# golden precision oracle table
# generated by scripts/gen_golden_precision.py
# each line: <input_raw>\t<expected_raw>
# input_raw is the storage integer of x at the tier scale.
# expected_raw is the half-to-even rounding of f(x) at the tier scale,
# computed by mpmath at max(700, 2*SCALE + 64)-digit precision.
3340839335747726792259881082625674477414603297157753288623747733874032102264552696	5779999425387278351454924781826522459755214910069017596703187231462047969578070
306249007335367667040644324299771147029543770540062726429017604495254636048022256	1749997163813037918263588804018912961337944921679187856926269812229107478855735
320410153318885208141447202926831373154704418797797619789952384652491638176003422	1790000428264991248746296854895554236447252273733895255311198280682758446524308
900000637409238947028194087872770966536423105513330961446809896622161737860451920	3000001062348543480975684121373998131325228205872677587064599129701454263245813
8353959112364622211642043214773017897508975754449768375456127703073279086461674489	9139999514422646954652879738624285094953658500805694892877582859683310117289427
7378810646136285951389395028291809685379772364206618637323005140019573688951214313	8590000376097946336683859814422917833816945218477181670671873023165161774961271
675999570705363471170571462366393309257555380501252495371638959873552674227311211	2599999174433260221396901144596102340179493990704871532332741765423748385723915
817960446356219933420792636377969195739425509049218111149371111688814669785619308	2860000780342935384459986351098997481616924698976506031712412341605458558259817
5416960563584311149743310417188044379553335988341306126595792098418538067950033770	7360000382869766637783620849252220832591590080935218276228978260049911361859242
3294760209942311574142082386410761389927508771170685266607317210229329597476387949	5740000182876575113029538222349560387965719855439242488899515963100366499755932
734410655006902914087241506370291353425818791307549035183550620440225433932451474	2710001208499551415075026683788742417629525875510320660668966468989841545023497
6037290301533475050089613446671411962681252848702008081355664104935786279665001670	7770000194036982808915407778595922005567682106783509252414638161087503068740660
2180889650643769126442926008887926643845303804335011018522225251830924149087506813	4669999625956911280106749568623758541066181062601649339596158835424209128176674
5155239720704239172091085285760493120983033646999486439996090534971307453938683253	7179999805504342193060581274619113626496427764662982840296702683764333981738683
5476000942843192754449237064177251921831952799130857368114308021183727167291793461	7400000637056183898912900459205424268459954141122822029094115460949484018322244
7638759640554063287487828153110779764709191337945676718861919791499296386474794151	8739999794367310674489437201897141849854449670583629202212918529082475292400077
222010470437569272401104134142452972426873975417788675848448154326012457608315033	1490001578648725030944295139414561424741630494585693247907993482270533906695568
7534239074408746653586012684865013422982016172489985768131992484992666520762429143	8679999466825298517315542955009606948464421812085541051630782462104416682665239
1713959066254767100205694867112043134428033580688184805699905103120121175243420734	4139998872288212472002562690807250461658491796968562581021901238230696310484796
8099999116720179649477905898632076531199924642206849443062190554604261445012260199	8999999509288975316526072948964614285868973323645209487866402303714199824636153
6839290010878488573492706084916405622553666151821991339126986850140375756923800844	8270000006577078941455205166084070986756804614866732025303190630452584803027517
750759838007725229439516863385284702593995873638680143769109751019314275256479631	2739999704393643231984855287372207035317395173951315843247019690610595991564762
524409398345389068919345506688562424730353499537126224118085222199326995076495446	2289998686343267466197057571922177990394931111500148084783274081223364136873615
8723560636633659920292298063063423106586857110613610060561875295805197897544004372	9340000340810304231866140793012757781424154932005227303491329838456402233352432
384159998187838196174453074007944410980933769543136053780070083031790476117677719	1959999995377138250095326525854016405628083571377823626387805304093589343162459
4998490525594683534789140209220050302631212442828095244876065506108436717231774476	7070000371707687212255068557888987455121339213846400048818759147260601862339169
6806249546344961775882704180082705844926324705782084831777025121475600996071212261	8249999725057548010028796093527674877195576797707056533738030414811533263992825
4788639356609453174163640269561112712918670556478977499537836642896535840944106218	6919999535122421649600690011846956937999968309715586127131678070325455248161693
3317759319059898336322699899689386031433825654609949091029652742316618447386524293	5759999408906131421116799257538978389328467755453356364665925464758658635177230
3069160659435642882367350095117737362921977199202491012896671400324192975278035267	5540000595158490488271182371263349641610388779309687572376922878448581488593173
8445610092256922104047874899231358531696725684676777907499758223103707790847674589	9190000050194190343907617231332149267192511439752936564484418755152392330087323
490411577865028482345775325361877760303366666401820188042409561871894754038247	70029392248185938568918984405030602709110138664598615481755015578369060464468
94111414640207002058885630505728057536383320401354023518763927224982255593760659281955925133662584246902145061486164388752348058738926202975338999975573	970110378463229317383034379091102032612899909498063050445998240879582927085036518524697210368196615096327402438610
97535992669456370131997803817692785706599267604056181665329127565036268138206106534921774517166390999741441111622410616733563317541634168097121284470624	987603122055901411638537261708730537937219190600694971196284687048113555824575691699352419232007099144295143892091
75675062279050502851468236217683731827345223794718289168633949846492097079141550572459913282389094132628913014447002588754985842932302254423194492599892	869914146792949349214234810108237285068028388298349007904456047158789811224979706907705929159134532654484832038730
