from __future__ import annotations
import chess
import struct
import os
import mmap
import random
import typing
from types import TracebackType
from typing import Callable, Container, Iterator, List, NamedTuple, Optional, Type, Union
StrOrBytesPath = Union[str, bytes, "os.PathLike[str]", "os.PathLike[bytes]"]
ENTRY_STRUCT = struct.Struct(">QHHI")
POLYGLOT_RANDOM_ARRAY = [
0x9D39247E33776D41, 0x2AF7398005AAA5C7, 0x44DB015024623547, 0x9C15F73E62A76AE2,
0x75834465489C0C89, 0x3290AC3A203001BF, 0x0FBBAD1F61042279, 0xE83A908FF2FB60CA,
0x0D7E765D58755C10, 0x1A083822CEAFE02D, 0x9605D5F0E25EC3B0, 0xD021FF5CD13A2ED5,
0x40BDF15D4A672E32, 0x011355146FD56395, 0x5DB4832046F3D9E5, 0x239F8B2D7FF719CC,
0x05D1A1AE85B49AA1, 0x679F848F6E8FC971, 0x7449BBFF801FED0B, 0x7D11CDB1C3B7ADF0,
0x82C7709E781EB7CC, 0xF3218F1C9510786C, 0x331478F3AF51BBE6, 0x4BB38DE5E7219443,
0xAA649C6EBCFD50FC, 0x8DBD98A352AFD40B, 0x87D2074B81D79217, 0x19F3C751D3E92AE1,
0xB4AB30F062B19ABF, 0x7B0500AC42047AC4, 0xC9452CA81A09D85D, 0x24AA6C514DA27500,
0x4C9F34427501B447, 0x14A68FD73C910841, 0xA71B9B83461CBD93, 0x03488B95B0F1850F,
0x637B2B34FF93C040, 0x09D1BC9A3DD90A94, 0x3575668334A1DD3B, 0x735E2B97A4C45A23,
0x18727070F1BD400B, 0x1FCBACD259BF02E7, 0xD310A7C2CE9B6555, 0xBF983FE0FE5D8244,
0x9F74D14F7454A824, 0x51EBDC4AB9BA3035, 0x5C82C505DB9AB0FA, 0xFCF7FE8A3430B241,
0x3253A729B9BA3DDE, 0x8C74C368081B3075, 0xB9BC6C87167C33E7, 0x7EF48F2B83024E20,
0x11D505D4C351BD7F, 0x6568FCA92C76A243, 0x4DE0B0F40F32A7B8, 0x96D693460CC37E5D,
0x42E240CB63689F2F, 0x6D2BDCDAE2919661, 0x42880B0236E4D951, 0x5F0F4A5898171BB6,
0x39F890F579F92F88, 0x93C5B5F47356388B, 0x63DC359D8D231B78, 0xEC16CA8AEA98AD76,
0x5355F900C2A82DC7, 0x07FB9F855A997142, 0x5093417AA8A7ED5E, 0x7BCBC38DA25A7F3C,
0x19FC8A768CF4B6D4, 0x637A7780DECFC0D9, 0x8249A47AEE0E41F7, 0x79AD695501E7D1E8,
0x14ACBAF4777D5776, 0xF145B6BECCDEA195, 0xDABF2AC8201752FC, 0x24C3C94DF9C8D3F6,
0xBB6E2924F03912EA, 0x0CE26C0B95C980D9, 0xA49CD132BFBF7CC4, 0xE99D662AF4243939,
0x27E6AD7891165C3F, 0x8535F040B9744FF1, 0x54B3F4FA5F40D873, 0x72B12C32127FED2B,
0xEE954D3C7B411F47, 0x9A85AC909A24EAA1, 0x70AC4CD9F04F21F5, 0xF9B89D3E99A075C2,
0x87B3E2B2B5C907B1, 0xA366E5B8C54F48B8, 0xAE4A9346CC3F7CF2, 0x1920C04D47267BBD,
0x87BF02C6B49E2AE9, 0x092237AC237F3859, 0xFF07F64EF8ED14D0, 0x8DE8DCA9F03CC54E,
0x9C1633264DB49C89, 0xB3F22C3D0B0B38ED, 0x390E5FB44D01144B, 0x5BFEA5B4712768E9,
0x1E1032911FA78984, 0x9A74ACB964E78CB3, 0x4F80F7A035DAFB04, 0x6304D09A0B3738C4,
0x2171E64683023A08, 0x5B9B63EB9CEFF80C, 0x506AACF489889342, 0x1881AFC9A3A701D6,
0x6503080440750644, 0xDFD395339CDBF4A7, 0xEF927DBCF00C20F2, 0x7B32F7D1E03680EC,
0xB9FD7620E7316243, 0x05A7E8A57DB91B77, 0xB5889C6E15630A75, 0x4A750A09CE9573F7,
0xCF464CEC899A2F8A, 0xF538639CE705B824, 0x3C79A0FF5580EF7F, 0xEDE6C87F8477609D,
