 0, 8380404, 8380410, 3, 1, 8380394, 24, 8380397, 16, 4, 8380409, 8380411, 8, 8380412, 8380413, 20, 13, 23, 8380390, 8380407, 15, 25, 8380402, 8380415, 16, 8380410, 16, 1, 3, 8380393, 13, 8380408, 9, 8380413, 12, 7, 8380414, 2, 8380412, 8380405, 7, 8380405, 8380402, 12, 4, 22, 8380370, 8380409, 8380392, 8380414, 8380397, 32, 0, 8380416, 8380399, 19, 8380404, 22, 8380411, 8, 8380399, 7, 0, 21, 8380405, 8380371, 20, 8380407, 17, 0, 8380392, 1, 20, 8380409, 8380397, 11, 8380380, 8380415, 8380402, 22, 7, 8380402, 6, 9, 8380406, 9, 8380404, 8380408, 8380399, 22, 8380397, 0, 1, 8, 8380416, 17, 8, 0, 8380411, 3, 13, 8380399, 8380405, 8380413, 8380413, 3, 8380403, 43, 15, 18, 18, 8380410, 8380404, 8380409, 8380395, 8380386, 8380411, 8380397, 18, 8, 17, 8380404, 4, 9, 11, 8380414, 8380393, 2, 8380396, 8380413, 0, 34, 17, 8380405, 36, 19, 11, 1, 8380386, 8380393, 7, 8380411, 8380397, 17, 22, 8380415, 22, 10, 8380411, 8380394, 8380415, 8380387, 4, 8380407, 18, 24, 15, 8380387, 15, 5, 5, 8380393, 8380405, 8380404, 1, 8380414, 8380408, 8380409, 9, 0, 8380409, 15, 8380414, 21, 8380395, 8380409, 8380412, 8380411, 8380403, 8380413, 8380376, 22, 31, 8380395, 2, 8380404, 24, 8380410, 3, 8380413, 8380402, 1, 20, 8380412, 15, 8380408, 23, 28, 8380416, 11, 12, 48, 8380407, 8380416, 8380409, 8380385, 8380410, 9, 8380413, 2, 8, 11, 8380414, 8380415, 8380398, 16, 8380410, 8380402, 3, 5, 10, 8380402, 17, 8380393, 12, 8380397, 8380390],
[1, 13, 8380413, 3, 8380406, 8380395, 33, 8380396, 4, 14, 2, 7, 8380411, 19, 40, 8380400, 15, 8380407, 17, 8380402, 8380404, 1, 8380376, 8380412, 4, 13, 5, 2, 8380401, 6, 12, 8380415, 8380404, 8380385, 2, 3, 25, 13, 2, 8380394, 17, 7, 1, 8380409, 8380416, 8380384, 3, 8380403, 12, 9, 4, 24, 8380412, 28, 8380385, 8380398, 8380413, 8380410, 3, 4, 8380403, 23, 8, 8380395, 0, 16, 3, 6, 8380411, 8380414, 4, 8380404, 8380395, 8380412, 8, 20, 11, 8380397, 10, 8380408, 3, 1, 10, 8380394, 8380410, 2, 8380416, 8380411, 8, 4, 8380410, 8380402, 8380403, 8380400, 8380398, 27, 8380385, 10, 3, 6, 8380407, 22, 8380389, 2, 8380415, 8380409, 11, 16, 8380387, 6, 4, 9, 20, 1, 8380408, 26, 8380416, 13, 6, 8380394, 8380415, 7, 9, 3, 8380399, 8380405, 0, 8380404, 8380396, 4, 8380380, 8380402, 8380416, 30, 8380401, 4, 8380375, 6, 8380403, 8380414, 3, 4, 8380398, 26, 16, 32, 28, 8380403, 4, 13, 8380402, 8380405, 29, 8380380, 16, 8380411, 13, 20, 8380404, 9, 11, 8380395, 3, 8380401, 8380407, 8, 8380410, 8380395, 10, 1, 16, 8380409, 8380410, 8380397, 6, 8380404, 8380414, 8380412, 8380397, 21, 1, 16, 8380396, 19, 8380415, 15, 8380406, 10, 8380391, 9, 0, 8380408, 12, 8380404, 16, 8380400, 14, 8380414, 8380408, 8380414, 8380402, 8380411, 17, 8380414, 21, 8380410, 8380393, 7, 20, 7, 12, 8380404, 8380416, 39, 2, 8380399, 8380412, 18, 8380410, 8380412, 8380408, 5, 11, 8380392, 8380413, 8380414, 12, 8380407, 8380407, 8380386, 46, 8380407, 19, 8380405, 11, 12, 34, 8380404, 8380413, 8380397, 23, 8380413, 13, 8380394, 8380412, 8380399, 8, 8380413, 8380415, 11, 8380407, 19, 11, 8380412, 11, 28]]
cs2: [[4, 3, 8380406, 31, 8380397, 22, 5, 8380403, 8380412, 8380397, 12, 19, 8380401, 8380405, 13, 8380396, 0, 9, 14, 8380401, 24, 15, 2, 8380412, 8380392, 16, 0, 8380400, 8380394, 34, 20, 8380406, 4, 8380402, 8380415, 8380402, 6, 3, 8380397, 8380415, 20, 8380407, 22, 8380402, 8380414, 34, 8380395, 8380408, 23, 13, 6, 8380408, 5, 2, 20, 8380408, 3, 0, 8380412, 1, 8380411, 5, 33, 8380400, 8380403, 28, 21, 8380396, 10, 8380411, 8380401, 8380414, 8380400, 8380415, 7, 6, 2, 24, 8380411, 12, 8380414, 8380411, 8380389, 8380392, 8380416, 22, 8380414, 7, 13, 14, 8380409, 3, 8380411, 6, 18, 8380412, 8380407, 8380407, 8380384, 48, 24, 8380410, 8380397, 8380398, 0, 8380407, 8380415, 2, 8380395, 8380391, 6, 9, 8380412, 3, 10, 8380406, 6, 15, 8380381, 17, 18, 8380385, 3, 20, 22, 8380413, 8380400, 8380394, 13, 8380413, 8380410, 20, 8, 0, 8380410, 4, 1, 8380380, 5, 12, 16, 8380413, 8380400, 8380416, 11, 8380410, 3, 8380397, 8380391, 15, 4, 6, 8380380, 8380412, 2, 30, 8, 8380407, 9, 11, 8380405, 8380407, 7, 4, 8380403, 9, 8380379, 4, 49, 8380397, 8380407, 1, 8380405, 0, 13, 8380390, 8380407, 8380414, 1, 22, 30, 20, 8380385, 8, 8380412, 8380381, 16, 7, 8380405, 8380416, 8380389, 8380410, 18, 8380371, 35, 8380403, 15, 8380390, 16, 8380379, 8380410, 8380401, 8380388, 10, 11, 19, 8380406, 8, 11, 8380415, 1, 8380380, 8380406, 8, 21, 16, 8380394, 8, 5, 0, 31, 8380400, 8380410, 31, 8380411, 8380413, 6, 8380390, 12, 8380411, 8380401, 10, 13, 8380413, 8380415, 8, 8380405, 8380411, 8380408, 11, 8380401, 8380397, 6, 27, 8380412, 19, 8, 8380398, 16, 8380416, 8380390, 20, 32, 8380403, 16, 9],
[8380408, 27, 8380398, 1, 8380411, 6, 8380406, 4, 1, 2, 8380399, 8380415, 8380410, 8380401, 38, 8380401, 8380411, 2, 5, 18, 12, 8380395, 24, 18, 8380403, 10, 8380403, 24, 8380395, 7, 8380415, 16, 12, 8380399, 8380416, 20, 8380397, 8380401, 38, 0, 8380409, 18, 23, 10, 0, 6, 33, 8380402, 8380390, 5, 8380402, 34, 8380397, 12, 11, 2, 13, 8380412, 8380413, 12, 8380406, 12, 8380413, 8380396, 8380414, 8380403, 8380412, 12, 14, 35, 24, 8380406, 28, 8380408, 8380401, 8380376, 8380407, 34, 8380406, 11, 20, 8380415, 24, 8380411, 8380415, 8380410, 8380400, 8380415, 8380412, 8380394, 8380412, 2, 2, 16, 8380410, 8380406, 25, 8380388, 1, 8380411, 9, 8, 24, 7, 14, 15, 27, 8380412, 10, 8380375, 13, 8, 8380409, 1, 8380411, 8380407, 8380415, 0, 8380395, 8380396, 8380409, 8380392, 8380400, 8380402, 8380414, 8380401, 17, 9, 27, 8380412, 2, 23, 8380391, 8380415, 9, 8380414, 15, 8380416, 8380407, 3, 8380409, 8380407, 8380414, 1, 12, 12, 4, 8380393, 8380406, 8380416, 8380388, 23, 12, 8380403, 18, 8, 8380411, 8380413, 28, 8380399, 19, 1, 22, 8380386, 8380416, 8380390, 8380410, 20, 3, 6, 37, 8380382, 8380408, 12, 6, 43, 8380410, 8380384, 13, 9, 1, 8380403, 13, 8380406, 8380376, 30, 8380416, 8380413, 8380412, 8380394, 16, 8380406, 8380411, 13, 8380409, 8380404, 20, 9, 0, 8380406, 8380405, 19, 8, 9, 8380398, 13, 8380407, 30, 8380397, 19, 8380389, 6, 8380414, 13, 8380400, 0, 7, 8380406, 8380402, 13, 9, 10, 6, 8380407, 28, 8380405, 1, 8380410, 8380400, 8380395, 8380407, 8380410, 8380404, 8380412, 16, 14, 8380413, 8380415, 8380391, 8380403, 8380400, 8380400, 8380396, 0, 5, 20, 8380402, 8380416, 8380405, 8380386, 8380416, 8380393, 8380414, 8380409, 5, 10],
[8380406, 8380385, 4, 20, 8380412, 8380411, 4, 8380411, 8380400, 4, 8, 8380374, 8380409, 8380415, 8380400, 8380392, 30, 16, 8380399, 42, 3, 2, 14, 8380387, 8380411, 17, 8380412, 13, 9, 16, 5, 19, 8380403, 9, 8380390, 8380402, 8380406, 8380409, 21, 8380383, 8380406, 14, 8380402, 7, 5, 19, 8380410, 23, 8, 8380403, 8380384, 27, 8380349, 25, 17, 13, 8380407, 8380399, 6, 12, 8380403, 38, 8380384, 8380388, 41, 8380388, 23, 1, 2, 37, 15, 0, 39, 8, 7, 8380407, 8380405, 8380414, 3, 8380390, 14, 8380405, 8380392, 8380411, 8380416, 8380398, 8380399, 8380401, 8380402, 8380413, 8380405, 8380414, 11, 15, 8380402, 1, 14, 8380402, 8380404, 15, 16, 8380400, 8380411, 8380391, 13, 8380395, 25, 8380384, 8380405, 8380409, 13, 8380412, 4, 8380412, 11, 29, 8380400, 8380410, 25, 3, 4, 8380396, 19, 10, 8380414, 16, 8380405, 1, 10, 8380406, 22, 8380407, 19, 8380402, 8380390, 14, 8380400, 8380386, 38, 8380403, 8380413, 24, 8380395, 8380388, 2, 8380396, 1, 8380391, 55, 8380380, 8380407, 8380409, 5, 8380406, 27, 8380414, 14, 26, 8380406, 8380409, 22, 8380407, 33, 8380411, 30, 25, 6, 23, 5, 8380406, 6, 8380400, 12, 8380412, 8380378, 9, 8380410, 13, 3, 35, 8380403, 6, 8380398, 20, 8380400, 8380390, 1, 8380410, 8380416, 6, 26, 8380381, 8, 0, 8380388, 17, 8380390, 8380412, 8380400, 19, 8380414, 8380379, 1, 33, 8380392, 8, 27, 30, 8380378, 40, 8380373, 25, 8380412, 9, 8380400, 8380411, 5, 8380400, 8380373, 4, 8380412, 17, 11, 7, 34, 5, 5, 8380402, 8380411, 13, 8380409, 8380411, 10, 1, 28, 8380414, 8380389, 28, 8380415, 22, 1, 8380409, 8380377, 12, 8380410, 17, 8380399, 14, 8380407, 1, 8380410, 26, 8380390, 1, 14, 8380415],
[8380411, 8380409, 32, 20, 6, 8380409, 8380409, 8380397, 25, 8380415, 8380400, 8380415, 42, 7, 8380396, 8, 33, 8380399, 8380411, 8380416, 1, 8380412, 8380413, 0, 8380386, 26, 13, 9, 8380391, 8380384, 8380411, 8380414, 32, 1, 6, 8380396, 8380399, 8380406, 8380407, 16, 19, 8380404, 15, 8380399, 8380414, 8380406, 8380400, 18, 8380415, 23, 27, 1, 0, 4, 4, 8380409, 8380399, 3, 5, 8380388, 8380398, 18, 8380380, 20, 8380406, 8380382, 19, 18, 8380391, 1, 8380395, 8380413, 7, 8380407, 13, 3, 12, 23, 8380403, 10, 8380409, 15, 8380405, 8380409, 8380403, 8380407, 8380400, 8380396, 19, 8380395, 12, 8380406, 8380403, 8380414, 8380390, 8380406, 16, 8380399, 8380377, 17, 8380405, 8380403, 6, 25, 8380406, 0, 21, 55, 19, 19, 8380405, 3, 14, 8380409, 8380414, 12, 8380409, 8380384, 5, 49, 8380415, 21, 4, 8380406, 8380389, 8380396, 8380397, 8380400, 8380390, 8380383, 8380413, 51, 8380387, 20, 18, 8380414, 8380396, 13, 8380409, 8380398, 22, 22, 25, 0, 8380403, 18, 4, 14, 12, 8380399, 8380411, 17, 8380402, 8380413, 28, 8380413, 8380407, 8380412, 8380414, 8380411, 34, 10, 8380406, 8380406, 30, 8380409, 8380398, 8380399, 8380414, 8380407, 19, 15, 8380412, 8, 8380408, 8380389, 30, 16, 18, 8380407, 8380395, 8380408, 8, 5, 8380398, 10, 32, 13, 8380414, 5, 8380386, 8380393, 9, 8380380, 8380405, 8380400, 22, 8380397, 8380413, 20, 8380414, 1, 8380393, 8380392, 8380412, 33, 8380414, 8380396, 4, 34, 44, 28, 28, 8380392, 8380405, 32, 8380403, 8380414, 10, 7, 8380388, 8380410, 18, 3, 8380408, 8380411, 8380414, 19, 8, 8380399, 8380397, 8380390, 8380389, 5, 8, 25, 8380402, 17, 8380411, 20, 8380416, 8380406, 16, 16, 8380406, 5, 6, 8380415, 8380413, 8380409, 30, 19, 14, 20, 8380411, 8380408],
[8380408, 8380404, 1, 18, 8380385, 19, 8380392, 8, 8380406, 9, 14, 2, 8380414, 19, 8380406, 8380407, 8380412, 1, 8380412, 14, 8380413, 5, 38, 8380412, 8380397, 13, 16, 0, 11, 8380402, 8380415, 39, 8380391, 2, 24, 21, 8380406, 15, 8380415, 12, 8380412, 8380399, 8380377, 27, 8380411, 8380416, 27, 8380400, 38, 8380410, 8380416, 18, 8380388, 0, 3, 2, 8380413, 8380394, 8380400, 8380415, 8380415, 8380411, 5, 8380416, 21, 8380392, 8380416, 8380402, 8380382, 7, 0, 8380407, 8380412, 8380411, 18, 8380406, 8380409, 9, 19, 8380413, 16, 8380403, 6, 8380410, 17, 8380390, 8380414, 8380414, 13, 17, 33, 8380404, 33, 26, 8380414, 11, 8, 13, 8380389, 14, 8380409, 8380409, 30, 8380413, 1, 18, 1, 8380399, 10, 8380371, 8380403, 8380399, 4, 8380399, 20, 2, 8380412, 8380389, 9, 8380410, 8380394, 8380411, 8380391, 23, 1, 24, 8380407, 8380402, 37, 2, 8, 8380416, 8380401, 8380400, 8, 8380406, 14, 32, 13, 8380405, 15, 30, 6, 8380411, 8380390, 3, 21, 43, 8380412, 27, 11, 8380415, 10, 8380405, 32, 8380406, 8380396, 23, 8380395, 5, 12, 8380409, 17, 25, 8380398, 23, 8380414, 8380362, 8380413, 9, 8380397, 3, 8380383, 10, 8380413, 8380401, 8380409, 8380400, 8380405, 7, 8380396, 11, 8380406, 8380410, 3, 5, 13, 13, 21, 22, 8380416, 19, 30, 8380404, 20, 1, 8380408, 25, 15, 31, 24, 8380399, 11, 15, 18, 8, 8380393, 0, 8380396, 9, 8380397, 8380410, 9, 24, 8380408, 17, 6, 8380405, 8380404, 8380364, 8380388, 8380402, 12, 8380401, 8380415, 8380392, 2, 8380412, 23, 5, 14, 17, 0, 8380408, 16, 8380384, 13, 1, 8, 21, 13, 8380398, 3, 8380408, 3, 8380403, 7, 16, 19, 12, 9, 8380391, 3, 8380410, 8380401, 30],
[8380400, 3, 8380411, 12, 6, 12, 5, 8, 6, 14, 19, 16, 21, 7, 13, 8380408, 6, 7, 8380398, 18, 8380399, 10, 12, 34, 16, 10, 24, 5, 8380401, 1, 8380387, 8380411, 8380403, 8380379, 8, 8380413, 5, 8380403, 8380391, 8380405, 8380394, 8380395, 8380414, 5, 4, 8380393, 8380394, 5, 25, 8380404, 12, 10, 3, 48, 34, 8380416, 23, 8380398, 0, 2, 8380394, 26, 5, 24, 1, 25, 6, 1, 8380402, 10, 8380407, 4, 8380409, 21, 23, 8380414, 8, 19, 6, 8380404, 8380415, 8380407, 8380414, 8380387, 8380410, 18, 30, 0, 8380387, 11, 8380414, 8380415, 8380406, 8380410, 8380407, 8380400, 8380400, 10, 15, 8380414, 15, 8380399, 4, 8380403, 8380400, 8380395, 8380391, 8380391, 18, 8380383, 25, 29, 6, 24, 8380397, 18, 22, 8380406, 8, 5, 7, 42, 0, 23, 42, 8380390, 8380415, 11, 8380407, 8380413, 11, 3, 8, 8380386, 8380413, 6, 18, 31, 8380414, 8380403, 7, 8380402, 34, 25, 8380387, 49, 8380413, 3, 8380405, 8380416, 2, 8380406, 8380376, 8380406, 8380408, 1, 8380406, 8380391, 8380411, 8380402, 8380387, 0, 8380416, 8380398, 3, 8380414, 8380409, 13, 11, 9, 8380414, 18, 12, 2, 8380392, 10, 22, 7, 23, 32, 7, 8380409, 21, 7, 12, 5, 8380396, 36, 26, 8380400, 25, 27, 33, 4, 7, 8380408, 8380408, 8380400, 8380399, 8380414, 8380407, 8380395, 8380403, 0, 8380377, 23, 8380406, 8380394, 9, 8380403, 2, 8380398, 8380381, 8380410, 8380399, 8380400, 8380413, 8380416, 8380403, 11, 2, 24, 6, 8380409, 0, 8380412, 2, 8380415, 8380384, 31, 11, 18, 29, 2, 5, 16, 7, 20, 29, 17, 13, 8380401, 8380401, 5, 38, 7, 31, 8380414, 8380409, 8380411, 7, 8380387, 8380398, 8380402, 8380413, 8380396]]
z: [[143772, 123656, 293463, 7962815, 162638, 130615, 8254548, 454692, 117418, 8029016, 7937213, 24642, 281101, 332539, 7957523, 8060313, 55471, 7986269, 7960328, 405391, 400225, 387815, 8023916, 310096, 8326181, 151862, 519702, 8106552, 441491, 7992435, 29297, 398273, 380800, 8310400, 242983, 8030637, 12515, 8331160, 8124656, 8301181, 259672, 8276198, 162435, 8246792, 11583, 182706, 470551, 8000653, 7880579, 110119, 8017055, 7975210, 8246156, 8055547, 7966150, 59380, 38580, 7949612, 7933398, 8189705, 159870, 284510, 8371776, 286438, 8070756, 8005229, 284296, 7887629, 8369540, 8026517, 8219208, 8004605, 517804, 7951555, 7934428, 109473, 7915952, 482722, 8180580, 22896, 8210526, 23527, 8358087, 69432, 389017, 249399, 8340002, 147072, 107695, 7881817, 136420, 518185, 92225, 7927386, 74780, 8271757, 445960, 7954895, 113196, 309500, 7955661, 8188744, 8035725, 295983, 441455, 103052, 8351550, 8084227, 412058, 8002752, 8378364, 8343226, 516352, 7998629, 150133, 439376, 7925006, 500971, 8011395, 8172211, 18820, 7926045, 8246338, 8270844, 198228, 383051, 8269264, 8028334, 8247402, 7996087, 433839, 7968613, 8015406, 456341, 7866632, 268726, 6913, 8282374, 7894281, 8328378, 8227847, 7969539, 8030192, 8154624, 8342926, 60383, 8253800, 8378740, 8160833, 189528, 8268337, 451560, 7857989, 15667, 8351569, 297121, 7872098, 8005729, 8336831, 169621, 8360521, 473778, 8151121, 8324692, 306792, 418157, 8265924, 136810, 8198596, 7856183, 205470, 7867259, 7902109, 8190260, 8155329, 7907132, 169095, 8186583, 228582, 63983, 8101422, 8253562, 8170752, 8053588, 8029731, 8050531, 7875359, 519011, 8193214, 390990, 7988427, 406163, 7956698, 8162071, 8347218, 443351, 393371, 8114488, 8086470, 363257, 210479, 303115, 441735, 396340, 215198, 164853, 72897, 363580, 8043771, 402831, 148221, 8063667, 306649, 7913832, 8353159, 7883555, 8334742, 8183001, 260740, 8175125, 8031299, 40485, 443226, 64875, 469340, 441146, 7899376, 291765, 8036579, 226740, 7902630, 8273949, 440073, 122120, 7951976, 20959, 8021609, 7971106, 344562, 8030487, 8111738, 8212258, 51161, 8258545, 196574, 293192, 448323, 379859, 7863219, 491415, 8140463, 7962312, 150893, 8211545, 518937, 7952634],
[8059338, 8054325, 478485, 190616, 96841, 440716, 411264, 8138281, 306706, 161846, 8207956, 277469, 8379587, 8128411, 8306406, 8045607, 293701, 8239243, 8051471, 8120559, 40017, 91634, 8164137, 8120221, 355600, 8310149, 14081, 280760, 7926345, 8343803, 399205, 7913904, 8280882, 200278, 458882, 29997, 162647, 8314453, 8374314, 8230575, 460423, 8077107, 441363, 292276, 122073, 488679, 7956539, 96787, 8059216, 300347, 8128416, 277770, 324173, 426082, 448937, 7916759, 7905387, 147017, 303276, 7988659, 97566, 66761, 8042283, 8219452, 7856947, 264017, 198064, 419626, 8219265, 8021223, 234471, 8148995, 488084, 28153, 21734, 8095315, 8063251, 299499, 8095839, 8334677, 7998541, 245194, 8201462, 44522, 8352397, 7929922, 55752, 8303270, 8011383, 7941571, 8213932, 171048, 8067946, 7890440, 8278138, 8139602, 163391, 7918713, 230606, 358234, 8190669, 8082831, 7879154, 515278, 8088783, 499128, 2314, 8286076, 7941660, 191344, 8213001, 7868974, 7998842, 8230137, 271621, 8153648, 7994409, 8167901, 7878916, 7995963, 8315657, 360363, 7867120, 124832, 275895, 8155773, 333895, 8120230, 336867, 476703, 8246278, 120774, 122298, 314263, 8305127, 437468, 7860187, 8025438, 8034319, 7359, 8286170, 22331, 33739, 8084894, 8038066, 65907, 225039, 52710, 316967, 7917219, 241491, 8026945, 258267, 8290591, 262208, 259592, 7904214, 8126458, 8042595, 309608, 8142248, 154317, 7989230, 8021135, 8100201, 459481, 44333, 8032552, 209848, 7991598, 8236869, 8130787, 250041, 8136567, 490740, 201430, 8345528, 7885349, 8325617, 428085, 126984, 189031, 7922561, 344762, 8233451, 173371, 8149284, 8357573, 126582, 331864, 8019071, 505909, 25840, 268422, 8200690, 226297, 8099295, 7909878, 8017255, 8380104, 6703, 107971, 8097820, 7925089, 124549, 148809, 8039418, 484599, 398453, 446611, 8194466, 53858, 465123, 8302073, 8215903, 7961514, 127078, 8008810, 8327894, 63403, 8081047, 227910, 373347, 79875, 8337192, 109756, 8072843, 287315, 8250610, 237129, 8231364, 482141, 7963830, 8379518, 8370592, 496787, 7891936, 307749, 204194, 8159797, 8116448, 210702, 8123755, 278586, 8177097, 244999, 8029850, 7973684, 8149880, 90669, 8070930, 112462, 148348, 301542, 8290883, 513829],
[134824, 8104893, 229093, 7914038, 7889383, 8122105, 306790, 85960, 8154601, 8090778, 8068180, 155248, 7985665, 481786, 8240036, 8353699, 8058569, 8365062, 8036905, 268425, 477048, 7975434, 514127, 475157, 7862917, 332267, 8330989, 11082, 8271262, 167097, 291267, 93802, 7893754, 197918, 8239699, 427970, 278495, 8123420, 8299350, 237083, 30744, 122195, 366734, 433538, 269442, 7950677, 101537, 7918129, 473721, 308542, 448170, 219672, 14278, 338359, 8123839, 8327111, 403754, 222137, 451100, 65280, 443162, 65685, 7964016, 7936115, 8014412, 53471, 104674, 8060035, 8168624, 8077369, 499356, 7924407, 476680, 8174801, 8315299, 375665, 349191, 368900, 398422, 7921429, 8063220, 343691, 7911423, 7994027, 8232563, 7897712, 309213, 8375434, 366150, 271757, 8024649, 429344, 183590, 482786, 8365153, 7875120, 7969012, 7943237, 43312, 8128192, 344475, 8026200, 246496, 8005415, 291074, 8260328, 8027940, 8325786, 8214874, 8131458, 342724, 82357, 8105685, 162838, 111198, 8325752, 345857, 8328295, 293403, 163499, 85437, 170211, 429428, 7992498, 7856197, 233113, 346551, 212492, 8007735, 499374, 8132049, 8328854, 7967412, 8133510, 50538, 8141456, 381702, 297808, 389015, 267177, 7936562, 230709, 8336633, 266552, 7938165, 8097110, 133750, 241300, 8110460, 7867742, 410355, 221437, 76184, 8272705, 155412, 8295215, 237247, 8330085, 8234396, 459250, 287804, 8228459, 8161827, 8238168, 7896782, 306485, 165927, 8156254, 8071748, 8378529, 132354, 130931, 105744, 8260091, 8226092, 257853, 8063097, 7864386, 405680, 7930777, 8309392, 122953, 195737, 18340, 7939372, 8058702, 310918, 329713, 8115136, 8248283, 44469, 8065764, 8314551, 8292692, 73403, 7990470, 7876339, 131780, 426783, 252537, 8077989, 8145198, 7924491, 103581, 8337052, 284880, 8159474, 367927, 7970708, 57070, 8269000, 7880430, 8081184, 8341607, 6028, 8326742, 258617, 8092068, 8172439, 96098, 8091757, 359442, 314553, 8172053, 8144098, 7890124, 7990674, 8166182, 356331, 8170993, 8240278, 8241740, 8116902, 8153388, 8309164, 8316923, 8199642, 146447, 8200878, 125439, 7981738, 7872295, 8359803, 521374, 66216, 342210, 176521, 8204181, 475087, 342261, 8303880, 8205641, 8281300, 335588, 8309877, 263831],
[105076, 443919, 8044095, 8016682, 7907494, 7967344, 232013, 7992532, 372497, 8162765, 13503, 147668, 8004375, 96105, 10471, 8269244, 8303016, 7976487, 464745, 7988596, 7952320, 8328284, 7892880, 8325987, 8238000, 7902484, 8277175, 29790, 8118640, 260422, 7905944, 112103, 8328774, 8020003, 8312866, 8264459, 8168980, 8003134, 7945984, 8286842, 485440, 289004, 8181004, 291717, 353105, 211537, 7976350, 55928, 267441, 205670, 7859854, 7918767, 504151, 358637, 308640, 291107, 8152457, 327216, 7986532, 116391, 8265622, 8224373, 8374271, 8315956, 8244033, 8150732, 485893, 459328, 7885721, 8105961, 8072437, 313274, 427929, 8190930, 514851, 181490, 7877627, 22605, 286241, 8088001, 8370302, 8315574, 322459, 196873, 8262740, 33481, 7858752, 473797, 189579, 8084985, 477709, 509578, 7918655, 7881223, 8218058, 7964823, 7870846, 7976209, 458575, 8375561, 8271714, 31112, 8155508, 318067, 8084583, 339656, 43353, 8377784, 80010, 8096154, 208866, 8046122, 145477, 8254746, 238749, 478993, 8293512, 7980109, 453209, 7919216, 518998, 104074, 8355968, 8022700, 8161385, 8056708, 454387, 8197323, 8072485, 219635, 269055, 8119857, 8302728, 8098206, 246927, 8270231, 522553, 8380235, 300781, 33191, 358671, 8125034, 7970785, 8058865, 80338, 8281671, 267726, 115519, 8085864, 8252454, 420643, 8326970, 8182556, 8107346, 8115792, 8316129, 8241402, 136841, 8078781, 8033746, 8167563, 14279, 193104, 9074, 7991410, 349729, 8291767, 8177852, 8101262, 8335184, 8285073, 142297, 8054506, 389742, 19302, 379395, 8121595, 8062382, 270339, 159716, 202201, 385898, 7935699, 7902803, 7944070, 318776, 8353280, 8302029, 8027656, 326173, 162124, 508188, 103535, 8223604, 7917351, 7959146, 8053482, 138413, 465619, 185871, 8309514, 162094, 252115, 7906507, 8313422, 7871198, 8080140, 8131590, 307497, 268655, 8305444, 32505, 8033815, 185236, 8359190, 513162, 8236108, 190052, 47157, 217253, 8345319, 7992043, 8160132, 7875385, 277146, 8159410, 8322833, 269808, 8134033, 222883, 124494, 303431, 8362645, 8130946, 7884925, 356152, 8019857, 8117758, 7896761, 110544, 8347367, 8362462, 318635, 300920, 8037993, 95180, 8008663, 283536, 249861, 8103321, 7879521, 11531, 7912536, 182547, 343405, 509644],
[8280167, 8183382, 7981272, 140587, 8131905, 8336906, 169368, 8259503, 6959, 8374380, 396768, 323466, 8234923, 140944, 1591, 8026813, 8357185, 381433, 211102, 8164711, 8067284, 8156928, 251946, 8038791, 8127856, 8108758, 7863541, 213144, 8087180, 8234345, 8120609, 476932, 469643, 8119853, 8252282, 242779, 455422, 8327248, 315529, 500126, 238274, 362230, 8144038, 397352, 8120461, 361771, 215362, 117234, 326202, 121265, 329880, 422725, 8098308, 349698, 8207912, 521451, 7917650, 8221894, 8018399, 329241, 418887, 273636, 222842, 7945466, 7985745, 500322, 341201, 8005324, 8042017, 8204796, 4355, 251481, 8049668, 8332492, 8208810, 80188, 8113001, 336564, 486706, 8272880, 7959409, 275435, 8136822, 122915, 8346258, 209220, 325983, 8181804, 7906986, 7892110, 8195640, 8310053, 401482, 7977011, 8009797, 352702, 484884, 8119269, 9220, 8186549, 8057240, 8335209, 7883137, 8334596, 7999830, 471680, 67218, 8279804, 7938521, 264940, 346770, 8041177, 273504, 445514, 7880639, 232624, 7937300, 122420, 206323, 497521, 8071430, 254612, 8082798, 8301735, 7989215, 173405, 7984922, 8017635, 8179667, 8198434, 2329, 138898, 22799, 382492, 8153831, 74164, 373776, 429916, 8339011, 8038841, 8248403, 8264300, 306680, 8188371, 8002325, 8069083, 7857388, 476833, 184576, 120365, 7970077, 316210, 101461, 8245173, 52432, 39592, 478130, 8069576, 7915175, 8163517, 8342671, 8271867, 8112471, 25100, 489470, 8223493, 7861960, 8247432, 7859869, 113284, 103885, 483623, 103624, 8003909, 201837, 442770, 470324, 8095252, 8096243, 7932580, 8367830, 8260678, 8277989, 8128595, 338069, 370275, 8002594, 202998, 8106253, 7863510, 8350195, 8355004, 329331, 8140657, 374523, 8258051, 8042666, 8208298, 8346773, 389534, 75286, 8257802, 8190753, 7941181, 323058, 8085399, 101549, 8262957, 126092, 8195429, 7881689, 8284634, 124092, 8027861, 382402, 8010862, 170043, 8225827, 144002, 224035, 515404, 213461, 8044274, 8252518, 8379310, 7901590, 8352296, 300390, 8125793, 139947, 7914872, 348748, 8313950, 8284926, 151582, 17586, 128752, 8162130, 283247, 8227059, 234117, 7989252, 256052, 91754, 7986704, 505118, 433888, 363668, 236660, 266971, 7869229, 464075, 8293171, 7949724, 122927, 351232]]
||z||: 524234, ||z|| too large
r0: [[-172830, -230199, -249934, -36994, -200682, 246659, -119995, -165336, 194290, 166606, 76097, -58268, 183807, -76055, -43533, -222635, -187478, 228396, 3262, -250294, 182720, -168752, -23559, -4223, 190710, 5549, 22770, -48172, -255583, 249297, -213753, -128721, -195864, 197228, -259971, 54051, -171216, 23303, 184076, 235124, 212154, -176119, 196402, -199649, 53701, 22125, 249821, 233408, -108101, -152666, 134365, -257363, 27038, -171939, -96380, -252191, 28236, -72638, 189924, -209534, -111732, 171636, 56283, -142383, -154101, -74416, -66014, 194384, -11811, 14941, 19769, -31862, 16332, -169320, -75341, -102048, -168561, 83107, -176903, -190576, 80102, 224709, 194400, 2307, -16285, -8711, 134087, 210065, -160678, 49959, 66281, 228303, -157936, 81027, 97078, -72812, 88150, -122124, -81251, -11878, 25955, -121568, 225379, 62442, -221664, -136989, -36944, 31525, 4658, -31997, -228365, -222308, 75326, -251419, -142384, 185172, 205818, 56681, 228207, -96980, 147292, 151411, 150904, -226567, -223814, -112882, 204799, -50439, -180881, 38358, -8842, -205444, 102156, 94169, 207318, -52431, 124121, -104917, 169793, -60670, -61093, 242607, 5041, 19283, 213384, 153250, 57303, -184146, -258677, 200526, 99111, -89272, -208614, -120105, -256798, 46207, 125037, -229297, 238430, 65885, -213579, 95977, -161138, -140785, -25021, 204740, 14840, 64669, -141953, -5590, -198586, -169541, 104275, -205246, -74739, -126421, -234135, -166212, -184019, -198067, 51815, 222299, -167562, 136846, -144823, -84602, 64621, -256835, -54155, 16897, -52368, 159807, 177576, -4488, 195039, 242433, 162367, -30323, 65326, -132909, 139192, 228865, -200821, 247793, -87023, 247775, 64188, -242384, 175427, -64586, 20033, 216184, 140621, 158507, -215602, -60700, -257117, -160038, -171128, 48233, -156252, -255974, 80946, 73171, 189764, -64235, -35813, 68072, 152820, -65327, 21268, 188461, 122511, 203203, -83705, 208843, -63170, 170562, 59761, 259973, 50433, 209259, 24176, -37348, -31817, -87845, 5137, -39498, -243857, 102048, -215671, 205424, -164784, -159427, -89899, 257311],
[159004, 231838, 94342, 224655, -126622, -58156, 258226, 19919, 202206, 101256, 175416, 29149, 186146, -7892, 36601, 116191, 178853, -165292, -71764, 142722, -159819, 1830, -197026, -19449, -216713, 226451, 141185, -32915, 117728, -48236, -162974, -163864, 109357, 44351, -129914, 149600, -131504, 110971, 22737, -111341, 206485, -21578, -107961, 44582, -242772, -79021, 254319, 150939, 162148, 22017, 107707, 213933, 155653, 78955, -22988, -212072, 211385, 52926, 19278, -14748, -220805, 72772, -57490, -251178, -144865, -12010, -19903, -776, 258752, -147396, -147540, 16079, 179843, 100993, -181397, -120835, -136260, 84814, 52629, -161706, 152470, 76036, 29829, 173692, -143852, 47763, 125513, 217767, -91921, 97192, -258122, -106999, -91362, -188008, 181194, 258776, -169085, -207439, 107497, -211783, 7632, -5371, -73218, 211862, -225691, 134217, 109380, 84810, -146403, -15672, 159587, 7575, 250284, -185256, -137089, 236895, -185607, 56713, -37095, 126657, -95366, 131923, 66434, 22310, 68068, -54416, 63508, -151427, -30382, 212702, -93483, -6697, -202801, 120211, 215609, -220185, -248226, 74506, -74535, 269, 32996, -132171, -168995, -112567, 159699, 4311, -42877, 224625, -183345, 80924, 52472, -183926, 66360, 18822, 202848, -239553, -55283, 175254, -31910, 84153, -254061, 720, 121785, 92113, -79883, -171150, 90962, 248222, -43494, -82515, 233753, -194236, 245005, 74138, 181057, -94909, 193189, 159894, -55366, -45321, 214626, -201940, 28062, -54899, 229526, 51294, -164385, 175027, -247472, -137400, -212320, -12216, -107754, 110143, -164960, -162093, -15228, 184899, -139072, -159732, -192271, -65981, -203472, 1985, 55377, -80066, -258398, -255339, 76057, -230635, 234154, -188520, 204628, -140242, -138166, -228586, 205365, 212365, 10789, 77912, -213477, 160143, -59960, 18554, -36492, -149767, 70097, -111465, 76561, 181390, 104201, -59932, -187987, 179373, 75505, 34377, -217878, -109639, 200029, -88744, -77038, -92121, 147314, 1600, -233098, -76958, 32941, -203262, -55658, 234023, 43717, -38273, 230366, -258969, 230783, 52680],
[-68415, -213788, 260628, -219115, -92148, -130265, 117087, 245292, 103992, 229860, -180284, 107548, -24990, -233860, 141435, 129118, -186177, 255359, -94560, -97310, 165947, 142474, -32615, 173594, -167082, -38617, 236488, -212327, 778, 59135, -233994, -163747, 127511, 40888, -116385, 181870, 154890, -241880, -258799, 49221, -51838, 205276, 1353, 24549, -259862, -150569, 215576, 94312, 119163, 1307, -213188, -66434, 52037, 63498, 112183, 9942, -139415, 92175, 119864, 157318, 178261, 24381, 199287, -18625, -238367, 110640, -193722, 78357, -166043, -126439, -172791, 68726, -129025, -108817, 210654, -153762, -53830, -183556, -239377, -30854, 196530, -42415, 118370, -52712, 59326, 187085, 260976, 68627, -49454, -173052, -28587, 190605, 30533, -29149, -54443, 103339, 213621, 110114, 57994, -254005, -154691, 134994, -222357, -135025, -196007, 79219, -192107, -97375, -215012, -110543, 143745, -260829, 101216, -216305, 116681, -55645, 122385, -53529, -190290, -18242, -107477, 227973, -92220, -74706, 29955, -46964, -255729, -235698, 141488, 149089, -68598, -171559, -144562, -177454, 86615, -74237, -257797, 160253, -201259, -105244, -100217, 215224, 53312, -251386, -177557, -137454, 218611, -245729, 150548, 13400, -26844, -59851, -95953, -253921, 8768, -8309, -143481, 202149, 174420, 14800, 139674, 237064, 127412, 110624, 131546, -127404, -124354, 207863, -208232, -57410, 8119, -64654, -128181, 49147, -28278, 101476, -139358, 259473, 87357, 38339, 88026, 61983, -103756, 179047, 235123, 11500, 14840, 43303, -12818, -30825, 116181, 150116, 33765, 22983, 61051, 234037, 208140, -202982, -172992, -14161, 20082, 17016, 103387, 100824, 107192, 130173, -146889, -70707, 27419, 225327, -1470, 166863, -226210, 80690, -247477, 129658, -91942, -171777, -107628, -96988, -110257, -240093, 4179, 194765, 146088, -223513, -64639, 124681, 129508, -56353, -129524, -194908, -117680, 205330, 154691, -92430, 114210, -29729, 119627, 62684, -210580, -240507, 186611, -108628, 226016, -31348, -162543, -212642, -77282, -206763, -202912, -118082, 10778, 243048, 80829, -40447],
[-15780, 201288, 25055, -125534, 24763, -75782, -204980, -209191, 235026, -66842, 183310, 195730, -128630, -31822, 77386, 119071, 147808, -114211, -32210, -253607, -184646, -37110, 202131, -74500, 113189, -111534, 176295, 242718, 130244, 71169, -1401, -127131, 214520, -121329, -57129, 166448, -172975, 208984, -118533, 37386, -130710, -49417, 21764, -93831, -42733, -187367, 27479, -235125, 65863, 26425, -115845, 236117, -259880, -213194, -85962, -184184, -130852, 166793, -80818, 79561, -134150, 68479, -240606, 231588, 90011, 171037, 155026, 257749, 255849, 213760, 27245, -241387, -59092, -65642, -242233, 259784, -35117, -207604, -116032, 164251, 29782, 49495, 157413, 5289, -223885, 87685, -165946, -132071, -35500, -69967, 167703, 2199, 25880, -225349, 180542, 169290, 89265, -253830, -192473, 241807, 103718, 252927, -52859, -147461, -224859, 92114, -22079, 4663, 32225, -58120, -14583, 257893, -21775, 43319, -130648, 109154, -167722, -165353, -142799, -6433, -25055, 219321, -248814, -183170, 213533, -247695, -219248, 85080, -246515, -154729, -87801, 243552, 28468, -159831, 101909, 205660, -246777, 79421, 42081, 225465, -38961, -82972, -180051, -185693, -135650, 132557, 72618, 257764, 220201, -89765, 94639, 223677, 84105, 148054, -125611, -121736, -152618, 72326, -118677, 113532, 157198, -64906, 163718, 32812, -243743, 253149, -191235, -82852, -247846, 58336, -36849, 43829, -166263, -208120, -24980, 63468, -47763, 125606, -115039, -38890, -34027, -21397, 71551, 8392, -65204, 156631, 61750, -64333, 11484, 178852, 68491, -190068, -164841, -126699, 175396, 249044, 41841, 147541, -108052, 173838, 220193, -75125, -233572, 203586, 86493, 130285, 70740, 210681, -239204, 64411, -71427, 139839, -14964, -65051, 108363, -256847, 230064, 181167, -248359, -129532, 255386, 156324, -88470, 223013, -178757, -244450, -16221, -6183, 146381, 165559, -130197, -89755, 208861, -81239, 191981, 238140, 21501, -248309, 113408, -209353, 132943, 74744, 123300, -120848, 43670, -234471, 177471, 174316, 233247, 15641, -57358, 76209, -136959, 215270, 226533, -147726],
[28984, 175536, -87316, 60148, 132601, 8378, -232208, 165555, -18592, -34076, -146289, 58514, 190092, 174975, -60855, -18772, -80721, -33760, 104301, 40432, 215178, -107064, 108065, 83384, -151130, 21721, 204823, 7114, -167573, -87795, 222662, 236171, 225291, 46453, 91651, 12492, -122713, 218943, 202570, -118015, 108001, 88580, 114580, 193794, -255841, -196444, 215161, -205757, -243208, 139171, 236092, -68109, -242192, 164686, 83653, -166802, 199904, -182597, 171739, 9698, 179616, -40770, 94774, -80012, -220168, -238430, 74086, -246388, -35375, -242146, -232981, 115990, -23766, -133351, -202391, 200073, 96191, 36571, -148280, -63047, 227400, -172018, -196005, -109087, 145103, -35222, 37875, 72598, 81720, 63289, -254083, -184696, -123540, 171826, 217793, -237265, 166603, -117192, 126467, -206397, -112696, 116605, 207760, 225299, -811, 261475, 9787, -122248, 187604, 203160, -31336, 53093, 75332, -199286, 64984, 116924, -258758, 49637, -148454, -203703, 190879, -200132, 167776, 104541, -184229, -3614, 169864, -252942, 248704, 188885, -197651, -180754, -162515, 164806, -35855, 133234, -118614, -130836, 58947, -226097, -169393, -24185, 249228, -209576, 108678, -259331, -9913, 44129, -177477, -111258, -133071, 179510, -194953, 71169, 94327, 225322, 77045, 157035, -50679, -256060, -116284, -74554, -24173, 135876, -176616, -143908, 229217, -250949, 236652, -217471, -239970, -104064, 122411, -214420, 119905, 159181, 252273, 141969, 156808, 178699, 19668, 65796, -208335, -117105, 132400, -56847, 45905, -55973, -220313, -70116, -119880, -1727, -180339, 165864, -48843, 53241, 261796, -14994, -200906, -78909, 30164, -169867, -150514, 70915, 216747, 193644, -202045, -195365, 176650, 83469, -159918, 152240, 84209, -146776, -124953, -16862, 160453, 50540, -164289, -153342, -146, -51149, -167124, 63990, -3702, -168007, 73493, -148007, 56643, -183679, -23103, 131775, 116995, 21391, -249244, -128794, 24602, 34179, 18257, 138592, -107374, -39815, 11657, -112429, -130040, -2683, -78667, -194585, 56822, -44876, -118640, -58514, 135531, 183187, -122809, 228816],
[63803, 239995, -153168, -86729, -125026, -106929, 212490, 32212, -74035, -7515, -179012, -162931, 101466, -188732, -190169, 220315, -48773, 159859, 48471, 68214, 1925, -122011, -213718, -181130, 136218, -241862, 78461, 134463, -135724, -37521, -56208, -104785, -101470, -239931, -105760, 240149, -193389, 15559, 186882, 197836, 52664, 217614, -235160, -39196, 183181, -33970, -67310, -87870, -27355, -97805, -251728, 230146, -245564, -94438, -92702, -257460, 19746, 204288, 31205, 195333, 102045, -207521, -91856, 200295, 64753, 74658, 235912, 223496, -232817, 55169, -91034, 52416, 114896, 170925, -41183, 13703, -193018, 256243, 242497, -84396, -39034, -22040, 62460, -27732, 53005, -220262, -85561, -132343, -68352, 197663, -209901, 224942, -78552, 54807, 199613, 95663, -172161, -60723, 171684, 145189, -192527, -175029, -168368, 45852, 158187, 59685, -112406, -174005, 154489, 215627, 115096, -12569, 243966, 60745, -172890, -14035, 130802, 194909, 234605, 133047, 116349, 243490, -125217, 97368, 162330, -87862, -54236, -188124, -138311, -220380, 256730, -66201, -61123, -198267, 137962, 52564, -171239, 31223, -172555, 125377, -77556, 139476, 261418, 260510, 207000, 88162, -145522, -233342, 81434, 34092, -156591, 88410, 48703, 187086, -177864, 192505, -185968, 87034, -105410, -41078, -70814, 67545, 63723, 56505, 115909, -14444, -191680, -212107, -20912, 191259, 129352, -238304, 12986, -24629, 220084, -120074, -228225, -115123, -208167, -135738, 39424, -121002, -157538, 175176, -160054, 104810, 186563, 29657, -177649, -323, -2869, 64182, -99564, 91289, -87955, 67090, 53177, 94591, -214885, -26224, -202273, -163565, 254495, 181548, -54281, 21530, -62292, 232579, 158508, 129625, -261473, 115684, 224514, -145060, -18153, 69366, -14863, -35585, -178209, 111515, -235321, -67978, -54003, -163866, 29514, 60577, 193374, -96620, -260087, -176740, -145037, 136670, 255235, 151430, 180259, -48831, -117710, 12792, -138784, -248004, -169590, 87706, -33490, 205419, 35597, 161236, -58759, 246819, 94566, -231297, 225330, -228650, -38340, -93193, 106254, -201297]]
||r0||261796, ||r0|| too large
Need new candidate round. ||z|| too large or ||r0|| too large.