43434687316627455641487771941392780710199520518873139351131831781346853064678108281477654768427505179605676822542664410135806277035878998806925616802111	659049977745447281048297548602773332264191166792493783329818112277004526523932480926059201761228642548463975414964
78519205059075341791137186418275137838148164557049960431951961047692198416793323977139755983226757603557070957310987807178173790557619526454914329357248	886110631123875760664486746295760318287677795142217120192470592830847835164985022425836898310452706428713914881683
15883231114256923231546948034138107132911313918514426071831262651925905275211323477714972572929563126956083629851285249441597058292709362517740033500016	398537716085402928725791939985974091866294363820631968125954499105275336662154597804298823286483425790242505938182
93473174773098585951706839336614937696291569971132816410671969027845885515857242015000277914033186220052545418422846617242099210248783326708055071949752	966815260394138513784796500480175062572600572244435435738206097014992613302670925330614259163267161522399770439520
30157365511032240589385927729413085752215743739969716724653495577963451487106705714542964169199716110569510871915713295127218316152002215104866940871263	549157222578673188749392990698700354136128451135975316523629658342080970917447699277398691651185692066915113148339
78139773746981278855200699318213042579607948900480245340336380494912756676347842741452426492297325986501227855712645790700140063683034908526859419642204	883967045465956716369947553673715672994993673956861955837703525380542763799802079318485989897333074394663998666898
68109999169188811311795819292052671617822157036033881208700921768061716083537904483973165643158237992194152660928085909900991435871312389677431641470489	825287823545148467446109005149882931469413401998351664300895440750607917804539235793849561146903287052360723417292
70853347870783539731170977697551276639079443396625727315722931824198599002976434950619417387447545118078989702634758137523976863752718245156885782296101	841744307202511110224057046822018235420091236295896454564135446568121011148524260514264889577194207403385980058971
63635498279643670544156837681221864723099031462637646913149586193039151174547762435100813464885834993334845727243042612545264170282324447595462866299294	797718611288740527051710772265108233106966863017963149582009737005722647992942011515073547490039650312312274526984
78035898874697096225318485993541493967346151946291435370721633660107308899536281633960470755413765137004133820032034401790160073555028044438459385769892	883379300610429156467986687524372127626815324497957848855815497047915593394234929338506646904198157150191516563509
21260540731314779461682832760044383604059028963696213050006859403048154516701865789487588835587293690679947303186239765831925850348034370215864026548272	461091538973713759271710862112369263594718132677339978109468893857887424934384916634983549094514059605119550799381
87131833205352115736478714546449965329416193691319592589933866317973766389354696260535190464511508582068651961133174462842213040780087150667743062166256	933444337951396627016888530100636918400635626239895367074704964498229437384506441306610002205063056282190963032976
84056646007254665355056846361663758240084322889279778078257097028705718574154964956882642112277717371886490010261829330440168253849740623111140216130910	916824116214525987394809684712154505905743991794404770972304966339924682634305975702627634601669989638696723404655
2885455448165332036389879502369136145835467099558756282164315513632515661183839701219914937996916193513566246248016907649517550788954438860308888463191	169866284122698464248631829418010281117167234721140284419705360211009244059104828849254643248765661680370879673190
26291141859347039469747418594413050586577576448451568106071943710879759055452410493045700698406397394628425631596230211234334838509165705210400594076396	512748884536544257412361765161782178435574841415023962718400652463018036658141276684768599083908875124329568986391
25314089777503683398799497910491332822033369917179877859487485185692597600118897554085268207679332261483582151772945115862428081636749244206621527927098	503131094025241928286942472453581035957963636580958370152483274112804251732428463318423201172717723316738625067321
34148599232143357224059475095165151233915141488734323881409307523635357783240758120624036997133354579841785560520650430440392762999028792668073510535173	584368028147873240781345634820111762314995206174800607798399054387938490365043823649468258695473342443365629692485
13221084229238660365061069755304970037341302779100890126316426006436683625104622081008624257226300936906045846889605248757143301144757934223439234853277	363608088870952654513081363511455819945454748297230309471326653657073113150209309582397476587529640566002340415853
20204859068761935919580291390419690164070612307507189816113559677080419603340010723933416163500837222269912370470945509218756258906247283155553825565808	449498154264975107245480597062077097689871569901788405401815419493534785498002563917204793579166517308243905567583
10532090486297508599590681553225862031359558171115025899313235510071723111356701589365508788760062633548859751170841008753262170264156529831559939616076	324531824114331021636317603514677957019837368158912998870514858541441476139360856080287337661743314913343844548932
89914693667988908928030143355292400004368172803869482162941851522352112790362360175285533904974733417481983632370248159962057925404156176236470172817408	948233587614301442110241962866793623982634187900842299626454214435766499923095646089121057799235513988316818484784
46017798768756614134803330539853299652035915253514801538499870292576878916149755606567162575102235758752955562575172827110623074194847823179382720961267	678364199886437212735531148863146070968100084090504097152362617185739321562311543439038379025803632219884687383573
8105732238287185485815968389720780910951637335742907354386256537568144556805981658010284970117823538070428292568273289304682062756759641488410644556250	284705676766150651438317062561566567196733056965123976299318141190189437470539005894881927035583839843007395171228
5661382943745898037299929524190175581905732858161194880518230538183731436668031124890207408917786142199541456625502860146518465371298582406359308339239	237936608022933243573165003640624400839080968723633461716709894593009118892503465653573513098850200363131830525495
