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SplitPext.hpp
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SplitPext.hpp
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#pragma once
#include <cstdint>
#include <immintrin.h>
#include <bit>
//Translation from C# into C++20 07.04.2023 - daniel infuehr
//Updates from talkchess discussion 22.07.2023:
//Mike Sherwin: Okay thanks I remember now. However, using one array with an offset for the other line I have shown to be slower than using two arrays. So the C# version that was faster could be faster still.
//And the C++ version never got a test because of a bug. Could someone please do a proper test of this.
//Martin Novak compiled into C++ code.
//History of this algo:
//Multiple people (Daniel Infuehr 2020, Thomas Jahn 2022) independendly had the same idea of using pext on each ray (not 2 at a time) to densify the resulting memory.
//Mike Sherwin had the idea to expand this idea with Split Index kindergarten horizontal.
namespace Chess_Lookup::SplitPext {
constexpr static std::uint64_t vertical_subset[64][64] = {
0x0101010101010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000001010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000101010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000001010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000010101010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000001010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000101010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000001010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0001010101010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000001010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000101010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000001010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000010101010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000001010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000101010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull, 0x0000000001010100ull, 0x0000000000000100ull, 0x0000000000010100ull, 0x0000000000000100ull,
0x0202020202020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000002020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000202020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000002020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000020202020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000002020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000202020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000002020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0002020202020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000002020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000202020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000002020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000020202020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000002020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000202020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull, 0x0000000002020200ull, 0x0000000000000200ull, 0x0000000000020200ull, 0x0000000000000200ull,
0x0404040404040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000004040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000404040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000004040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000040404040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000004040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000404040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000004040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0004040404040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000004040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000404040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000004040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000040404040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000004040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000404040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull, 0x0000000004040400ull, 0x0000000000000400ull, 0x0000000000040400ull, 0x0000000000000400ull,
0x0808080808080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000008080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000808080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000008080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000080808080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000008080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000808080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000008080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0008080808080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000008080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000808080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000008080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000080808080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000008080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000808080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull, 0x0000000008080800ull, 0x0000000000000800ull, 0x0000000000080800ull, 0x0000000000000800ull,
0x1010101010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000000010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000001010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000000010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000101010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000000010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000001010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000000010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0010101010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000000010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000001010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000000010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000101010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000000010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000001010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull, 0x0000000010101000ull, 0x0000000000001000ull, 0x0000000000101000ull, 0x0000000000001000ull,