y: [[-201659, 229740, -289229, 503274, 84816, 517884, 16167, 90087, -109900, 112949, 202968, -117516, -224481, 279096, -288761, -86933, 204501, 292285, -312247, 520445, 439706, 218627, -35448, 265158, 467161, -91174, 368895, 37966, 223046, 320840, 164436, -488084, 183244, 469942, 311465, -448812, -33067, -184833, -348036, -213874, 167541, -257506, 331600, 72590, 227101, -512223, 521095, 278087, 138476, 317084, 217401, -111427, 234829, -151377, -154908, -342852, 467432, 96856, -455255, -509601, -225181, -143053, 460649, -349841, -419978, -437576, -404490, 251362, -160128, -163652, -34510, 64654, 425122, 184046, 316785, 512956, 104531, -133267, -349173, -255563, 222630, 75631, -144475, -7100, -312909, -298932, 121645, -1739, 332421, 18841, 128410, -238160, 208459, -332647, 50428, 501935, 479505, 252718, -465651, 257395, 407311, 440348, -264081, -435714, -105048, 179561, -505697, 466770, 149208, -137405, -42308, -376585, 379015, 455655, 384850, 363184, 473646, 314608, -158284, 3898, 88338, 121357, 254585, -287009, -241031, 94707, -117977, -272274, 493095, 240769, -41707, 196490, 131270, -414862, 42571, -420711, -509561, 333979, -260690, -92932, 84010, -529, 513238, 253566, -401496, -315195, 131243, 348264, 387908, 297975, -176215, -77614, 103126, 84924, -217242, -447481, 473872, -243177, 394754, 492932, 248866, 95102, -24539, -483413, 13330, 408361, 417259, -6440, -161307, -17907, -491832, 237860, 16252, 14044, 384936, 141369, -181430, -334826, -492896, 273887, 451194, 134742, 411814, 125843, -251462, -40951, 406062, 463936, 86861, -240993, -61697, -345288, -18419, -1356, -57365, 358931, -137431, -317374, 343952, 61304, 516496, -89316, 85725, 65555, 82526, 210827, 291987, -4362, 46314, 385956, 269467, -399359, 265438, -412133, -36691, 230109, 167614, 369617, 71190, -323474, 519336, -285657, -493682, 362212, 347740, -102580, 370409, -135199, 345549, -58068, 222377, -77605, 27025, -198951, 445486, 7312, -268982, -315259, -350608, 272588, -306991, 135089, -392227, -264903, -146270, -422824, -354573, 167892, -144700, 102116, 75942, 293773, 442686, 53561, 9858, -240860],
[-515501, 346309, -172582, 194577, 173809, -327457, -370432, 35015, -389206, 4372, -110715, -273189, -519288, -237620, -411200, -262495, 439556, -207719, -142128, -112968, 103289, 246777, 478068, 345610, -83834, 429054, -396320, 513815, -336022, -62017, -135023, 519757, -202461, -56804, 3201, -414599, -90561, 492805, 259405, 492812, -404228, -517464, -376268, -323569, 71086, 295900, -250796, -411894, -469900, 473416, -2972, 402420, 126054, -88501, -326112, -174759, -48805, -170192, -521660, -19306, -490578, -225049, -456096, -500584, -1025, -485877, -385770, -139582, -267609, 440521, 16771, -518999, 214224, 432368, 233216, -410260, 508371, 183945, -512666, -45493, -168624, 117459, 261109, 346821, 15821, -316780, -402643, -293594, -481379, 417518, -442395, 246667, 374132, -305, 188858, 42550, 515750, -469240, -113643, -490026, 465250, -114127, -178884, -94953, -72637, 468932, -387715, -9853, 288555, 155239, -44306, 405220, 201583, 355048, 464307, -1308, -473833, 498969, 252050, -286784, -321173, -153244, 390653, -273595, -41230, 140620, -209204, 296590, -110146, -302107, -86322, 481385, 346588, -314756, -281504, 407780, -240305, -423112, 3924, 23429, 175075, 509423, -350998, -245191, -197130, 203387, -420308, -280923, 234920, 148185, 314523, -435385, 251111, -230943, 146154, 484950, 356547, -404636, -207193, 459093, -294950, -70761, 508483, 458106, 39679, -246582, -104681, 131801, -239237, -406584, 17529, 344756, 191711, 342453, -138799, 84022, 196017, -308863, 189816, 322569, -141330, -357580, -132626, 497499, 460937, 290752, -403319, 65490, 112896, -423594, 239250, -66309, -7802, -444124, 496133, 103565, -56859, -68234, 121156, -264502, -50995, -471, 26229, -149371, -121463, -395296, -513981, -149695, 162498, -305135, 448968, -474374, 5446, -201329, 306442, 56524, -451887, -301860, -26297, 65968, -489049, -365359, -460769, -454171, 300486, 60393, 448526, -346039, 51113, 435078, -207628, 289580, -160294, -25377, -448152, -58935, 340437, -39091, -127360, -226652, -233595, 521881, 520688, -54787, -230059, -351823, 384575, 376230, 66157, -132946, -507678, 182809, 419984, -188165, 130212, -458252],
[411033, 118432, -57884, 34774, 246514, -227729, 15408, 145618, 364149, 247840, 153092, 178403, 186981, -232581, 418980, 82216, -142006, -212994, 509863, -244214, -190796, 418035, 198565, 5382, 516419, 484689, -384467, -463227, 253180, -419693, 68434, -388968, -484828, 59019, 326624, 481660, 326047, -154838, 417907, 524126, -411030, 189968, -100540, -295221, 38880, -45614, -412923, -512812, -479096, -470766, 13637, -329463, -192134, 259632, 432612, 495344, 402214, -339079, 254688, 82490, 420949, -166964, -323505, -137427, -315502, -453798, 370987, 119337, 594, 431664, 523413, -273301, -256719, 350034, -264028, 442233, -138445, -3467, -198372, -296872, -367313, -255379, 121809, -477573, 102594, 223984, 269461, 72352, 337886, 16840, 462659, -115651, -170604, -32826, -380343, -98747, -38764, 13525, -493252, 178582, 355518, 346687, 332743, 415898, -285329, 144269, -54341, -56600, 222251, 124168, -420683, 324252, -25364, -7908, 509748, -153549, 388914, -51504, 372196, -198463, -514683, 411517, -85189, -179306, -37210, -7697, -348356, -129239, -266376, -88512, -452412, -335642, 217222, -122377, -261918, 103750, 70901, 82064, -380226, 31158, 134305, -130158, -454350, 196976, -423143, 96116, -68269, 504546, -181863, 521129, -158347, -46320, 176450, 410792, -259645, -37442, -478990, 167910, 105075, -50124, 213123, -230739, -493927, 203075, -62435, 491585, 52739, 446730, -510208, 51132, -401865, 205905, -168189, -287107, 17643, -108250, -42578, 237207, -108563, 150092, 340306, 112137, 416998, -169624, -201434, -512323, -331413, 421710, 23687, 296282, 160085, -250348, -10720, 339738, 154740, 264835, -82649, -507130, -424360, 476617, 62667, -433281, -425284, 391562, -371709, -57226, 307686, 132939, -326852, -36645, -34853, -145380, -332928, -416376, 462910, 20607, -127756, 72365, -66925, 62221, 204066, 451869, -111511, -226332, 296991, 153791, -348427, 307526, 318900, 198342, -81985, 276858, 33739, 385273, -465589, -209783, -148987, -422391, 90747, -310702, -335003, 472884, 344746, 454425, 205883, 226155, 59846, 23937, 227478, -64000, 112712, -139939, -423364, -278396, 93196, 95316],
[-425071, -8091, 334999, -479272, 420084, -283704, 150359, -269268, 265777, 221248, 418196, 261692, 391693, 74221, 182521, 124165, -366079, 225185, -388335, -396847, 234570, -357224, 202095, -64214, -124896, -517184, -362505, 57939, -361678, -489006, 263464, -122222, -493340, 322832, 135060, -370434, -515933, 414386, -241514, 147337, -262802, -80027, -38328, -297533, 182202, 221540, -332121, -443994, 275349, 241654, -32329, 503036, -87898, -287606, 448590, 20338, -142985, 140057, 501440, 231800, 89043, -56305, -309722, -273893, 64633, -97184, -242992, -329749, -356018, 394235, 124576, 33692, 389391, 267974, 4024, 440845, -332911, 17955, -252793, -216550, -162012, -83071, -115328, 459881, -160733, 216041, 379620, -45847, -190146, -326771, -215241, 200239, -57787, -224485, -168802, -223049, 217635, 497, 18775, 494926, 308847, -32661, 190271, 82666, 495047, -638, -74378, -485104, 269862, 495772, -341072, 315986, 84735, -59161, -285336, -505850, 292053, 447796, 84345, -142942, 394751, -313697, 409367, -89913, 71078, -113094, 36622, -468109, 314310, -111276, -184116, 441546, -486093, -75852, 286491, 43088, 168440, -333203, -439207, -458230, 265818, -322330, 421142, -424598, -385458, -237753, -192738, 223487, 169610, -52345, 78504, 445920, 300053, 121483, 262218, 415396, 13156, -76841, 513353, -40808, 304180, -518324, 142037, -339943, -73758, 517122, 107363, 437957, -96907, 100991, 385583, -159327, 43247, 158418, 505838, 437484, -252596, 28232, 500990, -321787, 86851, -73153, -253122, 435633, 402902, 265616, 409928, -72071, 335293, 155156, 106505, -10697, 312157, -198576, -445426, -210563, -247360, 108330, -128463, -224643, 177232, 198164, -381344, -255563, -141387, -415297, -63248, 438630, -79275, -268761, -459932, 519093, 310487, 373144, 438663, 16412, -22831, 447620, 155966, -128876, 303517, -343536, 218905, 95404, 403651, -50822, 342365, -368772, 168362, 51085, -173147, 37026, 379257, -193014, -187572, -147009, 381901, 235964, -281709, 456298, -416998, -29703, 402527, 164121, -198608, -141667, -376664, 385219, -396954, -334223, 265089, -30869, 197358, -83261, 483978, -471398],
[303224, -11846, -510477, -160274, 273368, -108071, -132161, -384581, 78928, 461825, -21469, 293493, 397455, -329275, 480596, -204583, -212077, 441036, 234681, 44858, -517993, -506701, -69149, 328241, -355204, 332661, 438134, 267291, 243178, 270003, 500558, -104068, -301510, -277056, -289963, -279456, -119438, -521855, 481448, 124944, 76312, 181477, -152807, -338064, 111796, 222159, 27095, 487843, -200572, -432043, -193271, 502598, -404451, -483015, 46206, 151805, 66390, 192104, 104579, 160330, -405093, -201744, -95001, 370515, 427500, -88233, 171615, 471014, 407619, 299505, -279593, -147844, -275594, 137893, -384383, 111392, 448054, 310464, -173102, -129940, 518630, -14594, 262644, -150986, 314484, -352108, 460227, -397517, 12792, 275860, 6134, 420029, -260968, -63378, 196191, -179423, 263757, -354945, -111969, 125171, -380705, 498352, -337991, -138556, 50141, 394826, -98621, -491095, 211042, -256989, -448812, -28188, -395830, 223650, 473431, -245284, -331218, 153049, 133138, 298992, -295320, -12070, -34584, 109623, 10213, 7583, -152235, -188333, 471646, 349392, -517510, -503746, -430786, 339513, 301593, -167466, 277483, 305255, 59338, -232125, 176824, 138790, 424600, -172424, -312713, -313529, -269850, 417658, 19770, 303356, 20500, 145603, -280293, -160031, -286632, -337408, 257558, -329590, -197557, -409330, -420878, -384710, -250806, -42913, 374915, 281594, -284199, -64458, 506084, 373239, 22005, 350796, -230311, -494470, 99493, 426748, 509137, -201552, -214414, 468608, 89778, -115848, -507684, 186442, 263324, -342686, -456805, -427199, -193895, -92805, 351209, -199074, 488975, -454915, 470212, -493062, 328933, 72208, 283579, -215771, -118915, -231259, 207755, 325586, 127630, -204627, -496230, -518914, -387379, 362419, 349829, -467391, -132512, -351724, 36185, 74521, -119374, 220487, 185920, 340677, 336479, 28521, 408982, -161480, -343248, 410824, -132082, -314457, 483277, 20392, 468983, -164621, -327367, -84924, 216648, 274337, -120834, -29557, 264169, -469414, 3111, 73204, -331130, 23389, -451608, -178575, -269680, 62829, 77172, 61557, 228320, -123969, 313320, -368695, -327547, -220570]]
NTT(y): [[7201786, 3449281, 6254867, 7825074, 1977123, 4799821, 5280827, 1894196, 8075650, 1657711, 5385752, 464853, 3813041, 1386845, 5691517, 2429777, 338890, 1263423, 5595470, 989811, 1408917, 4020424, 5403566, 683218, 5069632, 3181584, 840539, 2848374, 3031638, 4932898, 5523990, 572309, 8116844, 2751207, 1155868, 6295581, 7962798, 7552812, 2175641, 3270519, 3080919, 2651632, 4850794, 5629766, 7808423, 7907419, 3559437, 5411863, 6218969, 2341330, 4938141, 7332802, 5063123, 6308688, 5856207, 5983098, 6594913, 3054589, 408386, 4197788, 7469829, 724600, 1556506, 2000487, 5592277, 1201186, 4718137, 6029983, 8078956, 199587, 5122732, 1620705, 5242017, 5917, 4778240, 426494, 8366706, 1587007, 7837995, 1745822, 7702228, 4858631, 7952457, 6136782, 2253819, 2288240, 7062780, 4985033, 7716891, 3979764, 1661825, 3337126, 3836662, 3820071, 2923422, 3103472, 4042682, 7840413, 5753568, 4981119, 1606332, 5118455, 1687028, 4496189, 7400673, 1265544, 7805232, 6367198, 2540037, 4038887, 7827248, 4235184, 7783000, 694763, 4943664, 8238988, 1692300, 1717700, 8263657, 1327159, 2035981, 2672379, 5718135, 4607729, 8224545, 1379294, 7332671, 6519504, 435524, 1270912, 3738351, 5618172, 4077808, 6533147, 6710266, 5381879, 168720, 5385305, 2779134, 4583664, 1977865, 449081, 5694377, 3858033, 4698470, 8148545, 8119587, 2707017, 2803461, 122710, 8269457, 7762215, 7255170, 6129851, 6793552, 4710461, 7057695, 4756773, 6151506, 2598785, 3026059, 5338152, 3723084, 4761812, 3397330, 3035310, 8012796, 1682940, 2575908, 7636556, 164653, 717407, 1062269, 1748354, 7862856, 5434719, 2115309, 7415000, 3617008, 3713693, 767985, 5829947, 4801830, 5866644, 155647, 1983136, 6188716, 4382035, 1664617, 2563901, 1794840, 5065702, 2288878, 2432434, 2091993, 2336768, 3752205, 3705917, 453081, 8216529, 1702698, 5771096, 2935085, 1199278, 2067156, 8274276, 6402682, 3208619, 2625573, 5655829, 515148, 6689934, 6794230, 6373879, 2370446, 3285489, 4510339, 3406489, 3306611, 5418705, 6376114, 1622818, 888784, 2697530, 5937866, 2075805, 137942, 5172873, 4045317, 6612000, 2645903, 5678287, 2200378, 4377519, 6281484, 2681103, 4896601, 782622, 482355, 4321008, 4546069, 5192301, 7095978, 2402448, 7835100, 698915, 5753881, 5556028, 1308253, 2935783, 3813333, 5233827, 3368811, 5346022, 541146, 549056],
[6864270, 3414693, 8331767, 5615313, 7552214, 4809747, 1656411, 1300679, 6283763, 2203957, 7074871, 1676236, 301189, 2528813, 1633515, 1126621, 2613931, 8241862, 4804203, 7282380, 6151261, 5277303, 5515764, 2487850, 4888420, 5677478, 3371228, 4962627, 5113784, 3474961, 7099541, 4137740, 319294, 2051532, 4554803, 1785013, 359976, 3078960, 6516509, 2919388, 6845220, 6993135, 7022434, 6401006, 8190537, 458086, 7863814, 1133414, 4918678, 2716050, 6526422, 2306407, 626937, 7480737, 8064153, 3136431, 16971, 3420629, 4966268, 4287154, 5273403, 622838, 7845071, 727786, 96951, 7435128, 1218311, 5365163, 4715228, 6641653, 1462574, 7543400, 4652219, 4120798, 7421376, 1496821, 6543187, 3921637, 3726581, 6741272, 4953647, 7537687, 603506, 4744983, 6921533, 5208620, 3117085, 7361010, 1382490, 5180546, 2959796, 1652715, 8266681, 2088017, 1028350, 4370407, 2349226, 2050778, 4668658, 3383802, 2286225, 188036, 4772094, 8128911, 5816663, 5348967, 7625840, 1983213, 4855394, 2579518, 7363338, 2248636, 1814008, 978191, 8111079, 4179578, 2355142, 3390578, 7124314, 7421634, 2275415, 581064, 5897167, 1942433, 5575191, 108743, 2643397, 3561039, 7199158, 5399256, 4558366, 295499, 2208035, 1920857, 4671950, 5722669, 3510996, 10010, 4890474, 7522381, 1545259, 3641956, 213304, 6186841, 6317254, 7400069, 2653880, 3534443, 1002978, 8078666, 4413140, 783329, 2655104, 6912459, 5488857, 6051380, 5588021, 6897370, 4723543, 4931993, 7303180, 725425, 7081262, 5271010, 6691976, 6553641, 1099861, 6703825, 6113940, 1896282, 1635285, 7755885, 7617091, 6858199, 522467, 7033647, 370051, 6321469, 4000388, 109160, 2443332, 8163639, 3421161, 6450237, 5059172, 643704, 1926585, 941005, 5316184, 6255637, 5145989, 8304455, 874182, 3500745, 4485724, 3889902, 1751629, 4814079, 4007110, 2697585, 3666546, 2203132, 5665126, 6559981, 7091863, 2987883, 7595314, 5938965, 7970128, 4924444, 2752390, 815046, 552517, 5095443, 3068787, 8208054, 2100035, 3369128, 5590526, 1637343, 629381, 4068849, 662948, 3791456, 6577310, 3118335, 4172676, 6042490, 747083, 6641445, 1355208, 917017, 5609143, 127909, 1668513, 3865340, 2633474, 617031, 2639242, 2511919, 6833086, 3817741, 16493, 6016056, 4231696, 2778162, 1490399, 5441461, 1075825, 5267768, 4763173, 320874, 7916691, 3608943, 888693, 3337371],
[7247850, 2613821, 2753489, 2343097, 1207791, 3685947, 4828903, 7068786, 7658406, 2863104, 2567811, 5124603, 5176069, 7541964, 7457003, 879645, 425622, 7292789, 7893679, 5803915, 3370732, 6813799, 3653211, 3158167, 8076440, 3299003, 110438, 6814221, 1112684, 1997974, 1383670, 7836223, 5252264, 4965890, 7723591, 6507585, 6557865, 553622, 5342562, 1665156, 2497566, 4822774, 1367078, 698932, 5511982, 633196, 2698847, 4289686, 3489438, 2608624, 413481, 2327085, 3199655, 6128510, 241606, 1755723, 5933057, 2407993, 315171, 7277939, 7409161, 3646630, 2607946, 680711, 7738547, 907360, 2052037, 2957383, 3456957, 2164678, 2326591, 7239266, 2921858, 430009, 6000572, 6824523, 5023819, 5082664, 3606696, 7224344, 8186304, 1149529, 5524234, 1155209, 2338712, 3342099, 8355078, 2263193, 574521, 3331738, 2373094, 4840479, 8075946, 4801261, 3859240, 2420920, 6164906, 322966, 6246488, 2294947, 987465, 5000303, 2769479, 3819213, 636831, 8233358, 5312923, 4422607, 4616278, 1288490, 1382599, 566121, 6160127, 5297727, 2505857, 4712532, 1891141, 6653871, 1892775, 5333375, 7568530, 869859, 2216609, 3638869, 6489286, 1707300, 3118816, 5786258, 8076658, 5388235, 4133674, 2700677, 6693302, 2090269, 805356, 2499184, 6555591, 7325813, 5523402, 2690449, 117031, 3942522, 5402337, 203511, 8031678, 331126, 2165888, 7116626, 762212, 6329854, 4771340, 3445735, 2786013, 2941216, 6337539, 4449199, 8310004, 6046744, 2937380, 1397275, 4069817, 4666879, 1402663, 5648913, 4064332, 1513262, 5575158, 6998542, 5532954, 6631341, 1527544, 7816041, 2084402, 1768701, 1980766, 2027818, 2623653, 8238148, 713743, 7897386, 5669796, 7355960, 3509944, 1874023, 7838819, 2966097, 4322347, 7259048, 5423024, 7124972, 5167326, 624469, 1543660, 6200163, 4017861, 8226815, 1714147, 7909922, 4538588, 3110782, 813087, 278574, 2466134, 3259785, 5022099, 6195271, 7292277, 6667135, 5109944, 8266969, 1483473, 3444729, 2699417, 5072380, 1077581, 7886265, 6906584, 146520, 2415592, 2238455, 6842506, 1690613, 1181482, 5840650, 7229107, 3227835, 4826826, 6862353, 6104021, 8274708, 737353, 4827480, 7173943, 6581144, 4716537, 1934884, 4463675, 7737257, 617928, 10302, 1502478, 1920135, 5813403, 4770348, 1320439, 4111106, 8011522, 3877058, 2345418, 5588053, 3761994, 3852565, 4865217, 3354733, 6976999, 600194],
[973664, 3620268, 6465262, 4088998, 1225087, 7325921, 4883140, 1708371, 1129342, 5289567, 6585594, 8168700, 113682, 553667, 2224050, 7132790, 3174308, 6076626, 828372, 5077069, 2962260, 2417472, 1333796, 3297368, 3203725, 6329502, 5572764, 6567498, 633125, 2929555, 6484640, 465396, 4684113, 1027408, 6488665, 664505, 6347721, 3348625, 6651416, 7841774, 5549182, 7468420, 8137284, 2838361, 5842407, 6744813, 965575, 925640, 4078958, 8051261, 5520185, 4282074, 593245, 5881326, 717367, 2006993, 2156776, 7438868, 266290, 981094, 3549547, 3897443, 4962319, 5909675, 6907269, 4479713, 5561761, 1189819, 1632626, 4493705, 6223927, 5670737, 4657054, 2401868, 5762700, 7992676, 4496072, 6802854, 471145, 5974944, 7741281, 4685111, 1465478, 4833873, 2772420, 4566317, 7168217, 374281, 6615326, 3143718, 7506070, 5232536, 3945832, 1948181, 6003675, 3270537, 7255204, 6875089, 7972342, 1292542, 8130857, 5274548, 5965615, 736192, 1809441, 8008221, 5001018, 1558062, 4905031, 5659808, 5256396, 1454565, 3613820, 2830673, 4712145, 4282008, 4185050, 1671280, 1740807, 3284055, 4876607, 2982906, 1139307, 28814, 3729592, 3930989, 818185, 3332191, 4255281, 6821443, 5829999, 683249, 3335215, 2084887, 4784892, 2997012, 898200, 5222563, 6984547, 7857117, 7840140, 1254055, 2173892, 500873, 7957720, 2560602, 2021414, 3418837, 6168430, 5684938, 4644674, 4433757, 8374308, 5913765, 4048379, 4460942, 5198871, 4605212, 4463852, 7682295, 7139172, 6900251, 623009, 4096935, 1831640, 4320466, 737495, 5555839, 7743801, 7604291, 4115958, 7877210, 1048159, 4453758, 7357041, 2121758, 101317, 5871063, 4698497, 8193706, 5973795, 3072249, 4995669, 2206539, 4228577, 8027258, 6558097, 345323, 8314399, 1854727, 3606869, 7901679, 1636061, 5827231, 6240644, 3107656, 4148449, 87376, 7087876, 6376117, 8371120, 4947737, 3150067, 6395321, 101883, 6047948, 2444680, 2056021, 7337094, 5195116, 820213, 72394, 6591380, 3733809, 1115485, 2508284, 8127255, 833590, 2949183, 6589553, 5948247, 6583239, 4811577, 742610, 6843953, 2599306, 644696, 7611650, 4542889, 7487460, 6562135, 3146338, 238506, 5435648, 3810551, 6261260, 2123905, 6468092, 6372456, 6573557, 2331788, 1148312, 3143103, 7229221, 4162104, 7377989, 5096822, 1711004, 4857064, 5206965, 8245772, 4087905, 7390784, 2752971, 4941804, 8347163],
[2697336, 359868, 6682304, 4510575, 4939464, 5462763, 5009474, 471435, 2074562, 4335775, 5089740, 5577805, 3208610, 2696263, 2270204, 8194282, 376678, 3743581, 2411201, 8368713, 3457901, 5677672, 950168, 363705, 3527302, 5490583, 6516924, 2686920, 1396030, 6850570, 3879675, 5188354, 883124, 1078353, 2347819, 7289875, 1549916, 2556252, 7264835, 7899605, 6463501, 2080521, 6680465, 422772, 4210112, 6972914, 7138639, 109710, 5354813, 5881572, 4304970, 276344, 4901196, 4732868, 2743601, 1657321, 5020124, 2698173, 7208824, 2783711, 6719731, 7729534, 2631960, 2187699, 1820692, 5798321, 3628326, 5762166, 4275750, 1896030, 3051139, 6822845, 5290575, 1677111, 1610501, 4145977, 7903517, 1892930, 2125869, 7018820, 1066118, 8226501, 5531389, 811674, 3238555, 5936560, 7373992, 984250, 6295523, 3522836, 4239298, 3318262, 7696235, 8106159, 4565067, 4313073, 809795, 4994216, 3286428, 5632584, 186388, 4323813, 1909662, 4294970, 7444269, 3079308, 3480055, 623216, 3133238, 3539921, 8372888, 3392465, 2009332, 643450, 1845411, 6843560, 6527956, 5726715, 7109520, 2871265, 5301709, 7920140, 130307, 7450234, 2136713, 490955, 6960933, 7447170, 81731, 5804, 7829310, 7502714, 4536939, 948680, 5845455, 7432556, 6868247, 5340443, 7796841, 2813647, 4074138, 5779761, 6208549, 6664429, 563015, 6833301, 851779, 1858289, 7042569, 1713615, 1338367, 7754589, 1265735, 8120700, 8037838, 365979, 5652751, 1794454, 3292831, 5790592, 2920917, 6422130, 1352463, 6740790, 1547226, 2931642, 1681875, 348899, 2501497, 7726804, 7403302, 3524164, 55324, 4855468, 5997955, 1989604, 7250289, 7955284, 8297523, 7927323, 5725667, 7531042, 8219932, 7387402, 3564230, 8047569, 6825125, 4110484, 2349538, 5814220, 4399418, 1775668, 5787711, 8214704, 7399080, 1810681, 529070, 4634290, 830235, 3814861, 378669, 1213845, 4763240, 2292847, 7246455, 1150105, 4942002, 2436542, 2166874, 2451277, 7221312, 540629, 3579154, 2417257, 326285, 186876, 204943, 8067931, 1217454, 5435570, 1938599, 1339109, 539608, 5516089, 8166843, 6869267, 2049403, 3476348, 2124999, 4967753, 4318342, 3685562, 7353847, 2174134, 3496902, 7337134, 1690838, 7409778, 3984049, 2663719, 1095943, 8113763, 4059906, 3030030, 6343658, 1479749, 46810, 3953454, 4179560, 7327242, 7102775, 8027995, 6529160, 8248223, 5381176, 4314941]]
aHat * NTT(y): [[2753467, 534002, 434232, 4629917, 6092653, 6639983, 1250047, 5198985, 4438424, 6857051, 3668735, 105930, 2942107, 6104815, 3974798, 4011330, 4681128, 2559533, 4685866, 6153268, 2161780, 2860413, 1851559, 7948271, 8117305, 6195637, 3308465, 4779338, 5355243, 3844524, 2532208, 7500516, 4907650, 5977554, 7375693, 7127481, 6236002, 274693, 2294707, 2436618, 4507698, 7410294, 7847962, 2330093, 4002324, 3757820, 4377057, 4136729, 2249176, 1135239, 8282179, 6514350, 1286807, 2627793, 3386333, 5575744, 1436715, 5530259, 6849224, 7634436, 4658570, 5718651, 6546431, 7876447, 5648046, 2689976, 6565108, 3154699, 7372778, 2888577, 950962, 6596899, 4336771, 2778015, 1480608, 6227488, 5530148, 4215808, 6986830, 50306, 2430487, 2856715, 7120910, 1871196, 2933258, 7446308, 6732965, 5199214, 4490028, 1244830, 41126, 7437890, 2519834, 6202734, 3325133, 566399, 4499969, 8237112, 2731190, 2530918, 3036669, 5311151, 1542648, 6249693, 2861495, 4916165, 6300228, 7497608, 8309932, 6156321, 6487400, 8327638, 7371298, 5424612, 6663867, 5772210, 6629827, 7539007, 2514193, 5562023, 7068332, 5303117, 7707994, 8223, 3795723, 5478086, 2137588, 93822, 1638104, 1465221, 7329361, 1972062, 5138414, 4211961, 4468265, 4725477, 2651418, 6637244, 7985113, 4812949, 1271749, 929771, 559301, 4279472, 5629917, 1447503, 5998389, 2770958, 4641474, 6539054, 2659349, 1682418, 4441221, 616937, 707497, 5214798, 378973, 8098583, 7106900, 6398910, 6623818, 8358923, 6151615, 5488269, 4136087, 6478273, 3235936, 7798343, 673073, 7892010, 6327852, 4935689, 8115877, 2303200, 5632340, 3259233, 2615181, 1081444, 5918146, 3063766, 4188473, 5842080, 5811085, 327900, 6022066, 1763251, 3531723, 8358090, 3722438, 8351298, 6372689, 5875442, 1306913, 304229, 6166906, 7533690, 5513354, 5582126, 4376451, 3772240, 628409, 2377193, 8217663, 471967, 6283520, 4328352, 3835854, 813033, 1971779, 6443521, 848918, 1080191, 6969128, 1551203, 8259411, 1348926, 8327031, 3032129, 4785903, 6622204, 2691066, 1681069, 2286357, 2743601, 7624918, 7086407, 5473655, 290366, 6986130, 7944357, 6743012, 1051970, 4921902, 5626124, 1390814, 5606460, 6807058, 697693, 5992676, 4782714, 8221901, 4362453, 5408031, 2774289, 673142, 4562880, 8052447, 7726373, 8120915, 295912, 1051978, 4915487, 7957334, 4960889, 7380012, 7136705],
[7846773, 8162709, 8347187, 2063015, 1196673, 927161, 457152, 7553436, 5829571, 6986333, 6930569, 6731329, 5459988, 3942283, 5056821, 2774786, 6382794, 4548843, 5579897, 1056468, 846550, 195332, 7255290, 4221574, 5879568, 1693398, 963332, 4557934, 319504, 5698569, 1305516, 5230156, 6319514, 579159, 1528273, 5039317, 3287243, 1242787, 3397751, 4338213, 5640747, 6094696, 4381940, 6979513, 2743137, 4413422, 5378724, 5102355, 4353759, 4533942, 6754445, 7040408, 2241045, 4343392, 1647365, 4924843, 7820145, 4489397, 425347, 1823287, 745703, 1678346, 6811372, 7120690, 2369501, 2388826, 2260003, 4327180, 300116, 6108021, 6150586, 5484511, 3094553, 2645319, 162483, 4857690, 2006187, 2696197, 4983778, 5066142, 3089771, 1723080, 4299276, 3158842, 1208044, 58855, 131303, 7443525, 8180941, 223760, 1546883, 4695417, 3386409, 4610295, 102481, 869404, 2543051, 6350514, 3719013, 432148, 3876593, 700388, 7670197, 6314661, 7895188, 2192888, 2695537, 944940, 5469811, 5468504, 2766551, 4485943, 5911751, 765811, 2128993, 6050795, 63061, 3918430, 527273, 5626711, 5811825, 4094318, 4326925, 2047481, 7870587, 6089178, 6489393, 3785683, 3747740, 4210189, 7462417, 6370575, 7977048, 5247498, 147425, 15388, 7484408, 5897489, 5020674, 7632660, 2222486, 137875, 133331, 4536602, 660079, 82485, 1596064, 1003485, 4884695, 1967000, 2662850, 5230528, 4177034, 2183479, 7184697, 4101751, 353670, 4804217, 5688201, 3753395, 7349253, 3732339, 2770808, 3167477, 5428350, 5954990, 4134012, 7257936, 6945066, 447801, 7984599, 5041851, 2733024, 4272310, 2524029, 7560293, 7791760, 5658663, 7991654, 4370799, 3264101, 6411492, 4976112, 2471521, 606635, 5897965, 1291437, 4374075, 4693067, 6551526, 2566106, 7564658, 8304978, 5766003, 3057545, 3557167, 559327, 6611804, 6473956, 6270029, 1478165, 7574026, 8122177, 8005961, 3184129, 6882752, 933227, 8245873, 6190415, 2027754, 3216766, 6806951, 835660, 8129354, 1861489, 4096193, 1238455, 7670979, 762879, 185135, 4680821, 5893022, 3220010, 8229022, 4045031, 4072110, 6693702, 6059839, 5381035, 7590539, 97574, 8194802, 49736, 6411776, 6409640, 5531343, 355885, 5453374, 4955492, 5853115, 4819192, 2653370, 3398700, 3061506, 5571809, 2379084, 5884486, 6254662, 1362666, 8308299, 1978282, 449217, 3020366, 7641244, 6805872, 1712259],
[3601708, 1994715, 7241695, 6829094, 5880280, 6560843, 7196209, 2401869, 8152980, 214553, 2673432, 5451308, 399926, 2011330, 7562730, 5079233, 2925733, 3174912, 3328379, 6740019, 7730307, 7161628, 6032272, 3100783, 3446394, 4875725, 108911, 8273002, 4416413, 7879767, 3553955, 7454951, 993064, 7307133, 2907518, 6040241, 2279431, 6874393, 6764189, 7249798, 3349815, 589720, 4581831, 7121860, 8010918, 1127888, 6557982, 2506266, 7285941, 7644821, 5600421, 5739867, 8310486, 1891023, 3951662, 5642047, 6950383, 2851922, 6068222, 6489472, 6789928, 6421432, 7213874, 4358981, 8240568, 5611936, 3288902, 2679347, 4901585, 8175885, 4543325, 7242096, 1648109, 3963145, 106460, 1354320, 5440525, 2030561, 7507826, 3890832, 1579421, 8259196, 6166691, 5375662, 4421256, 2067801, 6818147, 1158340, 6937941, 7440494, 4451668, 4880725, 7079745, 5809160, 6083203, 2637931, 2086, 7858550, 7999020, 5805350, 540099, 8174679, 2224986, 2051663, 4747334, 1962946, 3939689, 7113804, 5976736, 1739661, 899549, 4470963, 2110255, 5334579, 8152121, 5060715, 819385, 3971676, 7780412, 4953980, 839552, 7651423, 1149519, 6675888, 1681861, 5526789, 2527593, 4678796, 6484160, 6435191, 2840097, 5114589, 3968689, 1292601, 2193905, 3138113, 3510916, 6593313, 382748, 2638276, 4831607, 520664, 411293, 7864577, 3972692, 5958299, 5212908, 5392628, 3850844, 7649981, 2081119, 2028025, 2213167, 6904375, 1165860, 1302905, 6712478, 4417226, 6689060, 5105791, 2130981, 1951822, 4115427, 8371045, 3466713, 5634739, 5676818, 2681761, 2283829, 5763899, 5071196, 6564657, 4892674, 4081600, 2127310, 6714530, 3256318, 4902023, 3911117, 1779208, 400663, 3827454, 3992220, 2101359, 1506073, 7201125, 5417283, 2203803, 1262258, 4139778, 271047, 4367666, 2260375, 6080926, 5823981, 2556633, 3105432, 4791828, 2707050, 5958155, 3956308, 6571850, 5165587, 6425200, 3325748, 4825662, 4335842, 7887365, 629137, 7542913, 7453015, 4589811, 8283281, 3036367, 341702, 1505867, 7450041, 7390832, 2645941, 798216, 2384848, 3483028, 5424462, 7569725, 5178226, 7886996, 3542793, 7565015, 6481139, 2372983, 1361670, 7047947, 1362557, 660472, 2152899, 6904483, 3838188, 2482476, 5680270, 305637, 6048625, 2347105, 1152057, 8013717, 3060628, 1643826, 2535233, 4259430, 350377, 2444443, 6199556, 5131144, 4828476, 6495968, 1306105, 3155761],
[3918565, 5971241, 1764749, 5338358, 7441993, 5773952, 562790, 6160104, 23542, 944781, 4941628, 5549968, 265384, 7329394, 7277009, 694316, 4622898, 6191746, 5927354, 4701758, 9898, 2798613, 904240, 3592583, 4508025, 6424837, 7091428, 5809992, 6321607, 6294948, 1588464, 1767958, 2266526, 5066598, 628971, 1528704, 3988719, 7675621, 1924701, 956201, 5894487, 2202967, 3721426, 31576, 2296753, 7289878, 2654334, 3097573, 5849876, 7334873, 5787258, 4144285, 4635310, 685606, 3994332, 3133928, 7795521, 2341525, 4188412, 6988048, 7440887, 1888581, 5958595, 4682223, 493188, 6388696, 5161371, 7322606, 961411, 3335760, 7344158, 456305, 3132338, 805085, 6995013, 1779019, 7439219, 2654111, 3469301, 8289304, 2526903, 4056502, 1127740, 547309, 2251974, 6459039, 5192796, 2672142, 4123288, 3696083, 5178942, 217058, 3797925, 6344251, 1059981, 382460, 4562194, 1740332, 6303302, 6927475, 1248196, 5864828, 7647620, 7778894, 7329507, 1546238, 4120725, 3440344, 3896109, 4878183, 1901393, 7694957, 1457839, 2856499, 611040, 7902178, 5054629, 4289935, 7234474, 2048466, 105819, 1692072, 2959026, 6726637, 1418817, 5930067, 6081567, 4439374, 3446020, 1262056, 3279150, 1800391, 5777498, 3878162, 4428744, 179549, 7786437, 6389493, 870072, 5606518, 786622, 8015378, 7441545, 7219377, 5979660, 8060688, 3474734, 4856331, 2679898, 2834090, 4559070, 6116854, 4429284, 5949379, 3874383, 2424550, 3642093, 7653803, 6286715, 6098774, 698753, 7633276, 3185280, 2161997, 591713, 2021545, 755085, 649866, 1800676, 4899097, 4402762, 5443452, 1354860, 575710, 3393616, 8364316, 8361077, 4234546, 5741955, 7346402, 677564, 1302157, 2331467, 390808, 145557, 2806951, 4000148, 1347837, 472240, 5544948, 3369463, 2311339, 6885342, 5225310, 8192012, 990075, 5504802, 679594, 507874, 3147003, 1605285, 2016347, 4297712, 4516778, 4242052, 4660532, 6727803, 2141884, 5051360, 3057100, 2333068, 1993445, 7200243, 6475497, 3022085, 3666859, 848320, 3714868, 4586616, 3412026, 7519501, 6304544, 2766331, 7674588, 4728228, 2213779, 2181478, 6894996, 3700707, 4019940, 796095, 877920, 5496885, 7225827, 2126049, 7381438, 6832817, 5357018, 3411344, 4023104, 4405132, 3487865, 307767, 5686616, 6801866, 5452247, 4019848, 2197126, 6833383, 6797733, 2505526, 376757, 8059039, 7537424, 1570598, 2774082],
[5313805, 6822608, 8178325, 8034389, 3619975, 3670940, 2019863, 6550148, 3338996, 3894367, 3954028, 6345117, 5594869, 4486438, 7509837, 233303, 6112001, 7487466, 6054465, 2324758, 5118687, 6594390, 7418722, 471263, 3568574, 4561619, 2946107, 6993778, 2905263, 4126487, 7380271, 7937898, 7151324, 7950776, 5772581, 6979591, 2242764, 1889425, 3132571, 6695929, 5881206, 7562073, 1708107, 2452154, 2270707, 1014804, 4715276, 8154933, 6179635, 35768, 5470564, 6277, 2603976, 4626394, 182189, 2353100, 2864784, 6832482, 1939959, 39187, 1813889, 7079187, 5948543, 2876855, 4973083, 5401420, 6874509, 3229038, 1427112, 6264609, 3268939, 1687110, 83363, 5056097, 594655, 5400137, 2579969, 227825, 7344207, 6101056, 2782584, 5295431, 941043, 1399534, 8067032, 1089869, 4524627, 3009288, 299253, 6740780, 7306854, 1642220, 6590008, 6697552, 7917390, 5883032, 2615357, 97764, 6494361, 1438782, 5114663, 6292478, 280152, 5505944, 3388533, 7208824, 899489, 6658094, 4313967, 146484, 837014, 5698872, 4021318, 6773239, 7407583, 1404110, 6159646, 5825141, 7151249, 3713650, 1226736, 3127097, 7186887, 2173051, 2274377, 3226325, 1404888, 5423625, 3412216, 7810852, 944445, 2117817, 4473804, 4809851, 7658186, 4345369, 3644011, 238677, 8148623, 285020, 288146, 6700579, 8364128, 837471, 7084057, 7494910, 1793216, 7083452, 1648275, 7075901, 952969, 5023765, 2341214, 1935999, 6698159, 3352076, 593306, 4588916, 2225660, 7787512, 5801919, 121120, 1215148, 6519921, 5443459, 7847105, 1949394, 2641467, 2038364, 2095834, 7246308, 2102112, 5471439, 650334, 3295265, 1492593, 6734014, 2275086, 6041039, 1838152, 6893049, 6981554, 4288393, 3305466, 2803013, 3070142, 4301483, 7446775, 205654, 373023, 3407593, 2415327, 3570856, 8088841, 3771630, 6540484, 6380957, 4377683, 4008627, 7015929, 6683886, 4365240, 5277719, 2391502, 8379439, 6541023, 6547643, 4312595, 6721430, 5918142, 6332259, 64892, 7820318, 2585617, 8056638, 337412, 3080249, 8340895, 87239, 7074083, 7306537, 4129560, 6405060, 2023986, 2072428, 2889357, 5586547, 2765648, 6109333, 661627, 1912217, 4787080, 1753005, 6758217, 6835396, 1689453, 3341813, 1891417, 1989092, 4388218, 759619, 2452756, 5033847, 283431, 3783385, 6312271, 4540195, 7407893, 6815253, 1960079, 775825, 7384698, 528780, 320928, 7882984, 6442086],