50692830929463826581405747094176402508453994019035356974236821866307024489594383448908463180910300349926638124246182027644949801007202277564016907976154	711988981160971525476561861936675548432298349723396711961829275641794664437871912267626056011649080085394730868881
30571464594486669708969316646053414898383538610737376881926286457148939232123126101319509155305753013595719399696855197210624400722743562014413285008286	552914682337941444802770444740288345017472788483218019063546824216262581976407998881862973023320932014253789265999
7056380224786900864208264534337413636810825145433041360672883502756783364170488663821516963163021868509838368167536210784057772524401079409776807294303	265638480359809709257144556894888193396185671983267344761868857517065236298998026504377206005177671215370153573060
88380012835920490653054969742339693092518444529203875258820231945992346846979468336496305706481474804052049506575676804412088786345225743889063199161491	940106445227988481388706440459233522191019848896116376968829333746225581263711114527393774334714403014447307305546
40703979142412165881501128722150012963036894909823816071890984479299042900835978278193162625666690392377517153109043662906711260572152145053927533728826	637996701734516538883714965579256318644575387184184866905964077288495889932605986188459696326634446868061437711390
31875119796420071216704398016291773227983180488556753639614428485121019569993258209283812306532694696650092993942320927760591305402347153093993374706302	564580550465742409962695303376159868506143629185155173841296946777113448415932934618980185043295544580080320972650
99025970911413460129244610512537631738800059232198889598790809305310272107307762544996120547705100582455999562592733172018512834978526289727308354618477	995117937288909791909909688053361357484666311784047894224753609778667640066217825743406217143829626142612589043850
15921472261921160087910088635549300974100178919458810852632269892904618969330649053916876357673035908565251688879929644131833457375203947649466517327223	399017195894126348464304851996893895983726090410575927129163229183918304333417673738118032135003840114392015324726
18346839856655126282294099899450396788770238088864535297230171550736414461751751428700707047235428373994757342613034212172398683128320177312307292796436	428332112462457410394990584508479745220841026989957310220084718249857628731026460230095078928100680930575952581029
52326723662097059913696040255534263719589301494010148380815795186128643990640917236590368376781776585840885803853896938146948138536101620019957405671655	723372128728340347809530712460651004996322920858523268728485036087515697984643786812351253041630821101904678566027
52654612357067930614161387718440429714799343590720949802542691157450469018232166688177274261656132939632202775506113256052062582063925235628383152182045	725634979566640865324473289296005961566622880666082135390490064943064506992210842299766027423645151771167843852206
38020738739759733534804723496651190405037557527292220388666911100281988293798972675684076585010629123263179735716823479563769830555446057255754115733222	616609590744092574682769266748250984304837307053672252922644548114778699814510936083730700274142371896550322043262
5489644768124983716594138139843916952294564175233647767309235840698401751781327770701211319222472813073346388363287394447411562957505743759725834878966	234299909691083400481271879148875717570455279051744096912260329147957269202876661059817328374146106112393665863238
22439202110384938788144751418177229166418438915277203655969673140460166054264612632468261384338935071622912359715551234093628032816546927116721201922956	473700349486729202984545613184466205047172653819216465654815674065171420187731148303687086385045341670745502367468
75446296961384857043218533104458460752323775956441421444669420207535034285187738559345350863917999287991595699097044310021141069972564985334275236704288	868598278615522338194940320977483056447053190164313098151165484962494687500232789642700922797863039066868742097690
90967123698132728049966967367384660463096002313036302116218454344597762126983764228603071097281175380730890442460538814512185487797374934322548733296399	953766867206723259687807527695284206060639453917986643552327191098296634333101641361744669696231549531573959141992
2743625271267772573757704869654226159263019889953656098726430360647542236095957266989228764256736680309390163270095496914057847555659587660332232612011	165638922698373421102836003103374332524075038560078429385162024268829891574243333217377174725825495315928952707631
82455742231927297075553750302511009298515466943584080352169132149555720795005011124511929006418055227460452922484170458967680253566007334223148237262411	908051442551176706601024119691645546435651616407420634788089590869807665554916133026724170369562554554766534018040
80070770633400684767352966129786802287648150956924251902340807780926513445821347323088067288340562039982902075090335587652706613799777232551867355580167	894822723411741957129534260853257742838502280138781952977427514171884662313646083948856980220019328466085666511437
85217688494782235873837195874832772632077371107767945965642482058917190576944090340213481828693972676562292338172679740329728287580378598895848081128699	923134272437017885165998542188977378608362330655768491968123397953113308558477868997996752067498683377705466478297
44623431326753550075833907882062514586450038649710924635890667798750832741952824802126234238432671926728844758928406126171210345453531036613248004603712	668007719467024947312193242342360022826052160411010243473550884498861827399064506570340643373229310668186921393461
22671450329079666963865985264303667798803854805802049263394606282102232022491704400046679538234478657143069221643796175990431895594590434266458970727053	476145464423212446542965573367463797676704647692860514402603754061084146667560740100196440410507468250114688559368
15770331209393926757461392503845673168817216387151999164656787439574819784584084694170236910303603887143301711153220938439981577235743194509937368302648	397118763210628550092267409339817482253607923760809829564391978429659487177660920852115714140734726372095185847377
14362359782772539564630481921977672284585978376990174730044766504433945932859035941134934444154761960242456187506109750418698165943268075452970438773005	378977041293698153815136011979888553271034145918532117822978878242278769268479155095479814138141073364198355264278
36815418272160953910234199538877703676828829800722166078313454180345214305358267878762634482728066836034767567092237317266349965675977457494030239941023	606757103560897372624359811385567823835843732759097518290048270603199373645786538309428934841996324139564174911793
