結果

問題 No.2444 一次変換と体積
ユーザー Aeren
提出日時 2023-08-26 04:16:56
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 21,296 bytes
コンパイル時間 3,926 ms
コンパイル使用メモリ 375,812 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-24 18:19:17
合計ジャッジ時間 4,721 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
other AC * 20
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ソースコード

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プレゼンテーションモードにする

#include <x86intrin.h>
#include <bits/stdc++.h>
using namespace std;
#if __cplusplus > 201703L
#include <ranges>
using namespace numbers;
#endif
template<int id>
struct modular_unfixed_base{
    static unsigned int _mod;
    static unsigned long long _inverse_mod;
    static unsigned int &mod(){
        return _mod;
    }
    static void precalc_barrett(){
        _inverse_mod = (unsigned long long)-1 / _mod + 1;
    }
    static void setup(unsigned int mod = 0){
        if(!mod) cin >> mod;
        _mod = mod;
        assert(_mod >= 1);
        precalc_barrett();
    }
    template<class T>
    static vector<modular_unfixed_base> precalc_power(T base, int SZ){
        vector<modular_unfixed_base> res(SZ + 1, 1);
        for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
        return res;
    }
    static vector<modular_unfixed_base> _INV;
    static void precalc_inverse(int SZ){
        if(_INV.empty()) _INV.assign(2, 1);
        for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);
    }
    // _mod must be a prime
    static modular_unfixed_base _primitive_root;
    static modular_unfixed_base primitive_root(){
        if(_primitive_root) return _primitive_root;
        if(_mod == 2) return _primitive_root = 1;
        if(_mod == 998244353) return _primitive_root = 3;
        unsigned int divs[20] = {};
        divs[0] = 2;
        int cnt = 1;
        unsigned int x = (_mod - 1) / 2;
        while(x % 2 == 0) x /= 2;
        for(auto i = 3; 1LL * i * i <= x; i += 2){
            if(x % i == 0){
                divs[cnt ++] = i;
                while(x % i == 0) x /= i;
            }
        }
        if(x > 1) divs[cnt ++] = x;
        for(auto g = 2; ; ++ g){
            bool ok = true;
            for(auto i = 0; i < cnt; ++ i){
                if((modular_unfixed_base(g).power((_mod - 1) / divs[i])) == 1){
                    ok = false;
                    break;
                }
            }
            if(ok) return _primitive_root = g;
        }
    }
    constexpr modular_unfixed_base(): data(){ }
    modular_unfixed_base(const double &x){ data = normalize(llround(x)); }
    modular_unfixed_base(const long double &x){ data = normalize(llround(x)); }
    template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base(const T &x){ data = normalize(x); }
    template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> static unsigned int normalize(const T &x){
        if(_mod == 1) return 0;
        assert(_inverse_mod);
        int sign = x >= 0 ? 1 : -1;
        unsigned int v = _mod <= sign * x ? sign * x - ((__uint128_t)(sign * x) * _inverse_mod >> 64) * _mod : sign * x;
        if(v >= _mod) v += _mod;
        if(sign == -1 && v) v = _mod - v;
        return v;
    }
    const unsigned int &operator()() const{ return data; }
    template<class T> operator T() const{ return data; }
    modular_unfixed_base &operator+=(const modular_unfixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }
    modular_unfixed_base &operator-=(const modular_unfixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }
    template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base &operator+=(const T &otr){ return *this += 
        modular_unfixed_base(otr); }
    template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base &operator-=(const T &otr){ return *this -= 
        modular_unfixed_base(otr); }
    modular_unfixed_base &operator++(){ return *this += 1; }
    modular_unfixed_base &operator--(){ return *this += _mod - 1; }
    modular_unfixed_base operator++(int){ modular_unfixed_base result(*this); *this += 1; return result; }
    modular_unfixed_base operator--(int){ modular_unfixed_base result(*this); *this += _mod - 1; return result; }
    modular_unfixed_base operator-() const{ return modular_unfixed_base(_mod - data); }
    modular_unfixed_base &operator*=(const modular_unfixed_base &rhs){
        data = normalize((unsigned long long)data * rhs.data);
        return *this;
    }
    template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr>
