結果

問題 No.1907 DETERMINATION
ユーザー yamada
提出日時 2025-08-31 06:08:59
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 543 ms / 4,000 ms
コード長 25,184 bytes
コンパイル時間 3,700 ms
コンパイル使用メモリ 341,364 KB
実行使用メモリ 7,720 KB
最終ジャッジ日時 2025-08-31 06:09:26
合計ジャッジ時間 25,591 ms
ジャッジサーバーID
(参考情報)
judge3 / judge2
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 4
other AC * 63
権限があれば一括ダウンロードができます

ソースコード

diff #

// Begin include: "../../template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
// Begin include: "util.hpp"
namespace yamada {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using lld = long double;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
template <typename T>
using VVV = vector<vector<vector<T>>>;
template <typename T>
using VVVV = vector<vector<vector<vector<T>>>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
using vvvl = vector<vector<vector<long long>>>;
using vvvvl = vector<vector<vector<vector<long long>>>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxpq = priority_queue<T, vector<T>, less<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
	template <typename... Args>
	P(Args... args) : pair<T, U>(args...) {}

	using pair<T, U>::first;
	using pair<T, U>::second;

	P &operator+=(const P &r) {
		first += r.first;
		second += r.second;
		return *this;
	}
	P &operator-=(const P &r) {
		first -= r.first;
		second -= r.second;
		return *this;
	}
	P &operator*=(const P &r) {
		first *= r.first;
		second *= r.second;
		return *this;
	}
	template <typename S>
		P &operator*=(const S &r) {
			first *= r, second *= r;
			return *this;
		}
	P operator+(const P &r) const { return P(*this) += r; }
	P operator-(const P &r) const { return P(*this) -= r; }
	P operator*(const P &r) const { return P(*this) *= r; }
	template <typename S>
		P operator*(const S &r) const {
			return P(*this) *= r;
		}
	P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
using vvp = VV<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T, typename U>
inline bool amin(T &x, U y) {
	return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
	return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
	return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
	return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
	return accumulate(begin(v), end(v), T(0));
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
	return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
	return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
	long long ret = 1, x = 10;
	for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
	return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
	return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
	vector<T> ret(v.size() + 1);
	if (rev) {
		for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
	} else {
		for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
	}
	return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
	vector<T> ret(v);
	sort(ret.begin(), ret.end());
	ret.erase(unique(ret.begin(), ret.end()), ret.end());
	return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
	vector<int> ord(N);
	iota(begin(ord), end(ord), 0);
	sort(begin(ord), end(ord), f);
	return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
	int max_val = *max_element(begin(v), end(v));
	vector<int> inv(max_val + 1, -1);
	for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
	return inv;
}

vector<int> mkiota(int n) {
	vector<int> ret(n);
	iota(begin(ret), end(ret), 0);
	return ret;
}

template <typename T>
T mkrev(const T &v) {
	T w{v};
	reverse(begin(w), end(w));
	return w;
}

template <typename T>
bool nxp(T &v) {
	return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
	vector<vector<T>> ret;
	vector<T> v;
	auto dfs = [&](auto rc, int i) -> void {
		if (i == (int)a.size()) {
			ret.push_back(v);
			return;
		}
		for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
	};
	dfs(dfs, 0);
	return ret;
}

template <typename T, typename U>
vector<U> Digit(T a, const U &x, int siz = -1) {
	vector<U> ret;
	while (a > 0) {
		ret.emplace_back(a % x);
		a /= x;
	}
	if (siz >= 0) while (ret.size() < siz) ret.emplace_back(0);
	return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
	T res = I;
	for (; n; f(a = a * a), n >>= 1) {
		if (n & 1) f(res = res * a);
	}
	return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
	return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
	T res = v;
	reverse(begin(res), end(res));
	return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
	using U = typename T::value_type;
	if(v.empty()) return {};
	int H = v.size(), W = v[0].size();
	vector res(W, T(H, U{}));
	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			res[j][i] = v[i][j];
		}
	}
	return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
	using U = typename T::value_type;
	int H = v.size(), W = v[0].size();
	vector res(W, T(H, U{}));
	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			if (clockwise) {
				res[W - 1 - j][i] = v[i][j];
			} else {
				res[j][H - 1 - i] = v[i][j];
			}
		}
	}
	return res;
}

