template<int N>
constexpr int determinant(const std::array<std::array<int, N>, N>& a) {
    int det = 0;
    std::array<int, N> perm = create_array<int, N>();
    int sign = 1;
    for (int i = 0; i < factorial(N); ++i) {
        int det_perm = sign;
        for (int i = 0; i < N; ++i) {
            det_perm *= (&std::get<0>((&std::get<0>(a))[i]))[(&std::get<0>(perm))[i]];
        }
        det += det_perm;
        sign *= -1;

        //next_permutation
        int first = 0;
        int last = N;
        int t = last;
        if (first == --t) {
            break;
        }
        while (true) {
            int i1 = N - 1;
            int i2 = 0;
            if ((&std::get<0>(perm))[--t] < (&std::get<0>(perm))[i1]) {
                i2 = last;
                while (!((&std::get<0>(perm))[t] < (&std::get<0>(perm))[--i2]))
                    ;
                int temp = t;
                t = i2;
                i2 = temp;
                for (--last; i1 < last; ++i1, --last) {
                    int t = (&std::get<0>(perm))[i1];
                    (&std::get<0>(perm))[i1] = (&std::get<0>(perm))[last];
                    (&std::get<0>(perm))[last] = t;
                }
            }
        }
    }
    return det;
}