29618957195881675346913551008269415766512976913476856960955375985563976803113940466308954131119956632482209704937573220261264046023078927371570406483701	544233012558790624370364865149407689108477752671663597248811597810534726724079987480573193902141330120200721493842
8869999182061644317348573667088076871359045015083915023512205343136337327574488008136230138875584218313759961075455677746507900879712157488084475547961	297825438504867215067429585751064301927689377419761708820904879442312542899826428161373480524075954327163145770158
66994647932678356151754769908925755437773385582208366113609014432944216950504608258075440800394630116784837486852851444655236994910242872987952502046509	818502583579785386078248090989441849504497997900364066095883415242467811334861076820587914638653071676152360997114
45850809992421836537714492421351540797220479448617136872048704970285012627268993892929792943686656958465691694651591042390143255999247848551758434902219	677132261765911110377980569451175708209072709241837706569554976693544932366813405979225536832322099443304388185882
78071734715168590609288230982498688629551376584421811339370333107984543796332270124587211252403106702300633627301331545380368127795769045435040068845304	883582111154184643213713391726899047209421256525842896976461695136016863242866303397113352367390708455425565831278
82996339766060433570175414328922675841344970053732279492186665553938728905577561926784393835380649662395174235618636341800638214700173659974935204529758	911023269549468937000245835960665583705021180924544650056166453367095894801353753159115968756539498773673246702532
73162166886852665313315538148685376291769265871145362865991917609451830856253987535773773939080808399795755401875016389689383052616805218475611800695929	855348857992180084919862154311190531587832769054479479373788270598812095099013914773131997831061504210740512634385
28058555377259115712439236323853352185556599695035325626801235605905575223160536085035915354220600620658546089267836826963974822927553416694027350535763	529703269550595805197151447575674652714866987171542277974325709842143505682184569629073106417518705104674222196332
92811788046860843132351701487386716738798268261099405592509654095005493844145847679983684340278990984448005366832048441337014508250145607650961120764228	963388748361017776384275966241833292532164387244047749959084695350330577921667067476549726704415884136701601921012
92105752507032565736885077053547557711519946298597393236889410252418000377563841283206138260552549255380325214049127940125507705008037764797099281578013	959717419384646606180281155702076129426580673122905853837708656321995901845030617366953344068635852325297155685172
67212178910814501956070121644458722129901393893531063406205118904646435364640064578284042499039192492926395530375484442858625506570044712138339717378318	819830341661093328652285648486403271908491349774182160483317503029075830368800866640886152310920012362103850177941
73391291195703184458359454040872453298051448563482944261116519000724987660473644980998308810641655448667901352660565308739810180801801259633072783658224	856687172751542863080700982739348914135668945004822094233212676134656736858755900609093711543722051635329880184955
8418135910364634326743684505437478084608907451653397980103746045489595818520627993	9175040005561084378733563318905439046340572961753783100874799363229858275679392
7440255890290167649501515758989347288761770845459706413591567572843490741067483206	8625691792714464736726168069063571767113060283713333007335103368803517672383168
4859165954441555191606782241188255031747232921910588866111793102094253237551503835	6970771804069873001688561671320892128812303271735308693841079917964780155798372
7386763797915658801339989048415396690835522358389543311077156195413543220909217854	8594628437527511172273940063482475620393674861174458779167547413963275183886072
5481376458343939612539642852207255598826233325880272518375976833620339454560401127	7403631850885036823151406315789366426277847553167449567815455771746052292053440
310168723918536924609734275977441334286576038965004320794525275985854805048899006	1761160764718930832818758281568479222901186890347662382466699541695803587692694
2828083748787460916244475651242370016132783159907366184227304430563746590477704141	5317973061973387728909489566294751696124655572436792804293244016074150364039341
2866763188720057882394894097846537513112244613429092801709424470608152350203088845	5354216271986085810463947147575637744842841315138155765676320616590518298491541
3154050644949054214130076213139399094412484903221251125817855613161178392894352666	5616093522146024781358639106956021288002836240228692776606458681933668005835166
1366004006933860151913149449624600301211045268316779324300318964311014522260508349	3695949143229462988322136827795127200145196623039017843000463314295284750984572
9714128673894127523659678934999430307046982743473055013950621840717170338357061255	9856027939232988763017268958367853605724883274231634609293432642536929703567933
5644989364101374514521969177909366187185578004239610071901100772481678150759139087	7513314424474310867799422803696909433107374462946487673400345403582265712969181
2378000904074150961973267610296262676723525901730894674051758837517996286446441683	4876475063069789719206424812804965547183817878090326439783090622099166653548673
1211821034978106643851486964177221530512566072447859842385207432596255941836225068	3481121995819891750568001446775316675508343192834054964182755303451132949811293
8817401241168821545860993093099693970771309211593503347664651119529547425322682636	9390101831806096843752116430561945398867665761466361969617799348510812272304108
5425368976799154280050904151786189142314760576875890960653858727004319194392848041	7365710404841582067703077533401115239258009765792687447723966322946840941110514
8023474740685413983711542379899858614344631145749905712497372946367229814930350273	8957385076396690217103604884176851758162753965810910587737072026252154001874900
5363502695399964103126555971716129334466919415606466815113763314734805469328533593	7323593855068673934285289746444512046889811423513030307651885320348547138295853
9673266905870319770548961496792686031828498007682420266755339899799838454950331915	9835276765739904571457281008861547662797243759722641278788822330708116220928325