0x799E81F05BC93F31, 0x86536B8CF3428A8C, 0x97D7374C60087B73, 0xA246637CFF328532,
0x043FCAE60CC0EBA0, 0x920E449535DD359E, 0x70EB093B15B290CC, 0x73A1921916591CBD,
0x56436C9FE1A1AA8D, 0xEFAC4B70633B8F81, 0xBB215798D45DF7AF, 0x45F20042F24F1768,
0x930F80F4E8EB7462, 0xFF6712FFCFD75EA1, 0xAE623FD67468AA70, 0xDD2C5BC84BC8D8FC,
0x7EED120D54CF2DD9, 0x22FE545401165F1C, 0xC91800E98FB99929, 0x808BD68E6AC10365,
0xDEC468145B7605F6, 0x1BEDE3A3AEF53302, 0x43539603D6C55602, 0xAA969B5C691CCB7A,
0xA87832D392EFEE56, 0x65942C7B3C7E11AE, 0xDED2D633CAD004F6, 0x21F08570F420E565,
0xB415938D7DA94E3C, 0x91B859E59ECB6350, 0x10CFF333E0ED804A, 0x28AED140BE0BB7DD,
0xC5CC1D89724FA456, 0x5648F680F11A2741, 0x2D255069F0B7DAB3, 0x9BC5A38EF729ABD4,
0xEF2F054308F6A2BC, 0xAF2042F5CC5C2858, 0x480412BAB7F5BE2A, 0xAEF3AF4A563DFE43,
0x19AFE59AE451497F, 0x52593803DFF1E840, 0xF4F076E65F2CE6F0, 0x11379625747D5AF3,
0xBCE5D2248682C115, 0x9DA4243DE836994F, 0x066F70B33FE09017, 0x4DC4DE189B671A1C,
0x51039AB7712457C3, 0xC07A3F80C31FB4B4, 0xB46EE9C5E64A6E7C, 0xB3819A42ABE61C87,
0x21A007933A522A20, 0x2DF16F761598AA4F, 0x763C4A1371B368FD, 0xF793C46702E086A0,
0xD7288E012AEB8D31, 0xDE336A2A4BC1C44B, 0x0BF692B38D079F23, 0x2C604A7A177326B3,
0x4850E73E03EB6064, 0xCFC447F1E53C8E1B, 0xB05CA3F564268D99, 0x9AE182C8BC9474E8,
0xA4FC4BD4FC5558CA, 0xE755178D58FC4E76, 0x69B97DB1A4C03DFE, 0xF9B5B7C4ACC67C96,
0xFC6A82D64B8655FB, 0x9C684CB6C4D24417, 0x8EC97D2917456ED0, 0x6703DF9D2924E97E,
0xC547F57E42A7444E, 0x78E37644E7CAD29E, 0xFE9A44E9362F05FA, 0x08BD35CC38336615,
0x9315E5EB3A129ACE, 0x94061B871E04DF75, 0xDF1D9F9D784BA010, 0x3BBA57B68871B59D,
0xD2B7ADEEDED1F73F, 0xF7A255D83BC373F8, 0xD7F4F2448C0CEB81, 0xD95BE88CD210FFA7,
0x336F52F8FF4728E7, 0xA74049DAC312AC71, 0xA2F61BB6E437FDB5, 0x4F2A5CB07F6A35B3,
0x87D380BDA5BF7859, 0x16B9F7E06C453A21, 0x7BA2484C8A0FD54E, 0xF3A678CAD9A2E38C,
0x39B0BF7DDE437BA2, 0xFCAF55C1BF8A4424, 0x18FCF680573FA594, 0x4C0563B89F495AC3,
0x40E087931A00930D, 0x8CFFA9412EB642C1, 0x68CA39053261169F, 0x7A1EE967D27579E2,
0x9D1D60E5076F5B6F, 0x3810E399B6F65BA2, 0x32095B6D4AB5F9B1, 0x35CAB62109DD038A,
0xA90B24499FCFAFB1, 0x77A225A07CC2C6BD, 0x513E5E634C70E331, 0x4361C0CA3F692F12,
0xD941ACA44B20A45B, 0x528F7C8602C5807B, 0x52AB92BEB9613989, 0x9D1DFA2EFC557F73,
0x722FF175F572C348, 0x1D1260A51107FE97, 0x7A249A57EC0C9BA2, 0x04208FE9E8F7F2D6,
0x5A110C6058B920A0, 0x0CD9A497658A5698, 0x56FD23C8F9715A4C, 0x284C847B9D887AAE,
0x04FEABFBBDB619CB, 0x742E1E651C60BA83, 0x9A9632E65904AD3C, 0x881B82A13B51B9E2,
0x506E6744CD974924, 0xB0183DB56FFC6A79, 0x0ED9B915C66ED37E, 0x5E11E86D5873D484,
0xF678647E3519AC6E, 0x1B85D488D0F20CC5, 0xDAB9FE6525D89021, 0x0D151D86ADB73615,
0xA865A54EDCC0F019, 0x93C42566AEF98FFB, 0x99E7AFEABE000731, 0x48CBFF086DDF285A,