0x2020202020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000000020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000002020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000000020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000202020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000000020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000002020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000000020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0020202020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000000020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000002020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000000020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000202020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000000020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000002020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull, 0x0000000020202000ull, 0x0000000000002000ull, 0x0000000000202000ull, 0x0000000000002000ull,
0x4040404040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000000040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000004040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000000040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000404040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000000040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000004040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000000040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0040404040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000000040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000004040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000000040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000404040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000000040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000004040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull, 0x0000000040404000ull, 0x0000000000004000ull, 0x0000000000404000ull, 0x0000000000004000ull,
0x8080808080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000000080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000008080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000000080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000808080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000000080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000008080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000000080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0080808080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000000080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000008080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000000080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000808080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000000080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000008080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull, 0x0000000080808000ull, 0x0000000000008000ull, 0x0000000000808000ull, 0x0000000000008000ull,
0x0101010101010001ull, 0x0101010101010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000001010001ull, 0x0000000001010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000101010001ull, 0x0000000101010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000001010001ull, 0x0000000001010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000010101010001ull, 0x0000010101010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000001010001ull, 0x0000000001010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000101010001ull, 0x0000000101010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000001010001ull, 0x0000000001010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0001010101010001ull, 0x0001010101010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000001010001ull, 0x0000000001010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000101010001ull, 0x0000000101010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000001010001ull, 0x0000000001010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000010101010001ull, 0x0000010101010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000001010001ull, 0x0000000001010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000101010001ull, 0x0000000101010001ull, 0x0000000000010001ull, 0x0000000000010001ull, 0x0000000001010001ull, 0x0000000001010001ull, 0x0000000000010001ull, 0x0000000000010001ull,
0x0202020202020002ull, 0x0202020202020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000002020002ull, 0x0000000002020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000202020002ull, 0x0000000202020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000002020002ull, 0x0000000002020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000020202020002ull, 0x0000020202020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000002020002ull, 0x0000000002020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000202020002ull, 0x0000000202020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000002020002ull, 0x0000000002020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0002020202020002ull, 0x0002020202020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000002020002ull, 0x0000000002020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000202020002ull, 0x0000000202020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000002020002ull, 0x0000000002020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000020202020002ull, 0x0000020202020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000002020002ull, 0x0000000002020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000202020002ull, 0x0000000202020002ull, 0x0000000000020002ull, 0x0000000000020002ull, 0x0000000002020002ull, 0x0000000002020002ull, 0x0000000000020002ull, 0x0000000000020002ull,