template <typename T, typename F>
T bisect(T ok, T bad, F pred) {
	if (ok == bad) return ok;
	if (!pred(ok)) return ok; 
	while (bad - ok > 1) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } 
	return bad;
}

template <typename T, typename F>
T bisect_double(T ok, T bad, F pred, int iter = 100) {
	if (ok == bad) return ok;
	if (!pred(ok)) return ok; 
	for (int i = 0; i < iter; i++){
		T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid;
	} 
	return bad;
}

template <typename T>
bool inLR(T L, T x, T R){ return (L <= x && x < R); }

bool YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); return b; }
bool YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); return b; }

template <typename mint>
void mout(mint a, int M = 100) {
	if (a == 0) { cout << 0 << "\n"; return; }
	for (int i = 0; i <= M; i++) for (int j = 1; j <= M; j++) {
		mint val = (mint)i / j;
		if (val == a) {
			if (j == 1) cout << i << "\n";
			else cout << i << "/" << j << "\n";
			return;
		}
		else if (val == -a) {
			if (j == 1) cout << -i << "\n";
			else cout << -i << "/" << j << "\n";
			return;
		}
	}
	cout << "NF\n";
}

template <typename mint>
void mout(std::vector<mint> A, int M = 100) {
	int N = A.size();
	for (int pos = 0; pos < N; pos++) {
		if (A[pos] == 0) { cout << 0 << (pos == N - 1 ? "\n" : " "); continue; }

		bool fn = false;
		for (int i = 0; i <= M; i++) {
			for (int j = 1; j <= M; j++) {
				mint val = (mint)i / j;
				if (val == A[pos]) {
					if (j == 1) cout << i << (pos == N - 1 ? "\n" : " ");
					else cout << i << "/" << j << (pos == N - 1 ? "\n" : " ");
					fn = true;
					break;
				}
				else if (val == -A[pos]) {
					if (j == 1) cout << -i << (pos == N - 1 ? "\n" : " ");
					else cout << -i << "/" << j << (pos == N - 1 ? "\n" : " ");
					fn = true;
					break;
				}
			}
			if (fn) break;
		}
		if (!fn) cout << "NF" << (pos == N - 1 ? "\n" : " ");
	}
}

bool is_square(uint64_t n) {
	if (n < 2) return true;
	uint64_t r = static_cast<uint64_t>(sqrtl(static_cast<long double>(n)));
	if (r * r == n) return true;
	++r;
	return r * r == n;
}

} // namespace yamada

// End include: "util.hpp"

// bit operation
// Begin include: "bitop.hpp"
namespace yamada {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace yamada
// End include: "bitop.hpp"

// inout
// Begin include: "inout.hpp"
namespace yamada {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
	int s = (int)v.size();
	for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
	return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
	for (auto &x : v) is >> x;
	return is;
}

istream &operator>>(istream &is, __int128_t &x) {
	string S;
	is >> S;
	x = 0;
	int flag = 0;
	for (auto &c : S) {
		if (c == '-') {
			flag = true;
			continue;
		}
		x *= 10;
		x += c - '0';
	}
	if (flag) x = -x;
	return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
	string S;
	is >> S;
	x = 0;
	for (auto &c : S) {
		x *= 10;
		x += c - '0';
	}
	return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
	if (x == 0) return os << 0;
	if (x < 0) os << '-', x = -x;
	string S;
	while (x) S.push_back('0' + x % 10), x /= 10;
	reverse(begin(S), end(S));
	return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
	if (x == 0) return os << 0;
	string S;
	while (x) S.push_back('0' + x % 10), x /= 10;
	reverse(begin(S), end(S));
	return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
	cin >> t;
	in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
	cout << t;
	if (sizeof...(u)) cout << sep;
	out(u...);
}

struct IoSetupYamada {
	IoSetupYamada() {
		cin.tie(nullptr);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(15);
		cerr << fixed << setprecision(7);
	}
} iosetupyamada;

}  // namespace yamada
// End include: "inout.hpp"

// macro
// Begin include: "macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define each3(x, y, z, v) for (auto&& [x, y, z] : v)
#define all(v) (v).begin(), (v).end()