[3558269, 3064545, 2536539, 2805485, 375953, 5108601, 3767194, 2161469, 7331407, 1787268, 623534, 8231484, 5203509, 1689160, 2422170, 6606545, 2030389, 5919526, 7307161, 466138, 1273813, 7327236, 186379, 2613136, 1788182, 6905676, 2078758, 184401, 6957156, 4346068, 2277856, 3887952, 7138746, 5677913, 7520643, 4727485, 3106842, 4740340, 3220910, 252650, 2938082, 2364823, 3396909, 2304607, 4507699, 5864867, 6215542, 5829195, 843714, 7789555, 1796582, 2391027, 714333, 7877918, 5745327, 6591453, 3281473, 1515008, 6916463, 62, 4303544, 4292481, 60268, 7941737, 7454982, 954237, 2420168, 3398549, 2787902, 6793894, 486470, 2356617, 5833546, 455166, 3801788, 2624646, 7983274, 4136223, 5849463, 2803846, 4623708, 1941782, 4032108, 350346, 2989170, 5295300, 4529997, 2332389, 7026766, 7086595, 1112353, 4503311, 2559076, 7392965, 7515957, 5032507, 7412182, 6351541, 3095208, 1200745, 7552729, 1126408, 4194346, 3998557, 209639, 331986, 5863698, 6583447, 2053286, 7848961, 7185068, 6683897, 1922171, 1533091, 439055, 5276802, 5568476, 104172, 3243166, 2029203, 3744605, 1488583, 6403256, 6489833, 3030370, 6888676, 4215839, 2141182, 7466347, 5272667, 1701983, 3893082, 8189825, 7798055, 8221606, 3519664, 1967881, 2053295, 38548, 1856047, 6819604, 5099061, 7135475, 83029, 4425764, 7793424, 1464499, 3603555, 824315, 112290, 3570167, 6297149, 997267, 4286260, 118184, 682768, 3833045, 7402206, 4302894, 7778932, 1509986, 1075214, 4309, 8089324, 4644856, 3312074, 5506995, 2157592, 7490873, 6982737, 5393612, 1566314, 6746469, 2515528, 2646930, 7339250, 1567709, 4643119, 4431063, 6925757, 582390, 7633636, 7446123, 6920390, 6339387, 7155054, 2326703, 5253143, 6002605, 4979960, 3602950, 3730409, 5634398, 323045, 2645199, 4904277, 179534, 3184357, 1972184, 6067731, 4007171, 2968924, 6655352, 8173534, 5330878, 3962795, 4820596, 2005378, 476017, 843332, 4265525, 2591730, 3364100, 7499411, 6606275, 8306732, 3575165, 4591531, 1840818, 5242527, 6466207, 625948, 2862251, 3803846, 5469627, 1632030, 558531, 6392861, 3229655, 2511183, 3390691, 3629089, 4530469, 402537, 6399754, 1792047, 4364122, 8126214, 5965718, 131287, 2694135, 5616886, 3160660, 4829126, 7561966, 8224386, 5847075, 3814198, 2289612, 138266, 2313612, 1207398, 7008730, 3052060, 1262727, 6184747]]
w = NTTInverse(aHat * NTT(y)): [[7176087, 2453101, 5436844, 1773792, 493702, 1886538, 7305009, 3449455, 764704, 787763, 5933737, 1006010, 6146373, 4926946, 7666382, 1234820, 2375419, 5648044, 4132594, 717266, 6470094, 5005570, 1965663, 3489637, 7833836, 6813616, 2661938, 2741072, 6700763, 1048459, 1945196, 665206, 5577744, 7815672, 2448359, 1675067, 2794452, 5109846, 768073, 7483535, 1574531, 1552938, 8160946, 7212069, 1884280, 3440988, 3632538, 345082, 2478239, 5934944, 2622312, 3687127, 1885569, 2679541, 7200289, 6478821, 1543852, 1482036, 4019148, 7342209, 8055406, 5970613, 7146141, 1281083, 5163093, 3670561, 629689, 1209455, 2324529, 797997, 7037088, 3133583, 6438700, 5524943, 4842146, 19437, 7823774, 6138299, 4151114, 7074923, 4771609, 5670916, 6515954, 1528361, 3500001, 8028303, 1158123, 4226485, 7046893, 7667994, 6723813, 1562456, 5528398, 5427140, 4456183, 5184947, 4072329, 1643984, 7088264, 2676550, 1396467, 7725634, 4014071, 5039271, 4478659, 3194992, 7792468, 5686508, 5519398, 6339694, 3630933, 1077624, 2637947, 7925664, 5094737, 1484727, 5624143, 2602333, 7873128, 4500854, 5072396, 1468171, 7377284, 3113000, 6994116, 2992110, 2391631, 7681205, 4950169, 6383294, 2739315, 8191179, 3419122, 3620572, 1143545, 4022400, 2795366, 6938193, 8319723, 1448750, 6115511, 5378533, 4332279, 1443284, 8315182, 4589887, 4748955, 6813117, 5123771, 4228504, 3910640, 4297274, 480403, 480382, 4159005, 6374306, 5030816, 4738855, 5558835, 1305591, 1670801, 2892743, 6139922, 7387772, 2503570, 5838861, 475350, 5695459, 4572301, 2632371, 3353925, 3937693, 858117, 4058667, 5172007, 7539807, 1230123, 3689545, 1840361, 47995, 152057, 3941989, 4480510, 1604200, 5674458, 2685694, 687831, 3606883, 993428, 2435498, 3497605, 2232102, 4375300, 1322056, 6783200, 318814, 4807389, 3366101, 6578095, 5547656, 3538625, 4693856, 3526402, 7908033, 5997190, 1462844, 3392868, 1041757, 3279496, 4714710, 7809, 1667026, 421907, 3515396, 3450901, 3248073, 7151944, 461200, 5214070, 2319016, 2233993, 8207799, 368889, 6465439, 4849080, 7204912, 2742594, 51758, 8029524, 2952314, 269834, 2255974, 7886895, 517529, 8331980, 5782392, 2065141, 5581895, 5495316, 5607784, 4771909, 3624870, 1216713, 7008424, 3057071, 2728274, 1210611, 5508004, 7142777, 6772707, 7498684, 2017129, 2420765, 677233, 2505831, 7198796],
[6377515, 3958736, 4607720, 1254925, 2363935, 5704429, 4135435, 4815556, 3206264, 5003461, 5213844, 6327296, 6078449, 1970178, 2848291, 226503, 7403749, 5980877, 2423655, 4532136, 463449, 6769279, 5101808, 1132450, 7682951, 3152443, 6977898, 284693, 6027908, 3168441, 3506979, 430361, 8284816, 3995412, 7135979, 3372648, 3790561, 2687358, 1824742, 585805, 1685190, 7892142, 3193055, 4053255, 976132, 5171258, 7406956, 3035861, 677208, 4143736, 956647, 4839238, 930729, 6193047, 7454134, 453512, 4169507, 3541439, 4596238, 178082, 6497432, 1995468, 482855, 4891607, 6273288, 5820776, 4761364, 4391310, 6642786, 8191496, 7019176, 3133610, 856128, 4002086, 6998071, 7169546, 115478, 6533104, 5931622, 7633618, 8206996, 4168140, 6830497, 4236540, 2767875, 2370790, 367334, 6578828, 6920584, 5643082, 315642, 5474798, 3939551, 2182409, 5508002, 1618509, 1613156, 4212699, 1050887, 1035992, 1878838, 3791486, 4350337, 4536824, 2472150, 458603, 2534079, 5690371, 4558128, 7395710, 6077322, 579251, 5053545, 5479280, 3891665, 51998, 6472664, 2396080, 3100661, 2662095, 877425, 7036058, 6511610, 4044433, 649814, 4305592, 1754691, 83045, 1559649, 2603889, 222869, 3183707, 5117223, 426830, 2652743, 2583326, 8260091, 2589805, 3375832, 2656264, 8000770, 5751891, 2282085, 3241533, 1353201, 3606605, 5891162, 3268271, 3373652, 6176612, 3978840, 860104, 6634859, 2086019, 6696882, 5402580, 7216430, 432304, 1080296, 8131409, 7675526, 6770989, 6067548, 2757478, 6759027, 7502529, 5138945, 998661, 7517548, 3111672, 6554503, 3582922, 2074795, 7158441, 4282844, 2763850, 8109464, 7391453, 3485872, 2831409, 5101932, 6798391, 8043402, 7149016, 6428394, 238246, 6321798, 6675654, 5490213, 1647602, 1841786, 5835129, 381555, 3728654, 2802517, 729474, 3206965, 7368197, 5223221, 5732234, 6377443, 419957, 5431252, 2975167, 1984155, 2297920, 4609864, 4325573, 4772137, 6373118, 3323922, 6560030, 1747007, 1580559, 263031, 1937519, 3233458, 4550761, 2209916, 1355684, 3521474, 7542169, 8271309, 1774375, 6158684, 5174610, 5436139, 2051628, 756046, 3968454, 5791599, 764164, 7955428, 3011535, 3574811, 3174409, 8058391, 968090, 184228, 4295777, 642131, 6993285, 6850467, 335434, 1667574, 3078127, 1666854, 5917978, 849710, 1334194, 813377, 6927512, 7783049, 4131608, 2552119, 7710802],
[282263, 1389765, 709183, 6136513, 1851211, 3570839, 1288402, 2498300, 1707845, 6987998, 4507974, 6245672, 5311409, 3558059, 1897591, 7637943, 7438234, 950822, 3849800, 6773437, 4262807, 5947579, 2478475, 5146894, 5289065, 4972547, 964686, 7445431, 3728859, 6563081, 6776978, 8304349, 899925, 3189889, 2952473, 232843, 2119889, 7203095, 6053978, 1605855, 1258392, 8216036, 6420995, 1833484, 4663562, 5654968, 5943830, 6818824, 7970535, 4900100, 6431613, 2393829, 7350070, 8109667, 7448650, 7573984, 3174055, 1624964, 781737, 5130191, 6291693, 3202208, 1963630, 3006212, 3290694, 2133002, 6993631, 5164189, 2735846, 1469986, 4954265, 6849429, 4899232, 3655875, 6361182, 2414026, 6061635, 1606191, 777499, 6440339, 5490841, 6621891, 1527671, 5401681, 3927852, 3708282, 5653730, 2587534, 2625259, 7079239, 5022565, 7166640, 3425073, 6061523, 737801, 4046193, 962522, 5918418, 5613878, 5970694, 2158525, 2188257, 6412161, 352457, 5003480, 7573204, 3071268, 1705624, 6443224, 5082912, 8160703, 6395479, 7612815, 313407, 1319495, 6303972, 2461728, 5233484, 5656266, 2430686, 2802599, 4081404, 6833779, 5347309, 4033063, 7715077, 8327641, 679277, 4065761, 6729446, 5662796, 7002807, 765693, 4904289, 4239108, 8181561, 2356172, 1208373, 3145942, 6854198, 4489910, 7659120, 4309437, 224111, 61490, 200749, 4790357, 6841087, 6811635, 1801444, 1814974, 8371955, 1916399, 1171915, 4271051, 178740, 6767398, 8059756, 3036776, 4802708, 2578426, 6670691, 6044490, 1292338, 7027463, 1788702, 5235813, 7370008, 495359, 3461442, 2492638, 2615729, 2822886, 5352688, 7392691, 5189971, 4755135, 2297201, 1123597, 709186, 6336535, 4907706, 8317748, 1626501, 493480, 1987279, 2716966, 3850857, 7929426, 823607, 1085890, 3723172, 4451368, 3745556, 3481156, 3204498, 1475634, 3180581, 5364750, 5468619, 7886262, 7846947, 6069330, 5854616, 3772634, 254975, 8199123, 5673367, 3452052, 6589640, 2733895, 3975158, 3806013, 3333090, 4539876, 6943304, 2261177, 3817733, 4452145, 476428, 1225274, 7239138, 1989125, 3482705, 8079831, 2742937, 3290721, 6812125, 293541, 2195356, 833600, 2465489, 4370990, 6908032, 6843618, 7176723, 5611574, 1032161, 4112196, 3493516, 3322601, 6422249, 4484605, 765289, 2204722, 3402790, 7250870, 7009320, 4175337, 402585, 1723875, 7731025, 4828924, 4371877, 1695224, 1940803],
[5875287, 6632421, 2890532, 7079728, 5304461, 6335027, 1521557, 6903226, 2033895, 739559, 7545997, 2208961, 3106698, 5907509, 7332867, 5171025, 1750982, 2372551, 1855645, 1057883, 4158850, 3930316, 3349187, 6790809, 5642959, 1632828, 2161428, 818833, 4698797, 501585, 2560105, 6726317, 2882979, 697071, 2100206, 6301205, 112743, 945770, 5818529, 3463043, 5266162, 2751596, 7136182, 318285, 7441441, 3901923, 5660833, 8089413, 2910244, 998927, 7614477, 2991084, 4075245, 171800, 195550, 4516930, 2211323, 4714769, 6469176, 1676113, 464321, 7447405, 7093915, 160127, 6404386, 5524355, 2342460, 5564022, 1200700, 3502461, 4511815, 625812, 3567187, 1428322, 5212307, 5875686, 4607563, 7639855, 4426071, 544974, 836215, 3134583, 1179854, 1236007, 5239635, 8194401, 1675163, 5789095, 4470949, 5040026, 2780624, 8239614, 2969036, 6992234, 2990258, 2522551, 5451240, 3984997, 60886, 6139183, 4459006, 4311577, 4760882, 1479177, 2272060, 3792713, 5690789, 6300667, 2198868, 8024944, 4622500, 195666, 3383997, 5709021, 5036274, 742858, 346659, 4893511, 8280630, 2625779, 3858733, 3797288, 7807815, 4767127, 83134, 5533123, 59272, 2593912, 3792245, 2710874, 1990765, 5831517, 152145, 4891471, 2525978, 837873, 4431013, 3539938, 3606861, 4042614, 992279, 7644228, 867087, 467601, 7842585, 5699266, 8214904, 6112450, 7249856, 116973, 2065561, 6881607, 7725578, 1858494, 4578002, 2581426, 1403458, 1346799, 4052915, 6042884, 6578509, 2464386, 7423731, 3418538, 1624680, 1841758, 2664368, 183573, 3962821, 7816009, 2446019, 6452774, 5854843, 7835015, 839790, 1229682, 7823812, 5458833, 1891723, 1938073, 5973536, 5508114, 5325164, 6045257, 6558552, 53996, 2345343, 3989507, 4711289, 7108192, 2446219, 4159458, 1183474, 35264, 2812862, 14846, 4324006, 3859727, 2096085, 4930909, 1482643, 5880719, 3527377, 3323983, 4583217, 3648018, 3654069, 4979168, 4123344, 1542152, 6449444, 2615632, 5953026, 1205702, 5910009, 6934356, 2299154, 6965014, 6877408, 4993085, 6144236, 5020160, 5606844, 268231, 3035297, 6656338, 1547531, 5086352, 8268611, 298404, 4411647, 7569412, 7123552, 3362985, 6122328, 4852737, 1266578, 5155740, 8180530, 6190975, 3045121, 2525104, 2252904, 1273587, 3743130, 53546, 4173548, 1026578, 3139916, 2132116, 3309956, 6242873, 4647202, 3259576, 6518298, 7334298],
[6661874, 418668, 1739485, 2853440, 5701355, 2208473, 1260024, 8333215, 1767406, 33103, 2786797, 3238808, 3724250, 1888342, 4565153, 5041520, 6600542, 3229968, 6968313, 4219596, 7340820, 6578268, 6016955, 2214049, 912213, 2282835, 1561761, 3648099, 7780218, 3377776, 7323979, 7456984, 3574212, 2205252, 1682988, 1488939, 7084873, 6632791, 4057469, 6261115, 5200090, 1502407, 5416109, 4004784, 2147191, 995228, 2545399, 3605031, 1617922, 6963812, 5269957, 1945925, 5230130, 4916142, 3928800, 6151980, 5525877, 7592713, 7895814, 5966463, 4104914, 6803559, 5408359, 5249108, 76066, 2995704, 451753, 2767103, 3726137, 5666105, 2290001, 2367140, 6842449, 6600967, 3788867, 5368637, 1234117, 1256343, 201840, 1074249, 507261, 2457613, 6014024, 117389, 3845080, 6240686, 8261055, 808060, 5477419, 2943632, 3829619, 4642745, 6501280, 3105866, 5559994, 931155, 328597, 6116052, 7752377, 2817218, 6710976, 2979545, 5889695, 7464494, 7971605, 1136386, 1358218, 5516145, 1022818, 7946598, 2793272, 1606731, 5649054, 5448360, 3435619, 4085643, 4397308, 5372992, 7270778, 5101506, 7531031, 3342870, 5909817, 6011810, 8212831, 4612082, 5370560, 7209563, 7658778, 6761641, 3003613, 2257511, 3019570, 6460280, 8200331, 3563076, 5252803, 4995245, 8210020, 3844880, 1158155, 3995384, 8227214, 787033, 8215365, 1627477, 5297977, 1187880, 2316633, 1569381, 1136040, 6750701, 334135, 4491860, 2239683, 4606187, 841337, 3684570, 5682745, 1410481, 4532455, 1238752, 2700494, 4336909, 2055979, 755257, 4792744, 6987910, 1424901, 4872184, 4037194, 1226260, 4766612, 2401893, 2027177, 3394235, 7652085, 8173831, 5817641, 2247881, 5158731, 4370046, 3537235, 6729646, 6240829, 1532792, 6690949, 7360963, 5263752, 2585052, 6187699, 4650736, 5654961, 2651488, 6904953, 3052903, 5097928, 3668232, 3417467, 5785059, 7806639, 634494, 5590426, 5777171, 2988007, 1808913, 8159836, 6412506, 3068567, 2634245, 5532616, 6122439, 1333717, 8264011, 6735866, 2048416, 3456794, 7683767, 6613642, 5196208, 7068567, 6320096, 2342140, 5008828, 4963417, 6839520, 3522657, 6928741, 7589762, 8295245, 1583773, 4233034, 5173292, 1434332, 7233094, 4150187, 2496848, 4088799, 2556107, 1653179, 3496936, 945800, 6894421, 1219054, 107967, 1595686, 6654027, 1892916, 3943011, 6500852, 4284810, 6860888, 3553895, 3777658, 3231224, 1621951],
[857445, 871618, 6472249, 6675283, 8161359, 4388115, 1704194, 2307391, 6863427, 5622255, 1146191, 250180, 880790, 4924912, 6283047, 4010770, 6841398, 8268097, 3805646, 4330563, 51961, 6082612, 1851032, 1609934, 3792730, 494544, 204471, 127992, 3558413, 4165858, 1335542, 1023303, 6331839, 2312851, 1190669, 826057, 448978, 7385698, 1985891, 2637921, 438417, 2859213, 6565950, 8173013, 2936538, 2933508, 6652005, 6198364, 1932225, 4142005, 8173930, 2820559, 5463914, 6854585, 5158443, 3313969, 2380477, 2005106, 6273920, 1847834, 5034534, 1553021, 7062390, 728814, 3487472, 3716198, 2668981, 3122880, 1568838, 2310641, 8354522, 6869259, 3664673, 145224, 6475282, 8076008, 588270, 2111630, 4472590, 6441994, 3160899, 5889429, 6518742, 8226449, 1713959, 4151238, 3259081, 7288531, 5293303, 2600706, 468825, 7598393, 2416518, 8248771, 4604332, 3078967, 7907375, 4057723, 4221117, 2649395, 668505, 3556842, 20862, 630087, 3987812, 7170626, 773032, 6537727, 7299358, 2121511, 2986090, 5005226, 2398431, 4767648, 901234, 5716713, 2781612, 3249264, 5681029, 6609866, 6781270, 4985807, 4310612, 6411386, 2695497, 4640263, 4868381, 6937539, 936772, 1693862, 3161698, 3929397, 4090036, 3471933, 5857005, 4612527, 5636321, 5536094, 1874394, 4776833, 2104835, 967126, 4132323, 3994956, 7587631, 3877694, 6790304, 2357593, 5107419, 781201, 4792739, 2192528, 455595, 5760663, 2434968, 7987233, 2289581, 1095464, 1943812, 6552879, 7854472, 4879915, 4467248, 3358609, 6026078, 5890453, 8066632, 4236922, 4182713, 966484, 5255267, 1576411, 4215775, 1921845, 3123789, 296862, 5628749, 6118279, 5216610, 7259005, 6498344, 1662899, 2915894, 1389776, 1828729, 7575774, 1708037, 3718103, 3662039, 7652845, 5603433, 7749290, 1166626, 5954997, 805739, 1678187, 1014585, 4688167, 2481287, 761240, 8177842, 3182138, 2414811, 8225196, 7080213, 2251882, 7201385, 1859024, 3509042, 336666, 4503412, 8281871, 6421984, 2294112, 7414833, 8571, 626249, 4656341, 872386, 6621926, 3120540, 4822259, 8129814, 3518472, 4607726, 47868, 3524739, 6894346, 7020948, 580843, 8086402, 8165096, 2684300, 3342028, 3817344, 670178, 6138986, 892443, 8336433, 7119514, 4104217, 1003818, 748618, 2534025, 565538, 692984, 276395, 7516959, 4651712, 1964401, 7060298, 4292819, 3909497, 1286170, 5921717, 4228798]]

w1: [[14, 5, 10, 3, 1, 4, 14, 7, 1, 2, 11, 2, 12, 9, 15, 2, 5, 11, 8, 1, 12, 10, 4, 7, 15, 13, 5, 5, 13, 2, 4, 1, 11, 15, 5, 3, 5, 10, 1, 14, 3, 3, 0, 14, 4, 7, 7, 1, 5, 11, 5, 7, 4, 5, 14, 12, 3, 3, 8, 14, 15, 11, 14, 2, 10, 7, 1, 2, 4, 2, 13, 6, 12, 11, 9, 0, 15, 12, 8, 14, 9, 11, 12, 3, 7, 15, 2, 8, 13, 15, 13, 3, 11, 10, 9, 10, 8, 3, 14, 5, 3, 15, 8, 10, 9, 6, 15, 11, 11, 12, 7, 2, 5, 15, 10, 3, 11, 5, 15, 9, 10, 3, 14, 6, 13, 6, 5, 15, 9, 12, 5, 0, 7, 7, 2, 8, 5, 13, 0, 3, 12, 10, 8, 3, 0, 9, 9, 13, 10, 8, 7, 8, 1, 1, 8, 12, 10, 9, 11, 2, 3, 6, 12, 14, 5, 11, 1, 11, 9, 5, 6, 8, 2, 8, 10, 14, 2, 7, 4, 0, 0, 8, 9, 3, 11, 5, 1, 7, 2, 5, 7, 4, 8, 3, 13, 1, 9, 6, 13, 11, 7, 9, 7, 15, 11, 3, 6, 2, 6, 9, 0, 3, 1, 7, 7, 6, 14, 1, 10, 4, 4, 0, 1, 12, 9, 14, 5, 0, 15, 6, 1, 4, 15, 1, 0, 11, 4, 11, 10, 11, 9, 7, 2, 13, 6, 5, 2, 11, 14, 13, 14, 4, 5, 1, 5, 14],
[12, 8, 9, 2, 5, 11, 8, 9, 6, 10, 10, 12, 12, 4, 5, 0, 14, 11, 5, 9, 1, 13, 10, 2, 15, 6, 13, 1, 12, 6, 7, 1, 0, 8, 14, 6, 7, 5, 3, 1, 3, 15, 6, 8, 2, 10, 14, 6, 1, 8, 2, 9, 2, 12, 14, 1, 8, 7, 9, 0, 12, 4, 1, 9, 12, 11, 9, 8, 13, 0, 13, 6, 2, 8, 13, 14, 0, 12, 11, 15, 0, 8, 13, 8, 5, 5, 1, 13, 13, 11, 1, 10, 8, 4, 11, 3, 3, 8, 2, 2, 4, 7, 8, 9, 5, 1, 5, 11, 9, 14, 12, 1, 10, 10, 7, 0, 12, 5, 6, 5, 2, 13, 12, 8, 1, 8, 3, 0, 3, 5, 0, 6, 10, 1, 5, 5, 0, 5, 6, 5, 15, 11, 4, 6, 3, 7, 11, 6, 6, 12, 8, 2, 13, 4, 13, 10, 14, 1, 2, 0, 15, 13, 12, 5, 13, 14, 10, 2, 14, 6, 13, 7, 4, 14, 8, 5, 15, 14, 7, 5, 10, 13, 15, 14, 12, 0, 12, 13, 10, 3, 4, 11, 1, 7, 5, 1, 6, 14, 10, 11, 12, 1, 10, 6, 4, 4, 9, 8, 9, 12, 6, 13, 3, 3, 1, 4, 6, 9, 4, 3, 7, 14, 0, 3, 12, 10, 10, 4, 1, 8, 11, 1, 15, 6, 7, 6, 15, 2, 0, 8, 1, 13, 13, 1, 3, 6, 3, 11, 2, 3, 2, 13, 15, 8, 5, 15],
[1, 3, 1, 12, 4, 7, 2, 5, 3, 13, 9, 12, 10, 7, 4, 15, 14, 2, 7, 13, 8, 11, 5, 10, 10, 9, 2, 14, 7, 13, 13, 0, 2, 6, 6, 0, 4, 14, 12, 3, 2, 0, 12, 4, 9, 11, 11, 13, 15, 9, 12, 5, 14, 15, 14, 14, 6, 3, 1, 10, 12, 6, 4, 6, 6, 4, 13, 10, 5, 3, 9, 13, 9, 7, 12, 5, 12, 3, 1, 12, 10, 13, 3, 10, 7, 7, 11, 5, 5, 14, 10, 14, 7, 12, 1, 8, 2, 11, 11, 11, 4, 4, 12, 1, 10, 14, 6, 3, 12, 10, 0, 12, 15, 1, 3, 12, 5, 10, 11, 5, 5, 8, 13, 10, 8, 15, 0, 1, 8, 13, 11, 13, 1, 9, 8, 0, 4, 2, 6, 13, 9, 15, 8, 0, 0, 0, 9, 13, 13, 3, 3, 0, 4, 2, 8, 0, 13, 15, 6, 9, 5, 13, 12, 2, 13, 3, 10, 14, 1, 7, 5, 5, 5, 10, 14, 10, 9, 4, 2, 1, 12, 9, 0, 3, 1, 4, 5, 7, 15, 2, 2, 7, 8, 7, 7, 6, 3, 6, 10, 10, 15, 15, 12, 11, 7, 0, 0, 11, 7, 13, 5, 8, 7, 6, 9, 13, 4, 7, 9, 1, 2, 14, 4, 7, 15, 5, 6, 13, 1, 4, 2, 5, 8, 13, 13, 14, 11, 2, 8, 7, 6, 12, 9, 1, 4, 6, 14, 13, 8, 1, 3, 15, 9, 8, 3, 4],
[11, 13, 6, 14, 10, 12, 3, 13, 4, 1, 14, 4, 6, 11, 14, 10, 3, 5, 4, 2, 8, 8, 6, 13, 11, 3, 4, 2, 9, 1, 5, 13, 6, 1, 4, 12, 0, 2, 11, 7, 10, 5, 14, 1, 14, 7, 11, 15, 6, 2, 15, 6, 8, 0, 0, 9, 4, 9, 12, 3, 1, 14, 14, 0, 12, 11, 4, 11, 2, 7, 9, 1, 7, 3, 10, 11, 9, 15, 8, 1, 2, 6, 2, 2, 10, 0, 3, 11, 9, 10, 5, 0, 6, 13, 6, 5, 10, 8, 0, 12, 9, 8, 9, 3, 4, 7, 11, 12, 4, 15, 9, 0, 6, 11, 10, 1, 1, 9, 0, 5, 7, 7, 15, 9, 0, 11, 0, 5, 7, 5, 4, 11, 0, 9, 5, 2, 8, 7, 7, 8, 2, 15, 2, 1, 15, 11, 0, 12, 14, 0, 4, 13, 15, 4, 9, 5, 3, 3, 8, 12, 13, 5, 14, 7, 3, 4, 5, 0, 8, 15, 5, 12, 11, 15, 2, 2, 15, 10, 4, 4, 11, 11, 10, 12, 13, 0, 4, 8, 9, 14, 5, 8, 2, 0, 5, 0, 8, 7, 4, 9, 3, 11, 7, 6, 9, 7, 7, 10, 8, 3, 12, 5, 11, 2, 11, 13, 4, 13, 13, 10, 12, 10, 11, 1, 6, 13, 3, 10, 0, 1, 8, 14, 14, 6, 12, 9, 2, 10, 0, 12, 6, 5, 4, 2, 7, 0, 8, 2, 6, 4, 6, 12, 9, 6, 12, 14],
[13, 1, 3, 5, 11, 4, 2, 0, 3, 0, 5, 6, 7, 4, 9, 10, 13, 6, 13, 8, 14, 13, 11, 4, 2, 4, 3, 7, 15, 6, 14, 14, 7, 4, 3, 3, 14, 13, 8, 12, 10, 3, 10, 8, 4, 2, 5, 7, 3, 13, 10, 4, 10, 9, 8, 12, 11, 14, 15, 11, 8, 13, 10, 10, 0, 6, 1, 5, 7, 11, 4, 5, 13, 13, 7, 10, 2, 2, 0, 2, 1, 5, 11, 0, 7, 12, 0, 2, 10, 6, 7, 9, 12, 6, 11, 2, 1, 12, 15, 5, 13, 6, 11, 14, 15, 2, 3, 11, 2, 15, 5, 3, 11, 10, 7, 8, 8, 10, 14, 10, 14, 6, 11, 11, 0, 9, 10, 14, 15, 13, 6, 4, 6, 12, 0, 7, 10, 10, 0, 7, 2, 8, 0, 2, 0, 3, 10, 2, 4, 3, 2, 13, 1, 9, 4, 9, 2, 7, 11, 3, 9, 2, 5, 8, 4, 1, 9, 13, 3, 9, 8, 2, 9, 5, 4, 6, 15, 0, 11, 4, 10, 8, 7, 13, 12, 3, 13, 14, 10, 5, 12, 9, 11, 5, 13, 6, 10, 7, 7, 11, 15, 1, 11, 11, 6, 3, 0, 12, 6, 5, 11, 12, 3, 0, 13, 4, 7, 15, 13, 10, 13, 12, 4, 10, 9, 13, 7, 13, 14, 0, 3, 8, 10, 3, 14, 8, 5, 8, 5, 3, 7, 2, 13, 2, 0, 3, 13, 4, 8, 12, 8, 13, 7, 7, 6, 3],
[2, 2, 12, 13, 0, 8, 3, 4, 13, 11, 2, 0, 2, 9, 12, 8, 13, 0, 7, 8, 0, 12, 4, 3, 7, 1, 0, 0, 7, 8, 3, 2, 12, 4, 2, 2, 1, 14, 4, 5, 1, 5, 13, 0, 6, 6, 13, 12, 4, 8, 0, 5, 10, 13, 10, 6, 5, 4, 12, 4, 10, 3, 13, 1, 7, 7, 5, 6, 3, 4, 0, 13, 7, 0, 12, 15, 1, 4, 9, 12, 6, 11, 12, 0, 3, 8, 6, 14, 10, 5, 1, 15, 5, 0, 9, 6, 15, 8, 8, 5, 1, 7, 0, 1, 8, 14, 1, 12, 14, 4, 6, 10, 5, 9, 2, 11, 5, 6, 11, 13, 13, 10, 8, 12, 5, 9, 9, 13, 2, 3, 6, 8, 8, 7, 11, 9, 11, 11, 4, 9, 4, 2, 8, 8, 14, 7, 13, 5, 10, 1, 9, 4, 1, 11, 5, 15, 4, 2, 4, 13, 15, 9, 9, 6, 12, 11, 15, 8, 8, 2, 10, 3, 8, 4, 6, 1, 11, 12, 10, 14, 12, 3, 6, 3, 3, 14, 3, 7, 7, 15, 11, 15, 2, 11, 2, 3, 2, 9, 5, 1, 0, 6, 5, 0, 14, 4, 14, 4, 7, 1, 9, 0, 12, 4, 14, 0, 1, 9, 2, 13, 6, 9, 0, 7, 9, 0, 7, 13, 13, 1, 15, 0, 5, 6, 7, 1, 12, 2, 0, 14, 8, 2, 1, 5, 1, 1, 1, 14, 9, 4, 13, 8, 7, 2, 11, 8]]
w1Encode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

cTilde: 10B3206713C7850609621506110EDE8FF646EF118B2C6CB23A36A0771122EFBAD5FAB4B2425B0A8FF4EEB0F85084F578
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
c: [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
cHat: [3645810, 7764467, 4545647, 6700250, 5211569, 7064580, 136201, 3754197, 6978672, 6615361, 964808, 4351899, 5876446, 3300010, 5854002, 4246643, 5286352, 5246453, 8233698, 3716177, 7557141, 5586754, 5482020, 549156, 8117854, 7477472, 6859174, 4665935, 4056248, 2138621, 2731257, 7686667, 1978666, 2154318, 5993959, 2476593, 6821691, 3548550, 647676, 5453922, 5206739, 8060447, 7770684, 5961383, 5099293, 6633544, 5646002, 3557095, 3512742, 206086, 5864240, 3588624, 6770431, 1781556, 5083792, 5605476, 7493036, 7805388, 6780731, 2910179, 3555113, 3024175, 8329352, 4699641, 7819072, 1611894, 1934923, 371131, 3264437, 2434068, 5958269, 579961, 1058992, 2334850, 4534149, 5143224, 871204, 2880275, 1533377, 6365899, 5212163, 6565294, 4980877, 4249337, 52601, 4516756, 3041068, 2716556, 3951992, 3200041, 7452226, 15289, 1175782, 7536250, 3218686, 7571641, 8320733, 3981485, 2395934, 3484697, 897601, 7095301, 7856197, 3371788, 7046495, 4864491, 2124696, 2456667, 5341980, 4099087, 4137909, 6361915, 837104, 2525714, 7936321, 6265789, 5284994, 2625186, 8032175, 5079229, 6182535, 5757387, 8125949, 4334955, 494803, 6803551, 1215230, 2336054, 2364952, 1212032, 3420765, 1736177, 386786, 7096632, 6970127, 6411757, 5188045, 3323532, 1970554, 2197874, 1207488, 6424620, 1708146, 184320, 3511793, 6255970, 5770042, 1780920, 4024826, 4624911, 3914672, 7348532, 6377081, 958746, 2692441, 2676610, 2302812, 4526757, 2048022, 1370089, 7840855, 7517013, 2810239, 1839442, 7738712, 1833397, 5925135, 938506, 2841593, 5644478, 554666, 6333849, 2593908, 4923561, 3983588, 5245699, 2601236, 6060554, 6278809, 7532190, 1606630, 4245840, 7597062, 1410424, 913214, 3877251, 6691546, 6216983, 7053344, 6136777, 1580377, 7142821, 457513, 8000803, 765682, 3268699, 5064478, 785242, 6506218, 3284042, 335399, 7519479, 6028018, 6971447, 372257, 1948709, 4810373, 1023287, 1059412, 7013597, 2278332, 7432780, 6779669, 5793474, 5632093, 2925853, 1368737, 3794375, 1622649, 7088496, 2377873, 4157614, 3267565, 2929544, 4655990, 1459002, 820207, 449629, 2614533, 152508, 7382441, 3888558, 2711356, 6244788, 2383798, 6898506, 1858282, 2678309, 4281789, 281533, 3116115, 5702026, 6125206, 4295173, 6357843, 6629311, 6499532, 6878147, 8032386, 4063742, 6763354, 2758753, 5373537, 1627092, 5905120, 2155560]
cs1: [[8380398, 8380390, 8380415, 8380413, 8380377, 8380406, 8380384, 0, 40, 6, 8380408, 8380396, 8380402, 8380408, 8380402, 50, 8, 8380408, 8380400, 8380395, 8380407, 8380413, 8380411, 8380404, 8380407, 11, 8, 5, 1, 8380404, 8380393, 8380399, 15, 8380414, 26, 8380393, 8380414, 0, 3, 9, 20, 16, 8380415, 8380383, 8380412, 8380396, 20, 2, 8380412, 8380395, 8380407, 22, 8380413, 4, 14, 20, 8380403, 8380411, 21, 8380405, 9, 34, 11, 8380408, 8380392, 8380406, 5, 8380393, 8380393, 11, 8380399, 10, 12, 8, 10, 8380402, 8380398, 8380404, 8380396, 27, 10, 24, 1, 7, 2, 8380416, 8380401, 8380403, 3, 18, 8380384, 8380403, 8380400, 45, 8380413, 8380405, 17, 1, 6, 8380414, 8380409, 8380414, 8380409, 36, 8380382, 3, 5, 7, 22, 8380414, 10, 3, 4, 8380395, 8380406, 8380403, 18, 8380408, 8380412, 41, 29, 7, 2, 14, 25, 8380397, 1, 10, 2, 7, 8380411, 7, 0, 33, 19, 8380395, 8380408, 8380416, 17, 7, 7, 5, 8380389, 8380408, 29, 10, 45, 11, 8, 8380391, 8380394, 8380402, 5, 8380406, 14, 31, 22, 19, 8380400, 8380377, 7, 2, 16, 8380410, 6, 10, 6, 8380401, 3, 2, 7, 8380414, 8380398, 8380407, 8380394, 8380393, 8380403, 8380412, 21, 17, 12, 8380405, 8380405, 14, 6, 10, 8380385, 2, 8380415, 8380378, 8380384, 8380414, 13, 3, 32, 35, 8380415, 8380414, 8380408, 8380385, 21, 5, 8380410, 8380397, 8380384, 19, 1, 2, 8380398, 8380403, 8380406, 8380416, 8380414, 2, 2, 31, 8380397, 8380412, 8380411, 30, 33, 8380395, 9, 7, 8380407, 8380390, 8380383, 8, 14, 2, 3, 8380392, 1, 8380392, 8380407, 0, 8380376, 5, 21, 24, 15, 4, 27, 10, 12, 8380415, 8380408, 22, 17, 8380379, 8380385, 8380410, 10, 8380385, 8380375, 27],
[7, 8380401, 18, 8380411, 16, 10, 8380395, 8380392, 2, 32, 27, 8380385, 6, 14, 6, 13, 9, 3, 8380404, 16, 0, 6, 56, 17, 10, 8380403, 14, 8380413, 8380402, 9, 23, 8, 32, 8380413, 8380405, 9, 8380407, 17, 8380379, 8380389, 8380412, 8380412, 5, 36, 8380402, 8, 8, 21, 8380387, 8380411, 8380410, 49, 2, 8380395, 8380405, 4, 4, 8380413, 10, 34, 8380386, 8380393, 15, 7, 8380386, 8380397, 8380402, 8380410, 21, 18, 28, 4, 8380387, 8, 8380414, 17, 10, 8380415, 2, 8380411, 3, 8380396, 22, 10, 4, 8380411, 11, 15, 4, 20, 12, 8380356, 18, 8380407, 23, 10, 9, 16, 15, 8380395, 8380411, 8380376, 8380408, 8380415, 24, 2, 8380416, 8380388, 5, 8380408, 1, 8380397, 8380413, 8380415, 8380415, 8380406, 12, 3, 8380413, 8380412, 8380393, 13, 4, 8380406, 8380404, 8380408, 8380401, 8380414, 8380408, 1, 21, 35, 8380397, 8380392, 9, 8380409, 8380407, 8380404, 8380415, 8380407, 8380406, 43, 5, 11, 16, 8380411, 2, 8380407, 8380396, 18, 2, 19, 8380384, 8380384, 8380396, 8380414, 8380409, 19, 17, 8380415, 8380385, 8380412, 11, 8380416, 8380400, 8380398, 8380414, 8380406, 16, 3, 9, 8380403, 8380402, 13, 8380406, 8380410, 3, 8380408, 1, 8380391, 8380416, 8380406, 8380409, 8380409, 8380415, 8380411, 37, 8380398, 19, 5, 1, 22, 8380403, 8380385, 17, 8380401, 8380404, 8380390, 8380413, 17, 8380401, 23, 9, 8380403, 18, 7, 8380416, 8380398, 8380403, 5, 8380414, 8380406, 8380390, 25, 8380414, 8380406, 11, 8380414, 8380397, 8380406, 1, 12, 21, 8380402, 8380389, 8380399, 8380407, 8380401, 8380401, 8380413, 0, 8380401, 3, 16, 14, 8380414, 8380410, 25, 10, 8380413, 2, 8380404, 8380408, 5, 8380416, 19, 8380406, 12, 13, 16, 3, 8380415, 10, 8380386, 8380376, 13],
[37, 23, 8380400, 0, 18, 12, 9, 8380403, 14, 8380414, 8380397, 8380414, 8380414, 8, 8380414, 8380390, 1, 8380402, 4, 30, 8380396, 11, 13, 20, 19, 16, 42, 1, 4, 8380412, 4, 8380398, 8, 8380415, 8380365, 8380404, 8380370, 8380400, 8380401, 8380415, 42, 6, 26, 14, 8380415, 18, 1, 28, 1, 8380402, 3, 8380401, 5, 8380406, 15, 8380413, 8380407, 7, 22, 8380412, 8380400, 8380402, 8380416, 8380395, 11, 32, 16, 10, 8380409, 19, 2, 8380413, 5, 3, 8380414, 20, 8380416, 8380397, 6, 8380407, 8380405, 8380375, 8380396, 8380409, 8380405, 34, 24, 28, 8380404, 8380403, 0, 8380407, 1, 8380402, 8380401, 5, 8380413, 8380401, 20, 2, 11, 8380376, 8380404, 34, 26, 8380408, 8380402, 8380395, 8380409, 8380413, 8380411, 10, 20, 27, 47, 40, 1, 24, 8380410, 1, 1, 11, 8380416, 8380410, 8380414, 8380399, 8380411, 3, 9, 8380401, 1, 1, 8380410, 8380410, 13, 8380408, 8380404, 9, 8380388, 25, 31, 16, 7, 8380374, 8380407, 15, 8380404, 35, 8380391, 8380383, 5, 0, 7, 8380405, 8380369, 8380389, 8380405, 20, 13, 24, 24, 16, 8380380, 8380407, 6, 8380408, 8380411, 8380400, 0, 11, 8380395, 8380413, 8380409, 8380410, 15, 9, 48, 11, 24, 8380390, 2, 8380415, 27, 11, 6, 21, 16, 8380393, 8380398, 8380398, 6, 1, 8380404, 8, 8380407, 8380377, 8380394, 10, 8, 15, 8380396, 8380393, 8380404, 8380408, 17, 8380392, 17, 9, 9, 8380400, 8380407, 8380407, 8380400, 8380409, 8380416, 8380410, 8380414, 8380392, 8380397, 8380410, 8380403, 31, 22, 12, 17, 8380403, 6, 8380400, 8380403, 38, 15, 2, 6, 3, 8380399, 8380397, 8380393, 8380397, 8380412, 11, 19, 4, 8380386, 14, 8380414, 39, 39, 8380400, 16, 8380403, 8380409, 17, 8380414, 4, 8380410, 8380395],
[8380394, 11, 2, 8380413, 8380390, 8380377, 8380401, 8380414, 11, 8380404, 7, 7, 14, 39, 20, 7, 8380393, 8380392, 14, 8380385, 0, 25, 13, 8380392, 3, 8380408, 8380410, 3, 0, 8, 5, 17, 12, 8380400, 1, 20, 22, 2, 8380414, 21, 7, 8380398, 6, 8380411, 8380401, 8380398, 8380415, 8380408, 8380416, 29, 26, 6, 8380397, 8380405, 8380416, 8380408, 7, 8380399, 3, 1, 29, 8380416, 2, 8380398, 8380392, 8380409, 8380381, 3, 8380396, 8380414, 8380412, 8380414, 9, 11, 6, 30, 0, 4, 8380407, 8380409, 8380391, 8, 8380409, 8380409, 8380375, 25, 8380412, 18, 8380411, 8380400, 8380397, 8380388, 8380396, 28, 5, 38, 19, 34, 21, 0, 8380416, 14, 8380411, 9, 7, 0, 0, 3, 3, 4, 8380414, 12, 7, 8380415, 5, 0, 8380415, 5, 21, 24, 8380390, 0, 2, 17, 31, 14, 0, 8380399, 8380384, 8380399, 8380400, 8380398, 17, 21, 16, 8380409, 18, 7, 8380386, 5, 14, 11, 16, 8380391, 18, 8380369, 8380412, 25, 8380405, 8380412, 8380385, 1, 8380410, 8380407, 16, 16, 8380398, 8380402, 9, 17, 24, 10, 8380416, 8380415, 16, 8380401, 8380407, 8380403, 12, 8380412, 5, 12, 12, 10, 8380408, 8380413, 8380409, 14, 8380406, 34, 5, 8380408, 8380413, 6, 28, 10, 3, 33, 8380408, 0, 8380411, 8380416, 8380386, 8380386, 8380400, 8380404, 13, 19, 22, 31, 6, 19, 13, 8380398, 4, 5, 0, 8380406, 5, 8, 8380404, 8380396, 7, 12, 5, 22, 14, 8380383, 5, 32, 8, 8380399, 8380397, 8380415, 11, 9, 10, 10, 8380391, 10, 1, 0, 8380416, 16, 8380408, 8380407, 31, 31, 8380407, 8380413, 16, 8, 8380407, 29, 19, 8380397, 8, 31, 22, 8380376, 8380401, 21, 8380416, 8380377, 0, 8380395],
[22, 8380408, 11, 8380397, 8380416, 8380393, 8380400, 8380388, 24, 1, 26, 8380399, 8380380, 10, 4, 8380405, 8380397, 8380388, 14, 22, 4, 8380409, 9, 27, 8380411, 8380402, 8380396, 16, 8380408, 2, 8380416, 8380415, 16, 34, 8380370, 18, 8380405, 24, 8380407, 16, 8380373, 2, 8380411, 8380416, 6, 8380404, 35, 20, 8380386, 8380401, 15, 8380410, 1, 8380413, 8380412, 21, 25, 8380404, 3, 8380396, 0, 8380407, 0, 8380411, 8, 8380411, 12, 8380405, 8380404, 17, 8380416, 8380405, 16, 8380393, 19, 8380404, 8380409, 8380394, 8380391, 8380411, 30, 27, 13, 8380415, 7, 8380401, 5, 8380404, 16, 21, 8380397, 8380416, 32, 8380415, 8380411, 8380386, 12, 8380406, 4, 8380392, 10, 18, 8380407, 12, 8380415, 28, 10, 8380388, 16, 1, 8380413, 14, 1, 23, 7, 3, 8380400, 5, 16, 11, 8380410, 1, 8380389, 8380405, 8380399, 18, 26, 29, 47, 8380399, 7, 7, 8380405, 2, 4, 8380402, 8380415, 8380389, 8380410, 8380402, 8380390, 9, 8380416, 8380395, 4, 17, 11, 14, 6, 5, 2, 19, 8380414, 27, 8380395, 8380397, 8380413, 8380393, 8380416, 17, 8380395, 5, 8380412, 7, 21, 14, 15, 6, 8380416, 20, 8380411, 8380415, 8380402, 7, 8380405, 12, 11, 1, 16, 8380393, 8380396, 8380398, 8380408, 9, 12, 0, 8380414, 25, 8380409, 24, 26, 11, 35, 0, 8380393, 9, 3, 15, 15, 17, 27, 8, 8380388, 8380389, 2, 8380413, 4, 3, 8380413, 9, 8, 8380392, 36, 8380399, 8380407, 4, 8380405, 17, 8380401, 6, 18, 8380399, 22, 21, 28, 38, 8380394, 8380416, 8380399, 32, 4, 8380399, 0, 8380400, 8380410, 17, 8380412, 38, 8380384, 13, 8380398, 8380393, 8380411, 23, 13, 11, 9, 33, 8380407, 6, 8380398, 26, 8, 6, 5, 8380395]]