    modular_unfixed_base &inplace_power(T e){
        if(e < 0) *this = 1 / *this, e = -e;
        modular_unfixed_base res = 1;
        for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
        return *this = res;
    }
    template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr>
    modular_unfixed_base power(T e) const{
        return modular_unfixed_base(*this).inplace_power(e);
    }
    modular_unfixed_base &operator/=(const modular_unfixed_base &otr){
        int a = otr.data, m = _mod, u = 0, v = 1;
        if(a < _INV.size()) return *this *= _INV[a];
        while(a){
            int t = m / a;
            m -= t * a; swap(a, m);
            u -= t * v; swap(u, v);
        }
        assert(m == 1);
        return *this *= u;
    }
    unsigned int data;
};
template<int id> unsigned int modular_unfixed_base<id>::_mod;
template<int id> unsigned long long modular_unfixed_base<id>::_inverse_mod;
template<int id> vector<modular_unfixed_base<id>> modular_unfixed_base<id>::_INV;
template<int id> modular_unfixed_base<id> modular_unfixed_base<id>::_primitive_root;
template<int id> bool operator==(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return lhs.data == rhs.data; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator==(const modular_unfixed_base<id> &lhs, T rhs){ 
    return lhs == modular_unfixed_base<id>(rhs); }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator==(T lhs, const modular_unfixed_base<id> &rhs){ 
    return modular_unfixed_base<id>(lhs) == rhs; }
template<int id> bool operator!=(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return !(lhs == rhs); }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator!=(const modular_unfixed_base<id> &lhs, T rhs){ 
    return !(lhs == rhs); }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator!=(T lhs, const modular_unfixed_base<id> &rhs){ 
    return !(lhs == rhs); }
template<int id> bool operator<(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return lhs.data < rhs.data; }
template<int id> bool operator>(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return lhs.data > rhs.data; }
template<int id> bool operator<=(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return lhs.data <= rhs.data; }
template<int id> bool operator>=(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return lhs.data >= rhs.data; }
template<int id> modular_unfixed_base<id> operator+(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return 
    modular_unfixed_base<id>(lhs) += rhs; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base<id> operator+(const modular_unfixed_base
    <id> &lhs, T rhs){ return modular_unfixed_base<id>(lhs) += rhs; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base<id> operator+(T lhs, const 
    modular_unfixed_base<id> &rhs){ return modular_unfixed_base<id>(lhs) += rhs; }
template<int id> modular_unfixed_base<id> operator-(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return 
    modular_unfixed_base<id>(lhs) -= rhs; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base<id> operator-(const modular_unfixed_base
    <id> &lhs, T rhs){ return modular_unfixed_base<id>(lhs) -= rhs; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base<id> operator-(T lhs, const 
    modular_unfixed_base<id> &rhs){ return modular_unfixed_base<id>(lhs) -= rhs; }
template<int id> modular_unfixed_base<id> operator*(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs){ return 
    modular_unfixed_base<id>(lhs) *= rhs; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base<id> operator*(const modular_unfixed_base
    <id> &lhs, T rhs){ return modular_unfixed_base<id>(lhs) *= rhs; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base<id> operator*(T lhs, const 
    modular_unfixed_base<id> &rhs){ return modular_unfixed_base<id>(lhs) *= rhs; }
template<int id> modular_unfixed_base<id> operator/(const modular_unfixed_base<id> &lhs, const modular_unfixed_base<id> &rhs) { return 
    modular_unfixed_base<id>(lhs) /= rhs; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base<id> operator/(const modular_unfixed_base
    <id> &lhs, T rhs) { return modular_unfixed_base<id>(lhs) /= rhs; }
template<int id, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_unfixed_base<id> operator/(T lhs, const 
    modular_unfixed_base<id> &rhs) { return modular_unfixed_base<id>(lhs) /= rhs; }
template<int id> istream &operator>>(istream &in, modular_unfixed_base<id> &number){
