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:heavy_check_mark: Math/tests/matrix_det.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/matrix_det"

#include <bits/stdc++.h>
#include "../../atcoder/modint.hpp"
using namespace std;
using namespace atcoder;

#include "../Matrix.h"
#include "../../buffered_reader.h"

#define REP(i, a) for (int i = 0, _##i = (a); i < _##i; ++i)

int32_t main() {
    ios::sync_with_stdio(0); cin.tie(0);
    int n = IO::get<int>();
    Matrix<modint998244353> a(n, n);
    REP(i,n) REP(j,n) {
        int x = IO::get<int>();
        a[i][j] = x;
    }
    auto tmp = a.gauss();
    cout << tmp.det().val() << endl;
    return 0;
}
#line 1 "Math/tests/matrix_det.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/matrix_det"

#include <bits/stdc++.h>
#line 1 "atcoder/modint.hpp"



#line 6 "atcoder/modint.hpp"
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#line 1 "atcoder/internal_math.hpp"



#line 5 "atcoder/internal_math.hpp"

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m < 2^31`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(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 (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#line 1 "atcoder/internal_type_traits.hpp"



#line 7 "atcoder/internal_type_traits.hpp"

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


#line 14 "atcoder/modint.hpp"

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder


#line 5 "Math/tests/matrix_det.test.cpp"
using namespace std;
using namespace atcoder;

#line 1 "Math/Matrix.h"
// Matrix, which works for both double and int {{{
// Copied partially from https://judge.yosupo.jp/submission/54653
//
// Tested:
// - (mat mul): https://judge.yosupo.jp/problem/matrix_product
// - (mat pow): https://oj.vnoi.info/problem/icpc21_mt_k
// - (mat pow): https://oj.vnoi.info/problem/icpc21_mb_h
// - (gauss): https://oj.vnoi.info/problem/vmrook
// - (inverse): https://oj.vnoi.info/problem/dtl_lsr
// - (inverse): https://judge.yosupo.jp/problem/inverse_matrix
// - (det): https://judge.yosupo.jp/problem/matrix_det

template<typename T>
struct Matrix {
    int n_row, n_col;
    vector<T> x;

    // accessors
    typename vector<T>::iterator operator [] (int r) {
        return x.begin() + r * n_col;
    }
    inline T get(int i, int j) const { return x[i * n_col + j]; }
    vector<T> at(int r) const {
        return vector<T> { x.begin() + r * n_col, x.begin() + (r+1) * n_col };
    }

    // constructors
    Matrix() = default;
    Matrix(int _n_row, int _n_col) : n_row(_n_row), n_col(_n_col), x(n_row * n_col) {}
    Matrix(const vector<vector<T>>& d) : n_row(d.size()), n_col(d.size() ? d[0].size() : 0) {
        for (auto& row : d) std::copy(row.begin(), row.end(), std::back_inserter(x));
    }

    // convert to 2d vec
    vector<vector<T>> vecvec() const {
        vector<vector<T>> ret(n_row);
        for (int i = 0; i < n_row; i++) {
            std::copy(x.begin() + i*n_col,
                    x.begin() + (i+1)*n_col,
                    std::back_inserter(ret[i]));
        }
        return ret;
    }
    operator vector<vector<T>>() const { return vecvec(); }

    static Matrix identity(int n) {
        Matrix res(n, n);
        for (int i = 0; i < n; i++) {
            res[i][i] = 1;
        }
        return res;
    }

    Matrix transpose() const {
        Matrix res(n_col, n_row);
        for (int i = 0; i < n_row; i++) {
            for (int j = 0; j < n_col; j++) {
                res[j][i] = this->get(i, j);
            }
        }
        return res;
    }

    Matrix& operator *= (const Matrix& r) { return *this = *this * r; }
    Matrix operator * (const Matrix& r) const {
        assert(n_col == r.n_row);
        Matrix res(n_row, r.n_col);

        for (int i = 0; i < n_row; i++) {
            for (int k = 0; k < n_col; k++) {
                for (int j = 0; j < r.n_col; j++) {
                    res[i][j] += this->get(i, k) * r.get(k, j);
                }
            }
        }
        return res;
    }

    Matrix pow(long long n) const {
        assert(n_row == n_col);
        Matrix res = identity(n_row);
        if (n == 0) return res;

        bool res_is_id = true;
        for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
            if (!res_is_id) res *= res;
            if ((n >> i) & 1) res *= (*this), res_is_id = false;
        }
        return res;
    }

    // Gauss
    template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>
    static int choose_pivot(const Matrix<T2> &mtr, int h, int c) noexcept {
        int piv = -1;
        for (int j = h; j < mtr.n_row; j++) {
            if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c)))) piv = j;
        }
        return piv;
    }
    template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>
    static int choose_pivot(const Matrix<T2> &mtr, int h, int c) noexcept {
        for (int j = h; j < mtr.n_row; j++) {
            if (mtr.get(j, c) != T(0)) return j;
        }
        return -1;
    }