cs2: [[8380391, 8380400, 8380408, 7, 8380383, 14, 3, 0, 0, 8380412, 3, 8, 5, 8380403, 8380403, 0, 8380412, 4, 8380413, 8380400, 12, 0, 8380386, 7, 1, 8380404, 13, 8380387, 23, 10, 8380400, 8380411, 8380413, 19, 14, 8380412, 11, 7, 8380404, 8380384, 8380390, 8380395, 8380398, 15, 18, 8380396, 8380405, 8380405, 25, 8380414, 8380408, 16, 9, 8, 8380403, 6, 8380415, 17, 8380402, 8380393, 8380410, 8, 8380399, 8380411, 8380416, 12, 8380406, 8380396, 13, 12, 8380382, 12, 20, 8380404, 8380405, 8380412, 8380390, 8380406, 8380406, 8380397, 8380415, 12, 24, 8380408, 8380401, 13, 8380378, 8380379, 8380413, 30, 13, 8380412, 16, 0, 21, 8380408, 15, 8380412, 8380402, 8380384, 18, 7, 18, 8, 8380395, 10, 8380410, 15, 15, 8380402, 8380410, 7, 24, 8380412, 8380413, 3, 8380400, 17, 8, 8380404, 14, 18, 8380399, 8380406, 8380411, 7, 8380403, 10, 28, 23, 2, 2, 18, 8380391, 8380379, 8380412, 10, 24, 19, 21, 8380390, 8380391, 8380395, 23, 26, 31, 8380405, 8380385, 8380385, 12, 8380408, 8380412, 2, 8380401, 8380416, 10, 7, 22, 8380368, 8380373, 8380412, 8380405, 23, 7, 8380413, 8, 8, 1, 8380403, 15, 8380400, 8380408, 8380408, 8380386, 18, 12, 8380412, 32, 8380410, 1, 3, 8380403, 2, 8380395, 24, 8380395, 8380413, 8380408, 8380405, 0, 8380411, 24, 8380414, 8380410, 26, 8380415, 8380414, 8380396, 8380412, 4, 5, 9, 0, 22, 8380392, 8380406, 19, 1, 8380404, 11, 8380407, 24, 8380413, 8380416, 8380407, 8380414, 8380402, 33, 12, 15, 8380391, 8380399, 8380405, 24, 16, 8380409, 4, 12, 2, 8380407, 8380392, 24, 8380416, 1, 2, 8380411, 11, 8380409, 32, 16, 15, 12, 8380404, 8380404, 8380395, 8380391, 8380403, 8380405, 20, 30, 11, 6, 1, 8380396, 0, 23],
[8380407, 8380407, 11, 27, 16, 8380410, 8380402, 8380397, 13, 1, 9, 2, 21, 8380393, 5, 8380411, 21, 8380416, 8380415, 11, 8380415, 8380413, 0, 8380373, 5, 39, 35, 26, 8380398, 8380399, 1, 10, 8380414, 8380411, 8380402, 10, 8380408, 21, 5, 38, 15, 12, 10, 1, 8380391, 7, 9, 8380413, 8380403, 0, 8380401, 8380391, 8380399, 36, 8380404, 7, 8380411, 8380412, 8380401, 8380394, 9, 8380403, 8380390, 4, 3, 20, 8380403, 4, 6, 8380408, 5, 9, 12, 8, 8380408, 8380415, 8380396, 7, 8380391, 8380396, 8380386, 8380380, 8380398, 0, 42, 20, 8380392, 8380414, 8380402, 15, 8380405, 7, 13, 3, 10, 0, 4, 8380400, 8380410, 0, 8380395, 8, 30, 10, 8380370, 8380391, 8380411, 8380403, 8380389, 26, 1, 8380398, 8380385, 8380408, 12, 8380408, 17, 13, 8380400, 25, 8380388, 8380403, 12, 8380397, 8380406, 8380395, 3, 8380372, 8380359, 4, 8380416, 14, 8380413, 8380415, 8380401, 8380371, 8380402, 15, 3, 8380388, 8380391, 8380409, 8380405, 24, 8380406, 20, 0, 7, 22, 8380402, 8380407, 8380410, 0, 8380399, 8380366, 14, 44, 13, 2, 8380416, 8380411, 8380374, 2, 8380410, 7, 8380403, 8380400, 5, 8380406, 11, 8380407, 2, 8380405, 8380413, 8380401, 11, 8380408, 10, 0, 33, 11, 3, 8380393, 8380411, 5, 8380399, 8380398, 8380389, 5, 14, 8380416, 16, 8380393, 8380404, 19, 8380415, 8380405, 8380398, 8380384, 8380391, 8380379, 24, 25, 8380390, 8380412, 8, 25, 8380406, 6, 8, 8380407, 8380395, 8380407, 8380415, 8380409, 8380388, 8380410, 8, 26, 11, 32, 8380401, 8380409, 8380396, 0, 5, 10, 8380403, 24, 8380411, 33, 8380413, 0, 3, 8380398, 8380415, 8380395, 6, 46, 8380384, 10, 8380414, 28, 16, 8380396, 6, 8380411, 5, 15, 8380389, 1, 14, 11, 35, 8380410, 24],
[8380397, 8380412, 35, 2, 10, 23, 16, 8380409, 10, 7, 8380413, 8380409, 25, 30, 8380387, 5, 8380408, 8380415, 8380392, 8380401, 2, 8380394, 8380399, 15, 2, 8380403, 8380398, 9, 8380399, 16, 3, 14, 1, 8380416, 8380400, 22, 25, 19, 8380406, 8380415, 30, 11, 32, 12, 8380404, 8380393, 8380385, 8380386, 1, 4, 8380414, 8380394, 11, 8380414, 12, 11, 8380409, 6, 13, 14, 8380406, 8380410, 14, 29, 8, 8380402, 9, 8380399, 8380391, 19, 8380412, 8380400, 8380401, 8380412, 18, 8380398, 20, 31, 8380369, 8, 16, 20, 2, 8380411, 8380390, 8380397, 8380405, 9, 4, 8380405, 2, 8380403, 8380398, 3, 5, 8380410, 21, 24, 8380380, 29, 8380394, 10, 8380387, 8380415, 50, 8380414, 6, 8380411, 8380390, 10, 8380397, 36, 8380412, 19, 8380416, 8380406, 13, 8380410, 23, 29, 0, 20, 15, 3, 32, 8380411, 2, 8380409, 8380415, 8380401, 13, 8380398, 8380412, 8380392, 2, 27, 44, 17, 5, 8380396, 8380412, 11, 8380416, 9, 9, 3, 2, 11, 17, 14, 0, 8380402, 8380397, 1, 8380407, 15, 1, 8380399, 8380416, 8380370, 19, 8380413, 8380402, 2, 8, 12, 8380402, 11, 8, 8380416, 5, 1, 2, 8380412, 8380407, 8380412, 1, 11, 27, 29, 8380409, 11, 8380405, 21, 8380389, 8380383, 9, 8380381, 2, 8380388, 20, 7, 9, 37, 5, 11, 7, 8380406, 10, 8380395, 18, 8380408, 19, 14, 2, 8380392, 36, 8380398, 28, 24, 23, 14, 8380413, 8380385, 20, 8380373, 21, 14, 6, 13, 8380400, 8380414, 39, 8380408, 2, 9, 8380400, 1, 54, 8380412, 31, 8380400, 22, 8380407, 8380382, 29, 3, 8380386, 8380407, 24, 34, 8380395, 30, 8380397, 8380400, 8380411, 8380399, 13, 8380400, 4, 17, 8380384, 31, 6, 8380416, 30],
[8380397, 8380412, 1, 8380412, 8380394, 9, 8380407, 2, 3, 8380413, 25, 8380405, 11, 8380403, 8380405, 2, 17, 5, 13, 15, 29, 0, 8, 8380415, 8380414, 2, 8380399, 8380389, 14, 8380411, 8380413, 8380397, 8380403, 8380390, 5, 32, 6, 8, 8380402, 8380406, 8380408, 8380387, 5, 18, 46, 8380403, 8380411, 8380413, 21, 2, 8380403, 14, 14, 16, 8380407, 8380414, 10, 8380407, 5, 8380402, 8380393, 8380404, 3, 35, 23, 8380413, 8380408, 8380406, 8380414, 8380408, 8380405, 19, 2, 8380399, 8380401, 13, 21, 9, 8380411, 8380409, 8380416, 8380382, 16, 5, 8380410, 27, 8380402, 8380397, 8380403, 8, 16, 0, 15, 1, 3, 9, 18, 8380405, 10, 8380404, 7, 8380403, 27, 11, 8380408, 0, 8380382, 14, 8380415, 0, 36, 8380382, 8380411, 8380416, 5, 8380404, 8380407, 8380413, 6, 9, 28, 21, 19, 20, 4, 4, 33, 20, 19, 8380398, 1, 8380398, 8380393, 8380415, 25, 8380410, 8380409, 8, 8380414, 8380389, 4, 8380412, 8380399, 8380413, 24, 3, 8380399, 8380404, 7, 10, 29, 13, 31, 6, 13, 8380400, 7, 17, 25, 27, 8380391, 8380397, 8380392, 8380408, 8380416, 8380405, 23, 19, 8380412, 8380398, 8380403, 38, 8380411, 8380416, 2, 18, 11, 8380402, 8380392, 8380416, 7, 8380415, 1, 34, 21, 12, 22, 17, 8380379, 14, 12, 29, 8380413, 8380414, 28, 8380404, 8380408, 33, 9, 31, 8380406, 8380413, 8380396, 9, 8380405, 8380407, 37, 8380399, 15, 10, 19, 22, 8380398, 20, 32, 8380386, 7, 8380398, 9, 8380405, 8380415, 12, 36, 8380411, 22, 29, 8380415, 8380412, 28, 8380398, 8380404, 11, 22, 8380407, 8380398, 8380414, 8380414, 8380398, 18, 8380397, 8380410, 12, 8380414, 8380401, 8380402, 8380397, 8380377, 8380391, 8, 40, 5, 0, 0, 8380388, 8380410, 39],
[19, 8380416, 17, 19, 12, 22, 8380409, 8380395, 6, 8380409, 8380408, 8380397, 1, 20, 31, 1, 25, 16, 1, 8380394, 1, 18, 8380409, 8380416, 8380405, 1, 3, 8380415, 17, 1, 8380394, 0, 8380411, 26, 23, 8380407, 1, 5, 17, 12, 14, 19, 8380407, 8380401, 8380388, 10, 8380414, 17, 13, 1, 7, 8380403, 7, 8380402, 8380383, 8380396, 8380400, 8, 15, 18, 1, 8, 31, 41, 5, 1, 37, 8380415, 8380373, 4, 8380406, 1, 13, 8380413, 0, 6, 22, 17, 8, 10, 13, 14, 8380406, 8, 8380407, 25, 26, 8380414, 11, 3, 8380414, 8380398, 8380382, 8380400, 10, 18, 8380404, 10, 4, 14, 2, 2, 8380405, 6, 8380403, 13, 8380390, 8380392, 8380405, 29, 8380404, 12, 8380409, 27, 8380412, 8380382, 8380399, 8380382, 8380411, 13, 9, 8380414, 8380415, 6, 8380388, 23, 48, 11, 16, 8380409, 8380416, 8380396, 8380405, 8380406, 0, 21, 8380389, 15, 23, 8380412, 10, 8380412, 23, 7, 9, 36, 0, 9, 5, 8380407, 8380402, 9, 6, 8380406, 8380400, 8380412, 8380408, 14, 11, 8380402, 8380405, 15, 2, 10, 8380413, 8380393, 8380414, 8380396, 10, 8380396, 2, 36, 8380402, 30, 8380407, 8380400, 8380406, 8380372, 8380399, 8380408, 21, 29, 8380378, 8380415, 8380413, 8380408, 16, 3, 7, 8380415, 8380391, 8380415, 2, 8380405, 8380409, 8380408, 23, 6, 18, 29, 8380415, 18, 8380409, 10, 20, 11, 21, 8380412, 8380397, 18, 8380404, 13, 18, 8380414, 21, 8380416, 8380386, 23, 8380389, 8380400, 12, 8380414, 8380391, 8380399, 8380416, 46, 8380414, 8380394, 8380405, 15, 9, 8380398, 12, 8380404, 3, 8380393, 8380388, 19, 8380400, 6, 8380393, 8, 3, 5, 4, 5, 2, 7, 8380397, 14, 2, 8380391, 15, 4, 8380407, 8380391],
[4, 17, 0, 8380391, 8380365, 3, 29, 19, 55, 17, 19, 6, 18, 0, 5, 8380393, 2, 8380414, 0, 13, 8380412, 11, 10, 8380400, 24, 18, 8380413, 8380408, 8380414, 8380400, 6, 8380396, 8380411, 8380403, 8380415, 7, 17, 8380413, 12, 8380408, 1, 8380413, 11, 0, 8380397, 8380401, 8380403, 21, 5, 4, 8380409, 3, 8380393, 8380372, 8380406, 45, 14, 29, 11, 35, 27, 3, 8380416, 8380401, 2, 2, 8380409, 8380413, 8, 46, 5, 2, 8380413, 6, 13, 8380402, 8380405, 8380411, 9, 22, 20, 8380415, 8380411, 8380390, 8380411, 8380385, 14, 19, 1, 8, 8380400, 8380378, 8380399, 8380403, 23, 8380380, 8380411, 8380407, 8380391, 8380411, 8, 9, 3, 19, 12, 12, 26, 8, 8380402, 8380391, 8380412, 14, 16, 2, 8380410, 8380392, 8380410, 8380410, 8380402, 45, 8380406, 8380404, 8380394, 8380403, 11, 13, 12, 5, 8380401, 14, 8380411, 36, 32, 10, 22, 8380411, 9, 8380416, 8380374, 8380388, 8380381, 16, 26, 8380411, 8380397, 8380387, 8380397, 8380403, 8380416, 7, 8380415, 8380408, 8380400, 7, 15, 8380405, 8380412, 8380399, 8380388, 8380404, 13, 31, 11, 8380396, 1, 8380415, 8380411, 8380404, 2, 8380399, 8380377, 8380398, 6, 49, 10, 8380409, 17, 8380384, 15, 8380397, 11, 16, 8380414, 8380399, 8380399, 8380407, 9, 42, 20, 8380415, 8380404, 8380411, 8380409, 2, 12, 29, 8380385, 0, 0, 8380392, 8380405, 8380402, 0, 8, 8380393, 25, 8380412, 7, 8380409, 8380396, 11, 5, 8380381, 8380408, 22, 21, 8380369, 8380411, 8380416, 8380401, 8380412, 8380384, 17, 3, 10, 10, 8380414, 18, 13, 9, 8380413, 8380401, 11, 10, 2, 8380409, 10, 37, 8380394, 8380412, 8380409, 8380411, 2, 8380400, 8380392, 8380410, 6, 12, 6, 8380404, 8380405, 8380394, 8380409, 2, 8380411, 9]]
z: [[8178739, 229713, 8091186, 503270, 84776, 517873, 16134, 90087, 8270557, 112955, 202959, 8262880, 8155921, 279087, 8091641, 8293534, 204509, 292276, 8068153, 520423, 439696, 218623, 8344963, 265145, 467151, 8289254, 368903, 37971, 223047, 320827, 164412, 7892315, 183259, 469939, 311491, 7931581, 8347347, 8195584, 8032384, 8166552, 167561, 8122927, 331598, 72556, 227096, 7868173, 521115, 278089, 138471, 317062, 217391, 8269012, 234825, 8229044, 8225523, 8037585, 467418, 96850, 7925183, 7870804, 8155245, 8237398, 460660, 8030567, 7960414, 7942830, 7975932, 251338, 8220265, 8216776, 8345889, 64664, 425134, 184054, 316795, 512941, 104512, 8247137, 8031223, 8124881, 222640, 75655, 8235943, 8373324, 8067510, 8081484, 121629, 8378664, 332424, 18859, 128377, 8142243, 208442, 8047815, 50424, 501923, 479522, 252719, 7914772, 257392, 407303, 440345, 8116328, 7944739, 8275334, 179564, 7874725, 466777, 149230, 8243009, 8338119, 8003835, 379019, 455633, 384839, 363170, 473664, 314599, 8222128, 3939, 88367, 121364, 254587, 8093422, 8139411, 94687, 8262441, 8108153, 493097, 240776, 8338704, 196497, 131270, 7965588, 42590, 7959684, 7870847, 333978, 8119744, 8287492, 84017, 8379893, 513210, 253557, 7978950, 8065232, 131288, 348275, 387916, 297949, 8204179, 8302788, 103131, 84913, 8163189, 7932967, 473894, 8137259, 394737, 492892, 248873, 95104, 8355894, 7896997, 13336, 408371, 417265, 8373961, 8219113, 8362512, 7888592, 237857, 16233, 14034, 384913, 141345, 8198973, 8045586, 7887542, 273904, 451206, 134730, 411802, 125857, 8128961, 8339476, 406030, 463938, 86859, 8139385, 8318687, 8035126, 8362011, 8379064, 8323084, 358966, 8242984, 8063040, 343943, 61272, 516517, 8291106, 85718, 65535, 82493, 210846, 291988, 8376057, 46295, 385942, 269456, 7981057, 265435, 7968286, 8343728, 230140, 167594, 369612, 71184, 8056973, 519369, 8094738, 7886744, 362219, 347730, 8277810, 370375, 8245226, 345563, 8322351, 222380, 8302787, 27026, 8181441, 445476, 7312, 8111394, 8065163, 8029830, 272612, 8073441, 135093, 7988217, 8115524, 8234159, 7957591, 8025835, 167914, 8235734, 102078, 75910, 293766, 442696, 53529, 9816, 8139584],
[7864923, 346293, 8207853, 194571, 173825, 8052970, 8009963, 34990, 7991213, 4404, 8269729, 8107196, 7861135, 8142811, 7969223, 8117935, 439565, 8172701, 8238276, 8267465, 103289, 246783, 478124, 345627, 8296593, 429040, 7984111, 513811, 8044380, 8318409, 8245417, 519765, 8177988, 8323609, 3189, 7965827, 8289846, 492822, 259367, 492784, 7976184, 7862948, 8004154, 8056884, 71071, 295908, 8129629, 7968544, 7910487, 473410, 8377438, 402469, 126056, 8291894, 8054293, 8205662, 8331616, 8210221, 7858767, 8361145, 7889808, 8155344, 7924336, 7879840, 8379361, 7894520, 7994632, 8240828, 8112829, 440539, 16799, 7861422, 214194, 432376, 233213, 7970174, 508381, 183943, 7867753, 8334918, 8211796, 117438, 261131, 346831, 15825, 8063631, 7977785, 8086838, 7899042, 417538, 7938034, 246606, 374150, 8380102, 188881, 42560, 515759, 7911193, 8266789, 7890369, 465244, 8266249, 8201524, 8285462, 8307804, 468934, 7992701, 8370535, 288560, 155230, 8336112, 405200, 201579, 355046, 464305, 8379098, 7906596, 498972, 252046, 8093628, 8059220, 8227186, 390657, 8106811, 8339174, 140611, 8171197, 296587, 8270262, 8078311, 8294116, 481420, 346568, 8065636, 8098922, 407772, 8140102, 7957292, 3922, 23419, 175064, 509466, 8029424, 8135237, 8183303, 203381, 7960111, 8099484, 234899, 148203, 314525, 7945051, 251078, 8149441, 146133, 484947, 356539, 7975800, 8173241, 459091, 8085435, 8309651, 508494, 458105, 39662, 8133816, 8275733, 131790, 8141196, 7973836, 17538, 344742, 191696, 342466, 8241607, 84015, 196020, 8071545, 189817, 322543, 8239086, 8022826, 8247783, 497491, 460935, 290746, 7977135, 65471, 112915, 7956828, 239251, 8314130, 8372601, 7936261, 496150, 103549, 8323545, 8312156, 121152, 8115932, 8329406, 8379969, 26238, 8231032, 8258972, 7985128, 7866435, 8230703, 162484, 8075287, 448965, 7906032, 5419, 8179113, 306439, 56513, 7928541, 8078554, 8354100, 65957, 7891369, 8015070, 7919669, 7926231, 300458, 60375, 448516, 8034362, 51097, 435074, 8172789, 289564, 8220126, 8355056, 7932279, 8321479, 340430, 8341351, 8253067, 8153761, 8146824, 521868, 520679, 8325635, 8150357, 8028613, 384564, 376242, 66170, 8247487, 7872742, 182807, 419994, 8192221, 130171, 7922178],
[411070, 118455, 8322516, 34774, 246532, 8152700, 15417, 145604, 364163, 247837, 153072, 178400, 186978, 8147844, 418977, 82189, 8238412, 8167408, 509867, 8136233, 8189600, 418046, 198578, 5402, 516438, 484705, 7995992, 7917191, 253184, 7960719, 68438, 7991430, 7895597, 59017, 326572, 481647, 326000, 8225562, 417891, 524124, 7969429, 189974, 8279903, 8085210, 38878, 8334821, 7967495, 7867633, 7901322, 7909636, 13640, 8050938, 8188288, 259621, 432627, 495340, 402204, 8041345, 254710, 82485, 420932, 8213438, 8056911, 8242968, 8064926, 7926651, 371003, 119347, 586, 431683, 523415, 8107112, 8123703, 350037, 8116386, 442253, 8241971, 8376930, 8182051, 8083535, 8013092, 8124996, 121788, 7902836, 102582, 224018, 269485, 72380, 337873, 16826, 462659, 8264756, 8209814, 8347576, 8000058, 8281675, 8341649, 13509, 7887185, 178584, 355529, 346646, 332730, 415932, 8095114, 144260, 8326061, 8323795, 222243, 124164, 7959728, 324262, 8355073, 8372536, 509795, 8226908, 388915, 8328937, 372189, 8181955, 7865735, 411528, 8295227, 8201104, 8343204, 8372702, 8032055, 8251181, 8114050, 8291889, 7928006, 8044776, 217215, 8258033, 8118512, 103741, 70888, 82073, 8000162, 31183, 134336, 8250275, 7926074, 196933, 7957264, 96131, 8312135, 504581, 8198528, 521095, 8222075, 8334097, 176457, 410780, 8120724, 8342947, 7901415, 167930, 105088, 8330317, 213147, 8149694, 7886453, 203065, 8317988, 491576, 52733, 446713, 7870209, 51143, 7978530, 205901, 8212220, 8093303, 17658, 8272176, 8337887, 237218, 8271878, 150065, 340308, 112135, 417025, 8210804, 8178989, 7868115, 8049020, 421686, 23668, 296263, 160091, 8130070, 8369684, 339746, 154730, 264795, 8297745, 7873297, 7956065, 476632, 62646, 7947112, 7955120, 391553, 8008725, 8323166, 307703, 132948, 8053574, 8343755, 8345554, 8235027, 8047472, 7964033, 462909, 20600, 8252658, 72340, 8313472, 62214, 204052, 451900, 8268928, 8154097, 297008, 153777, 8031996, 307509, 318886, 198380, 8298447, 276860, 33745, 385276, 7914810, 8170614, 8231406, 7958006, 90742, 8069726, 8045433, 472888, 344715, 454439, 205880, 226194, 59885, 23920, 227494, 8316403, 112704, 8240495, 7957050, 8102025, 93189, 95294],
[7955323, 8372337, 335001, 7901141, 420057, 8096673, 150343, 8111146, 265788, 221235, 418203, 261699, 391707, 74260, 182541, 124172, 8014314, 225160, 7992096, 7983538, 234570, 8023218, 202108, 8316178, 8255524, 7863224, 8017905, 57942, 8018739, 7891419, 263469, 8258212, 7887089, 322815, 135061, 8010003, 7864506, 414388, 8138900, 147358, 8117622, 8300371, 8342095, 8082878, 182186, 221521, 8048294, 7936414, 275348, 241683, 8348114, 503042, 8292499, 8092799, 448589, 20329, 8237439, 140039, 501443, 231801, 89072, 8324111, 8070697, 8106505, 64608, 8283225, 8137389, 8050671, 8024378, 394232, 124571, 33689, 389400, 267985, 4030, 440875, 8047506, 17959, 8127614, 8163859, 8218379, 8297354, 8265081, 459873, 8219642, 216066, 379615, 8334588, 8190265, 8053629, 8165156, 200210, 8322609, 8155960, 8211620, 8157406, 217654, 531, 18796, 494926, 308846, 8347770, 190265, 82675, 495054, 8379779, 8306039, 7895316, 269865, 495776, 8039342, 315998, 84742, 8321254, 8095086, 7874567, 292051, 447801, 84366, 8237499, 394724, 8066720, 409369, 8290521, 71109, 8267337, 36622, 7912290, 314277, 8269123, 8196284, 441527, 7894341, 8304586, 286507, 43080, 168458, 8047221, 7941179, 7922192, 265832, 8058098, 421158, 7955793, 7994977, 8142616, 8187674, 223512, 169598, 8328067, 78472, 445921, 300046, 121473, 262234, 415412, 13137, 8303561, 513362, 8339626, 304204, 7862103, 142036, 8040472, 8306675, 517106, 107353, 437943, 8283522, 100986, 385588, 8221102, 43259, 158428, 505829, 437480, 8127813, 28246, 500979, 8058664, 86856, 8307255, 8127291, 435639, 402930, 265626, 409931, 8308379, 335284, 155156, 106499, 8369719, 312126, 8181810, 7934974, 8169841, 8133070, 108349, 8251976, 8155805, 177238, 198183, 7999086, 8124835, 8239034, 7965125, 8317169, 438619, 8301147, 8111664, 7920472, 519072, 310494, 373156, 438668, 16434, 8357600, 447586, 155971, 8251573, 303525, 8036863, 218885, 95402, 403662, 8329604, 342375, 8011655, 168336, 51095, 8207271, 37026, 379256, 8187419, 8192836, 8233398, 381932, 235995, 8098698, 456294, 7963435, 8350722, 402517, 164150, 8181828, 8238730, 8003761, 385250, 7983485, 8046153, 265073, 8349569, 197357, 8297116, 483978, 7908997],
[303246, 8368562, 7869951, 8220123, 273367, 8272322, 8248239, 7995807, 78952, 461826, 8358974, 293475, 397418, 8051152, 480600, 8175822, 8168320, 441007, 234695, 44880, 7862428, 7873708, 8311277, 328268, 8025207, 332646, 438113, 267307, 243169, 270005, 500557, 8276347, 8078923, 8103395, 8090407, 8100979, 8260967, 7858586, 481438, 124960, 76268, 181479, 8227604, 8042352, 111802, 222146, 27130, 487863, 8179814, 7948358, 8187161, 502591, 7975967, 7897398, 46201, 151826, 66415, 192091, 104582, 160309, 7975324, 8178663, 8285416, 370509, 427508, 8292178, 171627, 471002, 407606, 299522, 8100823, 8232561, 8104839, 137869, 7996053, 111379, 448046, 310441, 8207289, 8250471, 518660, 8365850, 262657, 8229429, 314491, 8028293, 460232, 7982887, 12808, 275881, 6114, 420028, 8119481, 8317037, 196185, 8200963, 263769, 8025461, 8268452, 125146, 7999722, 498370, 8042416, 8241873, 50139, 394854, 8281806, 7889293, 211058, 8123429, 7931601, 8352243, 7984588, 223673, 473438, 8135136, 8049182, 153054, 133154, 299003, 8085090, 8368348, 8345805, 109611, 10195, 7601, 8228208, 8192113, 471693, 349374, 7862914, 7876678, 7949619, 339515, 301597, 8212936, 277481, 305227, 59331, 8148277, 176797, 138799, 424599, 8207971, 8067708, 8066905, 8110578, 417672, 19776, 303361, 20502, 145622, 8100121, 8220413, 8093763, 8042989, 257554, 8050803, 8182859, 7971104, 7959517, 7995712, 8129606, 8337511, 374936, 281608, 8096233, 8315965, 506083, 373259, 21999, 350794, 8150091, 7885954, 99481, 426760, 509148, 8178866, 8166019, 468584, 89757, 8264550, 7872724, 186451, 263336, 8037731, 7923609, 7953243, 8186514, 8287636, 351235, 8181354, 489010, 7925502, 470188, 7887364, 328936, 72223, 283594, 8164663, 8261529, 8149166, 207726, 325558, 127632, 8175786, 7884191, 7861506, 7993034, 362428, 349837, 7913001, 8247941, 8028675, 36175, 74525, 8261031, 220504, 185904, 340683, 336497, 28503, 409004, 8218958, 8037197, 410862, 8248312, 8065959, 483259, 20424, 468987, 8215778, 8053050, 8295476, 216641, 274354, 8259578, 8350898, 264136, 7911016, 3092, 73180, 8049281, 23412, 7928822, 8201853, 8110746, 62862, 77162, 61563, 228301, 8256474, 313328, 8011728, 8052875, 8159825]]
||z||: 524124, ||z|| too large
r0: [[-156751, -165762, 199093, 202457, -30040, -208580, -27858, -216977, 240928, -259784, 172198, -41550, -138944, 212976, -190244, 187268, -243456, -113496, -57610, 193507, 184770, -232190, -129410, -176802, -22805, 4541, 43045, 122222, -108348, 897, -149891, 141436, -183788, -40987, -170535, 103744, 175561, -127921, 244310, 150704, 3230, -18368, -219452, -120810, -210842, -225423, -33882, -178682, -140666, 173411, 3441, 20679, -209544, 60653, -132561, 193503, -27474, -89309, -171045, 9369, 198773, 209069, -186705, 233537, -74666, 4117, 105924, 161924, 229412, -249567, 228035, -9085, 153368, -236580, 128174, 19442, -32839, -147002, -39083, -257921, 57627, -90632, 230618, -42958, -166415, 171650, 110610, 36315, 237809, -188676, -85288, -8867, -233154, 189380, -257822, -52804, -117894, 72661, -244585, 57703, -174879, -131013, -176155, -198497, -235303, 52326, -64165, -75043, -242153, 54397, -35492, 30065, 19043, 69029, -143019, -86604, -137376, -16564, 16480, -213117, -165378, -103175, 44438, -29645, 185034, -150553, -227235, -175445, 236157, 97959, 120433, -189240, -247328, -45834, 96031, -167803, 176476, 129081, -60713, -122599, -169774, 140799, 142093, -128067, -65261, -124128, 34983, 4061, -113957, 38284, 244217, 107071, -43375, -43378, -31202, 88984, -206951, 24849, -202652, 258083, 99478, -249901, -145413, 54901, -115306, 77317, -48434, -66078, -141669, 13476, 211286, -252506, -189426, -131510, -65771, 206931, 182576, 23081, -254736, 47994, 152054, -248205, -233476, 32894, -87102, 66836, 164059, -59540, -54112, -183382, -168821, 136974, 185095, -249265, -25914, -204960, 93408, 223466, -230988, -213884, -127812, -20137, -140030, 51371, 235679, -108473, 250193, -5796, 136853, 715, 7819, 95674, -101865, -151035, -215521, 105420, -180905, -62609, -23702, 223897, 138915, -172600, -154875, 180103, 135080, -127944, 123710, 51746, 172882, -190332, -253917, 160846, 30256, -6248, -48439, 20862, -29974, -179633, 257524, -153768, 57910, -41574, 169174, 199349, -85563, 109420, 163073, -253520, -190107, -36411, 165809, -77981, -198116, 153478, -113049, -134091],
[92213, -231462, -106275, 207346, -254961, -57100, -54758, 101592, 63595, -234300, -23925, 41982, -206884, -124902, 229406, 226509, 70864, 219342, -195223, -181859, -60325, -39805, -135952, 84942, -173694, 9748, 168775, -239109, -257385, 25803, -159454, -93425, -95598, -194790, -196870, 229982, 124138, 68457, 253409, 61991, 113847, 35490, 50389, -136954, -71394, -66509, 74083, -106791, 153446, -46472, -90889, 125280, -116805, -92301, 121283, -70271, -20695, -124988, -117730, 178105, 212111, -99622, -40894, 177619, -12027, 59220, 47394, 201098, -166308, -188912, 210083, -9055, -191436, -188130, 188992, -163316, 115499, 247785, 170112, -223001, -173390, -22031, 21428, 46332, 148953, -248110, -156417, -230257, 111511, -118469, -208122, 237031, -250670, 87302, -253544, 47181, 41824, 22508, 3342, -11560, -216244, 125046, 160099, -177170, -146683, -65147, -84795, -71151, -155828, 62820, -207991, 55494, -184183, 241529, 225221, 52007, 187335, -222813, -41978, 43190, -170098, 226984, 226286, -145755, 126049, 115406, 183360, 83090, -11621, -14995, 222870, 41037, -120533, -96944, 33879, -35508, -120311, -29090, 233173, 37413, 144156, -9637, 186993, 98853, -218116, -59847, 129626, 125608, 230974, -108685, -211358, -187441, -174229, -9067, -112155, 164806, -116478, -91485, 32742, -249007, -181108, -38056, -217766, 138605, -50068, 169679, -98798, -48896, 184695, -30995, -254575, -83512, -20297, -174419, 92652, 144959, 252833, 58579, -180560, 212496, -135839, -10700, 186786, -183842, 143077, 238264, 36505, -133406, 252448, 76260, -253317, 73577, -142197, 62235, 183618, 205700, 64321, 35352, -14506, -29276, 92169, -103843, 193467, -167462, -110944, 202808, -104145, 135376, 58147, 87798, 181276, -249036, 175689, 9233, -260737, -157556, 90809, -163231, 114786, -215655, -144990, 209321, -109100, 203068, -126628, -63155, 198369, -43462, 232246, -221748, 30030, 240392, 98788, -131124, -91602, 31755, 201773, -79468, 184182, 105602, 118345, 184200, 41351, -188358, 96267, -64535, 95532, 156437, -197857, -237106, -234176, 118410, -73602, -58635, -66754, -145862],
[-241493, -181558, 185372, -148801, -243903, -95616, 240834, -120572, 136507, 178903, -206006, -39632, 73624, -108403, -197483, -218702, 105379, -96728, 183393, -35635, 72597, 186066, -140387, -90881, 51303, 258577, -82847, 112558, 62445, -246023, -32113, -76082, -147628, 47234, -190166, 232821, 24760, -129788, -231323, 34529, 210810, -164392, 135651, -261632, -50409, -106544, 182326, 9767, 113894, 186112, 146304, -225028, 17195, 253030, 115774, 241109, 31407, 53630, 257948, -107583, 6392, 59559, -131488, -136473, 148030, 37913, 184534, -73553, 116992, -101361, 240286, 40358, 185264, -10552, 75852, -204835, -223697, 34832, 253771, 155019, 253065, -187217, -43659, 163927, 261447, 41870, -107794, -31355, 6375, -253613, -215197, -166210, -241340, -223792, 214020, -144008, -85051, 156858, -147621, 209129, 63444, 93143, 126879, -171317, -234330, 240343, -71394, 134302, 157939, -154858, -219694, 110131, -243820, -210388, -251832, 18671, -157165, -4269, -105293, -188223, 183719, -108824, 24676, 109546, -157177, -141557, -52778, 155509, -124445, -79626, -98753, 193738, 241922, 190330, 48898, -198883, 261024, 160804, 3281, 45131, -224069, -197531, 119230, 224102, 61481, 200746, 76371, 31988, 2530, 230102, 243646, -8447, -178685, 124362, 80853, 178725, -41691, 203134, -105879, 88771, -40473, -138393, -240807, 244784, 218367, 217362, -1932, 37133, -28425, -204989, -126247, -3152, 204004, 114933, 59837, -47784, 41150, 202086, 76018, 185381, 51231, 193711, -62657, 55152, -30268, -107791, 98077, 184461, 72784, -223916, 38318, 56733, 261151, 79087, -185281, 61831, -95701, 37936, 126980, 230881, 29604, -9684, -216001, 93066, 106200, 255000, -181330, -88150, -214408, -219472, 114992, -215064, 139585, 190466, -174128, 134260, 166052, 151287, -261845, -47361, 177739, -93723, -106018, -183718, 223189, 124048, 148082, 3036, -230289, 100257, -213983, -153374, 180760, 98954, 34565, -156170, -149965, -15360, -78002, -172940, 179911, 136959, -229409, 241533, 109635, 260140, -81976, 200219, -14854, -121195, 152530, -125582, 114909, 181663, 123897, -154331],
[113771, -176662, -252125, -253131, 66724, 49706, -49761, 94136, -61212, 215787, 213108, 113869, -35969, 145987, 15, -66737, 179637, -246334, -239472, 10316, -31387, -259892, 206523, -18277, -118574, 61498, 66342, -228691, -15201, -22185, -58771, -82751, -259663, 173322, 5097, 15861, 112737, -101790, 57008, -203378, 28411, 132746, -196687, -205509, 108531, 235505, -100697, 232777, -232433, -48627, -242149, -151586, -114977, 171784, 195560, -197051, 116209, 795, 183859, 104800, -59431, 114554, -238952, 160092, 119051, -237177, 247365, -197503, 153151, -163962, -202157, 102017, -99247, -142988, -25437, 114137, -106442, -216794, 235869, 21206, -211336, -8038, 132286, 188450, 1882, -186043, 103850, 27579, -243021, -197742, 161728, -140803, -173635, 183145, -152401, -96338, 213462, -205199, 60876, -146116, -254985, 121383, 46871, -92162, 176965, 126281, -70712, 15341, 103766, 168304, -91520, 195701, 241347, -52514, -201491, 219095, -177107, 179531, -99793, 6890, 192273, 130835, -48844, 53123, 83130, -228417, 59239, -24988, 125794, 92013, -104340, 70000, 152169, 177489, -92927, -209672, 240813, -126502, -59568, -147566, -55277, -212407, -180447, -56171, -14079, -62273, -165495, -172849, -83015, 116963, -29572, 72506, -131093, -236616, -135995, -37437, -167877, -224546, -137318, -242455, -230553, -154474, 90892, -247885, 53353, -253334, 45465, 183554, -227382, -40612, -172847, 167424, 93313, -21624, -207764, 182112, -32839, 221088, -203356, -157030, 211993, -253420, 87403, -240089, -250557, 53984, 250217, -200718, -2657, -224686, -172673, -30779, 135926, 35267, 193954, 14859, 133807, 193262, 972, 216894, -88674, 119187, -139034, 181318, -130755, -18404, -12400, -258574, -66879, -29186, 164113, -3270, 191509, 158130, 148441, 125299, 204043, 155945, 68311, -244663, -141074, -217612, -154728, -255539, -107381, -152779, -23795, -151403, -111834, -225353, 221452, 236537, -209334, 220339, -162965, 138756, 219029, -82001, -199905, -94317, -97528, -93788, 157803, 226051, 76713, 53566, -16620, -20948, -2748, 36972, 167295, -42439, -66782, 116949, 232993, 1395],
[-147233, -105107, 168140, 234541, -60193, 113347, 212480, -47180, 196072, 33111, 167926, 96172, 57817, -206782, -148862, -196241, -208571, 87296, 159224, 29411, 7955, -230838, 255427, 118946, -135327, 187730, -9570, -18331, -76439, 235119, -8862, 124120, -92214, 110122, 111637, -82379, -247992, -176302, -132756, -24209, -37684, -68940, 178359, -185408, 52116, -52334, -73478, -61418, 46581, 154723, 32190, -149165, -7637, 202173, -261374, -133311, -235642, 259841, 39159, 204909, -85295, -5537, 170568, 11307, 76061, -146953, -72060, 148225, 59749, -95435, 194908, -251741, 33348, -208117, 122435, 130871, 186543, 208774, 201832, 26687, -16528, -161281, 252499, 117381, 178658, -44651, -119388, -239489, 239648, -199027, 163190, -71220, 216003, -36773, -201552, -116415, -195166, -169270, -104267, 198324, -98114, -163113, 128171, 131624, 114979, 88821, -213083, -245366, -24722, 89929, 174405, 35391, -112474, 210573, -230808, -104530, 207118, 135267, -62080, -136267, 198158, 200217, 148283, 250268, -167557, -101925, 132752, -123312, -197878, -47439, -139042, 162428, -123074, 174979, -180086, -103377, 15071, -242530, -170420, 178453, 110593, -194819, -153226, -260526, -165061, 56113, 60217, 140319, 221524, -1937, 88503, -58396, -189647, -222113, 144596, -107792, -206206, 18124, -78802, -160832, -181517, 191185, 81612, 146691, -39121, 231505, 78763, 178843, -146437, 158221, -153016, 178672, 52643, -217017, -67917, 251596, -204544, -206541, 56123, 152786, -79050, 179809, -129158, -79440, -44479, -38527, -118155, 28096, 25985, -33826, -97587, -63246, -106577, 32620, 95873, -89744, -139855, 1794, -248983, 23494, -49999, 110700, -171102, 15625, -154669, 237574, -220602, 127199, -74069, 15347, -228907, -162886, -237629, -116403, -73243, -46687, -209607, -172896, -195418, -41535, 259467, 34787, 247062, -228914, 249434, 30386, -143772, 119676, 256910, -85187, 12436, 42845, -64480, -136983, -99773, -39997, -122003, -101428, -62756, 81845, -169472, -101760, 85330, 171497, 107963, 24353, -155063, -202195, -247177, 215526, 94600, 51826, -112552, 111222, 88578, 50649],
[-190111, -175951, 186937, -133779, -219006, 197904, 132837, 212268, 54284, -139298, 98620, 250174, -166780, 210928, -2270, -179414, 32308, -112317, 139214, 140342, 51966, -202711, -244082, 38623, 126274, -29250, 204475, 128001, -108016, -24333, -235792, -24228, 46533, 217761, 143119, -221502, -74815, 52838, -109225, 19050, -85360, 240337, -243149, -207404, -206098, -209132, -157069, -86969, -162884, -48207, -206479, 201676, 226178, 45542, -79306, 171268, -238417, -90027, -11403, -247305, -203253, -18310, 253303, 205054, -178962, 49764, 50109, -19772, -2498, 215491, -25900, 60169, -1755, 145218, 189957, 219383, 64506, 16532, -241403, 156660, 18223, 127895, 233436, -153941, 142637, -38938, 116411, -44352, 55542, -18182, -54934, -258208, -202344, -131632, -109675, -63652, 50741, -132475, 30935, 30521, 144721, -109599, 20859, 106292, -202408, -162250, 249230, 252407, -33491, 26433, -156561, -232548, -220465, 53662, -146311, -44798, 162739, 106615, -80492, -199267, -27807, -251940, 120427, 126088, 76606, -73734, 154385, 128446, -110764, 122520, 19048, -260847, -100204, -194509, 95447, -101451, -125224, -225441, -220667, 62878, 9767, -80442, -57911, -195246, 254787, 211292, -18764, -261273, -130340, 257418, 78757, 97433, -68164, -880, -183927, 130605, 194482, 47930, -151263, -256196, -2181, 165900, -246747, 215974, -259235, 128919, 209998, 46727, -7497, -81050, 17547, 5102, 25561, -173308, -18877, -226906, -132804, -167000, -21165, -73839, 213021, 91555, -226759, -181534, 257419, 242920, 136700, 51629, -4413, -203793, -158090, -107344, 119082, 193459, -241825, 106830, -32935, -25817, -137593, 237489, -202563, 39497, -204069, -155229, -252627, 156753, -131474, -236087, -157382, -187089, -210583, -98551, 136708, 199017, 81947, 8550, 102521, -57637, -175165, -187146, -22111, 108308, -250620, -147963, -106268, 47858, -141690, 85240, 211847, 57058, 229766, -215305, 65409, 199362, 150910, 146410, -146336, -155146, -43961, -213345, -85983, -43728, 224840, -84838, 41787, 169215, -247387, 184083, -62278, -130690, 251222, 102634, 243073, 238616, 160187, 38581]]
||r0||261845, ||r0|| too large
Need new candidate round. ||z|| too large or ||r0|| too large.

