cube-hs 0.5.0.0 → 0.5.1.0

raw patch · 8 files changed

+2252/−1794 lines, 8 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• CHANGELOG.md +5/−1
• README.md +4/−1
• cbits/cube_amalg.min.cpp +2210/−1789
• cube-hs.cabal +2/−2
• src/Data/Cube.hs +4/−1
• src/Data/Cube/FFI.hs +6/−0
• src/Data/Cube/Internal.hs +19/−0
• test/Main.hs +2/−0

@@ -1,6 +1,10 @@ # Revision history for cube-hs -0.5.0.0+## 0.5.1.0+- Support for symmetric pruning table & customized table directory+- Upgrade underlying C++ library to v0.5.1++## 0.5.0.0 - Upgrade underlying C++ library to improve performance   ## 0.3.0 -- YYYY-mm-dd

@@ -50,7 +50,10 @@     let scrambledCube = foldl (&>) solvedCube turns     putStrLn $ "Scrambled Cube:     " ++ showCube scrambledCube -    -- 4. Solve the scrambled cube & verify+    -- 4a. build tables (`False` means without symmetry) under "cache" directory +    cubeInit False "cache"  ++    -- 4b. Solve the scrambled cube & verify solution     let solution = unsafeSolveFrom scrambledCube     let restoredCube = applyTurns scrambledCube solution 

@@ -2,1795 +2,2216 @@  * File: cube_amalg.min.cpp  * Project: cube  * Author: coshz <fsinhx@gmail.com>- * Version: v0.5.0- * Date: 2026-10-10- * Homepage: https://github.com/coshz/cube- * License: MIT- *- * Copyright (c) 2026 coshz <fsinhx@gmail.com>. All rights reserved.- */--#include <cstddef>-#include <vector>-#include <array>-#include <algorithm>-#include <utility>-#include <numeric>-#include <stdexcept>-#include <initializer_list>-#include <cassert>-#include <cstdint>-#include <string_view>-#include <set>-#include <filesystem>-#include <type_traits>-#include <limits>-#include <fstream>-#include <ios>-#include <tuple>-#include <cstdlib>-#include <chrono>-#include <optional>-#include <string>-#include <cstring>-#include <regex>-#include <sstream>-#include <stdbool.h>-#include <stdint.h>--namespace cube::math {-using std::size_t;-template<typename VectorLike>-auto decomposite(const VectorLike &xs) -> std::pair<-    std::vector<typename VectorLike::value_type>,-    std::vector<std::vector<typename VectorLike::value_type>>->-{-    using T = typename VectorLike::value_type;-    std::vector<T> fixed;-    std::vector<std::vector<T>> cycles;-    std::vector<bool> visited(xs.size(),false);-    for(int i = 0; i < xs.size(); ++i) {-        if(visited[i]) continue;-        std::vector<T> cycle;-        for(int j = xs[i]; j != i; j = xs[j]) {-            visited[j] = true;-            cycle.push_back(static_cast<T>(j));-        }-        visited[i] = true;-        cycle.push_back(static_cast<T>(i));-        if(cycle.size() > 1) cycles.push_back(cycle);-        else fixed.push_back(cycle[0]);-    }-    std::sort(cycles.begin(), cycles.end(), [](auto &v1, auto &v2){-        return v1.size() > v2.size();-    });-    return std::make_pair(fixed,cycles);-}-constexpr size_t factorial(size_t n)-{-    if(n>=21) throw std::invalid_argument("factorial(n) overflows for n >= 21");-    return n == 0 ? 1 : n * factorial(n-1);-}-constexpr size_t binomial(size_t n, size_t k)-{-    if(n < k)   return 0;-    if(n == k)  return 1;-    size_t r = 1, m = std::min(k, n-k);-    for(size_t i = 1; i <= m; i++) r *= n-i+1;-    for(size_t i = 1; i <= m; i++) r /= i;-    return r;-};-template<typename T, size_t N>-size_t orderOf(const std::array<T,N> &xs)-{-    size_t m = 1;-    auto cs = decomposite(xs);-    for(size_t i = 1; i < cs.size(); i++) { m = std::lcm(m, cs[i].size()); }-    return m;-}-template<typename T, size_t N>-constexpr size_t rankOf(const std::array<T,N> &xs)-{-    size_t r = 0;-    std::array<bool,N> used {false};-    for(size_t i = 0; i < N; i++)-    {-        int cnt = 0;-        for(int j=0; j < xs[i]; j++) if(!used[j]) cnt++;-        r += cnt * factorial(N - i - 1);-        used[xs[i]] = true;-    }-    return r;-}-template<typename T, size_t N>-constexpr std::array<T,N> fromRank(size_t r)-{-    std::array<T,N> A{};-    std::array<bool,N> used {false};-    for(size_t i = 0; i < N; i++)-    {-        size_t f = factorial(N - i - 1);-        size_t cnt = r / f;-        r %= f;-        for(size_t j = 0; j < N; j++)-        {-            if(used[j]) continue;-            if(cnt-- == 0) {-                A[i] = j;-                used[j] = true;-                break;-            }-        }-    }-    return A;-}-template<typename F, typename T, size_t N>-constexpr std::array<T,N+1> nestList(F &&f, T &&x)-{-    std::array<T,N+1> r;-    r[0] = x;-    for(auto i = 1; i <= N; i++) r[i] = f(r[i-1]);-    return r;-}-template<size_t Begin, size_t End, typename T, size_t N>-constexpr auto takeByRange(const std::array<T,N>& xs) -> std::array<T,End-Begin+1>-{-    static_assert(Begin <= End && End < N);-    std::array<T,End-Begin+1> ys;-    std::copy(xs.begin()+Begin,xs.begin()+End+1,ys.begin());-    return ys;-}-template<size_t B, typename Int, size_t N>-constexpr auto fromDigits(const std::array<Int,N> &xs) -> size_t-{-    auto pow = [](size_t base, size_t exp) -> size_t {-        size_t prod = 1;-        for(size_t i = 0; i < exp; i++) prod *= base;-        return prod;-    };-    size_t res = 0;-    for(size_t i = 0; i < N; i++) res += static_cast<size_t>(xs[i]) * pow(B, N-i-1);-    return res;-}-template<size_t B, size_t N, typename Int>-constexpr auto toDigits(size_t i) -> std::array<Int,N>-{-    auto pow = [](size_t base, size_t exp) -> size_t {-        size_t prod = 1;-        for(size_t i = 0; i < exp; i++) prod *= base;-        return prod;-    };-    std::array<Int,N> a {};-    for(size_t k = 0; k < N; k++) {-        size_t z = pow(B, N-1-k);-        a[k] = static_cast<Int>(i / z);-        i = i % z;-    }-    return a;-}-template<size_t N, size_t M>-constexpr auto lexicalOrderFromIndices(const std::array<size_t,M> &X) -> int-{-    static_assert(M<=N);-    int rank = 0;-    for(size_t i = 0; i < M; i++) rank += binomial(N-1-X[i],M-i);-    return rank;-}-template<size_t N, size_t M>-constexpr auto lexicalOrderToIndices(int rank) -> std::array<size_t,M>-{-    static_assert(M<=N);-    std::array<size_t,M> X {};-    size_t n=rank, k=0;-    for(size_t i = 0; i < M; i++) {-        while(binomial(N-1-k,M-i) > n || n >= binomial(N-k,M-i)) k++;-        X[i] = k;-        n -= binomial(N-1-k,M-i);-        k += 1;-    }-    return X;-}-template<size_t N, typename ArrayLike>-constexpr bool isValidPermutation(const ArrayLike& xs)-{-    if(xs.size() != N) return false;-    std::array<bool,N> visited{};-    for(auto i = 0; i < N; ++i) {-        size_t val = static_cast<size_t>(xs[i]);-        if(xs[i] < 0 || xs[i] >= N) return false;-        if(visited[val]) return false;-        visited[val] = true;-    }-    return true;-}-template<typename Array, typename Perm>-constexpr Array backpermute(const Array& src, const Perm& P)-{-    Array out{src};-    for (size_t i = 0; i < P.size(); ++i) { out[i] = src[P[i]]; }-    return out;-}-template<typename Array, typename Perm>-constexpr Array forepermute(const Array& src, const Perm& P)-{-    Array out{src};-    for (size_t i = 0; i < P.size(); ++i) { out[P[i]] = src[i]; }-    return out;-}-}-namespace cube::data {-enum Face       { U1,U2,U3,U4,U5,U6,U7,U8,U9,R1,R2,R3,R4,R5,R6,R7,R8,R9,F1,F2,F3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,D7,D8,D9,L1,L2,L3,L4,L5,L6,L7,L8,L9,B1,B2,B3,B4,B5,B6,B7,B8,B9 };-enum Layer      { U,R,F,D,L,B };-enum TurnMove   { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };-enum Symmetry   { S_URF3,S_F2,S_U4,S_LR2 };-enum ColorIndex { UCol,RCol,FCol,DCol,LCol,BCol,NoCol };-enum Corner     { URF,UFL,ULB,UBR,DFR,DLF,DBL,DRB };-enum Edge       { UR,UF,UL,UB,DR,DF,DL,DB,FR,FL,BL,BR };-struct OrientedCorner   { Corner c; unsigned o; };-struct OrientedEdge     { Edge e;   unsigned o; };-typedef ColorIndex      SingleFace[9];-typedef ColorIndex      CornerColorIndex[8][3];-typedef ColorIndex      EdgeColorIndex[12][2];-typedef ColorIndex      FaceletColor[54];-typedef Face            CentreFacelet[6];-typedef Face            CornerFacelet[8][3];-typedef Face            EdgeFacelet[12][2];-typedef Face            Facelet[54];-typedef OrientedCorner  CornerCubie[8];-typedef OrientedEdge    EdgeCubie[12];-typedef Corner          EdgeNeighbour[12][2];-const CornerColorIndex  CCI = {{UCol,RCol,FCol},{UCol,FCol,LCol},{UCol,LCol,BCol},{UCol,BCol,RCol},{DCol,FCol,RCol},{DCol,LCol,FCol},{DCol,BCol,LCol},{DCol,RCol,BCol}};-const EdgeColorIndex    ECI = {{UCol,RCol},{UCol,FCol},{UCol,LCol},{UCol,BCol},{DCol,RCol},{DCol,FCol}, {DCol,LCol},{DCol,BCol},{FCol,RCol},{FCol,LCol},{BCol,LCol},{BCol,RCol}};-const CentreFacelet     CC  = {U5,R5,F5,D5,L5,B5};-const CornerFacelet     CF  = {{U9,R1,F3},{U7,F1,L3},{U1,L1,B3},{U3,B1,R3},{D3,F9,R7},{D1,L9,F7},{D7,B9,L7},{D9,R9,B7}};-const EdgeFacelet       EF  = {{U6,R2},{U8,F2},{U4,L2},{U2,B2},{D6,R8},{D2,F8}, {D4,L8},{D8,B8},{F6,R4},{F4,L6},{B6,L4},{B4,R6}};-const EdgeNeighbour     EN  = {{URF,UBR},{UFL,URF},{ULB,UFL},{UBR,ULB},{DRB,DFR},{DFR,DLF}, {DLF,DBL},{DBL,DRB},{URF,DFR},{DLF,UFL},{DBL,ULB},{UBR,DRB}};-const Facelet FaceletMove[6] = {-    {U3,U6,U9,U2,U5,U8,U1,U4,U7,F1,F2,F3,R4,R5,R6,R7,R8,R9,L1,L2,L3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,D7,D8,D9,B1,B2,B3,L4,L5,L6,L7,L8,L9,R1,R2,R3,B4,B5,B6,B7,B8,B9},-    {U1,U2,B7,U4,U5,B4,U7,U8,B1,R3,R6,R9,R2,R5,R8,R1,R4,R7,F1,F2,U3,F4,F5,U6,F7,F8,U9,D1,D2,F3,D4,D5,F6,D7,D8,F9,L1,L2,L3,L4,L5,L6,L7,L8,L9,D9,B2,B3,D6,B5,B6,D3,B8,B9},-    {U1,U2,U3,U4,U5,U6,R1,R4,R7,D3,R2,R3,D2,R5,R6,D1,R8,R9,F3,F6,F9,F2,F5,F8,F1,F4,F7,L3,L6,L9,D4,D5,D6,D7,D8,D9,L1,L2,U9,L4,L5,U8,L7,L8,U7,B1,B2,B3,B4,B5,B6,B7,B8,B9},-    {U1,U2,U3,U4,U5,U6,U7,U8,U9,R1,R2,R3,R4,R5,R6,B7,B8,B9,F1,F2,F3,F4,F5,F6,R7,R8,R9,D3,D6,D9,D2,D5,D8,D1,D4,D7,L1,L2,L3,L4,L5,L6,F7,F8,F9,B1,B2,B3,B4,B5,B6,L7,L8,L9},-    {F1,U2,U3,F4,U5,U6,F7,U8,U9,R1,R2,R3,R4,R5,R6,R7,R8,R9,D1,F2,F3,D4,F5,F6,D7,F8,F9,B9,D2,D3,B6,D5,D6,B3,D8,D9,L3,L6,L9,L2,L5,L8,L1,L4,L7,B1,B2,U7,B4,B5,U4,B7,B8,U1},-    {L7,L4,L1,U4,U5,U6,U7,U8,U9,R1,R2,U1,R4,R5,U2,R7,R8,U3,F1,F2,F3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,R9,R6,R3,D7,L2,L3,D8,L5,L6,D9,L8,L9,B3,B6,B9,B2,B5,B8,B1,B4,B7}-};-const Facelet FaceletSym[4] = {-    {R9,R8,R7,R6,R5,R4,R3,R2,R1,F3,F6,F9,F2,F5,F8,F1,F4,F7,U3,U6,U9,U2,U5,U8,U1,U4,U7,L1,L2,L3,L4,L5,L6,L7,L8,L9,B7,B4,B1,B8,B5,B2,B9,B6,B3,D3,D6,D9,D2,D5,D8,D1,D4,D7},-    {D9,D8,D7,D6,D5,D4,D3,D2,D1,L9,L8,L7,L6,L5,L4,L3,L2,L1,F9,F8,F7,F6,F5,F4,F3,F2,F1,U9,U8,U7,U6,U5,U4,U3,U2,U1,R9,R8,R7,R6,R5,R4,R3,R2,R1,B9,B8,B7,B6,B5,B4,B3,B2,B1},-    {U3,U6,U9,U2,U5,U8,U1,U4,U7,F1,F2,F3,F4,F5,F6,F7,F8,F9,L1,L2,L3,L4,L5,L6,L7,L8,L9,D7,D4,D1,D8,D5,D2,D9,D6,D3,B1,B2,B3,B4,B5,B6,B7,B8,B9,R1,R2,R3,R4,R5,R6,R7,R8,R9},-    {U3,U2,U1,U6,U5,U4,U9,U8,U7,L3,L2,L1,L6,L5,L4,L9,L8,L7,F3,F2,F1,F6,F5,F4,F9,F8,F7,D3,D2,D1,D6,D5,D4,D9,D8,D7,R3,R2,R1,R6,R5,R4,R9,R8,R7,B3,B2,B1,B6,B5,B4,B9,B8,B7}-};-const CornerCubie CornerCubieMove[6] = {-    {{UBR,0},{URF,0},{UFL,0},{ULB,0},{DFR,0},{DLF,0},{DBL,0},{DRB,0}},-    {{DFR,2},{UFL,0},{ULB,0},{URF,1},{DRB,1},{DLF,0},{DBL,0},{UBR,2}},-    {{UFL,1},{DLF,2},{ULB,0},{UBR,0},{URF,2},{DFR,1},{DBL,0},{DRB,0}},-    {{URF,0},{UFL,0},{ULB,0},{UBR,0},{DLF,0},{DBL,0},{DRB,0},{DFR,0}},-    {{URF,0},{ULB,1},{DBL,2},{UBR,0},{DFR,0},{UFL,2},{DLF,1},{DRB,0}},-    {{URF,0},{UFL,0},{UBR,1},{DRB,2},{DFR,0},{DLF,0},{ULB,2},{DBL,1}}-};-const EdgeCubie EdgeCubieMove[6] = {-    {{UB,0},{UR,0},{UF,0},{UL,0},{DR,0},{DF,0},{DL,0},{DB,0},{FR,0},{FL,0},{BL,0},{BR,0}},-    {{FR,0},{UF,0},{UL,0},{UB,0},{BR,0},{DF,0},{DL,0},{DB,0},{DR,0},{FL,0},{BL,0},{UR,0}},-    {{UR,0},{FL,1},{UL,0},{UB,0},{DR,0},{FR,1},{DL,0},{DB,0},{UF,1},{DF,1},{BL,0},{BR,0}},-    {{UR,0},{UF,0},{UL,0},{UB,0},{DF,0},{DL,0},{DB,0},{DR,0},{FR,0},{FL,0},{BL,0},{BR,0}},-    {{UR,0},{UF,0},{BL,0},{UB,0},{DR,0},{DF,0},{FL,0},{DB,0},{FR,0},{UL,0},{DL,0},{BR,0}},-    {{UR,0},{UF,0},{UL,0},{BR,1},{DR,0},{DF,0},{DL,0},{BL,1},{FR,0},{FL,0},{UB,1},{DB,1}}-};-const CornerCubie CornerCubieSym[4] = {-    {{URF,1},{DFR,2},{DLF,1},{UFL,2},{UBR,2},{DRB,1},{DBL,2},{ULB,1}},-    {{DLF,0},{DFR,0},{DRB,0},{DBL,0},{UFL,0},{URF,0},{UBR,0},{ULB,0}},-    {{UBR,0},{URF,0},{UFL,0},{ULB,0},{DRB,0},{DFR,0},{DLF,0},{DBL,0}},-    {{UFL,3},{URF,3},{UBR,3},{ULB,3},{DLF,3},{DFR,3},{DRB,3},{DBL,3}}-};-const EdgeCubie EdgeCubieSym[4] = {-    {{UF,1},{FR,0},{DF,1},{FL,0},{UB,1},{BR,0},{DB,1},{BL,0},{UR,1},{DR,1},{DL,1},{UL,1}},-    {{DL,0},{DF,0},{DR,0},{DB,0},{UL,0},{UF,0},{UR,0},{UB,0},{FL,0},{FR,0},{BR,0},{BL,0}},-    {{UB,0},{UR,0},{UF,0},{UL,0},{DB,0},{DR,0},{DF,0},{DL,0},{BR,1},{FR,1},{FL,1},{BL,1}},-    {{UL,0},{UF,0},{UR,0},{UB,0},{DL,0},{DF,0},{DR,0},{DB,0},{FL,0},{FR,0},{BR,0},{BL,0}}-};-enum Constant {-    GN_HTM      = 20,-    GN_QTM      = 26,-    N_MOVE      = 18,-    N_TWIST     = 2187,-    N_FLIP      = 2048,-    N_SLICE     = 495,-    N_CORNER    = 40320,-    N_EDGE8     = 40320,-    N_EDGE4     = 24,-    N_SYM       = 48,-    N_SYM_D4h   = 16,-    EQ_FLIPSLICE= 64430,-    EQ_CORNER   = 2768,-};-using std::size_t;-using namespace cube::math;-template<size_t N,typename T=int>-struct Perm-{-    using value_type = T;-    static constexpr size_t size() { return N; }-    constexpr Perm() noexcept-    {-        for(size_t i = 0; i < N; ++i) X[i] = static_cast<T>(i);-    }-    constexpr Perm(const std::array<T,N>& xs) noexcept-    :X{xs}-    {-        assert(isValidPermutation<N>(xs) && "array must be a valid permutation");-    }-    constexpr Perm(std::initializer_list<T> xs) noexcept-    {-        assert(xs.size() == N && "size mismatch");-        auto dit = X.begin();-        for(auto it = xs.begin(); it != xs.end(); it++, dit++) { *dit = *it; }-        assert(isValidPermutation<N>(X) && "invalid permutation list");-    }-    template<typename ArrayLike>-    constexpr ArrayLike act_right(const ArrayLike& src) const noexcept-    {-        return backpermute(src,this->X);-    }-    friend constexpr Perm operator*(const Perm &P, const Perm& Q) noexcept-    {-        return Q.act_right(P);-    }-    constexpr Perm& operator*=(const Perm& rhs) noexcept-    {-        return *this = *this * rhs;-    }-    friend constexpr bool operator==(const Perm &lhs, const Perm& rhs) noexcept-    {-        return lhs.X == rhs.X;-    }-    constexpr Perm operator~() const-    {-        return { forepermute(Perm::id.X, this->X) };-    }-    constexpr T& operator[](size_t idx)             { return X[idx]; }-    constexpr const T& operator[](size_t idx) const { return X[idx]; }-    bool parity() const-    {-        const auto [fixed, cs] = decomposite(this->X);-        int s = 1;-        for(auto &c:cs) s *= (c.size() % 2 == 0) ? -1 : 1;-        return s == 1;-    }-    size_t order() const { return orderOf(X); }-    constexpr size_t rank() const { return rankOf(X); }-    static constexpr Perm<N,T> fromRank(size_t i)-    { return { cube::math::fromRank<T,N>(i) }; }-    static const Perm id;-    std::array<T,N> X{};-};-template<size_t N,typename T>-inline constexpr Perm<N,T> Perm<N,T>::id{};-template<size_t N, size_t L, typename T=int>-struct CArray-{-    using value_type = T;-    static constexpr size_t period = N;-    static constexpr size_t size() noexcept { return L; }-    constexpr CArray() noexcept {}-    constexpr CArray(const std::array<T,L> &arr) noexcept-    :xs{arr}-    {-        auto n = static_cast<T>(N);-        for(size_t i = 0; i < L; i++) { xs[i] = (xs[i] % n + n) % n; }-    }-    constexpr CArray(std::initializer_list<T> list) noexcept-    {-        auto n = static_cast<T>(N);-        std::size_t i = 0;-        for(T val : list) { if(i < L) { xs[i++] = (val % n + n) % n; } }-    }-    constexpr T& operator[](size_t idx) noexcept             { return xs[idx]; }-    constexpr const T& operator[](size_t idx) const noexcept { return xs[idx]; }-    friend constexpr bool operator==(const CArray& lhs, const CArray& rhs) noexcept-    {-        return lhs.xs == rhs.xs;-    }-    constexpr CArray& operator+=(const CArray& rhs)-    {-        for(size_t i = 0; i < L; i++) xs[i] = (xs[i] + rhs.xs[i]) % N;-        return *this;-    }-    friend constexpr CArray operator+(CArray lhs, const CArray& rhs)-    {-        return lhs += rhs;-    }-    constexpr CArray operator~() const noexcept-    {-        CArray<N,L,T> inv {};-        auto n = static_cast<T>(N);-        for(size_t i = 0; i < L; i++) inv[i] = (n - xs[i]) % n;-        return inv;-    }-    constexpr T sum() const noexcept-    {-        T s = 0;-        for(size_t i = 0; i < L; i++) s += xs[i];-        return s % N;-    }-    static const CArray id;-    std::array<T,L> xs {};-};-template<size_t N, size_t L, typename T>-inline constexpr CArray<N,L,T> CArray<N,L,T>::id{};-template<size_t N, size_t L, typename T>-constexpr CArray<N,L,T> operator*(const CArray<N,L,T> &xs, const Perm<L,T> &P)-{-    return P.act_right(xs);-}-template<size_t N, size_t L, typename T>-constexpr CArray<N,L,T>& operator*=(CArray<N,L,T> &xs, const Perm<L,T> &P)-{-    return xs = P.act_right(xs);-}-template<typename T, size_t N, size_t... Ns>-struct ArrayHelper {-    using type = std::array<typename ArrayHelper<T,Ns...>::type,N>;-};-template<typename T, size_t N>-struct ArrayHelper<T,N> {-    using type = std::array<T,N>;-};-template<typename T, size_t... Ns>-struct NArray-{-    using value_type = T;-    static constexpr size_t size = (Ns * ...);-    static constexpr size_t dim = sizeof...(Ns);-    static constexpr std::array<size_t,dim> shape { Ns... };-    typename ArrayHelper<T,Ns...