0x0404040404040004ull, 0x0404040404040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000004040004ull, 0x0000000004040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000404040004ull, 0x0000000404040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000004040004ull, 0x0000000004040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000040404040004ull, 0x0000040404040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000004040004ull, 0x0000000004040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000404040004ull, 0x0000000404040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000004040004ull, 0x0000000004040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0004040404040004ull, 0x0004040404040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000004040004ull, 0x0000000004040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000404040004ull, 0x0000000404040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000004040004ull, 0x0000000004040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000040404040004ull, 0x0000040404040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000004040004ull, 0x0000000004040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000404040004ull, 0x0000000404040004ull, 0x0000000000040004ull, 0x0000000000040004ull, 0x0000000004040004ull, 0x0000000004040004ull, 0x0000000000040004ull, 0x0000000000040004ull,
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0x1000101010101010ull, 0x1000101010101000ull, 0x1000101010100000ull, 0x1000101010100000ull, 0x1000101010000000ull, 0x1000101010000000ull, 0x1000101010000000ull, 0x1000101010000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000101010101010ull, 0x1000101010101000ull, 0x1000101010100000ull, 0x1000101010100000ull, 0x1000101010000000ull, 0x1000101010000000ull, 0x1000101010000000ull, 0x1000101010000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000101000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull, 0x1000100000000000ull,
0x2000202020202020ull, 0x2000202020202000ull, 0x2000202020200000ull, 0x2000202020200000ull, 0x2000202020000000ull, 0x2000202020000000ull, 0x2000202020000000ull, 0x2000202020000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000202020202020ull, 0x2000202020202000ull, 0x2000202020200000ull, 0x2000202020200000ull, 0x2000202020000000ull, 0x2000202020000000ull, 0x2000202020000000ull, 0x2000202020000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000202000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull, 0x2000200000000000ull,
0x4000404040404040ull, 0x4000404040404000ull, 0x4000404040400000ull, 0x4000404040400000ull, 0x4000404040000000ull, 0x4000404040000000ull, 0x4000404040000000ull, 0x4000404040000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000404040404040ull, 0x4000404040404000ull, 0x4000404040400000ull, 0x4000404040400000ull, 0x4000404040000000ull, 0x4000404040000000ull, 0x4000404040000000ull, 0x4000404040000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000404000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull, 0x4000400000000000ull,
0x8000808080808080ull, 0x8000808080808000ull, 0x8000808080800000ull, 0x8000808080800000ull, 0x8000808080000000ull, 0x8000808080000000ull, 0x8000808080000000ull, 0x8000808080000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000808080808080ull, 0x8000808080808000ull, 0x8000808080800000ull, 0x8000808080800000ull, 0x8000808080000000ull, 0x8000808080000000ull, 0x8000808080000000ull, 0x8000808080000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000808000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull, 0x8000800000000000ull,
0x0001010101010101ull, 0x0001010101010100ull, 0x0001010101010000ull, 0x0001010101010000ull, 0x0001010101000000ull, 0x0001010101000000ull, 0x0001010101000000ull, 0x0001010101000000ull, 0x0001010100000000ull, 0x0001010100000000ull, 0x0001010100000000ull, 0x0001010100000000ull, 0x0001010100000000ull, 0x0001010100000000ull, 0x0001010100000000ull, 0x0001010100000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001010000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull,
0x0002020202020202ull, 0x0002020202020200ull, 0x0002020202020000ull, 0x0002020202020000ull, 0x0002020202000000ull, 0x0002020202000000ull, 0x0002020202000000ull, 0x0002020202000000ull, 0x0002020200000000ull, 0x0002020200000000ull, 0x0002020200000000ull, 0x0002020200000000ull, 0x0002020200000000ull, 0x0002020200000000ull, 0x0002020200000000ull, 0x0002020200000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002020000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull,
0x0004040404040404ull, 0x0004040404040400ull, 0x0004040404040000ull, 0x0004040404040000ull, 0x0004040404000000ull, 0x0004040404000000ull, 0x0004040404000000ull, 0x0004040404000000ull, 0x0004040400000000ull, 0x0004040400000000ull, 0x0004040400000000ull, 0x0004040400000000ull, 0x0004040400000000ull, 0x0004040400000000ull, 0x0004040400000000ull, 0x0004040400000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004040000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull,
0x0008080808080808ull, 0x0008080808080800ull, 0x0008080808080000ull, 0x0008080808080000ull, 0x0008080808000000ull, 0x0008080808000000ull, 0x0008080808000000ull, 0x0008080808000000ull, 0x0008080800000000ull, 0x0008080800000000ull, 0x0008080800000000ull, 0x0008080800000000ull, 0x0008080800000000ull, 0x0008080800000000ull, 0x0008080800000000ull, 0x0008080800000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008080000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull,
0x0010101010101010ull, 0x0010101010101000ull, 0x0010101010100000ull, 0x0010101010100000ull, 0x0010101010000000ull, 0x0010101010000000ull, 0x0010101010000000ull, 0x0010101010000000ull, 0x0010101000000000ull, 0x0010101000000000ull, 0x0010101000000000ull, 0x0010101000000000ull, 0x0010101000000000ull, 0x0010101000000000ull, 0x0010101000000000ull, 0x0010101000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010100000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull,
0x0020202020202020ull, 0x0020202020202000ull, 0x0020202020200000ull, 0x0020202020200000ull, 0x0020202020000000ull, 0x0020202020000000ull, 0x0020202020000000ull, 0x0020202020000000ull, 0x0020202000000000ull, 0x0020202000000000ull, 0x0020202000000000ull, 0x0020202000000000ull, 0x0020202000000000ull, 0x0020202000000000ull, 0x0020202000000000ull, 0x0020202000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020200000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull,
0x0040404040404040ull, 0x0040404040404000ull, 0x0040404040400000ull, 0x0040404040400000ull, 0x0040404040000000ull, 0x0040404040000000ull, 0x0040404040000000ull, 0x0040404040000000ull, 0x0040404000000000ull, 0x0040404000000000ull, 0x0040404000000000ull, 0x0040404000000000ull, 0x0040404000000000ull, 0x0040404000000000ull, 0x0040404000000000ull, 0x0040404000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040400000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull,