y: [[-341989, 66464, -128125, 119754, 9605, -224492, -271124, 454096, -374398, 307617, 449750, 105469, 466088, 129670, -139977, -204735, -501883, 162902, 421503, -297264, 65203, -518147, 222648, -179778, 37599, 425303, -211775, -331067, -220570, 274800, -370693, 400479, -328150, 110109, 158543, -279494, -389551, -76521, 245788, -431616, 182234, -156980, -41850, -245934, -8079, 470432, -235575, -101881, 101241, -125632, 491712, -243509, 123798, 380236, -56071, -296255, -115620, -181972, 51438, 159330, 277312, 429108, 287413, 395763, 345972, -165267, -293566, -443148, 76179, -387295, -446237, 98940, -212198, -91319, 159428, 315082, -10095, 385722, 410023, 432312, 389029, 405, 57416, -212533, 301027, 67323, -73642, 434438, 359528, 82130, -242127, 37398, -40065, 244967, -334641, 281404, -476106, 37699, 210800, 248885, 176486, 336180, 340398, -145235, 192079, 88414, -40905, 211399, -155957, -124943, 102567, 504593, -440798, 445337, -71618, -35431, -375812, -226307, 519313, -196194, 348191, 314479, -299101, 198298, 32761, 366353, -80897, -398634, -413167, 434265, 334341, -264377, 243348, -388504, -376176, -290760, -88046, -283248, 92136, 75263, 248989, 507739, 52837, 413151, -488820, 292773, 203218, -49813, -238294, 406263, 522793, 96724, -472402, -232368, 485981, -99494, 266256, 61913, -476273, 94603, -30971, 136967, 419707, 31273, 123783, -174657, -1882, 428823, 256787, 40892, -347766, 123053, 315108, 463410, -8298, 483446, -324626, -279306, -399029, -343879, 184426, -321375, -357183, 415784, 215883, 101518, -182789, -270770, -133189, 105517, -92633, 479101, -211577, 38974, 66155, 82904, -55619, -492062, -490549, 501607, -226023, -34105, -270971, -376431, -283438, 309691, 303532, 393849, 201824, -349511, -254313, 458279, 329331, 254193, 417654, -86525, 284505, -91365, 410178, -479387, -306679, -348816, -202677, -352920, -161103, -44442, -10077, 363468, 366011, 79782, -170688, 116693, 14263, -298064, -231147, 260346, -155584, 7054, 450937, 31742, 413488, 58064, 249549, 93808, -340566, 241423, -13854, 287089, -304350, -196874, 152370, -302019, -516612, -135720, -111066, 198382],
[476062, -440388, -274398, -386415, -152513, -399396, -353322, -164772, -329340, 352094, 507669, -247894, 446554, 431522, -508106, -283785, -493657, -403733, -180282, 137613, 330062, 481795, -498614, -373084, 370932, -228028, 103828, 446272, 216387, 61135, -397942, 385553, -77912, -154174, -159577, -431479, 102362, -419892, -416991, 16229, -260692, 56130, 490912, 462975, -136335, 399915, 191394, 389672, -124709, -150167, 339960, 364828, -201143, 290277, 507481, -175093, 362562, 264735, 343715, -77663, 403360, 314441, 283333, -221491, 505927, -85583, 94173, 421520, 37913, 199793, -326225, -118427, -96960, 153050, 441827, -416564, -63979, -431871, -219594, 83525, 306836, -434447, 89303, 25085, -472737, 184745, -436058, 371057, -343660, 164751, 372512, -87782, 92739, -506008, -351094, 88010, -171039, -335355, 332127, 416623, 356974, 303429, 57865, 227642, 54487, -161576, -452030, -510143, 488609, -82973, -520221, -418740, -480411, -208967, 508859, 93064, -366045, 205288, -374422, -368939, -145858, 433261, -328629, 65217, 211501, -405001, -43403, -414397, -504424, -203176, -139774, 111078, -123422, -280754, -283654, 29768, 381259, -124897, 510340, -234631, -114995, -276975, -313627, -430859, 346668, -255292, -20716, 243633, -392616, -70290, 92225, -322592, 255671, 205957, -392242, 374124, -85313, -31682, 61981, 258180, -523453, -196079, 72453, 355839, 283674, -332157, -315774, 74590, -90498, 307462, 464624, 186335, -388968, 417497, 436082, 56816, -113409, 416982, -172742, 319980, 63131, 10919, 339462, -347545, 237912, 432039, 496541, -283563, 485896, -12068, 420296, -495516, -122208, 158931, 87411, 307747, 243289, 405473, -144681, 113932, -149255, -193185, 350428, 469404, 274722, 357757, 78966, 242087, 404154, -234280, -202454, -171890, 92188, 340707, 4317, -160792, -491378, -387996, -316392, -480842, 180469, 422781, 43727, -446077, -169658, -130977, -523828, 215349, 510933, 441989, 287622, -459885, 184165, -447682, -276428, 448727, -191983, -68149, 410545, -64907, 53662, -164580, -347433, 503560, 132377, -366737, 452712, 159404, -50129, 420248, -50996, 163877, -262689, 441319, 151827, -365304],
[-435352, -47839, 103490, -156704, -42967, -130203, -298743, -310624, 424095, -10020, 161760, 259650, 201015, 86289, -401264, -482165, 421874, 467622, 318524, 104215, -465236, -342717, 194702, -142682, 156020, 317445, 389067, 29639, -406564, 119810, 126788, -228757, -517465, 451918, -152878, 479357, 54881, -35270, 285085, -290941, 496083, -514905, -199901, -249886, -467587, 258912, 93198, 448233, 493335, 237635, -211595, -133705, -245236, -218002, 280702, -18604, -34179, 184142, -125303, -489863, -57035, -140992, 257401, -413445, -25429, -420215, -130261, 327862, 238740, -379504, 193279, -361578, -120974, -80034, 522480, -103959, -113996, 458650, -186115, -399297, 105558, 235842, -118609, 342531, 231583, 359962, -459140, -327025, -360085, 513168, 102706, 150343, 498551, 523546, -39154, -108380, 455300, 92504, 330429, -100609, 142335, 95141, -207513, 300610, 65717, 506940, -488095, -349260, -112407, -332345, 144813, 136871, -262845, -81149, 470470, 169890, -355172, 66125, -219913, -37241, 315895, 413367, -48267, -158604, -298415, 260022, 361142, -144472, 160235, -451026, -104026, 222321, -256284, -22967, 193980, -172112, 171226, -523320, 163050, -489922, -19167, -348948, 465235, -142409, -421751, -308950, 468309, -115252, -492206, 370043, 52621, 512055, -205851, -328369, -465570, 458497, -384944, 364446, -384760, -252863, -204856, -337408, 40244, 472136, 376044, 134816, 448693, 299475, -105891, 27981, 374492, -31176, 62323, -140832, -53056, 195703, -314844, -54085, 490589, -229282, 463185, -251015, 229666, -356361, 42729, -418111, -83453, 458641, -446963, -507029, 321384, 329319, -389043, 123957, 477968, 451734, 269541, 460437, 108733, -416705, -372440, 335945, -372622, 58126, 50324, -393233, -118208, -18327, 43917, 345448, 457222, 242781, -288756, -233661, -55437, 279852, 383713, -304791, 427041, 401646, 82997, -61675, 226387, 301570, -306324, 428020, -43609, -412529, 438571, 319375, -141872, -319691, 260721, -271652, -254042, 71766, -76581, -463367, -155230, 40039, -188191, -140853, -201458, -431194, 155129, -396435, 265806, 408127, 188592, -202395, -484332, 435971, 213644, -51132, 366518, -484572],
[-519015, -322411, -357569, 286649, -82536, 73412, -254009, 68522, -263163, 482653, 131287, -12184, 197431, -409188, 129129, -113796, -495595, 141406, -52579, -386393, -238008, -127531, 356845, 457589, 208353, -135585, -239776, 494370, 64358, -225169, -504856, 251559, -270250, -393365, 399223, 261545, 151786, -306076, 252460, -14137, -145105, -473465, 345168, -376087, -58201, 449656, 310614, -488988, 189287, -266637, -396501, 114220, 385074, 394145, 258363, -304863, 289671, -71634, 227577, -374888, -473421, -264375, -198861, 187732, -223469, -320180, 479231, -105110, -508728, 255183, 518977, -62508, -473503, 69378, 115081, 498401, -134626, 287146, -37384, 441631, -449404, -81481, -471452, -452857, 336216, -329222, 292433, -154940, 445689, -214922, 198718, -238255, -86433, -384152, 429342, -114591, -24823, 43336, 56829, 461446, 255848, 194060, -12287, -176503, -270745, 142934, -159183, 337805, -117218, 155121, 40088, -347200, 25279, 129532, -401755, 151952, -341443, 513925, -493895, -460087, -458078, -218316, -246211, -194254, 199828, -18797, 375886, 520428, 356851, 147698, 237470, 179949, 450269, 304845, 295312, 69013, 107141, -401983, 186110, 324632, 379941, -89959, -374722, 414209, -469034, -524032, -204538, 268832, 245091, 446258, 449110, 102003, 207479, -8364, 414098, 199357, -17298, 68200, -478041, 193524, -272745, -411323, 481633, -269803, -282203, 324129, -342397, 192104, 81565, 500887, -519706, -523904, 140755, 276720, -394307, 5472, 397830, 391226, -243931, 520688, 28156, -278258, 244430, -403093, -63728, 208726, 165090, -498903, -367541, 306555, -165615, -480755, -158655, -18211, 495968, 136046, -152994, -251891, 171453, 292664, -519891, 225988, 319643, -44700, -107785, -383902, 455008, 66559, -423407, -304011, -395415, -18161, 274745, -418580, -30900, 21918, 347126, 104935, 203404, 123816, 373890, 292676, 187415, -270497, 320137, -438885, 71212, 278349, -64973, -465187, -492572, 520733, -391570, -97147, -205685, -477802, 471490, 275416, -376573, 15946, 73325, -222079, -161401, -294979, 453237, -79612, -403830, -462335, -495749, 208036, 446684, -238800, 11145, 215720, -77983, 460549],
[-229453, -96359, -32206, 256599, 198168, -501142, 381592, 329973, 180899, -24984, 179002, -428940, 280137, 471222, 155012, 110538, -309558, -507948, -357972, 254923, -191957, -284410, 283431, 452495, 364536, -346800, -320578, -117766, 257817, -198913, 230650, 231072, -143126, 495112, 297076, -449637, -139480, 51305, -271700, -276418, 261803, 275773, -341898, -202651, 488675, -260173, -424384, -461256, 6894, -327911, 313014, 209377, 398468, 233011, 85824, 215610, -425669, -7344, 104369, -315587, 406359, -296726, -1121, 361959, -104802, -451054, -25335, -468816, -83466, 431902, 500654, 90661, -4289, 112776, 170133, 24728, 100654, -327649, 130524, 343618, -235105, 323999, -66876, 92352, -137059, -268234, -155389, 479650, -77903, -180225, 12705, 144798, -304922, 331552, -371278, -41306, 283117, 432149, -99319, -387404, 46093, -152710, -153619, -283283, 315474, -367903, -419337, -121320, -395789, -88181, 282831, -55984, -149042, 269978, -294159, -322044, 37731, -297134, -330138, -414374, -80431, 385243, 267376, 272267, 39881, 228910, -457570, 361322, -6165, 84550, -33179, 296694, 510810, -93907, -363106, -298251, -498298, -438985, -307627, 243044, 66867, 283277, -401105, 415320, -448306, -328031, 443573, 7494, 60689, -35503, -347647, -384073, -284627, 134550, -371038, 420229, -410298, 168524, 391337, 494837, -331753, 440487, -86262, 205201, -50784, 351886, 107827, -94570, -489081, -488287, 424123, 267610, 44858, 209874, -285913, -239490, -272084, 246224, 49954, 359242, 61094, -91558, -196970, 255224, 221907, 475479, 168073, 463307, -518842, -85657, 306228, -402572, -452460, 211256, 483755, -151443, 136440, 328717, -203357, -403536, 372005, -152629, -207389, 249182, -403944, 24962, 146631, 5137, 362565, 110547, -186953, 425379, -204576, 521376, -296707, 239662, -501694, 54612, 208455, -80118, 48878, -295081, -369500, 465276, 433838, -504286, 471630, 354404, 205500, 200409, 295206, 234963, 318207, -286572, -289921, 161552, 372872, -160163, 344987, -111831, -51003, -68187, -485702, 90042, -116782, -166260, 89878, -145975, -334232, -416287, -131852, -516520, -26184, 246740, -91613, 100419]]
NTT(y): [[1160348, 1930630, 2168100, 5297506, 4565745, 445884, 1255355, 5644455, 4697489, 2006528, 783229, 6489857, 1973321, 4466817, 7236069, 1024033, 6099408, 2108572, 7577793, 3619421, 7239187, 5810589, 7065917, 5133517, 6048576, 2704419, 4384313, 7487926, 4332443, 7717418, 2018067, 1497461, 6534780, 7585636, 5193025, 1428990, 1409316, 5696708, 464625, 5315753, 2155090, 1055636, 1432464, 4731792, 2032007, 5523717, 7440289, 8321320, 3451952, 4306699, 7476008, 8230828, 816251, 6186301, 1570913, 8089116, 6663330, 250262, 2726494, 3888810, 4503896, 3378936, 3908943, 5297258, 6467405, 517899, 6435343, 6943425, 1422757, 5017573, 3241682, 6356087, 4895036, 2806698, 6571734, 3471769, 3736465, 8251275, 4125633, 5074400, 6580470, 2315559, 3977454, 925589, 2194253, 657919, 7073620, 8232268, 1446766, 2607061, 888403, 1717321, 1043731, 5600106, 546395, 7676672, 7523513, 5076714, 1544614, 480998, 2889874, 3978981, 2607444, 7574645, 2054581, 3792179, 2410492, 3740221, 6393926, 6448821, 5952769, 4906393, 1645679, 1186631, 228285, 7685683, 7783443, 3693749, 2414518, 6285128, 6733687, 1203592, 3154723, 1863687, 7169426, 214441, 6993006, 1434268, 6817436, 2790092, 8101324, 3443936, 1099407, 225349, 2032441, 554060, 657263, 2824334, 1092013, 5018900, 4818598, 7841114, 2910217, 1623682, 7566639, 2549198, 7378232, 6218689, 6752964, 5639819, 2848745, 6118499, 4339010, 1117655, 356076, 625116, 488992, 1875646, 7101154, 6905602, 2584573, 1211610, 1636833, 1641630, 7361328, 3087828, 4444202, 5726592, 6315272, 4917919, 6882725, 8134165, 5510556, 3438519, 1392645, 1701461, 405810, 5459327, 2545016, 3599582, 5471481, 1923370, 7373081, 1744633, 7547401, 5193430, 1683136, 8110212, 6557040, 2553173, 3577420, 4654239, 974951, 6914365, 7971, 2233862, 3465958, 6160709, 859314, 1230387, 2453529, 5304122, 808344, 3303511, 3325299, 8321660, 3649507, 627032, 1248017, 459613, 3837208, 2394758, 6053234, 2036199, 2790468, 6346731, 6326880, 6478737, 5968763, 3857155, 1506612, 6338907, 3045221, 4313648, 2258800, 48542, 6674581, 4602563, 3272476, 6828767, 4587616, 1737425, 1268488, 2654207, 7717249, 5524136, 324681, 8101939, 1700561, 2337680, 6678032, 3073948, 8376095, 3315014, 5996447, 5710853, 2956642, 8361140, 7335385, 6705413, 1552442, 5123869, 2885368, 1929504, 4842051, 860863],
[3060042, 1885637, 134490, 149529, 7075888, 3343833, 1434, 4188038, 1867630, 5199970, 5504915, 2905030, 2262972, 6183564, 2921497, 5313000, 1651530, 6974193, 4390297, 7677740, 6791341, 2513938, 495122, 2966283, 6987744, 6499211, 7703189, 2550513, 1937368, 103711, 4189119, 3611363, 5584007, 3316243, 4975955, 7222053, 2333120, 3992023, 7109988, 3551679, 2837642, 3437687, 3756978, 8283947, 2923012, 4958225, 7345762, 2765653, 2590992, 2509576, 1243406, 5959441, 7457239, 4718194, 6217477, 4024101, 7397652, 46155, 6283569, 1172362, 2448240, 6781638, 5165530, 6443491, 1338531, 2096210, 280759, 2793041, 1195776, 2003646, 4863065, 2058286, 3721125, 5068106, 2666963, 5101462, 1083870, 896423, 6735550, 1870914, 3639395, 1224807, 8320390, 6956943, 6076549, 1950506, 4233936, 4506291, 5885153, 5168582, 943453, 302754, 599363, 6732844, 317918, 7739887, 1839520, 6543296, 4499825, 7963610, 4965121, 7102726, 358727, 1742312, 5286969, 4276000, 7796754, 315486, 127232, 2110699, 690987, 4133565, 4160720, 4414282, 3213253, 4796022, 2206945, 7747966, 8284933, 2161242, 5423436, 7058518, 3914460, 4143117, 360169, 4170696, 1291206, 7256678, 2698637, 4519557, 7256582, 34103, 3645439, 7398048, 5507110, 2651165, 1359951, 3354059, 2335742, 7465799, 281236, 3987603, 4766523, 692102, 6222967, 627313, 4403719, 2592524, 6720112, 6930783, 6597269, 6125608, 5139060, 1606554, 4025931, 7481974, 7384249, 669685, 8072345, 4787405, 384628, 5835300, 5918420, 2020862, 748111, 2362374, 4234841, 2366947, 6724571, 6809263, 5505506, 7368080, 5702459, 2721853, 2320947, 2545486, 1329699, 6608796, 6949342, 4312991, 3749431, 6417803, 6229789, 5887677, 3007234, 114734, 1180733, 299491, 6544370, 6100629, 1678017, 6636832, 467065, 863810, 2470619, 911606, 416913, 6111997, 1597748, 4292206, 1570646, 1073737, 5838297, 6297722, 5341229, 1347526, 8111913, 1357011, 543839, 1002980, 5870602, 8089278, 7195546, 2887850, 2163003, 4434451, 6113137, 8182776, 996580, 4739634, 2101124, 7020662, 67800, 1624253, 7983021, 735882, 4299942, 677395, 7531277, 3637419, 1558671, 4236385, 4269542, 3204972, 7510626, 2213355, 7769931, 3221697, 2008656, 1004473, 5409487, 3839903, 433619, 8313890, 5979475, 305346, 7341880, 4920014, 7559211, 4298724, 5770084, 4173952, 4260018, 6285880, 247670, 5890026],
[5774149, 1066056, 4140412, 3289608, 8079364, 930707, 7562508, 4639369, 7172420, 3645866, 5601960, 4767320, 7171540, 846555, 5605802, 966835, 6319912, 7657299, 6724271, 4204592, 6199311, 1496140, 2600247, 6460036, 575333, 3140761, 2904946, 4189420, 128810, 6277829, 8287700, 2632100, 2328978, 2270411, 2002140, 8196219, 4838449, 7476699, 4839058, 7534547, 7603728, 2229654, 1538848, 5448552, 1222259, 2290175, 4588603, 5418479, 6888593, 67305, 3077630, 6559304, 8061856, 2653731, 2454480, 3716828, 4708789, 6096144, 5396258, 3681897, 7467156, 4935992, 2496386, 6248758, 7495139, 1666863, 7602076, 5390064, 5447301, 6336485, 3699481, 2211020, 2419868, 1453591, 2615131, 3925369, 825927, 5736430, 5423621, 6254954, 6821239, 2329018, 3028946, 3711979, 4371555, 6982840, 3047527, 3472949, 474076, 7036304, 281011, 7723295, 888135, 8070854, 4187236, 7339035, 4154604, 1910138, 5246081, 4995817, 615533, 7088701, 5231837, 5236370, 1829183, 7160374, 3121699, 1033463, 3826144, 7695547, 3099322, 2968862, 24303, 3138159, 6760871, 7837143, 1526795, 8145496, 7287541, 1340234, 7079702, 2083330, 2020024, 1214786, 4387985, 3409602, 8149466, 6633728, 3642563, 6694772, 3887305, 3810114, 7136633, 6632348, 1772669, 1943660, 4172689, 3520596, 3640142, 209007, 5509852, 7180105, 6866326, 8261673, 2898176, 6112304, 6078359, 69387, 5697492, 3110395, 1934616, 6024109, 3122875, 6622067, 4826977, 6924294, 5161335, 2584102, 6170187, 866542, 7774132, 3950266, 4999375, 443161, 6510817, 497947, 2674616, 1546069, 1046341, 5372414, 210093, 7364185, 3155144, 1456933, 7766600, 2333304, 31877, 1872636, 6110672, 492198, 1805611, 7741508, 4697577, 6993366, 6420912, 7252901, 7693800, 2056764, 6111668, 3968137, 5531450, 71296, 5998240, 5071713, 6417306, 4363567, 6115877, 4643270, 2301731, 7891196, 8014678, 331171, 7505871, 7066445, 6019200, 7083623, 5718159, 1343372, 2561800, 3683200, 7545830, 36815, 5741841, 7899689, 1260479, 4245183, 5225179, 1579746, 1870472, 5243726, 2235202, 6758748, 7246537, 4745341, 2341749, 1647664, 5213512, 5845293, 71654, 5892405, 540594, 8183201, 1385311, 8013194, 3128688, 8015745, 6146353, 3289, 278563, 6359999, 7882191, 6044578, 1717058, 6360372, 7548843, 3673434, 5081116, 6476909, 2737732, 6472586, 2037464, 1780154, 6277377, 2811130, 3371746, 4409392],
[4884018, 1834104, 1716750, 2134675, 738715, 6500881, 3749506, 7756242, 4798984, 839580, 4374288, 6594349, 4957820, 3833268, 4854717, 5026124, 4887971, 8266063, 2374510, 4534390, 4244940, 6700412, 5064932, 1740653, 3176286, 5407052, 2804426, 1549771, 4399965, 4171397, 6389351, 3622456, 6890740, 6265030, 7612059, 7563094, 2935736, 612148, 1658284, 7056162, 3627422, 46727, 4290518, 3832242, 764848, 69260, 6348056, 4659881, 7937436, 4467591, 2648158, 6169157, 190998, 7454502, 5029339, 4254842, 4537968, 7951857, 3783101, 2126483, 4547054, 7915148, 2423385, 7618507, 7677942, 5702247, 8177294, 7132576, 3483220, 6490409, 650210, 5023470, 7178639, 7851519, 3348538, 8262357, 5524369, 3337396, 5153700, 1261737, 618698, 548658, 284206, 4462996, 1314300, 7247478, 7985859, 4376482, 992439, 7046636, 2983925, 169681, 3196057, 3405797, 1124945, 1956314, 1077179, 5158564, 6840842, 3763672, 6245051, 3941601, 4456194, 1878173, 5185875, 4110884, 784991, 3986669, 6137913, 2215286, 6736283, 8224310, 7259680, 3256347, 5004191, 3055523, 148234, 3300753, 335896, 4456298, 2197933, 8149121, 3756425, 4384875, 1988363, 6597655, 2767942, 2778572, 6178698, 5954103, 2098717, 1929657, 1080781, 2430868, 4762626, 1921557, 5515714, 2614585, 1548034, 6946369, 4789019, 2479307, 7325766, 5050663, 8065239, 771043, 7696791, 1647168, 2463096, 8021411, 5972364, 1970237, 2621257, 3058563, 4687385, 4527811, 729552, 3593186, 1765160, 1390247, 5020568, 5849086, 2284479, 7126032, 4486257, 2506657, 5437624, 1458586, 2124866, 5632939, 2064428, 1403507, 7299445, 3619294, 7728761, 1801451, 5119570, 4028255, 4703594, 4642233, 6210484, 4454894, 8176971, 3046636, 1162585, 5164136, 1852596, 3782889, 2022539, 2789384, 6704683, 8311660, 3611938, 1901375, 161779, 6623672, 4972046, 7432013, 3888990, 3912506, 6401667, 586786, 4911268, 6063911, 4636930, 7467328, 5724121, 3194433, 679305, 6852234, 2698033, 4610376, 2397698, 1107943, 1720503, 7888978, 4155617, 6314998, 2903304, 725006, 984046, 7468695, 104672, 3636843, 1843773, 159582, 7714271, 989419, 7772945, 7420366, 4422276, 7245700, 7539715, 8108492, 404083, 4889689, 331663, 7651071, 3472997, 6204687, 3424557, 1293236, 3499656, 86280, 4174855, 2586568, 3291416, 8007273, 8297728, 2172045, 6273072, 4529772, 2253785, 1737799, 6210496, 4791729],
[6300625, 312709, 7578314, 4765512, 5751332, 4473565, 3955687, 3515825, 4594367, 5238976, 5518107, 5471968, 3280055, 7655980, 4331616, 3305848, 5170484, 6039557, 3529582, 3872605, 6968974, 878158, 4276178, 5398104, 2703136, 511500, 1843188, 5528909, 808888, 2649800, 736520, 1262056, 3168021, 5960115, 5966518, 1308195, 5139002, 8091225, 7510786, 2751482, 3943316, 1067330, 1092904, 324466, 1906433, 7580573, 2685963, 980522, 4633648, 3198832, 3494682, 5539354, 5443297, 228931, 7074133, 2117040, 4114490, 3068429, 1800101, 3026425, 1490119, 2663247, 2915700, 5884700, 1414492, 17814, 4345193, 6718994, 2454231, 101225, 8171875, 3159896, 2912813, 3356721, 5585506, 5406749, 4413548, 6033024, 3840004, 7309261, 3002178, 6415963, 2662900, 2358526, 6978814, 1116450, 832446, 4943467, 1834107, 4196476, 2082330, 2554159, 7311437, 7655818, 6660009, 7612985, 6127265, 99726, 7850133, 2440820, 4505669, 7136745, 8231094, 2055540, 5283729, 5215513, 305318, 7104242, 6418317, 4616753, 387723, 3533863, 3310249, 1381530, 443639, 2930808, 6782267, 6562021, 1978114, 856783, 3258832, 469270, 831083, 2220615, 5175299, 3121028, 4997764, 5234907, 2898491, 2300691, 7599061, 461501, 8284733, 4499695, 3896556, 4681300, 2143461, 7581633, 4784895, 4772926, 414363, 6311651, 6045824, 1820495, 3220247, 5435900, 1465383, 7601787, 5335546, 5813372, 2461461, 6024770, 7968758, 2526943, 2031286, 7289566, 3110973, 2249455, 695280, 4078542, 6641982, 5351834, 2393854, 3964745, 5790908, 4343694, 8374311, 7710563, 2451668, 2718810, 5978852, 1599885, 6005592, 6116176, 7043536, 4721455, 2413116, 7950752, 6405175, 4483383, 313775, 3941148, 7287860, 7553938, 6005005, 5332276, 1180785, 7515906, 4537302, 5123954, 7486283, 3181913, 4018585, 4247209, 5482573, 1987034, 2183623, 3837230, 2552000, 5388682, 3862657, 4306902, 3965088, 349803, 1666953, 3928016, 1930270, 2911743, 6529876, 1631003, 1988573, 2120731, 6820531, 445217, 5478013, 8374074, 8010527, 8105859, 8202009, 6634652, 2579927, 2676622, 3322662, 3405046, 2362947, 111194, 698365, 4050605, 2845439, 2125681, 2387255, 7967629, 7229835, 7998874, 5497650, 2981832, 1095984, 6617355, 4573597, 7222248, 2031925, 407883, 4419308, 3536144, 6549188, 6625328, 391764, 4067977, 4021279, 6441201, 3821424, 7964685, 6794320, 4969648, 7769158, 3263343]]
aHat * NTT(y): [[6383167, 5388895, 2753697, 7297636, 8193380, 949578, 3459689, 6103335, 829318, 4258269, 1698316, 3262886, 3590053, 1723822, 6050049, 2340081, 2218936, 259632, 1286750, 5466208, 988301, 8096862, 5400869, 7843951, 544667, 3729221, 3181090, 7477757, 7234999, 3144824, 3422397, 7496682, 7205760, 2031660, 1902463, 2490207, 3379182, 2377919, 8354703, 61079, 940468, 3886339, 171178, 7302, 5372084, 7149079, 6905624, 3290960, 7716549, 3730890, 7596310, 4278976, 2654522, 3090463, 5676014, 1642393, 1367713, 2171794, 3419248, 7527308, 2567194, 5900759, 6534760, 3978735, 784637, 7783178, 7573035, 316463, 8008707, 6597969, 3184917, 6689194, 3852923, 3158655, 4104357, 4568209, 509166, 5726701, 7643893, 6642698, 6182097, 2108793, 7581757, 1388000, 2917137, 5479500, 2989279, 2529343, 2061120, 4046367, 1750307, 4350690, 7714129, 3363587, 3034005, 663129, 5918737, 5246228, 6253675, 7806540, 971594, 3130342, 4162808, 6120696, 7032106, 3826217, 5802039, 7649684, 3156467, 5240308, 3459432, 7134258, 8286546, 2631657, 4038870, 5630242, 6224126, 2130379, 7616416, 5588551, 4354877, 6023940, 2240747, 6522625, 7826219, 4996770, 2114352, 1915659, 7529728, 3256594, 1309651, 2864241, 589743, 6127320, 722138, 2289674, 5630098, 2628131, 2152628, 194322, 2784820, 6400690, 4590700, 1982280, 6608424, 6401463, 7598923, 6983302, 4513353, 7887498, 5882936, 3943037, 986851, 5298858, 956212, 3992880, 2809729, 1813991, 4836414, 185443, 1434314, 3434373, 4825956, 1214105, 3520492, 7549833, 6070798, 4243209, 2655259, 1043873, 4111640, 1506852, 248628, 2643368, 1286258, 4940456, 4950386, 3640142, 8250262, 7317648, 8065174, 2681034, 532707, 5070762, 803901, 7375392, 2009538, 1621746, 5057476, 4018633, 3544149, 3073713, 4857797, 3511131, 4811242, 2201335, 7982771, 4773407, 8042258, 3042893, 3111363, 1317773, 716108, 5913349, 920281, 7604962, 683475, 5685011, 7155386, 7760488, 7158805, 5817109, 3937982, 4008700, 6587600, 2570949, 4897663, 6447709, 3875971, 3923382, 4189429, 1199558, 4864103, 7769414, 2984751, 1879171, 4396923, 885658, 6021467, 2225556, 3348034, 192503, 4392196, 7620587, 41616, 4239951, 1608337, 3876200, 5068357, 3186542, 1116787, 1312402, 2852819, 4374178, 3999669, 1030743, 218940, 4851045, 6836136, 306443, 7964414, 1089812, 6995773, 4833481, 4088502, 110861],
[5793986, 6902600, 4839869, 1261213, 2711946, 506657, 3827849, 5672508, 3750631, 7084312, 1015653, 8270028, 8068153, 7227542, 6804588, 3544048, 6854119, 4293689, 7138567, 1977861, 3526826, 4145215, 1047497, 2124417, 7562477, 1288891, 958637, 4349398, 7848641, 2646240, 2145125, 1186676, 3811205, 6464815, 1771375, 808596, 6886051, 7233550, 502795, 8024157, 712890, 3249628, 7960960, 6143486, 1754222, 74487, 108063, 5783563, 3430513, 8157026, 2638585, 75730, 7799412, 5909299, 639594, 7011278, 478257, 2643538, 4433917, 487377, 7814650, 2250363, 5720640, 836424, 4371993, 7969718, 1013177, 4287138, 176937, 7651853, 1513838, 656301, 8132741, 7548005, 3512998, 2917901, 6979858, 5859132, 1934510, 3705832, 6535028, 11512, 181023, 292694, 1629752, 7034193, 2131041, 5100432, 3347647, 8278231, 616283, 1826243, 4399060, 8149267, 5103285, 3209413, 3350252, 7064339, 7218063, 5966979, 6087801, 2253443, 4442952, 2614934, 4625841, 8346675, 2562989, 5206532, 5404807, 5763019, 3725826, 7928415, 1779421, 7865657, 1659185, 1310146, 8185468, 2689562, 6344988, 4007332, 6387721, 4118892, 6298201, 2999166, 4209452, 6743782, 1718916, 862703, 5666252, 1624297, 2587554, 6522551, 752, 4001327, 2927532, 5226134, 7591106, 6815112, 5462522, 1250844, 3652852, 3292605, 1928510, 8339124, 6107431, 2387249, 1154116, 2858652, 1970860, 1599260, 4235014, 884032, 4555033, 7601326, 2761366, 2484567, 6574928, 5775877, 3320815, 4710681, 8046937, 2099353, 4617623, 667310, 3249792, 8199409, 7958315, 4756773, 253126, 3521574, 7821009, 7021709, 4091628, 8357027, 4708139, 27197, 1737578, 2205643, 2756687, 5652735, 2094240, 7738568, 3858293, 7861911, 5598764, 47404, 2159839, 6618611, 7886497, 3817029, 3780821, 6800744, 544239, 993109, 3341063, 6061360, 7257567, 2793495, 5169212, 1331937, 7104982, 3442302, 4169922, 7161824, 7401011, 3714816, 136756, 5504753, 6882836, 6331987, 5798500, 1238678, 6356290, 4472767, 6870401, 354034, 751974, 4469861, 4149625, 2447129, 3845554, 3478916, 8149174, 6953642, 5330169, 1610268, 7578438, 5123733, 5335317, 3893807, 5299948, 1847630, 1098431, 5781978, 8258102, 7326373, 5662517, 7977819, 4567952, 718042, 7150706, 5331435, 8133645, 5238144, 7169390, 1415687, 131939, 3784623, 7816882, 8378356, 7703997, 6435528, 3664500, 5431220, 544829, 3250088],
[6620406, 1208938, 2483134, 4159659, 4242017, 2153241, 4688238, 85178, 4434058, 7370349, 107259, 2984188, 4557561, 7355519, 7582650, 4222455, 531967, 2338919, 3773193, 6326513, 45444, 6930578, 2776498, 2108715, 2675689, 4374398, 4089536, 1020221, 3814410, 3454860, 1430833, 4392253, 2927573, 2920781, 5873486, 6671816, 6152611, 5409260, 1927145, 1691262, 2242207, 78590, 4687686, 7248034, 6185562, 6890480, 3857614, 8167119, 1456238, 2790686, 5403540, 4141184, 4779354, 5848791, 3501984, 286755, 7404398, 7542145, 3084471, 428227, 7354232, 4295890, 6777404, 3293599, 2826983, 4232595, 7494886, 582273, 2670748, 1533550, 5618948, 6123072, 3401165, 1351274, 391116, 4952047, 2887173, 7379326, 3815131, 4265378, 5345258, 2818808, 2503356, 5931100, 4307332, 7690422, 2796910, 5105521, 2440158, 8211370, 5898216, 1983418, 5353500, 3139189, 722112, 3268746, 1233076, 6659561, 5246850, 2414724, 640747, 4260240, 3373968, 7357419, 6090269, 5366655, 3984808, 482294, 4706322, 7705587, 2011809, 3105124, 3979429, 6008877, 7522102, 703470, 1386029, 8004138, 8239622, 7798330, 6970283, 6586951, 2379280, 217546, 2246680, 3316593, 159975, 7296769, 7226031, 1377459, 4967249, 1334910, 5497582, 4214349, 98489, 4680946, 6767066, 7546405, 5627336, 7714574, 4962570, 6303796, 5366617, 496578, 1025896, 3908096, 3870619, 3787218, 4437520, 7037379, 4433508, 2651258, 4087734, 5560235, 1109368, 7777054, 3715094, 2244756, 1368685, 7247961, 753070, 6447420, 4642588, 4460071, 5932529, 1887745, 5027593, 81854, 6867933, 1576963, 7951284, 6362119, 329829, 1769716, 802392, 918154, 6248965, 2123985, 1835338, 6026940, 6668779, 6473678, 7824360, 3872735, 6654676, 4552204, 5045179, 3834912, 7278423, 4452364, 6594753, 251463, 3112166, 6532689, 2462479, 2664036, 2835749, 592268, 752290, 6949532, 1736710, 2261030, 421663, 4653007, 1261821, 2138407, 3245533, 8178667, 693264, 6101230, 1689913, 7673514, 6506189, 7008588, 7078334, 4838916, 7075484, 1836249, 7289778, 6098669, 2465569, 3724275, 6109653, 6988669, 2893268, 4288653, 7842298, 4540321, 3744338, 3863786, 6649425, 4965334, 4330105, 4533788, 4618018, 1063504, 3594989, 8077891, 242302, 2254372, 4869909, 6896494, 2501350, 5640858, 2602676, 6474793, 5662286, 4886610, 1330610, 7002374, 4695611, 1179242, 2121193, 5138098, 3401215, 2603542],
[333269, 6985229, 7829399, 2044999, 7494349, 2575821, 4228064, 3486301, 7088336, 7938171, 5932947, 3900646, 1235313, 420100, 6028493, 3184812, 1774290, 3861296, 4760124, 5856533, 1782609, 7506087, 4676519, 2018507, 758832, 4378820, 3152403, 3243819, 2247988, 2270578, 3696063, 966665, 1044500, 2387649, 4798962, 2503731, 2989366, 2575889, 8379453, 6597217, 2002454, 797454, 3292808, 2654019, 6020701, 1491569, 1714154, 6135966, 5874237, 2739563, 2247865, 6426262, 1211267, 848667, 4793729, 4382223, 5674089, 1555448, 5319165, 7580784, 3093352, 4265289, 7701453, 2080728, 2531871, 4332135, 7191074, 1654746, 6779582, 5096278, 4932905, 4202631, 8133658, 1344809, 6905317, 6344315, 5240022, 5384524, 7884117, 5630446, 3644020, 6903321, 8124046, 5346511, 3096251, 4099574, 5005381, 1671681, 567112, 1708632, 6116799, 7098378, 4577204, 6108672, 5034371, 4450274, 8089595, 69771, 250783, 7242483, 5826638, 2189811, 2259622, 6471961, 6807324, 2311094, 7601816, 4473107, 301870, 1155847, 3369821, 279831, 5202662, 7503844, 2500147, 6678856, 3914391, 1313764, 3567858, 118113, 2214764, 546045, 3828404, 7375457, 6259262, 2839116, 7511620, 4061989, 6520612, 3066830, 99, 2380562, 4573427, 41227, 6437796, 3727253, 7631734, 3364833, 4212888, 4882589, 7661673, 6649688, 6752186, 1403848, 3759092, 7181794, 453273, 1912763, 7515759, 2486028, 4701083, 4152407, 5785245, 258702, 3917604, 5102171, 445303, 7657292, 4550905, 6330029, 1844585, 7182890, 1943102, 1268355, 6182948, 3517994, 6501331, 4219213, 2314346, 3517583, 1945324, 6004228, 7623995, 2941871, 4394556, 1947980, 2207700, 3455089, 3069141, 1740526, 5446583, 5514836, 3245962, 3396104, 3133486, 8245093, 1738626, 920729, 7646709, 1769950, 8333748, 7881342, 424613, 2689209, 891151, 1872610, 797548, 6231512, 1817422, 257148, 7128854, 2386366, 7493453, 4270980, 665666, 4597083, 4162080, 877071, 1584948, 401058, 5863515, 6953058, 6521964, 5705932, 6277122, 6099733, 5870028, 8194636, 472218, 1928227, 6410077, 1465318, 3950810, 7599153, 5172774, 3105375, 2454814, 2108655, 6931233, 2704750, 2287054, 1680701, 4098766, 506508, 5501385, 3116557, 5689431, 6803397, 8007114, 8106903, 909301, 5800427, 2466851, 5560967, 5726254, 715695, 3327159, 5802348, 7591122, 7897997, 3420132, 3661269, 5962014, 5818429, 4824912, 7888478],
[8002922, 6356476, 3200704, 495403, 5361520, 5766923, 5502000, 2114204, 6581657, 3282423, 6757782, 38825, 6257035, 8056386, 7712436, 5855541, 3748426, 6506943, 8329139, 4464736, 6507534, 2755142, 5613066, 750993, 86661, 643315, 2372501, 6971248, 7225574, 2103651, 4958557, 4296738, 2358267, 3953711, 7408981, 7420558, 1405987, 4816642, 7917780, 1637588, 163113, 2746611, 7050095, 4273868, 6469559, 4756221, 7595366, 7836711, 4324483, 8032092, 5084901, 1803445, 3802007, 5106146, 8193263, 1297966, 371192, 4009023, 751843, 5168520, 960959, 2012265, 1545558, 3153065, 2155998, 6139555, 6175634, 4953204, 2037103, 4700911, 5542920, 8327103, 5556920, 5076642, 4337003, 3241027, 3250913, 6240628, 471278, 342677, 5597821, 5335341, 6363946, 2333691, 7875492, 7414343, 403850, 4101607, 4996111, 1526654, 1777407, 510032, 1084541, 6675366, 7589179, 5146888, 6618169, 6568566, 7851947, 6749223, 311456, 92078, 7456259, 6918398, 986611, 6764198, 3821153, 6775638, 5062655, 5313616, 1365167, 1058491, 2329189, 7096056, 531201, 7714036, 2964619, 366539, 4946754, 4880287, 7101834, 3658654, 4560025, 3268280, 7257937, 3519829, 197800, 7796453, 2513366, 5326129, 7361208, 7467539, 1021952, 271166, 3926680, 5693804, 4953979, 4785847, 8181723, 88166, 6396951, 3621240, 2958356, 7917715, 940434, 6199043, 1869959, 4560213, 4220883, 4993433, 3456257, 655933, 4942873, 7729710, 2889092, 99109, 4254805, 4397892, 566716, 7638269, 712702, 3021649, 7459784, 1474592, 6663551, 5497495, 1612528, 3951166, 3464720, 3082792, 8328908, 4906116, 4892144, 1064079, 292156, 4406608, 1372725, 4643784, 6815209, 2576189, 5219012, 4551660, 5759911, 4191285, 4924128, 6663549, 7369862, 2619701, 6693097, 3172635, 1825821, 2593380, 6689077, 1954577, 3525818, 3567008, 7020430, 5176667, 7753976, 7608986, 4888751, 5172767, 4266370, 2213132, 4133048, 1947774, 3093950, 2160885, 2160568, 5344784, 3190244, 1327760, 7765530, 7592291, 5390090, 5593052, 7258840, 7873222, 3441562, 4200566, 6601638, 6047736, 8140218, 3940247, 8160023, 5354035, 525909, 6019834, 6014077, 8130485, 2528636, 3101749, 5707436, 1271089, 1909479, 489462, 3962750, 4410120, 5522107, 738910, 8368031, 6637792, 4290537, 2657149, 4414023, 269274, 6354856, 326716, 8339688, 540728, 4790387, 4361147, 97487, 6036048, 945225, 5138131],
[5661106, 6573239, 2821408, 1276722, 389504, 2855086, 2901224, 6027529, 2089902, 5734306, 3917272, 4420067, 2741469, 7123306, 5328861, 7184809, 5922403, 3792987, 7131702, 6508181, 2565521, 7491204, 7133083, 547108, 1852366, 4524962, 1432494, 8290920, 4589713, 4495051, 221710, 5784450, 1736795, 1104784, 1835790, 1071539, 4068236, 523615, 7163351, 7839177, 7889739, 1951983, 6200379, 1539219, 3736368, 3682694, 4625534, 6025719, 6753962, 5822712, 5298992, 4395515, 2647628, 2291255, 336547, 571109, 8185190, 5155211, 1415484, 7409345, 1242353, 4197744, 1472701, 4417687, 2597418, 5229397, 733629, 8233169, 4858942, 1384871, 2892543, 225120, 5172733, 307803, 1338300, 6026762, 781775, 824139, 4026478, 7005871, 7689104, 6388512, 6823305, 4643865, 6944299, 2813514, 1473472, 4646648, 1987275, 6076897, 3062119, 3824871, 2109975, 395803, 7261372, 1730157, 3812823, 8349213, 1970837, 5109369, 4705527, 1617612, 295474, 1034626, 5947989, 2527807, 5567015, 738044, 5948512, 6398457, 3511141, 7698933, 8020920, 5436925, 2216585, 1675400, 6119146, 3032202, 593676, 4425066, 3989838, 2929091, 6032384, 713368, 6836074, 4577996, 1867829, 8309037, 2612140, 1009446, 2930066, 1556459, 7943715, 2546794, 7244935, 405521, 7302373, 4109582, 3144291, 5621685, 4226472, 5292180, 838588, 6774508, 5653012, 5209670, 6552046, 6066805, 1836991, 948331, 7986259, 1007182, 7359344, 3613107, 4180413, 6459660, 1341670, 6212693, 2871479, 4430008, 5649720, 2772868, 1029216, 4856589, 3699559, 7100015, 2238327, 3261094, 2419540, 5746032, 2752415, 6333743, 5167956, 4502061, 5055476, 5632396, 280655, 2089899, 3876685, 2717944, 8017917, 2162935, 7173919, 7752411, 5891939, 5432384, 3156272, 85495, 4537958, 5934925, 1102270, 7273041, 2908968, 6232318, 945818, 4273456, 347409, 298043, 4136190, 7843207, 2453465, 5912303, 720358, 4294949, 3462945, 549110, 2612011, 4542721, 1249730, 1633754, 905703, 5755286, 3826540, 5637689, 5822804, 6245349, 622956, 3114559, 4005669, 2168127, 3601606, 1668296, 6514298, 4874225, 5385419, 4731276, 3169463, 5791864, 139722, 1598059, 7784919, 2471949, 3648693, 1692137, 7220683, 4748937, 5943103, 6749762, 4239522, 748420, 7642073, 1720391, 2545623, 7905944, 2836641, 523160, 4322759, 2806726, 3140490, 5332117, 6124119, 6427564, 7998811, 3289837, 6726546, 5368865]]
w = NTTInverse(aHat * NTT(y)): [[3560581, 47893, 5288591, 8200619, 834849, 7173375, 1229664, 1212957, 5814018, 7972724, 865753, 2705887, 6967047, 1169987, 6299165, 2230927, 5747033, 968539, 7018837, 3963319, 2940446, 3297448, 471067, 6816052, 6537345, 2510066, 803714, 5477691, 4353991, 1779710, 3416902, 7795092, 352184, 5298713, 1075954, 2871019, 8292845, 7057442, 4601559, 2188293, 5575364, 7510678, 7555217, 1332707, 4508805, 8098440, 1394701, 1975635, 6945976, 1602371, 7817644, 2955713, 269908, 1914372, 4589100, 5937317, 1665225, 873525, 5321045, 4613091, 6430865, 2885704, 7140271, 7589428, 3646, 6681174, 6702006, 6113787, 1966082, 6076989, 3708196, 277882, 4253560, 2816010, 605068, 917566, 4857420, 3253206, 8215493, 6525914, 1667093, 6822873, 4342734, 2270832, 5890261, 6961974, 6619113, 6499398, 4720204, 1529218, 7927435, 203781, 3762654, 4114760, 3435889, 1711170, 6593691, 7410879, 167293, 2246084, 283037, 4536424, 6355651, 4549400, 6495131, 4078178, 2101613, 1417406, 439205, 7210791, 3215811, 6024296, 7379998, 1165848, 1601525, 3794345, 5657793, 2967781, 1982254, 5119236, 6609683, 5828617, 3427811, 6013991, 6638842, 5222433, 5300374, 3908028, 2166583, 6214637, 8324449, 647385, 4104189, 7168943, 5847217, 2795008, 2006675, 1619465, 4193706, 5402444, 6316706, 4028331, 211220, 809342, 6517500, 4166658, 19994, 4348610, 1677739, 7598879, 5980119, 4459704, 6001555, 3529244, 8089376, 5135326, 6438497, 1967075, 5287711, 5292117, 5052047, 1103132, 6140519, 5948513, 5995476, 6354, 1076114, 5085041, 478804, 4184563, 3752466, 2195167, 395822, 4019811, 5060103, 4648674, 2077720, 6682998, 6246277, 5968220, 6499937, 6008370, 1495549, 596465, 1140002, 5195674, 1596165, 7690383, 7132355, 8115414, 7240498, 8096549, 4024327, 8284365, 4749927, 1417427, 2608184, 7253097, 2985448, 221501, 5312702, 7829279, 4642597, 2920620, 1444049, 5767437, 5568386, 4488731, 5351482, 3188181, 5603141, 7893555, 474242, 359226, 1212081, 7973926, 7576472, 3913522, 1823000, 2702354, 3036837, 6110663, 1402859, 6688171, 3725517, 3381884, 2539286, 3221850, 4687665, 1135633, 4830850, 2518811, 8168301, 2930008, 344314, 7425812, 5972476, 3264369, 7274883, 6060673, 1825258, 2485475, 935043, 3201054, 7080142, 1311164, 5343774, 4198060, 7668976, 5190034, 3274382, 3364560, 937807, 4630638, 4105309, 1965713],