>::type data;-    auto & operator[](size_t i) {-        return data[i];-    }-    const auto & operator[](size_t i) const {-        return data[i];-    }-};-}-namespace cube {-using namespace cube::data;-typedef std::int8_t cube_value_t;-typedef Perm<54,    cube_value_t>   FacePerm;-typedef Perm<8,     cube_value_t>   CornerPerm;-typedef Perm<12,    cube_value_t>   EdgePerm;-typedef CArray<3, 8,cube_value_t>   CornerOri;-typedef CArray<2,12,cube_value_t>   EdgeOri;-struct ColorState;-struct FaceCube;-struct CubieCube;-constexpr CornerPerm operator*(const CornerPerm &cp, const CubieCube &cc);-constexpr CornerOri  operator*(const CornerOri  &co, const CubieCube &cc);-constexpr EdgePerm   operator*(const EdgePerm   &ep, const CubieCube &cc);-constexpr EdgeOri    operator*(const EdgeOri    &eo, const CubieCube &cc);-struct ColorState-{-    std::array<Layer,54> s;-    Layer & operator[](size_t i) noexcept           { return s[i]; }-    const Layer operator[](size_t i) const noexcept { return s[i]; }-    static ColorState fromString(std::string_view cube);-    static bool is_valid_config(std::string_view cube);-    FaceCube  toFaceCube() const;-    CubieCube toCubieCube() const;-    static const ColorState id;-};-inline const ColorState ColorState::id = {{U,U,U,U,U,U,U,U,U,R,R,R,R,R,R,R,R,R,F,F,F,F,F,F,F,F,F,D,D,D,D,D,D,D,D,D,L,L,L,L,L,L,L,L,L,B,B,B,B,B,B,B,B,B}};-struct FaceCube-{-    FacePerm f;-    CubieCube toCubieCube() const;-    friend constexpr FaceCube operator*(const FaceCube &lhs, const FaceCube &rhs)-    { return { lhs.f * rhs.f }; }-    constexpr FaceCube& operator*=(const FaceCube &rhs)-    { return *this = *this * rhs; }-    constexpr FaceCube operator~() const-    { return { ~f }; }-    friend bool operator==(const FaceCube &lhs, const FaceCube &rhs)-    { return lhs.f == rhs.f; }-    static const FaceCube id;-};-struct CubieCube-{-    CornerPerm  cp;-    CornerOri   co;-    EdgePerm    ep;-    EdgeOri     eo;-    FaceCube toFaceCube() const;-    bool isSolvable() const-    {  return cp.parity() == ep.parity() && co.sum() == 0 && eo.sum() == 0; }-    friend constexpr CubieCube operator*(const CubieCube &a, const CubieCube &b)-    { return { a.cp*b, a.co*b, a.ep*b, a.eo*b }; }-    constexpr CubieCube& operator*=(const CubieCube &rhs)-    { return *this = *this * rhs; }-    constexpr CubieCube operator~() const-    {-        auto cp_inv = ~cp;-        auto ep_inv = ~ep;-        return { cp_inv, ~(co*cp_inv), ep_inv, ~(eo*ep_inv) };-    }-    friend bool operator==(const CubieCube &lhs, const CubieCube &rhs)-    { return lhs.cp == rhs.cp && lhs.co == rhs.co && lhs.ep == rhs.ep && lhs.eo == rhs.eo; }-    static const CubieCube id;-};-inline constexpr CornerPerm operator*(const CornerPerm &cp, const CubieCube &cc) { return cp * cc.cp;}-inline constexpr CornerOri  operator*(const CornerOri &co,  const CubieCube &cc) { return co * cc.cp + cc.co; }-inline constexpr EdgePerm   operator*(const EdgePerm &ep,   const CubieCube &cc) { return ep * cc.ep; }-inline constexpr EdgeOri    operator*(const EdgeOri &eo,    const CubieCube &cc) { return eo * cc.ep + cc.eo; }-inline constexpr CornerPerm    eCP = {0,1,2,3,4,5,6,7};-inline constexpr EdgePerm      eEP = {0,1,2,3,4,5,6,7,8,9,10,11};-inline constexpr CornerOri     eCO = {0,0,0,0,0,0,0,0};-inline constexpr EdgeOri       eEO = {0,0,0,0,0,0,0,0,0,0,0,0};-inline constexpr FacePerm      eFP = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53};-inline const FaceCube   FaceCube::id = FaceCube{eFP};-inline const CubieCube  CubieCube::id = CubieCube{eCP,eCO,eEP,eEO};-inline constexpr CubieCube mU = {{3,0,1,2,4,5,6,7},{0,0,0,0,0,0,0,0},{3,0,1,2,4,5,6,7,8,9,10,11},{0,0,0,0,0,0,0,0,0,0,0,0}};-inline constexpr CubieCube mR = {{4,1,2,0,7,5,6,3},{2,0,0,1,1,0,0,2},{8,1,2,3,11,5,6,7,4,9,10,0},{0,0,0,0,0,0,0,0,0,0,0,0}};-inline constexpr CubieCube mF = {{1,5,2,3,0,4,6,7},{1,2,0,0,2,1,0,0},{0,9,2,3,4,8,6,7,1,5,10,11},{0,1,0,0,0,1,0,0,1,1,0,0}};-inline constexpr CubieCube mD = {{0,1,2,3,5,6,7,4},{0,0,0,0,0,0,0,0},{0,1,2,3,5,6,7,4,8,9,10,11},{0,0,0,0,0,0,0,0,0,0,0,0}};-inline constexpr CubieCube mL = {{0,2,6,3,4,1,5,7},{0,1,2,0,0,2,1,0},{0,1,10,3,4,5,9,7,8,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0}};-inline constexpr CubieCube mB = {{0,1,3,7,4,5,2,6},{0,0,1,2,0,0,2,1},{0,1,2,11,4,5,6,10,8,9,3,7},{0,0,0,1,0,0,0,1,0,0,1,1}};-inline constexpr std::array<CubieCube,18>-    ElementaryMove = { mU,mU*mU,mU*mU*mU,mR,mR*mR,mR*mR*mR,mF,mF*mF,mF*mF*mF,mD,mD*mD,mD*mD*mD,mL,mL*mL,mL*mL*mL,mB,mB*mB,mB*mB*mB };-inline constexpr FaceCube pU = {{6,3,0,7,4,1,8,5,2,45,46,47,12,13,14,15,16,17,9,10,11,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,39,40,41,42,43,44,36,37,38,48,49,50,51,52,53}};-inline constexpr FaceCube pR = {{0,1,20,3,4,23,6,7,26,15,12,9,16,13,10,17,14,11,18,19,29,21,22,32,24,25,35,27,28,51,30,31,48,33,34,45,36,37,38,39,40,41,42,43,44,8,46,47,5,49,50,2,52,53}};-inline constexpr FaceCube pF = {{0,1,2,3,4,5,44,41,38,6,10,11,7,13,14,8,16,17,24,21,18,25,22,19,26,23,20,15,12,9,30,31,32,33,34,35,36,37,27,39,40,28,42,43,29,45,46,47,48,49,50,51,52,53}};-inline constexpr FaceCube pD = {{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,24,25,26,18,19,20,21,22,23,42,43,44,33,30,27,34,31,28,35,32,29,36,37,38,39,40,41,51,52,53,45,46,47,48,49,50,15,16,17}};-inline constexpr FaceCube pL = {{53,1,2,50,4,5,47,7,8,9,10,11,12,13,14,15,16,17,0,19,20,3,22,23,6,25,26,18,28,29,21,31,32,24,34,35,42,39,36,43,40,37,44,41,38,45,46,33,48,49,30,51,52,27}};-inline constexpr FaceCube pB = {{11,14,17,3,4,5,6,7,8,9,10,35,12,13,34,15,16,33,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,39,42,2,37,38,1,40,41,0,43,44,51,48,45,52,49,46,53,50,47}};-inline constexpr std::array<FaceCube,18>-    ElementaryPerm = { pU,pU*pU,pU*pU*pU,pR,pR*pR,pR*pR*pR,pF,pF*pF,pF*pF*pF,pD,pD*pD,pD*pD*pD,pL,pL*pL,pL*pL*pL,pB,pB*pB,pB*pB*pB };-inline FaceCube operator*(const FaceCube &c, const std::vector<TurnMove> &ms)-{-    FaceCube fc = c;-    for (auto m : ms) fc = fc * ElementaryPerm[m];-    return fc;-}-inline CubieCube operator*(const CubieCube &c, const std::vector<TurnMove> &ms)-{-    CubieCube cc = c;-    for (auto m : ms) cc = cc * ElementaryMove[m];-    return cc;-}-inline ColorState operator*(const ColorState &c, const std::vector<TurnMove> &ms)-{-    ColorState cs = c;-    for (auto m : ms) cs = ElementaryPerm[m].f.act_right(cs);-    return cs;-}-}-namespace cube {-using namespace cube::data;-ColorState ColorState::fromString(std::string_view cube)-{-    assert(is_valid_config(cube) && "invalid cube config");-    std::array<Layer,54> xs{};-    std::transform(cube.cbegin(), cube.cend(), xs.begin(), [](char c) {-        switch(c) {-        case 'U': return U;-        case 'R': return R;-        case 'F': return F;-        case 'D': return D;-        case 'L': return L;-        case 'B': return B;-        default: throw std::invalid_argument("invalid cube config");-        }-    });-    return { xs };-}-bool ColorState::is_valid_config(std::string_view cfg)-{-    if(cfg.size() != 54) return false;-    std::set<char> vs { cfg[CC[0]],cfg[CC[1]],cfg[CC[2]],cfg[CC[3]],cfg[CC[4]],cfg[CC[5]] };-    if(vs.size() != 6) return false;-    for(size_t i = 0, x = 0; i < 8; i++) {-        for(x = 0; x < 24; x++) {-            if(cfg[CC[CCI[i][0]]] == cfg[CF[x/3][x%3]]-               && cfg[CC[CCI[i][1]]] == cfg[CF[x/3][(x+1)%3]]-               && cfg[CC[CCI[i][2]]] == cfg[CF[x/3][(x+2)%3]]) break;-        }-        if(x >= 24) return false;-    }-    for(size_t i = 0, y = 0; i < 12; i++) {-        for(y = 0; y < 24; y++) {-            if(cfg[CC[ECI[i][0]]] == cfg[EF[y/2][y%2]]-               && cfg[CC[ECI[i][1]]] == cfg[EF[y/2][(y+1)%2]]) break;-        }-        if(y >= 24) return false;-    }-    return true;-}-FaceCube ColorState::toFaceCube() const-{-    FacePerm fp{};-    for(int i = 0; i < 6; ++i) {-        fp[CC[i]] = s[CC[i]];-    }-    for(int i = 0; i < 8; i++) {-        for(int x = 0; x < 24; x++) {-            if(s[CC[CCI[i][0]]] == s[CF[x/3][x%3]]-            && s[CC[CCI[i][1]]] == s[CF[x/3][(x+1)%3]]-            && s[CC[CCI[i][2]]] == s[CF[x/3][(x+2)%3]])-            {-                fp[CF[x/3][x%3]]      = CF[i][0];-                fp[CF[x/3][(x+1)%3]]  = CF[i][1];-                fp[CF[x/3][(x+2)%3]]  = CF[i][2];-                break;-            }-        }-    }-    for(int i = 0; i < 12; i++) {-        for(int y = 0; y < 24; y++) {-            if(s[CC[ECI[i][0]]] == s[EF[y/2][y%2]]-            && s[CC[ECI[i][1]]] == s[EF[y/2][(y+1)%2]])-            {-                fp[EF[y/2][y%2]]      = EF[i][0];-                fp[EF[y/2][(y+1)%2]]  = EF[i][1];-                break;-            }-        }-    }-    return { fp };-}-CubieCube ColorState::toCubieCube() const-{-    return toFaceCube().toCubieCube();-}-CubieCube FaceCube::toCubieCube() const-{-    CubieCube cc{};-    const FaceCube &fc = *this;-    for(int i = 0; i < 8; i++) {-        for(int x = 0; x < 24; x++) {-            if(fc.f[CF[i][0]] == CF[x/3][x%3]) {-                cc.cp[i] = x/3, cc.co[i] = (3-x%3)%3;-                break;-            }-        }-    }-    for(int i = 0; i < 12; i++){-        for(int y = 0; y < 24; y++){-            if(fc.f[EF[i][0]] == EF[y/2][y%2]) {-                cc.ep[i] = y/2, cc.eo[i] = (2-y%2)%2;-                break;-            }-        }-    }-    return cc;-}-FaceCube CubieCube::toFaceCube() const-{-    FaceCube fc{};-    const CubieCube &cc = *this;-    for(int i = 0; i < 6; i++) {-        fc.f[CC[i]] = CC[i];-    }-    for(int i = 0; i < 8; i++) for(int j = 0; j < 3; j++) {-        fc.f[CF[i][j]] = CF[cc.cp[i]][(j-cc.co[i]+3)%3];-    }-    for(int i = 0; i < 12; i++) for(int j = 0; j < 2; j++) {-        fc.f[EF[i][j]] = EF[cc.ep[i]][(j-cc.eo[i]+2)%2];-    }-    return fc;-}-}-namespace cube::pdb {-struct Coord-{-    int twist, flip, slice;-    int corner, edge4, edge8;-    static const Coord id;-    static CornerOri    twist2co(int);-    static int          co2twist(const CornerOri &);-    static EdgeOri      flip2eo(int);-    static int          eo2flip(const EdgeOri &);-    static CornerPerm   corner2cp(int);-    static int          cp2corner(const CornerPerm &);-    static int          ep2slice(const EdgePerm &);-    static int          ep2edge4(const EdgePerm &);-    static int          ep2edge8(const EdgePerm &);-    static EdgePerm     slice2ep(int);-    static EdgePerm     edge42ep(int);-    static EdgePerm     edge82ep(int);-    static EdgePerm     see2ep(int,int,int);-    static Coord        CubieCube2Coord(const CubieCube &);-    static CubieCube    Coord2CubieCube(const Coord &);-};-constexpr bool operator==(const Coord &c1, const Coord &c2)-{-    return c1.twist == c2.twist && c1.flip == c2.flip && c1.slice == c2.slice-        && c1.corner == c2.corner && c1.edge4 == c2.edge4 && c1.edge8 == c2.edge8;-}-inline constexpr Coord Coord::id = { 0,0,0,0,0,0 };-}-namespace cube::pdb {-using namespace cube::math;-using namespace cube::data;-inline bool isSliceEdge(size_t idx)-{-    return FR <= idx && idx <= BR;-}-int Coord::co2twist(const CornerOri &co)-{-    return static_cast<int>(fromDigits<3>(takeByRange<1,7>(co.xs)));-}-CornerOri Coord::twist2co(int i)-{-    CornerOri co;-    auto sub1to7 = CArray<3,7,CornerOri::value_type>{toDigits<3,7,CornerOri::value_type>(i)};-    std::copy(sub1to7.xs.begin(),sub1to7.xs.end(),co.xs.begin()+1);-    co[0] = (3 - sub1to7.sum()) % 3;-    return co;-}-int Coord::eo2flip(const EdgeOri &eo)-{-    return static_cast<int>(fromDigits<2>(takeByRange<1,11>(eo.xs)));-}-EdgeOri Coord::flip2eo(int i)-{-    EdgeOri eo;-    auto sub1to11 = CArray<2,11,CornerOri::value_type>{toDigits<2,11,CornerOri::value_type>(i)};-    std::copy(sub1to11.xs.begin(),sub1to11.xs.end(),eo.xs.begin()+1);-    eo[0] = (2 - sub1to11.sum()) % 2;-    return eo;-}-int Coord::ep2slice(const EdgePerm &ep)-{-    int x[4],slice=0,N=12;-    for(int i = 0, j = 0; i < N; i++) {-        if(isSliceEdge(ep[i])) x[j++] = i;-    }-    for(int i = 0; i < 4; i++) slice += binomial(N-1-x[i],4-i);-    return slice;-}-int Coord::ep2edge4(const EdgePerm &ep)-{-    Perm<4,EdgePerm::value_type> edge4_perm;-    for(int i = 0, j = 0; i < 4; i++, j++) {-        while(!isSliceEdge(ep[j])) j++;-        edge4_perm[i] = ep[j] - 8;-    }-    return static_cast<int>(edge4_perm.rank());-}-int Coord::ep2edge8(const EdgePerm &ep)-{-    Perm<8,EdgePerm::value_type> edge8_perm;-    for(size_t i = 0, j = 0; i < 8; i++, j++) {-        while(isSliceEdge(ep[j]) || ep[j] == (EdgePerm::value_type) ~0UL) j++;-        edge8_perm[i] = ep[j] - 0;-    }-    return static_cast<int>(edge8_perm.rank());-}-int Coord::cp2corner(const CornerPerm &cp)-{-    return static_cast<int>(cp.rank());-}-CornerPerm Coord::corner2cp(int i)-{-    return CornerPerm::fromRank(i);-}-EdgePerm Coord::slice2ep(int i)-{-    auto si = lexicalOrderToIndices<12,4>(i);-    EdgePerm ep;-    for(size_t i = 0, j = 0; i < 12; i++){-        ep[i] = (i == si[j]) ? 8 + j++ : (EdgePerm::value_type) ~0UL;-    }-    return ep;-}-EdgePerm Coord::edge42ep(int i)-{-    EdgePerm ep;-    auto e4 = Perm<4,EdgePerm::value_type>::fromRank(i);-    for(size_t i = 0; i < 12; i++){-        ep[i] = (i < 8) ? (EdgePerm::value_type) ~0UL : e4[i-8] + 8;-    }-    return ep;-}-EdgePerm Coord::edge82ep(int i)-{-    EdgePerm ep;-    auto e8 = Perm<8,EdgePerm::value_type>::fromRank(i);-    for(size_t i = 0; i < 12; i++){-        ep[i] = (i < 8) ? e8[i] + 0 : (EdgePerm::value_type) ~0UL;-    }-    return ep;-}-EdgePerm Coord::see2ep(int slice, int edge4, int edge8)-{-    auto e4 = Perm<4,EdgePerm::value_type>::fromRank(edge4);-    auto e8 = Perm<8,EdgePerm::value_type>::fromRank(edge8);-    auto slice_indices = lexicalOrderToIndices<12,4>(slice);-    EdgePerm ep;-    for(size_t i = 0, j = 0, x = 0, y = 0; i < 12; i++) {-        ep[i] = (i == slice_indices[j] && ++j) ? e4[x++]+8: e8[y++]+0;-    }-    return ep;-}-Coord Coord::CubieCube2Coord(const CubieCube &cc)-{-    return {-        Coord::co2twist(cc.co),-        Coord::eo2flip(cc.eo),-        Coord::ep2slice(cc.ep),-        Coord::cp2corner(cc.cp),-        Coord::ep2edge4(cc.ep),-        Coord::ep2edge8(cc.ep)-    };-}-CubieCube Coord::Coord2CubieCube(const Coord &c)-{-    return {-        Coord::corner2cp(c.corner),-        Coord::twist2co(c.twist),-        Coord::see2ep(c.slice,c.edge4,c.edge8),-        Coord::flip2eo(c.flip)-    };-}-}-namespace cube::config {-void set_table_dir(std::filesystem::path dir);-auto get_table_dir() -> std::filesystem::path;-}-namespace cube::pdb {-using namespace cube::data;-namespace fs = std::filesystem;-typedef uint16_t    mt_value_t;-typedef uint8_t     pt_value_t;-template <typename Table> void save_to(const Table &table, fs::path path);-template <typename Table> void load_from(Table &table, fs::path path);-template<class T>-class Singleton-{-public:-    Singleton(const Singleton&) = delete;-    Singleton(Singleton&&) = delete;-    Singleton& operator=(const Singleton&) = delete;-    Singleton& operator=(Singleton&&) = delete;-    static T& instance() {-        static T obj {};-        return obj;-    }-protected:-    Singleton() = default;-    ~Singleton() = default;-};-template<typename T=mt_value_t>-struct TableMove-{-    static_assert(std::is_integral<T>::value);-    static_assert(std::numeric_limits<T>::digits >= 16);-    using value_t = T;-    TableMove(fs::path dir = {});-    TableMove(const TableMove &) = delete;-    ~TableMove();-    TableMove& operator=(const TableMove &) = delete;-    template<typename Table, typename F1, typename F2>-    std::enable_if_t<Table::shape[0] == N_MOVE, void>-    buildMoveTable(Table &t, F1&& coord2i, F2&& i2coord, fs::path filename);-    static bool is_ready(fs::path);-    const fs::path tdir;-    NArray<T,N_MOVE,N_TWIST>   *pTMTwist;-    NArray<T,N_MOVE,N_FLIP>    *pTMFlip;-    NArray<T,N_MOVE,N_SLICE>   *pTMSlice;-    NArray<T,N_MOVE,N_CORNER>  *pTMCorner;-    NArray<T,N_MOVE,N_EDGE4>   *pTMEdge4;-    NArray<T,N_MOVE,N_EDGE8>   *pTMEdge8;-};-template<typename T=pt_value_t>-struct TablePrunning-{-    using value_type = T;-    TablePrunning(fs::path dir = {});-    TablePrunning(const TablePrunning &) = delete;-    ~TablePrunning();-    TablePrunning operator=(const TablePrunning &) = delete;-    template<typename Table, typename MT1, typename MT2>-    std::enable_if_t<Table::shape[0] == MT1::shape[1] && Table::shape[1] == MT2::shape[1]>-    buildPrunningTable(Table &t, const MT1 &mt1, const MT2 &mt2, fs::path filename);-    static bool is_ready(fs::path);-    const fs::path tdir;-    NArray<T,N_SLICE,N_FLIP>   *pTPSliceFlip;-    NArray<T,N_SLICE,N_TWIST>  *pTPSliceTwist;-    NArray<T,N_EDGE4,N_EDGE8>  *pTPEdge4Edge8;-    NArray<T,N_EDGE4,N_CORNER> *pTPEdge4Corner;-};-template<typename T=mt_value_t>-using SingletonTM = Singleton<TableMove<T>>;-template<typename T=pt_value_t>-using SingletonTP = Singleton<TablePrunning<T>>;-inline const auto &get_TM() { return SingletonTM<>::instance(); }-inline const auto &get_TP() { return SingletonTP<>::instance(); }-inline bool tables_ready(fs::path dir = {})-{-    return TableMove<>::is_ready(dir) && TablePrunning<>::is_ready(dir);-}-inline void preload_tables()-{-    (void) get_TM();-    (void) get_TP();-}-}-#if defined(VERBOSE) && VERBOSE-#define VPRINT(...) printf(__VA_ARGS__)-#else-#define VPRINT(...)-#endif-namespace cube::pdb {-using namespace cube::data;-auto table_dir_or_default(fs::path dir) -> fs::path-{-    return dir.empty() ? cube::config::get_table_dir() : dir;-}-template <typename Table>-void save_to(const Table &table, fs::path path)-{-    std::ofstream f(path, std::ios::binary);-    if(f.is_open()) {-        f.write(reinterpret_cast<const char*>(&table.data), sizeof(table.data));-        f.close();-    }-}-template <typename Table>-void load_from(Table &table, fs::path path)-{-    VPRINT("loading table from %s...", path.c_str());-    std::ifstream f(path,std::ios::binary);-    f.read(reinterpret_cast<char*>(&table.data), sizeof(table.data));-    f.close();-    VPRINT("done.\n");-}-template<typename T>-template<typename Table, typename F1, typename F2>-std::enable_if_t<Table::shape[0] == N_MOVE>-TableMove<T>::buildMoveTable(Table &t, F1&& coord2i, F2&& i2coord, fs::path filename)-{-    VPRINT("creating move table %s of shape (%zu,%zu)... ",-           filename.c_str(), t.shape[0], t.shape[1]);-    for(size_t i = 0; i < t.shape[0]; i++) for(size_t j = 0; j < t.shape[1]; j++) {-        t[i][j] = coord2i(i2coord(j) * ElementaryMove[i]);-    }-    if(filename != "") save_to(t, tdir/filename);-    VPRINT("done.\n");-}-template<typename T>-TableMove<T>::TableMove(fs::path dir)-:tdir{table_dir_or_default(dir)}-{-    VPRINT("INIT MOVE TABLES -- \n");-    pTMTwist     = new NArray<T,N_MOVE,N_TWIST>;-    pTMFlip      = new NArray<T,N_MOVE,N_FLIP>;-    pTMSlice     = new NArray<T,N_MOVE,N_SLICE>;-    pTMCorner    = new NArray<T,N_MOVE,N_CORNER>;-    pTMEdge4     = new NArray<T,N_MOVE,N_EDGE4>;-    pTMEdge8     = new NArray<T,N_MOVE,N_EDGE8>;-    if(!is_ready(tdir)) {-        if(!fs::exists(tdir)) fs::create_directories(tdir);-        buildMoveTable(*pTMTwist, Coord::co2twist, Coord::twist2co, "tm_twist.dat");-        buildMoveTable(*pTMFlip, Coord::eo2flip, Coord::flip2eo, "tm_flip.dat");-        buildMoveTable(*pTMSlice, Coord::ep2slice, Coord::slice2ep, "tm_slice.dat");-        buildMoveTable(*pTMCorner, Coord::cp2corner, Coord::corner2cp, "tm_corner.dat");-        buildMoveTable(*pTMEdge4, Coord::ep2edge4, Coord::edge42ep, "tm_edge4.dat");-        buildMoveTable(*pTMEdge8, Coord::ep2edge8, Coord::edge82ep, "tm_edge8.dat");-    } else {-        load_from(*pTMTwist, tdir/"tm_twist.dat");-        load_from(*pTMFlip, tdir/"tm_flip.dat");-        load_from(*pTMSlice, tdir/"tm_slice.dat");-        load_from(*pTMCorner, tdir/"tm_corner.dat");-        load_from(*pTMEdge4, tdir/"tm_edge4.dat");-        load_from(*pTMEdge8, tdir/"tm_edge8.dat");-    }-    VPRINT("-- DONE.\n");-}-template<typename T>-TableMove<T>::~TableMove()-{-    delete pTMTwist;-    delete pTMFlip;-    delete pTMSlice;-    delete pTMCorner;-    delete pTMEdge4;-    delete pTMEdge8;-}-template<typename T>-bool TableMove<T>::is_ready(fs::path tdir)-{-    tdir = table_dir_or_default(tdir);-    return fs::exists(tdir/"tm_twist.dat") &&-           fs::exists(tdir/"tm_flip.dat") &&-           fs::exists(tdir/"tm_slice.dat") &&-           fs::exists(tdir/"tm_corner.dat") &&-           fs::exists(tdir/"tm_edge4.dat") &&-           fs::exists(tdir/"tm_edge8.dat");-}-template<typename T>-template<typename Table, typename MT1, typename MT2>-std::enable_if_t<Table::shape[0] == MT1::shape[1] && Table::shape[1] == MT2::shape[1]>-TablePrunning<T>::buildPrunningTable(-    Table &t, const MT1 &mt1, const MT2 &mt2, fs::path filename)-{-    VPRINT("creating prunning table %s of shape (%zu,%zu):\n",-           filename.c_str(), mt1.shape[1], mt2.shape[1]);-    std::fill_n(&t.data[0][0], t.size, (typename Table::value_type) ~0UL);-    t[0][0] = 0;-    typename Table::value_type depth = 0;-    size_t count = 1;-    VPRINT("\tdepth %2d: %10zu / %-10zu.\n", depth, count, t.size);-    while(count < t.size)-    {-        for(size_t i = 0; i < t.shape[0]; i++) for(size_t j = 0; j < t.shape[1]; j++)-        if(t[i][j] == depth) {-            for(auto k = 0; k < N_MOVE; k++) {-                auto ii = mt1[k][i], jj = mt2[k][j];-                if(t[ii][jj] == (typename Table::value_type)~0UL) { t[ii][jj] = depth + 1; count++; }-            }-        }-        depth++;-        VPRINT("\tdepth %2d: %10zu / %-10zu.