0x0080808080808080ull, 0x0080808080808000ull, 0x0080808080800000ull, 0x0080808080800000ull, 0x0080808080000000ull, 0x0080808080000000ull, 0x0080808080000000ull, 0x0080808080000000ull, 0x0080808000000000ull, 0x0080808000000000ull, 0x0080808000000000ull, 0x0080808000000000ull, 0x0080808000000000ull, 0x0080808000000000ull, 0x0080808000000000ull, 0x0080808000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080800000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull,
};
constexpr static std::uint64_t horizontal_subset[64][64] = {
0x00000000000000feull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000000eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000001eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000000eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000003eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000000eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000001eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000000eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000007eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000000eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000001eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000000eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000003eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000000eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000001eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull, 0x000000000000000eull, 0x0000000000000002ull, 0x0000000000000006ull, 0x0000000000000002ull,
0x00000000000000fdull, 0x00000000000000fdull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000000dull, 0x000000000000000dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000001dull, 0x000000000000001dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000000dull, 0x000000000000000dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000003dull, 0x000000000000003dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000000dull, 0x000000000000000dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000001dull, 0x000000000000001dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000000dull, 0x000000000000000dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000007dull, 0x000000000000007dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000000dull, 0x000000000000000dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000001dull, 0x000000000000001dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000000dull, 0x000000000000000dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000003dull, 0x000000000000003dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000000dull, 0x000000000000000dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000001dull, 0x000000000000001dull, 0x0000000000000005ull, 0x0000000000000005ull, 0x000000000000000dull, 0x000000000000000dull, 0x0000000000000005ull, 0x0000000000000005ull,
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0xfe00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x0e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x1e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x0e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x3e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x0e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x1e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x0e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x7e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x0e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x1e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x0e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x3e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x0e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x1e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull, 0x0e00000000000000ull, 0x0200000000000000ull, 0x0600000000000000ull, 0x0200000000000000ull,
0xfd00000000000000ull, 0xfd00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x0d00000000000000ull, 0x0d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x1d00000000000000ull, 0x1d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x0d00000000000000ull, 0x0d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x3d00000000000000ull, 0x3d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x0d00000000000000ull, 0x0d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x1d00000000000000ull, 0x1d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x0d00000000000000ull, 0x0d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x7d00000000000000ull, 0x7d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x0d00000000000000ull, 0x0d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x1d00000000000000ull, 0x1d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x0d00000000000000ull, 0x0d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x3d00000000000000ull, 0x3d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x0d00000000000000ull, 0x0d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x1d00000000000000ull, 0x1d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull, 0x0d00000000000000ull, 0x0d00000000000000ull, 0x0500000000000000ull, 0x0500000000000000ull,
0xfb00000000000000ull, 0xfa00000000000000ull, 0xfb00000000000000ull, 0xfa00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x1b00000000000000ull, 0x1a00000000000000ull, 0x1b00000000000000ull, 0x1a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x3b00000000000000ull, 0x3a00000000000000ull, 0x3b00000000000000ull, 0x3a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x1b00000000000000ull, 0x1a00000000000000ull, 0x1b00000000000000ull, 0x1a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x7b00000000000000ull, 0x7a00000000000000ull, 0x7b00000000000000ull, 0x7a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x1b00000000000000ull, 0x1a00000000000000ull, 0x1b00000000000000ull, 0x1a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x3b00000000000000ull, 0x3a00000000000000ull, 0x3b00000000000000ull, 0x3a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x1b00000000000000ull, 0x1a00000000000000ull, 0x1b00000000000000ull, 0x1a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull, 0x0b00000000000000ull, 0x0a00000000000000ull,