5884852295704077399185992847758801903202271082564764046873516442182176356812172754	7671279095238340628825936505849346639913641534043261026368949564453482542358080
2207726247263382860430821816153266744220537148297573931844042844430165271584600256	4698644748502894489104213853449777682153872988065295506708608036061261763108448
7215877939347640546442422330466688056283543423541000356782662743944114085012372240	8494632387188771423487180308415005233907123917391274903021583688803247783327281
6642808968781360533353387189178054436390903155727849204605506813368406320921851523	8150342918418439486410747134160819031219065697938067945818335506969136450469980
9372572143376443294845454867269218343442918330366511491777509541080572070310802456	9681204544568017386790371739562123059036144044502825763129460117185015165197555
190248433572785013817304555336517592957662565909453958030076422564090793067602600	1379305744107465876746721007891428928370257968747372252829589075162687862471761
3591140054853562986100590527107289827353414278413253823310547855741342309372525551	5992612164034614868579096242840566227004403386889568051868533910385767301185383
1108111645118153044927724221542990588084039747374533584513412103904590767844260085	3328831093819800651808735239232499972320983176907083597698494997433847579340738
6487470750250531881258707569243311592312626715692299470141916935521133195165936632	8054483689381046776457248782354859605093720168501467458665165413888595330942024
5366350025771156346645286929367674624182202573313111156083032518897139742378833972	7325537540529811759463877431253361423971445068897345542193796743665183199295743
1396145778004512540448873168583919224712441992200844751220446261716097821573967068	3736503416303151917203657468961208498709027655188967501721817797794788808262839
3193445137819495548380667145222807336920067533939188643464524609067405436205548977	5651057545114450122697659825515240261141643549283657579666856112430838967399221
7904425073354301419256437647450347683591826593887345333799878914422388048332295085	8890683367072691684666037235193998009523802040052942192497243655768901253453223
0	0
1	100000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000000000
40000000000000000000000000000000000000000000000000000000000000000000000000000	20000000000000000000000000000000000000000000000000000000000000000000000000000
90000000000000000000000000000000000000000000000000000000000000000000000000000	30000000000000000000000000000000000000000000000000000000000000000000000000000
160000000000000000000000000000000000000000000000000000000000000000000000000000	40000000000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000000000000
50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	707106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456

# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
## category: half-ULP-tie
3237754326860544009700160800555457830245475412140468284601141838285196102270548794	5690126823595888894798937984111244344611611681119836407267391980523122739499332
7704761081454823900526052189442445060063215554504484785298453545761126811255211599	8777676846099327607967549909544704564552143162240254057189845681011805335070188
2996755572487394234181818209505573207464713370139047767284993814670807446094891276	5474263030296767019042023582804043970723530993651002754287914404824197464327108
7970830479473284553122166174184911972968664345805755223396740764744501279151454056	8927950761217987672332221048892515277588531800458839558179878289398099047574109
3427363502131881417293545589420130307624686956132401014225874113277063403435636508	5854368883263063922467409478653564701481352991921121237798155955512556817367056
3215936711179338743181487510248198957497013774172534692669672705801127507032672946	5670922950613364437568196828455290434695992520191189579136925959502034357717672
5795792754277800215714375835169513821153822207067801479792546843535351707211681292	7613010412627714392567005265844063961579441824246858509549050562196628440864502
6718691929943972428546034544774613623411190586269407870586519705387596026518905430	8196762732898868305844989854495491453240516950409464800345713570542064406044001
1633753308921676072958463001929747679324017973341604371659528185673709524473440593	4041971435972396963963090719340133144972729666428568725681045025765175638435034
9782929148021953559946102558992187753623718400148697664692757389334795629335859278	9890869096303900411835390351303470414078877668391003175939669040142130592919202
7548481329243367396390294489035952950825471525759644334019757522409857257392218303	8688199657721596925105184813321231886116233820349012031495902096342358175107174
9592295919658177651481570011795675346970589973395987704940360874582335724924849229	9794026710019825983036108498031317162283313144817619401756441671180844149003217
5322322184819473881533211720213993891904028645326163799818461051583588273732615032	7295424720206133332240705120419588264765155822490424517490496119326354935148833
8122227763467055558781509815051778917007111748177441362970527945194075625875932868	9012340297318480394078358911590124700990954447544168333834137429474447546883271
8043248021833260521715265227448986789834128740588802670211393113570515322582275563	8968415702805741665681290062187340839141644872749444711959408156866718636867179
9666217076306139195638020535547381234276037159770497891145414303311948568402808697	9831692161731946332287348959141445096217277960737101829166741828679317307074342
7428506776872438130044223639451775022415514034730218882650621957262274589865840433	8618878567930075048972272914365390104945357535891946552068471940857006188463510
1799057432305001632567254361224720247822632795351227922642417303974828778857084335	4241529714979021141983453427222249704058087918689206111063991686197804413419222
344166242410084834043059864017083102495458204384673894074542594392459602152579838	1855171804470100375730377442958643893815974476376645130719059451811695371286127
1973896067795147629260906011051269088030582147026536539159355449191985428269171335	4442855014284336995981950423290208586260537714655266760039415890244504627797477
8833121071984029603488395104662583485856392976344023846464810100124483176254165836	9398468530555406186723459455706404357561937605348066190086697006646299696536818
9230461131392020875129830563901140063667257689768811150514856811746292206886005064	9607528886967772669487330735213818973202089309099310641993577395056257343399050