\n", depth, count, t.size);-    }-    if(filename != "") save_to(t, tdir/filename);-    VPRINT("done.\n");-}-template<typename T>-TablePrunning<T>::TablePrunning(fs::path dir)-:tdir{table_dir_or_default(dir)}-{-    VPRINT("INIT PRUNNING TABLES -- \n");-    pTPSliceFlip     = new NArray<T,N_SLICE,N_FLIP>;-    pTPSliceTwist    = new NArray<T,N_SLICE,N_TWIST>;-    pTPEdge4Edge8    = new NArray<T,N_EDGE4,N_EDGE8>;-    pTPEdge4Corner   = new NArray<T,N_EDGE4,N_CORNER>;-    if(!is_ready(tdir)) {-        const auto &TM = get_TM();-        buildPrunningTable(*pTPSliceTwist, *TM.pTMSlice, *TM.pTMTwist, "tp_slicetwist.dat");-        buildPrunningTable(*pTPSliceFlip, *TM.pTMSlice, *TM.pTMFlip, "tp_sliceflip.dat");-        buildPrunningTable(*pTPEdge4Corner, *TM.pTMEdge4, *TM.pTMCorner, "tp_edge4corner.dat");-        buildPrunningTable(*pTPEdge4Edge8, *TM.pTMEdge4, *TM.pTMEdge8, "tp_edge4edge8.dat");-    } else {-        load_from(*pTPSliceTwist, tdir/"tp_slicetwist.dat");-        load_from(*pTPSliceFlip, tdir/"tp_sliceflip.dat");-        load_from(*pTPEdge4Corner,tdir/"tp_edge4corner.dat");-        load_from(*pTPEdge4Edge8, tdir/"tp_edge4edge8.dat");-    }-    VPRINT("-- DONE.\n");-}-template<typename T>-TablePrunning<T>::~TablePrunning()-{-    delete pTPSliceFlip;-    delete pTPSliceTwist;-    delete pTPEdge4Edge8;-    delete pTPEdge4Corner;-}-template<typename T>-bool TablePrunning<T>::is_ready(fs::path tdir)-{-    tdir = table_dir_or_default(tdir);-    return fs::exists(tdir/"tp_slicetwist.dat") &&-           fs::exists(tdir/"tp_sliceflip.dat") &&-           fs::exists(tdir/"tp_edge4corner.dat") &&-           fs::exists(tdir/"tp_edge4edge8.dat");-}-template struct TableMove<>;-template struct TablePrunning<>;-}-namespace cube::solver {-using namespace cube::data;-using namespace cube::pdb;-enum enum_phase { Ph1=0, Ph2=1 };-struct solve_session-{-    const Coord root;-    const size_t good_enough;-    const size_t max_step;-};-class TwoPhaseSolver-{-public:-    auto solve(const Coord &c, int max_step = DS)-        -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>;-protected:-    template<enum_phase PhX>-    bool search_phase(const Coord &c, size_t togo);-    template<enum_phase PhX>-    static Coord transform(const Coord &c, const TurnMove &m);-    template<enum_phase PhX>-    static size_t distance(const Coord &c);-    static constexpr int D0 = 12, D1 = 18, DS = D0+D1;-    template<enum_phase PhX> static constexpr auto& D = std::get<PhX>(std::tie(D0,D1));-    static constexpr std::array<TurnMove,18> EM0-        = { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };-    static constexpr std::array<TurnMove,10> EM1-        = { Ux1,Ux2,Ux3,Rx2,Fx2,Dx1,Dx2,Dx3,Lx2,Bx2 };-    template<enum_phase PhX>-    static constexpr auto& EM = std::get<PhX>(std::tie(EM0,EM1));-protected:-    template<enum_phase PhX>-    void reset_ph_sofar() { sofar_[PhX].fill(-1); }-    template<enum_phase PhX>-    void set_ph_sofar(int step, int move) { sofar_[PhX][step] = move; }-    template<enum_phase PhX>-    int get_ph_sofar(int step) { return sofar_[PhX][step]; }-    template<enum_phase PhX>-    void set_ph_solution(size_t L)-    {-        rsolution_[PhX].first = L;-        std::copy(sofar_[PhX].begin(), sofar_[PhX].begin()+L, rsolution_[PhX].second.begin());-    }-    template<enum_phase PhX>-    auto get_ph_solution() const -> std::vector<TurnMove>-    {-        size_t n = rsolution_[PhX].first;-        if(n == 0) return {};-        std::vector<TurnMove> sol(n);-        for(auto i = 0; i < n; i++) {-            sol[i] = static_cast<TurnMove>(rsolution_[PhX].second[n-1-i]);-        }-        return sol;-    }-    Coord ph2_origin(Coord c) const;-private:-    std::array<std::array<int,DS+2>,2>                  sofar_;-    std::array<std::pair<size_t,std::array<int,DS>>,2>  rsolution_;-};-class TwoPhaseOptimSolver: public TwoPhaseSolver-{-public:-    auto solve(const Coord &c, size_t good = 0)-        -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>;-    int start_search_ph1(const Coord& c, size_t d, size_t d_orig, size_t maxL);-    bool start_search_ph2(const Coord& c, size_t togo);-private:-    Coord root_;-    size_t good_;-};-}-namespace cube::solver {-#define TM cube::pdb::get_TM()-#define TP cube::pdb::get_TP()-inline bool is_dull_pair(const TurnMove A, const int B)-{-    if(!(B >= Ux1 && B <= Bx3)) return false;-    return (A/3 == B/3) || (A/3 == B/3+3);-}-template<enum_phase I>-Coord TwoPhaseSolver::transform(const Coord &c, const TurnMove &m)-{-    if constexpr (I == Ph1)-    return Coord {-        (*TM.pTMTwist)[m][c.twist], (*TM.pTMFlip)[m][c.flip], (*TM.pTMSlice)[m][c.slice],-        -1,-1,-1-    };-    else-    return Coord {-        0,0,0,-        (*TM.pTMCorner)[m][c.corner], (*TM.pTMEdge4)[m][c.edge4], (*TM.pTMEdge8)[m][c.edge8]-    };-}-template<enum_phase I>-size_t TwoPhaseSolver::distance(const Coord &c)-{-    if constexpr (I == Ph1)-    return std::max((*TP.pTPSliceTwist)[c.slice][c.twist],-                    (*TP.pTPSliceFlip)[c.slice][c.flip]);-    else-    return std::max((*TP.pTPEdge4Corner)[c.edge4][c.corner],-                    (*TP.pTPEdge4Edge8)[c.edge4][c.edge8]);-}-template<enum_phase PhX>-bool TwoPhaseSolver::search_phase(const Coord &c, size_t togo)-{-    if(togo < distance<PhX>(c)) return false;-    if(togo == 0) return distance<PhX>(c) == 0;-    for(auto m: EM<PhX>)-    {-        if(is_dull_pair(m,get_ph_sofar<PhX>(togo))) continue;-        set_ph_sofar<PhX>(togo-1,m);-        bool ret = search_phase<PhX>(transform<PhX>(c,m), togo-1);-        if(ret) return true;-    }-    return false;-}-Coord TwoPhaseSolver::ph2_origin(Coord c) const-{-    int corner = c.corner, edge4, edge8;-    auto ep = Coord::see2ep(c.slice,c.edge4,c.edge8);-    for(auto &m : get_ph_solution<Ph1>())-    {-        corner = (*TM.pTMCorner)[m][corner];-        ep = ep * ElementaryMove[m].ep;-    }-    edge4 = Coord::ep2edge4(ep);-    edge8 = Coord::ep2edge8(ep);-    return Coord { 0,0,0,corner,edge4,edge8 };-}-auto TwoPhaseSolver::solve(const Coord &c, int step)-    -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>-{-    reset_ph_sofar<Ph1>();-    reset_ph_sofar<Ph2>();-    const size_t maxL = std::clamp(step,0,DS);-    for(auto d1 = distance<Ph1>(c); d1 <= maxL; d1++)-    {-        bool ret1 = search_phase<Ph1>(c,d1);-        if(!ret1) continue;-        set_ph_solution<Ph1>(d1);-        auto c2 = ph2_origin(c);-        for(auto d2 = distance<Ph2>(c2); d2 <= maxL-d1; d2++)-        {-            bool ret2 = search_phase<Ph2>(c2,d2);-            if(!ret2) continue;-            set_ph_solution<Ph2>(d2);-            return {true, get_ph_solution<Ph1>(), get_ph_solution<Ph2>()};-        }-    }-    return {false, {}, {}};-}-auto TwoPhaseOptimSolver::solve(const Coord &c, size_t good)-    -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>-{-    good_ = good;-    root_ = c;-    size_t bestL = DS + 1;-    reset_ph_sofar<Ph1>();-    for(auto togo = distance<Ph1>(c); togo < bestL; ++togo)-    {-        int l = start_search_ph1(c,togo,togo,bestL-1);-        if(l >= 0) bestL = std::min(bestL,static_cast<size_t>(l));-        if(bestL <= good_) break;-    }-    if(bestL > DS) return {false, {}, {}};-    else return { true, get_ph_solution<Ph1>(), get_ph_solution<Ph2>() };-}-int TwoPhaseOptimSolver::start_search_ph1(const Coord& c, size_t d, size_t d_orig, size_t maxL)-{-    if(d < distance<Ph1>(c)) return -1;-    if(d == 0) {-        set_ph_solution<Ph1>(d_orig);-        auto c2 = ph2_origin(root_);-        reset_ph_sofar<Ph2>();-        for(auto togo = distance<Ph2>(c2); togo <= maxL; ++togo)-        {-            bool succ = start_search_ph2(c2,togo);-            if(succ) {-                set_ph_solution<Ph2>(togo);-                return togo;-            }-        }-        return -1;-    }-    int bestL = maxL + 1;-    for(auto m: EM<Ph1>)-    {-        if(is_dull_pair(m, get_ph_sofar<Ph1>(d))) continue;-        set_ph_sofar<Ph1>(d-1,m);-        auto l = start_search_ph1(transform<Ph1>(c,m), d-1, d_orig, bestL-2);-        if(l >= 0 && bestL > l+1) {-            bestL = l+1;-        }-        if(bestL + d_orig - d <= good_) break;-        if(d >= bestL) break;-    }-    return bestL > static_cast<int>(maxL) ? -1 : bestL;-}-bool TwoPhaseOptimSolver::start_search_ph2(const Coord& c, size_t togo)-{   if(togo < distance<Ph2>(c)) return false;-    if(togo == 0) return distance<Ph2>(c) == 0;-    for(auto m: EM<Ph2>)-    {-        if(is_dull_pair(m, get_ph_sofar<Ph2>(togo))) continue;-        set_ph_sofar<Ph2>(togo-1,m);-        bool ret = start_search_ph2(transform<Ph2>(c,m), togo-1);-        if(ret) return true;-    }-    return false;-}-}-namespace cube::utils {-inline auto get_cache_dir() -> std::filesystem::path-{-#ifdef _WIN32-    const char* localAppData = std::getenv("LOCALAPPDATA");-    if (localAppData) return std::filesystem::path(localAppData);-#elif __APPLE__-    const char* home = std::getenv("HOME");-    if (home) return std::filesystem::path(home) / "Library" / "Caches";-#else-    const char* xdgCache = std::getenv("XDG_CACHE_HOME");-    if (xdgCache) return std::filesystem::path(xdgCache);-    const char* home = std::getenv("HOME");-    if (home) return std::filesystem::path(home) / ".cache";-#endif-    throw std::runtime_error("Unable to determine cache path");-}-template<typename F, typename... Args>-inline auto time_execution(F&& f, Args&&... args)-{-    using Rf = std::invoke_result_t<F, Args...>;-    auto start = std::chrono::high_resolution_clock::now();-    auto duration_from_start = [start](){-        auto end = std::chrono::high_resolution_clock::now();-        return std::chrono::duration_cast<std::chrono::microseconds>(end-start);-    };-    if constexpr (std::is_void_v<Rf>) {-        std::forward<F>(f)(std::forward<Args>(args)...);-        return std::make_pair(-            duration_from_start(),-            std::nullopt-        );-    } else {-        auto result = std::forward<F>(f)(std::forward<Args>(args)...);-        return std::make_pair(-            duration_from_start(),-            std::make_optional(result)-        );-    }-}-}-namespace cube::config-{-namespace fs = std::filesystem;-static fs::path& get_custom_dir_storage()-{-    static fs::path custom_dir = "";-    return custom_dir;-}-void set_table_dir(fs::path dir)-{-    get_custom_dir_storage() = dir;-}-fs::path get_table_dir()-{-    const auto user_dir = get_custom_dir_storage();-    if(!user_dir.empty()) return user_dir;-    if(const char *env = std::getenv("CUBE_TABLE_DIR")) {-        if(env[0] != '\0') return fs::path(env);-    }-    try {-        return utils::get_cache_dir() / "cube.coshz" / "tables";-    } catch (...) {-        return fs::absolute("tables");-    }-}-}-namespace cube::internal-{-using namespace cube::data;-std::string apply_maneuver(std::string_view s, const std::vector<TurnMove>& ms);-auto parse_maneuver(std::string_view s) -> std::vector<TurnMove>;-inline auto operator""_Tm(const char* ts, size_t n) -> std::vector<TurnMove>-{-    return parse_maneuver(std::string(ts,n));-}-bool is_valid_maneuver(std::string_view);-}-namespace cube {-using namespace cube::data;-namespace internal {-std::string apply_maneuver(std::string_view s, const std::vector<TurnMove> &ms)-{-    assert(s.size() == 54 && "invalid cube length");-    char buf[2][54];-    std::memcpy(buf[0], s.data(), 54);-    size_t curr = 0;-    for(const auto &m : ms)-    {-        const auto& p   = ElementaryPerm[m].f;-        const char* src = buf[curr];-        char*       dst = buf[1-curr];-        for(int i = 0; i < 54; ++i) dst[i] = src[p[i]];-        curr = 1-curr;-    }-    return std::string(buf[curr],54);-}-auto parse_maneuver(std::string_view s) -> std::vector<TurnMove>-{-    assert(is_valid_maneuver(s) && "invalid maneuver");-    auto expand = [](std::string_view in) -> std::string {-        static const std::regex group_re(R"(\(([^)]+)\)(?:\{(\d+)\})?)");-        std::string res;-        auto start = in.cbegin();-        std::match_results<std::string_view::const_iterator> m;-        while (std::regex_search(start, in.cend(), m, group_re)) {-            res.append(start, m[0].first);-            int repeat = m[2].matched ? std::stoi(m[2].str()) : 1;-            for (int i = 0; i < repeat; ++i) res += m[1].str();-            start = m[0].second;-        }-        res.append(start, in.cend());-        return res;-    };-    auto char_to_move = [](char c) -> TurnMove {-        switch(c) {-        case 'U': return Ux1;-        case 'R': return Rx1;-        case 'F': return Fx1;-        case 'D': return Dx1;-        case 'L': return Lx1;-        case 'B': return Bx1;-        default: throw std::invalid_argument("char_to_move: ???");-        }-    };-    std::string in = expand(s);-    std::vector<TurnMove> ms;-    ms.reserve(in.size());-    for (char c : in)-    {-        switch (c) {-        case ' ': break;-        case '2':-            ms.back() = static_cast<TurnMove>(ms.back() + 1);-            break;-        case '\'':-            ms.back() = static_cast<TurnMove>(ms.back() + 2);-            break;-        default:-            ms.push_back(char_to_move(c));-            break;-        }-    }-    return ms;-}-bool is_valid_maneuver(std::string_view s)-{-    static const std::regex pat(-        R"(\s*(([UDLRFB]['23]?|\(([UDLRFB]['23]?\s*)+\)(\{\d+\})?)\s*)*)"-    );-    return std::regex_match(s.begin(), s.end(), pat);-}-}-}-#ifndef CUBE_EXPORT_H-#define CUBE_EXPORT_H-#ifdef CUBE_STATIC_DEFINE-#  define CUBE_EXPORT-#  define CUBE_NO_EXPORT-#else-#  ifndef CUBE_EXPORT-#    ifdef cube_shared_EXPORTS-#      define CUBE_EXPORT __attribute__((visibility("default")))-#    else-#      define CUBE_EXPORT __attribute__((visibility("default")))-#    endif-#  endif-#  ifndef CUBE_NO_EXPORT-#    define CUBE_NO_EXPORT __attribute__((visibility("hidden")))-#  endif-#endif-#ifndef CUBE_DEPRECATED-#  define CUBE_DEPRECATED __attribute__ ((__deprecated__))-#endif-#ifndef CUBE_DEPRECATED_EXPORT-#  define CUBE_DEPRECATED_EXPORT CUBE_EXPORT CUBE_DEPRECATED-#endif-#ifndef CUBE_DEPRECATED_NO_EXPORT-#  define CUBE_DEPRECATED_NO_EXPORT CUBE_NO_EXPORT CUBE_DEPRECATED-#endif-#if 0-#  ifndef CUBE_NO_DEPRECATED-#    define CUBE_NO_DEPRECATED-#  endif-#endif-#endif-#ifndef __cplusplus-#error "This is a C++ header; please use a C++ compiler OR include cube/cube.h instead"-#endif-namespace cube {-constexpr std::string_view cubeId = "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB";-enum class SolveResult : int32_t {-    Success       = 0,-    Unsolvable    = 1,-    NotFound      = 2,-    InvalidSrc    = 3,-    InvalidTgt    = 4,-    UnknownErr    = 5-};-CUBE_EXPORT constexpr std::string_view to_string(SolveResult status) noexcept {-    switch (status) {-    case SolveResult::Success:      return "Success";-    case SolveResult::Unsolvable:   return "The cube configuration is unsolvable";-    case SolveResult::NotFound:     return "No solution found within the step limit";-    case SolveResult::InvalidSrc:   return "Invalid source color configuration";-    case SolveResult::InvalidTgt:   return "Invalid target color configuration";-    case SolveResult::UnknownErr:   return "Unknown error";-    }-}-enum class PermFormat : int {-    Face  = 0,-    Cubie = 1,-    Cycle = 2-};-struct Solution {-    SolveResult status;-    std::string maneuver;-    bool is_success() const noexcept-    {-        return status == SolveResult::Success;-    }-};-CUBE_EXPORT bool is_solvable(std::string_view color_cube);-[[nodiscard]] CUBE_EXPORT Solution solve(-    std::string_view src,-    std::string_view tgt = cubeId,-    int good = 22-);-[[nodiscard]] CUBE_EXPORT std::string apply_maneuver(-    std::string_view maneuver,-    std::string_view cube = cubeId-);-[[nodiscard]] CUBE_EXPORT std::string show_permutation(-    std::string_view ms_or_cube,-    PermFormat format = PermFormat::Cycle-);-}-namespace cube {-CUBE_EXPORT void set_table_dir(std::filesystem::path dir);-CUBE_EXPORT auto get_table_dir() -> std::filesystem::path;-CUBE_EXPORT bool tables_ready();-CUBE_EXPORT void preload_tables();-CUBE_EXPORT bool is_valid_config(std::string_view cube);-CUBE_EXPORT bool is_valid_maneuver(std::string_view maneuver);-}-namespace cube::show {-using std::size_t;-using namespace cube::data;-template<size_t N>-using StringArr = std::array<std::string_view,N>;-inline constexpr StringArr< 8> CornerToString       = { "urf", "ufl", "ulb", "ubr", "dfr", "dlf", "dbl", "drb" };-inline constexpr StringArr<12> EdgeToString         = { "ur","uf","ul","ub","dr","df","dl","db","fr","fl","bl","br" };-inline constexpr StringArr< 6> CenterToString       = { "u", "r", "f", "d", "l", "b" };-inline constexpr StringArr< 3> OrientationToString  = { "", "+", "-" };-inline constexpr StringArr<18> Move2Str             = { "U","U2","U'","R","R2","R'","F","F2","F'","D","D2","D'","L","L2","L'","B","B2","B'" };-inline constexpr StringArr<54> Face2Str             = { "U1","U2","U3","U4","U5","U6","U7","U8","U9","R1","R2","R3","R4","R5","R6","R7","R8","R9","F1","F2","F3","F4","F5","F6","F7","F8","F9","D1","D2","D3","D4","D5","D6","D7","D8","D9","L1","L2","L3","L4","L5","L6","L7","L8","L9","B1","B2","B3","B4","B5","B6","B7","B8","B9" };-inline constexpr std::string_view ColorSet          = "URFDLB";-inline constexpr std::string_view CornerSet         = "ABCDEFGH";-inline constexpr std::string_view EdgeSet           = "opqrstuvwxyz";-enum class CubeFormat {-    Face,-    Cubie,-    Cycle-};-template<typename Array, typename Formatter>-inline std::string seq2str_fmt(const Array &xs,-                           Formatter && fmt,-                           std::string_view sep="",-                           std::string_view pre="",-                           std::string_view suf="")-{-    const size_t len = xs.size();-    if(len == 0) { return std::string(pre) + std::string(suf); }-    std::stringstream ss;-    ss << pre << fmt(xs[0]);-    for(size_t i = 1; i < len; ++i) ss << sep << fmt(xs[i]);-    ss << suf;-    return ss.str();-}-template<typename Container>-inline std::string seq2str(const Container &xs,-                           std::string_view sep="",-                           std::string_view pre="",-                           std::string_view suf="")-{-    auto default_formatter = [](const auto& val) {-        using T = std::decay_t<decltype(val)>;-        if constexpr (std::is_same_v<T,uint8_t> || std::is_same_v<T,int8_t>) {-            return static_cast<int>(val);-        } else {-            return val;-        }-    };-    return seq2str_fmt(xs, default_formatter, sep, pre, suf);-}-inline std::string to_string(const ColorState& cs)-{-    return seq2str_fmt(cs.s, [](auto v) {-        switch(v){-        case U: return 'U';-        case R: return 'R';-        case F: return 'F';-        case D: return 'D';-        case L: return 'L';-        case B: return 'B';-        default: throw std::invalid_argument("to_string(ColorState): ???");-        }-    });-}-inline std::string to_string(const FaceCube& fc, bool use_digit=true)-{-    if(use_digit){-        return seq2str(fc.f);-    } else {-        return seq2str_fmt(fc.f, [](auto v) { return Face2Str[v]; });-    }-}-inline std::string to_string(const CubieCube& cc, CubeFormat fmt)-{-    switch(fmt){-    case CubeFormat::Face:-        return to_string(cc.toFaceCube(), false);-    case CubeFormat::Cubie:-        return seq2str_fmt(cc.cp, [](auto