0xf700000000000000ull, 0xf600000000000000ull, 0xf400000000000000ull, 0xf400000000000000ull, 0xf700000000000000ull, 0xf600000000000000ull, 0xf400000000000000ull, 0xf400000000000000ull, 0x1700000000000000ull, 0x1600000000000000ull, 0x1400000000000000ull, 0x1400000000000000ull, 0x1700000000000000ull, 0x1600000000000000ull, 0x1400000000000000ull, 0x1400000000000000ull, 0x3700000000000000ull, 0x3600000000000000ull, 0x3400000000000000ull, 0x3400000000000000ull, 0x3700000000000000ull, 0x3600000000000000ull, 0x3400000000000000ull, 0x3400000000000000ull, 0x1700000000000000ull, 0x1600000000000000ull, 0x1400000000000000ull, 0x1400000000000000ull, 0x1700000000000000ull, 0x1600000000000000ull, 0x1400000000000000ull, 0x1400000000000000ull, 0x7700000000000000ull, 0x7600000000000000ull, 0x7400000000000000ull, 0x7400000000000000ull, 0x7700000000000000ull, 0x7600000000000000ull, 0x7400000000000000ull, 0x7400000000000000ull, 0x1700000000000000ull, 0x1600000000000000ull, 0x1400000000000000ull, 0x1400000000000000ull, 0x1700000000000000ull, 0x1600000000000000ull, 0x1400000000000000ull, 0x1400000000000000ull, 0x3700000000000000ull, 0x3600000000000000ull, 0x3400000000000000ull, 0x3400000000000000ull, 0x3700000000000000ull, 0x3600000000000000ull, 0x3400000000000000ull, 0x3400000000000000ull, 0x1700000000000000ull, 0x1600000000000000ull, 0x1400000000000000ull, 0x1400000000000000ull, 0x1700000000000000ull, 0x1600000000000000ull, 0x1400000000000000ull, 0x1400000000000000ull,
0xef00000000000000ull, 0xee00000000000000ull, 0xec00000000000000ull, 0xec00000000000000ull, 0xe800000000000000ull, 0xe800000000000000ull, 0xe800000000000000ull, 0xe800000000000000ull, 0xef00000000000000ull, 0xee00000000000000ull, 0xec00000000000000ull, 0xec00000000000000ull, 0xe800000000000000ull, 0xe800000000000000ull, 0xe800000000000000ull, 0xe800000000000000ull, 0x2f00000000000000ull, 0x2e00000000000000ull, 0x2c00000000000000ull, 0x2c00000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2f00000000000000ull, 0x2e00000000000000ull, 0x2c00000000000000ull, 0x2c00000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x6f00000000000000ull, 0x6e00000000000000ull, 0x6c00000000000000ull, 0x6c00000000000000ull, 0x6800000000000000ull, 0x6800000000000000ull, 0x6800000000000000ull, 0x6800000000000000ull, 0x6f00000000000000ull, 0x6e00000000000000ull, 0x6c00000000000000ull, 0x6c00000000000000ull, 0x6800000000000000ull, 0x6800000000000000ull, 0x6800000000000000ull, 0x6800000000000000ull, 0x2f00000000000000ull, 0x2e00000000000000ull, 0x2c00000000000000ull, 0x2c00000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2f00000000000000ull, 0x2e00000000000000ull, 0x2c00000000000000ull, 0x2c00000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull, 0x2800000000000000ull,
0xdf00000000000000ull, 0xde00000000000000ull, 0xdc00000000000000ull, 0xdc00000000000000ull, 0xd800000000000000ull, 0xd800000000000000ull, 0xd800000000000000ull, 0xd800000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xdf00000000000000ull, 0xde00000000000000ull, 0xdc00000000000000ull, 0xdc00000000000000ull, 0xd800000000000000ull, 0xd800000000000000ull, 0xd800000000000000ull, 0xd800000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0xd000000000000000ull, 0x5f00000000000000ull, 0x5e00000000000000ull, 0x5c00000000000000ull, 0x5c00000000000000ull, 0x5800000000000000ull, 0x5800000000000000ull, 0x5800000000000000ull, 0x5800000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5f00000000000000ull, 0x5e00000000000000ull, 0x5c00000000000000ull, 0x5c00000000000000ull, 0x5800000000000000ull, 0x5800000000000000ull, 0x5800000000000000ull, 0x5800000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull, 0x5000000000000000ull,
0xbf00000000000000ull, 0xbe00000000000000ull, 0xbc00000000000000ull, 0xbc00000000000000ull, 0xb800000000000000ull, 0xb800000000000000ull, 0xb800000000000000ull, 0xb800000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xbf00000000000000ull, 0xbe00000000000000ull, 0xbc00000000000000ull, 0xbc00000000000000ull, 0xb800000000000000ull, 0xb800000000000000ull, 0xb800000000000000ull, 0xb800000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xb000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull, 0xa000000000000000ull,
0x7f00000000000000ull, 0x7e00000000000000ull, 0x7c00000000000000ull, 0x7c00000000000000ull, 0x7800000000000000ull, 0x7800000000000000ull, 0x7800000000000000ull, 0x7800000000000000ull, 0x7000000000000000ull, 0x7000000000000000ull, 0x7000000000000000ull, 0x7000000000000000ull, 0x7000000000000000ull, 0x7000000000000000ull, 0x7000000000000000ull, 0x7000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x6000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull, 0x4000000000000000ull,
};
constexpr static std::uint64_t diagonal_subset[64][64] = {
0x8040201008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000000008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000001008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000000008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000201008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000000008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000001008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000000008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0040201008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000000008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000001008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000000008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000201008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000000008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000001008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull, 0x0000000008040200ull, 0x0000000000000200ull, 0x0000000000040200ull, 0x0000000000000200ull,