[6961642, 3484739, 2479972, 1449358, 8013470, 4837783, 7805497, 2836973, 1408896, 7993132, 3700401, 1086372, 2082514, 4723986, 3024999, 1584431, 5086733, 6534440, 6662558, 6686379, 3870275, 4677946, 4136813, 8270140, 879277, 3670254, 8345816, 336602, 7967744, 7726550, 3616238, 4050373, 1776309, 5580633, 4430706, 3399863, 278515, 347199, 7471497, 4590175, 2252110, 3611252, 2809445, 3175375, 6479949, 3987081, 1675252, 5670162, 1790023, 7067593, 3151621, 5531241, 2155057, 5858397, 2893870, 5917925, 6395490, 3991043, 8323549, 3426396, 3986170, 4252519, 4490997, 2592727, 7113470, 2982476, 5647700, 5145743, 8261597, 6921792, 7511841, 2447065, 873877, 3723981, 2712988, 2953526, 7638227, 7064500, 3521836, 3657185, 328989, 5486054, 1214093, 6384798, 1049971, 6339330, 7014976, 1320357, 231029, 4576685, 41902, 5588335, 7893691, 2948868, 7480709, 5660302, 2284937, 3446783, 6265836, 649368, 1278124, 173855, 3041040, 19969, 4413062, 6923047, 6589253, 3279261, 4182101, 8043041, 5823495, 3337812, 2393085, 5526652, 4779217, 1634990, 7682900, 7312253, 2261502, 3600536, 881105, 5057144, 5248203, 3430020, 4965277, 1489581, 4381682, 5689774, 4412375, 4980102, 6194320, 2563916, 1641029, 6195354, 8165958, 7866565, 2239219, 3295823, 6505220, 5601528, 3775603, 518322, 1056137, 2875427, 5891809, 6798457, 7792185, 5887914, 964893, 3253677, 4986017, 7808080, 7467912, 5625014, 6234290, 1823425, 2340269, 5836329, 2140921, 4347475, 5148510, 3487715, 590995, 4601511, 1614104, 239228, 3482779, 5563011, 510939, 1283481, 8347221, 2493439, 7070049, 6442850, 4901772, 5940119, 5395991, 2336639, 2848985, 3652179, 2065301, 2794226, 5191502, 4545973, 3651233, 531349, 2338577, 894736, 6920476, 4903608, 1405740, 6724784, 5187308, 5784424, 4172409, 4948190, 3354463, 7612631, 2506172, 5603382, 6713447, 2735253, 4879748, 7639983, 2424189, 5164997, 2726431, 2894678, 3483015, 1231417, 3943949, 7402314, 6951291, 7268549, 5582547, 4314671, 3415701, 1888974, 8172665, 6681366, 8333275, 4986530, 8063276, 3438475, 2851017, 7696109, 6696056, 7111145, 5786721, 2020099, 3988339, 6996409, 6653730, 4743711, 1944706, 6257845, 3208406, 5762026, 409630, 5814578, 4840761, 4971672, 2827966, 1128233, 5857920, 7301381, 6449539, 5458030, 897079, 4575349, 1215354, 2185679, 2751570, 153840, 1127663, 31614],
[5096358, 422070, 3170040, 6476022, 5911345, 7986735, 2113252, 7663839, 2065385, 7854462, 7812243, 3611040, 2679424, 4523455, 3713978, 4505890, 926983, 147714, 2925664, 1660502, 1015544, 654887, 204317, 2974297, 189811, 2540669, 5860645, 1293791, 2309477, 5948909, 6658992, 1289208, 3600121, 1839961, 744193, 1945126, 4048464, 3662296, 8102655, 1125312, 4664713, 6465638, 8306464, 1418408, 3866891, 2250370, 7509810, 4038944, 2889596, 2150982, 1857313, 4802959, 3318030, 4129799, 3784580, 2916867, 5238015, 479458, 5917104, 2225189, 3327893, 2318020, 6644540, 5216054, 945640, 1384138, 623374, 3547217, 2200796, 5782269, 5887322, 5793678, 576357, 1960632, 4159218, 5833760, 3695305, 3515657, 5769278, 5672041, 6366965, 5444125, 4361363, 8121299, 269831, 5878556, 2179526, 4806772, 4726746, 3887114, 6252576, 2763463, 7287204, 8239720, 5332741, 7467010, 1531080, 309107, 2825868, 4862944, 6866240, 4270958, 2185881, 1114348, 6903714, 8189693, 8061318, 2556445, 7376134, 3701575, 6684008, 6058225, 3672822, 4115488, 4752006, 145903, 6313143, 2532818, 7544706, 6287779, 6778084, 7076655, 7957409, 8017176, 2387687, 1162073, 6473806, 564878, 2147155, 7247584, 4324527, 3486663, 8349401, 42332, 6531065, 3817554, 1594275, 6232985, 4672619, 4737752, 6537235, 5965074, 3108576, 8134567, 3987056, 5016888, 4912676, 6629206, 1647598, 4206028, 1203621, 7867596, 7595540, 7533561, 7090887, 1595691, 3325617, 2435049, 5377599, 3424203, 6626239, 5097768, 5884191, 5151559, 3243445, 6762359, 4072641, 7768207, 3327939, 2841264, 5011722, 1530358, 2253580, 4293661, 2984613, 7183142, 2300536, 6773074, 7429307, 4740280, 4451160, 2600791, 4853681, 8338857, 4609106, 8228015, 695592, 1012199, 6337226, 169199, 7826370, 17044, 7329286, 6908146, 5156911, 2668033, 6825389, 4418449, 1387011, 4278996, 3577606, 2710166, 7054483, 3027135, 5144246, 354693, 5693778, 837278, 6042024, 6619496, 739186, 6228943, 7256241, 3595784, 5548110, 7320505, 4893032, 224626, 4144287, 8270774, 5585253, 2142355, 6958797, 8014502, 7734836, 905113, 7603650, 5216809, 7811624, 4062677, 289663, 6159566, 6060985, 2251615, 3930569, 5928478, 719498, 2079625, 468508, 2479217, 1673009, 6305862, 8029123, 7790039, 4855199, 1494007, 5943930, 4746973, 5289579, 5837713, 5570777, 660330, 5063442, 6816136, 7401711, 5839623],
[704273, 5776085, 2600625, 1078246, 3077689, 4016262, 6143076, 2814363, 2007902, 718889, 6315143, 5611001, 770448, 1006217, 2380057, 5993455, 1499884, 2510093, 3055077, 6383997, 7335234, 1897201, 7126676, 1060138, 3570341, 5621485, 4109110, 6774372, 5313807, 2322296, 179011, 8298742, 5857566, 6374357, 1146815, 6922826, 3110595, 2933514, 7831594, 4020690, 39560, 3620157, 7418598, 3864034, 1018115, 7206187, 4645005, 1376609, 2305551, 2753562, 4840839, 5201172, 1271620, 6623737, 5144377, 6150656, 5714850, 7852361, 3269106, 5460272, 6291934, 1883313, 7601969, 6166014, 7218828, 3016717, 2582125, 322787, 5354252, 352696, 6607577, 7704960, 4176995, 6368893, 725937, 6213310, 2060432, 3668989, 3976494, 1838006, 3970154, 6895099, 5596020, 7404413, 3642522, 4373247, 2334782, 2239907, 7344370, 931268, 3890890, 6849156, 3367981, 3199985, 8097010, 7198090, 6593243, 6086047, 1629682, 2605764, 231285, 7331630, 1856787, 4405266, 8180110, 232993, 3066755, 1110723, 1137087, 844480, 360130, 3130612, 3970194, 6295411, 7707905, 1586503, 3784741, 4916926, 7927390, 6043553, 1809522, 45024, 3981154, 684652, 5281117, 781944, 4482335, 5123982, 5675172, 3336658, 1018129, 5465053, 5502181, 1897364, 8075790, 2162090, 1317013, 7149635, 4400947, 6386109, 4466326, 2545059, 1517489, 5437827, 8267557, 5950926, 2827346, 6391776, 2817502, 323230, 4294534, 398434, 6767654, 7012504, 7811744, 5331354, 5006953, 3331026, 5195867, 1981906, 7708855, 6165657, 2974611, 7269533, 942973, 2073723, 3901212, 1691482, 37414, 3901020, 360184, 4107696, 6579878, 5701040, 5978545, 7461908, 6083150, 2627786, 641211, 2922861, 3126498, 7721401, 7632081, 2549884, 1726727, 3973143, 1909862, 6699946, 4005440, 1459097, 341886, 940931, 7155103, 7931745, 8135242, 4566384, 791477, 5707083, 4333437, 408252, 393997, 4752773, 7564053, 5308611, 6278397, 3456360, 1356824, 5091302, 1386904, 5952371, 6803713, 3292952, 5381139, 2616410, 1087287, 6702625, 5863702, 2295817, 969269, 2144980, 7800354, 3842637, 1098122, 2064427, 2846131, 2107047, 4760328, 4690298, 112343, 7952602, 1140400, 2440225, 5234035, 3413665, 7863268, 6616032, 3611122, 2385948, 7209573, 5463402, 4759871, 1880773, 236638, 4450394, 1593713, 3048047, 73828, 8184230, 6533947, 2234954, 1953596, 8062595, 1907606, 2189734, 395202, 4604308],
[3613665, 3422873, 1730137, 4425630, 1807693, 2072178, 5552526, 8069541, 1839440, 3881383, 3529565, 5943798, 4459292, 8360561, 4002504, 4938829, 6556823, 5231116, 1092411, 564561, 4387299, 7491967, 5300401, 5641994, 359422, 5732668, 1230552, 3361077, 1326898, 2974415, 6289856, 6206119, 6592133, 5498431, 7174769, 3616225, 788790, 5956531, 2192787, 439069, 6065035, 2716272, 7214867, 6273613, 7384407, 7434380, 7686243, 104554, 4765126, 5968179, 6057059, 6588805, 8117286, 6049247, 1771492, 4191016, 3611300, 3011553, 4420930, 4447018, 7124454, 6867246, 1749149, 2203846, 6703127, 1447917, 6436318, 1692011, 2291578, 2876848, 4130676, 4015780, 2326462, 1124561, 1900747, 920906, 3555623, 8309887, 5502508, 6813400, 5708917, 1316140, 1940846, 7912974, 5596430, 1671495, 6143436, 6713727, 6140098, 5898400, 532019, 3866667, 4946911, 6200001, 8352985, 1328075, 4774734, 2549466, 1075390, 6190731, 6158586, 4144719, 2738197, 6898525, 8188803, 6242611, 435252, 305708, 6722922, 5636074, 4610338, 6973490, 1478679, 2173633, 3567260, 4089162, 7936307, 3235472, 6685602, 3465068, 1069452, 3231388, 1473631, 279144, 2943212, 5576138, 5991558, 5827368, 8087992, 1265812, 1747692, 2087966, 8371997, 4766254, 3796463, 891130, 5865960, 1277452, 5879363, 8254700, 3980450, 6244336, 4083854, 4141485, 2488231, 4466629, 3263556, 2398503, 2796671, 862841, 165730, 3280413, 3685203, 3528368, 3894637, 229385, 4527799, 6132368, 67987, 5674424, 1528089, 3498247, 6661515, 4112767, 3384026, 5433189, 1062052, 7786653, 198027, 6546258, 415637, 6671155, 6288900, 6365882, 2436805, 1774041, 137863, 5362215, 1864283, 6028153, 8147904, 7896054, 1511383, 1405614, 1449602, 2930764, 2821658, 5379695, 4210407, 6220193, 3821030, 8040041, 3497992, 3570805, 8193286, 3181360, 5030155, 702118, 5610832, 4656790, 6269843, 3886761, 5643012, 6398921, 8012343, 1197002, 5905263, 559546, 5107350, 6662446, 1242427, 3849841, 1287793, 6947627, 6488924, 1535700, 1192573, 4695166, 2222302, 8029771, 8270055, 7640146, 2728890, 7303873, 722843, 5352439, 6497969, 7859722, 1472723, 694897, 3414080, 5286740, 6587156, 4921312, 8191030, 3323565, 355314, 6739809, 2462264, 1993441, 3945428, 4570654, 6680459, 8281205, 6795615, 6440093, 7756294, 7669209, 4775686, 7193631, 3709886, 3348792, 1587237, 6015981, 7366448, 6551765],
[3091295, 302460, 2319179, 3122367, 195581, 1653957, 2849648, 5808127, 3114670, 3607370, 3964281, 7728063, 3014534, 2250510, 4249954, 803192, 1090359, 5150345, 6966784, 2402593, 6287862, 1057218, 4314541, 4762512, 7170223, 3871709, 4099455, 1177180, 6473978, 4123591, 5947177, 8123569, 3262501, 966252, 4921457, 4179500, 121687, 5417066, 1344204, 2075093, 986674, 139857, 4024509, 667631, 7134233, 2658370, 6661809, 2911611, 346059, 7490518, 1357325, 188991, 5173577, 124296, 62955, 3575803, 1147827, 2808550, 3879413, 1316239, 1551728, 1612884, 1503550, 1581638, 4325252, 8267491, 2079654, 3775032, 4394182, 1705982, 663087, 6890226, 4288042, 7654884, 872629, 925007, 6379675, 261703, 1115376, 2328826, 576687, 2639328, 2090639, 3279025, 22171, 5945590, 2241826, 364298, 463703, 5489614, 627217, 652356, 1481830, 673709, 5795042, 6521338, 6707501, 7491103, 817257, 503570, 8044756, 7191420, 8102199, 3301042, 1175039, 3579581, 48366, 1665725, 1762058, 6266878, 7649525, 1732491, 7743552, 7280460, 8130751, 4654330, 6520048, 6919414, 2690958, 6181350, 1646868, 1384884, 1248670, 1050673, 7372059, 6209385, 4725695, 5354441, 6726069, 482663, 5094710, 7778712, 5245259, 600121, 7724059, 1081459, 4936424, 707986, 4658852, 8339672, 5060099, 5170933, 8315859, 8209185, 6963764, 3972477, 3142098, 6040064, 2134207, 352545, 1328796, 3131583, 5793515, 3859730, 2001804, 1120625, 516475, 3887911, 5708153, 4343385, 5923057, 2384733, 254505, 5936727, 6977748, 3095137, 4951127, 5678529, 5807105, 7959348, 2513922, 1603202, 1784340, 7169513, 818905, 2165469, 1171097, 1844403, 1474606, 3463776, 314806, 6200799, 5984361, 5175056, 2905720, 4769158, 8343819, 2676529, 4191877, 1468760, 5698425, 620062, 3423297, 1898007, 7420177, 3514014, 8038510, 5191428, 2158712, 4136628, 2327661, 1582861, 6981377, 829241, 3585017, 3070000, 3888781, 2598875, 7741465, 3741547, 1694808, 4155121, 6529649, 7651713, 4533788, 6355492, 1565749, 7811549, 5149638, 3506758, 1040557, 7489820, 3864747, 2044442, 3027174, 7559442, 1091508, 4726288, 5328101, 1693165, 8195524, 1792806, 5585489, 5905929, 3794503, 7180440, 5667120, 6919859, 791559, 5772061, 7755425, 4168604, 7309471, 12123, 8328017, 1651763, 5164827, 997835, 6895367, 249889, 4656083, 5246296, 1173750, 3712555, 6889404, 5969362]]

w1: [[7, 0, 10, 0, 2, 14, 2, 2, 11, 15, 2, 5, 13, 2, 12, 4, 11, 2, 13, 8, 6, 6, 1, 13, 12, 5, 2, 10, 8, 3, 7, 15, 1, 10, 2, 5, 0, 13, 9, 4, 11, 14, 14, 3, 9, 15, 3, 4, 13, 3, 15, 6, 1, 4, 9, 11, 3, 2, 10, 9, 12, 6, 14, 14, 0, 13, 13, 12, 4, 12, 7, 1, 8, 5, 1, 2, 9, 6, 0, 12, 3, 13, 8, 4, 11, 13, 13, 12, 9, 3, 15, 0, 7, 8, 7, 3, 13, 14, 0, 4, 1, 9, 12, 9, 12, 8, 4, 3, 1, 14, 6, 12, 14, 2, 3, 7, 11, 6, 4, 10, 13, 11, 7, 11, 13, 10, 10, 7, 4, 12, 0, 1, 8, 14, 11, 5, 4, 3, 8, 10, 12, 8, 0, 2, 12, 8, 0, 8, 3, 15, 11, 9, 11, 7, 15, 10, 12, 4, 10, 10, 10, 2, 12, 11, 11, 0, 2, 10, 1, 8, 7, 4, 1, 8, 10, 9, 4, 13, 12, 11, 12, 11, 3, 1, 2, 10, 3, 15, 14, 15, 14, 15, 8, 0, 9, 3, 5, 14, 6, 0, 10, 15, 9, 6, 3, 11, 11, 9, 10, 6, 11, 15, 1, 1, 2, 15, 14, 7, 3, 5, 6, 12, 3, 13, 7, 6, 5, 6, 9, 2, 9, 5, 0, 6, 1, 14, 11, 6, 14, 12, 3, 5, 2, 6, 14, 3, 10, 8, 15, 10, 6, 6, 2, 9, 8, 4],
[13, 7, 5, 3, 15, 9, 15, 5, 3, 15, 7, 2, 4, 9, 6, 3, 10, 12, 13, 13, 7, 9, 8, 0, 2, 7, 0, 1, 15, 15, 7, 8, 3, 11, 8, 6, 1, 1, 14, 9, 4, 7, 5, 6, 12, 8, 3, 11, 3, 13, 6, 11, 4, 11, 6, 11, 12, 8, 0, 7, 8, 8, 9, 5, 14, 6, 11, 10, 0, 13, 14, 5, 2, 7, 5, 6, 15, 13, 7, 7, 1, 10, 2, 12, 2, 12, 13, 3, 0, 9, 0, 11, 15, 6, 14, 11, 4, 7, 12, 1, 2, 0, 6, 0, 8, 13, 13, 6, 8, 15, 11, 6, 5, 11, 9, 3, 15, 14, 4, 7, 2, 10, 10, 7, 9, 3, 8, 11, 8, 10, 12, 5, 3, 12, 0, 15, 4, 6, 12, 11, 7, 1, 2, 5, 11, 13, 15, 11, 2, 6, 10, 15, 14, 11, 12, 3, 4, 11, 4, 8, 10, 7, 1, 9, 3, 0, 7, 11, 1, 2, 0, 5, 13, 12, 9, 11, 10, 4, 5, 7, 4, 5, 10, 9, 7, 1, 4, 2, 13, 9, 3, 13, 10, 11, 8, 9, 6, 15, 5, 11, 13, 5, 9, 15, 5, 10, 5, 6, 7, 2, 8, 14, 13, 14, 11, 8, 7, 4, 0, 13, 0, 10, 15, 7, 5, 15, 13, 14, 11, 4, 8, 13, 13, 9, 4, 12, 6, 11, 1, 11, 9, 9, 5, 2, 11, 14, 12, 10, 2, 9, 2, 4, 5, 0, 2, 0],
[10, 1, 6, 12, 11, 15, 4, 15, 4, 15, 15, 7, 5, 9, 7, 9, 2, 0, 6, 3, 2, 1, 0, 6, 0, 5, 11, 2, 4, 11, 13, 2, 7, 4, 1, 4, 8, 7, 15, 2, 9, 12, 0, 3, 7, 4, 14, 8, 6, 4, 4, 9, 6, 8, 7, 6, 10, 1, 11, 4, 6, 4, 13, 10, 2, 3, 1, 7, 4, 11, 11, 11, 1, 4, 8, 11, 7, 7, 11, 11, 12, 10, 8, 0, 1, 11, 4, 9, 9, 7, 12, 5, 14, 0, 10, 14, 3, 1, 5, 9, 13, 8, 4, 2, 13, 0, 15, 5, 14, 7, 13, 12, 7, 8, 9, 0, 12, 5, 14, 12, 13, 14, 15, 15, 5, 2, 12, 1, 4, 14, 8, 7, 0, 0, 12, 7, 3, 12, 9, 9, 12, 11, 6, 0, 8, 10, 9, 13, 3, 8, 2, 15, 15, 14, 14, 3, 6, 5, 10, 7, 13, 10, 11, 10, 6, 13, 8, 15, 6, 5, 10, 3, 4, 8, 6, 14, 4, 13, 14, 9, 8, 5, 9, 0, 9, 0, 1, 2, 12, 0, 15, 0, 14, 13, 10, 5, 13, 8, 3, 8, 7, 5, 13, 6, 10, 1, 11, 2, 12, 13, 1, 12, 14, 7, 11, 14, 9, 0, 8, 0, 11, 4, 13, 15, 15, 2, 15, 10, 15, 8, 1, 12, 12, 4, 8, 11, 1, 4, 1, 5, 3, 12, 15, 15, 9, 3, 11, 9, 10, 11, 11, 1, 10, 13, 14, 11],
[1, 11, 5, 2, 6, 8, 12, 5, 4, 1, 12, 11, 1, 2, 5, 11, 3, 5, 6, 12, 14, 4, 14, 2, 7, 11, 8, 13, 10, 4, 0, 0, 11, 12, 2, 13, 6, 6, 15, 8, 0, 7, 14, 7, 2, 14, 9, 3, 4, 5, 9, 10, 2, 13, 10, 12, 11, 15, 6, 10, 12, 4, 15, 12, 14, 6, 5, 1, 10, 1, 13, 15, 8, 12, 1, 12, 4, 7, 8, 4, 8, 13, 11, 14, 7, 8, 4, 4, 14, 2, 7, 13, 6, 6, 15, 14, 13, 12, 3, 5, 0, 14, 4, 8, 0, 0, 6, 2, 2, 2, 1, 6, 8, 12, 15, 3, 7, 9, 15, 12, 3, 0, 8, 1, 10, 1, 9, 10, 11, 6, 2, 10, 11, 4, 15, 4, 3, 14, 8, 12, 9, 5, 3, 10, 0, 11, 5, 12, 5, 1, 8, 1, 13, 13, 15, 10, 10, 6, 10, 4, 15, 12, 6, 14, 2, 4, 7, 3, 0, 7, 1, 8, 13, 11, 11, 14, 12, 5, 1, 6, 6, 15, 15, 5, 3, 8, 4, 13, 8, 3, 1, 2, 14, 15, 0, 9, 2, 11, 8, 1, 1, 9, 14, 10, 12, 7, 3, 10, 3, 11, 13, 6, 10, 5, 2, 13, 11, 4, 2, 4, 15, 7, 2, 4, 5, 4, 9, 9, 0, 15, 2, 5, 10, 7, 15, 13, 7, 5, 14, 10, 9, 4, 0, 8, 3, 6, 0, 0, 12, 4, 4, 15, 4, 4, 1, 9],
[7, 7, 3, 8, 3, 4, 11, 15, 4, 7, 7, 11, 9, 0, 8, 9, 13, 10, 2, 1, 8, 14, 10, 11, 1, 11, 2, 6, 3, 6, 12, 12, 13, 10, 14, 7, 2, 11, 4, 1, 12, 5, 14, 12, 14, 14, 15, 0, 9, 11, 12, 13, 15, 12, 3, 8, 7, 6, 8, 8, 14, 13, 3, 4, 13, 3, 12, 3, 4, 5, 8, 8, 4, 2, 4, 2, 7, 0, 11, 13, 11, 3, 4, 15, 11, 3, 12, 13, 12, 11, 1, 7, 9, 12, 0, 3, 9, 5, 2, 12, 12, 8, 5, 13, 0, 12, 1, 1, 13, 11, 9, 13, 3, 4, 7, 8, 15, 6, 13, 7, 2, 6, 3, 1, 6, 11, 11, 11, 15, 2, 3, 4, 0, 9, 7, 2, 11, 2, 11, 0, 8, 12, 8, 8, 5, 9, 6, 5, 5, 2, 0, 6, 7, 7, 7, 0, 9, 12, 0, 11, 3, 7, 13, 8, 6, 10, 2, 15, 0, 12, 1, 13, 12, 12, 5, 3, 0, 10, 4, 12, 0, 15, 3, 3, 3, 6, 5, 10, 8, 12, 7, 15, 7, 7, 0, 6, 10, 1, 11, 9, 12, 7, 11, 12, 15, 2, 11, 1, 10, 13, 2, 7, 2, 13, 12, 3, 2, 9, 4, 15, 0, 15, 5, 14, 1, 10, 12, 15, 3, 1, 7, 10, 13, 9, 0, 6, 1, 13, 5, 4, 8, 9, 13, 0, 13, 12, 15, 15, 9, 14, 7, 6, 3, 11, 14, 13],
[6, 1, 4, 6, 0, 3, 5, 11, 6, 7, 8, 15, 6, 4, 8, 2, 2, 10, 13, 5, 12, 2, 8, 9, 14, 7, 8, 2, 12, 8, 11, 0, 6, 2, 9, 8, 0, 10, 3, 4, 2, 0, 8, 1, 14, 5, 13, 6, 1, 14, 3, 0, 10, 0, 0, 7, 2, 5, 7, 3, 3, 3, 3, 3, 8, 0, 4, 7, 8, 3, 1, 13, 8, 15, 2, 2, 12, 0, 2, 4, 1, 5, 4, 6, 0, 11, 4, 1, 1, 10, 1, 1, 3, 1, 11, 12, 13, 14, 2, 1, 15, 14, 15, 6, 2, 7, 0, 3, 3, 12, 15, 3, 15, 14, 0, 9, 12, 13, 5, 12, 3, 3, 2, 2, 14, 12, 9, 10, 13, 1, 10, 15, 10, 1, 15, 2, 9, 1, 9, 0, 10, 10, 0, 0, 13, 8, 6, 12, 4, 1, 3, 6, 11, 7, 4, 2, 1, 7, 11, 8, 11, 5, 0, 11, 13, 6, 9, 11, 11, 15, 5, 3, 3, 14, 2, 4, 2, 4, 3, 7, 1, 12, 11, 10, 6, 9, 0, 5, 8, 3, 11, 1, 7, 4, 14, 7, 15, 10, 4, 8, 4, 3, 13, 2, 7, 6, 7, 5, 15, 7, 3, 8, 12, 15, 9, 12, 3, 15, 10, 7, 2, 14, 7, 4, 6, 14, 2, 9, 10, 3, 0, 3, 11, 11, 7, 14, 11, 13, 2, 11, 15, 8, 14, 0, 0, 3, 10, 2, 13, 0, 9, 10, 2, 7, 13, 11]]
w1Encode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

cTilde: 765AB68AC204B255699618463D65D693A1845D574181D1403972888A76B3A553F79FEFD05FF22F37A99C525FCE21F283
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
c: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1]
cHat: [7697636, 1304167, 3143043, 85116, 8042507, 4596675, 4883028, 3726575, 8346936, 3126137, 5967592, 3809195, 8123177, 5908107, 706054, 5801063, 2838270, 8239964, 4241496, 60602, 50092, 69397, 1948883, 1880956, 2845997, 8026707, 6877645, 8268845, 8275650, 6073602, 1340711, 7321070, 1760166, 2415040, 6907118, 4882128, 4911996, 1503219, 5765478, 1264484, 4741842, 2748186, 3716580, 984221, 4296663, 1349212, 7532645, 1195901, 2982898, 7128083, 6630759, 683299, 7245579, 794503, 6121664, 5644943, 418808, 3438417, 6712607, 7386647, 8083030, 5245429, 1864829, 4275295, 851434, 3629055, 6123265, 5826055, 138135, 4513773, 2021722, 4337747, 3674854, 4886678, 8312413, 5637757, 3145972, 2947478, 3479015, 1301260, 2861478, 117338, 4515896, 6037872, 1869025, 3820331, 873222, 1712911, 5809085, 1177662, 4860561, 6967091, 2583834, 4712152, 1802060, 3641516, 1682099, 6783366, 4392824, 3527811, 3887959, 8302943, 315084, 7170207, 4018559, 5033985, 212217, 5899680, 3089349, 7519477, 2985200, 3367707, 999188, 4834843, 3467509, 6670077, 6275668, 1400365, 3248508, 2861002, 2775686, 5405093, 7522027, 5767165, 4069683, 5528306, 628368, 1496816, 6461093, 2024183, 4059993, 892265, 8046234, 4593705, 4811641, 5312964, 3398982, 6055791, 7739228, 2597791, 5142163, 5638808, 3798159, 4137253, 2778395, 6380083, 3448622, 8298681, 101913, 7383430, 962108, 83596, 2604891, 70272, 5934110, 3519532, 1441675, 8361631, 2764042, 8320364, 6850205, 5741156, 2022274, 48444, 2215734, 3752657, 1502099, 2857379, 8125333, 2082959, 1427368, 185150, 4288283, 1078563, 7882134, 2755862, 555240, 5250242, 6047762, 2363257, 229707, 2536807, 4657452, 45750, 6715136, 7849401, 3335201, 6872402, 5262666, 7814443, 5715872, 2529210, 1833890, 8149650, 2602783, 3507212, 1495787, 175709, 1037870, 8055259, 3812733, 2826283, 7916225, 2095505, 7761282, 6552140, 5280086, 3652854, 1477474, 1737168, 1896077, 2102498, 6823468, 3934389, 1849891, 564637, 488022, 3976904, 8155982, 5076302, 6095157, 1362531, 2330093, 6026084, 6409827, 2879815, 1626977, 7393474, 7738584, 7828981, 5589091, 3432961, 2764021, 2144367, 1752218, 6173004, 4071607, 7921448, 3180477, 7187411, 3163155, 18859, 4489661, 4080780, 5664455, 1417835, 3490159, 1398652, 3588983, 1169145, 7827560, 4425621, 5129479, 584985, 382330, 7867952]
cs1: [[1, 33, 8380400, 8380409, 8380401, 2, 41, 8380409, 8380415, 8380408, 9, 8380396, 14, 8380411, 37, 30, 8380399, 7, 29, 5, 8380412, 8380397, 4, 8380398, 11, 0, 18, 7, 8380401, 48, 6, 8380394, 15, 15, 8380407, 5, 5, 13, 7, 8380408, 20, 22, 8380414, 8380390, 8380411, 11, 5, 5, 4, 24, 35, 21, 8380408, 8380395, 8380402, 16, 8380409, 14, 8380387, 6, 9, 8380391, 4, 8380409, 2, 35, 8380397, 8380394, 11, 17, 7, 0, 19, 9, 0, 8380414, 8380394, 8380415, 8380408, 16, 8380402, 7, 8380401, 8380403, 8380385, 8380408, 8380406, 10, 8380393, 8380416, 17, 6, 39, 13, 8380374, 8380413, 14, 5, 8380389, 8380401, 8380402, 4, 8380399, 8380404, 8380404, 5, 7, 11, 5, 22, 8380393, 8380400, 8380387, 12, 22, 6, 6, 8380406, 8380408, 8380415, 19, 8380397, 8380387, 8380410, 8380403, 3, 8380409, 8380414, 8380407, 8380382, 11, 30, 8380413, 2, 0, 8380401, 8380407, 19, 8380405, 8380402, 33, 8380406, 8380415, 19, 34, 8380406, 8380409, 8380405, 16, 8380400, 8380388, 8380398, 29, 21, 8380416, 8380403, 10, 8380403, 12, 8380406, 0, 11, 8380413, 8380386, 8380396, 6, 35, 8380410, 42, 8, 18, 17, 8380413, 8380399, 5, 8380408, 8380400, 8380409, 21, 8380399, 8380407, 3, 0, 39, 24, 8380399, 8380414, 14, 12, 8380387, 8380408, 9, 8380416, 4, 8380406, 1, 36, 8380398, 8380393, 0, 3, 20, 8380390, 8380415, 11, 37, 21, 8380366, 16, 38, 27, 8380400, 8380400, 9, 8380399, 12, 8380391, 8380406, 31, 31, 8, 8380385, 8380410, 4, 8380407, 8380412, 8380413, 18, 16, 8380407, 17, 12, 8, 2, 7, 8380405, 10, 21, 8380397, 6, 8380387, 8380412, 18, 13, 8380398, 10, 8, 8380413, 8380409, 1, 8380399, 23, 0, 4, 8380393, 32],
[9, 8380392, 8380375, 29, 8380405, 8380374, 2, 8380398, 47, 4, 8380386, 0, 8380405, 12, 16, 8380409, 21, 8380411, 8380402, 35, 7, 8, 8380414, 1, 8380376, 4, 10, 3, 8380369, 8380404, 26, 8380407, 4, 9, 8380406, 30, 1, 8380411, 8380401, 4, 7, 25, 4, 21, 8380412, 8380413, 8380401, 8380393, 8380379, 3, 5, 8380411, 0, 8380377, 23, 12, 8380401, 8380403, 8380412, 8380398, 1, 14, 10, 8380416, 8380407, 8380407, 26, 25, 8380414, 8380415, 0, 20, 9, 9, 5, 8380399, 8380410, 8380395, 0, 29, 8380378, 8380392, 10, 24, 17, 8380405, 1, 18, 8380415, 8380394, 8380414, 8380415, 8380413, 5, 12, 12, 1, 21, 8380404, 0, 8380412, 8380398, 8380411, 10, 8380408, 0, 7, 10, 5, 16, 12, 8380406, 8, 8380415, 8380416, 11, 8380415, 12, 24, 8380401, 7, 8380410, 16, 8380385, 8380415, 12, 8380408, 8380416, 8380404, 1, 19, 15, 23, 8380397, 41, 5, 8380397, 8380416, 8380412, 8380407, 5, 22, 16, 8380414, 25, 8380390, 5, 0, 10, 3, 8380394, 8380401, 31, 14, 12, 8380409, 8380398, 12, 14, 27, 8380393, 10, 53, 4, 8380374, 7, 8380405, 0, 24, 23, 8380401, 8380404, 8380394, 17, 6, 8380397, 8380411, 8380404, 6, 4, 8380393, 29, 8380412, 8380386, 8380407, 27, 8380405, 8380414, 23, 8380415, 34, 6, 8380416, 8380409, 15, 13, 8380406, 8380414, 12, 8380393, 6, 8380403, 9, 12, 0, 12, 11, 8380409, 8380409, 21, 8380414, 9, 4, 8380407, 30, 12, 3, 8380395, 8380382, 16, 0, 9, 9, 8380408, 13, 20, 8380397, 10, 8380415, 8380382, 20, 12, 8380398, 35, 8380390, 8380405, 8380397, 17, 8, 8380409, 8380391, 16, 7, 25, 8380411, 8380405, 8380398, 8380413, 9, 37, 1, 8380405, 8380416, 8380415, 0, 3],
[8380400, 8380396, 8380409, 8380389, 11, 8380396, 8380413, 8380402, 5, 37, 3, 5, 31, 18, 3, 5, 1, 12, 1, 8380414, 8380398, 8380409, 25, 8380391, 3, 8380391, 21, 8380391, 8380410, 8380396, 8380406, 15, 7, 21, 8380388, 9, 19, 5, 17, 8380414, 8380412, 10, 8380412, 36, 6, 6, 8380394, 8380386, 8380415, 8380383, 7, 8380404, 26, 8380396, 8380414, 9, 8380408, 8380405, 9, 8380371, 17, 75, 8380413, 10, 8380402, 8380415, 31, 3, 8380405, 8380406, 5, 0, 2, 8380388, 1, 8380406, 8380414, 8, 29, 0, 8380401, 8380405, 12, 4, 8380395, 8, 14, 1, 13, 7, 8380406, 1, 8380395, 5, 1, 8380391, 4, 8380404, 8380415, 25, 8380411, 8380395, 23, 27, 15, 8380387, 8380390, 45, 15, 8380405, 8380376, 6, 8380397, 8380416, 8380396, 8380413, 8380400, 11, 12, 8380408, 2, 8, 8380399, 8380414, 17, 16, 12, 4, 4, 22, 9, 9, 8380412, 8380410, 8380416, 12, 8380384, 29, 15, 13, 15, 8380402, 8380397, 0, 8380413, 6, 8380408, 8380397, 5, 8380385, 29, 35, 8380389, 8380382, 8380405, 8380408, 5, 15, 8380402, 39, 8380414, 8380395, 26, 8380414, 5, 9, 8380382, 30, 31, 9, 2, 8380395, 31, 8380392, 8380413, 8380405, 6, 8380408, 8380416, 12, 8380386, 27, 8380387, 8380396, 15, 15, 12, 3, 8, 10, 3, 8380398, 10, 8380414, 18, 8380414, 26, 52, 22, 8380379, 8380408, 1, 0, 8380400, 8380408, 6, 8380409, 8380415, 8380388, 8380408, 2, 7, 8380411, 8380403, 44, 0, 24, 8380412, 8380409, 12, 24, 8380411, 11, 8380399, 8380375, 8380403, 14, 0, 8380408, 8380400, 13, 14, 15, 25, 17, 21, 8380405, 17, 40, 0, 26, 8380407, 8380413, 8380399, 21, 8380409, 8380407, 8380400, 8380412, 13, 8380411, 8380410, 8380387, 7, 8380395, 8380410],
[7, 8380413, 6, 13, 7, 8380408, 9, 4, 1, 8380412, 1, 10, 10, 8380395, 44, 8380363, 8380415, 37, 24, 11, 8380415, 19, 8380415, 8380399, 8380408, 23, 16, 8380386, 10, 8380412, 6, 8380396, 0, 8380415, 8380412, 12, 8380412, 8380402, 18, 8380410, 8380397, 8380392, 20, 8380406, 8380407, 0, 8380403, 23, 8380415, 10, 4, 1, 8380403, 3, 3, 8380413, 8380408, 4, 8380402, 23, 6, 2, 8380407, 8380415, 8380416, 9, 8380406, 8380384, 0, 8380415, 7, 20, 18, 18, 8380390, 8380405, 8380395, 3, 8380406, 8380395, 8380399, 19, 8, 8380413, 23, 16, 2, 7, 8380411, 8380403, 8380402, 0, 2, 32, 8380415, 20, 8380414, 3, 8380409, 8380410, 8380404, 15, 8380374, 8380375, 8380407, 3, 6, 17, 10, 18, 19, 26, 8380414, 4, 8380403, 15, 5, 8380416, 8380393, 8380413, 8380411, 8380416, 15, 15, 8380416, 8380413, 8380414, 8380413, 8380406, 24, 12, 8380404, 4, 8380404, 11, 6, 8380406, 7, 8380395, 8380405, 10, 8380413, 8380402, 8380395, 8380408, 17, 8380407, 28, 7, 8380399, 2, 14, 31, 8380400, 8380405, 8380385, 1, 10, 32, 8380414, 8380407, 14, 9, 8380382, 8380406, 8380399, 1, 4, 4, 8380381, 37, 8380398, 13, 3, 0, 3, 8380414, 0, 8380413, 8380383, 8380387, 0, 8380413, 8380412, 5, 8380400, 9, 25, 10, 6, 8380394, 8380409, 2, 8380408, 18, 8380416, 8380416, 1, 8380414, 21, 14, 8380385, 8380380, 1, 11, 7, 8380405, 8380393, 33, 12, 8380393, 8380409, 15, 8380415, 8380416, 0, 8380409, 8380413, 31, 15, 8380412, 8380395, 22, 5, 7, 8380406, 8380413, 12, 5, 8380411, 16, 8380393, 8380402, 25, 6, 8380405, 14, 13, 8380374, 1, 1, 9, 8380385, 3, 4, 8380395, 8380415, 13, 0, 8380413, 7, 19, 8380393, 8380406, 25, 8380412],
[1, 8380412, 8380404, 12, 0, 8380408, 8380413, 17, 8380390, 8380415, 19, 0, 15, 1, 8380415, 8380398, 1, 2, 8380415, 28, 8380406, 7, 16, 3, 4, 8380397, 8, 8380407, 8380407, 8380415, 8380407, 8380398, 8380412, 8380414, 1, 8380413, 15, 26, 8380416, 1, 8380412, 17, 4, 8380411, 1, 14, 8, 8380411, 8380388, 18, 8380411, 8380408, 8380411, 8380396, 5, 18, 8380402, 14, 4, 8380411, 8380412, 8380402, 8380387, 17, 8380415, 8380410, 8380385, 23, 8380410, 17, 6, 8380410, 8380401, 10, 43, 4, 8380397, 15, 2, 23, 5, 8380372, 8380414, 8380407, 8380401, 10, 8380398, 5, 8380413, 8380395, 8380410, 0, 33, 6, 14, 10, 21, 4, 8380391, 8380406, 11, 8380411, 38, 8380390, 35, 8380403, 8380386, 8380387, 6, 4, 8380403, 8380406, 8380406, 14, 23, 8380386, 35, 12, 10, 8380399, 4, 22, 9, 8380400, 8380390, 1, 3, 8380390, 8380391, 8380408, 13, 19, 8380401, 5, 8380401, 16, 4, 8380405, 32, 13, 8380404, 4, 8380401, 0, 23, 31, 8380404, 8380416, 8380388, 19, 8380411, 8380396, 8380409, 15, 8380401, 27, 5, 8380390, 4, 8380388, 8380390, 8380416, 8380412, 8380402, 15, 3, 8380412, 13, 9, 8380414, 0, 8380393, 39, 31, 8380403, 8380408, 9, 1, 8380414, 8380393, 8380404, 17, 25, 2, 8380393, 8380411, 8, 2, 8380410, 8380404, 17, 15, 0, 8380382, 8380416, 8380414, 8380385, 8380399, 8380409, 16, 5, 11, 8380365, 6, 8380409, 3, 8380416, 8380408, 27, 30, 8380412, 45, 8380407, 6, 8380404, 24, 8380384, 8380404, 8380416, 8380404, 38, 8380402, 8380368, 24, 8380389, 39, 8380392, 8380408, 8380414, 11, 8380409, 8380405, 8380394, 8380409, 17, 11, 8380409, 8380416, 8380401, 8380416, 20, 8380407, 4, 8380416, 23, 8380410, 8380398, 14, 37, 8380395, 13, 8380410, 8380408, 8380414, 8380383, 8380362]]
cs2: [[8, 30, 8380413, 8380401, 11, 2, 18, 8380403, 8380410, 27, 14, 12, 4, 7, 8380415, 17, 2, 8380395, 16, 1, 8380413, 23, 1, 25, 8380413, 9, 8380389, 8380404, 8380407, 50, 2, 8380402, 0, 10, 8, 8380416, 8380410, 18, 8380407, 31, 12, 11, 8380408, 8380408, 8380401, 8380408, 14, 17, 17, 25, 8380391, 1, 8380412, 8380397, 23, 8380414, 8380398, 8380415, 16, 8380408, 4, 8380402, 8380388, 0, 28, 2, 8380397, 8380397, 19, 18, 4, 8380414, 10, 8380407, 8380403, 20, 30, 8380387, 8380415, 10, 16, 8380398, 8380402, 8380411, 0, 6, 8380409, 8380407, 24, 19, 8380409, 8380403, 27, 13, 8380360, 8380413, 4, 8380415, 8380413, 8380409, 1, 7, 8380405, 5, 1, 16, 10, 8380390, 15, 12, 2, 8380415, 8380399, 29, 7, 8380413, 8380381, 40, 23, 8380411, 0, 8380374, 8380410, 9, 6, 8380409, 6, 17, 20, 11, 8380376, 0, 24, 8380400, 8380412, 1, 22, 8380400, 8380409, 8380391, 8380401, 8380408, 20, 14, 4, 8380410, 8380412, 8380404, 28, 8, 10, 8380399, 4, 29, 12, 9, 8380412, 8380401, 8380401, 8380408, 30, 8380390, 8380416, 8380408, 8380416, 24, 3, 30, 8380403, 4, 8380398, 7, 8380381, 3, 8380413, 2, 8380404, 24, 8380390, 0, 23, 8, 8380397, 6, 17, 9, 8380408, 6, 15, 2, 8380402, 8380412, 19, 18, 7, 8380410, 8380406, 8380412, 8380393, 7, 8380392, 18, 26, 8380414, 7, 8380413, 10, 7, 4, 8380389, 10, 0, 5, 8380404, 5, 8380409, 4, 9, 8380410, 4, 8, 8380408, 8380410, 12, 33, 8380401, 8380415, 20, 13, 11, 8380392, 8, 8380411, 8380375, 8380400, 3, 8380410, 15, 5, 6, 8380416, 2, 8380403, 13, 26, 8380387, 8380401, 35, 2, 3, 8, 8380396, 8380393, 1, 8380403, 8380414],
[8380416, 38, 8380403, 4, 8380403, 8380389, 8380416, 8380415, 10, 8380385, 10, 2, 8380415, 1, 8380413, 27, 8380414, 28, 8380405, 8380386, 15, 8380408, 8380406, 8380409, 21, 0, 8380396, 12, 8380412, 29, 31, 8380374, 16, 8380386, 8380390, 0, 29, 8380398, 8380410, 8380415, 28, 19, 11, 8380416, 8380400, 8380399, 8380411, 16, 10, 8380395, 29, 8380415, 8380415, 25, 8380398, 8380390, 16, 22, 19, 21, 8, 8380406, 8380414, 4, 8380413, 8380403, 5, 5, 8380404, 10, 13, 8380412, 8380368, 8380406, 15, 0, 0, 27, 15, 11, 8380408, 8, 8380402, 23, 8380416, 0, 1, 8380412, 21, 17, 3, 12, 8380402, 8380408, 8380392, 11, 8380394, 5, 8380400, 29, 19, 8380404, 8380413, 8380410, 3, 52, 24, 8380402, 0, 2, 21, 8380393, 32, 8380416, 8380403, 26, 8380414, 8380416, 8380399, 10, 36, 8380396, 8380404, 8380413, 8, 8380411, 18, 13, 8380416, 8, 33, 7, 8380416, 14, 27, 7, 8380405, 42, 20, 5, 8380392, 16, 4, 11, 8380392, 8380396, 32, 26, 0, 21, 8380381, 8380410, 8380401, 8380414, 17, 21, 27, 10, 12, 17, 8380392, 8380415, 8380408, 9, 15, 22, 27, 6, 5, 8380412, 6, 11, 8380394, 8380413, 8380414, 8380411, 3, 8380408, 4, 8380396, 10, 8380401, 6, 8380414, 14, 8380399, 8380402, 8380405, 26, 8380395, 14, 8380393, 12, 8380399, 9, 16, 8380416, 3, 8380393, 13, 24, 9, 8380408, 8380380, 14, 18, 9, 8380380, 3, 25, 3, 8380402, 13, 8380402, 7, 8380408, 6, 8380414, 6, 1, 8380382, 8380414, 4, 8380406, 8380402, 8, 8380394, 8380403, 19, 8, 13, 48, 2, 8380415, 8380404, 8380388, 18, 14, 8380399, 8380411, 11, 38, 8380411, 1, 8380399, 8380402, 28, 8380370, 11, 8380398, 8380392, 7, 10, 9, 4, 8380416],
[8380408, 36, 1, 8380412, 8380413, 15, 38, 8380380, 8380404, 4, 21, 8380392, 8380415, 8380407, 19, 10, 8380416, 8380414, 12, 8380409, 15, 8380393, 29, 46, 8380403, 8380406, 18, 0, 25, 8380407, 23, 8380403, 28, 8380389, 19, 8380375, 8380389, 8380404, 8380380, 8380385, 33, 0, 8380400, 8380413, 25, 11, 3, 8380415, 23, 15, 2, 10, 22, 8380412, 2, 8380389, 6, 3, 8380412, 8380398, 8380412, 8380402, 6, 19, 8380390, 8, 8380396, 10, 4, 8380394, 8380413, 8380407, 8380416, 0, 6, 8380397, 1, 10, 8380399, 5, 8380413, 4, 8380410, 8380389, 12, 8380399, 7, 31, 8380415, 8380408, 6, 8380415, 8380403, 12, 20, 8380396, 8380403, 3, 16, 8380398, 21, 7, 15, 17, 32, 7, 8380357, 31, 8380412, 8380398, 8380407, 8380414, 28, 8380380, 10, 8380404, 8380410, 30, 8380388, 1, 8380395, 27, 6, 12, 32, 10, 8380390, 21, 8380415, 8380411, 8380414, 8380406, 8380393, 40, 8380410, 32, 8, 8380390, 8380407, 12, 8380411, 6, 8380384, 6, 8380390, 10, 8380410, 5, 8380390, 5, 8380403, 8380411, 12, 8380411, 30, 8380400, 8, 7, 16, 8380409, 8380415, 13, 8380392, 6, 8380394, 8380399, 20, 8380383, 25, 8380411, 8380404, 8380406, 8380388, 8380398, 8380416, 15, 23, 8380393, 8380415, 14, 21, 8380392, 4, 8380391, 10, 1, 11, 8380390, 17, 8380402, 8380401, 1, 14, 17, 8380406, 8380397, 37, 8380398, 11, 20, 8380404, 6, 13, 8380405, 10, 8380401, 8380375, 5, 8380405, 8380408, 8380415, 8380398, 8, 8380403, 30, 8380407, 0, 5, 16, 8380412, 8380414, 17, 8380408, 8380412, 5, 8380402, 19, 4, 20, 8380412, 7, 8380416, 3, 2, 1, 0, 10, 8380372, 28, 8380415, 2, 8380386, 51, 26, 8380383, 0, 2, 8380400, 0, 8380404, 29, 8380389, 19, 8, 8380404, 8],
[1, 32, 14, 21, 8380409, 24, 18, 8380409, 1, 8380399, 8380389, 41, 14, 8380382, 8380375, 22, 8380397, 8380372, 8380411, 5, 8, 12, 8380389, 8380410, 13, 3, 2, 8380394, 8380413, 16, 1, 21, 8380414, 1, 8380408, 8380406, 8380416, 8380416, 35, 8380408, 9, 8380407, 24, 14, 8380411, 8380412, 8380412, 8380412, 8380395, 8380395, 8380400, 6, 24, 8380389, 19, 3, 1, 8380378, 8380385, 17, 8380415, 9, 3, 8380397, 24, 8380402, 3, 24, 8380414, 8380403, 8380410, 23, 8380411, 8380408, 8380388, 13, 57, 8380415, 6, 8380415, 8380409, 17, 9, 8380412, 8380400, 4, 8380407, 8380397, 0, 1, 15, 8380394, 8380408, 3, 11, 27, 8380415, 8, 8380404, 8380404, 25, 8380412, 4, 8380387, 1, 3, 24, 9, 35, 8380408, 23, 16, 8380408, 4, 8380397, 8380391, 22, 13, 10, 6, 15, 8380384, 8380379, 8380408, 10, 8380376, 8380384, 32, 8380405, 8380394, 3, 8380390, 6, 18, 20, 10, 8380409, 12, 6, 8380407, 8380416, 1, 12, 12, 8380396, 7, 34, 8, 8380387, 10, 8380368, 5, 8380404, 8380360, 8380405, 5, 8380389, 14, 8380415, 8380398, 8380406, 8380401, 13, 8380410, 8380403, 24, 8380406, 8, 8380415, 18, 8380403, 8380416, 8380399, 5, 31, 19, 4, 8380395, 8380406, 5, 8380408, 0, 9, 8380414, 8380410, 6, 8380409, 8380414, 8380410, 8380404, 8380414, 8380394, 8380383, 8380401, 1, 25, 8380412, 16, 4, 4, 8380397, 8380409, 8380410, 20, 5, 8380372, 8380411, 46, 30, 8380405, 8380415, 8380415, 8, 7, 1, 8, 12, 12, 8380391, 8380388, 8380409, 10, 3, 8380401, 8380405, 25, 8380414, 8380390, 8380391, 8380402, 8380411, 5, 0, 8380390, 30, 26, 8380410, 7, 25, 37, 8380413, 8380394, 9, 2, 0, 8380410, 25, 8380414, 31, 5, 8380408, 1, 8380390, 8380415, 8380397, 4],
[8380402, 8380381, 5, 26, 8380400, 8380404, 8380407, 9, 8380404, 8380397, 8380413, 8380403, 33, 8380385, 18, 8380414, 7, 8380377, 8380392, 29, 12, 5, 8380389, 14, 43, 8380412, 8, 0, 8380404, 9, 8380405, 8380414, 8380412, 0, 8380411, 8380388, 6, 29, 23, 8380388, 2, 8380403, 8380389, 8380402, 8380400, 8380402, 26, 7, 8380407, 39, 8380395, 8380415, 17, 16, 8380382, 0, 25, 8380403, 8380412, 11, 8380373, 6, 6, 8380407, 8380385, 22, 11, 8380394, 8380381, 4, 8380408, 19, 8380406, 18, 10, 8380414, 8380398, 0, 4, 8380402, 8380411, 2, 36, 15, 0, 8380411, 8380381, 33, 8380398, 4, 8380416, 5, 8380416, 8380414, 18, 1, 8380396, 29, 10, 25, 7, 8380416, 1, 8380399, 8380410, 8380399, 8380407, 8380408, 8380407, 28, 8380409, 4, 8380407, 10, 8, 8380412, 12, 21, 8380408, 8380415, 8380406, 1, 5, 9, 8380408, 24, 14, 8380407, 8380412, 8380388, 8, 8380409, 0, 23, 5, 7, 8380415, 8380410, 9, 10, 8380402, 8380406, 4, 8380407, 8380411, 8380409, 8380403, 8380407, 19, 8380415, 23, 15, 7, 8380400, 8380411, 8380402, 8380397, 8380414, 39, 8380405, 28, 20, 8380405, 24, 8380388, 8380380, 8380416, 4, 3, 8, 8380405, 8380401, 27, 8380397, 2, 8380408, 3, 6, 19, 4, 8380408, 8380401, 8380404, 8380406, 40, 7, 21, 8380392, 0, 17, 8380400, 8380405, 17, 18, 1, 8380415, 8380416, 8380415, 7, 8380394, 8380401, 14, 29, 8380403, 4, 8380410, 8380387, 26, 8380409, 8380411, 18, 1, 8, 8380404, 8380389, 7, 8380414, 0, 8380415, 27, 34, 27, 8380410, 8380406, 0, 19, 8380400, 8380396, 20, 3, 8380388, 7, 8380406, 6, 8380413, 5, 8380403, 15, 15, 8380388, 2, 8380399, 8380403, 29, 8380392, 19, 8380398, 8380399, 27, 8380399, 3, 8380412, 8380411, 29, 15, 19],
[5, 8380402, 12, 8380409, 17, 2, 6, 5, 13, 8380412, 8380414, 23, 11, 8380409, 8380393, 8380405, 8380397, 21, 8380374, 8380405, 0, 13, 8, 6, 5, 8380415, 3, 19, 8380405, 9, 9, 8380395, 25, 32, 8380416, 8380408, 8380406, 8380405, 8380408, 8380391, 8380392, 0, 8380415, 8380394, 8380387, 6, 44, 8380414, 8380408, 8380394, 17, 8380408, 1, 8380414, 7, 14, 8380404, 8380405, 27, 18, 21, 8380384, 0, 8380415, 8380390, 3, 8380389, 8380404, 9, 8380412, 8380404, 0, 35, 5, 8380414, 3, 8380403, 16, 3, 21, 28, 3, 2, 30, 8380392, 8380395, 8380402, 40, 8380406, 11, 2, 1, 19, 8380401, 8380393, 8380413, 8380381, 8380414, 8380408, 29, 41, 9, 8380413, 8380387, 2, 8380411, 8380410, 8380391, 8380404, 42, 8380412, 22, 8380384, 5, 8380411, 8380415, 8380410, 11, 22, 13, 11, 16, 35, 8380413, 39, 9, 8380379, 8380407, 40, 5, 21, 8380404, 8380402, 8380406, 8380404, 9, 8380409, 8380381, 8380405, 18, 18, 30, 8380411, 8380400, 16, 8380386, 5, 7, 2, 8380405, 28, 23, 8380413, 8380415, 18, 24, 8380394, 8380410, 4, 4, 8380409, 8380404, 8380391, 10, 8380391, 8380407, 8380403, 6, 3, 19, 8380410, 26, 2, 8380409, 9, 8380379, 33, 38, 8380413, 24, 23, 24, 8380415, 8380389, 2, 31, 9, 8380377, 8380399, 8380409, 8380409, 8380414, 8380406, 13, 15, 8380412, 10, 1, 31, 8380400, 16, 3, 8380398, 8380409, 15, 4, 52, 8380392, 8380402, 8380415, 8380406, 8380416, 8380402, 8380411, 10, 17, 8380403, 12, 23, 5, 8380388, 8380387, 18, 13, 8380410, 8380416, 16, 10, 16, 8380399, 8380405, 10, 8380400, 9, 8380395, 24, 15, 8380415, 8380374, 8380414, 8380402, 4, 5, 8380413, 3, 33, 20, 33, 29, 25, 6, 8380415, 4, 3, 8380387, 8380397]]