5986235919803787175383536203025293627420021530857624997015326175816870915263230111	7737076915608237105037581861386241491439189427335768289907070642015853612067187
673771422474068394059505536931726159345225478486707941061498273176893435258292161	2595710735952811044772908118800075169715495383442602979422115860738165204646235
7920356749066752662582042432576331155913779455409411159403106199198340459734859018	8899638615734210059847545838454361481806410303385334771442628797269072260860383
7928220920792378400109386652565650393176996282940833377127392238209547794526753337	8904055772956713909505966031420670787495971878299348516131425678647390685984827
3458228524154707051149286406829906269506502655208330379556607772180706317150721356	5880670475511025478453774187089623812762272031889391808685671124820198619947554
1946116962387943166802097432460546680004018798176883365550976615163771915846848200	4411481567895238488278548254637896622466886954127432914705140394293274203750834
1008713905370915438586024919534494289003255199952665376055994561158461628318839257	3176025669560804161521049074330642003199347443824878001529489646284136389406702
5598889161869515335154330133910081992267840147915314514597912398333369518802509133	7482572526791514725300559404075544266195464666960772925657133757228563334494986
5642874819196781860302123073994451596961601775416690402576973576160176001826573405	7511907094205027413706934918301664057108661287245452813869229065906686783810866
6052528091632262891519675394013690038504189542677263436927745901040546786555724685	7779799542168334616915790026205582316236968331783447124549430562080616558775159
3635588658936177985384579392824546478228134862561215416558042176720581923360310012	6029584279978328643069014724886989606749401889628055675736032880454102118115249
7471526675573629147254110870165574338799516571524854840366656541986573198478328403	8643799324124565275974562421116032175602103618021914486500690192137973888580684
3019189303281313377361281899974274295332515611943982129618918977099109973983404267	5494715009244167685508546194110368885394139472230655740271826611748805202119478
9360684317156799641395118477608418024314209122727538656734153000478433236040653232	9675062954398177786254466537428675867306840545706112816729641764011396522880255
8330346286387523252590522072221484248287568157031330408655190615678741183288331028	9127073072123134510053698987995166890547506535517414849003161246756019895626153
2969691460296192552452028269075094501122412403532169642672483056118327195284520204	5449487554161576899758359884513227565462728961383109719560802368367957272811813
6204243576161619388775973525671463759259944577425472299144149912113567545078157312	7876702086636017611302305692841456209316547933377628864452619941731849639950339
4618447148385590443233769304316853555259842130230983881763891951240184468238719883	6795915794347065365375923511282768865495615588181236468915122574913900541926935
## category: catastrophic cancellation
9999999999999999999999999999999999999999999999999999999999999999999999999932	9999999999999999999999999999999999999999999999999999999999999999999999999966
9999999999999999999999999999999999999999999990000000000000000000000000000000	9999999999999999999999999999999999999999999995000000000000000000000000000000
9999999999999990000000000000000000000000000000000000000000000000000000000000	9999999999999994999999999999998749999999999999374999999999999609375000000000
10000000000000000000000010000000000000000000000000000000000000000000000000000	10000000000000000000000004999999999999999999999998750000000000000000000000625
9999999999999999999999999999999999999999999999999999999999999999999999999900	9999999999999999999999999999999999999999999999999999999999999999999999999950
10000000000000000000000000000000000000000010000000000000000000000000000000000	10000000000000000000000000000000000000000005000000000000000000000000000000000
9999999999999999999999999999999999999999999999999999999999999999999999999985	9999999999999999999999999999999999999999999999999999999999999999999999999992
9999999999900000000000000000000000000000000000000000000000000000000000000000	9999999999949999999999874999999999374999999996093749999972656249999794921875
9999999999999999999999999999999999999999999999999999999999999999999999999000	9999999999999999999999999999999999999999999999999999999999999999999999999500
10000000000000000000000000000001000000000000000000000000000000000000000000000	10000000000000000000000000000000499999999999999999999999999999987500000000000
9999999999999999999999999999999999999999999999999999999999999999999999999997	9999999999999999999999999999999999999999999999999999999999999999999999999998
10000000000000000000000000000000000000000000000000000000000000000000000100000	10000000000000000000000000000000000000000000000000000000000000000000000050000
10000000000000000000000000000000000000000000000000000000000000000000001000000	10000000000000000000000000000000000000000000000000000000000000000000000500000
9999999999999999999999999999999999999999999999999900000000000000000000000000	9999999999999999999999999999999999999999999999999950000000000000000000000000
9999999999999999999999999999999999999999999999999999999999999999999999000000	9999999999999999999999999999999999999999999999999999999999999999999999500000
10000000000000000000000000000000000000000000000000000000000000000000000001000	10000000000000000000000000000000000000000000000000000000000000000000000000500
10000000000000000000000000000000000000000100000000000000000000000000000000000	10000000000000000000000000000000000000000050000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000001000000000	10000000000000000000000000000000000000000000000000000000000000000000500000000
9999999999999999999999999999999999999999999999999999990000000000000000000000	9999999999999999999999999999999999999999999999999999995000000000000000000000
9999999999999999999999990000000000000000000000000000000000000000000000000000	9999999999999999999999994999999999999999999999998749999999999999999999999375
10000000000000000000000000000000000000000000000000000000000000000000000000023	10000000000000000000000000000000000000000000000000000000000000000000000000011
9999999999999999999000000000000000000000000000000000000000000000000000000000	9999999999999999999499999999999999999987499999999999999999375000000000000000
9999999999999999999999999999999999999999999999999999999999999999999999900000	9999999999999999999999999999999999999999999999999999999999999999999999950000