0x0080402010080400ull, 0x0000000000000400ull, 0x0000000000080400ull, 0x0000000000000400ull, 0x0000000010080400ull, 0x0000000000000400ull, 0x0000000000080400ull, 0x0000000000000400ull, 0x0000002010080400ull, 0x0000000000000400ull, 0x0000000000080400ull, 0x0000000000000400ull, 0x0000000010080400ull, 0x0000000000000400ull, 0x0000000000080400ull, 0x0000000000000400ull, 0x0000402010080400ull, 0x0000000000000400ull, 0x0000000000080400ull, 0x0000000000000400ull, 0x0000000010080400ull, 0x0000000000000400ull, 0x0000000000080400ull, 0x0000000000000400ull, 0x0000002010080400ull, 0x0000000000000400ull, 0x0000000000080400ull, 0x0000000000000400ull, 0x0000000010080400ull, 0x0000000000000400ull, 0x0000000000080400ull, 0x0000000000000400ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000804020100800ull, 0x0000000000000800ull, 0x0000000000100800ull, 0x0000000000000800ull, 0x0000000020100800ull, 0x0000000000000800ull, 0x0000000000100800ull, 0x0000000000000800ull, 0x0000004020100800ull, 0x0000000000000800ull, 0x0000000000100800ull, 0x0000000000000800ull, 0x0000000020100800ull, 0x0000000000000800ull, 0x0000000000100800ull, 0x0000000000000800ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000008040201000ull, 0x0000000000001000ull, 0x0000000000201000ull, 0x0000000000001000ull, 0x0000000040201000ull, 0x0000000000001000ull, 0x0000000000201000ull, 0x0000000000001000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000000080402000ull, 0x0000000000002000ull, 0x0000000000402000ull, 0x0000000000002000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000000000804000ull, 0x0000000000004000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull, 0x0000000000008000ull,
0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x4020100804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000000804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000100804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000000804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0020100804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000000804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000100804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000000804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x4020100804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000000804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000100804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000000804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0020100804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000000804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000100804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull, 0x0000000804020000ull, 0x0000000000020000ull, 0x0000000004020000ull, 0x0000000000020000ull,
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0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull, 0x0001000000000000ull,
0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull, 0x0002010000000000ull, 0x0002000000000000ull,
0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004020100000000ull, 0x0004020000000000ull, 0x0004000000000000ull, 0x0004000000000000ull,
0x0008040201000000ull, 0x0008040200000000ull, 0x0008040000000000ull, 0x0008040000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008040201000000ull, 0x0008040200000000ull, 0x0008040000000000ull, 0x0008040000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008040201000000ull, 0x0008040200000000ull, 0x0008040000000000ull, 0x0008040000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008040201000000ull, 0x0008040200000000ull, 0x0008040000000000ull, 0x0008040000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008040201000000ull, 0x0008040200000000ull, 0x0008040000000000ull, 0x0008040000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008040201000000ull, 0x0008040200000000ull, 0x0008040000000000ull, 0x0008040000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008040201000000ull, 0x0008040200000000ull, 0x0008040000000000ull, 0x0008040000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008040201000000ull, 0x0008040200000000ull, 0x0008040000000000ull, 0x0008040000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull,
0x0010080402010000ull, 0x0010080402000000ull, 0x0010080400000000ull, 0x0010080400000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010080402010000ull, 0x0010080402000000ull, 0x0010080400000000ull, 0x0010080400000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010080402010000ull, 0x0010080402000000ull, 0x0010080400000000ull, 0x0010080400000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010080402010000ull, 0x0010080402000000ull, 0x0010080400000000ull, 0x0010080400000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010080000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull,
0x0020100804020100ull, 0x0020100804020000ull, 0x0020100804000000ull, 0x0020100804000000ull, 0x0020100800000000ull, 0x0020100800000000ull, 0x0020100800000000ull, 0x0020100800000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020100804020100ull, 0x0020100804020000ull, 0x0020100804000000ull, 0x0020100804000000ull, 0x0020100800000000ull, 0x0020100800000000ull, 0x0020100800000000ull, 0x0020100800000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020100000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020000000000000ull,
0x0040201008040201ull, 0x0040201008040200ull, 0x0040201008040000ull, 0x0040201008040000ull, 0x0040201008000000ull, 0x0040201008000000ull, 0x0040201008000000ull, 0x0040201008000000ull, 0x0040201000000000ull, 0x0040201000000000ull, 0x0040201000000000ull, 0x0040201000000000ull, 0x0040201000000000ull, 0x0040201000000000ull, 0x0040201000000000ull, 0x0040201000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040200000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull, 0x0040000000000000ull,
};
constexpr static std::uint64_t antidiagonal_subset[64][64] = {
0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull, 0x0000000000000100ull,
0x0000000000010200ull, 0x0000000000000200ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000000001020400ull, 0x0000000000000400ull, 0x0000000000020400ull, 0x0000000000000400ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000000102040800ull, 0x0000000000000800ull, 0x0000000000040800ull, 0x0000000000000800ull, 0x0000000002040800ull, 0x0000000000000800ull, 0x0000000000040800ull, 0x0000000000000800ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0000010204081000ull, 0x0000000000001000ull, 0x0000000000081000ull, 0x0000000000001000ull, 0x0000000004081000ull, 0x0000000000001000ull, 0x0000000000081000ull, 0x0000000000001000ull, 0x0000000204081000ull, 0x0000000000001000ull, 0x0000000000081000ull, 0x0000000000001000ull, 0x0000000004081000ull, 0x0000000000001000ull, 0x0000000000081000ull, 0x0000000000001000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0001020408102000ull, 0x0000000000002000ull, 0x0000000000102000ull, 0x0000000000002000ull, 