#define rep1(a) for (long long _ = 0; _ < (long long)(a); ++_)
#define rep2(i, a) for (long long i = 0; i < (long long)(a); ++i)
#define rep3(i, a, b) for (long long i = a; i < (long long)(b); ++i)
#define rep4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rep1r(a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define rep2r(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define rep3r(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i)
#define overload3(a, b, c, d, ...) d
#define repr(...) overload3(__VA_ARGS__, rep3r, rep2r, rep1r)(__VA_ARGS__)

#define eb emplace_back
#define mkp make_pair
#define mkt make_tuple
#define fi first
#define se second

#define vv(type, name, h, ...)  \
	vector<vector<type> > name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
	vector<vector<vector<type>>> name( \
			h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)  \
	vector<vector<vector<vector<type>>>> name( \
			a, vector<vector<vector<type>>>( \
				b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

#define ini(...)   \
	int __VA_ARGS__; \
	in(__VA_ARGS__)
#define inl(...)         \
	long long __VA_ARGS__; \
	in(__VA_ARGS__)
#define ins(...)      \
	string __VA_ARGS__; \
	in(__VA_ARGS__)
#define in2(s, t)                           \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i]);                         \
	}
#define in3(s, t, u)                        \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i], u[i]);                   \
	}
#define in4(s, t, u, v)                     \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i], u[i], v[i]);             \
	}
#define die(...)             \
	do {                       \
		yamada::out(__VA_ARGS__);\
		return;                  \
	} while (0)
// End include: "macro.hpp"

namespace yamada {
void solve();
}
int main() { yamada::solve(); }
// End include: "../../template/template.hpp"
// Begin include: "../../matrix/first-degree-matrix-determinant.hpp"

// Begin include: "characteristric-polynomial.hpp"

// calculate det(a - xI)
template <typename mint>
vector<mint> CharacteristicPolynomial(vector<vector<mint>> a) {
  int N = a.size();

  for (int j = 0; j < N - 2; j++) {
    for (int i = j + 1; i < N; i++) {
      if (a[i][j] != 0) {
        swap(a[j + 1], a[i]);
        for (int k = 0; k < N; k++) swap(a[k][j + 1], a[k][i]);
        break;
      }
    }
    if (a[j + 1][j] != 0) {
      mint inv = mint(1) / a[j + 1][j];
      for (int i = j + 2; i < N; i++) {
        if (a[i][j] == 0) continue;
        mint coe = inv * a[i][j];
        for (int l = j; l < N; l++) a[i][l] -= coe * a[j + 1][l];
        for (int k = 0; k < N; k++) a[k][j + 1] += coe * a[k][i];
      }
    }
  }

  vector<vector<mint>> p(N + 1);
  p[0] = {mint(1)};
  for (int i = 1; i <= N; i++) {
    p[i].resize(i + 1);
    for (int j = 0; j < i; j++) {
      p[i][j + 1] -= p[i - 1][j];
      p[i][j] += p[i - 1][j] * a[i - 1][i - 1];
    }
    mint x = 1;
    for (int m = 1; m < i; m++) {
      x *= -a[i - m][i - m - 1];
      mint coe = x * a[i - m - 1][i - 1];
      for (int j = 0; j < i - m; j++) p[i][j] += coe * p[i - m - 1][j];
    }
  }
  return p[N];
}
// End include: "characteristric-polynomial.hpp"

// det(M0 + xM1)
template <typename mint>
vector<mint> FirstDegreeMatrixDeterminant(vector<vector<mint>>& M0, vector<vector<mint>>& M1) {
	const int N = M0.size();
	int multiply_by_x = 0;
	mint detAdetBinv = 1;
	for (int p = 0; p < N; ++p) {
		int pivot = -1;
		for (int r = p; r < N; ++r) if (M1[r][p] != mint()) {
			pivot = r;
			break;
		}
		if (pivot < 0) {
			++multiply_by_x;
			if (multiply_by_x > N) return std::vector<mint>(N + 1);
			for (int r = 0; r < p; ++r) {
				mint v = M1[r][p];
				M1[r][p] = 0;
				for (int i = 0; i < N; ++i) M0[i][p] -= v * M0[i][r];
			}
			for (int i = 0; i < N; ++i) swap(M0[i][p], M1[i][p]);
			--p;
			continue;
		}