0x7F9B6AF1EBF78BAF, 0x58627E1A149BBA21, 0x2CD16E2ABD791E33, 0xD363EFF5F0977996,
0x0CE2A38C344A6EED, 0x1A804AADB9CFA741, 0x907F30421D78C5DE, 0x501F65EDB3034D07,
0x37624AE5A48FA6E9, 0x957BAF61700CFF4E, 0x3A6C27934E31188A, 0xD49503536ABCA345,
0x088E049589C432E0, 0xF943AEE7FEBF21B8, 0x6C3B8E3E336139D3, 0x364F6FFA464EE52E,
0xD60F6DCEDC314222, 0x56963B0DCA418FC0, 0x16F50EDF91E513AF, 0xEF1955914B609F93,
0x565601C0364E3228, 0xECB53939887E8175, 0xBAC7A9A18531294B, 0xB344C470397BBA52,
0x65D34954DAF3CEBD, 0xB4B81B3FA97511E2, 0xB422061193D6F6A7, 0x071582401C38434D,
0x7A13F18BBEDC4FF5, 0xBC4097B116C524D2, 0x59B97885E2F2EA28, 0x99170A5DC3115544,
0x6F423357E7C6A9F9, 0x325928EE6E6F8794, 0xD0E4366228B03343, 0x565C31F7DE89EA27,
0x30F5611484119414, 0xD873DB391292ED4F, 0x7BD94E1D8E17DEBC, 0xC7D9F16864A76E94,
0x947AE053EE56E63C, 0xC8C93882F9475F5F, 0x3A9BF55BA91F81CA, 0xD9A11FBB3D9808E4,
0x0FD22063EDC29FCA, 0xB3F256D8ACA0B0B9, 0xB03031A8B4516E84, 0x35DD37D5871448AF,
0xE9F6082B05542E4E, 0xEBFAFA33D7254B59, 0x9255ABB50D532280, 0xB9AB4CE57F2D34F3,
0x693501D628297551, 0xC62C58F97DD949BF, 0xCD454F8F19C5126A, 0xBBE83F4ECC2BDECB,
0xDC842B7E2819E230, 0xBA89142E007503B8, 0xA3BC941D0A5061CB, 0xE9F6760E32CD8021,
0x09C7E552BC76492F, 0x852F54934DA55CC9, 0x8107FCCF064FCF56, 0x098954D51FFF6580,
0x23B70EDB1955C4BF, 0xC330DE426430F69D, 0x4715ED43E8A45C0A, 0xA8D7E4DAB780A08D,
0x0572B974F03CE0BB, 0xB57D2E985E1419C7, 0xE8D9ECBE2CF3D73F, 0x2FE4B17170E59750,
0x11317BA87905E790, 0x7FBF21EC8A1F45EC, 0x1725CABFCB045B00, 0x964E915CD5E2B207,
0x3E2B8BCBF016D66D, 0xBE7444E39328A0AC, 0xF85B2B4FBCDE44B7, 0x49353FEA39BA63B1,
0x1DD01AAFCD53486A, 0x1FCA8A92FD719F85, 0xFC7C95D827357AFA, 0x18A6A990C8B35EBD,
0xCCCB7005C6B9C28D, 0x3BDBB92C43B17F26, 0xAA70B5B4F89695A2, 0xE94C39A54A98307F,
0xB7A0B174CFF6F36E, 0xD4DBA84729AF48AD, 0x2E18BC1AD9704A68, 0x2DE0966DAF2F8B1C,
0xB9C11D5B1E43A07E, 0x64972D68DEE33360, 0x94628D38D0C20584, 0xDBC0D2B6AB90A559,
0xD2733C4335C6A72F, 0x7E75D99D94A70F4D, 0x6CED1983376FA72B, 0x97FCAACBF030BC24,
0x7B77497B32503B12, 0x8547EDDFB81CCB94, 0x79999CDFF70902CB, 0xCFFE1939438E9B24,
0x829626E3892D95D7, 0x92FAE24291F2B3F1, 0x63E22C147B9C3403, 0xC678B6D860284A1C,
0x5873888850659AE7, 0x0981DCD296A8736D, 0x9F65789A6509A440, 0x9FF38FED72E9052F,
0xE479EE5B9930578C, 0xE7F28ECD2D49EECD, 0x56C074A581EA17FE, 0x5544F7D774B14AEF,
0x7B3F0195FC6F290F, 0x12153635B2C0CF57, 0x7F5126DBBA5E0CA7, 0x7A76956C3EAFB413,
0x3D5774A11D31AB39, 0x8A1B083821F40CB4, 0x7B4A38E32537DF62, 0x950113646D1D6E03,
0x4DA8979A0041E8A9, 0x3BC36E078F7515D7, 0x5D0A12F27AD310D1, 0x7F9D1A2E1EBE1327,
0xDA3A361B1C5157B1, 0xDCDD7D20903D0C25, 0x36833336D068F707, 0xCE68341F79893389,
0xAB9090168DD05F34, 0x43954B3252DC25E5, 0xB438C2B67F98E5E9, 0x10DCD78E3851A492,
