#include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; const int inf=1<<30; const ll INF=1LL<<62; using P = pair; typedef pair PP; const ll MOD=998244353; const int MAXN=100000; class NTT{ private: long long int mod; const long long root=3; long long int add(const long long int x, const long long int y) { return (x + y < mod ? x + y : x + y - mod); } long long int sub(const long long int x, const long long int y) { return (x >= y) ? (x - y) : ( mod- y + x); } long long int mul(const long long int x, const long long int y) { return x * y % mod; } long long int mod_pow(long long int x, long long int n) { long long int res = 1; while(n > 0){ if(n & 1){ res = mul(res, x); } x = mul(x, x); n >>= 1; } return res; } long long int inverse(const long long int x) { return mod_pow(x, mod- 2); } void ntt(std::vector& a, const bool rev = false){ unsigned int i, j, k, l, p, q, r, s; const unsigned int size = a.size(); if(size == 1) return; std::vector b(size); r = rev ? ( mod- 1 - ( mod- 1) / size) : ( mod- 1) / size; s = mod_pow(root, r); std::vector kp(size / 2 + 1, 1); for(i = 0; i < size / 2; ++i) kp[i + 1] = mul(kp[i], s); for(i = 1, l = size / 2; i < size; i <<= 1, l >>= 1){ for(j = 0, r = 0; j < l; ++j, r += i){ for(k = 0, s = kp[i * j]; k < i; ++k){ p = a[k + r], q = a[k + r + size / 2]; b[k + 2 * r] = add(p, q); b[k + 2 * r + i] = mul(sub(p, q), s); } } swap(a, b); } if(rev){ s = inverse(size); for(i = 0; i < size; i++){ a[i] = mul(a[i], s); } } } public: NTT(long long int mod_=998244353): mod(mod_){}; // //vector c = ntt(a,b)みたいにして使う std::vector operator()(const std::vector& a, const std::vector& b){ const int size = (int)a.size() + (int)b.size() - 1; ll t = 1; while(t < size){ t <<= 1; } std::vector A(t, 0), B(t, 0); for(int i = 0; i < (int)a.size(); i++){ A[i] = a[i]; } for(int i = 0; i < (int)b.size(); i++){ B[i] = b[i]; } ntt(A), ntt(B); for (int i = 0; i < t; i++){ A[i] = mul(A[i], B[i]); } ntt(A, true); A.resize(size); return A; } //vector c; // res[j]= ∑(a[i+j]*b[i])(i=[0,b.size())) j=[0,a.size()) std::vector filter(const std::vector& a,const std::vector& b){ std::vector revb=b; int lena=a.size(),lenb=b.size(); assert(lena>=lenb); std::reverse(revb.begin(),revb.end()); std::vector filt=this->operator()(a,revb); std::vector res; for(int i=lenb-1;i= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;}//後ろのconstはメンバxを変更しないことを示す mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} bool operator==(const mint a) const {return a.x==x;} mint pow(unsigned long long int t) const { assert(t>=0); if (!t) return 1; //aがtで割り切れない場合には t%=(mod-1)をして良い mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; std::istream& operator>>(std::istream& is, mint& a) { return is >> a.x;} std::ostream& operator<<(std::ostream& os, const mint& a) { return os << a.x;} struct combination { std::vector fact, ifact; combination(int n):fact(n+1),ifact(n+1) { assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } }; int main(){ int N; cin>>N; vector A(N); queue> que; for(int i=0;i>A[i]; A[i]%=MOD; que.push({1,A[i]}); } NTT ntt; while(que.size()>1){ vector a=que.front();que.pop(); vector b=que.front();que.pop(); NTT ntt; vector c=ntt(a,b); que.push(c); } vector data = que.front(); mint ans=0; for(int i=1;i<=N;i++){ ans+=(mint)data[i]*mint(i).pow(N-i); } cout<