9999999999999999999999999999999999999999999999999999999999999999999999999975	9999999999999999999999999999999999999999999999999999999999999999999999999987
9999999999999999999999999999999999999999999999999999999000000000000000000000	9999999999999999999999999999999999999999999999999999999500000000000000000000
9999990000000000000000000000000000000000000000000000000000000000000000000000	9999994999998749999374999609374726562294921713867056579480743315467754383017
10000000100000000000000000000000000000000000000000000000000000000000000000000	10000000049999999875000000624999996093750027343749794921876611328111907959093
9999999999999999000000000000000000000000000000000000000000000000000000000000	9999999999999999499999999999999987499999999999999374999999999999960937500000
9999000000000000000000000000000000000000000000000000000000000000000000000000	9999499987499374960934765419905760409436788821373106490134281689772710330308
9999999999999999999999999999999999999999990000000000000000000000000000000000	9999999999999999999999999999999999999999995000000000000000000000000000000000
9999999999999999999999999999999999999999999999999999999999999999999999999980	9999999999999999999999999999999999999999999999999999999999999999999999999990
10000000000000000000000000000010000000000000000000000000000000000000000000000	10000000000000000000000000000004999999999999999999999999999998750000000000000
9999999999999999999999999999999999999999999999999000000000000000000000000000	9999999999999999999999999999999999999999999999999500000000000000000000000000
10000000000000000000000000000000000000000000000000000010000000000000000000000	10000000000000000000000000000000000000000000000000000005000000000000000000000
10000010000000000000000000000000000000000000000000000000000000000000000000000	10000004999998750000624999609375273437294922036132681579698943999061664562155
9999999999999999999999999999999999900000000000000000000000000000000000000000	9999999999999999999999999999999999949999999999999999999999999999999999875000
10000000000000000000000000000000000000100000000000000000000000000000000000000	10000000000000000000000000000000000000050000000000000000000000000000000000000
9999900000000000000000000000000000000000000000000000000000000000000000000000	9999949999874999374996093722656044920263658782849883105842210699574327427574
9990000000000000000000000000000000000000000000000000000000000000000000000000	9994998749374609101357260611157896686502888143690733873785809756305648067110
10000000000000000000000000000000000000000000010000000000000000000000000000000	10000000000000000000000000000000000000000000005000000000000000000000000000000
## category: asymptote stress
1000000000000000000000000000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504852792594438639
100000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279259443864
1000000000000000000000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575048527925944386
10000000000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504852792594439
100000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279259444
1000000000000000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575048527925944
10000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504852792594
100000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279259
1000000000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575048527926
10000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504852793
100000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279
1000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575048528
10000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504853
100000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485
1000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575049
10000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857505
100000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750
1000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575
10000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826858
100000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682686
1000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000
## category: inverse-identity
2500000000000000000000000000000000000000000000000000000000000000000000000000	5000000000000000000000000000000000000000000000000000000000000000000000000000
490000000000000000000000000000000000000000000000000000000000000000000000000000	70000000000000000000000000000000000000000000000000000000000000000000000000000
## category: perfect-power ± ULP
9999999999999999999999999999999999999999999999999999999999999999999999999999	9999999999999999999999999999999999999999999999999999999999999999999999999999
10000000000000000000000000000000000000000000000000000000000000000000000000001	10000000000000000000000000000000000000000000000000000000000000000000000000000
39999999999999999999999999999999999999999999999999999999999999999999999999999	20000000000000000000000000000000000000000000000000000000000000000000000000000
40000000000000000000000000000000000000000000000000000000000000000000000000001	20000000000000000000000000000000000000000000000000000000000000000000000000000
89999999999999999999999999999999999999999999999999999999999999999999999999999	30000000000000000000000000000000000000000000000000000000000000000000000000000
90000000000000000000000000000000000000000000000000000000000000000000000000001	30000000000000000000000000000000000000000000000000000000000000000000000000000
159999999999999999999999999999999999999999999999999999999999999999999999999999	40000000000000000000000000000000000000000000000000000000000000000000000000000
160000000000000000000000000000000000000000000000000000000000000000000000000001	40000000000000000000000000000000000000000000000000000000000000000000000000000
249999999999999999999999999999999999999999999999999999999999999999999999999999	50000000000000000000000000000000000000000000000000000000000000000000000000000
250000000000000000000000000000000000000000000000000000000000000000000000000000	50000000000000000000000000000000000000000000000000000000000000000000000000000
250000000000000000000000000000000000000000000000000000000000000000000000000001	50000000000000000000000000000000000000000000000000000000000000000000000000000
489999999999999999999999999999999999999999999999999999999999999999999999999999	70000000000000000000000000000000000000000000000000000000000000000000000000000