0xDBC27AB5447822BF, 0x9B3CDB65F82CA382, 0xB67B7896167B4C84, 0xBFCED1B0048EAC50,
0xA9119B60369FFEBD, 0x1FFF7AC80904BF45, 0xAC12FB171817EEE7, 0xAF08DA9177DDA93D,
0x1B0CAB936E65C744, 0xB559EB1D04E5E932, 0xC37B45B3F8D6F2BA, 0xC3A9DC228CAAC9E9,
0xF3B8B6675A6507FF, 0x9FC477DE4ED681DA, 0x67378D8ECCEF96CB, 0x6DD856D94D259236,
0xA319CE15B0B4DB31, 0x073973751F12DD5E, 0x8A8E849EB32781A5, 0xE1925C71285279F5,
0x74C04BF1790C0EFE, 0x4DDA48153C94938A, 0x9D266D6A1CC0542C, 0x7440FB816508C4FE,
0x13328503DF48229F, 0xD6BF7BAEE43CAC40, 0x4838D65F6EF6748F, 0x1E152328F3318DEA,
0x8F8419A348F296BF, 0x72C8834A5957B511, 0xD7A023A73260B45C, 0x94EBC8ABCFB56DAE,
0x9FC10D0F989993E0, 0xDE68A2355B93CAE6, 0xA44CFE79AE538BBE, 0x9D1D84FCCE371425,
0x51D2B1AB2DDFB636, 0x2FD7E4B9E72CD38C, 0x65CA5B96B7552210, 0xDD69A0D8AB3B546D,
0x604D51B25FBF70E2, 0x73AA8A564FB7AC9E, 0x1A8C1E992B941148, 0xAAC40A2703D9BEA0,
0x764DBEAE7FA4F3A6, 0x1E99B96E70A9BE8B, 0x2C5E9DEB57EF4743, 0x3A938FEE32D29981,
0x26E6DB8FFDF5ADFE, 0x469356C504EC9F9D, 0xC8763C5B08D1908C, 0x3F6C6AF859D80055,
0x7F7CC39420A3A545, 0x9BFB227EBDF4C5CE, 0x89039D79D6FC5C5C, 0x8FE88B57305E2AB6,
0xA09E8C8C35AB96DE, 0xFA7E393983325753, 0xD6B6D0ECC617C699, 0xDFEA21EA9E7557E3,
0xB67C1FA481680AF8, 0xCA1E3785A9E724E5, 0x1CFC8BED0D681639, 0xD18D8549D140CAEA,
0x4ED0FE7E9DC91335, 0xE4DBF0634473F5D2, 0x1761F93A44D5AEFE, 0x53898E4C3910DA55,
0x734DE8181F6EC39A, 0x2680B122BAA28D97, 0x298AF231C85BAFAB, 0x7983EED3740847D5,
0x66C1A2A1A60CD889, 0x9E17E49642A3E4C1, 0xEDB454E7BADC0805, 0x50B704CAB602C329,
0x4CC317FB9CDDD023, 0x66B4835D9EAFEA22, 0x219B97E26FFC81BD, 0x261E4E4C0A333A9D,
0x1FE2CCA76517DB90, 0xD7504DFA8816EDBB, 0xB9571FA04DC089C8, 0x1DDC0325259B27DE,
0xCF3F4688801EB9AA, 0xF4F5D05C10CAB243, 0x38B6525C21A42B0E, 0x36F60E2BA4FA6800,
0xEB3593803173E0CE, 0x9C4CD6257C5A3603, 0xAF0C317D32ADAA8A, 0x258E5A80C7204C4B,
0x8B889D624D44885D, 0xF4D14597E660F855, 0xD4347F66EC8941C3, 0xE699ED85B0DFB40D,
0x2472F6207C2D0484, 0xC2A1E7B5B459AEB5, 0xAB4F6451CC1D45EC, 0x63767572AE3D6174,
0xA59E0BD101731A28, 0x116D0016CB948F09, 0x2CF9C8CA052F6E9F, 0x0B090A7560A968E3,
0xABEEDDB2DDE06FF1, 0x58EFC10B06A2068D, 0xC6E57A78FBD986E0, 0x2EAB8CA63CE802D7,
0x14A195640116F336, 0x7C0828DD624EC390, 0xD74BBE77E6116AC7, 0x804456AF10F5FB53,
0xEBE9EA2ADF4321C7, 0x03219A39EE587A30, 0x49787FEF17AF9924, 0xA1E9300CD8520548,
0x5B45E522E4B1B4EF, 0xB49C3B3995091A36, 0xD4490AD526F14431, 0x12A8F216AF9418C2,
0x001F837CC7350524, 0x1877B51E57A764D5, 0xA2853B80F17F58EE, 0x993E1DE72D36D310,
0xB3598080CE64A656, 0x252F59CF0D9F04BB, 0xD23C8E176D113600, 0x1BDA0492E7E4586E,
0x21E0BD5026C619BF, 0x3B097ADAF088F94E, 0x8D14DEDB30BE846E, 0xF95CFFA23AF5F6F4,
0x3871700761B3F743, 0xCA672B91E9E4FA16, 0x64C8E531BFF53B55, 0x241260ED4AD1E87D,
0x106C09B972D2E822, 0x7FBA195410E5CA30, 0x7884D9BC6CB569D8, 0x0647DFEDCD894A29,