		if (pivot != p) {
			M1[pivot].swap(M1[p]);
			M0[pivot].swap(M0[p]);
			detAdetBinv *= -1;
		}

		mint v = M1[p][p], vinv = v.inverse();
		detAdetBinv *= v;
		for (int c = 0; c < N; ++c) {
			M0[p][c] *= vinv;
			M1[p][c] *= vinv;
		}

		for (int r = 0; r < N; ++r) {
			if (r == p) continue;
			mint v = M1[r][p];
			for (int c = 0; c < N; ++c) {
				M0[r][c] -= M0[p][c] * v;
				M1[r][c] -= M1[p][c] * v;
			}
		}
	}

	for (auto &vec : M0) for (auto &x : vec) x = -x;
	auto poly = CharacteristicPolynomial(M0);
	for (auto &x : poly) x *= detAdetBinv * (N % 2 ? -1 : 1);

	poly.erase(poly.begin(), poly.begin() + multiply_by_x);
	poly.resize(N + 1);
	return poly;
}
// End include: "../../matrix/first-degree-matrix-determinant.hpp"
// Begin include: "../../modint/montgomery-modint.hpp"

template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  static_assert(r * mod == 1, "this code has bugs.");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint operator+() const { return mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  constexpr mint inverse() const {
    int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
    while (y > 0) {
      t = x / y;
      x -= t * y, u -= t * v;
      tmp = x, x = y, y = tmp;
      tmp = u, u = v, v = tmp;
    }
    return mint{u};
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }

  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};
// End include: "../../modint/montgomery-modint.hpp"
// Begin include: "../../matrix/matrix.hpp"

// Begin include: "inverse-matrix.hpp"

// Begin include: "gauss-elimination.hpp"

#include <utility>
#include <vector>
using namespace std;

// {rank, det(非正方行列の場合は未定義)} を返す
// 型が double や Rational でも動くはず?(未検証)
//
// pivot 候補 : [0, pivot_end)
template <typename T>
std::pair<int, T> GaussElimination(vector<vector<T>> &a, int pivot_end = -1,
                                   bool diagonalize = false) {
  if (a.empty()) return {0, 1};
  int H = a.size(), W = a[0].size(), rank = 0;
  if (pivot_end == -1) pivot_end = W;
  T det = 1;
  for (int j = 0; j < pivot_end; j++) {
    int idx = -1;
    for (int i = rank; i < H; i++) {
      if (a[i][j] != T(0)) {
        idx = i;
        break;
      }
    }
    if (idx == -1) {
      det = 0;
      continue;
    }
    if (rank != idx) det = -det, swap(a[rank], a[idx]);
    det *= a[rank][j];
    if (diagonalize && a[rank][j] != T(1)) {
      T coeff = T(1) / a[rank][j];
      for (int k = j; k < W; k++) a[rank][k] *= coeff;
    }
    int is = diagonalize ? 0 : rank + 1;
    for (int i = is; i < H; i++) {
      if (i == rank) continue;
      if (a[i][j] != T(0)) {
        T coeff = a[i][j] / a[rank][j];
        for (int k = j; k < W; k++) a[i][k] -= a[rank][k] * coeff;
      }
    }
    rank++;
  }
  return make_pair(rank, det);
}
// End include: "gauss-elimination.hpp"

template <typename mint>
vector<vector<mint>> inverse_matrix(const vector<vector<mint>>& a) {
  int N = a.size();
  assert(N > 0);
  assert(N == (int)a[0].size());

  vector<vector<mint>> m(N, vector<mint>(2 * N));
  for (int i = 0; i < N; i++) {
    copy(begin(a[i]), end(a[i]), begin(m[i]));
    m[i][N + i] = 1;
  }

  auto [rank, det] = GaussElimination(m, N, true);
  if (rank != N) return {};

  vector<vector<mint>> b(N);
  for (int i = 0; i < N; i++) {
    copy(begin(m[i]) + N, end(m[i]), back_inserter(b[i]));
  }
  return b;
}
// End include: "inverse-matrix.hpp"

template <class T>
struct Matrix {
	vector<vector<T> > A;