z: [[8038429, 66497, 8252275, 119746, 9589, 8155927, 8109334, 454088, 8006017, 307608, 449759, 105448, 466102, 129664, 8240477, 8175712, 7878516, 162909, 421532, 8083158, 65198, 7862250, 222652, 8200620, 37610, 425303, 8168660, 8049357, 8159831, 274848, 8009730, 400456, 8052282, 110124, 158533, 8100928, 7990871, 8303909, 245795, 7948792, 182254, 8223459, 8338564, 8134456, 8372332, 470443, 8144847, 8278541, 101245, 8254809, 491747, 8136929, 123789, 380214, 8324331, 8084178, 8264789, 8198459, 51408, 159336, 277321, 429082, 287417, 395755, 345974, 8215185, 8086831, 7937246, 76190, 7993139, 7934187, 98940, 8168238, 8289107, 159428, 315079, 8370299, 385720, 410014, 432328, 389014, 412, 57400, 8167870, 300995, 67314, 8306764, 434448, 359504, 82129, 8138307, 37404, 8340391, 244980, 8045733, 281400, 7904325, 37704, 210772, 248869, 176471, 336184, 340380, 8235169, 192066, 88419, 8339519, 211410, 8224465, 8255496, 102543, 504576, 7939589, 445349, 8308821, 8344992, 8004611, 8154099, 519304, 8184221, 348210, 314459, 8081286, 198291, 32747, 366356, 8299512, 7981780, 7967240, 434230, 334352, 8116070, 243344, 7991915, 8004241, 8089641, 8292361, 8097188, 92124, 75248, 249022, 507728, 52835, 413170, 7891631, 292762, 203210, 8330592, 8142139, 406246, 522764, 96705, 7908044, 8148070, 485980, 8280909, 266266, 61899, 7904156, 94592, 8349446, 136978, 419703, 31242, 123762, 8205766, 8378570, 428816, 256829, 40900, 8032669, 123070, 315104, 463392, 8372124, 483437, 8055774, 8101103, 7981409, 8036520, 184416, 8059045, 8023234, 415823, 215907, 101500, 8197625, 8109661, 8247240, 105487, 8287775, 479110, 8168839, 38978, 66144, 82905, 8324834, 7888336, 7889844, 501607, 8154397, 8346332, 8109419, 8003984, 8096990, 309728, 303553, 393798, 201840, 8030944, 8126131, 458262, 329314, 254202, 417636, 8293904, 284479, 8289041, 410209, 7901061, 8073746, 8031569, 8177733, 8027501, 8219304, 8335970, 8370336, 363486, 366027, 79772, 8209746, 116705, 14271, 8082355, 8149277, 260334, 8224843, 7075, 450917, 31748, 413458, 58059, 249567, 93821, 8039832, 241433, 8366571, 287085, 8076059, 8183544, 152352, 8078421, 7863805, 8244701, 8269327, 198414],
[476071, 7940004, 8105977, 7994031, 8227892, 7980978, 8027097, 8215626, 8051124, 352098, 507638, 8132523, 446542, 431534, 7872327, 8096624, 7886781, 7976678, 8200120, 137648, 330069, 481803, 7881800, 8007334, 370891, 8152393, 103838, 446275, 216339, 61122, 7982501, 385543, 8302509, 8226252, 8220829, 7948968, 102363, 7960519, 7963410, 16233, 8119732, 56155, 490916, 462996, 8244077, 399911, 191378, 389648, 8255670, 8230253, 339965, 364822, 8179274, 290237, 507504, 8205336, 362546, 264721, 343710, 8302735, 403361, 314455, 283343, 8158925, 505917, 8294824, 94199, 421545, 37910, 199791, 8054192, 8262010, 8283466, 153059, 441832, 7963835, 8316431, 7948524, 8160823, 83554, 306797, 7945945, 89313, 25109, 7907697, 184733, 7944360, 371075, 8036755, 164728, 372509, 8292633, 92735, 7874414, 8029335, 88022, 8209379, 8045083, 332114, 416623, 356969, 303410, 57859, 227652, 54478, 8218841, 7928394, 7870284, 488614, 8297460, 7860208, 7961666, 7900014, 8171448, 508858, 93075, 8014370, 205300, 8006019, 8011462, 8234566, 433254, 8051804, 65185, 211499, 7975428, 8337005, 7966019, 7875980, 8177242, 8240662, 111093, 8257018, 8099643, 8096804, 29773, 381239, 8255519, 510335, 8145776, 8265427, 8103464, 8066806, 7949555, 346693, 8125098, 8359706, 243633, 7987811, 8310130, 92202, 8057809, 255702, 205971, 7988187, 374116, 8295085, 8348747, 61995, 258207, 7856940, 8184348, 72506, 355843, 283631, 8048267, 8064631, 74590, 8289943, 307485, 464608, 186322, 7991426, 417514, 436088, 56796, 8267002, 416969, 8207681, 319984, 63107, 10948, 339457, 8032841, 237902, 432066, 496529, 8096851, 485919, 8368347, 420330, 7884907, 8258208, 158923, 87426, 307760, 243278, 405470, 8235748, 113908, 8231168, 8187218, 350437, 469416, 274722, 357769, 78977, 242079, 404146, 8146158, 8177960, 8208536, 92192, 340697, 4347, 8219637, 7889042, 7992399, 8063990, 7899591, 180469, 422790, 43736, 7934331, 8210772, 8249460, 7856569, 215359, 510931, 441954, 287642, 7920544, 184146, 7932770, 8103962, 448715, 8188414, 8312285, 410553, 8315502, 53636, 8215853, 8032991, 503585, 132371, 8013668, 452693, 159400, 8330297, 420285, 8329422, 163865, 8117727, 441317, 151827, 8015116],
[7945048, 8332557, 103482, 8223685, 8337461, 8250193, 8081670, 8069778, 424100, 8370434, 161763, 259655, 201046, 86307, 7979156, 7898257, 421875, 467634, 318525, 104212, 7915162, 8037692, 194727, 8237709, 156023, 317419, 389088, 29613, 7973846, 119789, 126777, 8151675, 7862959, 451939, 8227510, 479366, 54900, 8345152, 285102, 8089473, 496078, 7865522, 8180511, 8130567, 7912836, 258918, 93175, 448202, 493333, 237601, 8168829, 8246699, 8135207, 8162394, 280699, 8361822, 8346229, 184130, 8255123, 7890508, 8323399, 8239500, 257397, 7966982, 8354973, 7960200, 8250187, 327865, 238728, 8000902, 193284, 8018839, 8259445, 8300354, 522481, 8276447, 8266418, 458658, 8194331, 7981120, 105542, 235830, 8261820, 342535, 231561, 359970, 7921291, 8053393, 8020345, 513175, 102695, 150344, 498529, 523551, 8341264, 8272011, 455304, 92491, 330427, 8279833, 142329, 95119, 8172927, 300637, 65732, 506910, 7892295, 8031202, 8268025, 8048060, 144772, 136877, 8117552, 8299267, 470449, 169886, 8025228, 66136, 8160516, 8343167, 315897, 413375, 8332132, 8221810, 8082019, 260038, 361154, 8235949, 160239, 7929413, 8276400, 222330, 8124128, 8357443, 193979, 8208317, 171193, 7857126, 163065, 7890508, 8361265, 8031454, 465215, 8238008, 7958662, 8071473, 468300, 8265145, 7888216, 370011, 52650, 512090, 8174538, 8052013, 7914835, 458488, 7995478, 364461, 7995642, 8127593, 8175558, 8042987, 40270, 472133, 376049, 134825, 448658, 299505, 8274557, 27990, 374494, 8349219, 62354, 8239560, 8327357, 195691, 8065579, 8326323, 490588, 8151147, 463154, 8129429, 229636, 8024035, 42744, 7962321, 8296976, 458644, 7933462, 7873398, 321387, 329300, 7991384, 123954, 477986, 451731, 269567, 460489, 108755, 7963674, 8007968, 335946, 8007795, 58109, 50315, 7987190, 8262201, 8362088, 43888, 345439, 457224, 242788, 8091655, 8146742, 8325024, 279852, 383737, 8075621, 427033, 401658, 83021, 8318736, 226398, 301552, 8074051, 428006, 8336822, 7967888, 438562, 319358, 8238558, 8060740, 260736, 8108790, 8126392, 71787, 8303824, 7917067, 8225227, 40039, 8192252, 8239554, 8178955, 7949205, 155150, 7983974, 265796, 408110, 188587, 8178035, 7896079, 435964, 213614, 8329292, 366496, 7895838],
[7861409, 8058002, 8022854, 286662, 8297888, 73403, 8126417, 68526, 8117255, 482648, 131288, 8368243, 197441, 7971207, 129173, 8266567, 7884820, 141443, 8327862, 7994035, 8142407, 8252905, 356843, 457571, 208344, 8244855, 8140657, 494339, 64368, 8155243, 7875567, 251538, 8110167, 7987050, 399218, 261557, 151781, 8074326, 252478, 8366273, 8235292, 7906927, 345188, 8004319, 8322206, 449656, 310600, 7891452, 189285, 8113790, 7983920, 114221, 385060, 394148, 258366, 8075550, 289662, 8308787, 227562, 8005552, 7907002, 8116044, 8181546, 187730, 8156947, 8060246, 479220, 8275274, 7871689, 255181, 518984, 8317929, 7906932, 69396, 115054, 498389, 8245769, 287149, 8343022, 441609, 7930995, 8298955, 7908973, 7927556, 336239, 8051211, 292435, 8225484, 445683, 8165481, 198703, 8142162, 8293986, 7996297, 429340, 8265846, 8355591, 43339, 56821, 461439, 255835, 194075, 8368087, 8203872, 8109662, 142937, 8221240, 337822, 8263209, 155139, 40107, 8033243, 25276, 129536, 7978648, 151967, 8038979, 513924, 7886498, 7920326, 7922333, 8162100, 8134221, 8186178, 199827, 8361616, 375883, 520424, 356840, 147722, 237482, 179936, 450273, 304832, 295323, 69019, 107130, 7978441, 186088, 324620, 379951, 8290454, 8005680, 414187, 7911374, 7856402, 8175869, 268860, 245098, 446240, 449112, 102017, 207510, 8372036, 414086, 199325, 8363120, 68210, 7902408, 193521, 8107662, 7969108, 481642, 8110579, 8098203, 324111, 8038021, 192108, 81569, 500851, 7860748, 7856494, 140768, 276723, 7986110, 5475, 397827, 391226, 8136482, 520654, 28126, 8102159, 244426, 7977319, 8316694, 208709, 165099, 7881539, 8012886, 306561, 8214779, 7899654, 8221764, 8362197, 495986, 136045, 8227422, 8128527, 171450, 292685, 7860540, 225956, 319606, 8335718, 8272643, 7996522, 454996, 66535, 7957043, 8076418, 7984978, 8362248, 274760, 7961835, 8349516, 21918, 347118, 104931, 203435, 123831, 373885, 292654, 187437, 8109925, 320144, 7941521, 71208, 278361, 8315449, 7915224, 7887861, 520709, 7988832, 8283295, 8174738, 7902603, 471504, 275429, 8003801, 15947, 73326, 8158347, 8218984, 8085441, 453241, 8300783, 7976585, 7918095, 7884668, 208032, 446691, 8141636, 11121, 215709, 8302459, 460544],
[8150965, 8284053, 8348198, 256611, 198168, 7879266, 381588, 329990, 180872, 8355431, 179021, 7951477, 280152, 471223, 155010, 110519, 8070860, 7872471, 8022443, 254951, 8188449, 8096014, 283447, 452498, 364540, 8033597, 8059847, 8262641, 257807, 8181502, 230640, 231053, 8237286, 495109, 297077, 7930776, 8240952, 51331, 8108716, 8104000, 261798, 275790, 8038523, 8177760, 488676, 8120258, 7956041, 7919155, 6865, 8052524, 313008, 209368, 398462, 232990, 85829, 215628, 7954733, 8373087, 104373, 8064824, 406354, 8083676, 8379266, 361976, 8275613, 7929356, 8355050, 7911624, 8296944, 431919, 500660, 90654, 8376112, 112786, 170176, 24732, 100634, 8052783, 130526, 343641, 8145317, 323954, 8313538, 92342, 8243342, 8112193, 8225009, 479655, 8302510, 8200170, 12698, 144798, 8075528, 331558, 8009153, 8339121, 283138, 432153, 8281072, 7993002, 46104, 8227701, 8226836, 8097107, 315509, 8012500, 7961049, 8259067, 7984634, 8292240, 282817, 8324422, 8231364, 269992, 8086281, 8058342, 37766, 8083295, 8050289, 7966025, 8299990, 385265, 267385, 272250, 39854, 228911, 7922850, 361295, 8374226, 84541, 8347251, 296713, 510794, 8286515, 8017295, 8082182, 7882123, 7941420, 8072822, 243057, 66854, 283281, 7979296, 415320, 7932134, 8052417, 443560, 7493, 60660, 8344933, 8032764, 7996323, 8095782, 134565, 8009363, 420256, 7970124, 168497, 391341, 494808, 8048637, 440486, 8294150, 205186, 8329648, 351889, 107822, 8285860, 7891345, 7892127, 424123, 267586, 44897, 209905, 8094490, 8140918, 8108342, 246225, 49951, 359218, 61081, 8288876, 8183472, 255226, 221883, 475473, 168081, 463309, 7861568, 8294747, 306245, 7977860, 7927957, 211221, 483754, 8228971, 136408, 328699, 8177052, 7976897, 372010, 8227799, 8172976, 249188, 7976465, 24965, 146630, 5128, 362592, 110577, 8193459, 425424, 8175831, 521382, 8083697, 239686, 7878690, 54599, 208454, 8300286, 48916, 8085321, 8010868, 465300, 433810, 7876170, 471605, 354395, 205497, 200420, 295198, 234951, 318184, 8093837, 8090513, 161563, 372864, 8220253, 344971, 8268585, 8329434, 8312220, 7894719, 90041, 8263658, 8214150, 89859, 8234456, 8046222, 7964108, 8248578, 7863890, 8354224, 246737, 8288770, 100364]]
||z||: 524015, ||z|| check passed
r0: [[-105859, 47863, 50835, -179782, -212714, -159491, 182094, 165419, 52489, 116057, -181813, 86995, 157955, 122428, 13855, 135806, -14505, -78991, 209733, -226890, -202206, 154769, -52710, 6939, 252037, -108823, -243810, 239944, 163793, 208332, -249532, -61533, -171592, 60943, 28394, 252140, -87565, 248336, -112415, 93158, -186184, 177803, 222362, -238612, -205163, 241809, -176641, -119486, 136871, 31018, -38970, -186944, -253863, -180712, -124907, 175784, 93916, -174025, 83269, -100884, 145549, -256937, -192564, 256564, 3618, -127916, -107062, -171505, -129041, -208341, 41760, -245891, 63342, 197140, 81306, -130006, 143406, 110580, -164922, 240592, 95749, 13804, 152541, 175734, 128725, 152880, -189967, 214096, 6196, -42129, 70803, 203795, 96195, -75461, -230486, 139846, -215401, 78017, 167297, 150988, -240740, -177567, 70351, -164589, 209818, -112046, 6499, -153895, -84586, -122085, 73153, -261014, 47152, 118267, 30190, 127917, -103707, -174915, -112873, -118518, -199405, 67124, -238614, 252446, -170252, -15319, 62608, 241579, 71459, -70686, -55927, 123609, -86043, -163904, 85686, 176127, -88451, 48154, 3506, 164710, 31410, -161868, 211200, -238224, 232184, -23543, 19999, 158415, 106383, -257769, 218573, -254262, 240015, -137217, 232724, -102443, 153190, -128013, 49967, 54366, -185743, 55607, -144792, 186986, 233941, 6330, 28559, -152749, -44958, -5649, 86053, 100056, -127918, -170400, -177653, -65312, -17371, -126114, -39008, 206684, 214602, 246826, -75759, 72683, 92433, -42095, 24846, -166263, -200524, 258772, -92351, 239914, -165900, -96070, 35936, -153894, -10685, -79762, -157184, 221494, 74967, -27379, -71413, -222033, -127286, 5905, -193160, -225260, 113718, 45553, -158405, 36915, -49539, -164537, 164524, 117294, 243604, 247081, 251679, 83470, -105827, -174640, -168462, -120929, 59052, 239244, -79592, 79174, -26332, 88070, 116891, -100077, -212110, -212606, -179445, 92945, 210947, 121698, -57986, -224645, 253931, -133407, -112495, 58385, -252748, -260134, 106030, 7817, -187666, -47729, 131718, 221925, -109721, -83347, -84885, -129388],
[152555, -181731, -138894, -121974, 156844, 123827, -51142, 218095, -162442, 136524, 33959, 38818, -12588, 10001, -117653, 13076, -151024, 249100, -146518, -122678, 203828, -36029, -53384, -110269, -168296, 3822, -34580, -187186, 111109, -130119, -50225, -139792, 204965, -180872, 240525, 257207, -245290, -176558, 138640, -123807, 156978, -55199, 190554, 32720, 194654, -203109, 103930, -91390, 218685, 258527, 8936, -230293, 59955, 96836, -248767, 156416, 110162, -199187, -56887, -240057, -204046, 62322, -222984, -26157, -219390, -160166, -113841, -92022, -118807, 112694, 178964, -171810, -173626, 57560, 94093, -189130, -218413, 255385, -144611, -9258, -194778, 248286, 166556, 99463, 2420, 54018, 205887, -250966, 231008, -137316, 41899, -173213, 37066, -193779, 147870, -101245, 189856, -219654, -19459, 125563, 230553, 173868, -101612, 19976, 222851, 113907, -219859, 136620, -8107, 186399, 61938, 195180, -225827, -234883, 65247, 63636, -173737, -20610, 166416, -65906, -166483, -180595, 10456, -236408, 251285, -81741, 191456, -71775, 222168, -257666, -91025, -54971, 69702, -89972, -214486, 9918, 144127, 153125, 219888, -160013, 109196, -5470, 8581, 256536, 130298, -10610, -64487, 126352, -82659, 111000, -251707, -48553, 135064, -136519, -51039, 252076, 245138, 74783, 45805, 157250, -89225, -178715, 67228, -112482, 42761, 239206, -183680, -198531, -12842, 235934, -33202, -125452, 260984, 157542, 187791, 178589, 158228, 241544, 230101, -14232, -29813, 175362, -46264, -168008, -15213, 7591, 243488, -152804, 111362, 189646, -165602, -84280, -50464, 22906, -17808, 234190, 211808, -244012, -112684, -158167, -95665, 116364, 165773, -216620, -194705, -72781, 107542, -247941, -183420, 183840, -246262, 69465, 142190, -64300, -178996, 124472, -250737, -206127, -207758, -127723, -47107, -251227, 206632, -227946, 232152, -160539, -113009, -221705, 25166, -75013, -201882, 187273, -155360, 29729, -150385, -27438, 65732, 476, -114128, 53048, 126766, 257650, 209092, 80680, 96402, -31468, 164199, 220317, -150484, -138616, 167827, 90568, 132680, 153831, 80107, 31615],
[-141393, -101742, 27383, 190715, 149813, 130080, 18110, -192764, -29706, -2182, -44418, -55367, 60546, -190519, 47527, -208104, -120568, 147717, -217004, 89182, -32023, 131135, 204288, -168405, 189825, -78200, 99091, 246239, 214348, 187383, -150119, 241670, -66339, -255115, 220398, -149936, -141716, -4123, 246052, 77792, -49304, 180326, -73936, -152916, 200434, 155255, 176943, -151262, -253083, 55863, -237793, 88965, 175352, -60404, 118146, -225761, 249, -44321, 155573, 130104, 185242, 222931, -164554, -21725, -101885, -187198, 99619, -119225, 105688, 20756, 125790, 32152, 52582, -134472, -30996, 72244, 28872, -150785, 7760, -89500, 81657, 206361, 171162, -259090, -253957, 117038, 84415, 92757, 12764, 220691, -32742, 144585, -45646, -140709, 94961, 134167, -40234, -214672, 206972, 148979, 57131, 80743, 90762, 66779, 94594, -190731, 204738, -62466, 43275, 35162, -125070, -227084, 6362, -74683, 38012, 145916, 27838, -86092, 211871, 2466, -30982, -256236, 100763, 160524, -231225, 114511, 188521, 41081, 52053, -85274, 134322, -179758, -30992, 42292, 245760, 151090, 22939, -52300, -41355, 23756, 251929, 203532, -34047, -245856, -203125, -220882, 198699, -179887, 76297, 15815, 156083, 10962, -261112, 200703, -242007, 24380, 182953, -183838, 139823, -242221, -182847, -140005, 122680, -86207, 100812, -46711, -117587, -88399, 185258, 222390, -226025, -40959, 158505, 103472, -158042, -149737, 205409, -35990, 96445, 26282, 260931, -18064, 139693, -41534, -104888, -152403, 171805, -35326, 51897, 169214, -30254, 17043, -3592, 99041, -80838, 49173, 16264, 228260, -184328, 88768, -88813, 91280, 245382, -115509, -93524, -169067, -67716, -210279, -243276, -189583, 215412, -56350, -76631, -70634, -213456, -12349, 179048, 224621, -45937, -109638, -176280, 47234, 149718, 157867, -121809, -142424, -253009, -20955, -45036, -127526, -234120, -125745, -224330, 156509, -259640, 166942, 195712, -15434, -55296, -139661, 101679, 20581, 172432, -66627, 141249, -77321, 182392, 33006, 51819, 76190, -190788, 136582, -174337, 7040, 68860, 78079],
[180496, 14517, -18269, 30673, -64959, -173970, -142254, 195491, -87203, 195131, 29859, -150576, 246658, -41300, -238781, 231897, -71424, -108742, -87573, 98680, 2362, -197915, -206160, 12593, -96104, -140054, -81100, -34693, 76051, 227176, 179010, -81696, 96033, 89044, 99272, 113749, -32060, -209141, -25081, -169509, 39551, -46265, 85710, 197588, -29431, -126672, -68974, -194714, 210469, 134704, 126872, -36594, 224044, -185323, -93402, -134659, -46687, -4240, 126482, 222495, 6624, -211800, -254674, -119278, -114060, -125924, -36758, -201013, 116495, -171066, -201504, -151703, -13207, 83590, 202190, -72015, -34729, 2559, -213720, -257096, -220046, 85994, -165525, 71554, -23893, 183035, 239688, 144823, 11506, -116285, 224443, 40091, 225334, 57326, 240359, -134801, -215843, -199273, 58367, -13103, 231260, -1229, -238321, 215088, -200308, 232990, -75925, 63162, 89500, -203063, -163669, -12060, -220005, 10095, -148715, 15201, 118287, 202929, 70740, -241765, 238179, 45057, -209016, 160885, 43347, 258209, -231616, -113810, -86352, 194025, -29426, 227320, -259361, -197758, 219130, 66976, -254307, -183241, 210733, 100807, -247657, -73822, -53851, 200055, -112839, 189383, 208432, 106456, 198652, -200556, 104375, -125347, -41421, 203473, -44884, 93589, -230779, 188356, -41891, -113179, -147774, -119639, -168058, -63324, -104565, -21405, 234791, 120146, 37416, 234570, -163578, -82511, -229192, -60501, 216978, 129025, -202166, 8928, 117446, -219800, -16149, -135239, -224568, -68993, 155406, -217071, -185234, -109139, -184761, -112218, -181887, -106598, -177727, 75121, -245176, -147625, -256070, -54469, 143225, -115528, -129759, 38797, 231196, 70831, -6920, -210027, -214498, -146504, -184454, 190847, -5373, 150298, 143371, -2477, 39734, -106471, 102154, 200701, -78257, 49905, -56278, 176195, 50567, -30661, 227263, 11918, 46347, -23659, 112369, 95977, 92854, -178660, -3725, -252740, 6598, -193082, -55303, -232939, -123316, 225605, 45891, -214308, 236629, 260184, 22385, -94602, 73803, -196184, 248604, 139845, -141499, 205954, -187471, 94632, -128554, -109680],
[-52752, -243523, 158804, 235396, 236382, -22913, -209000, 212892, -255651, 214971, -136863, 182276, -254725, -19824, -187722, 224848, -252272, -6604, 44884, 40756, 197079, 159098, 62669, -119556, -164397, -28863, 182992, 218421, -244417, -168250, 4556, -79190, -216950, 260671, -158089, -50178, -258768, 194966, 97660, -84678, -220279, 97406, -117969, -11684, 51560, 101531, -170423, 104547, 51152, 206604, -228231, -220281, 260629, -236081, 200199, 808, -55157, -131089, 230727, 256799, -208366, 58152, 177815, 108752, -105929, -123433, 150995, 120706, 196510, 257964, -59523, -174447, 231369, 76991, -194367, -126643, -110790, -70530, -259032, 4327, -52613, -255190, -154294, 56319, -165106, 100173, -141840, -95394, -145195, 136860, 8244, 200230, 232928, -85308, -27450, -243254, 60771, -69443, 27828, -94606, -126733, -45488, 119316, 89455, -191607, -42683, -88514, -218059, -86156, -125490, -103638, 164398, -92639, 78519, -99180, -101041, 79655, 92795, -123477, -201362, 21911, 88731, -97702, -244641, -199435, -185422, 230008, 65842, 231357, 218289, 176356, -7130, -8420, 52247, 130026, -156429, 104426, 229907, 117818, -125727, -209743, -40965, -106358, -48713, -130643, -247347, 120914, -220367, 177772, -184709, 165707, 137742, 18764, -138047, 228211, 229400, -186165, -152941, 67948, -87100, -43267, -168205, -147561, -77465, 241399, 195466, 14501, -69991, 198024, 260938, -108127, -137917, 3561, 80590, -182077, 202722, 137860, 124449, -230840, -257163, -232504, 39430, -59932, -165703, -121766, -211899, 202757, 141960, 20199, -65136, 154615, 183413, -168457, -95645, -187132, 38706, -207604, 178344, -150711, -57171, -15453, 220315, -118553, 113623, 155699, 149457, 143757, 35744, -130402, -146636, 194857, 183408, 240233, 138552, 203640, -35635, 145024, -18818, 127200, 173104, -110396, -216521, 110017, -28980, 199067, 114660, 212674, 3103, -98625, 171118, -252323, 48973, -221921, 207322, -189383, 180904, -168448, -69294, -156631, -101634, -244782, -143312, -128615, -99241, -13448, 154762, -100327, -187413, 61675, -139215, 43451, 206141, 15915, 254416, 33569, -257342],
[-51366, -221301, 224063, -20281, 195564, 82627, 230762, 46586, -27999, -59057, -225924, -128600, -128133, 155414, 59770, -244348, 42827, -87436, 157739, -216275, 2550, 9653, 124325, 48522, -162646, 205279, -90756, 129609, 188678, -66626, 185632, -256826, 119820, -81332, 207474, -10699, 121698, 179318, -227115, -19985, -60853, 139857, -165697, 143878, -198601, 39484, -147323, -231042, -177708, 157677, -214020, 189000, -64184, 124299, 62948, -90643, 100288, 189682, 212954, -255107, -19621, 41589, -67778, 10312, 135071, -112929, -15422, 108613, 203965, 134659, 139324, 81138, 97799, -201761, -174920, -122548, 94377, 261687, 67821, 233701, 52883, 20445, -4467, 136339, 22196, 184076, 146737, -159518, -60062, 251843, 103439, 128579, -89517, 149949, 33530, 236030, -101551, 158242, -230286, -20235, 188075, -141453, 245563, 158416, 127485, -86845, 48373, 94423, 190743, -18476, -207110, 161141, -113055, -52409, -249660, -59652, 234743, 110315, 72056, -103975, 75529, -186460, 201083, 3125, 39156, -75936, 11749, 116691, -83059, -41118, -143071, -77915, 7514, 76356, -132568, 33898, 222448, 184246, -55120, -40763, -177679, -66857, -64552, -171215, 154660, -217700, -563, -245255, 39101, -171219, -242560, -11096, 31983, 193300, -93318, 73049, -7278, 221486, -53387, 153173, 161529, -234134, 254531, 175181, 168686, -47509, 237157, -83013, 45566, 102689, -104951, 31848, 213010, -163343, -228656, 70403, 123512, -250739, -96718, -202680, -208993, -84537, 222827, -62676, -236938, 55143, -36607, 57689, 1687, -102560, -63103, 96289, -243124, -197110, 87298, -152413, 181860, -46333, 63577, -53563, 232541, 11530, 172308, -218303, -81430, -72660, 222297, -19980, -115160, 75117, 123491, -35086, 244352, -204921, -180206, 70163, -5565, -45103, -88145, -159679, -6966, 156986, 198297, -50675, -115475, 226579, 43940, 12294, 90325, 121855, -184881, 221468, -176030, 144384, 128093, -152448, -94431, 110773, -255950, 10528, -101200, -21608, -23398, 12127, -52403, 80402, -72953, -49750, 86250, 249864, -57907, 8538, 126194, 46120, 80346, 207846]]
||r0||261687, ||r0|| check passed
cHat * t0Hat: [[5283921, 1325226, 2851471, 2452202, 6625370, 3047221, 5713202, 7651499, 3066858, 1710013, 4612629, 3053574, 3803431, 7459755, 321431, 3276443, 7023201, 2039862, 1712229, 1273686, 1858157, 5670663, 1183303, 2251352, 7470335, 4111173, 3100311, 7292866, 1524347, 5101013, 4188801, 3332046, 4461260, 1701921, 1946466, 2459795, 5977031, 8301562, 8201704, 7311034, 6729058, 34750, 3785171, 6403190, 3585151, 4528075, 4824486, 6632280, 1906080, 475641, 7769066, 6500856, 1413966, 2950357, 3167622, 894714, 6703153, 4964526, 6279191, 8037811, 7296629, 869144, 5578711, 5369902, 5773855, 7850915, 2005087, 1481561, 2668516, 8151581, 8239803, 6320248, 1448380, 4370817, 7445925, 2560904, 7630553, 5553889, 6249313, 8065020, 7074113, 2616275, 281882, 7602353, 1435615, 6435337, 4616854, 8085065, 9066, 2782196, 7684325, 2729552, 3843366, 5895007, 6643692, 6352720, 1695115, 780170, 2787355, 5698254, 1221312, 4328101, 4029677, 4273444, 2848008, 1121183, 353978, 5246991, 1666285, 5511170, 818593, 718726, 5668898, 1825281, 6983743, 5252390, 8174101, 6842815, 405083, 2552447, 5504662, 2192611, 6018434, 8348868, 5583876, 4993841, 1332629, 5998470, 8247297, 2990257, 1867101, 457765, 7233359, 6580576, 3240493, 5663542, 3599050, 3601677, 7769298, 3105617, 2731586, 3539699, 4982563, 6808563, 7569361, 2587665, 2706060, 6345187, 5849639, 1579828, 2595894, 4476336, 1357180, 2768225, 2421296, 1395904, 4937234, 5710473, 6896872, 6663097, 5608354, 809381, 6873817, 5594963, 777210, 2084498, 4443335, 6053371, 3450801, 5553603, 5786359, 7986543, 5123054, 4022443, 6011479, 3016441, 1835313, 5215531, 6549509, 4742837, 7938910, 4717838, 3766318, 8177107, 6797528, 175259, 1599643, 551645, 4713190, 721688, 5859106, 6399876, 6193440, 6299427, 4144029, 2526863, 1434961, 4555731, 6833372, 8099844, 1732741, 1085380, 2075382, 4671992, 1486927, 5218668, 6556290, 4319283, 1302078, 95303, 2981544, 7931050, 3850637, 952340, 8299193, 6088011, 7848068, 1701944, 6875613, 2870173, 4300030, 789594, 937881, 3116187, 1736703, 375352, 3677669, 7170559, 6868731, 182543, 5932015, 6121123, 3824196, 7180225, 5196119, 5944556, 237291, 4137542, 2117420, 516250, 1079461, 2130763, 1822906, 22428, 700735, 565510, 3308379, 989728, 1563260, 3064689, 654281, 1661349, 7308580, 4603594, 2295562, 6527518],
[6315724, 7354088, 7631684, 4709365, 891294, 5617250, 3274359, 6364818, 3120150, 2348412, 7576824, 7110681, 11595, 4283223, 798241, 6091744, 2253617, 4901931, 8092292, 1844897, 3295484, 7230029, 3132955, 1210694, 1338096, 349800, 2476432, 7076900, 7357732, 1221960, 5850286, 8151859, 7121119, 2463251, 3528923, 905021, 1205403, 3212215, 775815, 4487441, 223038, 3859259, 5354973, 52114, 770932, 1329152, 4571328, 2680166, 2041219, 7782574, 1657899, 7287754, 161530, 1284862, 7182907, 2553122, 6415998, 7229045, 7455303, 1983955, 2135628, 4859888, 2982321, 1264569, 2908629, 527544, 6484919, 4698552, 7132052, 6988765, 4819058, 1156119, 2910896, 3919652, 6781155, 8007003, 2736631, 4074487, 2283377, 4198334, 4699961, 3054275, 2416811, 5178581, 8213099, 5284733, 6006769, 4405391, 3110389, 2529453, 2584441, 3237016, 3445878, 3997068, 229628, 993970, 4614156, 1844768, 1960672, 8373200, 2645393, 2011259, 111391, 5603673, 7081080, 2024960, 99629, 1506795, 3663258, 4080501, 6203342, 1923735, 3393479, 4445974, 182650, 4243714, 146397, 7395507, 5059151, 650350, 2179588, 2936454, 5893701, 1779198, 4132023, 7363025, 4566746, 426455, 4218481, 5440985, 734451, 1041198, 528392, 3798157, 7273072, 6403466, 4513103, 2723876, 1038339, 880702, 6473959, 6505814, 1247186, 2558689, 1701360, 2427067, 8125347, 8142512, 8229301, 3494370, 3912595, 4440811, 19278, 7551118, 2262845, 518691, 1133802, 3024407, 3686497, 6059242, 390013, 5216587, 1597934, 4658562, 2025550, 2620226, 2855904, 3835847, 4781044, 1877872, 852372, 2818228, 4584977, 3661598, 5544907, 217809, 7498506, 2768293, 988083, 3227293, 611680, 3619692, 3866227, 5719379, 394011, 6049343, 370637, 6728427, 3021720, 7728815, 8248453, 1485819, 3988055, 761128, 5853379, 7868155, 535324, 1459706, 4770042, 6709068, 1582147, 4483181, 1071650, 655950, 802244, 1062818, 7394890, 2887449, 1230444, 7884773, 4779130, 272539, 1468385, 7479006, 5773159, 7895747, 2516088, 674941, 2675768, 796145, 5454677, 367708, 7442567, 4356721, 871761, 7741086, 4443151, 8145406, 3148550, 1097589, 5403366, 468049, 7706763, 288532, 3222814, 7647432, 3062153, 8291254, 4374027, 7888033, 1846348, 8087128, 4676258, 329247, 4833197, 6427444, 503619, 2718158, 7619821, 2490179, 4944037, 1784082, 2037282, 2905464, 2926953, 2129682],
[4731210, 4771054, 3352283, 7067112, 834035, 214619, 7335764, 3663659, 5761238, 5679014, 202452, 2421445, 3704026, 7901873, 2096480, 6930831, 2506475, 5046226, 6906970, 3201751, 1759491, 5101961, 72905, 2033687, 6968319, 5896655, 127509, 4213820, 1204226, 7116845, 3342066, 2778469, 7870201, 2476139, 4411910, 5165080, 4226671, 1548784, 6394688, 7844767, 1244156, 7962833, 2163621, 1573553, 3656144, 5995758, 3492310, 4390558, 66173, 2385971, 3985283, 2066201, 776432, 2964066, 6867921, 4104861, 6591964, 3560276, 5247492, 67923, 6596706, 6602225, 7192421, 6874645, 2601101, 4402331, 5476912, 4023656, 7790969, 3277340, 8356407, 368135, 7287311, 7278839, 4255826, 3621989, 4228492, 8104177, 3823018, 5515190, 4754819, 7986913, 3895896, 7988486, 750688, 6431827, 7671618, 1802560, 1673078, 1400770, 1907225, 2894396, 2593750, 2292525, 763585, 8073127, 6170549, 3646334, 6090263, 5807161, 5018049, 5221347, 6212183, 8171649, 4376812, 4295671, 723817, 6929809, 693507, 215770, 1690683, 5271279, 4253705, 6032586, 2123084, 2493457, 4932885, 5758074, 5374458, 8280905, 5685876, 2436047, 7140236, 4071315, 1959070, 6022201, 1900314, 6203865, 4949651, 4959698, 4423796, 4892605, 236144, 3158635, 4331731, 2289910, 2030501, 1437036, 2309413, 7764882, 202913, 7798144, 3347434, 5414501, 1816525, 1968448, 1658467, 1375559, 928871, 4091618, 1953942, 7097831, 2643350, 4426525, 137126, 8261564, 2851107, 7277813, 3328397, 4273481, 1353122, 6422914, 143301, 5227750, 1101521, 1655804, 1835013, 7993059, 2652556, 1864907, 6379005, 8297180, 6953154, 3628678, 82252, 3953628, 1875211, 7007058, 2751785, 5971365, 6359793, 5552132, 4080071, 5648907, 5762800, 508642, 7766367, 4533312, 2437571, 2208609, 6033074, 1827877, 4995270, 1572607, 1200472, 6175924, 5975422, 4881397, 4314060, 4863376, 2056138, 5559739, 5639708, 1618266, 4821978, 7344123, 3019208, 970160, 3193961, 7577319, 979268, 698558, 1298892, 6277147, 5463178, 4020213, 8336142, 4702813, 2787020, 7836534, 6834225, 1942570, 2085930, 3477662, 4506377, 2389248, 4212443, 1371756, 3207245, 7423804, 6298822, 1492495, 3723635, 2161699, 2994283, 1373739, 2343353, 4047884, 4532258, 7281376, 1950627, 2825031, 6535924, 1421606, 6769967, 2582819, 6533885, 4996988, 6330781, 5710328, 1239063, 77082, 8373317, 495209, 5567167, 386302],
[733987, 230719, 1436820, 3105951, 6205497, 2133283, 6938566, 1069453, 6255597, 531533, 8003704, 2850404, 5370150, 7679119, 4149910, 8356166, 151816, 5699006, 2767269, 5132474, 8227574, 4592750, 4744407, 7668690, 4761709, 4603614, 5137553, 4539209, 2625297, 3631065, 8091348, 6321142, 7387081, 5234941, 3699135, 1470731, 8130857, 5541512, 2193558, 5999032, 826447, 4297312, 7826579, 3997252, 4140012, 4713429, 2623197, 2015255, 4295613, 2819742, 3348195, 2853287, 3656875, 2505654, 6507732, 1952398, 2809302, 2937737, 3991846, 3441020, 3228765, 693321, 5475, 3478590, 7920134, 155670, 3682289, 6496199, 7416012, 1199554, 1606990, 2692817, 96826, 4792003, 4145173, 7733402, 3499556, 6869208, 4505077, 3920110, 6060549, 2874957, 5422002, 7789978, 5930279, 38443, 1127204, 5669600, 5001393, 5005676, 5717319, 1980049, 6952211, 2291676, 7289091, 6207355, 4925783, 25933, 8344294, 82731, 2079639, 4100048, 3592265, 4441306, 6564270, 6474109, 3520160, 344254, 1028079, 1475455, 7631177, 3616530, 4139470, 1522573, 5779315, 6065664, 6273111, 4578577, 1050710, 7913617, 22279, 6905599, 4205404, 1006898, 6028589, 1417777, 6952521, 4633753, 6661929, 1072824, 7155906, 3363137, 427633, 2600489, 5707219, 500180, 7395749, 5365318, 8185642, 2583821, 1171580, 5136604, 3521230, 2559807, 178547, 1124372, 5336770, 7819033, 606380, 7932049, 7069811, 2587533, 2178249, 4256187, 1726820, 5557507, 5822857, 6988983, 7082220, 6392037, 7616006, 8032111, 2878877, 6955954, 6404467, 5787255, 6025412, 2841503, 5107603, 4065557, 1356992, 2380678, 781306, 4055933, 2146576, 5689173, 2099856, 5431529, 4322167, 5931233, 3381061, 7514134, 4006956, 7900084, 3941475, 2513937, 6786763, 4172090, 1917615, 497639, 5908243, 3507751, 675393, 1393811, 7198147, 3331467, 1205012, 156627, 364734, 5402309, 7810760, 3074589, 7691308, 1687677, 3505668, 119266, 2520707, 7817725, 7668878, 3729883, 5943317, 1843104, 7295425, 7147888, 3943338, 6275750, 4244318, 3789615, 3576087, 2736385, 3341839, 5771715, 5185144, 7206023, 5363347, 2020489, 3027113, 643644, 889214, 3454897, 6857619, 1101234, 1781454, 1478172, 7847782, 3722870, 7978478, 3554660, 720038, 2253480, 6469204, 4427066, 1581570, 4822804, 3112449, 1799383, 2708015, 898308, 6379465, 1245116, 3064916, 356426, 8309601, 7569787, 2772052, 7740418],
[754154, 6695511, 8372662, 2373360, 244098, 3176263, 5785889, 4799551, 3636845, 6735761, 8097297, 4935160, 3824983, 3903990, 1998970, 3955627, 7088855, 4943690, 1568001, 7817595, 804277, 2914685, 2089005, 225065, 124432, 2450407, 2647794, 4340990, 4264202, 8064875, 3791261, 7655388, 7452784, 1301273, 7150250, 6804262, 4267553, 4359909, 1294891, 911819, 7346622, 3389911, 6856516, 7348678, 7029204, 5191423, 2019681, 5808576, 1281645, 2375011, 5911671, 1537761, 1661925, 871945, 4826527, 2220838, 6770496, 2531723, 4954185, 7242624, 7854623, 2749044, 5345462, 2803371, 7094568, 1365206, 3591108, 4935819, 108286, 7916628, 5634729, 1979002, 2077249, 2638313, 5831252, 3572488, 4369324, 5898299, 5227583, 22653, 781952, 7558230, 6897948, 5390206, 6241791, 2460631, 5590923, 5774583, 2376784, 5295922, 8103877, 6626399, 88129, 4430079, 7178471, 3957353, 3833769, 1665330, 5315458, 1576140, 6944650, 417825, 6085110, 6749835, 355456, 2206153, 6071769, 1005031, 2174117, 3539691, 4792761, 879426, 4742711, 6050402, 2769014, 7993897, 2077889, 8352380, 6506161, 1759683, 2577921, 4356006, 2520029, 5192286, 4495792, 3072082, 6149919, 6536525, 6854670, 5623325, 7817437, 346804, 6634637, 7604058, 6904570, 1209755, 5833713, 3825109, 3244115, 6895788, 5207529, 787707, 7722706, 8092061, 24795, 6491114, 4874354, 1960019, 7879357, 6278169, 4074613, 3494560, 4130656, 3126959, 5723556, 4747002, 7921891, 556810, 3816330, 1830439, 3795370, 587279, 1427106, 1772921, 8173944, 1507860, 4762778, 5400150, 7163015, 3139642, 6288127, 6914078, 5244372, 5147140, 4803735, 599895, 7504827, 2037663, 8029339, 5600109, 6820435, 681058, 7342938, 6797209, 1098068, 3926630, 1279659, 1498535, 4269767, 2498206, 4225001, 1131144, 3760106, 5302580, 2550219, 7834920, 7573255, 4761168, 1986542, 3117959, 3487739, 3879836, 5435830, 7330582, 5357785, 27820, 1986969, 7698917, 4404291, 4101946, 29563, 5469339, 349397, 6971467, 6176278, 8144181, 2682162, 4500533, 2614011, 3647541, 6394889, 4580925, 8164432, 3080418, 6499851, 710058, 373753, 356219, 7324678, 2083754, 6750012, 3616354, 629521, 3903633, 7317681, 4212618, 538268, 7778490, 7817553, 7954212, 8331676, 5760826, 2907514, 150621, 7904720, 4951921, 2070979, 6673155, 4410000, 4832337, 5621873, 5020297, 5684588, 7296546, 6422687, 3817361],
[18089, 4147725, 2716887, 5827831, 640946, 5502429, 1946328, 983814, 5997468, 4302149, 2578816, 5267307, 6048047, 4827448, 4482214, 6755951, 2362362, 2166840, 5923149, 2631026, 4077603, 2494491, 4433969, 3361215, 2163877, 6819215, 6109737, 1876041, 2041323, 5927118, 3351039, 727392, 1344754, 6966636, 2631908, 3954699, 4621403, 8294496, 4225740, 731528, 3157337, 5314259, 6132895, 7265655, 4308757, 542037, 706462, 6495848, 7707012, 7820681, 6158962, 3046119, 1184855, 2405644, 6013720, 5116014, 1298567, 4068714, 2206826, 6069031, 5047232, 7130600, 6311214, 5222892, 5073757, 5257714, 3431718, 2485911, 6254603, 6877932, 2657985, 4376356, 8034373, 3335591, 1262696, 2232102, 6799826, 6435943, 4522715, 5498365, 5030240, 1603116, 2815124, 6475350, 1488229, 601391, 7911391, 3431414, 3645548, 2235785, 3103191, 6827019, 5678348, 1345109, 2766087, 6486983, 8118562, 3569350, 2950236, 7183920, 7098835, 2083141, 5633814, 3107375, 32440, 1997634, 5309210, 459021, 5596415, 2300413, 3289478, 4281742, 6347922, 6463677, 268093, 2070248, 5028444, 4632151, 7449235, 1910702, 4560625, 3552168, 4585653, 2784145, 8125473, 7944432, 1729842, 5795682, 3811102, 1276484, 619886, 478758, 7995384, 3199740, 1549113, 5230350, 1326032, 4483632, 109717, 5194557, 5459540, 2020163, 3108033, 1110160, 1491251, 4819947, 7047659, 4845177, 381160, 7506361, 3213591, 7054442, 7380587, 6213274, 2396277, 7529153, 2345272, 6427944, 4476512, 6892387, 4553614, 8342046, 1048981, 5221745, 6818248, 4627882, 7300384, 2440090, 2162035, 6765459, 6798731, 5855553, 5599734, 7220910, 4044362, 5877241, 3845445, 2947320, 6429767, 2554719, 4248516, 308275, 2507982, 4949556, 3319916, 7610938, 7474056, 7161506, 2599375, 2299792, 6974639, 6392687, 6595467, 146745, 6897535, 3164219, 1114225, 4387693, 6146772, 6660280, 8084306, 6640512, 2019732, 5271488, 8035793, 2305708, 3741820, 1912100, 945750, 5359388, 5471310, 7662045, 1808592, 610512, 1441543, 119029, 1080938, 307685, 2500309, 7747445, 3343480, 7341069, 5325691, 7428491, 4269389, 6902137, 5418565, 2996572, 1646733, 383595, 4299606, 7482770, 6918712, 5977396, 1938123, 1365910, 6314865, 4427162, 2461892, 1629012, 7749879, 1967710, 4270079, 2546754, 2681194, 7171807, 683058, 4858729, 5415704, 3018172, 7077154, 4588586, 7448106, 3791893, 1014796, 3736883]]