0x63573FF03E224774, 0x4FC8E9560F91B123, 0x1DB956E450275779, 0xB8D91274B9E9D4FB,
0xA2EBEE47E2FBFCE1, 0xD9F1F30CCD97FB09, 0xEFED53D75FD64E6B, 0x2E6D02C36017F67F,
0xA9AA4D20DB084E9B, 0xB64BE8D8B25396C1, 0x70CB6AF7C2D5BCF0, 0x98F076A4F7A2322E,
0xBF84470805E69B5F, 0x94C3251F06F90CF3, 0x3E003E616A6591E9, 0xB925A6CD0421AFF3,
0x61BDD1307C66E300, 0xBF8D5108E27E0D48, 0x240AB57A8B888B20, 0xFC87614BAF287E07,
0xEF02CDD06FFDB432, 0xA1082C0466DF6C0A, 0x8215E577001332C8, 0xD39BB9C3A48DB6CF,
0x2738259634305C14, 0x61CF4F94C97DF93D, 0x1B6BACA2AE4E125B, 0x758F450C88572E0B,
0x959F587D507A8359, 0xB063E962E045F54D, 0x60E8ED72C0DFF5D1, 0x7B64978555326F9F,
0xFD080D236DA814BA, 0x8C90FD9B083F4558, 0x106F72FE81E2C590, 0x7976033A39F7D952,
0xA4EC0132764CA04B, 0x733EA705FAE4FA77, 0xB4D8F77BC3E56167, 0x9E21F4F903B33FD9,
0x9D765E419FB69F6D, 0xD30C088BA61EA5EF, 0x5D94337FBFAF7F5B, 0x1A4E4822EB4D7A59,
0x6FFE73E81B637FB3, 0xDDF957BC36D8B9CA, 0x64D0E29EEA8838B3, 0x08DD9BDFD96B9F63,
0x087E79E5A57D1D13, 0xE328E230E3E2B3FB, 0x1C2559E30F0946BE, 0x720BF5F26F4D2EAA,
0xB0774D261CC609DB, 0x443F64EC5A371195, 0x4112CF68649A260E, 0xD813F2FAB7F5C5CA,
0x660D3257380841EE, 0x59AC2C7873F910A3, 0xE846963877671A17, 0x93B633ABFA3469F8,
0xC0C0F5A60EF4CDCF, 0xCAF21ECD4377B28C, 0x57277707199B8175, 0x506C11B9D90E8B1D,
0xD83CC2687A19255F, 0x4A29C6465A314CD1, 0xED2DF21216235097, 0xB5635C95FF7296E2,
0x22AF003AB672E811, 0x52E762596BF68235, 0x9AEBA33AC6ECC6B0, 0x944F6DE09134DFB6,
0x6C47BEC883A7DE39, 0x6AD047C430A12104, 0xA5B1CFDBA0AB4067, 0x7C45D833AFF07862,
0x5092EF950A16DA0B, 0x9338E69C052B8E7B, 0x455A4B4CFE30E3F5, 0x6B02E63195AD0CF8,
0x6B17B224BAD6BF27, 0xD1E0CCD25BB9C169, 0xDE0C89A556B9AE70, 0x50065E535A213CF6,
0x9C1169FA2777B874, 0x78EDEFD694AF1EED, 0x6DC93D9526A50E68, 0xEE97F453F06791ED,
0x32AB0EDB696703D3, 0x3A6853C7E70757A7, 0x31865CED6120F37D, 0x67FEF95D92607890,
0x1F2B1D1F15F6DC9C, 0xB69E38A8965C6B65, 0xAA9119FF184CCCF4, 0xF43C732873F24C13,
0xFB4A3D794A9A80D2, 0x3550C2321FD6109C, 0x371F77E76BB8417E, 0x6BFA9AAE5EC05779,
0xCD04F3FF001A4778, 0xE3273522064480CA, 0x9F91508BFFCFC14A, 0x049A7F41061A9E60,
0xFCB6BE43A9F2FE9B, 0x08DE8A1C7797DA9B, 0x8F9887E6078735A1, 0xB5B4071DBFC73A66,
0x230E343DFBA08D33, 0x43ED7F5A0FAE657D, 0x3A88A0FBBCB05C63, 0x21874B8B4D2DBC4F,
0x1BDEA12E35F6A8C9, 0x53C065C6C8E63528, 0xE34A1D250E7A8D6B, 0xD6B04D3B7651DD7E,
0x5E90277E7CB39E2D, 0x2C046F22062DC67D, 0xB10BB459132D0A26, 0x3FA9DDFB67E2F199,
0x0E09B88E1914F7AF, 0x10E8B35AF3EEAB37, 0x9EEDECA8E272B933, 0xD4C718BC4AE8AE5F,
0x81536D601170FC20, 0x91B534F885818A06, 0xEC8177F83F900978, 0x190E714FADA5156E,
0xB592BF39B0364963, 0x89C350C893AE7DC1, 0xAC042E70F8B383F2, 0xB49B52E587A1EE60,
0xFB152FE3FF26DA89, 0x3E666E6F69AE2C15, 0x3B544EBE544C19F9, 0xE805A1E290CF2456,