	Matrix() = default;
	Matrix(int n, int m) : A(n, vector<T>(m, T())) {}
	Matrix(int n) : A(n, vector<T>(n, T())){};

	int H() const { return A.size(); }

	int W() const { return A[0].size(); }

	int size() const { return A.size(); }

	inline const vector<T> &operator[](int k) const { return A[k]; }

	inline vector<T> &operator[](int k) { return A[k]; }

	static Matrix I(int n) {
		Matrix mat(n);
		for (int i = 0; i < n; i++) mat[i][i] = 1;
		return (mat);
	}

	Matrix &operator+=(const Matrix &B) {
		int n = H(), m = W();
		assert(n == B.H() && m == B.W());
		for (int i = 0; i < n; i++)
			for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
		return (*this);
	}

	Matrix &operator-=(const Matrix &B) {
		int n = H(), m = W();
		assert(n == B.H() && m == B.W());
		for (int i = 0; i < n; i++)
			for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
		return (*this);
	}

	Matrix &operator*=(const Matrix &B) {
		int n = H(), m = B.W(), p = W();
		assert(p == B.H());
		vector<vector<T> > C(n, vector<T>(m, T{}));
		for (int i = 0; i < n; i++)
			for (int k = 0; k < p; k++)
				for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];
		A.swap(C);
		return (*this);
	}

	Matrix &operator^=(long long k) {
		Matrix B = Matrix::I(H());
		while (k > 0) {
			if (k & 1) B *= *this;
			*this *= *this;
			k >>= 1LL;
		}
		A.swap(B.A);
		return (*this);
	}

	Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }

	Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }

	Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }

	Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }

	bool operator==(const Matrix &B) const {
		assert(H() == B.H() && W() == B.W());
		for (int i = 0; i < H(); i++)
			for (int j = 0; j < W(); j++)
				if (A[i][j] != B[i][j]) return false;
		return true;
	}

	bool operator!=(const Matrix &B) const {
		assert(H() == B.H() && W() == B.W());
		for (int i = 0; i < H(); i++)
			for (int j = 0; j < W(); j++)
				if (A[i][j] != B[i][j]) return true;
		return false;
	}

	Matrix inverse() const {
		assert(H() == W());
		Matrix B(H());
		B.A = inverse_matrix(A);
		return B;
	}

	Matrix transpose() const {
		Matrix B(W(), H());
		for (int i = 0; i < W(); ++i)
			for (int j = 0; j < H(); ++j)
				B[i][j] = A[j][i];
		return B;
	}

	friend ostream &operator<<(ostream &os, const Matrix &p) {
		int n = p.H(), m = p.W();
		for (int i = 0; i < n; i++) {
			os << (i ? "   " : "") << "[";
			for (int j = 0; j < m; j++) {
				os << p[i][j] << (j + 1 == m ? "]\n" : ",");
			}
		}
		return (os);
	}

	T determinant() const {
		Matrix B(*this);
		assert(H() == W());
		T ret = 1;
		for (int i = 0; i < H(); i++) {
			int idx = -1;
			for (int j = i; j < W(); j++) {
				if (B[j][i] != 0) {
					idx = j;
					break;
				}
			}
			if (idx == -1) return 0;
			if (i != idx) {
				ret *= T(-1);
				swap(B[i], B[idx]);
			}
			ret *= B[i][i];
			T inv = T(1) / B[i][i];
			for (int j = 0; j < W(); j++) {
				B[i][j] *= inv;
			}
			for (int j = i + 1; j < H(); j++) {
				T a = B[j][i];
				if (a == 0) continue;
				for (int k = i; k < W(); k++) {
					B[j][k] -= B[i][k] * a;
				}
			}
		}
		return ret;
	}
};

/**
 * @brief 行列ライブラリ
 */
// End include: "../../matrix/matrix.hpp"

using mint = LazyMontgomeryModInt<998244353>;
using mat = Matrix<mint>;
void yamada::solve()
{
	inl(N);
	vv(mint,A,N,N);
	vv(mint,B,N,N);
	in(A,B);
	auto ans=FirstDegreeMatrixDeterminant(A,B);
	each(a,ans)out(a);
}
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