v) { return CornerSet[v]; }) +-               seq2str_fmt(cc.co, [](auto v) { return static_cast<char>('0'+v); }) +-               seq2str_fmt(cc.ep, [](auto v) { return EdgeSet[v]; }) +-               seq2str_fmt(cc.eo, [](auto v) { return static_cast<char>('0'+v);});-    default:-        const auto [fixed_corner,cycles_corner] = decomposite(cc.cp);-        const auto [fixed_edge, cycles_edge ]   = decomposite(cc.ep);-        std::string s1, s2;-        s1.reserve(64);-        s2.reserve(64);-        auto append_fixed = [&](std::string& out, const auto& fixed, const auto& ori_arr, auto name_table) {-            for(auto idx: fixed) {-                if(ori_arr[idx] == 0) continue;-                out += '(';-                out += OrientationToString[ori_arr[idx]];-                out += name_table[idx];-                out += ')';-            }-        };-        auto append_cycles = [&](std::string& out, const auto& cycles, const auto& ori_arr, auto name_table) {-            for(const auto& cycle: cycles) {-                const size_t N = cycle.size();-                if(N == 0) continue;-                out += '(';-                for(int i = 0; i < N; i++) {-                    if(i > 0) out += ',';-                    size_t prev_idx = cycle[(N-1+i)%N];-                    out += OrientationToString[ori_arr[prev_idx]];-                    out += name_table[cycle[i]];-                }-                out += ')';-            }-        };-        append_fixed(s1, fixed_corner, cc.co, CornerToString);-        append_cycles(s1, cycles_corner, cc.co, CornerToString);-        append_fixed(s2, fixed_edge, cc.eo, EdgeToString);-        append_cycles(s2, cycles_edge, cc.eo, EdgeToString);-        return s1.empty() && s2.empty() ? "id" : s1 + s2;-    }-}-inline std::string to_string(const std::vector<TurnMove>& ms)-{-    return seq2str_fmt(ms, [](auto v){-        return Move2Str[v];-    }, " ");-}-}-namespace cube {-using namespace cube::data;-namespace fs = std::filesystem;-void set_table_dir(fs::path dir) { config::set_table_dir(dir); }-auto get_table_dir() -> fs::path { return config::get_table_dir(); }-bool tables_ready() { return pdb::tables_ready(); }-void preload_tables() { pdb::preload_tables(); }-bool is_valid_config(std::string_view cube) { return ColorState::is_valid_config(cube); }-bool is_valid_maneuver(std::string_view maneuver) { return internal::is_valid_maneuver(maneuver); }-cube::solver::TwoPhaseOptimSolver TPS;-Solution solve(std::string_view src, std::string_view tgt, int good)-{-    if (src != cubeId && !is_valid_config(src)) return {SolveResult::InvalidSrc, ""};-    if (tgt != cubeId && !is_valid_config(tgt)) return {SolveResult::InvalidTgt, ""};-    if (src == tgt) return {SolveResult::Success, ""};-    auto cc_src = ColorState::fromString(src).toCubieCube();-    auto cc_tgt = ColorState::fromString(tgt).toCubieCube();-    CubieCube cc = ~cc_tgt * cc_src;-    if (!cc.isSolvable()) return {SolveResult::Unsolvable, ""};-    const auto& [found, s1, s2] = TPS.solve(pdb::Coord::CubieCube2Coord(cc), good < 0 ? 0 : good);-    if (!found) return {SolveResult::NotFound, ""};-    std::vector<TurnMove> sol;-    size_t n1 = s1.size(), n2 = s2.size();-    if (!s1.empty() && !s2.empty() && s1[n1 - 1] / 3 == s2[0] / 3) {-        sol.insert(sol.end(), s1.begin(), s1.end() - 1);-        int m = (s1[n1 - 1] + s2[0] - s2[0] / 3 * 6 + 2) % 4;-        if (m != 0) sol.push_back(static_cast<TurnMove>(s2[0] / 3 * 3 + m - 1));-        sol.insert(sol.end(), s2.begin() + 1, s2.end());-    } else {-        sol.insert(sol.end(), s1.begin(), s1.end());-        sol.insert(sol.end(), s2.begin(), s2.end());-    }-    return {SolveResult::Success, show::to_string(sol)};-}-bool is_solvable(std::string_view color_cube) {-    return is_valid_config(color_cube) &&-           ColorState::fromString(color_cube).toCubieCube().isSolvable();-}-std::string apply_maneuver(std::string_view maneuver, std::string_view cube_state) {-    if (cube_state.size() != 54 || !is_valid_maneuver(maneuver)) {-        throw std::invalid_argument("Invalid cube format or maneuver string.");-    }-    const auto ms = internal::parse_maneuver(maneuver);-    return internal::apply_maneuver(cube_state, ms);-}-std::string show_permutation(std::string_view ms_or_cube, PermFormat format) {-    std::string cube_str;-    if (is_valid_config(ms_or_cube)) {-        cube_str = ms_or_cube;-    } else if (is_valid_maneuver(ms_or_cube)) {-        auto ms = internal::parse_maneuver(ms_or_cube);-        cube_str = internal::apply_maneuver(cubeId, ms);-    } else {-        throw std::invalid_argument("Input is neither a valid configuration nor a valid maneuver.");-    }-    auto cc = ColorState::fromString(cube_str).toCubieCube();-    return show::to_string(cc, show::CubeFormat(static_cast<int>(format)));-}-}-#define CUBE_VERSION_FULL  v0.5.0-#define CUBE_VERSION_MAJOR 0-#define CUBE_VERSION_MINOR 5-#define CUBE_VERSION_PATCH 0-#define CUBE_VERSION_BUILD-#ifdef __cplusplus-    #define Default(x) = x-#else-    #define Default(x)-#endif-#define CUBE_BS 128-#define CUBE_ID "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB"-#ifndef CF_ENUM-    #if defined(__cplusplus)-        #define CF_ENUM(_type, _name) \-            int __CF_ENUM_##_name; \-            enum _name : _type-    #elif defined(__clang__) || defined(__OBJC__)-        #define CF_ENUM(_type, _name) \-            enum _name : _type _name; \-            enum _name: _type-    #else-        #define CF_ENUM(_type, _name) \-            _type _name; \-            enum-    #endif-#endif-typedef CF_ENUM(int32_t,SolveResult) {-    SolveResultSuccess = 0,-    SolveResultUnsolvable = 1,-    SolveResultNotFound = 2,-    SolveResultInvalidSrc = 3,-    SolveResultInvalidTgt = 4,-    SolveResultUnknownErr = 5-};-static inline const char* solve_result_info(SolveResult sr)-{-    switch(sr) {-    case SolveResultSuccess:    return "Success.";-    case SolveResultUnsolvable: return "The cube configuration is unsolvable.";-    case SolveResultNotFound:   return "No solution found within the step limit.";-    case SolveResultInvalidSrc: return "Invalid source color configuration.";-    case SolveResultInvalidTgt: return "Invalid target color configuration.";-    case SolveResultUnknownErr: return "Unknown error.";-    default:                    return "???";-    }-}-#ifdef __cplusplus-extern "C" {-#endif-CUBE_EXPORT const char *solve_result_to_string(int32_t sr);-CUBE_EXPORT SolveResult solve(-    char*       buf,-    const char* src         Default(CUBE_ID),-    const char* tgt         Default(CUBE_ID),-    int         good        Default(22)-);-CUBE_EXPORT bool solvable(-    const char* color_cube  Default(CUBE_ID)-);-CUBE_EXPORT bool facecube(-    char* buf,-    const char* maneuver    Default(""),-    const char *cube        Default(CUBE_ID)-);-CUBE_EXPORT bool permutation(-    char*       buf,-    const char* ms_or_cube  Default(CUBE_ID),-    int         format      Default(2)-);-#ifdef __cplusplus-}-#endif-extern "C" {+ * Version: v0.5.1+ * Date: 2026-11-06+ * Homepage: https://github.com/coshz/cube+ * License: MIT+ *+ * Copyright (c) 2026 coshz <fsinhx@gmail.com>. All rights reserved.+ */++#include <cstddef>+#include <vector>+#include <array>+#include <algorithm>+#include <utility>+#include <numeric>+#include <stdexcept>+#include <initializer_list>+#include <cassert>+#include <type_traits>+#include <cstdint>+#include <string_view>+#include <set>+#include <memory>+#include <filesystem>+#include <cstdio>+#include <limits>+#include <queue>+#include <exception>+#include <fstream>+#include <ios>+#include <iostream>+#include <tuple>+#include <cstdlib>+#include <mutex>+#include <string>+#include <cstring>+#include <regex>+#include <sstream>+#include <stdbool.h>+#include <stdint.h>++namespace cube::math {+using std::size_t;+template<typename VectorLike>+auto decomposite(const VectorLike &xs) -> std::pair<+    std::vector<typename VectorLike::value_type>,+    std::vector<std::vector<typename VectorLike::value_type>>+>+{+    using T = typename VectorLike::value_type;+    std::vector<T> fixed;+    std::vector<std::vector<T>> cycles;+    std::vector<bool> visited(xs.size(),false);+    for(int i = 0; i < xs.size(); ++i) {+        if(visited[i]) continue;+        std::vector<T> cycle;+        for(int j = xs[i]; j != i; j = xs[j]) {+            visited[j] = true;+            cycle.push_back(static_cast<T>(j));+        }+        visited[i] = true;+        cycle.push_back(static_cast<T>(i));+        if(cycle.size() > 1) cycles.push_back(cycle);+        else fixed.push_back(cycle[0]);+    }+    std::sort(cycles.begin(), cycles.end(), [](auto &v1, auto &v2){+        return v1.size() > v2.size();+    });+    return std::make_pair(fixed,cycles);+}+constexpr size_t factorial(size_t n)+{+    if(n>=21) throw std::invalid_argument("factorial(n) overflows for n >= 21");+    return n == 0 ? 1 : n * factorial(n-1);+}+constexpr size_t binomial(size_t n, size_t k)+{+    if(n < k)   return 0;+    if(n == k)  return 1;+    size_t r = 1, m = std::min(k, n-k);+    for(size_t i = 1; i <= m; i++) r *= n-i+1;+    for(size_t i = 1; i <= m; i++) r /= i;+    return r;+};+template<typename T, size_t N>+size_t orderOf(const std::array<T,N> &xs)+{+    size_t m = 1;+    auto cs = decomposite(xs);+    for(size_t i = 1; i < cs.size(); i++) { m = std::lcm(m, cs[i].size()); }+    return m;+}+template<typename T, size_t N>+constexpr size_t rankOf(const std::array<T,N> &xs)+{+    size_t r = 0;+    std::array<bool,N> used {false};+    for(size_t i = 0; i < N; i++)+    {+        int cnt = 0;+        for(int j=0; j < xs[i]; j++) if(!used[j]) cnt++;+        r += cnt * factorial(N - i - 1);+        used[xs[i]] = true;+    }+    return r;+}+template<typename T, size_t N>+constexpr std::array<T,N> fromRank(size_t r)+{+    std::array<T,N> A{};+    std::array<bool,N> used {false};+    for(size_t i = 0; i < N; i++)+    {+        size_t f = factorial(N - i - 1);+        size_t cnt = r / f;+        r %= f;+        for(size_t j = 0; j < N; j++)+        {+            if(used[j]) continue;+            if(cnt-- == 0) {+                A[i] = j;+                used[j] = true;+                break;+            }+        }+    }+    return A;+}+template<typename F, typename T, size_t N>+constexpr std::array<T,N+1> nestList(F &&f, T &&x)+{+    std::array<T,N+1> r;+    r[0] = x;+    for(auto i = 1; i <= N; i++) r[i] = f(r[i-1]);+    return r;+}+template<size_t Begin, size_t End, typename T, size_t N>+constexpr auto takeByRange(const std::array<T,N>& xs) -> std::array<T,End-Begin+1>+{+    static_assert(Begin <= End && End < N);+    std::array<T,End-Begin+1> ys;+    std::copy(xs.begin()+Begin,xs.begin()+End+1,ys.begin());+    return ys;+}+template<size_t B, typename Int, size_t N>+constexpr auto fromDigits(const std::array<Int,N> &xs) -> size_t+{+    auto pow = [](size_t base, size_t exp) -> size_t {+        size_t prod = 1;+        for(size_t i = 0; i < exp; i++) prod *= base;+        return prod;+    };+    size_t res = 0;+    for(size_t i = 0; i < N; i++) res += static_cast<size_t>(xs[i]) * pow(B, N-i-1);+    return res;+}+template<size_t B, size_t N, typename Int>+constexpr auto toDigits(size_t i) -> std::array<Int,N>+{+    auto pow = [](size_t base, size_t exp) -> size_t {+        size_t prod = 1;+        for(size_t i = 0; i < exp; i++) prod *= base;+        return prod;+    };+    std::array<Int,N> a {};+    for(size_t k = 0; k < N; k++) {+        size_t z = pow(B, N-1-k);+        a[k] = static_cast<Int>(i / z);+        i = i % z;+    }+    return a;+}+template<size_t N, size_t M>+constexpr auto lexicalOrderFromIndices(const std::array<size_t,M> &X) -> int+{+    static_assert(M<=N);+    int rank = 0;+    for(size_t i = 0; i < M; i++) rank += binomial(N-1-X[i],M-i);+    return rank;+}+template<size_t N, size_t M>+constexpr auto lexicalOrderToIndices(int rank) -> std::array<size_t,M>+{+    static_assert(M<=N);+    std::array<size_t,M> X {};+    size_t n=rank, k=0;+    for(size_t i = 0; i < M; i++) {+        while(binomial(N-1-k,M-i) > n || n >= binomial(N-k,M-i)) k++;+        X[i] = k;+        n -= binomial(N-1-k,M-i);+        k += 1;+    }+    return X;+}+template<size_t N, typename ArrayLike>+constexpr bool isValidPermutation(const ArrayLike& xs)+{+    if(xs.size() != N) return false;+    std::array<bool,N> visited{};+    for(auto i = 0; i < N; ++i) {+        size_t val = xs[i];+        if(xs[i] < 0 || xs[i] >= N) return false;+        if(visited[val]) return false;+        visited[val] = true;+    }+    return true;+}+template<typename Array, typename Perm>+constexpr Array backpermute(const Array& src, const Perm& P)+{+    Array out{src};+    for (size_t i = 0; i < P.size(); ++i) { out[i] = src[P[i]]; }+    return out;+}+template<typename Array, typename Perm>+constexpr Array forepermute(const Array& src, const Perm& P)+{+    Array out{src};+    for (size_t i = 0; i < P.size(); ++i) { out[P[i]] = src[i]; }+    return out;+}+}+namespace cube::data {+enum Face       { U1,U2,U3,U4,U5,U6,U7,U8,U9,R1,R2,R3,R4,R5,R6,R7,R8,R9,F1,F2,F3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,D7,D8,D9,L1,L2,L3,L4,L5,L6,L7,L8,L9,B1,B2,B3,B4,B5,B6,B7,B8,B9 };+enum Layer      { U,R,F,D,L,B };+enum TurnMove   { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };+enum Symmetry   { S_URF3,S_F2,S_U4,S_LR2 };+enum ColorIndex { UCol,RCol,FCol,DCol,LCol,BCol,NoCol };+enum Corner     { URF,UFL,ULB,UBR,DFR,DLF,DBL,DRB };+enum Edge       { UR,UF,UL,UB,DR,DF,DL,DB,FR,FL,BL,BR };+struct OrientedCorner   { Corner c; unsigned o; };+struct OrientedEdge     { Edge e;   unsigned o; };+typedef ColorIndex      SingleFace[9];+typedef ColorIndex      CornerColorIndex[8][3];+typedef ColorIndex      EdgeColorIndex[12][2];+typedef ColorIndex      FaceletColor[54];+typedef Face            CentreFacelet[6];+typedef Face            CornerFacelet[8][3];+typedef Face            EdgeFacelet[12][2];+typedef Face            Facelet[54];+typedef OrientedCorner  CornerCubie[8];+typedef OrientedEdge    EdgeCubie[12];+typedef Corner          EdgeNeighbour[12][2];+const CornerColorIndex  CCI = {{UCol,RCol,FCol},{UCol,FCol,LCol},{UCol,LCol,BCol},{UCol,BCol,RCol},{DCol,FCol,RCol},{DCol,LCol,FCol},{DCol,BCol,LCol},{DCol,RCol,BCol}};+const EdgeColorIndex    ECI = {{UCol,RCol},{UCol,FCol},{UCol,LCol},{UCol,BCol},{DCol,RCol},{DCol,FCol}, {DCol,LCol},{DCol,BCol},{FCol,RCol},{FCol,LCol},{BCol,LCol},{BCol,RCol}};+const CentreFacelet     CC  = {U5,R5,F5,D5,L5,B5};+const CornerFacelet     CF  = {{U9,R1,F3},{U7,F1,L3},{U1,L1,B3},{U3,B1,R3},{D3,F9,R7},{D1,L9,F7},{D7,B9,L7},{D9,R9,B7}};+const EdgeFacelet       EF  = {{U6,R2},{U8,F2},{U4,L2},{U2,B2},{D6,R8},{D2,F8}, {D4,L8},{D8,B8},{F6,R4},{F4,L6},{B6,L4},{B4,R6}};+const EdgeNeighbour     EN  = {{URF,UBR},{UFL,URF},{ULB,UFL},{UBR,ULB},{DRB,DFR},{DFR,DLF}, {DLF,DBL},{DBL,DRB},{URF,DFR},{DLF,UFL},{DBL,ULB},{UBR,DRB}};+const Facelet FaceletMove[6] = {+    {U3,U6,U9,U2,U5,U8,U1,U4,U7,F1,F2,F3,R4,R5,R6,R7,R8,R9,L1,L2,L3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,D7,D8,D9,B1,B2,B3,L4,L5,L6,L7,L8,L9,R1,R2,R3,B4,B5,B6,B7,B8,B9},+    {U1,U2,B7,U4,U5,B4,U7,U8,B1,R3,R6,R9,R2,R5,R8,R1,R4,R7,F1,F2,U3,F4,F5,U6,F7,F8,U9,D1,D2,F3,D4,D5,F6,D7,D8,F9,L1,L2,L3,L4,L5,L6,L7,L8,L9,D9,B2,B3,D6,B5,B6,D3,B8,B9},+    {U1,U2,U3,U4,U5,U6,R1,R4,R7,D3,R2,R3,D2,R5,R6,D1,R8,R9,F3,F6,F9,F2,F5,F8,F1,F4,F7,L3,L6,L9,D4,D5,D6,D7,D8,D9,L1,L2,U9,L4,L5,U8,L7,L8,U7,B1,B2,B3,B4,B5,B6,B7,B8,B9},+    {U1,U2,U3,U4,U5,U6,U7,U8,U9,R1,R2,R3,R4,R5,R6,B7,B8,B9,F1,F2,F3,F4,F5,F6,R7,R8,R9,D3,D6,D9,D2,D5,D8,D1,D4,D7,L1,L2,L3,L4,L5,L6,F7,F8,F9,B1,B2,B3,B4,B5,B6,L7,L8,L9},+    {F1,U2,U3,F4,U5,U6,F7,U8,U9,R1,R2,R3,R4,R5,R6,R7,R8,R9,D1,F2,F3,D4,F5,F6,D7,F8,F9,B9,D2,D3,B6,D5,D6,B3,D8,D9,L3,L6,L9,L2,L5,L8,L1,L4,L7,B1,B2,U7,B4,B5,U4,B7,B8,U1},+    {L7,L4,L1,U4,U5,U6,U7,U8,U9,R1,R2,U1,R4,R5,U2,R7,R8,U3,F1,F2,F3,F4,F5,F6,F7,F8,F9,D1,D2,D3,D4,D5,D6,R9,R6,R3,D7,L2,L3,D8,L5,L6,D9,L8,L9,B3,B6,B9,B2,B5,B8,B1,B4,B7}+};+const Facelet FaceletSym[4] = {+    {R9,R8,R7,R6,R5,R4,R3,R2,R1,F3,F6,F9,F2,F5,F8,F1,F4,F7,U3,U6,U9,U2,U5,U8,U1,U4,U7,L1,L2,L3,L4,L5,L6,L7,L8,L9,B7,B4,B1,B8,B5,B2,B9,B6,B3,D3,D6,D9,D2,D5,D8,D1,D4,D7},+    {D9,D8,D7,D6,D5,D4,D3,D2,D1,L9,L8,L7,L6,L5,L4,L3,L2,L1,F9,F8,F7,F6,F5,F4,F3,F2,F1,U9,U8,U7,U6,U5,U4,U3,U2,U1,R9,R8,R7,R6,R5,R4,R3,R2,R1,B9,B8,B7,B6,B5,B4,B3,B2,B1},+    {U3,U6,U9,U2,U5,U8,U1,U4,U7,F1,F2,F3,F4,F5,F6,F7,F8,F9,L1,L2,L3,L4,L5,L6,L7,L8,L9,D7,D4,D1,D8,D5,D2,D9,D6,D3,B1,B2,B3,B4,B5,B6,B7,B8,B9,R1,R2,R3,R4,R5,R6,R7,R8,R9},+    {U3,U2,U1,U6,U5,U4,U9,U8,U7,L3,L2,L1,L6,L5,L4,L9,L8,L7,F3,F2,F1,F6,F5,F4,F9,F8,F7,D3,D2,D1,D6,D5,D4,D9,D8,D7,R3,R2,R1,R6,R5,R4,R9,R8,R7,B3,B2,B1,B6,B5,B4,B9,B8,B7}+};+const CornerCubie CornerCubieMove[6] = {+    {{UBR,0},{URF,0},{UFL,0},{ULB,0},{DFR,0},{DLF,0},{DBL,0},{DRB,0}},+    {{DFR,2},{UFL,0},{ULB,0},{URF,1},{DRB,1},{DLF,0},{DBL,0},{UBR,2}},+    {{UFL,1},{DLF,2},{ULB,0},{UBR,0},{URF,2},{DFR,1},{DBL,0},{DRB,0}},+    {{URF,0},{UFL,0},{ULB,0},{UBR,0},{DLF,0},{DBL,0},{DRB,0},{DFR,0}},+    {{URF,0},{ULB,1},{DBL,2},{UBR,0},{DFR,0},{UFL,2},{DLF,1},{DRB,0}},+    {{URF,0},{UFL,0},{UBR,1},{DRB,2},{DFR,0},{DLF,0},{ULB,2},{DBL,1}}+};+const EdgeCubie EdgeCubieMove[6] = {+    {{UB,0},{UR,0},{UF,0},{UL,0},{DR,0},{DF,0},{DL,0},{DB,0},{FR,0},{FL,0},{BL,0},{BR,0}},+    {{FR,0},{UF,0},{UL,0},{UB,0},{BR,0},{DF,0},{DL,0},{DB,0},{DR,0},{FL,0},{BL,0},{UR,0}},+    {{UR,0},{FL,1},{UL,0},{UB,0},{DR,0},{FR,1},{DL,0},{DB,0},{UF,1},{DF,1},{BL,0},{BR,0}},+    {{UR,0},{UF,0},{UL,0},{UB,0},{DF,0},{DL,0},{DB,0},{DR,0},{FR,0},{FL,0},{BL,0},{BR,0}},+    {{UR,0},{UF,0},{BL,0},{UB,0},{DR,0},{DF,0},{FL,0},{DB,0},{FR,0},{UL,0},{DL,0},{BR,0}},+    {{UR,0},{UF,0},{UL,0},{BR,1},{DR,0},{DF,0},{DL,0},{BL,1},{FR,0},{FL,0},{UB,1},{DB,1}}+};+const CornerCubie CornerCubieSym[4] = {+    {{URF,1},{DFR,2},{DLF,1},{UFL,2},{UBR,2},{DRB,1},{DBL,2},{ULB,1}},+    {{DLF,0},{DFR,0},{DRB,0},{DBL,0},{UFL,0},{URF,0},{UBR,0},{ULB,0}},+    {{UBR,0},{URF,0},{UFL,0},{ULB,0},{DRB,0},{DFR,0},{DLF,0},{DBL,0}},+    {{UFL,3},{URF,3},{UBR,3},{ULB,3},{DLF,3},{DFR,3},{DRB,3},{DBL,3}}+};+const EdgeCubie EdgeCubieSym[4] = {+    {{UF,1},{FR,0},{DF,1},{FL,0},{UB,1},{BR,0},{DB,1},{BL,0},{UR,1},{DR,1},{DL,1},{UL,1}},+    {{DL,0},{DF,0},{DR,0},{DB,0},{UL,0},{UF,0},{UR,0},{UB,0},{FL,0},{FR,0},{BR,0},{BL,0}},+    {{UB,0},{UR,0},{UF,0},{UL,0},{DB,0},{DR,0},{DF,0},{DL,0},{BR,1},{FR,1},{FL,1},{BL,1}},+    {{UL,0},{UF,0},{UR,0},{UB,0},{DL,0},{DF,0},{DR,0},{DB,0},{FL,0},{FR,0},{BR,0},{BL,0}}+};+enum Constant {+    GN_HTM      = 20,+    GN_QTM      = 26,+    N_MOVE      = 18,+    N_TWIST     = 2187,+    N_FLIP      = 2048,+    N_SLICE     = 495,+    N_CORNER    = 40320,+    N_EDGE8     = 40320,+    N_EDGE4     = 24,+    N_SYM       = 48,+    N_SYM_D4h   = 16,+    EQ_FLIPSLICE= 64430,+    EQ_CORNER   = 2768,+};+using std::size_t;+using namespace cube::math;+template<size_t N,typename T=int>+struct Perm+{+    using value_type = T;+    static constexpr size_t size() { return N; }+    constexpr Perm() noexcept+    {+        for(size_t i = 0; i < N; ++i) X[i] = static_cast<T>(i);+    }+    constexpr Perm(const std::array<T,N>& xs) noexcept+        :X{xs}+    {+        assert(isValidPermutation<N>(xs) && "array must be a valid permutation");+    }+    constexpr Perm(std::initializer_list<T> xs) noexcept+    {+        assert(xs.size() == N && "size mismatch");+        auto dit = X.begin();+        for(auto it = xs.begin(); it != xs.end(); it++, dit++) { *dit = *it; }+        assert(isValidPermutation<N>(X) && "invalid permutation list");+    }+    template<typename ArrayLike>+    constexpr ArrayLike act_right(const ArrayLike& src) const noexcept+    {+        return backpermute(src,this->X);+    }+    friend constexpr bool operator==(const Perm &lhs, const Perm& rhs) noexcept { return lhs.X == rhs.X; }+    friend constexpr Perm operator*(const Perm &P, const Perm& Q) noexcept      { return Q.act_right(P); }+    constexpr Perm&     operator*=(const Perm& rhs) noexcept    { return *this = *this * rhs; }+    constexpr Perm      operator~() const noexcept              { return { forepermute(Perm::id.X, this->X) }; }+    constexpr T&        operator[](size_t idx) noexcept         { return X[idx]; }+    constexpr const T&  operator[](size_t idx) const noexcept   { return X[idx]; }+    bool parity() const+    {+        const auto [fixed, cs] = decomposite(this->X);+        int s = 1;+        for(auto &c:cs) s *= (c.size() % 2 == 0) ? -1 : 1;+        return s == 1;+    }+    size_t order() const { return orderOf(X); }+    constexpr size_t rank() const { return rankOf(X); }+    static constexpr Perm<N,T> fromRank(size_t i) { return { cube::math::fromRank<T,N>(i) }; }+    static const Perm id;+    std::array<T,N> X{};+};+template<size_t N,typename T>+inline constexpr Perm<N,T> Perm<N,T>::id{};+template<size_t N, size_t L, typename T=int>+struct CArray+{+    using value_type = T;+    static constexpr size_t period = N;+    static constexpr size_t size() noexcept { return L; }+    constexpr CArray() noexcept {}+    constexpr CArray(const std::array<T,L> &arr) noexcept+        :xs{arr}+    {+        auto n = static_cast<T>(N);+        for(size_t i = 0; i < L; i++) { xs[i] = (xs[i] % n + n) % n; }+    }+    constexpr CArray(std::initializer_list<T> list) noexcept+    {+        auto n = static_cast<T>(N);+        std::size_t i = 0;+        for(T val : list) { if(i < L) { xs[i++] = (val % n + n) % n; } }+    }+    constexpr T& operator[](size_t idx) noexcept             { return xs[idx]; }+    constexpr const T& operator[](size_t idx) const noexcept { return xs[idx]; }+    constexpr CArray& operator+=(const CArray& rhs)+    {+        for(size_t i = 0; i < L; i++) xs[i] = (xs[i] + rhs.xs[i]) % N;+        return *this;+    }+    friend constexpr bool operator==(const CArray& lhs, const CArray& rhs) noexcept { return lhs.xs == rhs.xs; }+    friend constexpr CArray operator+(CArray lhs, const CArray& rhs) noexcept { return lhs += rhs; }+    constexpr CArray operator~() const noexcept+    {+        CArray<N,L,T> inv {};+        auto n = static_cast<T>(N);+        for(size_t i = 0; i < L; i++) inv[i] = (n - xs[i]) % n;+        return inv;+    }+    constexpr T sum() const noexcept+    {+        T s = 0;+        for(size_t i = 0; i < L; i++) s += xs[i];+        return s % N;+    }+    static const CArray id;+    std::array<T,L> xs {};+};+template<size_t N, size_t L, typename T>+inline constexpr CArray<N,L,T> CArray<N,L,T>::id{};+template<size_t N, size_t L, typename T>+constexpr CArray<N,L,T> operator*(const CArray<N,L,T> &xs, const Perm<L,T> &P)+{+    return P.act_right(xs);+}+template<size_t N, size_t L, typename T>+constexpr CArray<N,L,T>& operator*=(CArray<N,L,T> &xs, const Perm<L,T> &P)+{+    return xs = P.act_right(xs);+}+template<typename T, size_t N, size_t... Ns>+struct ArrayHelper+{+    using type = std::array<typename ArrayHelper<T,Ns...>::type,N>;+};+template<typename T, size_t N>+struct ArrayHelper<T,N>+{+    using type = std::array<T,N>;+};+template<typename T, size_t... Ns>+struct NArray+{+    using value_type = T;+    static constexpr size_t size = (Ns * ...);+    static constexpr size_t dim = sizeof...(Ns);+    static constexpr std::array<size_t,dim> shape { Ns... };+    typename ArrayHelper<T,Ns...>::type storage;+    auto& operator[](size_t i) noexcept             { return storage[i]; }+    const auto& operator[](size_t i) const noexcept { return storage[i]; }+    template<typename U, std::enable_if_t<std::is_integral_v<U>,int> = 0>+    auto& operator[](const std::array<U,dim>& indices) noexcept+    {+        return std::apply(+            [this](auto... args) -> decltype(auto) { return (*this)(args...); },+            indices+        );+    }+    template<typename U, std::enable_if_t<std::is_integral_v<U>,int> = 0>+    const auto& operator[](const std::array<U,dim>& indices) const noexcept+    { return const_cast<NArray*>(this)->operator[](indices); }+    template<typename... Is, std::enable_if_t<sizeof...(Is)==dim, int> = 0>+    decltype(auto) operator()(Is... is) noexcept+    { return at<0>(storage, {size_t(is)...}); }+    template<typename... Is, std::enable_if_t<sizeof...(Is)==dim, int> = 0>+    decltype(auto) operator()(Is... is) const noexcept+    { return at<0>(storage, {size_t(is)...}); }+    template<typename F> void for_each(F&& f)       { for_each_rec(storage, f); }+    template<typename F> void for_each(F&& f) const { for_each_rec(storage, f); }+    void fill(const T &val) { for_each([&val](T& e){ e = val; }); }+private:+    template<size_t I, typename Arr>+    static decltype(auto) at(Arr&& arr, const std::array<size_t,dim>& indices)+    {+        if constexpr (I+1==dim) return arr[indices[I]];+        else                    return at<I+1>(arr[indices[I]], indices);+    }+    template<typename Arr, typename F>+    static void for_each_rec(Arr&& arr, F&& f)+    {+        for(auto& e: arr)+        {+            if constexpr (std::is_same_v<std::remove_reference_t<decltype(e)>,T>) {+                f(e);+            } else {+                for_each_rec(e,f);+            }+        }+    }+};+}+namespace cube {+using namespace cube::data;+typedef std::int8_t cube_value_t;+typedef Perm<54,    cube_value_t>   FacePerm;+typedef Perm<8,     cube_value_t>   CornerPerm;+typedef Perm<12,    cube_value_t>   EdgePerm;+typedef CArray<3, 8,cube_value_t>   CornerOri;+typedef CArray<2,12,cube_value_t>   EdgeOri;+struct ColorState;+struct FaceCube;+struct CubieCube;+constexpr CornerPerm operator*(const CornerPerm &cp, const CubieCube &cc);+constexpr CornerOri  operator*(const CornerOri  &co, const CubieCube &cc);+constexpr EdgePerm   operator*(const EdgePerm   &ep, const CubieCube &cc);+constexpr EdgeOri    operator*(const EdgeOri    &eo, const CubieCube &cc);+struct ColorState+{+    std::array<Layer,54> s;+    Layer & operator[](size_t i) noexcept           { return s[i]; }+    const Layer operator[](size_t i) const noexcept { return s[i]; }+    static ColorState fromString(std::string_view cube);+    static bool is_valid_config(std::string_view cube);+    FaceCube  toFaceCube() const;+    CubieCube toCubieCube() const;+    static const ColorState id;+};+inline const ColorState ColorState::id = {{U,U,U,U,U,U,U,U,U,R,R,R,R,R,R,R,R,R,F,F,F,F,F,F,F,F,F,D,D,D,D,D,D,D,D,D,L,L,L,L,L,L,L,L,L,B,B,B,B,B,B,B,B,B}};+struct FaceCube+{+    FacePerm f;+    CubieCube toCubieCube() const;+    friend constexpr FaceCube operator*(const FaceCube &lhs, const FaceCube &rhs)+    { return { lhs.f * rhs.f }; }+    constexpr FaceCube& operator*=(const FaceCube &rhs)+    { return *this = *this * rhs; }+    constexpr FaceCube operator~() const+    { return { ~f }; }+    friend bool operator==(const FaceCube &lhs, const FaceCube &rhs)+    { return lhs.f == rhs.f; }+    static const FaceCube id;+};+struct CubieCube+{+    CornerPerm  cp;+    CornerOri   co;+    EdgePerm    ep;+    EdgeOri     eo;+    FaceCube toFaceCube() const;+    bool isSolvable() const+    {  return cp.parity() == ep.parity() && co.sum() == 0 && eo.sum() == 0; }+    friend constexpr CubieCube operator*(const CubieCube &a, const CubieCube &b)+    { return { a.cp*b, a.co*b, a.ep*b, a.eo*b }; }+    constexpr CubieCube& operator*=(const CubieCube &rhs)+    { return *this = *this * rhs; }+    constexpr CubieCube operator~() const+    {+        auto cp_inv = ~cp;+        auto ep_inv = ~ep;+        return { cp_inv, ~(co*cp_inv), ep_inv, ~(eo*ep_inv) };+    }+    friend bool operator==(const CubieCube &lhs, const CubieCube &rhs)+    { return lhs.cp == rhs.cp && lhs.co == rhs.co && lhs.ep == rhs.ep && lhs.eo == rhs.eo; }+    static const CubieCube id;+};+inline constexpr CornerPerm operator*(const CornerPerm &cp, const CubieCube &cc) { return cp * cc.cp; }+inline constexpr CornerOri  operator*(const CornerOri &co,  const CubieCube &cc) { return co * cc.cp + cc.co; }+inline constexpr EdgePerm   operator*(const EdgePerm &ep,   const CubieCube &cc) { return ep * cc.ep; }+inline constexpr EdgeOri    operator*(const EdgeOri &eo,    const CubieCube &cc) { return eo * cc.ep + cc.eo; }+inline constexpr CornerPerm    eCP = {0,1,2,3,4,5,6,7};+inline constexpr EdgePerm      eEP = {0,1,2,3,4,5,6,7,8,9,10,11};+inline constexpr CornerOri     eCO = {0,0,0,0,0,0,0,0};+inline constexpr EdgeOri       eEO = {0,0,0,0,0,0,0,0,0,0,0,0};+inline constexpr FacePerm      eFP = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53};+inline constexpr FaceCube   FaceCube::id = FaceCube{eFP};+inline constexpr CubieCube  CubieCube::id = CubieCube{eCP,eCO,eEP,eEO};+inline constexpr CubieCube mU = {{3,0,1,2,4,5,6,7},{0,0,0,0,0,0,0,0},{3,0,1,2,4,5,6,7,8,9,10,11},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube mR = {{4,1,2,0,7,5,6,3},{2,0,0,1,1,0,0,2},{8,1,2,3,11,5,6,7,4,9,10,0},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube mF = {{1,5,2,3,0,4,6,7},{1,2,0,0,2,1,0,0},{0,9,2,3,4,8,6,7,1,5,10,11},{0,1,0,0,0,1,0,0,1,1,0,0}};+inline constexpr CubieCube mD = {{0,1,2,3,5,6,7,4},{0,0,0,0,0,0,0,0},{0,1,2,3,5,6,7,4,8,9,10,11},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube mL = {{0,2,6,3,4,1,5,7},{0,1,2,0,0,2,1,0},{0,1,10,3,4,5,9,7,8,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube mB = {{0,1,3,7,4,5,2,6},{0,0,1,2,0,0,2,1},{0,1,2,11,4,5,6,10,8,9,3,7},{0,0,0,1,0,0,0,1,0,0,1,1}};+inline constexpr std::array<CubieCube,18>+    ElementaryMove = { mU,mU*mU,mU*mU*mU,mR,mR*mR,mR*mR*mR,mF,mF*mF,mF*mF*mF,mD,mD*mD,mD*mD*mD,mL,mL*mL,mL*mL*mL,mB,mB*mB,mB*mB*mB };+inline constexpr FaceCube pU = {{6,3,0,7,4,1,8,5,2,45,46,47,12,13,14,15,16,17,9,10,11,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,39,40,41,42,43,44,36,37,38,48,49,50,51,52,53}};+inline constexpr FaceCube pR = {{0,1,20,3,4,23,6,7,26,15,12,9,16,13,10,17,14,11,18,19,29,21,22,32,24,25,35,27,28,51,30,31,48,33,34,45,36,37,38,39,40,41,42,43,44,8,46,47,5,49,50,2,52,53}};+inline constexpr FaceCube pF = {{0,1,2,3,4,5,44,41,38,6,10,11,7,13,14,8,16,17,24,21,18,25,22,19,26,23,20,15,12,9,30,31,32,33,34,35,36,37,27,39,40,28,42,43,29,45,46,47,48,49,50,51,52,53}};+inline constexpr FaceCube pD = {{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,24,25,26,18,19,20,21,22,23,42,43,44,33,30,27,34,31,28,35,32,29,36,37,38,39,40,41,51,52,53,45,46,47,48,49,50,15,16,17}};+inline constexpr FaceCube pL = {{53,1,2,50,4,5,47,7,8,9,10,11,12,13,14,15,16,17,0,19,20,3,22,23,6,25,26,18,28,29,21,31,32,24,34,35,42,39,36,43,40,37,44,41,38,45,46,33,48,49,30,51,52,27}};+inline constexpr FaceCube pB = {{11,14,17,3,4,5,6,7,8,9,10,35,12,13,34,15,16,33,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,39,42,2,37,38,1,40,41,0,43,44,51,48,45,52,49,46,53,50,47}};+inline constexpr std::array<FaceCube,18>+    ElementaryPerm = { pU,pU*pU,pU*pU*pU,pR,pR*pR,pR*pR*pR,pF,pF*pF,pF*pF*pF,pD,pD*pD,pD*pD*pD,pL,pL*pL,pL*pL*pL,pB,pB*pB,pB*pB*pB };+inline constexpr std::array<TurnMove,N_MOVE> turn_entries = { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };+inline constexpr std::array<TurnMove,N_MOVE> turn_inv_entries = { Ux3,Ux2,Ux1,Rx3,Rx2,Rx1,Fx3,Fx2,Fx1,Dx3,Dx2,Dx1,Lx3,Lx2,Lx1,Bx3,Bx2,Bx1 };+inline constexpr TurnMove operator~(TurnMove m) { return turn_inv_entries[m]; }+inline FaceCube operator*(const FaceCube &c, const std::vector<TurnMove> &ms)+{+    FaceCube fc = c;+    for (auto m : ms) fc = fc * ElementaryPerm[m];+    return fc;+}+inline CubieCube operator*(const CubieCube &c, const std::vector<TurnMove> &ms)+{+    CubieCube cc = c;+    for (auto m : ms) cc = cc * ElementaryMove[m];+    return cc;+}+inline ColorState operator*(const ColorState &c, const std::vector<TurnMove> &ms)+{+    ColorState cs = c;+    for (auto m : ms) cs = ElementaryPerm[m].f.act_right(cs);+    return cs;+}+}+namespace cube {+using namespace cube::data;+ColorState ColorState::fromString(std::string_view cube)+{+    assert(is_valid_config(cube) && "invalid cube config");+    std::array<Layer,54> xs{};+    std::transform(cube.cbegin(), cube.cend(), xs.begin(), [](char c) {+        switch(c) {+        case 'U': return U;+        case 'R': return R;+        case 'F': return F;+        case 'D': return D;+        case 'L': return L;+        case 'B': return B;+        default: throw std::invalid_argument("invalid cube config");+        }+    });+    return { xs };+}+bool ColorState::is_valid_config(std::string_view cfg)+{+    if(cfg.size() != 54) return false;+    std::set<char> vs { cfg[CC[0]],cfg[CC[1]],cfg[CC[2]],cfg[CC[3]],cfg[CC[4]],cfg[CC[5]] };+    if(vs.size() != 6) return false;+    for(size_t i = 0, x = 0; i < 8; i++) {+        for(x = 0; x < 24; x++) {+            if(cfg[CC[CCI[i][0]]] == cfg[CF[x/3][x%3]]+               && cfg[CC[CCI[i][1]]] == cfg[CF[x/3][(x+1)%3]]+               && cfg[CC[CCI[i][2]]] == cfg[CF[x/3][(x+2)%3]]) break;+        }+        if(x >= 24) return false;+    }+    for(size_t i = 0, y = 0; i < 12; i++) {+        for(y = 0; y < 24; y++) {+            if(cfg[CC[ECI[i][0]]] == cfg[EF[y/2][y%2]]+               && cfg[CC[ECI[i][1]]] == cfg[EF[y/2][(y+1)%2]]) break;+        }+        if(y >= 24) return false;+    }+    return true;+}+FaceCube ColorState::toFaceCube() const+{+    FacePerm fp{};+    for(int i = 0; i < 6; ++i) {+        fp[CC[i]] = s[CC[i]];+    }+    for(int i = 0; i < 8; i++) {+        for(int x = 0; x < 24; x++) {+            if(s[CC[CCI[i][0]]] == s[CF[x/3][x%3]]+            && s[CC[CCI[i][1]]] == s[CF[x/3][(x+1)%3]]+            && s[CC[CCI[i][2]]] == s[CF[x/3][(x+2)%3]])+            {+                fp[CF[x/3][x%3]]      = CF[i][0];+                fp[CF[x/3][(x+1)%3]]  = CF[i][1];+                fp[CF[x/3][(x+2)%3]]  = CF[i][2];+                break;+            }+        }+    }+    for(int i = 0; i < 12; i++) {+        for(int y = 0; y < 24; y++) {+            if(s[CC[ECI[i][0]]] == s[EF[y/2][y%2]]+            && s[CC[ECI[i][1]]] == s[EF[y/2][(y+1)%2]])+            {+                fp[EF[y/2][y%2]]      = EF[i][0];+                fp[EF[y/2][(y+1)%2]]  = EF[i][1];+                break;+            }+        }+    }+    return { fp };+}+CubieCube ColorState::toCubieCube() const+{+    return toFaceCube().toCubieCube();+}+CubieCube FaceCube::toCubieCube() const+{+    CubieCube cc{};+    const FaceCube &fc = *this;+    for(int i = 0; i < 8; i++) {+        for(int x = 0; x < 24; x++) {+            if(fc.f[CF[i][0]] == CF[x/3][x%3]) {+                cc.cp[i] = x/3, cc.co[i] = (3-x%3)%3;+                break;+            }+        }+    }+    for(int i = 0; i < 12; i++){+        for(int y = 0; y < 24; y++){+            if(fc.f[EF[i][0]] == EF[y/2][y%2]) {+                cc.ep[i] = y/2, cc.eo[i] = (2-y%2)%2;+                break;+            }+        }+    }+    return cc;+}+FaceCube CubieCube::toFaceCube() const+{+    FaceCube fc{};+    const CubieCube &cc = *this;+    for(int i = 0; i < 6; i++) {+        fc.f[CC[i]] = CC[i];+    }+    for(int i = 0; i < 8; i++) for(int j = 0; j < 3; j++) {+        fc.f[CF[i][j]] = CF[cc.cp[i]][(j-cc.co[i]+3)%3];+    }+    for(int i = 0; i < 12; i++) for(int j = 0; j < 2; j++) {+        fc.f[EF[i][j]] = EF[cc.ep[i]][(j-cc.eo[i]+2)%2];+    }+    return fc;+}+}+namespace cube::pdb {+struct Coord+{+    int twist, flip, slice;+    int corner, edge4, edge8;+    static const Coord id;+    static CornerOri    twist2co(int);+    static int          co2twist(const CornerOri &);+    static EdgeOri      flip2eo(int);+    static int          eo2flip(const EdgeOri &);+    static CornerPerm   corner2cp(int);+    static int          cp2corner(const CornerPerm &);+    static int          ep2slice(const EdgePerm &);+    static int          ep2edge4(const EdgePerm &);+    static int          ep2edge8(const EdgePerm &);+    static EdgePerm     slice2ep(int);+    static EdgePerm     edge42ep(int);+    static EdgePerm     edge82ep(int);+    static EdgePerm     see2ep(int,int,int);+    static Coord        CubieCube2Coord(const CubieCube &);+    static CubieCube    Coord2CubieCube(const Coord &);+};+constexpr bool operator==(const Coord &c1, const Coord &c2)+{+    return c1.twist == c2.twist && c1.flip == c2.flip && c1.slice == c2.slice+        && c1.corner == c2.corner && c1.edge4 == c2.edge4 && c1.edge8 == c2.edge8;+}+inline constexpr Coord Coord::id = { 0,0,0,0,0,0 };+template<size_t coord_size>+using MoveTableLayout = NArray<uint16_t,N_MOVE,coord_size>;+using MoveTwist = MoveTableLayout<N_TWIST>;+using MoveFlip  = MoveTableLayout<N_FLIP>;+using MoveSlice = MoveTableLayout<N_SLICE>;+using MoveEdge4 = MoveTableLayout<N_EDGE4>;+using MoveEdge8 = MoveTableLayout<N_EDGE8>;+using MoveCorner= MoveTableLayout<N_CORNER>;+inline int transform_twist(TurnMove m, int twist)   { return Coord::co2twist(Coord::twist2co(twist) * ElementaryMove[m]); }+inline int transform_flip(TurnMove m, int flip)     { return Coord::eo2flip(Coord::flip2eo(flip) * ElementaryMove[m]); }+inline int transform_slice(TurnMove m, int slice)   { return Coord::ep2slice(Coord::slice2ep(slice) * ElementaryMove[m]); }+inline int transform_corner(TurnMove m, int corner) { return Coord::cp2corner(Coord::corner2cp(corner) * ElementaryMove[m]); }+inline int transform_edge4(TurnMove m, int edge4)   { return Coord::ep2edge4(Coord::edge42ep(edge4) * ElementaryMove[m]); }+inline int transform_edge8(TurnMove m, int edge8)   { return Coord::ep2edge8(Coord::edge82ep(edge8) * ElementaryMove[m]); }+}+namespace cube::pdb {+using namespace cube::math;+using namespace cube::data;+inline bool isSliceEdge(size_t idx)+{+    return FR <= idx && idx <= BR;+}+int Coord::co2twist(const CornerOri &co)+{+    return int(fromDigits<3>(takeByRange<1,7>(co.xs)));+}+CornerOri Coord::twist2co(int i)+{+    CornerOri co;+    auto sub1to7 = CArray<3,7,CornerOri::value_type>{toDigits<3,7,CornerOri::value_type>(i)};+    std::copy(sub1to7.xs.begin(),sub1to7.xs.end(),co.xs.begin()+1);+    co[0] = (3 - sub1to7.sum()) % 3;+    return co;+}+int Coord::eo2flip(const EdgeOri &eo)+{+    return int(fromDigits<2>(takeByRange<1,11>(eo.xs)));+}+EdgeOri Coord::flip2eo(int i)+{+    EdgeOri eo;+    auto sub1to11 = CArray<2,11,CornerOri::value_type>{toDigits<2,11,CornerOri::value_type>(i)};+    std::copy(sub1to11.xs.begin(),sub1to11.xs.end(),eo.xs.begin()+1);+    eo[0] = (2 - sub1to11.sum()) % 2;+    return eo;+}+int Coord::ep2slice(const EdgePerm &ep)+{+    int x[4],slice=0,N=12;+    for(int i = 0, j = 0; i < N; i++) {+        if(isSliceEdge(ep[i])) x[j++] = i;+    }+    for(int i = 0; i < 4; i++) slice += binomial(N-1-x[i],4-i);+    return slice;+}+int Coord::ep2edge4(const EdgePerm &ep)+{+    Perm<4,EdgePerm::value_type> edge4_perm;+    for(int i = 0, j = 0; i < 4; i++, j++) {+        while(!isSliceEdge(ep[j])) j++;+        edge4_perm[i] = ep[j] - 8;+    }+    return int(edge4_perm.rank());+}+int Coord::ep2edge8(const EdgePerm &ep)+{+    Perm<8,EdgePerm::value_type> edge8_perm;+    for(size_t i = 0, j = 0; i < 8; i++, j++) {+        while(isSliceEdge(ep[j]) || ep[j] == (EdgePerm::value_type) ~0UL) j++;+        edge8_perm[i] = ep[j] - 0;+    }+    return int(edge8_perm.rank());+}+int Coord::cp2corner(const CornerPerm &cp)+{+    return int(cp.rank());+}+CornerPerm Coord::corner2cp(int i)+{+    return CornerPerm::fromRank(i);+}+EdgePerm Coord::slice2ep(int i)+{+    auto si = lexicalOrderToIndices<12,4>(i);+    EdgePerm ep;+    for(size_t i = 0, j = 0, k = 0; i < 12; i++) {+        ep[i] = (j < 4 && i == si[j]) ? 