ct0: [[8352065, 11234, 8375999, 8341752, 8378553, 6922, 8379575, 8373695, 4764, 8371266, 8377810, 9960, 16746, 8365463, 8368640, 15037, 36637, 8377991, 8360965, 8356500, 7581, 7529, 13984, 8375264, 3125, 8379745, 2832, 8369650, 8358958, 9725, 13820, 8355623, 8379132, 8370404, 13139, 8374929, 8378505, 8360003, 16882, 11155, 8365535, 242, 7155, 20646, 13401, 6710, 17491, 8376426, 8366915, 8369454, 8366295, 8376160, 22347, 8357602, 8379278, 14047, 8376623, 18350, 8375016, 8380052, 1455, 8368844, 38432, 8370335, 18010, 8372216, 8368077, 11820, 15611, 15095, 8354547, 34675, 8376987, 8374369, 8373625, 8367085, 8371827, 7776, 8367794, 8360528, 9663, 21524, 15612, 8375139, 8378343, 38945, 14643, 4197, 8352459, 8369565, 13403, 45233, 8364796, 7519, 8365771, 5594, 229, 8369366, 8611, 8365163, 8362156, 8369178, 8364279, 12917, 11799, 15657, 8366972, 4796, 8352244, 6650, 184, 8370071, 8357121, 24182, 875, 9950, 8361968, 8363903, 8372643, 8374906, 2915, 6762, 13556, 8379180, 7582, 1169, 20101, 13195, 8375088, 8364953, 4404, 14294, 13897, 14672, 8364376, 25323, 8377072, 2755, 8378658, 8379730, 10123, 8366406, 8359002, 15703, 8369218, 8355975, 5717, 8380231, 8366493, 8373777, 9685, 8339385, 3911, 8373686, 8333833, 3359, 20411, 12242, 16852, 8331865, 8376417, 37632, 16791, 9985, 8365558, 6098, 10124, 4143, 8368939, 8356810, 8377959, 4404, 8364450, 827, 8358546, 8371535, 8360949, 8344534, 2458, 1755, 11366, 7940, 8377129, 247, 11259, 8375765, 16699, 8367513, 21275, 8361232, 8359466, 22734, 14923, 8376558, 8379009, 13445, 11483, 8348349, 8376539, 29906, 21612, 8346217, 17326, 14818, 3903, 8362834, 8364172, 8353979, 8046, 8377067, 8373251, 8373446, 8309, 2421, 3030, 8352032, 8375417, 67653, 8364590, 8360159, 12464, 19148, 23077, 8347573, 8364201, 5018, 8370911, 7787, 8374243, 2249, 7000, 29255, 8364894, 7902, 7399, 8375431, 8365702, 23701, 8378811, 8379531, 8358226, 27854, 19701, 8365407, 8373434, 29835, 4180, 8377606, 8350572, 11691, 8372008, 28216, 20654, 8375863, 2083, 13350],
[4997, 24605, 8354528, 8332814, 17430, 3943, 2613, 8356685, 8354655, 8364104, 8372115, 8367986, 8372874, 15704, 8352296, 8376312, 13198, 18760, 21827, 19209, 3527, 13291, 7348, 10497, 579, 8368809, 16720, 8913, 8365267, 12808, 508, 4857, 8356488, 8369081, 8370110, 24727, 8367654, 8366360, 8357604, 14041, 21434, 8375517, 8378190, 12896, 8356321, 13902, 14107, 8370502, 8673, 8355709, 8346069, 2204, 19914, 141, 8368404, 1803, 1910, 26788, 8353542, 11387, 8379667, 8356096, 4438, 15724, 7694, 8357408, 8360856, 7175, 8367885, 7544, 8357418, 5048, 4401, 17425, 8361291, 8365401, 26912, 9355, 8359137, 8373815, 8374770, 12053, 2811, 8364028, 8369279, 8373259, 22932, 7241, 8371452, 8369655, 8369096, 8365141, 8370388, 11544, 13282, 8575, 17666, 34739, 8375543, 8354, 8368912, 8379336, 8364300, 309, 8366029, 8374970, 13603, 6042, 8363122, 8364120, 8379646, 4967, 8373317, 2306, 10558, 13037, 8374498, 8369521, 55, 37548, 8374616, 8363967, 3261, 29273, 23871, 8358483, 8347210, 8368951, 8372629, 8349864, 8364003, 8373703, 40424, 8365423, 5545, 5789, 4972, 8351741, 8354309, 10974, 13306, 8363069, 12589, 8367628, 13033, 17624, 8379590, 8371013, 10719, 8509, 4951, 8364499, 13270, 14423, 12961, 8349161, 8371654, 27715, 8367529, 8364386, 22914, 8365575, 31662, 11673, 8376495, 8375569, 11438, 8378842, 8366475, 956, 8371728, 23220, 8372160, 8361457, 21049, 36239, 8348115, 8373619, 1934, 8348811, 8371667, 8371799, 8363513, 8379456, 16260, 2002, 9278, 8359813, 24591, 8356024, 8363683, 40540, 13410, 8374160, 8368093, 41942, 7326, 8358375, 4321, 32171, 8369282, 8371881, 22497, 8373903, 913, 10449, 8371367, 9462, 4859, 8368460, 29423, 8371319, 8378374, 23228, 8367045, 8366640, 16632, 8375881, 8376939, 733, 3919, 10842, 8378332, 8354339, 5434, 14850, 9409, 14673, 1050, 8374359, 18335, 8563, 8374771, 8364962, 14599, 8375530, 8352151, 2423, 15723, 4403, 8349587, 27021, 25846, 24645, 8335621, 8377760, 5742, 8376192, 6348, 3887, 8375624, 9239, 3183, 8373354, 8365815, 3928],
[8378221, 8369934, 3947, 8338150, 8368919, 8373174, 753, 30720, 3301, 12286, 28622, 540, 8368428, 9709, 4007, 8364672, 8355187, 9361, 8374787, 27624, 2115, 8371053, 8347408, 8379122, 8379282, 8344759, 14339, 8378841, 8347580, 8374916, 7467, 8360502, 6938, 22291, 528, 11792, 25825, 8353617, 166, 432, 7273, 8368237, 8362781, 10431, 22633, 8367796, 8375992, 422, 34695, 9219, 4285, 8359127, 8378946, 8377054, 8359543, 8371138, 20859, 6833, 8363754, 8366494, 17375, 8360334, 8376525, 8336301, 8344705, 6980, 8379735, 8370194, 8357382, 4417, 10577, 15931, 8357083, 6432, 31194, 8365812, 5918, 11378, 8344, 14908, 8358581, 8367498, 8376464, 17438, 5231, 8366321, 8356562, 18159, 8376240, 8371978, 8359619, 11368, 8375903, 18809, 8357371, 7289, 2932, 1231, 5831, 8371717, 8365420, 8369352, 8353751, 14382, 4600, 5209, 8374138, 8376372, 8059, 4998, 8362997, 4973, 21988, 16446, 8351507, 13437, 21390, 8376564, 16743, 8368297, 1020, 8344974, 3460, 8367782, 3359, 32654, 8367483, 8361110, 23224, 8352669, 8378304, 8369669, 8378169, 5329, 2249, 8370483, 8354193, 8365187, 17311, 8379162, 8371728, 48968, 11997, 8335432, 24405, 26946, 8435, 12647, 8373474, 8378410, 16690, 4869, 60, 481, 5345, 30012, 221, 8366780, 8365955, 8378580, 2923, 16495, 4986, 15200, 8361548, 8378877, 39104, 10704, 8368036, 18284, 8357085, 8369870, 25564, 8363409, 8373015, 5472, 11784, 8369257, 8375073, 8374152, 4551, 2229, 12708, 35949, 8379085, 9755, 649, 8369497, 22583, 8366051, 20942, 31320, 18486, 8371011, 8368727, 8365104, 8374837, 8369516, 8376410, 8335284, 26666, 8377898, 35868, 3285, 8369606, 13227, 8377369, 4979, 14443, 6745, 8363818, 8373239, 13411, 8362857, 14884, 4101, 12427, 6547, 30518, 18054, 13209, 8370525, 8362327, 2947, 1384, 8363712, 2362, 8367299, 8363577, 4050, 8374488, 11570, 8346975, 8377500, 8363343, 17886, 8355848, 6703, 8355460, 8366698, 8376957, 15980, 14059, 20642, 20362, 806, 8374079, 7906, 8376262, 12498, 8375456, 10896, 8375264, 56, 8369542, 8369440],
[8358998, 8374460, 23095, 8372778, 8350324, 8372276, 8372678, 11765, 8356729, 8354456, 8342075, 11969, 8367207, 8832, 8360949, 8374756, 18837, 8379872, 15031, 34746, 4576, 18157, 8363297, 8375243, 8372433, 19965, 8378276, 2251, 8370904, 8376615, 15752, 8358161, 8369143, 8352893, 8376176, 10700, 8355785, 8365839, 5268, 8366916, 8372403, 8379046, 1374, 4661, 8358843, 17303, 8373411, 8372100, 8369812, 8362224, 18577, 6178, 8363718, 3701, 15421, 13086, 8375992, 8913, 8367971, 32062, 109, 8334959, 12053, 8182, 4582, 8377389, 8379982, 8376363, 1989, 7200, 2642, 8365592, 8369464, 14975, 8375214, 8356925, 8380391, 19008, 31289, 8356940, 8379084, 15572, 1554, 16461, 8379370, 8363752, 8697, 8761, 17698, 27099, 4512, 8376613, 8358447, 18709, 8379567, 13330, 2094, 8366889, 8369832, 8376969, 6865, 11757, 8360924, 8359458, 4118, 6268, 26872, 8347816, 8372661, 17222, 11529, 8370051, 8363617, 15177, 20180, 13778, 32566, 8359095, 18942, 8279, 19873, 8373706, 8353196, 8380163, 11801, 12082, 12094, 8366544, 8377106, 1604, 11304, 8373096, 8376716, 6299, 26078, 8370546, 13983, 8379683, 15357, 23070, 8372249, 140, 15481, 8372980, 8366391, 5696, 8371511, 17729, 8363581, 8376744, 8366427, 16275, 14190, 8377465, 8367668, 8376667, 8372268, 13853, 2752, 8376706, 8350194, 31012, 8369507, 10054, 18610, 28325, 10832, 8355152, 6350, 15435, 8362795, 17075, 15483, 8360983, 3268, 8378550, 6808, 22044, 8378556, 8360248, 8351601, 2624, 8367045, 12124, 8360779, 35242, 4692, 12041, 8371852, 15468, 42283, 23984, 8375998, 20443, 8852, 8364965, 17692, 8373115, 8379272, 18266, 8361758, 1984, 8362275, 8367351, 21234, 11162, 8366978, 1880, 13120, 8371984, 5986, 8356582, 8380054, 26582, 8262, 15025, 8341687, 12438, 34901, 668, 8375947, 3785, 8373960, 5501, 8378704, 8379916, 8363552, 18482, 34044, 5696, 8350048, 8375873, 25069, 8368825, 8376938, 17709, 8358515, 26400, 8359738, 7334, 19264, 11677, 946, 6095, 8374787, 8378572, 14569, 8348360, 8374688, 2393, 8370786, 8376759, 32568, 12523, 16797, 8357256],
[3392, 25473, 8347605, 11687, 8356349, 29438, 8364685, 8360038, 22734, 18260, 8361007, 2048, 4038, 24733, 6710, 8375744, 8348524, 21335, 8475, 8354011, 8375271, 10066, 14311, 8350506, 8361823, 8362858, 27432, 8370112, 8373269, 26108, 8360560, 38546, 27288, 8374042, 12764, 22258, 5388, 8367023, 1433, 1850, 8375699, 8352629, 8358835, 8338838, 8377351, 8360303, 8364034, 8374148, 2736, 8376987, 1406, 28931, 32691, 8368160, 8363045, 8373898, 16612, 1800, 8355501, 40646, 8379886, 2428, 20200, 8346916, 20635, 29526, 8364737, 8352461, 8380265, 8363832, 22740, 5942, 8376988, 12704, 16220, 8373186, 106, 8371067, 3407, 8354161, 8377083, 8369114, 2298, 16369, 8369180, 6573, 8378274, 8372810, 12251, 8372563, 28452, 8367116, 17438, 604, 8377176, 8362937, 4463, 5181, 8380382, 8371087, 2429, 1807, 16950, 4024, 8368196, 8350724, 19081, 13135, 8360038, 8369598, 26876, 29136, 8380245, 8358333, 8369920, 14049, 22763, 8346337, 8376055, 8374857, 8371687, 8379956, 8359391, 31574, 14047, 8375608, 27180, 5081, 16901, 20620, 2078, 8370809, 4386, 8369109, 8374208, 8357862, 8365917, 15488, 8328437, 31101, 30665, 8373735, 8325800, 15577, 9993, 4532, 2943, 8373943, 19426, 8369017, 8354304, 24469, 8359412, 14306, 8373288, 8368881, 8359525, 14957, 8378292, 8374360, 8368206, 4528, 8366671, 40, 8379564, 36416, 8367732, 8363842, 8343985, 3582, 1408, 8371646, 6571, 8375526, 8375632, 15831, 8354114, 1924, 37767, 15635, 8342224, 5299, 26765, 30363, 8369394, 8360415, 8376308, 46882, 3389, 8362820, 6810, 174, 8378756, 3285, 8366646, 8360492, 6861, 1812, 8367480, 25181, 16489, 8355816, 8361466, 8369642, 30627, 10283, 8371002, 8378407, 7938, 8373168, 8365484, 5167, 8345247, 3777, 4445, 8361207, 8376957, 5657, 1539, 25282, 8377046, 392, 7803, 8371827, 10468, 23611, 8340852, 8361131, 23160, 8848, 32214, 8361859, 8377182, 14916, 21140, 8379066, 8373546, 8374001, 14191, 20040, 8376694, 7066, 34733, 8366980, 8376900, 8376268, 7110, 6581, 8358354, 8361587, 21591, 8356320, 16157, 8361125, 12101, 185],
[2134, 8355348, 17721, 9694, 29213, 43685, 4838, 8354709, 8375621, 8370910, 8376779, 8342477, 8379591, 8352488, 22678, 8371153, 615, 4605, 17846, 2630, 8354023, 9940, 8369561, 8347402, 18207, 5514, 762, 8378465, 1173, 13213, 15970, 14051, 8370083, 20364, 8358438, 14423, 5200, 8339761, 8504, 8866, 8365984, 8367316, 3891, 22518, 8344687, 8350353, 8371493, 6268, 8361035, 8360972, 5115, 6115, 21494, 12338, 2433, 27128, 8366655, 8373688, 8358970, 22418, 579, 8368562, 8357982, 18029, 9807, 8363079, 8367759, 8369616, 16411, 9645, 8377343, 8366326, 8363358, 7112, 8372155, 8357804, 2574, 18335, 16132, 18299, 8376394, 8367124, 8245, 3267, 8352832, 15251, 4152, 8377313, 8365645, 3867, 8364968, 8368253, 8373858, 8370778, 2718, 8369098, 13561, 6208, 7047, 25042, 8367510, 8369345, 7878, 12886, 8375217, 9985, 970, 106, 8355993, 27543, 8378228, 6311, 8376772, 1193, 3547, 8362300, 8379877, 8378800, 8370206, 8364831, 16693, 27259, 8353191, 8376478, 8374636, 678, 11380, 19647, 8368043, 34162, 63, 26742, 3051, 8372579, 8368545, 8362209, 6645, 16103, 21846, 8372112, 14652, 8366152, 8363118, 18561, 6190, 8366038, 4105, 8362960, 27201, 7024, 2126, 8354017, 8379806, 8364439, 9911, 563, 6996, 8375455, 8366268, 8375851, 8366945, 8358564, 39819, 8350012, 8346310, 8379714, 13269, 5045, 8360503, 8366440, 8373865, 18670, 5456, 29092, 16876, 8362253, 8376417, 31071, 5310, 8363344, 8371911, 8368572, 6359, 8368441, 389, 2290, 8370738, 8348395, 8369469, 30924, 32631, 1759, 8355913, 8377316, 3707, 4873, 8362742, 14461, 1748, 8378620, 8377462, 17298, 8367015, 8359786, 8374293, 8373300, 7628, 14253, 23611, 8353087, 8361123, 6501, 7268, 8374545, 8371333, 3919, 20316, 8359831, 8377830, 31027, 8365783, 8358202, 8370706, 126, 8370745, 30898, 8370982, 8369208, 12798, 8378118, 8374149, 8380246, 5131, 8110, 8377766, 11483, 3334, 18393, 8377118, 8341040, 8380331, 7690, 8374703, 8371916, 8377366, 3513, 8354384, 10827, 8373879, 18188, 4823, 8353098, 8377649, 6348, 2677, 6506]]
-ct0: [[28352, 8369183, 4418, 38665, 1864, 8373495, 842, 6722, 8375653, 9151, 2607, 8370457, 8363671, 14954, 11777, 8365380, 8343780, 2426, 19452, 23917, 8372836, 8372888, 8366433, 5153, 8377292, 672, 8377585, 10767, 21459, 8370692, 8366597, 24794, 1285, 10013, 8367278, 5488, 1912, 20414, 8363535, 8369262, 14882, 8380175, 8373262, 8359771, 8367016, 8373707, 8362926, 3991, 13502, 10963, 14122, 4257, 8358070, 22815, 1139, 8366370, 3794, 8362067, 5401, 365, 8378962, 11573, 8341985, 10082, 8362407, 8201, 12340, 8368597, 8364806, 8365322, 25870, 8345742, 3430, 6048, 6792, 13332, 8590, 8372641, 12623, 19889, 8370754, 8358893, 8364805, 5278, 2074, 8341472, 8365774, 8376220, 27958, 10852, 8367014, 8335184, 15621, 8372898, 14646, 8374823, 8380188, 11051, 8371806, 15254, 18261, 11239, 16138, 8367500, 8368618, 8364760, 13445, 8375621, 28173, 8373767, 8380233, 10346, 23296, 8356235, 8379542, 8370467, 18449, 16514, 7774, 5511, 8377502, 8373655, 8366861, 1237, 8372835, 8379248, 8360316, 8367222, 5329, 15464, 8376013, 8366123, 8366520, 8365745, 16041, 8355094, 3345, 8377662, 1759, 687, 8370294, 14011, 21415, 8364714, 11199, 24442, 8374700, 186, 13924, 6640, 8370732, 41032, 8376506, 6731, 46584, 8377058, 8360006, 8368175, 8363565, 48552, 4000, 8342785, 8363626, 8370432, 14859, 8374319, 8370293, 8376274, 11478, 23607, 2458, 8376013, 15967, 8379590, 21871, 8882, 19468, 35883, 8377959, 8378662, 8369051, 8372477, 3288, 8380170, 8369158, 4652, 8363718, 12904, 8359142, 19185, 20951, 8357683, 8365494, 3859, 1408, 8366972, 8368934, 32068, 3878, 8350511, 8358805, 34200, 8363091, 8365599, 8376514, 17583, 16245, 26438, 8372371, 3350, 7166, 6971, 8372108, 8377996, 8377387, 28385, 5000, 8312764, 15827, 20258, 8367953, 8361269, 8357340, 32844, 16216, 8375399, 9506, 8372630, 6174, 8378168, 8373417, 8351162, 15523, 8372515, 8373018, 4986, 14715, 8356716, 1606, 886, 22191, 8352563, 8360716, 15010, 6983, 8350582, 8376237, 2811, 29845, 8368726, 8409, 8352201, 8359763, 4554, 8378334, 8367067],
[8375420, 8355812, 25889, 47603, 8362987, 8376474, 8377804, 23732, 25762, 16313, 8302, 12431, 7543, 8364713, 28121, 4105, 8367219, 8361657, 8358590, 8361208, 8376890, 8367126, 8373069, 8369920, 8379838, 11608, 8363697, 8371504, 15150, 8367609, 8379909, 8375560, 23929, 11336, 10307, 8355690, 12763, 14057, 22813, 8366376, 8358983, 4900, 2227, 8367521, 24096, 8366515, 8366310, 9915, 8371744, 24708, 34348, 8378213, 8360503, 8380276, 12013, 8378614, 8378507, 8353629, 26875, 8369030, 750, 24321, 8375979, 8364693, 8372723, 23009, 19561, 8373242, 12532, 8372873, 22999, 8375369, 8376016, 8362992, 19126, 15016, 8353505, 8371062, 21280, 6602, 5647, 8368364, 8377606, 16389, 11138, 7158, 8357485, 8373176, 8965, 10762, 11321, 15276, 10029, 8368873, 8367135, 8371842, 8362751, 8345678, 4874, 8372063, 11505, 1081, 16117, 8380108, 14388, 5447, 8366814, 8374375, 17295, 16297, 771, 8375450, 7100, 8378111, 8369859, 8367380, 5919, 10896, 8380362, 8342869, 5801, 16450, 8377156, 8351144, 8356546, 21934, 33207, 11466, 7788, 30553, 16414, 6714, 8339993, 14994, 8374872, 8374628, 8375445, 28676, 26108, 8369443, 8367111, 17348, 8367828, 12789, 8367384, 8362793, 827, 9404, 8369698, 8371908, 8375466, 15918, 8367147, 8365994, 8367456, 31256, 8763, 8352702, 12888, 16031, 8357503, 14842, 8348755, 8368744, 3922, 4848, 8368979, 1575, 13942, 8379461, 8689, 8357197, 8257, 18960, 8359368, 8344178, 32302, 6798, 8378483, 31606, 8750, 8618, 16904, 961, 8364157, 8378415, 8371139, 20604, 8355826, 24393, 16734, 8339877, 8367007, 6257, 12324, 8338475, 8373091, 22042, 8376096, 8348246, 11135, 8536, 8357920, 6514, 8379504, 8369968, 9050, 8370955, 8375558, 11957, 8350994, 9098, 2043, 8357189, 13372, 13777, 8363785, 4536, 3478, 8379684, 8376498, 8369575, 2085, 26078, 8374983, 8365567, 8371008, 8365744, 8379367, 6058, 8362082, 8371854, 5646, 15455, 8365818, 4887, 28266, 8377994, 8364694, 8376014, 30830, 8353396, 8354571, 8355772, 44796, 2657, 8374675, 4225, 8374069, 8376530, 4793, 8371178, 8377234, 7063, 14602, 8376489],
[2196, 10483, 8376470, 42267, 11498, 7243, 8379664, 8349697, 8377116, 8368131, 8351795, 8379877, 11989, 8370708, 8376410, 15745, 25230, 8371056, 5630, 8352793, 8378302, 9364, 33009, 1295, 1135, 35658, 8366078, 1576, 32837, 5501, 8372950, 19915, 8373479, 8358126, 8379889, 8368625, 8354592, 26800, 8380251, 8379985, 8373144, 12180, 17636, 8369986, 8357784, 12621, 4425, 8379995, 8345722, 8371198, 8376132, 21290, 1471, 3363, 20874, 9279, 8359558, 8373584, 16663, 13923, 8363042, 20083, 3892, 44116, 35712, 8373437, 682, 10223, 23035, 8376000, 8369840, 8364486, 23334, 8373985, 8349223, 14605, 8374499, 8369039, 8372073, 8365509, 21836, 12919, 3953, 8362979, 8375186, 14096, 23855, 8362258, 4177, 8439, 20798, 8369049, 4514, 8361608, 23046, 8373128, 8377485, 8379186, 8374586, 8700, 14997, 11065, 26666, 8366035, 8375817, 8375208, 6279, 4045, 8372358, 8375419, 17420, 8375444, 8358429, 8363971, 28910, 8366980, 8359027, 3853, 8363674, 12120, 8379397, 35443, 8376957, 12635, 8377058, 8347763, 12934, 19307, 8357193, 27748, 2113, 10748, 2248, 8375088, 8378168, 9934, 26224, 15230, 8363106, 1255, 8689, 8331449, 8368420, 44985, 8356012, 8353471, 8371982, 8367770, 6943, 2007, 8363727, 8375548, 8380357, 8379936, 8375072, 8350405, 8380196, 13637, 14462, 1837, 8377494, 8363922, 8375431, 8365217, 18869, 1540, 8341313, 8369713, 12381, 8362133, 23332, 10547, 8354853, 17008, 7402, 8374945, 8368633, 11160, 5344, 6265, 8375866, 8378188, 8367709, 8344468, 1332, 8370662, 8379768, 10920, 8357834, 14366, 8359475, 8349097, 8361931, 9406, 11690, 15313, 5580, 10901, 4007, 45133, 8353751, 2519, 8344549, 8377132, 10811, 8367190, 3048, 8375438, 8365974, 8373672, 16599, 7178, 8367006, 17560, 8365533, 8376316, 8367990, 8373870, 8349899, 8362363, 8367208, 9892, 18090, 8377470, 8379033, 16705, 8378055, 13118, 16840, 8376367, 5929, 8368847, 33442, 2917, 17074, 8362531, 24569, 8373714, 24957, 13719, 3460, 8364437, 8366358, 8359775, 8360055, 8379611, 6338, 8372511, 4155, 8367919, 4961, 8369521, 5153, 8380361, 10875, 10977],
[21419, 5957, 8357322, 7639, 30093, 8141, 7739, 8368652, 23688, 25961, 38342, 8368448, 13210, 8371585, 19468, 5661, 8361580, 545, 8365386, 8345671, 8375841, 8362260, 17120, 5174, 7984, 8360452, 2141, 8378166, 9513, 3802, 8364665, 22256, 11274, 27524, 4241, 8369717, 24632, 14578, 8375149, 13501, 8014, 1371, 8379043, 8375756, 21574, 8363114, 7006, 8317, 10605, 18193, 8361840, 8374239, 16699, 8376716, 8364996, 8367331, 4425, 8371504, 12446, 8348355, 8380308, 45458, 8368364, 8372235, 8375835, 3028, 435, 4054, 8378428, 8373217, 8377775, 14825, 10953, 8365442, 5203, 23492, 26, 8361409, 8349128, 23477, 1333, 8364845, 8378863, 8363956, 1047, 16665, 8371720, 8371656, 8362719, 8353318, 8375905, 3804, 21970, 8361708, 850, 8367087, 8378323, 13528, 10585, 3448, 8373552, 8368660, 19493, 20959, 8376299, 8374149, 8353545, 32601, 7756, 8363195, 8368888, 10366, 16800, 8365240, 8360237, 8366639, 8347851, 21322, 8361475, 8372138, 8360544, 6711, 27221, 254, 8368616, 8368335, 8368323, 13873, 3311, 8378813, 8369113, 7321, 3701, 8374118, 8354339, 9871, 8366434, 734, 8365060, 8357347, 8168, 8380277, 8364936, 7437, 14026, 8374721, 8906, 8362688, 16836, 3673, 13990, 8364142, 8366227, 2952, 12749, 3750, 8149, 8366564, 8377665, 3711, 30223, 8349405, 10910, 8370363, 8361807, 8352092, 8369585, 25265, 8374067, 8364982, 17622, 8363342, 8364934, 19434, 8377149, 1867, 8373609, 8358373, 1861, 20169, 28816, 8377793, 13372, 8368293, 19638, 8345175, 8375725, 8368376, 8565, 8364949, 8338134, 8356433, 4419, 8359974, 8371565, 15452, 8362725, 7302, 1145, 8362151, 18659, 8378433, 18142, 13066, 8359183, 8369255, 13439, 8378537, 8367297, 8433, 8374431, 23835, 363, 8353835, 8372155, 8365392, 38730, 8367979, 8345516, 8379749, 4470, 8376632, 6457, 8374916, 1713, 501, 16865, 8361935, 8346373, 8374721, 30369, 4544, 8355348, 11592, 3479, 8362708, 21902, 8354017, 20679, 8373083, 8361153, 8368740, 8379471, 8374322, 5630, 1845, 8365848, 32057, 5729, 8378024, 9631, 3658, 8347849, 8367894, 8363620, 23161],
[8377025, 8354944, 32812, 8368730, 24068, 8350979, 15732, 20379, 8357683, 8362157, 19410, 8378369, 8376379, 8355684, 8373707, 4673, 31893, 8359082, 8371942, 26406, 5146, 8370351, 8366106, 29911, 18594, 17559, 8352985, 10305, 7148, 8354309, 19857, 8341871, 8353129, 6375, 8367653, 8358159, 8375029, 13394, 8378984, 8378567, 4718, 27788, 21582, 41579, 3066, 20114, 16383, 6269, 8377681, 3430, 8379011, 8351486, 8347726, 12257, 17372, 6519, 8363805, 8378617, 24916, 8339771, 531, 8377989, 8360217, 33501, 8359782, 8350891, 15680, 27956, 152, 16585, 8357677, 8374475, 3429, 8367713, 8364197, 7231, 8380311, 9350, 8377010, 26256, 3334, 11303, 8378119, 8364048, 11237, 8373844, 2143, 7607, 8368166, 7854, 8351965, 13301, 8362979, 8379813, 3241, 17480, 8375954, 8375236, 35, 9330, 8377988, 8378610, 8363467, 8376393, 12221, 29693, 8361336, 8367282, 20379, 10819, 8353541, 8351281, 172, 22084, 10497, 8366368, 8357654, 34080, 4362, 5560, 8730, 461, 21026, 8348843, 8366370, 4809, 8353237, 8375336, 8363516, 8359797, 8378339, 9608, 8376031, 11308, 6209, 22555, 14500, 8364929, 51980, 8349316, 8349752, 6682, 54617, 8364840, 8370424, 8375885, 8377474, 6474, 8360991, 11400, 26113, 8355948, 21005, 8366111, 7129, 11536, 20892, 8365460, 2125, 6057, 12211, 8375889, 13746, 8380377, 853, 8344001, 12685, 16575, 36432, 8376835, 8379009, 8771, 8373846, 4891, 4785, 8364586, 26303, 8378493, 8342650, 8364782, 38193, 8375118, 8353652, 8350054, 11023, 20002, 4109, 8333535, 8377028, 17597, 8373607, 8380243, 1661, 8377132, 13771, 19925, 8373556, 8378605, 12937, 8355236, 8363928, 24601, 18951, 10775, 8349790, 8370134, 9415, 2010, 8372479, 7249, 14933, 8375250, 35170, 8376640, 8375972, 19210, 3460, 8374760, 8378878, 8355135, 3371, 8380025, 8372614, 8590, 8369949, 8356806, 39565, 19286, 8357257, 8371569, 8348203, 18558, 3235, 8365501, 8359277, 1351, 6871, 6416, 8366226, 8360377, 3723, 8373351, 8345684, 13437, 3517, 4149, 8373307, 8373836, 22063, 18830, 8358826, 24097, 8364260, 19292, 8368316, 8380232],
[8378283, 25069, 8362696, 8370723, 8351204, 8336732, 8375579, 25708, 4796, 9507, 3638, 37940, 826, 27929, 8357739, 9264, 8379802, 8375812, 8362571, 8377787, 26394, 8370477, 10856, 33015, 8362210, 8374903, 8379655, 1952, 8379244, 8367204, 8364447, 8366366, 10334, 8360053, 21979, 8365994, 8375217, 40656, 8371913, 8371551, 14433, 13101, 8376526, 8357899, 35730, 30064, 8924, 8374149, 19382, 19445, 8375302, 8374302, 8358923, 8368079, 8377984, 8353289, 13762, 6729, 21447, 8357999, 8379838, 11855, 22435, 8362388, 8370610, 17338, 12658, 10801, 8364006, 8370772, 3074, 14091, 17059, 8373305, 8262, 22613, 8377843, 8362082, 8364285, 8362118, 4023, 13293, 8372172, 8377150, 27585, 8365166, 8376265, 3104, 14772, 8376550, 15449, 12164, 6559, 9639, 8377699, 11319, 8366856, 8374209, 8373370, 8355375, 12907, 11072, 8372539, 8367531, 5200, 8370432, 8379447, 8380311, 24424, 8352874, 2189, 8374106, 3645, 8379224, 8376870, 18117, 540, 1617, 10211, 15586, 8363724, 8353158, 27226, 3939, 5781, 8379739, 8369037, 8360770, 12374, 8346255, 8380354, 8353675, 8377366, 7838, 11872, 18208, 8373772, 8364314, 8358571, 8305, 8365765, 14265, 17299, 8361856, 8374227, 14379, 8376312, 17457, 8353216, 8373393, 8378291, 26400, 611, 15978, 8370506, 8379854, 8373421, 4962, 14149, 4566, 13472, 21853, 8340598, 30405, 34107, 703, 8367148, 8375372, 19914, 13977, 6552, 8361747, 8374961, 8351325, 8363541, 18164, 4000, 8349346, 8375107, 17073, 8506, 11845, 8374058, 11976, 8380028, 8378127, 9679, 32022, 10948, 8349493, 8347786, 8378658, 24504, 3101, 8376710, 8375544, 17675, 8365956, 8378669, 1797, 2955, 8363119, 13402, 20631, 6124, 7117, 8372789, 8366164, 8356806, 27330, 19294, 8373916, 8373149, 5872, 9084, 8376498, 8360101, 20586, 2587, 8349390, 14634, 22215, 9711, 8380291, 9672, 8349519, 9435, 11209, 8367619, 2299, 6268, 171, 8375286, 8372307, 2651, 8368934, 8377083, 8362024, 3299, 39377, 86, 8372727, 5714, 8501, 3051, 8376904, 26033, 8369590, 6538, 8362229, 8375594, 27319, 2768, 8374069, 8377740, 8373911]]
w - cs2 + ct0: [[3532221, 59097, 5284177, 8161970, 832974, 7180295, 1228804, 1206249, 5818789, 7963546, 863132, 2715835, 6983789, 1155026, 6287390, 2245947, 5783668, 966135, 6999369, 3939401, 2948031, 3304954, 485050, 6810874, 6540474, 2509385, 806574, 5466937, 4332542, 1789385, 3430720, 7770313, 350899, 5288690, 1089085, 2865532, 8290940, 7037010, 4618451, 2199417, 5560470, 7510909, 7562381, 1353362, 4522222, 8105159, 1412178, 1971627, 6932457, 1591383, 7803548, 2951455, 292260, 1891577, 4587938, 5951367, 1661450, 891877, 5315628, 4612735, 6432316, 2874146, 7178732, 7579346, 21628, 6672971, 6689686, 6125627, 1981674, 6092066, 3682322, 312560, 4250120, 2809972, 598290, 904214, 4848800, 3261012, 8202872, 6506015, 1676740, 6844416, 4358361, 2265560, 5888187, 7000913, 6633764, 6503605, 4692222, 1518347, 7940846, 249028, 3747006, 4122266, 3421300, 1716768, 6593916, 7399830, 175908, 2230838, 264775, 4525178, 6339525, 4562312, 6506929, 4093819, 2088158, 1422229, 411017, 7217429, 3215993, 6013952, 7356720, 1190001, 1602393, 3804299, 5639380, 2951227, 1974457, 5113731, 6612598, 5835422, 3441374, 6012745, 6646418, 5223610, 5320469, 3921206, 2161234, 6199162, 8328894, 661679, 4118062, 7183632, 5831181, 2820330, 2003308, 1622237, 4191955, 5401783, 6326845, 4014329, 189785, 825031, 6506297, 4142223, 25716, 4348437, 1663787, 7592231, 5989794, 4418690, 6005462, 3522484, 8042780, 5138676, 6458913, 1979333, 5304579, 5243574, 5048017, 1140791, 6157311, 5958507, 5980618, 12428, 1086235, 5089154, 467340, 4160952, 3750027, 2199564, 379891, 4020635, 5038236, 4639790, 2058265, 6647091, 6248762, 5969975, 6511280, 6016302, 1492281, 596706, 1151244, 5191013, 1612873, 7677473, 7153615, 8096227, 7219562, 8119288, 4039231, 8280488, 4748512, 1430879, 2619678, 7221034, 2981594, 251400, 5334339, 7795061, 4659897, 2935441, 1447945, 5749858, 5552131, 4462286, 5359524, 3184859, 5595965, 7886584, 482546, 361660, 1215106, 7945549, 7571468, 3981166, 1807180, 2682092, 3049293, 6129820, 1425943, 6655315, 3709268, 3386918, 2529782, 3229617, 4681478, 1137871, 4837875, 2548058, 8152784, 2937952, 351730, 7420823, 5957768, 3288055, 7273272, 6059781, 1803068, 2513327, 954758, 3186031, 7073133, 1341029, 5347970, 4195214, 7639129, 5201722, 3265965, 3392797, 958485, 4626083, 4107406, 1979066],
[6966640, 3509306, 2454097, 1401751, 8030914, 4841754, 7808111, 2813243, 1383124, 7976851, 3692089, 1073939, 2074973, 4739689, 2996882, 1580299, 5099934, 6553172, 6684397, 6705619, 3873787, 4691246, 4144172, 8280645, 879835, 3658646, 8362557, 345503, 7952599, 7739329, 3616715, 4055273, 1752364, 5569328, 4420426, 3424590, 265723, 333161, 7448691, 4604218, 2273516, 3606333, 2807207, 3188272, 6455870, 4001001, 1689365, 5660231, 1798686, 7042907, 3117244, 5533447, 2174973, 5858513, 2881876, 5919755, 6397384, 4017809, 8296655, 3437762, 3985412, 4228209, 4495438, 2608447, 7121168, 2959481, 5628134, 5152913, 8249078, 6929326, 7488829, 2452118, 878327, 3741417, 2693847, 2938510, 7665139, 7073828, 3500541, 3650572, 323351, 5498099, 1216919, 6368386, 1038834, 6332172, 7037907, 1327603, 222043, 4565906, 30578, 5573047, 7883677, 2960421, 7494016, 5668866, 2302626, 3481517, 6260979, 657693, 1266600, 172787, 3024927, 20285, 4398671, 6917548, 6602832, 3285318, 4164806, 8026742, 5822703, 3342803, 2385953, 5528959, 4789789, 1648001, 7676984, 7301358, 2261575, 3638074, 875268, 5040715, 5251477, 3459297, 4989140, 1467653, 4348457, 5678295, 4404588, 4949541, 6177873, 2557195, 1681454, 6180346, 8171476, 7872347, 2244203, 3267105, 6479092, 5612497, 3788934, 500958, 1068722, 2862627, 5904867, 6816102, 7791326, 5878484, 975612, 3262165, 4991004, 7792169, 7481198, 5639440, 6247234, 1792148, 2331479, 5864034, 2128021, 4331427, 5171449, 3472875, 622666, 4613175, 1610167, 234358, 3494190, 5561430, 496992, 1284442, 8338526, 2516648, 7061815, 6423894, 4922824, 5976364, 5363686, 2329850, 2850915, 3620594, 2056541, 2785624, 5174592, 4545015, 3667479, 533369, 2347870, 874144, 6945041, 4879237, 1388992, 6765348, 5200706, 5778185, 4160076, 4990116, 3361790, 7590586, 2510517, 5635540, 6702288, 2726708, 4902254, 7633506, 2425088, 5175428, 2717372, 2904177, 3487871, 1219435, 3973369, 7393231, 6949235, 7291792, 5569168, 4300903, 3432327, 1884441, 8169181, 6682098, 8337229, 4997375, 8061187, 3412408, 2856466, 7710951, 6705488, 7125832, 5787752, 2014033, 4006661, 7004924, 6648082, 4728258, 1959318, 6252987, 3180122, 5764435, 425371, 5818987, 4809920, 4998655, 2853818, 1152877, 5813142, 7298739, 6455253, 5453852, 903416, 4579255, 1210586, 2194911, 2754743, 146768, 1113057, 35543],
[5094171, 411551, 3173986, 6433760, 5899851, 7979477, 2113967, 7694596, 2068699, 7866744, 7840844, 3611605, 2667437, 4533174, 3717966, 4490135, 901754, 157078, 2920022, 1688134, 1017644, 645547, 171279, 2972956, 188690, 2505022, 5874966, 1292215, 2276615, 5943418, 6666436, 1269307, 3607031, 1862280, 744702, 1956960, 4074317, 3635509, 8102858, 1125776, 4671953, 6453458, 8288845, 1428843, 3889499, 2237738, 7505382, 4039368, 2924268, 2160186, 1861596, 4781659, 3316537, 4126441, 3763704, 2907616, 5258868, 486288, 5900446, 2211285, 3345273, 2297952, 6640642, 5171919, 909955, 1391110, 622713, 3536984, 2177757, 5786709, 5897903, 5809619, 553024, 1967064, 4190406, 5819175, 3701222, 3527025, 5777640, 5686944, 6345133, 5431202, 4357417, 8138765, 275050, 5864478, 2155664, 4824900, 4722571, 3878684, 6231772, 2774833, 7282704, 8258517, 5309675, 7474320, 1534026, 310335, 2831683, 4854263, 6851222, 4259886, 2159200, 1128713, 6908282, 8194895, 8055099, 2552369, 7384198, 3706592, 6666598, 6063201, 3694782, 4131971, 4723086, 159353, 6334540, 2528935, 7561478, 6275658, 6779126, 7041185, 7960863, 8004529, 2391014, 1194717, 6460899, 545550, 2170381, 7219842, 4322417, 3475926, 8347177, 47621, 6533321, 3807588, 1568043, 6217782, 4689940, 4736485, 6528552, 6014036, 3120606, 8089576, 4011488, 5043824, 4921118, 6641848, 1640682, 4204016, 1220325, 7872471, 7595588, 7534048, 7096202, 1625720, 3325830, 2421405, 5363121, 3422374, 6629164, 5114250, 5889202, 5166753, 3224599, 6760837, 4111725, 7778945, 3315533, 2859554, 4988403, 1519822, 2279173, 4276672, 2977212, 7188599, 2312297, 6761938, 7423965, 4734001, 4455690, 2603045, 4866385, 8374832, 4607764, 8237769, 696230, 1001306, 6359792, 154848, 7847328, 48363, 7347758, 6898723, 5145232, 2652740, 6819772, 4407567, 1382993, 4233843, 3604285, 2707641, 7090338, 3030432, 5133425, 367936, 5690772, 842252, 6056479, 6626250, 722589, 6221784, 7269644, 3578238, 5562964, 7324616, 4905459, 231168, 4174789, 8288833, 5598465, 2132446, 6940716, 8017454, 7736215, 888423, 7605993, 5203687, 7794764, 4066732, 283727, 6171137, 6027540, 2248696, 3913494, 5946364, 694919, 2086373, 443523, 2465500, 1669547, 6321873, 8043131, 7810655, 4875595, 1494813, 5937590, 4754896, 5285424, 5850224, 5565787, 671254, 5058270, 6816184, 7390849, 5828638],
[682853, 5770096, 2623706, 1070586, 3047604, 4008097, 6135319, 2826136, 1984213, 692946, 6276829, 5622929, 757224, 1015084, 2360631, 5987772, 1518741, 2509593, 3070114, 6418738, 7339802, 1915346, 7109584, 1054971, 3562344, 5641447, 4106967, 6776646, 5304298, 2318478, 194762, 8276465, 5846295, 6346832, 1142583, 6933537, 3085964, 2918937, 7836827, 4007198, 31537, 3618796, 7419948, 3868681, 996547, 7223495, 4638004, 1368297, 2294968, 2735391, 4859433, 5207344, 1254897, 6627466, 5159779, 6163739, 5710424, 7861313, 3256692, 5492317, 6292045, 1837846, 7614019, 6174216, 7223386, 3013704, 2581687, 318709, 5356244, 359910, 6610226, 7690112, 4166048, 6383877, 720763, 6189805, 2060349, 3687999, 4007777, 1814531, 3968829, 6910654, 5597565, 7420879, 3641492, 4356578, 2343489, 2248688, 7362068, 958366, 3895387, 6845375, 3346020, 3218691, 8096149, 7211393, 6595339, 6072511, 1619110, 2602329, 238125, 7343392, 1837290, 4384337, 8184227, 239258, 3093603, 1078113, 1129296, 861711, 371636, 3120230, 3953403, 6310584, 7728105, 1600307, 3817285, 4895591, 7946322, 6051826, 1829380, 38346, 3953971, 684407, 5292908, 794067, 4494462, 5110077, 5671873, 3338285, 1029430, 5457759, 5498474, 1903645, 8101848, 2152209, 1331004, 7148889, 4416298, 6409189, 4458159, 2545198, 1532958, 5430378, 8253552, 5956615, 2818406, 6409497, 2800696, 319547, 4280593, 414704, 6781857, 7009609, 7799007, 5327599, 4998832, 3344865, 5198621, 1978214, 7678643, 6196685, 2963688, 7279594, 961597, 2102024, 3912055, 1666209, 43766, 3916437, 342576, 4124772, 6595379, 5681601, 5981782, 7460022, 6089954, 2649852, 639361, 2902687, 3097691, 7724025, 7618700, 2562011, 1707096, 4008379, 1914562, 6711990, 3996882, 1474578, 384172, 964938, 7150718, 7952204, 8144093, 4550907, 809174, 5699765, 4332288, 426514, 375358, 4754765, 7545918, 5295525, 6299626, 3467567, 1343391, 5093136, 1399994, 5943950, 6809701, 3269119, 5380768, 2642985, 1095548, 6717642, 5824960, 2308243, 1004196, 2145677, 7795892, 3846412, 1091662, 2069944, 2844430, 2106521, 4743466, 4708807, 146413, 7958313, 1110037, 2435676, 5259104, 3402100, 7859759, 6633715, 3589227, 2412341, 7188869, 5470699, 4779139, 1892473, 237575, 4456487, 1588083, 3046209, 88372, 8152176, 6528187, 2237342, 1943974, 8058936, 1940201, 2202259, 412019, 4581143],
[3617072, 3448382, 1697320, 4437291, 1783642, 2101629, 5536804, 8049153, 1862187, 3899663, 3510159, 5945860, 4463297, 4909, 4009196, 4934159, 6524923, 5252491, 1100911, 538126, 4382141, 7502028, 5314740, 5612069, 340785, 5715114, 1257976, 3350772, 1319763, 3000514, 6270011, 6244668, 6619426, 5492056, 7187539, 3638512, 794172, 5943108, 2194197, 440948, 6060315, 2688498, 7193313, 6232049, 7381358, 7414281, 7669834, 98278, 4767872, 5964710, 6058487, 6617738, 8149960, 6036974, 1754155, 4184497, 3627887, 3013367, 4396019, 4487653, 7123967, 6869668, 1769343, 2170355, 6723794, 1477421, 6420627, 1664078, 2291462, 2860259, 4153425, 4021703, 2323044, 1137247, 1916957, 913678, 3555748, 8300537, 5505911, 6787159, 5705589, 1304835, 1943108, 7929328, 5585193, 1678074, 6141329, 6706087, 6152368, 5890542, 560472, 3853361, 4964350, 6200608, 8349726, 1310594, 4779218, 2554618, 1075345, 6181376, 6161008, 4146527, 2755146, 6902567, 8176589, 6212936, 454343, 318852, 6702553, 5625227, 4637222, 7002622, 1478517, 2151539, 3556755, 4103216, 7959058, 3201371, 6681249, 3459510, 1060733, 3230926, 1452600, 310709, 2957268, 5571305, 6018724, 5832459, 8104898, 1286461, 1749762, 2078366, 8376383, 4754923, 3790249, 868568, 5851462, 1292947, 5827374, 8285791, 4011130, 6237665, 4029233, 4157072, 2498230, 4471169, 3266513, 2392039, 2816078, 851443, 139594, 3304867, 3664191, 3542691, 3887514, 217864, 4506927, 6147328, 65823, 5668379, 1515850, 3502755, 6647781, 4112783, 3383202, 5469642, 1049368, 7770074, 161592, 6549832, 417057, 6662400, 6295444, 6361011, 2432018, 1789881, 111557, 5364133, 1902031, 6043784, 8109720, 7901369, 1538161, 1435988, 1438539, 2910755, 2817528, 5426602, 4213796, 6202579, 3827857, 8040227, 3496314, 3574072, 8179514, 3161437, 5037017, 703932, 5597888, 4681994, 6286348, 3862146, 5624032, 6388160, 8042966, 1207292, 5895878, 557510, 5115296, 6655203, 1227476, 3855007, 1252615, 6951417, 6493397, 1516483, 1189116, 4700823, 2223843, 8055026, 8266650, 7640511, 2736700, 7295294, 733311, 5376031, 6458421, 7840457, 1495863, 703742, 3446323, 5268175, 6583932, 4936222, 8212174, 3322209, 348457, 6733378, 2476440, 2013510, 3941703, 4577738, 6715206, 8267739, 6792123, 6435925, 7763423, 7675808, 4753596, 7174819, 3731474, 3324700, 1603400, 5996660, 7378534, 6551931],
[3093424, 277406, 2336888, 3132069, 224777, 1697640, 2854480, 5782414, 3109861, 3597868, 3960646, 7690100, 3013697, 2222589, 4272656, 793940, 1090994, 5154929, 6984673, 2405235, 6261468, 1067145, 4303677, 4729491, 7188425, 3877225, 4100214, 1175209, 6475163, 4136795, 5963138, 8137642, 3252142, 986584, 4899479, 4193932, 126898, 5376422, 1352717, 2083985, 972266, 126756, 4028402, 690172, 7098533, 2628300, 6652841, 2917882, 326686, 7471096, 1362423, 195115, 5195070, 136637, 65381, 3602917, 1134078, 2801833, 3857939, 1338639, 1552286, 1601062, 1481115, 1599669, 4335086, 8250150, 2067024, 3764244, 4410584, 1715632, 660026, 6876135, 4270948, 7661991, 864370, 902391, 6382263, 280022, 1131505, 2347104, 572636, 2626032, 2098882, 3282262, 8375028, 5960863, 2245993, 361154, 448942, 5493470, 611766, 640191, 1475252, 664086, 5797784, 6510023, 6721098, 7497314, 824313, 528583, 8031808, 7180339, 8110081, 3313958, 1169837, 3589572, 49343, 1665857, 1737647, 6294379, 7647341, 1738780, 7739940, 7281648, 8134304, 4636215, 6519515, 6917786, 2680725, 6165751, 1663550, 1412127, 1221409, 1046738, 7366239, 6210054, 4737113, 5374098, 6713655, 516820, 5094752, 7805467, 5248325, 592294, 7712200, 1063242, 4943077, 724125, 4680710, 8331349, 5074733, 5156638, 8298566, 8227763, 6969938, 3958129, 3146198, 6022600, 2161406, 359581, 1330894, 3105160, 5792908, 3843754, 2011697, 1121164, 523494, 3882956, 5694000, 4338815, 5909593, 2362893, 294350, 5906312, 6943667, 3094444, 4964410, 5683568, 5787188, 7945352, 2507377, 1621846, 1789794, 7198613, 835772, 2147343, 1167064, 1875436, 1479920, 3446679, 306277, 6188930, 5990722, 5163108, 2906107, 4771417, 8334131, 2644547, 4180947, 1499692, 5731064, 621824, 3398804, 1894893, 7423869, 3518892, 8020825, 5205888, 2160429, 4134848, 2324690, 1600156, 6967994, 808618, 3578878, 3062879, 3896357, 2613153, 7765091, 3714219, 1675525, 4161623, 6536932, 7645847, 4524694, 6359394, 1586079, 7790951, 5147028, 3537780, 1025952, 7467635, 3855018, 2044555, 3017509, 7590341, 1082057, 4715069, 5340883, 1690884, 8189268, 1792625, 5590637, 5914030, 3791874, 7191899, 5670439, 6938254, 788303, 5732687, 7755354, 4176290, 7303752, 3626, 8324963, 1655243, 5138774, 1008629, 6888800, 268052, 4660900, 5218979, 1170978, 3718900, 6892111, 5975888]]
h: [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]]
||h||: 35, Hint check passed
||ct0||: 67653, ||ct0|| check passed

signature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