0x24B33C9D7ED25117, 0xE74733427B72F0C1, 0x0A804D18B7097475, 0x57E3306D881EDB4F,
0x4AE7D6A36EB5DBCB, 0x2D8D5432157064C8, 0xD1E649DE1E7F268B, 0x8A328A1CEDFE552C,
0x07A3AEC79624C7DA, 0x84547DDC3E203C94, 0x990A98FD5071D263, 0x1A4FF12616EEFC89,
0xF6F7FD1431714200, 0x30C05B1BA332F41C, 0x8D2636B81555A786, 0x46C9FEB55D120902,
0xCCEC0A73B49C9921, 0x4E9D2827355FC492, 0x19EBB029435DCB0F, 0x4659D2B743848A2C,
0x963EF2C96B33BE31, 0x74F85198B05A2E7D, 0x5A0F544DD2B1FB18, 0x03727073C2E134B1,
0xC7F6AA2DE59AEA61, 0x352787BAA0D7C22F, 0x9853EAB63B5E0B35, 0xABBDCDD7ED5C0860,
0xCF05DAF5AC8D77B0, 0x49CAD48CEBF4A71E, 0x7A4C10EC2158C4A6, 0xD9E92AA246BF719E,
0x13AE978D09FE5557, 0x730499AF921549FF, 0x4E4B705B92903BA4, 0xFF577222C14F0A3A,
0x55B6344CF97AAFAE, 0xB862225B055B6960, 0xCAC09AFBDDD2CDB4, 0xDAF8E9829FE96B5F,
0xB5FDFC5D3132C498, 0x310CB380DB6F7503, 0xE87FBB46217A360E, 0x2102AE466EBB1148,
0xF8549E1A3AA5E00D, 0x07A69AFDCC42261A, 0xC4C118BFE78FEAAE, 0xF9F4892ED96BD438,
0x1AF3DBE25D8F45DA, 0xF5B4B0B0D2DEEEB4, 0x962ACEEFA82E1C84, 0x046E3ECAAF453CE9,
0xF05D129681949A4C, 0x964781CE734B3C84, 0x9C2ED44081CE5FBD, 0x522E23F3925E319E,
0x177E00F9FC32F791, 0x2BC60A63A6F3B3F2, 0x222BBFAE61725606, 0x486289DDCC3D6780,
0x7DC7785B8EFDFC80, 0x8AF38731C02BA980, 0x1FAB64EA29A2DDF7, 0xE4D9429322CD065A,
0x9DA058C67844F20C, 0x24C0E332B70019B0, 0x233003B5A6CFE6AD, 0xD586BD01C5C217F6,
0x5E5637885F29BC2B, 0x7EBA726D8C94094B, 0x0A56A5F0BFE39272, 0xD79476A84EE20D06,
0x9E4C1269BAA4BF37, 0x17EFEE45B0DEE640, 0x1D95B0A5FCF90BC6, 0x93CBE0B699C2585D,
0x65FA4F227A2B6D79, 0xD5F9E858292504D5, 0xC2B5A03F71471A6F, 0x59300222B4561E00,
0xCE2F8642CA0712DC, 0x7CA9723FBB2E8988, 0x2785338347F2BA08, 0xC61BB3A141E50E8C,
0x150F361DAB9DEC26, 0x9F6A419D382595F4, 0x64A53DC924FE7AC9, 0x142DE49FFF7A7C3D,
0x0C335248857FA9E7, 0x0A9C32D5EAE45305, 0xE6C42178C4BBB92E, 0x71F1CE2490D20B07,
0xF1BCC3D275AFE51A, 0xE728E8C83C334074, 0x96FBF83A12884624, 0x81A1549FD6573DA5,
0x5FA7867CAF35E149, 0x56986E2EF3ED091B, 0x917F1DD5F8886C61, 0xD20D8C88C8FFE65F,
0x31D71DCE64B2C310, 0xF165B587DF898190, 0xA57E6339DD2CF3A0, 0x1EF6E6DBB1961EC9,
0x70CC73D90BC26E24, 0xE21A6B35DF0C3AD7, 0x003A93D8B2806962, 0x1C99DED33CB890A1,
0xCF3145DE0ADD4289, 0xD0E4427A5514FB72, 0x77C621CC9FB3A483, 0x67A34DAC4356550B,
0xF8D626AAAF278509
]
class ZobristHasher:
def __init__(self, array: List[int]) -> None:
assert len(array) >= 781
self.array = array
def hash_board(self, board: chess.BaseBoard) -> int:
zobrist_hash = 0
for pivot, squares in enumerate(board.occupied_co):
for square in chess.scan_reversed(squares):
piece_index = (typing.cast(chess.PieceType, board.piece_type_at(square)) - 1) * 2 + pivot
zobrist_hash ^= self.array[64 * piece_index + square]
return zobrist_hash
def hash_castling(self, board: chess.Board) -> int:
zobrist_hash = 0
# Hash in the castling flags.
if board.has_kingside_castling_rights(chess.WHITE):
zobrist_hash ^= self.array[768]
if board.has_queenside_castling_rights(chess.WHITE):
zobrist_hash ^= self.array[768 + 1]
if board.has_kingside_castling_rights(chess.BLACK):
zobrist_hash ^= self.array[768 + 2]
if board.has_queenside_castling_rights(chess.BLACK):
zobrist_hash ^= self.array[768 + 3]
return zobrist_hash
def hash_ep_square(self, board: chess.Board) -> int:
# Hash in the en passant file.
if board.ep_square:
# But only if there's actually a pawn ready to capture it. Legality
# of the potential capture is irrelevant.
if board.turn == chess.WHITE:
ep_mask = chess.shift_down(chess.BB_SQUARES[board.ep_square])
else:
ep_mask = chess.shift_up(chess.BB_SQUARES[board.ep_square])
ep_mask = chess.shift_left(ep_mask) | chess.shift_right(ep_mask)
if ep_mask & board.pawns & board.occupied_co[board.turn]:
return self.array[772 + chess.square_file(board.ep_square)]
return 0
def hash_turn(self, board: chess.Board) -> int:
# Hash in the turn.
return self.array[780] if board.turn == chess.WHITE else 0
def __call__(self, board: chess.Board) -> int:
return (self.hash_board(board) ^ self.hash_castling(board) ^
self.hash_ep_square(board) ^ self.hash_turn(board))
[docs]
def zobrist_hash(board: chess.Board, *, _hasher: Callable[[chess.Board], int] = ZobristHasher(POLYGLOT_RANDOM_ARRAY)) -> int:
"""
Calculates the Polyglot Zobrist hash of the position.
A Zobrist hash is an XOR of pseudo-random values picked from
an array. Which values are picked is decided by features of the
position, such as piece positions, castling rights and en passant
squares.
"""
return _hasher(board)
[docs]
class Entry(NamedTuple):
"""An entry from a Polyglot opening book."""
key: int
"""The Zobrist hash of the position."""
raw_move: int
"""
The raw binary representation of the move. Use
:data:`~chess.polyglot.Entry.move` instead.
"""
weight: int
"""An integer value that can be used as the weight for this entry."""
learn: int
"""Another integer value that can be used for extra information."""
move: chess.Move
"""The :class:`~chess.Move`."""
class _EmptyMmap(bytearray):
def size(self) -> int:
return 0
def close(self) -> None:
pass
def madvise(self, option: int) -> None:
pass
def _randint(rng: Optional[random.Random], a: int, b: int) -> int:
return random.randint(a, b) if rng is None else rng.randint(a, b)
[docs]
class MemoryMappedReader:
"""Maps a Polyglot opening book to memory."""
def __init__(self, filename: StrOrBytesPath) -> None:
fd = os.open(filename, os.O_RDONLY | getattr(os, "O_BINARY", 0))
try:
self.mmap: Union[mmap.mmap, _EmptyMmap] = mmap.mmap(fd, 0, access=mmap.ACCESS_READ)
except (ValueError, OSError):
self.mmap = _EmptyMmap() # Workaround for empty opening books.
finally:
os.close(fd)
if self.mmap.size() % ENTRY_STRUCT.size != 0:
raise IOError(f"invalid file size: ensure {filename!r} is a valid polyglot opening book")
try:
# Unix
self.mmap.madvise(mmap.MADV_RANDOM)
except AttributeError:
pass
def __enter__(self) -> MemoryMappedReader:
return self
def __exit__(self, exc_type: Optional[Type[BaseException]], exc_value: Optional[BaseException], traceback: Optional[TracebackType]) -> None:
return self.close()
def __len__(self) -> int:
return self.mmap.size() // ENTRY_STRUCT.size
def __getitem__(self, index: int) -> Entry:
if index < 0:
index = len(self) + index
try:
key, raw_move, weight, learn = ENTRY_STRUCT.unpack_from(self.mmap, index * ENTRY_STRUCT.size)
except struct.error:
raise IndexError()