    long long x;
    in >> x;
    number.data = modular_unfixed_base<id>::normalize(x);
    return in;
}
// #define _PRINT_AS_FRACTION
template<int id> ostream &operator<<(ostream &out, const modular_unfixed_base<id> &number){
#ifdef LOCAL
#ifdef _PRINT_AS_FRACTION
    out << number();
    cerr << "(";
    for(auto d = 1; ; ++ d){
        if((number * d).data <= 1000000){
            cerr << (number * d).data << "/" << d;
            break;
        }
        else if((-number * d).data <= 1000000){
            cerr << "-" << (-number * d).data << "/" << d;
            break;
        }
    }
    cerr << ")";
    return out;
#else
    return out << number();
#endif
#else
    return out << number();
#endif
}
#undef _PRINT_AS_FRACTION
using modular = modular_unfixed_base<0>;
// T must support +=, -=, *, *=, ==, and !=
template<class T, size_t N, size_t M>
struct matrix_fixed_base{
    using ring_t = T;
    using domain_t = array<T, M>;
    using range_t = array<T, N>;
    static constexpr int n = N, m = M;
    array<array<T, M>, N> data;
    array<T, M> &operator()(int i){
        assert(0 <= i && i < n);
        return data[i];
    }
    const array<T, M> &operator()(int i) const{
        assert(0 <= i && i < n);
        return data[i];
    }
    T &operator()(int i, int j){
        assert(0 <= i && i < n && 0 <= j && j < m);
        return data[i][j];
    }
    const T &operator()(int i, int j) const{
        assert(0 <= i && i < n && 0 <= j && j < m);
        return data[i][j];
    }
    operator vector<vector<T>>() const{
        return data;
    }
    bool operator==(const matrix_fixed_base &a) const{
        assert(n == a.n && m == a.m);
        return data == a.data;
    }
    bool operator!=(const matrix_fixed_base &a) const{
        assert(n == a.n && m == a.m);
        return data != a.data;
    }
    matrix_fixed_base &operator+=(const matrix_fixed_base &a){
        assert(n == a.n && m == a.m);
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] += a(i, j);
        return *this;
    }
    matrix_fixed_base operator+(const matrix_fixed_base &a) const{
        assert(n == a.n && m == a.m);
        return matrix_fixed_base(*this) += a;
    }
    matrix_fixed_base &operator-=(const matrix_fixed_base &a){
        assert(n == a.n && m == a.m);
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] += a(i, j);
        return *this;
    }
    matrix_fixed_base operator-(const matrix_fixed_base &a) const{
        assert(n == a.n && m == a.m);
        return matrix_fixed_base(*this) += a;
    }
    template<size_t N2, size_t M2>
    matrix_fixed_base<T, N, M2> operator*(const matrix_fixed_base<T, N2, M2> &a) const{
        assert(m == a.n);
        int l = M2;
        matrix_fixed_base<T, N, M2> res;
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) for(auto k = 0; k < l; ++ k) res(i, k) += data[i][j] * a(j, k);
        return res;
    }
    template<size_t N2, size_t M2>
    matrix_fixed_base &operator*=(const matrix_fixed_base<T, N2, M2> &a){
        return *this = *this * a;
    }
    matrix_fixed_base &operator*=(T c){
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] *= c;
        return *this;
    }
    matrix_fixed_base operator*(T c) const{
        return matrix_fixed_base(*this) *= c;
    }
    template<class U, typename enable_if<is_integral<U>::value>::type* = nullptr>
    matrix_fixed_base &inplace_power(U e){
        assert(n == m && e >= 0);
        matrix_fixed_base res(1, 0);
        for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
        return *this = res;
    }
    template<class U>
    matrix_fixed_base power(U e) const{
        return matrix_fixed_base(*this).inplace_power(e);
    }
    matrix_fixed_base &inplace_transpose(){
        assert(n == m);
        for(auto i = 0; i < n; ++ i) for(auto j = i + 1; j < n; ++ j) swap(data[i][j], data[j][i]);
        return *this;
    }
    matrix_fixed_base transpose() const{
        if(n == m) return matrix_fixed_base(*this).inplace_transpose();
        matrix_fixed_base<T, M, N> res;
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res(j, i) = data[i][j];
        return res;
    }
    // Multiply a column vector v on the right
    range_t operator*(const domain_t &v) const{
        range_t res;
        res.fill(T(0));
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[i] += data[i][j] * v[j];
        return res;
    }
    // Assumes T is either a floating, integral, or a modular type.