490000000000000000000000000000000000000000000000000000000000000000000000000001	70000000000000000000000000000000000000000000000000000000000000000000000000000
1209999999999999999999999999999999999999999999999999999999999999999999999999999	110000000000000000000000000000000000000000000000000000000000000000000000000000
1210000000000000000000000000000000000000000000000000000000000000000000000000000	110000000000000000000000000000000000000000000000000000000000000000000000000000
1210000000000000000000000000000000000000000000000000000000000000000000000000001	110000000000000000000000000000000000000000000000000000000000000000000000000000
2559999999999999999999999999999999999999999999999999999999999999999999999999999	160000000000000000000000000000000000000000000000000000000000000000000000000000
2560000000000000000000000000000000000000000000000000000000000000000000000000000	160000000000000000000000000000000000000000000000000000000000000000000000000000
2560000000000000000000000000000000000000000000000000000000000000000000000000001	160000000000000000000000000000000000000000000000000000000000000000000000000000
5289999999999999999999999999999999999999999999999999999999999999999999999999999	230000000000000000000000000000000000000000000000000000000000000000000000000000
5290000000000000000000000000000000000000000000000000000000000000000000000000000	230000000000000000000000000000000000000000000000000000000000000000000000000000
5290000000000000000000000000000000000000000000000000000000000000000000000000001	230000000000000000000000000000000000000000000000000000000000000000000000000000
9609999999999999999999999999999999999999999999999999999999999999999999999999999	310000000000000000000000000000000000000000000000000000000000000000000000000000
9610000000000000000000000000000000000000000000000000000000000000000000000000000	310000000000000000000000000000000000000000000000000000000000000000000000000000
9610000000000000000000000000000000000000000000000000000000000000000000000000001	310000000000000000000000000000000000000000000000000000000000000000000000000000
40959999999999999999999999999999999999999999999999999999999999999999999999999999	640000000000000000000000000000000000000000000000000000000000000000000000000000
40960000000000000000000000000000000000000000000000000000000000000000000000000000	640000000000000000000000000000000000000000000000000000000000000000000000000000
40960000000000000000000000000000000000000000000000000000000000000000000000000001	640000000000000000000000000000000000000000000000000000000000000000000000000000
98009999999999999999999999999999999999999999999999999999999999999999999999999999	990000000000000000000000000000000000000000000000000000000000000000000000000000
98010000000000000000000000000000000000000000000000000000000000000000000000000000	990000000000000000000000000000000000000000000000000000000000000000000000000000
98010000000000000000000000000000000000000000000000000000000000000000000000000001	990000000000000000000000000000000000000000000000000000000000000000000000000000
99999999999999999999999999999999999999999999999999999999999999999999999999999999	1000000000000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000000000000000001	1000000000000000000000000000000000000000000000000000000000000000000000000000000
161289999999999999999999999999999999999999999999999999999999999999999999999999999	1270000000000000000000000000000000000000000000000000000000000000000000000000000
## category: constant edges
19999999999999999999999999999999999999999999999999999999999999999999999999999	14142135623730950488016887242096980785696718753769480731766797379907324784621
20000000000000000000000000000000000000000000000000000000000000000000000000000	14142135623730950488016887242096980785696718753769480731766797379907324784621
20000000000000000000000000000000000000000000000000000000000000000000000000001	14142135623730950488016887242096980785696718753769480731766797379907324784621
29999999999999999999999999999999999999999999999999999999999999999999999999999	17320508075688772935274463415058723669428052538103806280558069794519330169088
30000000000000000000000000000000000000000000000000000000000000000000000000000	17320508075688772935274463415058723669428052538103806280558069794519330169088
30000000000000000000000000000000000000000000000000000000000000000000000000001	17320508075688772935274463415058723669428052538103806280558069794519330169088
49999999999999999999999999999999999999999999999999999999999999999999999999999	22360679774997896964091736687312762354406183596115257242708972454105209256378
50000000000000000000000000000000000000000000000000000000000000000000000000000	22360679774997896964091736687312762354406183596115257242708972454105209256378
50000000000000000000000000000000000000000000000000000000000000000000000000001	22360679774997896964091736687312762354406183596115257242708972454105209256378
31415926535897932384626433832795028841971693993751058209749445923078164062861	17724538509055160272981674833411451827975494561223871282138077898529112845910
31415926535897932384626433832795028841971693993751058209749445923078164062862	17724538509055160272981674833411451827975494561223871282138077898529112845910
31415926535897932384626433832795028841971693993751058209749445923078164062863	17724538509055160272981674833411451827975494561223871282138077898529112845911
27182818284590452353602874713526624977572470936999595749669676277240766303534	16487212707001281468486507878141635716537761007101480115750793116406610211942
27182818284590452353602874713526624977572470936999595749669676277240766303535	16487212707001281468486507878141635716537761007101480115750793116406610211942
27182818284590452353602874713526624977572470936999595749669676277240766303536	16487212707001281468486507878141635716537761007101480115750793116406610211942
4999999999999999999999999999999999999999999999999999999999999999999999999999	7071067811865475244008443621048490392848359376884740365883398689953662392310
5000000000000000000000000000000000000000000000000000000000000000000000000000	7071067811865475244008443621048490392848359376884740365883398689953662392311
5000000000000000000000000000000000000000000000000000000000000000000000000001	7071067811865475244008443621048490392848359376884740365883398689953662392311
20000000000000000000000000000000000000000000000000000000000000000000000000000	14142135623730950488016887242096980785696718753769480731766797379907324784621
