#include using namespace std; //using namespace atcoder; struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define FOR(i, begin, end) for(int i=(begin);i<(end);i++) #define REP(i, n) FOR(i,0,n) #define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--) #define IREP(i, n) IFOR(i,0,n) #define Sort(v) sort(v.begin(), v.end()) #define Reverse(v) reverse(v.begin(), v.end()) #define all(v) v.begin(),v.end() #define SZ(v) ((int)v.size()) #define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x)) #define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x)) #define chmax(a, b) a = max(a, b) #define chmin(a, b) a = min(a, b) #define bit(n) (1LL<<(n)) #define debug(x) cout << #x << "=" << x << endl; #define vdebug(v) { cout << #v << "=" << endl; REP(i_debug, (int)v.size()){ cout << v[i_debug] << ","; } cout << endl; } #define mdebug(m) { cout << #m << "=" << endl; REP(i_debug, (int)m.size()){ REP(j_debug, (int)m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;} } #define pb push_back #define fi first #define se second #define int long long #define INF 1000000000000000000 template istream &operator>>(istream &is, vector &v){ for (auto &x : v) is >> x; return is; } template ostream &operator<<(ostream &os, vector &v){ for(int i = 0; i < (int)v.size(); i++) { cout << v[i]; if(i != (int)v.size() - 1) cout << endl; }; return os; } template ostream &operator<<(ostream &os, pair p){ cout << '(' << p.first << ',' << p.second << ')'; return os; } template void Out(T x) { cout << x << endl; } template void chOut(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); } using vec = vector; using mat = vector; using Pii = pair; using v_bool = vector; using v_Pii = vector; //int dx[4] = {1,0,-1,0}; //int dy[4] = {0,1,0,-1}; //char d[4] = {'D','R','U','L'}; //const int mod = 1000000007; const int mod = 998244353; template struct ModInt{ using ll = long long; ll val; void setval(ll v) { val = v % MOD; }; ModInt(): val(0) {} ModInt(ll v) { setval(v); }; ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); } ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); } ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); } ModInt operator/(const ModInt &x) const { return *this * x.inv(); } ModInt operator-() const { return ModInt(MOD - val); } ModInt operator+=(const ModInt &x) { return *this = *this + x; } ModInt operator-=(const ModInt &x) { return *this = *this - x; } ModInt operator*=(const ModInt &x) { return *this = *this * x; } ModInt operator/=(const ModInt &x) { return *this = *this / x; } bool operator==(const ModInt &x) const { return (*this).val == x.val; } friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; } friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; } ModInt pow(ll n) const { ModInt a = 1; if(n == 0) return a; int i0 = 64 - __builtin_clzll(n); for(int i = i0 - 1; i >= 0; i--){ a = a * a; if((n >> i) & 1) a *= (*this); } return a; } ModInt inv() const { return this->pow(MOD - 2); } }; using mint = ModInt; mint pow(mint x, long long n) { return x.pow(n); } //using mint = double; //for debug using mvec = vector; using mmat = vector; struct Combination{ vector fact, invfact; Combination(int N){ fact = vector({mint(1)}); invfact = vector({mint(1)}); fact_initialize(N); } void fact_initialize(int N){ int i0 = fact.size(); if(i0 >= N + 1) return; fact.resize(N + 1); invfact.resize(N + 1); for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i; invfact[N] = (mint)1 / fact[N]; for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); } mint nCr(int n, int r){ if(n < 0 || r < 0 || r > n) return mint(0); if((int)fact.size() < n + 1) fact_initialize(n); return fact[n] * invfact[r] * invfact[n - r]; } mint nPr(int n, int r){ if(n < 0 || r < 0 || r > n) return mint(0); if((int)fact.size() < n + 1) fact_initialize(n); return fact[n] * invfact[n - r]; } mint Catalan(int n){ if(n < 0) return 0; else if(n == 0) return 1; if((int)fact.size() < 2 * n + 1) fact_initialize(2 * n); return fact[2 * n] * invfact[n + 1] * invfact[n]; } }; template T determinant(vector> A){ int N = A.size(); for(int j = 0; j < N; j++) assert((int)A[j].size() == N); T m1 = 0; m1 -= 1; // -1, mintでバグらないように T d = 1; for(int j = 0; j < N; j++){ int i0 = -1; for(int i = j; i < N; i++) if(!(A[i][j] == 0)){ i0 = i; break; } if(i0 == -1) return 0; if(i0 != j){ d *= m1; A[j].swap(A[i0]); } d *= A[j][j]; for(int i = j + 1; i < N; i++){ if(A[i][j] == 0) continue; T alpha = A[i][j] / A[j][j]; for(int k = j; k < N; k++){ A[i][k] -= A[j][k] * alpha; } } } return d; } //solve Ax=b template bool solve_equation(vector> A, vector b, vector &x){ if(A.size() == 0){ assert(b.size() == 0); fill(x.begin(), x.end(), 0); return true; } int N = A.size(), M = A[0].size(); for(int i = 0; i < N; i++) assert((int)A[i].size() == M); assert((int)b.size() == N); int i_now = 0; for(int j = 0; j < M; j++){ int i0 = -1; for(int i = i_now; i < N; i++) if(!(A[i][j] == 0)){ i0 = i; break; } if(i0 == -1) continue; if(i0 != i_now){ A[i_now].swap(A[i0]); swap(b[i_now], b[i0]); } for(int i = i_now + 1; i < N; i++){ if(A[i][j] == 0) continue; T alpha = A[i][j] / A[i_now][j]; for(int k = j; k < M; k++){ A[i][k] -= A[i_now][k] * alpha; } b[i] -= b[i_now] * alpha; } i_now++; if(i_now == N) break; } const int rank = i_now; for(int i = rank; i < N; i++) if(!(b[i] == 0)) return false; x = vector(M, 0); for(int i = rank - 1; i >= 0; i--){ int j0 = -1; for(int j = 0; j < M; j++) if(!(A[i][j] == 0)){ j0 = j; break; } for(int j = j0 + 1; j < M; j++){ b[i] -= A[i][j] * x[j]; } x[j0] = b[i] / A[i][j0]; } return true; } signed main(){ int N; cin >> N; vector> M0(N, vector(N)), M1(N, vector(N)); cin >> M0 >> M1; vector> A(N + 1, vector(N + 1)); vector b(N + 1), ans; FOR(x, 0, N + 1){ mint p = 1; REP(j, N + 1){ A[x][j] = p; p *= x; } auto M = M0; REP(i, N) REP(j, N) M[i][j] += M1[i][j] * x; b[x] = determinant(M); } assert(solve_equation(A, b, ans)); cout << ans << endl; return 0; }