0x0000000008102000ull, 0x0000000000002000ull, 0x0000000000102000ull, 0x0000000000002000ull, 0x0000000408102000ull, 0x0000000000002000ull, 0x0000000000102000ull, 0x0000000000002000ull, 0x0000000008102000ull, 0x0000000000002000ull, 0x0000000000102000ull, 0x0000000000002000ull, 0x0000020408102000ull, 0x0000000000002000ull, 0x0000000000102000ull, 0x0000000000002000ull, 0x0000000008102000ull, 0x0000000000002000ull, 0x0000000000102000ull, 0x0000000000002000ull, 0x0000000408102000ull, 0x0000000000002000ull, 0x0000000000102000ull, 0x0000000000002000ull, 0x0000000008102000ull, 0x0000000000002000ull, 0x0000000000102000ull, 0x0000000000002000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0102040810204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000010204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000810204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000010204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000040810204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000010204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000810204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000010204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0002040810204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000010204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000810204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000010204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000040810204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000010204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000810204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull, 0x0000000010204000ull, 0x0000000000004000ull, 0x0000000000204000ull, 0x0000000000004000ull,
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0x0002040810204080ull, 0x0002040810204000ull, 0x0002040810200000ull, 0x0002040810200000ull, 0x0002040810000000ull, 0x0002040810000000ull, 0x0002040810000000ull, 0x0002040810000000ull, 0x0002040800000000ull, 0x0002040800000000ull, 0x0002040800000000ull, 0x0002040800000000ull, 0x0002040800000000ull, 0x0002040800000000ull, 0x0002040800000000ull, 0x0002040800000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002040000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull, 0x0002000000000000ull,
0x0004081020408000ull, 0x0004081020400000ull, 0x0004081020000000ull, 0x0004081020000000ull, 0x0004081000000000ull, 0x0004081000000000ull, 0x0004081000000000ull, 0x0004081000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004081020408000ull, 0x0004081020400000ull, 0x0004081020000000ull, 0x0004081020000000ull, 0x0004081000000000ull, 0x0004081000000000ull, 0x0004081000000000ull, 0x0004081000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004080000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull, 0x0004000000000000ull,
0x0008102040800000ull, 0x0008102040000000ull, 0x0008102000000000ull, 0x0008102000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008102040800000ull, 0x0008102040000000ull, 0x0008102000000000ull, 0x0008102000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008102040800000ull, 0x0008102040000000ull, 0x0008102000000000ull, 0x0008102000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008102040800000ull, 0x0008102040000000ull, 0x0008102000000000ull, 0x0008102000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008100000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull, 0x0008000000000000ull,
0x0010204080000000ull, 0x0010204000000000ull, 0x0010200000000000ull, 0x0010200000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010204080000000ull, 0x0010204000000000ull, 0x0010200000000000ull, 0x0010200000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010204080000000ull, 0x0010204000000000ull, 0x0010200000000000ull, 0x0010200000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010204080000000ull, 0x0010204000000000ull, 0x0010200000000000ull, 0x0010200000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010204080000000ull, 0x0010204000000000ull, 0x0010200000000000ull, 0x0010200000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010204080000000ull, 0x0010204000000000ull, 0x0010200000000000ull, 0x0010200000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010204080000000ull, 0x0010204000000000ull, 0x0010200000000000ull, 0x0010200000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010204080000000ull, 0x0010204000000000ull, 0x0010200000000000ull, 0x0010200000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull, 0x0010000000000000ull,
0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull, 0x0020408000000000ull, 0x0020400000000000ull, 0x0020000000000000ull, 0x0020000000000000ull,
0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull, 0x0040800000000000ull, 0x0040000000000000ull,
0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull, 0x0080000000000000ull,
0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
};
constexpr static std::uint64_t horizontal_mask[64] = {
0x000000000000007eull, 0x000000000000007eull, 0x000000000000007eull, 0x000000000000007eull, 0x000000000000007eull, 0x000000000000007eull, 0x000000000000007eull, 0x000000000000007eull,
0x0000000000007e00ull, 0x0000000000007e00ull, 0x0000000000007e00ull, 0x0000000000007e00ull, 0x0000000000007e00ull, 0x0000000000007e00ull, 0x0000000000007e00ull, 0x0000000000007e00ull,
0x00000000007e0000ull, 0x00000000007e0000ull, 0x00000000007e0000ull, 0x00000000007e0000ull, 0x00000000007e0000ull, 0x00000000007e0000ull, 0x00000000007e0000ull, 0x00000000007e0000ull,
0x000000007e000000ull, 0x000000007e000000ull, 0x000000007e000000ull, 0x000000007e000000ull, 0x000000007e000000ull, 0x000000007e000000ull, 0x000000007e000000ull, 0x000000007e000000ull,
0x0000007e00000000ull, 0x0000007e00000000ull, 0x0000007e00000000ull, 0x0000007e00000000ull, 0x0000007e00000000ull, 0x0000007e00000000ull, 0x0000007e00000000ull, 0x0000007e00000000ull,
0x00007e0000000000ull, 0x00007e0000000000ull, 0x00007e0000000000ull, 0x00007e0000000000ull, 0x00007e0000000000ull, 0x00007e0000000000ull, 0x00007e0000000000ull, 0x00007e0000000000ull,
0x007e000000000000ull, 0x007e000000000000ull, 0x007e000000000000ull, 0x007e000000000000ull, 0x007e000000000000ull, 0x007e000000000000ull, 0x007e000000000000ull, 0x007e000000000000ull,
0x7e00000000000000ull, 0x7e00000000000000ull, 0x7e00000000000000ull, 0x7e00000000000000ull, 0x7e00000000000000ull, 0x7e00000000000000ull, 0x7e00000000000000ull, 0x7e00000000000000ull,