8 + j++ : k++;+    }+    return ep;+}+EdgePerm Coord::edge42ep(int i)+{+    EdgePerm ep;+    auto e4 = Perm<4,EdgePerm::value_type>::fromRank(i);+    for(size_t i = 0; i < 12; i++) {+        ep[i] = (i < 8) ? i : e4[i-8] + 8;+    }+    return ep;+}+EdgePerm Coord::edge82ep(int i)+{+    EdgePerm ep;+    auto e8 = Perm<8,EdgePerm::value_type>::fromRank(i);+    for(size_t i = 0; i < 12; i++) {+        ep[i] = (i < 8) ? e8[i] + 0 : i;+    }+    return ep;+}+EdgePerm Coord::see2ep(int slice, int edge4, int edge8)+{+    auto e4 = Perm<4,EdgePerm::value_type>::fromRank(edge4);+    auto e8 = Perm<8,EdgePerm::value_type>::fromRank(edge8);+    auto s = lexicalOrderToIndices<12,4>(slice);+    EdgePerm ep;+    for(size_t i = 0, j = 0, x = 0, y = 0; i < 12; i++) {+        ep[i] = (j >=4 || i != s[j]) ? e8[y++]+0 : (++j,e4[x++]+8);+    }+    return ep;+}+Coord Coord::CubieCube2Coord(const CubieCube &cc)+{+    return {+        Coord::co2twist(cc.co),+        Coord::eo2flip(cc.eo),+        Coord::ep2slice(cc.ep),+        Coord::cp2corner(cc.cp),+        Coord::ep2edge4(cc.ep),+        Coord::ep2edge8(cc.ep)+    };+}+CubieCube Coord::Coord2CubieCube(const Coord &c)+{+    return {+        Coord::corner2cp(c.corner),+        Coord::twist2co(c.twist),+        Coord::see2ep(c.slice,c.edge4,c.edge8),+        Coord::flip2eo(c.flip)+    };+}+}+namespace cube::config {+void set_table_dir(std::filesystem::path dir);+auto get_table_dir() -> std::filesystem::path;+bool use_symmetry();+void use_symmetry(bool v);+}+namespace cube::symmetry {+using cube::CubieCube;+using namespace cube::pdb;+inline constexpr CubieCube S_U4 = {{3,0,1,2,7,4,5,6},{0,0,0,0,0,0,0,0},{3,0,1,2,7,4,5,6,11,8,9,10},{0,0,0,0,0,0,0,0,1,1,1,1}};+inline constexpr CubieCube S_RL = {{1,0,3,2,5,4,7,6},{0,0,0,0,0,0,0,0},{2,1,0,3,6,5,4,7,9,8,11,10},{0,0,0,0,0,0,0,0,0,0,0,0}};+inline constexpr CubieCube S_F2 = {{5,4,7,6,1,0,3,2},{0,0,0,0,0,0,0,0},{6,5,4,7,2,1,0,3,9,8,11,10},{0,0,0,0,0,0,0,0,0,0,0,0}};+enum Sym: uint8_t+{+    Id, U1, U2, U3,+    RL, RL_U1, RL_U2, RL_U3,+    FF, FF_U1, FF_U2, FF_U3,+    FF_RL, FF_RL_U1, FF_RL_U2, FF_RL_U3+};+constexpr bool is_mirror(Sym s) { return (RL <= s && s <= RL_U3) || (FF_RL <= s && s <= FF_RL_U3); }+inline constexpr std::array<Sym,N_SYM_D4h> sym_entries      = { Id,U1,U2,U3,RL,RL_U1,RL_U2,RL_U3,FF,FF_U1,FF_U2,FF_U3,FF_RL,FF_RL_U1,FF_RL_U2,FF_RL_U3 };+inline constexpr std::array<Sym,N_SYM_D4h> sym_inv_entries  = { Id,U3,U2,U1,RL,RL_U1,RL_U2,RL_U3,FF,FF_U1,FF_U2,FF_U3,FF_RL,FF_RL_U3,FF_RL_U2,FF_RL_U1 };+constexpr Sym operator~(Sym s) { return sym_inv_entries[s]; }+inline constexpr std::array<CubieCube,N_SYM_D4h> SymmetricMove = {+    CubieCube::id, S_U4, S_U4*S_U4, S_U4*S_U4*S_U4,+    S_RL, S_RL*S_U4, S_RL*S_U4*S_U4, S_RL*S_U4*S_U4*S_U4,+    S_F2, S_F2*S_U4, S_F2*S_U4*S_U4, S_F2*S_U4*S_U4*S_U4,+    S_F2*S_RL, S_F2*S_RL*S_U4, S_F2*S_RL*S_U4*S_U4, S_F2*S_RL*S_U4*S_U4*S_U4+};+typedef uint16_t                    corner_t;+typedef std::array<uint16_t,2>      flipslice_t;+typedef struct{uint16_t eq; Sym s;} corner_eq_t;+typedef struct{uint16_t eq; Sym s;} flipslice_eq_t;+template<size_t coord_size>+using ConjTableLayout = NArray<uint16_t,N_SYM_D4h,coord_size>;+using TwistConj     = ConjTableLayout<N_TWIST>;+using SliceConj     = NArray<uint16_t,N_SYM_D4h,N_SLICE>;+using Edge4Conj     = NArray<uint16_t,N_SYM_D4h,N_EDGE4>;+using Edge8Conj     = NArray<uint16_t,N_SYM_D4h,N_EDGE8>;+using CornerConj    = NArray<uint16_t,N_SYM_D4h,N_CORNER>;+using FlipSliceConj = NArray<flipslice_t,N_SYM_D4h,N_FLIP,N_SLICE>;+struct SymReduction+{+    using CornerDom     = NArray<corner_eq_t,N_CORNER>;+    using EqCornerDom   = NArray<corner_t,EQ_CORNER>;+    using FlipSliceDom  = NArray<flipslice_eq_t,N_FLIP,N_SLICE>;+    using EqFlipSliceDom= NArray<flipslice_t,EQ_FLIPSLICE>;+    typedef uint16_t SymMask;+    using CornerStab    = NArray<SymMask,EQ_CORNER>;+    using FlipSliceStab = NArray<SymMask,EQ_FLIPSLICE>;+public:+    static auto make_trans_edge8_corner(+        const CornerDom& emb, const EqCornerDom& rep, const Edge8Conj& conj,+        const MoveEdge8& tran_edge8, const MoveCorner& tran_corner+    ) {+        return [&](TurnMove m, const std::pair<uint16_t,uint16_t>& ec) -> std::pair<uint16_t,uint16_t> {+            auto [edge8, c_corner] = ec;+            auto corner = rep(c_corner);+            auto [eq, s] = emb(tran_corner(m,corner));+            return { conj(~s,tran_edge8(m,edge8)), eq };+        };+    }+    static auto make_trans_twist_flipslice(+        const FlipSliceDom& emb, const EqFlipSliceDom& rep, const TwistConj& conj,+        const MoveTwist& tran_twist, const MoveFlip& tran_flip, const MoveSlice& tran_slice+    ) {+        return [&](TurnMove m, const std::pair<uint16_t,uint16_t>& tfs) -> std::pair<uint16_t,uint16_t> {+            auto [twist, c_flipslice] = tfs;+            auto [flip, slice] = rep(c_flipslice);+            auto [eq, s] = emb(tran_flip(m,flip),tran_slice(m,slice));+            return { conj(~s,tran_twist(m,twist)), eq };+        };+    }+    static void build_emb_corner(CornerDom&, const CornerConj&);+    static void build_rep_corner(EqCornerDom&, const CornerDom&);+    static void build_emb_flipslice(FlipSliceDom&, const FlipSliceConj&);+    static void build_rep_flipslice(EqFlipSliceDom&, const FlipSliceDom&);+    static void build_stab_corner(CornerStab&, const EqCornerDom&, const CornerConj&);+    static void build_stab_flipslice(FlipSliceStab&, const EqFlipSliceDom&, const FlipSliceConj&);+};+inline int conjugate_slice(Sym s, int slice)    { return Coord::ep2slice(SymmetricMove[~s].ep * Coord::slice2ep(slice) * SymmetricMove[s].ep); }+inline int conjugate_edge4(Sym s, int edge4)    { return Coord::ep2edge4(SymmetricMove[~s].ep * Coord::edge42ep(edge4) * SymmetricMove[s].ep); }+inline int conjugate_edge8(Sym s, int edge8)    { return Coord::ep2edge8(SymmetricMove[~s].ep * Coord::edge82ep(edge8) * SymmetricMove[s].ep); }+inline int conjugate_corner(Sym s, int corner)  { return Coord::cp2corner(SymmetricMove[~s].cp * Coord::corner2cp(corner) * SymmetricMove[s].cp); }+inline int conjugate_twist(Sym s, int twist)+{+    auto co = Coord::twist2co(twist) * SymmetricMove[s];+    return Coord::co2twist(is_mirror(s) ? ~co : co);+}+inline flipslice_t conjugate_flipslice(Sym s, const flipslice_t& fs)+{+    auto c = CubieCube { {},{},Coord::slice2ep(fs[1]),Coord::flip2eo(fs[0]) };+    c = SymmetricMove[~s] * c * SymmetricMove[s];+    return { uint16_t(Coord::eo2flip(c.eo)), uint16_t(Coord::ep2slice(c.ep)) };+}+}+namespace cube::pdb::table {+using namespace cube::data;+using namespace cube::symmetry;+#if CUBE_ENABLE_TRACE+#   define VTRACE(...) fprintf(stderr,__VA_ARGS__)+#else+#   define VTRACE(...) do{}while(0)+#endif+template<size_t coord_size>+struct MoveTableBase: MoveTableLayout<coord_size>+{+    static constexpr size_t size = coord_size;+    template<typename F> void build(F&& tran_fn)+    {+        for(size_t x = 0; x < coord_size; ++x)+            for(auto m: turn_entries)+                (*this)(m,x) = tran_fn(m,x);+    }+};+template<size_t coord_size>+struct ConjTableBase: ConjTableLayout<coord_size>+{+    static constexpr size_t size = coord_size;+    template<typename F> void build(F&& conj_fn)+    {+        for(size_t x = 0; x < coord_size; ++x)+            for(auto s: sym_entries)+                (*this)[s][x] = conj_fn(s,x);+    }+};+template<size_t... Ns>+struct PrunTableBase: NArray<uint8_t,Ns...>+{+    using index_type = std::array<size_t,PrunTableBase::dim>;+    template<typename...MTs>+    void build_disjU(MTs&&... tables)+    {+        static_assert(sizeof...(tables) == PrunTableBase::dim);+        auto ts = std::tie(tables...);+        auto next = [ts](TurnMove m, const index_type&c) -> index_type {+            index_type c_next;+            size_t idx = 0;+            std::apply([&](auto&&... tbl){+                ( (c_next[idx] = tbl[m][c[idx]], ++idx),... );+            },ts);+            return c_next;+        };+        auto orbit = [](const index_type& c, auto&& visit) { visit(c); };+        build(next,orbit);+    }+    template<typename TranX, typename ConjX,+             typename TranY, typename EmbY, typename RepY, typename StabY>+    void build_XxEqY(TranX&& Tx, ConjX&& conj, TranY&& Ty, EmbY&& emb, RepY&& rep, StabY&& stab)+    {+        static_assert(sizeof...(Ns) == 2 && "only dim=2 is implemented");+        auto next = [&](TurnMove m, const index_type& c) -> index_type {+            auto [x, eqY] = c;+            auto y = rep(eqY);+            auto [eq, s] = emb[Ty(m,y)];+            return { conj(~s,Tx(m,x)), eq };+        };+        auto orbit = [&](const index_type& c, auto&& visit) {+            const auto [x,eqY] = c;+            for(auto s: sym_entries)+            {+                if(stab(eqY) & (1u << s)) visit(index_type{conj(s,x),eqY});+            }+        };+        build(next,orbit);+    }+    template<typename NextFn, typename OrbitFn>+    void build(NextFn&& next_fn, OrbitFn&& orbit_fn)+    {+        constexpr auto unvisited = std::numeric_limits<uint8_t>::max();+        this->fill(unvisited);+        std::queue<index_type> q;+        size_t discovered = 0, depth = 0;+        auto visit_fn = [&](const index_type& c) {+            auto& entry = (*this)[c];+            if(entry == unvisited) { entry = depth; ++discovered; }+        };+        index_type starting {};+        orbit_fn(starting,visit_fn);+        q.push(starting);+        while(!q.empty())+        {+            VTRACE("[depth %3zu] visited: %9zu / %-9zu\n",+                depth, discovered, PrunTableBase::size+            );+            ++depth;+            const auto n_depth = q.size();+            for(auto _ = 0; _ < n_depth; ++_)+            {+                auto c = q.front(); q.pop();+                for(auto m: turn_entries) {+                    const auto c_next = next_fn(m,c);+                    if((*this)[c_next] == unvisited) {+                        orbit_fn(c_next,visit_fn);+                        q.push(c_next);+                    }+                }+            }+        }+    }+};+}+#define TABLE_MAGIC 8677391316305539925+#define TABLE_VERSION 1+namespace cube::pdb::table {+namespace fs = std::filesystem;+template<typename> inline constexpr bool always_false_v = false;+enum class MoveKind { Twist, Flip, Slice, Edge4, Edge8, Corner, Count };+enum class ConjKind { TwistConj, SliceConj, Edge4Conj, Edge8Conj, CornerConj, FlipSliceConj, Count };+enum class EqKind   { RepCorner, RepFlipSlice, EmbCorner, EmbFlipSlice, Count };+enum class StabKind { CornerStab, FlipSliceStab, Count };+enum class PrunKind { SliceFlip, SliceTwist, Edge4Edge8, Edge4Corner, Edge8EqCorner, TwistEqFlipSlice, Count };+template<auto K> struct table_meta;+template<auto K> using table_t = typename table_meta<K>::type;+template<auto K> constexpr std::string_view tag_v = table_meta<K>::value;+#define Unwrap(...) __VA_ARGS__+#define spec_table_meta(Kind,Type,Tag) \+    template<> struct table_meta<Kind> \+    {                                  \+        using type = Unwrap Type;      \+        static constexpr std::string_view value = Tag; \+    };+spec_table_meta(MoveKind::Twist,        (MoveTableBase<N_TWIST>),       "TmTwist")+spec_table_meta(MoveKind::Flip,         (MoveTableBase<N_FLIP>),        "TmFlip")+spec_table_meta(MoveKind::Slice,        (MoveTableBase<N_SLICE>),       "TmSlice")+spec_table_meta(MoveKind::Edge4,        (MoveTableBase<N_EDGE4>),       "TmEdge4")+spec_table_meta(MoveKind::Edge8,        (MoveTableBase<N_EDGE8>),       "TmEdge8")+spec_table_meta(MoveKind::Corner,       (MoveTableBase<N_CORNER>),      "TmCorner")+spec_table_meta(ConjKind::TwistConj,    (ConjTableBase<N_TWIST>),       "TcTwist")+spec_table_meta(ConjKind::SliceConj,    (ConjTableBase<N_SLICE>),       "TcSlice")+spec_table_meta(ConjKind::Edge4Conj,    (ConjTableBase<N_EDGE4>),       "TcEdge4")+spec_table_meta(ConjKind::Edge8Conj,    (ConjTableBase<N_EDGE8>),       "TcEdge8")+spec_table_meta(ConjKind::CornerConj,   (ConjTableBase<N_CORNER>),      "TcCorner")+spec_table_meta(ConjKind::FlipSliceConj,(FlipSliceConj),                "TcFlipSlice")+spec_table_meta(EqKind::RepCorner,      (SymReduction::EqCornerDom),    "TeRepCorner")+spec_table_meta(EqKind::RepFlipSlice,   (SymReduction::EqFlipSliceDom), "TeRepFlipSlice")+spec_table_meta(EqKind::EmbCorner,      (SymReduction::CornerDom),      "TeEmbCorner")+spec_table_meta(EqKind::EmbFlipSlice,   (SymReduction::FlipSliceDom),   "TeEmbFlipSlice")+spec_table_meta(StabKind::CornerStab,   (SymReduction::CornerStab),     "TsCorner")+spec_table_meta(StabKind::FlipSliceStab,(SymReduction::FlipSliceStab),  "TsFlipSlice")+spec_table_meta(PrunKind::SliceFlip,        (PrunTableBase<N_SLICE,N_FLIP>),        "TpSliceFlip")+spec_table_meta(PrunKind::SliceTwist,       (PrunTableBase<N_SLICE,N_TWIST>),       "TpSliceTwist")+spec_table_meta(PrunKind::Edge4Edge8,       (PrunTableBase<N_EDGE4,N_EDGE8>),       "TpEdge4Edge8")+spec_table_meta(PrunKind::Edge4Corner,      (PrunTableBase<N_EDGE4,N_CORNER>),      "TpEdge4Corner")+spec_table_meta(PrunKind::Edge8EqCorner,    (PrunTableBase<N_EDGE8,EQ_CORNER>),     "TpEdge8EqCorner")+spec_table_meta(PrunKind::TwistEqFlipSlice, (PrunTableBase<N_TWIST,EQ_FLIPSLICE>),  "TpTwistEqFlipSlice")+#undef Unwrap+#undef spec_table_meta+template<size_t... Is> auto make_mk_tuple(std::index_sequence<Is...>) -> std::tuple<std::unique_ptr<table_t<static_cast<MoveKind>(Is)>>...>;+template<size_t... Is> auto make_ck_tuple(std::index_sequence<Is...>) -> std::tuple<std::unique_ptr<table_t<static_cast<ConjKind>(Is)>>...>;+template<size_t... Is> auto make_ek_tuple(std::index_sequence<Is...>) -> std::tuple<std::unique_ptr<table_t<static_cast<EqKind>(Is)>>...>;+template<size_t... Is> auto make_sk_tuple(std::index_sequence<Is...>) -> std::tuple<std::unique_ptr<table_t<static_cast<StabKind>(Is)>>...>;+template<size_t... Is> auto make_pk_tuple(std::index_sequence<Is...>) -> std::tuple<std::unique_ptr<table_t<static_cast<PrunKind>(Is)>>...>;+using MoveTables= decltype(make_mk_tuple(std::make_index_sequence<size_t(MoveKind::Count)>{}));+using ConjTables= decltype(make_ck_tuple(std::make_index_sequence<size_t(ConjKind::Count)>{}));+using EqTables  = decltype(make_ek_tuple(std::make_index_sequence<size_t(EqKind::Count)>{}));+using StabTables= decltype(make_sk_tuple(std::make_index_sequence<size_t(StabKind::Count)>{}));+using PrunTables= decltype(make_pk_tuple(std::make_index_sequence<size_t(PrunKind::Count)>{}));+using Tables    = decltype(std::tuple_cat(+    std::declval<MoveTables>(),+    std::declval<ConjTables>(),+    std::declval<EqTables>(),+    std::declval<StabTables>(),+    std::declval<PrunTables>()+));+template<auto K>+constexpr size_t index_v = []() constexpr {+    using T = decltype(K);+    constexpr size_t C_Move = size_t(MoveKind::Count)+                    ,C_Conj = size_t(ConjKind::Count)+                    ,C_Eq   = size_t(EqKind::Count)+                    ,C_Stab = size_t(StabKind::Count);+    if constexpr (std::is_same_v<T, MoveKind>)  return size_t(K);+    if constexpr (std::is_same_v<T, ConjKind>)  return size_t(K) + C_Move;+    if constexpr (std::is_same_v<T, EqKind>)    return size_t(K) + C_Move + C_Conj;+    if constexpr (std::is_same_v<T, StabKind>)  return size_t(K) + C_Move + C_Conj + C_Eq;+    if constexpr (std::is_same_v<T, PrunKind>)  return size_t(K) + C_Move + C_Conj + C_Eq + C_Stab;+}();+class TablePool+{+    Tables tables_;+public:+    static const TablePool& instance() { return instance_mut(); }+    template<auto K> const auto& get() const+    {+        const auto& slot = std::get<index_v<K>>(tables_);+        if(!slot) {+            VTRACE("fatal: table %s is not initialized\n", tag_v<K>.data());+            std::terminate();+        }+        return *slot;+    }+    template<auto K, typename Builder> const auto& ensure(Builder&& builder)+    {+        auto& slot = std::get<index_v<K>>(tables_);+        if(!slot) {+            slot = std::make_unique<table_t<K>>();+            builder(*slot);+        }+        return *slot;+    }+    template<auto... K> void clean() { (std::get<index_v<K>>(tables_).reset(),...); }+private:+    friend class TableProvider;+    static TablePool& instance_mut() { static TablePool pool; return pool; }+};+enum class LoadStatus { Ok, Missing, Incompatible, Corrupted, OsErr };+template<auto K> struct table_with_header;+class TableProvider+{+    fs::path tdir_;+    TablePool& pool_;+public:+    template<bool use_symmetry>+    static const TableProvider& make(fs::path dir = {})+    {+        static TableProvider tp (+            dir.empty() ? cube::config::get_table_dir() : dir,+            std::bool_constant<use_symmetry>()+        );+        return tp;+    }+    template<auto K> [[nodiscard]] const auto& get() const { return pool_.get<K>(); }+private:+    template<bool use_symmetry>+    TableProvider(fs::path dir, std::bool_constant<use_symmetry>)+        : tdir_{dir}+        , pool_{TablePool::instance_mut()}+    { load_or_build<use_symmetry>(); }+    template<bool use_symmetry>+    void load_or_build()+    {+        ensure_all<+            MoveKind::Twist, MoveKind::Flip, MoveKind::Slice,+            MoveKind::Edge4, MoveKind::Edge8, MoveKind::Corner+        >();+        if constexpr (!use_symmetry) {+            ensure_all<+                PrunKind::SliceFlip, PrunKind::SliceTwist,+                PrunKind::Edge4Edge8, PrunKind::Edge4Corner+            >();+        } else {+            ensure_all<+                EqKind::EmbCorner, EqKind::EmbFlipSlice,+                ConjKind::TwistConj, ConjKind::Edge8Conj,+                PrunKind::TwistEqFlipSlice,+                PrunKind::Edge4Edge8, PrunKind::Edge8EqCorner+            >();+            pool_.clean<+                ConjKind::CornerConj, ConjKind::FlipSliceConj,+                StabKind::CornerStab, StabKind::FlipSliceStab,+                EqKind::RepCorner, EqKind::RepFlipSlice+            >();+        }+    }+    template<auto K>+    static constexpr bool should_persist()+    {+        using T = std::remove_cv_t<decltype(K)>;+        if constexpr (std::is_same_v<T, MoveKind> || std::is_same_v<T, PrunKind>) return true;+        else if constexpr (std::is_same_v<T, EqKind>) return K == EqKind::EmbCorner || K == EqKind::EmbFlipSlice;+        else if constexpr (std::is_same_v<T, ConjKind>) return K == ConjKind::TwistConj || K == ConjKind::Edge8Conj;+        else return false;+    }+    template<auto K> const auto& ensure()+    {+        return pool_.ensure<K>([this](table_t<K>& t){+            auto status = load_from<K>(t,tdir_);+            if(status == LoadStatus::Ok) return;+            if(!fs::exists(tdir_)) fs::create_directories(tdir_);+            if constexpr (std::is_same_v<decltype(K), PrunKind>) { VTRACE("[pdb] building pruning table %s...\n", tag_v<K>.data()); }+            build_table<K>(t);+            if constexpr (std::is_same_v<decltype(K), PrunKind>) { VTRACE("[pdb] done.