    // If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    // Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
    // Returns {REF matrix, determinant, rank}
    tuple<matrix_fixed_base &, T, int> inplace_REF(){
        if(n == 0) return {*this, T(1), 0};
        T det = 1;
        int rank = 0;
        for(auto j = 0; j < m; ++ j){
            if constexpr(is_floating_point_v<T>){
                static const T eps = 1e-9;
                int pivot = rank;
                for(auto i = rank + 1; i < n; ++ i) if(abs(data[pivot][j]) < abs(data[i][j])) pivot = i;
                if(rank != pivot){
                    swap(data[rank], data[pivot]);
                    det *= -1;
                }
                if(abs(data[rank][j]) <= eps) continue;
                det *= data[rank][j];
                T inv = 1 / data[rank][j];
                for(auto i = rank + 1; i < n; ++ i) if(abs(data[i][j]) > eps){
                    T coef = data[i][j] * inv;
                    for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
                }
            }
            else{
                for(auto i = rank + 1; i < n; ++ i) while(data[i][j]){
                    T q;
                    if constexpr(is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) q = data[rank][j] / data[i][j];
                    else q = data[rank][j].data / data[i][j].data;
                    if(q) for(auto k = j; k < m; ++ k) data[rank][k] -= q * data[i][k];
                    swap(data[rank], data[i]);
                    det *= -1;
                }
                if(rank == j) det *= data[rank][j];
                else det = T(0);
                if(data[rank][j]) ++ rank;
            }
        }
        return {*this, det, rank};
    }
    // Assumes T is either a floating, integral, or a modular type.
    // If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    // Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
    // Returns {REF matrix, determinant, rank}
    tuple<matrix_fixed_base, T, int> REF() const{
        return matrix_fixed_base(*this).inplace_REF();
    }
    // Assumes T is a field.
    // O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    // Returns {REF matrix, determinant, rank}
    tuple<matrix_fixed_base &, T, int> inplace_REF_field(){
        if(n == 0) return {*this, T(1), 0};
        T det = T(1);
        int rank = 0;
        for(auto j = 0; j < m; ++ j){
            int pivot = -1;
            for(auto i = rank; i < n; ++ i) if(data[i][j] != T(0)){
                pivot = i;
                break;
            }
            if(!~pivot){
                det = T(0);
                continue;
            }
            if(rank != pivot){
                swap(data[rank], data[pivot]);
                det *= -1;
            }
            det *= data[rank][j];
            T inv = 1 / data[rank][j];
            for(auto i = rank + 1; i < n; ++ i) if(data[i][j] != T(0)){
                T coef = data[i][j] * inv;
                for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[j][k];
            }
            ++ rank;
        }
        return {*this, det, rank};
    }
    // Assumes T is a field.
    // O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    // Returns {REF matrix, determinant, rank}
    tuple<matrix_fixed_base, T, int> REF_field() const{
        return matrix_fixed_base(*this).inplace_REF_field();
    }
    // Assumes T is a field.
    // O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    optional<matrix_fixed_base> inverse(auto find_inverse) const{
        assert(n == m);
        if(n == 0) return *this;
        auto a = data;
        array<array<T, N>, N> res{};
        for(auto i = 0; i < n; ++ i) res[i][i] = T(1);
        for(auto j = 0; j < n; ++ j){
            int rank = j, pivot = -1;
            for(auto i = rank; i < n; ++ i) if(a[i][j] != T(0)){
                pivot = i;
                break;
            }
            if(!~pivot) return {};
            swap(a[rank], a[pivot]), swap(res[rank], res[pivot]);
            T inv = 1 / a[rank][j];
            for(auto k = j; k < n; ++ k) a[rank][k] *= inv, res[rank][k] *= inv;
            for(auto i = 0; i < n; ++ i) if(i != j && a[i][j] != T(0)){
                T d = a[i][j];
                for(auto k = j; k < n; ++ k) a[i][k] -= d * a[j][k], res[i][k] -= d * res[j][k];
            }
        }
        return res;
    }
    // Assumes T is either a floating, integral, or a modular type.
    // If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    // Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
    T determinant() const{
        assert(n == m);
        return get<1>(REF());
    }
    // Assumes T is a field.
    // O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    T determinant_field() const{
        assert(n == m);
        return get<1>(REF_field());
    }
    // Assumes T is either a floating, integral, or a modular type.
    // If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    // Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
    int rank() const{
        return get<2>(REF());
    }
    // Assumes T is a field.