    // return upper triangle matrix
    [[nodiscard]] Matrix gauss() const {
        int c = 0;
        Matrix mtr(*this);
        vector<int> ws;
        ws.reserve(n_col);

        for (int h = 0; h < n_row; h++) {
            if (c == n_col) break;
            int piv = choose_pivot(mtr, h, c);
            if (piv == -1) {
                c++;
                h--;
                continue;
            }
            if (h != piv) {
                for (int w = 0; w < n_col; w++) {
                    swap(mtr[piv][w], mtr[h][w]);
                    mtr[piv][w] *= -1; // for determinant
                }
            }
            ws.clear();
            for (int w = c; w < n_col; w++) {
                if (mtr[h][w] != 0) ws.emplace_back(w);
            }
            const T hcinv = T(1) / mtr[h][c];
            for (int hh = 0; hh < n_row; hh++) {
                if (hh != h) {
                    const T coeff = mtr[hh][c] * hcinv;
                    for (auto w : ws) mtr[hh][w] -= mtr[h][w] * coeff;
                    mtr[hh][c] = 0;
                }
            }
            c++;
        }
        return mtr;
    }

    // For upper triangle matrix
    T det() const {
        T ret = 1;
        for (int i = 0; i < n_row; i++) {
            ret *= get(i, i);
        }
        return ret;
    }

    // return rank of inverse matrix. If rank < n -> not invertible
    int inverse() {
        assert(n_row == n_col);
        vector<vector<T>> ret = identity(n_row), tmp = *this;
        int rank = 0;

        for (int i = 0; i < n_row; i++) {
            int ti = i;
            while (ti < n_row && tmp[ti][i] == 0) ++ti;
            if (ti == n_row) continue;
            else ++rank;

            ret[i].swap(ret[ti]);
            tmp[i].swap(tmp[ti]);

            T inv = T(1) / tmp[i][i];
            for (int j = 0; j < n_col; j++) ret[i][j] *= inv;
            for (int j = i+1; j < n_col; j++) tmp[i][j] *= inv;

            for (int h = 0; h < n_row; h++) {
                if (i == h) continue;
                const T c = -tmp[h][i];
                for (int j = 0; j < n_col; j++) ret[h][j] += ret[i][j] * c;
                for (int j = i+1; j < n_col; j++) tmp[h][j] += tmp[i][j] * c;
            }
        }

        *this = ret;
        return rank;
    }

    // sum of all elements in this matrix
    T sum_all() {
        return submatrix_sum(0, 0, n_row, n_col);
    }

    // sum of [r1, r2) x [c1, c2)
    T submatrix_sum(int r1, int c1, int r2, int c2) {
        T res {0};
        for (int r = r1; r < r2; ++r) {
            res += std::accumulate(
                    x.begin() + r * n_col + c1,
                    x.begin() + r * n_col + c2,
                    T{0});
        }
        return res;
    }
};
template<typename T>
ostream& operator << (ostream& cout, const Matrix<T>& m) {
    cout << m.n_row << ' ' << m.n_col << endl;
    for (int i = 0; i < m.n_row; ++i) {
        cout << "row [" << i << "] = " << m.at(i) << endl;
    }
    return cout;
}
// }}}
#line 1 "buffered_reader.h"
// Buffered reader {{{
namespace IO {
    const int BUFSIZE = 1<<14;
    char buf[BUFSIZE + 1], *inp = buf;

    bool reacheof;
    char get_char() {
        if (!*inp && !reacheof) {
            memset(buf, 0, sizeof buf);
            int tmp = fread(buf, 1, BUFSIZE, stdin);
            if (tmp != BUFSIZE) reacheof = true;
            inp = buf;
        }
        return *inp++;
    }
    template<typename T>
    T get() {
        int neg = 0;
        T res = 0;
        char c = get_char();
        while (!std::isdigit(c) && c != '-' && c != '+') c = get_char();
        if (c == '+') { neg = 0; }
        else if (c == '-') { neg = 1; }
        else res = c - '0';

        c = get_char();
        while (std::isdigit(c)) {
            res = res * 10 + (c - '0');
            c = get_char();
        }
        return neg ? -res : res;
    }
};
// Helper methods
int ri() {
    return IO::get<int>();
}
// }}}
#line 10 "Math/tests/matrix_det.test.cpp"

#define REP(i, a) for (int i = 0, _##i = (a); i < _##i; ++i)

int32_t main() {
    ios::sync_with_stdio(0); cin.tie(0);
    int n = IO::get<int>();
    Matrix<modint998244353> a(n, n);
    REP(i,n) REP(j,n) {
        int x = IO::get<int>();
        a[i][j] = x;
    }
    auto tmp = a.gauss();
    cout << tmp.det().val() << endl;
    return 0;
}
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