\n"); }+            if constexpr (should_persist<K>()) save_to<K>(t,tdir_);+        });+    }+    template<auto... Ks> void ensure_all() { (ensure<Ks>(), ...); }+    template<MoveKind K> void build_table(table_t<K>& t)+    {+        if constexpr (K == MoveKind::Twist)   { t.build(transform_twist); }+        if constexpr (K == MoveKind::Flip)    { t.build(transform_flip); }+        if constexpr (K == MoveKind::Slice)   { t.build(transform_slice); }+        if constexpr (K == MoveKind::Edge4)   { t.build(transform_edge4); }+        if constexpr (K == MoveKind::Edge8)   { t.build(transform_edge8); }+        if constexpr (K == MoveKind::Corner)  { t.build(transform_corner); }+    }+    template<ConjKind K> void build_table(table_t<K>& t)+    {+        if constexpr (K == ConjKind::TwistConj)  { t.build(conjugate_twist); }+        if constexpr (K == ConjKind::SliceConj)  { t.build(conjugate_slice); }+        if constexpr (K == ConjKind::Edge4Conj)  { t.build(conjugate_edge4); }+        if constexpr (K == ConjKind::Edge8Conj)  { t.build(conjugate_edge8); }+        if constexpr (K == ConjKind::CornerConj) { t.build(conjugate_corner); }+        if constexpr (K == ConjKind::FlipSliceConj) {+            for(int flip = 0; flip < N_FLIP; ++flip) {+                for(int slice = 0; slice < N_SLICE; ++slice) {+                    for(auto s: sym_entries)+                        t[s][flip][slice] = conjugate_flipslice(s, {uint16_t(flip),uint16_t(slice)});+                }+            }+        }+    }+    template<StabKind K> void build_table(table_t<K>& t)+    {+        if constexpr(K == StabKind::CornerStab) {+            SymReduction::build_stab_corner(t,+                ensure<EqKind::RepCorner>(), ensure<ConjKind::CornerConj>()+            );+        }+        if constexpr(K == StabKind::FlipSliceStab) {+            SymReduction::build_stab_flipslice(t,+                ensure<EqKind::RepFlipSlice>(), ensure<ConjKind::FlipSliceConj>()+            );+        }+    }+    template<EqKind K> void build_table(table_t<K>& t)+    {+        if constexpr (K == EqKind::EmbCorner)   { SymReduction::build_emb_corner(t, ensure<ConjKind::CornerConj>()); }+        if constexpr (K == EqKind::RepCorner)   { SymReduction::build_rep_corner(t, ensure<EqKind::EmbCorner>()); }+        if constexpr (K == EqKind::EmbFlipSlice){ SymReduction::build_emb_flipslice(t, ensure<ConjKind::FlipSliceConj>()); }+        if constexpr (K == EqKind::RepFlipSlice){ SymReduction::build_rep_flipslice(t, ensure<EqKind::EmbFlipSlice>()); }+    }+    template<PrunKind K> void build_table(table_t<K>& t)+    {+        if constexpr (K == PrunKind::SliceTwist)    { t.build_disjU(ensure<MoveKind::Slice>(), ensure<MoveKind::Twist>()); return; }+        if constexpr (K == PrunKind::SliceFlip)     { t.build_disjU(ensure<MoveKind::Slice>(), ensure<MoveKind::Flip>()); return ; }+        if constexpr (K == PrunKind::Edge4Corner)   { t.build_disjU(ensure<MoveKind::Edge4>(), ensure<MoveKind::Corner>()); return; }+        if constexpr (K == PrunKind::Edge4Edge8)    { t.build_disjU(ensure<MoveKind::Edge4>(), ensure<MoveKind::Edge8>()); return; }+        if constexpr (K == PrunKind::Edge8EqCorner) {+            t.build_XxEqY(+                ensure<MoveKind::Edge8>(), ensure<ConjKind::Edge8Conj>(),+                ensure<MoveKind::Corner>(), ensure<EqKind::EmbCorner>(), ensure<EqKind::RepCorner>(), ensure<StabKind::CornerStab>()+            );+        }+        if constexpr (K == PrunKind::TwistEqFlipSlice) {+            const auto& tran_flip = ensure<MoveKind::Flip>();+            const auto& tran_slice = ensure<MoveKind::Slice>();+            auto tran_flipslice = [&tran_flip,&tran_slice](TurnMove m, const flipslice_t& fs) -> flipslice_t {+                return { tran_flip(m,fs[0]), tran_slice(m,fs[1]) };+            };+            t.build_XxEqY(+                ensure<MoveKind::Twist>(), ensure<ConjKind::TwistConj>(),+                tran_flipslice,+                ensure<EqKind::EmbFlipSlice>(), ensure<EqKind::RepFlipSlice>(), ensure<StabKind::FlipSliceStab>()+            );+        }+    }+    template<auto K>+    static bool save_to(const table_t<K>& table, const fs::path& dir)+    {+        static_assert(std::is_trivially_copyable_v<table_t<K>>);+        std::ofstream f(dir / tag_v<K>, std::ios::binary);+        if(!f) return false;+        return table_with_header<K>::write(f, table);+    }+    template <auto K>+    static auto load_from(table_t<K>& table, const fs::path& dir) -> LoadStatus+    {+        static_assert(std::is_trivially_copyable_v<table_t<K>>);+        std::ifstream f(dir / tag_v<K>, std::ios::binary);+        if(!f) return LoadStatus::Missing;+        return table_with_header<K>::read(f, table);+    }+};+template<auto K>+struct table_with_header+{+    struct meta_info { uint64_t filetag, checksum; };+    static constexpr auto encode_filetag(std::array<uint32_t,2> vk) -> uint64_t+    {+        const auto& [ver,kind] = vk;+        return TABLE_MAGIC ^ ((uint64_t(ver) << 32) | uint64_t(kind));+    }+    [[maybe_unused]]+    static auto decode_filetag(uint64_t tag) -> std::array<uint32_t,2>+    {+        const uint64_t vk = tag ^ TABLE_MAGIC;+        return { uint32_t(vk >> 32), uint32_t(vk & 0xffffffff) };+    }+    static constexpr uint64_t filetag_v = encode_filetag({uint32_t(TABLE_VERSION),uint32_t(index_v<K>)});+    static auto read(std::ifstream& is, table_t<K>& t) -> LoadStatus+    {+        meta_info header{};+        if(!is.read(reinterpret_cast<char*>(&header), sizeof(header))) return LoadStatus::OsErr;+        if(!(header.filetag == filetag_v)) return LoadStatus::Incompatible;+        if(!is.read(reinterpret_cast<char*>(&t.storage), sizeof(t.storage))) return LoadStatus::OsErr;+        if(fnv1a(&t.storage, sizeof(t.storage)) != header.checksum) return LoadStatus::Corrupted;+        return LoadStatus::Ok;+    }+    static auto write(std::ofstream& os, const table_t<K>& t) -> bool+    {+        const auto header = meta_info{filetag_v, fnv1a(&t.storage, sizeof(t.storage))};+        os.write(reinterpret_cast<const char*>(&header), sizeof(header));+        os.write(reinterpret_cast<const char*>(&t.storage), sizeof(t.storage));+        return bool(os);+    }+private:+    static uint64_t fnv1a(const void* data, size_t n)+    {+        const auto* p = static_cast<const uint8_t*>(data);+        uint64_t h = 1469598103934665603ull;+        for(size_t i = 0; i < n; ++i) { h ^= p[i]; h *= 1099511628211ull; }+        return h;+    }+};+}+namespace cube::pdb::ops {+using namespace cube::data;+using namespace cube::pdb::table;+using cube::config::use_symmetry;+enum Phase { Ph1=0, Ph2=1 };+struct CoordOps+{+    template<Phase PhX>+    static auto transform(const Coord&, TurnMove) -> Coord;+    template<Phase PhX>+    static auto distance(const Coord&) -> uint8_t;+    template<Phase PhX>+    static auto origin(const CubieCube& cc, const std::vector<TurnMove>& sol = {}) -> Coord;+};+template<Phase PhX>+auto CoordOps::transform(const Coord& c, TurnMove m) -> Coord+{+    const TablePool& pool = TablePool::instance();+    if constexpr (PhX == Ph1)+        return {+            pool.get<MoveKind::Twist>()(m,c.twist),+            pool.get<MoveKind::Flip>()(m,c.flip),+            pool.get<MoveKind::Slice>()(m,c.slice),+            -1,-1,-1+        };+    else+        return {+            0,0,0,+            pool.get<MoveKind::Corner>()(m,c.corner),+            pool.get<MoveKind::Edge4>()(m,c.edge4),+            pool.get<MoveKind::Edge8>()(m,c.edge8)+        };+}+template<Phase PhX>+auto CoordOps::distance(const Coord& c) -> uint8_t+{+    const TablePool& pool = TablePool::instance();+    if constexpr (PhX == Ph1) {+        if (!use_symmetry()) {+            return std::max(+                pool.get<PrunKind::SliceTwist>()(c.slice,c.twist),+                pool.get<PrunKind::SliceFlip>()(c.slice,c.flip)+            );+        } else {+            const auto [eq, s] = pool.get<EqKind::EmbFlipSlice>()(c.flip,c.slice);+            return pool.get<PrunKind::TwistEqFlipSlice>()(+                pool.get<ConjKind::TwistConj>()(~s,c.twist),+                eq+            );+        }+    } else {+        if (!use_symmetry()) {+            return std::max(+                pool.get<PrunKind::Edge4Corner>()(c.edge4,c.corner),+                pool.get<PrunKind::Edge4Edge8>()(c.edge4,c.edge8)+            );+        } else {+            const auto [eq, s] = pool.get<EqKind::EmbCorner>()(c.corner);+            return std::max(+                pool.get<PrunKind::Edge4Edge8>()(c.edge4,c.edge8),+                pool.get<PrunKind::Edge8EqCorner>()(+                    pool.get<ConjKind::Edge8Conj>()(~s,c.edge8),+                    eq+                )+            );+        }+    }+}+template<Phase PhX>+auto CoordOps::origin(const CubieCube& cc, const std::vector<TurnMove>& sol) -> Coord+{+    if constexpr (PhX == Ph1) return Coord::CubieCube2Coord(cc);+    else {+        const TablePool& pool = TablePool::instance();+        Coord c = Coord::CubieCube2Coord(cc);+        int corner = c.corner, edge4, edge8;+        auto ep = cc.ep;+        for(auto m: sol)+        {+            corner = pool.get<MoveKind::Corner>()(m,corner);+            ep = ep * ElementaryMove[m].ep;+        }+        edge4 = Coord::ep2edge4(ep);+        edge8 = Coord::ep2edge8(ep);+        return { 0,0,0,corner,edge4,edge8 };+    }+}+}+namespace cube::solver {+using namespace cube::data;+using namespace cube::pdb;+using namespace cube::pdb::table;+using cube::pdb::ops::Phase;+class SearchContext+{+public:+    SearchContext(const CubieCube& cc = CubieCube::id, size_t good = 22)+        : root_(cc), tgtlen_(good)+    {}+    CubieCube   root() const    { return root_; }+    size_t      tgtlen() const  { return tgtlen_; }+    template<Phase PhX>+    void reset() { path_[PhX].fill(-1); }+    template<Phase PhX> void record(int step, int move){ path_[PhX][step] = move; }+    template<Phase PhX> int  recall(int step) const    { return path_[PhX][step]; }+    template<Phase PhX>+    void commit(size_t L)+    {+        rsolution_[PhX].first = L;+        std::copy(path_[PhX].begin(), path_[PhX].begin()+L, rsolution_[PhX].second.begin());+    }+    template<Phase PhX>+    auto extract() const -> std::vector<TurnMove>+    {+        size_t n = rsolution_[PhX].first;+        if(n == 0) return {};+        std::vector<TurnMove> sol(n);+        for(auto i = 0; i < n; i++) {+            sol[i] = static_cast<TurnMove>(rsolution_[PhX].second[n-1-i]);+        }+        return sol;+    }+    static constexpr int D0 = 12, D1 = 18, DS = D0+D1;+    template<Phase PhX> static constexpr auto D = std::get<PhX>(std::tie(D0,D1));+    static constexpr std::array<TurnMove,18> EM0+        = { Ux1,Ux2,Ux3,Rx1,Rx2,Rx3,Fx1,Fx2,Fx3,Dx1,Dx2,Dx3,Lx1,Lx2,Lx3,Bx1,Bx2,Bx3 };+    static constexpr std::array<TurnMove,10> EM1+        = { Ux1,Ux2,Ux3,Rx2,Fx2,Dx1,Dx2,Dx3,Lx2,Bx2 };+    template<Phase PhX>+    static constexpr auto& EM = std::get<PhX>(std::tie(EM0,EM1));+private:+    CubieCube root_;+    size_t tgtlen_;+    std::array<std::array<int,DS+2>,2>                  path_;+    std::array<std::pair<size_t,std::array<int,DS>>,2>  rsolution_;+};+class KociembaSolver+{+public:+    static auto solve(const CubieCube &cc, size_t good)+        -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>;+protected:+    static int start_search_ph1(SearchContext& ctx, const Coord& c, size_t d, size_t d_orig, size_t maxL);+    static bool start_search_ph2(SearchContext& ctx, const Coord& c, size_t togo);+};+}+namespace cube::solver {+using namespace cube::pdb::ops;+inline bool is_dull_pair(const TurnMove A, const int B)+{+    if(!(B >= Ux1 && B <= Bx3)) return false;+    return (A/3 == B/3) || (A/3 == B/3+3);+}+auto KociembaSolver::solve(const CubieCube &cc, size_t good)+    -> std::tuple<bool,std::vector<TurnMove>,std::vector<TurnMove>>+{+    size_t bestL = SearchContext::DS + 1;+    auto ctx = SearchContext(cc,good);+    ctx.reset<Ph1>();+    auto c = CoordOps::origin<Ph1>(cc);+    for(auto togo = CoordOps::distance<Ph1>(c); togo < bestL; ++togo)+    {+        int l = start_search_ph1(ctx, c,togo,togo,bestL-1);+        if(l >= 0) bestL = std::min(bestL,size_t(l));+        if(bestL <= ctx.tgtlen()) break;+    }+    if(bestL > SearchContext::DS) return {false, {}, {}};+    else return { true, ctx.extract<Ph1>(), ctx.extract<Ph2>() };+}+int KociembaSolver::start_search_ph1(+    SearchContext& ctx, const Coord& c, size_t d, size_t d_orig, size_t maxL)+{+    if(d < CoordOps::distance<Ph1>(c)) return -1;+    if(d == 0) {+        ctx.commit<Ph1>(d_orig);+        ctx.reset<Ph2>();+        auto c2 = CoordOps::origin<Ph2>(ctx.root(), ctx.extract<Ph1>());+        for(auto togo = CoordOps::distance<Ph2>(c2); togo <= maxL; ++togo)+        {+            bool succ = start_search_ph2(ctx,c2,togo);+            if(succ) {+                ctx.commit<Ph2>(togo);+                return togo;+            }+        }+        return -1;+    }+    int bestL = maxL + 1;+    for(auto m: SearchContext::EM<Ph1>)+    {+        if(is_dull_pair(m, ctx.recall<Ph1>(d))) continue;+        ctx.record<Ph1>(d-1,m);+        auto l = start_search_ph1(ctx, CoordOps::transform<Ph1>(c,m), d-1, d_orig, bestL-2);+        if(l >= 0 && bestL > l+1) {+            bestL = l+1;+        }+        if(bestL + d_orig - d <= ctx.tgtlen()) break;+        if(d >= bestL) break;+    }+    return bestL > int(maxL) ? -1 : bestL;+}+bool KociembaSolver::start_search_ph2(+    SearchContext& ctx, const Coord& c, size_t togo)+{   if(togo < CoordOps::distance<Ph2>(c)) return false;+    if(togo == 0) return CoordOps::distance<Ph2>(c) == 0;+    for(auto m: SearchContext::EM<Ph2>)+    {+        if(is_dull_pair(m, ctx.recall<Ph2>(togo))) continue;+        ctx.record<Ph2>(togo-1,m);+        bool ret = start_search_ph2(ctx, CoordOps::transform<Ph2>(c,m), togo-1);+        if(ret) return true;+    }+    return false;+}+}+namespace cube::config+{+namespace fs = std::filesystem;+namespace {+bool& use_symmetry_ref()+{+    static bool val_ = CUBE_USE_SYMMETRY;+    return val_;+}+fs::path& get_custom_dir_storage()+{+    static fs::path custom_dir = {};+    return custom_dir;+}+auto get_cache_dir() -> std::filesystem::path+{+#ifdef _WIN32+    const char* localAppData = std::getenv("LOCALAPPDATA");+    if (localAppData) return std::filesystem::path(localAppData);+#elif __APPLE__+    const char* home = std::getenv("HOME");+    if (home) return std::filesystem::path(home) / "Library" / "Caches";+#else+    const char* xdgCache = std::getenv("XDG_CACHE_HOME");+    if (xdgCache) return std::filesystem::path(xdgCache);+    const char* home = std::getenv("HOME");+    if (home) return std::filesystem::path(home) / ".cache";+#endif+    throw std::runtime_error("Unable to determine cache path");+}+}+bool use_symmetry() { return use_symmetry_ref(); }+void use_symmetry(bool v)+{+    static std::once_flag once;+    std::call_once(once, [v]() { use_symmetry_ref() = v; });+}+void set_table_dir(fs::path dir)+{+    static std::once_flag once;+    std::call_once(once, [dir]() { get_custom_dir_storage() = dir; });+}+fs::path get_table_dir()+{+    const auto user_dir = get_custom_dir_storage();+    if(!user_dir.empty()) return user_dir;+    if(const char *env = std::getenv("CUBE_TABLE_DIR")) {+        if(env[0] != '\0') return fs::path(env);+    }+    try {+        return get_cache_dir() / "cube.coshz" / "tables";+    } catch (...) {+        return fs::absolute("tables");+    }+}+}+namespace cube::internal+{+using namespace cube::data;+std::string apply_maneuver(std::string_view s, const std::vector<TurnMove>& ms);+auto parse_maneuver(std::string_view s) -> std::vector<TurnMove>;+inline auto operator""_Tm(const char* ts, size_t n) -> std::vector<TurnMove>+{+    return parse_maneuver(std::string(ts,n));+}+bool is_valid_maneuver(std::string_view);+}+namespace cube {+using namespace cube::data;+namespace internal {+std::string apply_maneuver(std::string_view s, const std::vector<TurnMove> &ms)+{+    assert(s.size() == 54 && "invalid cube length");+    char buf[2][54];+    std::memcpy(buf[0], s.data(), 54);+    size_t curr = 0;+    for(const auto &m : ms)+    {+        const auto& p   = ElementaryPerm[m].f;+        const char* src = buf[curr];+        char*       dst = buf[1-curr];+        for(int i = 0; i < 54; ++i) dst[i] = src[p[i]];+        curr = 1-curr;+    }+    return std::string(buf[curr],54);+}+auto parse_maneuver(std::string_view s) -> std::vector<TurnMove>+{+    assert(is_valid_maneuver(s) && "invalid maneuver");+    auto expand = [](std::string_view in) -> std::string {+        static const std::regex group_re(R"(\(([^)]+)\)(?:\{(\d+)\})?)");+        std::string res;+        auto start = in.cbegin();+        std::match_results<std::string_view::const_iterator> m;+        while (std::regex_search(start, in.cend(), m, group_re)) {+            res.append(start, m[0].first);+            int repeat = m[2].matched ? std::stoi(m[2].str()) : 1;+            for (int i = 0; i < repeat; ++i) res += m[1].str();+            start = m[0].second;+        }+        res.append(start, in.cend());+        return res;+    };+    auto char_to_move = [](char c) -> TurnMove {+        switch(c) {+        case 'U': return Ux1;+        case 'R': return Rx1;+        case 'F': return Fx1;+        case 'D': return Dx1;+        case 'L': return Lx1;+        case 'B': return Bx1;+        default: throw std::invalid_argument("char_to_move: ???");+        }+    };+    std::string in = expand(s);+    std::vector<TurnMove> ms;+    ms.reserve(in.size());+    for (char c : in)+    {+        switch (c) {+        case ' ': break;+        case '2':+            ms.back() = static_cast<TurnMove>(ms.back() + 1);+            break;+        case '\'':+            ms.back() = static_cast<TurnMove>(ms.back() + 2);+            break;+        default:+            ms.push_back(char_to_move(c));+            break;+        }+    }+    return ms;+}+bool is_valid_maneuver(std::string_view s)+{+    static const std::regex pat(+        R"(\s*(([UDLRFB]['23]?|\(([UDLRFB]['23]?\s*)+\)(\{\d+\})?)