    // O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    int rank_field() const{
        return get<2>(REF_field());
    }
    // O(n * 2^n)
    T permanent() const{
        static_assert(n <= 30 && n == m);
        T perm = n ? 0 : 1;
        array<T, N> sum{};
        for(auto order = 1; order < 1 << n; ++ order){
            int j = __lg(order ^ order >> 1 ^ order - 1 ^ order - 1 >> 1), sign = (order ^ order >> 1) & 1 << j ? 1 : -1;
            T prod = order & 1 ? -1 : 1;
            if((order ^ order >> 1) & 1 << j) for(auto i = 0; i < n; ++ i) prod *= sum[i] += data[i][j];
            else for(auto i = 0; i < n; ++ i) prod *= sum[i] -= data[i][j];
            perm += prod;
        }
        return perm * (n & 1 ? -1 : 1);
    }
    template<class output_stream>
    friend output_stream &operator<<(output_stream &out, const matrix_fixed_base &a){
        out << "{";
        for(auto i = 0; i < a.n; ++ i){
            out << "{";
            for(auto j = 0; j < a.m; ++ j){
                out << a(i, j);
                if(j != a.m - 1) out << ", ";
            }
            out << "}";
            if(i != a.n - 1) out << ", ";
        }
        return out << "}";
    }
    matrix_fixed_base(): matrix_fixed_base(T(0), T(0)){ }
    matrix_fixed_base(const T &init_diagonal, const T &init_off_diagonal){
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] = i == j ? init_diagonal : init_off_diagonal;
    }
    matrix_fixed_base(const array<array<T, M>, N> &arr): data(arr){ }
    static matrix_fixed_base additive_identity(){
        return matrix_fixed_base(T(1), T(0));
    }
    static matrix_fixed_base multiplicative_identity(){
        return matrix_fixed_base(T(0), T(0));
    }
};
template<class T, size_t N, size_t M>
matrix_fixed_base<T, N, M> operator*(T c, matrix_fixed_base<T, N, M> a){
    for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) a(i, j) = c * a(i, j);
    return a;
}
// Multiply a row vector v on the left
template<class T, size_t N, size_t M>
typename matrix_fixed_base<T, N, M>::domain_t operator*(const typename matrix_fixed_base<T, N, M>::range_t &v, const matrix_fixed_base<T, N, M> &a){
    typename matrix_fixed_base<T, N, M>::domain_t res;
    res.fill(T(0));
    for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) res[j] += v[i] * a(i, j);
    return res;
}
template<class T>
using matrix = matrix_fixed_base<T, 3, 3>;
int main(){
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(ios::badbit | ios::failbit);
    int n;
    cin >> n;
    modular::setup();
    matrix<__int128_t> mat_int;
    for(auto i = 0; i < 3; ++ i){
        for(auto j = 0; j < 3; ++ j){
            long long x;
            cin >> x;
            mat_int(i, j) = x;
        }
    }
    auto det = mat_int.determinant();
    if(!mat_int.determinant()){
        mat_int.inplace_power(min(n, 3));
        mat_int.inplace_transpose();
        auto [ref, det, rank] = mat_int.REF();
        assert(rank <= 2);
        if(rank == 0){
            cout << "0\n";
        }
        else if(rank == 1){
            if(ranges::min(ref(0)) >= 0 || ranges::max(ref(0)) <= 0){
                cout << "0\n";
            }
            else{
                cout << "infty\n";
            }
        }
        else{
            array<__int128_t, 3> normal;
            for(auto j = 0; j < 3; ++ j){
                int x = (j + 1) % 3, y = (j + 2) % 3;
                normal[j] = __int128_t(1) * ref(0, x) * ref(1, y) - __int128_t(1) * ref(0, y) * ref(1, x);
            }
            assert(ranges::count(normal, 0) <= 2);
            if(ranges::min(normal) > 0 || ranges::min(normal) < 0 || ranges::count(normal, 0) == 2){
                cout << "0\n";
            }
            else{
                cout << "infty\n";
            }
        }
        return 0;
    }
    cout << modular(abs((long long)det)).power(n) << "\n";
    return 0;
}
/*
*/
////////////////////////////////////////////////////////////////////////////////////////
//                                                                                    //
//                                   Coded by Aeren                                   //
//                                                                                    //
////////////////////////////////////////////////////////////////////////////////////////
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