};
constexpr static std::uint64_t vertical_mask[64]{
0x0001010101010100ull, 0x0002020202020200ull, 0x0004040404040400ull, 0x0008080808080800ull, 0x0010101010101000ull, 0x0020202020202000ull, 0x0040404040404000ull, 0x0080808080808000ull,
0x0001010101010100ull, 0x0002020202020200ull, 0x0004040404040400ull, 0x0008080808080800ull, 0x0010101010101000ull, 0x0020202020202000ull, 0x0040404040404000ull, 0x0080808080808000ull,
0x0001010101010100ull, 0x0002020202020200ull, 0x0004040404040400ull, 0x0008080808080800ull, 0x0010101010101000ull, 0x0020202020202000ull, 0x0040404040404000ull, 0x0080808080808000ull,
0x0001010101010100ull, 0x0002020202020200ull, 0x0004040404040400ull, 0x0008080808080800ull, 0x0010101010101000ull, 0x0020202020202000ull, 0x0040404040404000ull, 0x0080808080808000ull,
0x0001010101010100ull, 0x0002020202020200ull, 0x0004040404040400ull, 0x0008080808080800ull, 0x0010101010101000ull, 0x0020202020202000ull, 0x0040404040404000ull, 0x0080808080808000ull,
0x0001010101010100ull, 0x0002020202020200ull, 0x0004040404040400ull, 0x0008080808080800ull, 0x0010101010101000ull, 0x0020202020202000ull, 0x0040404040404000ull, 0x0080808080808000ull,
0x0001010101010100ull, 0x0002020202020200ull, 0x0004040404040400ull, 0x0008080808080800ull, 0x0010101010101000ull, 0x0020202020202000ull, 0x0040404040404000ull, 0x0080808080808000ull,
0x0001010101010100ull, 0x0002020202020200ull, 0x0004040404040400ull, 0x0008080808080800ull, 0x0010101010101000ull, 0x0020202020202000ull, 0x0040404040404000ull, 0x0080808080808000ull,
};
constexpr static std::uint64_t antidiagonal_mask[64] = {
0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000200ull, 0x0000000000020400ull, 0x0000000002040800ull, 0x0000000204081000ull, 0x0000020408102000ull, 0x0002040810204000ull,
0x0000000000000000ull, 0x0000000000000200ull, 0x0000000000020400ull, 0x0000000002040800ull, 0x0000000204081000ull, 0x0000020408102000ull, 0x0002040810204000ull, 0x0004081020400000ull,
0x0000000000000200ull, 0x0000000000020400ull, 0x0000000002040800ull, 0x0000000204081000ull, 0x0000020408102000ull, 0x0002040810204000ull, 0x0004081020400000ull, 0x0008102040000000ull,
0x0000000000020400ull, 0x0000000002040800ull, 0x0000000204081000ull, 0x0000020408102000ull, 0x0002040810204000ull, 0x0004081020400000ull, 0x0008102040000000ull, 0x0010204000000000ull,
0x0000000002040800ull, 0x0000000204081000ull, 0x0000020408102000ull, 0x0002040810204000ull, 0x0004081020400000ull, 0x0008102040000000ull, 0x0010204000000000ull, 0x0020400000000000ull,
0x0000000204081000ull, 0x0000020408102000ull, 0x0002040810204000ull, 0x0004081020400000ull, 0x0008102040000000ull, 0x0010204000000000ull, 0x0020400000000000ull, 0x0040000000000000ull,
0x0000020408102000ull, 0x0000040810204000ull, 0x0000081020400000ull, 0x0000102040000000ull, 0x0000204000000000ull, 0x0000400000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0002040810204000ull, 0x0004081020400000ull, 0x0008102040000000ull, 0x0010204000000000ull, 0x0020400000000000ull, 0x0040000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull,
};
constexpr static std::uint64_t diagonal_mask[64] = {
0x0040201008040200ull, 0x0000402010080400ull, 0x0000004020100800ull, 0x0000000040201000ull, 0x0000000000402000ull, 0x0000000000004000ull, 0x0000000000000000ull, 0x0000000000000000ull,
0x0020100804020000ull, 0x0040201008040200ull, 0x0000402010080400ull, 0x0000004020100800ull, 0x0000000040201000ull, 0x0000000000402000ull, 0x0000000000004000ull, 0x0000000000000000ull,
0x0010080402000000ull, 0x0020100804020000ull, 0x0040201008040200ull, 0x0000402010080400ull, 0x0000004020100800ull, 0x0000000040201000ull, 0x0000000000402000ull, 0x0000000000004000ull,
0x0008040200000000ull, 0x0010080402000000ull, 0x0020100804020000ull, 0x0040201008040200ull, 0x0000402010080400ull, 0x0000004020100800ull, 0x0000000040201000ull, 0x0000000000402000ull,
0x0004020000000000ull, 0x0008040200000000ull, 0x0010080402000000ull, 0x0020100804020000ull, 0x0040201008040200ull, 0x0000402010080400ull, 0x0000004020100800ull, 0x0000000040201000ull,
0x0002000000000000ull, 0x0004020000000000ull, 0x0008040200000000ull, 0x0010080402000000ull, 0x0020100804020000ull, 0x0040201008040200ull, 0x0000402010080400ull, 0x0000004020100800ull,
0x0000000000000000ull, 0x0002000000000000ull, 0x0004020000000000ull, 0x0008040200000000ull, 0x0010080402000000ull, 0x0020100804020000ull, 0x0040201008040200ull, 0x0000402010080400ull,
0x0000000000000000ull, 0x0000000000000000ull, 0x0002000000000000ull, 0x0004020000000000ull, 0x0008040200000000ull, 0x0010080402000000ull, 0x0020100804020000ull, 0x0040201008040200ull,
};
constexpr static std::uint32_t horizontal_shift_table[64] = {
1, 1, 1, 1, 1, 1, 1, 1,
9, 9, 9, 9, 9, 9, 9, 9,
17, 17, 17, 17, 17, 17, 17, 17,
25, 25, 25, 25, 25, 25, 25, 25,
33, 33, 33, 33, 33, 33, 33, 33,
41, 41, 41, 41, 41, 41, 41, 41,
49, 49, 49, 49, 49, 49, 49, 49,
57, 57, 57, 57, 57, 57, 57, 57,
};
// I currently don't count horizontal_mask into Size because it is currently not used
static constexpr uint64_t Size = (64 * 64 * 4 + 64 * 3) * sizeof(std::uint64_t) + 64 * sizeof(std::uint32_t);
static std::uint64_t rook_horizontal(int square, std::uint64_t occupancy) {
return horizontal_subset[square][(occupancy >> horizontal_shift_table[square]) & 63]; // test confirms horizontal pext is slower
//return horizontal_subset[square][_pext_u64(occupancy, horizontal_mask[square])];
}
static std::uint64_t rook_vertical(int square, std::uint64_t occupancy) {
return vertical_subset[square][_pext_u64(occupancy, vertical_mask[square])];
}
static std::uint64_t bishop_antidiagonal(int square, std::uint64_t occupancy) {
return antidiagonal_subset[square][_pext_u64(occupancy, antidiagonal_mask[square])];
}
static std::uint64_t bishop_diagonal(int square, std::uint64_t occupancy) {
return diagonal_subset[square][_pext_u64(occupancy, diagonal_mask[square])];
}
static std::uint64_t rook(int square, std::uint64_t occupancy) {
return rook_horizontal(square, occupancy) | rook_vertical(square, occupancy);
}
static std::uint64_t bishop(int square, std::uint64_t occupancy) {
return bishop_antidiagonal(square, occupancy) | bishop_diagonal(square, occupancy);
}
static std::uint64_t Queen(int square, std::uint64_t occupancy) {
return bishop(square, occupancy) | rook(square, occupancy);
}
}