\s*)*)"+    );+    return std::regex_match(s.begin(), s.end(), pat);+}+}+}+namespace cube::symmetry {+void SymReduction::build_emb_corner(CornerDom& emb, const CornerConj& conj)+{+    static_assert(EQ_CORNER <= std::numeric_limits<uint16_t>::max());+    constexpr auto unvisited = corner_eq_t { std::numeric_limits<uint16_t>::max(),Id };+    emb.fill(unvisited);+    for(int c = 0, eq = -1; c < N_CORNER; ++c)+    {+        if(emb[c].eq != unvisited.eq) continue;+        emb[c] = { uint16_t(++eq), Id };+        for(Sym s: sym_entries)+        {+            if(s == Id) continue;+            auto &entry = emb[conj(s,c)];+            if(entry.eq == unvisited.eq) entry = { uint16_t(eq), s };+        }+    }+}+void SymReduction::build_rep_corner(EqCornerDom& rep, const CornerDom& emb)+{+    const auto unvisited = std::numeric_limits<uint16_t>::max();+    rep.fill(unvisited);+    for(int corner = 0; corner < N_CORNER; ++corner)+    {+        auto eq = emb[corner].eq;+        if(rep[eq] == unvisited) rep[eq] = corner;+    }+}+void SymReduction::build_emb_flipslice(FlipSliceDom& emb, const FlipSliceConj& conj)+{+    static_assert(EQ_FLIPSLICE <= std::numeric_limits<uint16_t>::max());+    constexpr auto unvisited = flipslice_eq_t { std::numeric_limits<uint16_t>::max(),Id };+    emb.fill(unvisited);+    for(int flip = 0, eq = -1; flip < N_FLIP; ++flip)+        for(int slice = 0; slice < N_SLICE; ++slice)+    {+        if(emb(flip,slice).eq != unvisited.eq) continue;+        emb(flip,slice) = { uint16_t(++eq), Id };+        for(auto s: sym_entries)+        {+            if(s == Id) continue;+            auto fs = conj(s,flip,slice);+            auto &entry = emb(fs[0],fs[1]);+            if(entry.eq == unvisited.eq) entry = { uint16_t(eq), s };+        }+    }+}+void SymReduction::build_rep_flipslice(EqFlipSliceDom& rep, const FlipSliceDom& emb)+{+    const auto unvisited = flipslice_t { std::numeric_limits<uint16_t>::max(),std::numeric_limits<uint16_t>::max() };+    rep.fill(unvisited);+    for(int flip = 0; flip < N_FLIP; ++flip)+        for(int slice = 0; slice < N_SLICE; ++slice)+        {+            auto eq = emb(flip,slice).eq;+            if(rep[eq] == unvisited) rep[eq] = { uint16_t(flip), uint16_t(slice) };+        }+}+void SymReduction::build_stab_corner(CornerStab& stab, const EqCornerDom& rep, const CornerConj& conj)+{+    for (int eq = 0; eq < EQ_CORNER; ++eq)+    {+        SymMask mask = 0;+        const auto c = rep[eq];+        for (Sym s : sym_entries)+        {+            if (conj[s][c] == c) mask |= SymMask(1u << s);+        }+        stab[eq] = mask;+    }+}+void SymReduction::build_stab_flipslice(FlipSliceStab& stab, const EqFlipSliceDom& rep, const FlipSliceConj& conj)+{+    for (int eq = 0; eq < EQ_FLIPSLICE; ++eq)+    {+        SymMask mask = 0;+        const auto fs = rep[eq];+        for (Sym s : sym_entries)+        {+            if (conj(s,fs[0],fs[1]) == fs) mask |= SymMask(1u << s);+        }+        stab[eq] = mask;+    }+}+}+#ifndef CUBE_EXPORT_H+#define CUBE_EXPORT_H+#ifdef CUBE_STATIC_DEFINE+#  define CUBE_EXPORT+#  define CUBE_NO_EXPORT+#else+#  ifndef CUBE_EXPORT+#    ifdef cube_shared_EXPORTS+#      define CUBE_EXPORT __attribute__((visibility("default")))+#    else+#      define CUBE_EXPORT __attribute__((visibility("default")))+#    endif+#  endif+#  ifndef CUBE_NO_EXPORT+#    define CUBE_NO_EXPORT __attribute__((visibility("hidden")))+#  endif+#endif+#ifndef CUBE_DEPRECATED+#  define CUBE_DEPRECATED __attribute__ ((__deprecated__))+#endif+#ifndef CUBE_DEPRECATED_EXPORT+#  define CUBE_DEPRECATED_EXPORT CUBE_EXPORT CUBE_DEPRECATED+#endif+#ifndef CUBE_DEPRECATED_NO_EXPORT+#  define CUBE_DEPRECATED_NO_EXPORT CUBE_NO_EXPORT CUBE_DEPRECATED+#endif+#if 0+#  ifndef CUBE_NO_DEPRECATED+#    define CUBE_NO_DEPRECATED+#  endif+#endif+#endif+#define CUBE_VERSION        "0.5.1"+#define CUBE_VERSION_FULL   "0.5.1"+#define CUBE_VERSION_MAJOR  0+#define CUBE_VERSION_MINOR  5+#define CUBE_VERSION_PATCH  1+#define CUBE_VER_BIT_MAJOR_ 5+#define CUBE_VER_BIT_MINOR_ 7+#define CUBE_VER_BIT_PATCH_ 4+#define CUBE_VER_SFT_MAJOR_ (CUBE_VER_BIT_MINOR_ + CUBE_VER_BIT_PATCH_)+#define CUBE_VER_SFT_MINOR_ CUBE_VER_BIT_PATCH_+#define CUBE_VER_SFT_PATCH_ 0+#define CUBE_VER_MSK_MAJOR_ ((1U << CUBE_VER_BIT_MAJOR_) - 1)+#define CUBE_VER_MSK_MINOR_ ((1U << CUBE_VER_BIT_MINOR_) - 1)+#define CUBE_VER_MSK_PATCH_ ((1U << CUBE_VER_BIT_PATCH_) - 1)+#if 0 > CUBE_VERSION_MAJOR || CUBE_VERSION_MAJOR > CUBE_VER_MSK_MAJOR_+#   error "CUBE_VERSION_MAJOR out of range [0..31]"+#endif+#if 0 > CUBE_VERSION_MINOR || CUBE_VERSION_MINOR > CUBE_VER_MSK_MINOR_+#   error "CUBE_VERSION_MINOR out of range [0..127]"+#endif+#if 0 > CUBE_VERSION_PATCH || CUBE_VERSION_PATCH > CUBE_VER_MSK_PATCH_+#   error "CUBE_VERSION_PATCH out of range [0..15]"+#endif+#define CUBE_VERSION_CODE (\+    ((CUBE_VERSION_MAJOR & CUBE_VER_MSK_MAJOR_) << CUBE_VER_SFT_MAJOR_) | \+    ((CUBE_VERSION_MINOR & CUBE_VER_MSK_MINOR_) << CUBE_VER_SFT_MINOR_) | \+    ((CUBE_VERSION_PATCH & CUBE_VER_MSK_PATCH_) << CUBE_VER_SFT_PATCH_) )+#ifndef __cplusplus+#error "This is a C++ header; please use a C++ compiler OR include cube/cube.h instead"+#endif+namespace cube {+constexpr std::string_view cubeId = "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB";+enum class SolveResult : int32_t {+    Success       = 0,+    Unsolvable    = 1,+    NotFound      = 2,+    InvalidSrc    = 3,+    InvalidTgt    = 4,+    UnknownErr    = 5+};+CUBE_EXPORT constexpr std::string_view to_string(SolveResult status) noexcept {+    switch (status) {+    case SolveResult::Success:      return "Success";+    case SolveResult::Unsolvable:   return "The cube configuration is unsolvable";+    case SolveResult::NotFound:     return "No solution found within the step limit";+    case SolveResult::InvalidSrc:   return "Invalid source color configuration";+    case SolveResult::InvalidTgt:   return "Invalid target color configuration";+    case SolveResult::UnknownErr:   return "Unknown error";+    }+}+enum class PermFormat : int {+    Face  = 0,+    Cubie = 1,+    Cycle = 2+};+struct Solution {+    SolveResult status;+    std::string maneuver;+    bool is_success() const noexcept+    {+        return status == SolveResult::Success;+    }+};+CUBE_EXPORT bool is_solvable(std::string_view color_cube);+[[nodiscard]] CUBE_EXPORT Solution solve(+    std::string_view src,+    std::string_view tgt = cubeId,+    int good = 22+);+[[nodiscard]] CUBE_EXPORT std::string apply_maneuver(+    std::string_view maneuver,+    std::string_view cube = cubeId+);+[[nodiscard]] CUBE_EXPORT std::string show_permutation(+    std::string_view ms_or_cube,+    PermFormat format = PermFormat::Cycle+);+}+#ifndef CUBE_USE_SYMMETRY+#   define CUBE_USE_SYMMETRY 1+#endif+namespace cube {+CUBE_EXPORT void cube_init(+    bool use_symmetry = CUBE_USE_SYMMETRY,+    std::string_view dir = {}+);+CUBE_EXPORT void set_table_dir(std::filesystem::path dir);+CUBE_EXPORT auto get_table_dir() -> std::filesystem::path;+CUBE_EXPORT bool is_valid_config(std::string_view cube);+CUBE_EXPORT bool is_valid_maneuver(std::string_view maneuver);+}+namespace cube::show {+using std::size_t;+using namespace cube::data;+template<size_t N>+using StringArr = std::array<std::string_view,N>;+inline constexpr StringArr< 8> CornerToString       = { "urf", "ufl", "ulb", "ubr", "dfr", "dlf", "dbl", "drb" };+inline constexpr StringArr<12> EdgeToString         = { "ur","uf","ul","ub","dr","df","dl","db","fr","fl","bl","br" };+inline constexpr StringArr< 6> CenterToString       = { "u", "r", "f", "d", "l", "b" };+inline constexpr StringArr< 3> OrientationToString  = { "", "+", "-" };+inline constexpr StringArr<18> Move2Str             = { "U","U2","U'","R","R2","R'","F","F2","F'","D","D2","D'","L","L2","L'","B","B2","B'" };+inline constexpr StringArr<54> Face2Str             = { "U1","U2","U3","U4","U5","U6","U7","U8","U9","R1","R2","R3","R4","R5","R6","R7","R8","R9","F1","F2","F3","F4","F5","F6","F7","F8","F9","D1","D2","D3","D4","D5","D6","D7","D8","D9","L1","L2","L3","L4","L5","L6","L7","L8","L9","B1","B2","B3","B4","B5","B6","B7","B8","B9" };+inline constexpr std::string_view ColorSet          = "URFDLB";+inline constexpr std::string_view CornerSet         = "ABCDEFGH";+inline constexpr std::string_view EdgeSet           = "opqrstuvwxyz";+enum class CubeFormat {+    Face,+    Cubie,+    Cycle+};+template<typename Array, typename Formatter>+inline std::string seq2str_fmt(const Array &xs,+                           Formatter && fmt,+                           std::string_view sep="",+                           std::string_view pre="",+                           std::string_view suf="")+{+    const size_t len = xs.size();+    if(len == 0) { return std::string(pre) + std::string(suf); }+    std::stringstream ss;+    ss << pre << fmt(xs[0]);+    for(size_t i = 1; i < len; ++i) ss << sep << fmt(xs[i]);+    ss << suf;+    return ss.str();+}+template<typename Container>+inline std::string seq2str(const Container &xs,+                           std::string_view sep="",+                           std::string_view pre="",+                           std::string_view suf="")+{+    auto default_formatter = [](const auto& val) {+        using T = std::decay_t<decltype(val)>;+        if constexpr (std::is_same_v<T,uint8_t> || std::is_same_v<T,int8_t>) {+            return int(val);+        } else {+            return val;+        }+    };+    return seq2str_fmt(xs, default_formatter, sep, pre, suf);+}+inline std::string to_string(const ColorState& cs)+{+    return seq2str_fmt(cs.s, [](auto v) {+        switch(v){+        case U: return 'U';+        case R: return 'R';+        case F: return 'F';+        case D: return 'D';+        case L: return 'L';+        case B: return 'B';+        default: throw std::invalid_argument("to_string(ColorState): ???");+        }+    });+}+inline std::string to_string(const FaceCube& fc, bool use_digit=true)+{+    if(use_digit){+        return seq2str(fc.f);+    } else {+        return seq2str_fmt(fc.f, [](auto v) { return Face2Str[v]; });+    }+}+inline std::string to_string(const CubieCube& cc, CubeFormat fmt)+{+    switch(fmt){+    case CubeFormat::Face:+        return to_string(cc.toFaceCube(), false);+    case CubeFormat::Cubie:+        return seq2str_fmt(cc.cp, [](auto v) { return CornerSet[v]; }) ++               seq2str_fmt(cc.co, [](auto v) { return char('0'+v); }) ++               seq2str_fmt(cc.ep, [](auto v) { return EdgeSet[v]; }) ++               seq2str_fmt(cc.eo, [](auto v) { return char('0'+v);});+    default:+        const auto [fixed_corner,cycles_corner] = decomposite(cc.cp);+        const auto [fixed_edge, cycles_edge ]   = decomposite(cc.ep);+        std::string s1, s2;+        s1.reserve(64);+        s2.reserve(64);+        auto append_fixed = [&](std::string& out, const auto& fixed, const auto& ori_arr, auto name_table) {+            for(auto idx: fixed) {+                if(ori_arr[idx] == 0) continue;+                out += '(';+                out += OrientationToString[ori_arr[idx]];+                out += name_table[idx];+                out += ')';+            }+        };+        auto append_cycles = [&](std::string& out, const auto& cycles, const auto& ori_arr, auto name_table) {+            for(const auto& cycle: cycles) {+                const size_t N = cycle.size();+                if(N == 0) continue;+                out += '(';+                for(int i = 0; i < N; i++) {+                    if(i > 0) out += ',';+                    size_t prev_idx = cycle[(N-1+i)%N];+                    out += OrientationToString[ori_arr[prev_idx]];+                    out += name_table[cycle[i]];+                }+                out += ')';+            }+        };+        append_fixed(s1, fixed_corner, cc.co, CornerToString);+        append_cycles(s1, cycles_corner, cc.co, CornerToString);+        append_fixed(s2, fixed_edge, cc.eo, EdgeToString);+        append_cycles(s2, cycles_edge, cc.eo, EdgeToString);+        return s1.empty() && s2.empty() ? "id" : s1 + s2;+    }+}+inline std::string to_string(const std::vector<TurnMove>& ms)+{+    return seq2str_fmt(ms, [](auto v){+        return Move2Str[v];+    }, " ");+}+}+namespace cube {+using namespace cube::data;+using namespace cube::pdb;+using namespace cube::solver;+namespace fs = std::filesystem;+void set_table_dir(fs::path dir) { config::set_table_dir(dir); }+auto get_table_dir() -> fs::path { return config::get_table_dir(); }+bool is_valid_config(std::string_view cube) { return ColorState::is_valid_config(cube); }+bool is_valid_maneuver(std::string_view maneuver) { return internal::is_valid_maneuver(maneuver); }+void cube_init(bool use_symmetry, std::string_view dir)+{+    static std::once_flag once;+    std::call_once(once, [=]() {+        config::use_symmetry(use_symmetry);+        if(!dir.empty()) config::set_table_dir(dir);+        if(use_symmetry) table::TableProvider::make<true>();+        else table::TableProvider::make<false>();+    });+}+Solution solve(std::string_view src, std::string_view tgt, int good)+{+    if (src != cubeId && !is_valid_config(src)) return {SolveResult::InvalidSrc, ""};+    if (tgt != cubeId && !is_valid_config(tgt)) return {SolveResult::InvalidTgt, ""};+    if (src == tgt) return {SolveResult::Success, ""};+    auto cc_src = ColorState::fromString(src).toCubieCube();+    auto cc_tgt = ColorState::fromString(tgt).toCubieCube();+    CubieCube cc = ~cc_tgt * cc_src;+    if (!cc.isSolvable()) return {SolveResult::Unsolvable, ""};+    cube_init(CUBE_USE_SYMMETRY);+    const auto& [found, s1, s2] = KociembaSolver::solve(cc, good < 0 ? 0 : good);+    if (!found) return {SolveResult::NotFound, ""};+    std::vector<TurnMove> sol;+    size_t n1 = s1.size(), n2 = s2.size();+    if (!s1.empty() && !s2.empty() && s1[n1 - 1] / 3 == s2[0] / 3) {+        sol.insert(sol.end(), s1.begin(), s1.end() - 1);+        int m = (s1[n1 - 1] + s2[0] - s2[0] / 3 * 6 + 2) % 4;+        if (m != 0) sol.push_back(static_cast<TurnMove>(s2[0] / 3 * 3 + m - 1));+        sol.insert(sol.end(), s2.begin() + 1, s2.end());+    } else {+        sol.insert(sol.end(), s1.begin(), s1.end());+        sol.insert(sol.end(), s2.begin(), s2.end());+    }+    return {SolveResult::Success, show::to_string(sol)};+}+bool is_solvable(std::string_view color_cube) {+    return is_valid_config(color_cube) &&+           ColorState::fromString(color_cube).toCubieCube().isSolvable();+}+std::string apply_maneuver(std::string_view maneuver, std::string_view cube_state) {+    if (cube_state.size() != 54 || !is_valid_maneuver(maneuver)) {+        throw std::invalid_argument("Invalid cube format or maneuver string.");+    }+    const auto ms = internal::parse_maneuver(maneuver);+    return internal::apply_maneuver(cube_state, ms);+}+std::string show_permutation(std::string_view ms_or_cube, PermFormat format) {+    std::string cube_str;+    if (is_valid_config(ms_or_cube)) {+        cube_str = ms_or_cube;+    } else if (is_valid_maneuver(ms_or_cube)) {+        auto ms = internal::parse_maneuver(ms_or_cube);+        cube_str = internal::apply_maneuver(cubeId, ms);+    } else {+        throw std::invalid_argument("Input is neither a valid configuration nor a valid maneuver.");+    }+    auto cc = ColorState::fromString(cube_str).toCubieCube();+    return show::to_string(cc, show::CubeFormat(int(format)));+}+}+#ifdef __cplusplus+    #define Default(x) = x+#else+    #define Default(x)+#endif+#define CUBE_BS 128+#define CUBE_ID "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB"+#ifndef CF_ENUM+    #if defined(__cplusplus)+        #define CF_ENUM(_type, _name) \+            int __CF_ENUM_##_name; \+            enum _name : _type+    #elif defined(__clang__) || defined(__OBJC__)+        #define CF_ENUM(_type, _name) \+            enum _name : _type _name; \+            enum _name: _type+    #else+        #define CF_ENUM(_type, _name) \+            _type _name; \+            enum+    #endif+#endif+typedef CF_ENUM(int32_t,SolveResult) {+    SolveResultSuccess = 0,+    SolveResultUnsolvable = 1,+    SolveResultNotFound = 2,+    SolveResultInvalidSrc = 3,+    SolveResultInvalidTgt = 4,+    SolveResultUnknownErr = 5+};+static inline const char* solve_result_info(SolveResult sr)+{+    switch(sr) {+    case SolveResultSuccess:    return "Success.";+    case SolveResultUnsolvable: return "The cube configuration is unsolvable.";+    case SolveResultNotFound:   return "No solution found within the step limit.";+    case SolveResultInvalidSrc: return "Invalid source color configuration.";+    case SolveResultInvalidTgt: return "Invalid target color configuration.";+    case SolveResultUnknownErr: return "Unknown error.";+    default:                    return "???";+    }+}+#ifdef __cplusplus+extern "C" {+#endif+CUBE_EXPORT const char *solve_result_to_string(int32_t sr);+CUBE_EXPORT void cube_init(+    bool use_symmetry   Default(CUBE_USE_SYMMETRY),+    const char* dir     Default(0)+);+CUBE_EXPORT SolveResult solve(+    char*       buf,+    const char* src         Default(CUBE_ID),+    const char* tgt         Default(CUBE_ID),+    int         good        Default(22)+);+CUBE_EXPORT bool solvable(+    const char* color_cube  Default(CUBE_ID)+);+CUBE_EXPORT bool facecube(+    char* buf,+    const char* maneuver    Default(""),+    const char *cube        Default(CUBE_ID)+);+CUBE_EXPORT bool permutation(+    char*       buf,+    const char* ms_or_cube  Default(CUBE_ID),+    int         format      Default(2)+);+#ifdef __cplusplus+}+#endif+extern "C" {+void cube_init(bool use_symmetry, const char* dir)+{+    cube::cube_init(use_symmetry, dir ? std::string_view(dir) : std::string_view{});+} const char* solve_result_to_string(int sr) {     return solve_result_info(static_cast<SolveResult>(sr));

@@ -20,7 +20,7 @@ -- PVP summary:     +-+------- breaking API changes --                  | | +----- non-breaking API additions --                  | | | +--- code changes with no API change-version:            0.5.0.0+version:            0.5.1.0  -- A short (one-line) description of the package. synopsis:           High-performance, type-safe Rubik's Cube solver with C FFI bindings.@@ -88,7 +88,7 @@      cxx-sources:        cbits/cube_amalg.min.cpp     include-dirs:       cbits-    cxx-options:        -std=c++17 -O3+    cxx-options:        -std=c++17 -O3 -DCUBE_USE_SYMMETRY=1 -DCUBE_ENABLE_TRACE=1  test-suite cube-hs-test     -- Import common warning flags.

@@ -27,7 +27,9 @@ --     let scrambledCube = foldl (&>) cubeId scrambledTurns --     putStrLn $ "Scrambled state: " ++ showCube scrambledCube -----     -- 4. Solve using zero-cost C FFI solver and verify restoration+--     -- 4a. build tables (`False` means without symmetry) under "cache" directory+--     cubeInit False "cache"  +--     -- 4b. Solve the scrambled cube & verify solution --     let sol = unsafeSolveFrom scrambledCube --     putStrLn $ "Optimal solution steps: " ++ showTurns sol --     putStrLn $ "Is fully restored? " ++ show (applyTurns scrambledCube sol == cubeId)@@ -51,6 +53,7 @@ , showTurns , parseTurns   -- * Solving Interface (C FFI)+, cubeInit , rawSolve , solve , unsafeSolve

@@ -3,6 +3,12 @@ import Foreign.C.Types (CInt(..), CBool(..)) import Foreign.C.String (CString) +foreign import ccall "cube_init"+    c_cube_init +        :: CBool    -- use symmetry +        -> CString  -- table directory+        -> IO ()+ foreign import ccall "solve"     c_solve          :: CString  -- buffer

@@ -23,6 +23,7 @@ , applyTurns , showTurns , parseTurns+, cubeInit , rawSolve , solve , unsafeSolve@@ -104,6 +105,24 @@         Dx1 -> "D"; Dx2 -> "D2"; Dx3 -> "D'"         Lx1 -> "L"; Lx2 -> "L2"; Lx3 -> "L'"         Bx1 -> "B"; Bx2 -> "B2"; Bx3 -> "B'"++-- | Initialize the cube library by loading or building lookup tables.+--+-- @useSym@: 'False' uses compact tables (<10 MB, fast build, slower+-- solving); 'True' uses symmetry tables (~260 MB, slow build, fasters olving).+--+-- @dir@: directory to read\/write table files; empty means the default.+-- Tables are loaded if present, otherwise built there.+--+-- Only the first call takes effect; later calls are no-ops. The first +-- 'c_solve' invokes it implicitly with defaults.+--+-- Warning: @useSym = True@ may take minutes and write ~260 MB on first run.+cubeInit :: Bool -> FilePath -> IO ()+cubeInit useSymmetry tableDir = do+    let cb = if useSymmetry then 1 else 0+    withCString tableDir $ \cstr -> do+        c_cube_init cb cstr  -- | Uses Kociemba's two-phase algorithm. The search stops as soon as any solution  -- of length at most `good` is found, trading optimality for speed. 

@@ -23,6 +23,8 @@      assertTest "Standard initial cube is legal"                  (isLegalCubeString initStr)++    cubeInit False "cache"          let identityMoves = unsafeSolveFrom cubeId     assertTest "Solving already solved cube returns no moves"