# Extract source and target square.
to_square = raw_move & 0x3f
from_square = (raw_move >> 6) & 0x3f
# Extract the promotion type.
promotion_part = (raw_move >> 12) & 0x7
promotion = promotion_part + 1 if promotion_part else None
# Piece drop.
if from_square == to_square:
promotion, drop = None, promotion
else:
drop = None
# Entry with move (not normalized).
move = chess.Move(from_square, to_square, promotion, drop)
return Entry(key, raw_move, weight, learn, move)
def __iter__(self) -> Iterator[Entry]:
for i in range(len(self)):
yield self[i]
def bisect_key_left(self, key: int) -> int:
lo = 0
hi = len(self)
while lo < hi:
mid = (lo + hi) // 2
mid_key, _, _, _ = ENTRY_STRUCT.unpack_from(self.mmap, mid * ENTRY_STRUCT.size)
if mid_key < key:
lo = mid + 1
else:
hi = mid
return lo
def __contains__(self, entry: Entry) -> bool:
return any(current == entry for current in self.find_all(entry.key, minimum_weight=entry.weight))
[docs]
def find_all(self, board: Union[chess.Board, int], *, minimum_weight: int = 1, exclude_moves: Container[chess.Move] = []) -> Iterator[Entry]:
"""Seeks a specific position and yields corresponding entries."""
try:
key = int(board) # type: ignore
context: Optional[chess.Board] = None
except (TypeError, ValueError):
context = typing.cast(chess.Board, board)
key = zobrist_hash(context)
i = self.bisect_key_left(key)
size = len(self)
while i < size:
entry = self[i]
i += 1
if entry.key != key:
break
if entry.weight < minimum_weight:
continue
if context:
move = context._from_chess960(context.chess960, entry.move.from_square, entry.move.to_square, entry.move.promotion, entry.move.drop)
entry = Entry(entry.key, entry.raw_move, entry.weight, entry.learn, move)
if exclude_moves and entry.move in exclude_moves:
continue
if context and not context.is_legal(entry.move):
continue
yield entry
[docs]
def find(self, board: Union[chess.Board, int], *, minimum_weight: int = 1, exclude_moves: Container[chess.Move] = []) -> Entry:
"""
Finds the main entry for the given position or Zobrist hash.
The main entry is the (first) entry with the highest weight.
By default, entries with weight ``0`` are excluded. This is a common
way to delete entries from an opening book without compacting it. Pass
*minimum_weight* ``0`` to select all entries.
:raises: :exc:`IndexError` if no entries are found. Use
:func:`~chess.polyglot.MemoryMappedReader.get()` if you prefer to
get ``None`` instead of an exception.
"""
try:
return max(self.find_all(board, minimum_weight=minimum_weight, exclude_moves=exclude_moves), key=lambda entry: entry.weight)
except ValueError:
raise IndexError()
def get(self, board: Union[chess.Board, int], default: Optional[Entry] = None, *, minimum_weight: int = 1, exclude_moves: Container[chess.Move] = []) -> Optional[Entry]:
try:
return self.find(board, minimum_weight=minimum_weight, exclude_moves=exclude_moves)
except IndexError:
return default
[docs]
def choice(self, board: Union[chess.Board, int], *, minimum_weight: int = 1, exclude_moves: Container[chess.Move] = [], random: Optional[random.Random] = None) -> Entry:
"""
Uniformly selects a random entry for the given position.
:raises: :exc:`IndexError` if no entries are found.
"""
chosen_entry = None
for i, entry in enumerate(self.find_all(board, minimum_weight=minimum_weight, exclude_moves=exclude_moves)):
if chosen_entry is None or _randint(random, 0, i) == i:
chosen_entry = entry
if chosen_entry is None:
raise IndexError()
return chosen_entry
[docs]
def weighted_choice(self, board: Union[chess.Board, int], *, exclude_moves: Container[chess.Move] = [], random: Optional[random.Random] = None) -> Entry:
"""
Selects a random entry for the given position, distributed by the
weights of the entries.
:raises: :exc:`IndexError` if no entries are found.
"""
total_weights = sum(entry.weight for entry in self.find_all(board, exclude_moves=exclude_moves))
if not total_weights:
raise IndexError()
choice = _randint(random, 0, total_weights - 1)
current_sum = 0
for entry in self.find_all(board, exclude_moves=exclude_moves):
current_sum += entry.weight
if current_sum > choice:
return entry
assert False
[docs]
def close(self) -> None:
"""Closes the reader."""
self.mmap.close()
[docs]
def open_reader(path: StrOrBytesPath) -> MemoryMappedReader:
"""
Creates a reader for the file at the given path.
The following example opens a book to find all entries for the start
position:
>>> import chess
>>> import chess.polyglot
>>>
>>> board = chess.Board()
>>>
>>> with chess.polyglot.open_reader("data/polyglot/performance.bin") as reader:
... for entry in reader.find_all(board):
... print(entry.move, entry.weight, entry.learn)
e2e4 1 0
d2d4 1 0
c2c4 1 0
"""
return MemoryMappedReader(path)