#include using namespace std; #include using namespace atcoder; using mint=atcoder::modint998244353; #define int long long template struct FormalPowerSeries:vector{ using vector::vector; using vector::operator=; using fps=FormalPowerSeries; using sfps=vector>; fps& operator+=(const fps& g){ if(g.size()>this->size())this->resize(g.size()); for(int i=0;i<(int)g.size();i++)(*this)[i]+=g[i]; return *this; } fps& operator+=(const mint& v){ if(this->empty())this->resize(1); (*this)[0]+=v; return *this; } fps operator+(const fps& g)const{return fps(*this)+=g;} fps operator+(const mint& v)const{return fps(*this)+=v;} friend fps operator+(const mint& v,const fps& f){return f+v;} fps& operator+=(const int& v){*this+=mint(v);return *this;} fps operator+(const int& v){return fps(*this)+=v;;} friend fps operator+(const int& v,const fps& f){return f+v;} fps& operator-=(const fps& g){ if(g.size()>this->size())this->resize(g.size()); for(int i=0;i<(int)g.size();i++)(*this)[i]-=g[i]; return *this; } fps& operator-=(const mint& v){ if(this->empty())this->resize(1); (*this)[0]-=v; return *this; } fps operator-(const fps& g)const{return fps(*this)-=g;} fps operator-(const mint& v)const{return fps(*this)-=v;} friend fps operator-(const mint& v,const fps& f){return -(f-v);} fps& operator-=(const int& v){*this-=v;return *this;} fps operator-(const int& v){return fps(*this)-=v;} friend fps operator-(const int& v,const fps& f){return -(f-v);} fps operator-()const{return fps(*this)*=-1;} fps& operator*=(const mint& v){for(auto&e:*this)e*=v;return *this;} fps operator*(const mint& v)const{return fps(*this)*=v;} friend fps operator*(const mint& v,const fps& f){return f*v;} fps& operator*=(const int& v){*this*=mint(v);return *this;} fps operator*(const int& v)const{return fps(*this)*=v;} friend fps operator*(const int&v,const fps& f){return f*v;} fps& operator<<=(const int d){ this->insert(this->begin(),d,0); return *this; } fps operator<<(const int d)const{return fps(*this)<<=d;} fps& operator>>=(const int d){ this->erase(this->begin(),this->begin()+min((int)this->size(),d)); return *this; } fps operator>>(const int d)const{return fps(*this)>>=d;} //fast fps& operator*=(const fps& g){ *this=atcoder::convolution(*this,g); return *this; } //naive // fps& operator*=(const fps& g){ // this->resize(this->size()+g.size()-1); // for(int i=(int)this->size()-1;i>=0;i--){ // for(int j=1;j<=(int)g.size();j++){ // if(i+j>=(int)this->size())break; // (*this)[i+j]+=(*this)[i]*g[j]; // } // (*this)[i]*=g[0]; // } // return *this; // } fps operator*(const fps& g)const{return fps(*this)*=g;} fps inv(int d)const{ fps g={(*this)[0].inv()}; for(int k=1;ksize())).pre(this->size());} fps& operator/=(const mint& v){for(auto&e:*this)e/=v;return *this;} fps operator/(const fps& g)const{return fps(*this)/=g;} fps operator/(const mint& v)const{return fps(*this)/=v;} fps quotient(const fps& g)const{ if(this->size()rev()/g.rev()).pre(this->size()-g.size()+1)).rev(); } fps reminder(const fps& g)const{return fps(*this-this->quotient(g)*g).pre(g.size()-1);} pair quotient_reminder(const fps& g)const{ pair res; res.first=this->quotient(g); res.second=fps(*this-res.first*g).pre(g.size()-1); return res; } void shrink(){ while(this->size()&&this->back()==mint(0))this->pop_back(); } fps rev()const{fps g(*this);reverse(g.begin(),g.end());return g;} fps dot(fps g)const{ fps res(min(this->size(),g.size())); for(int i=0;i<(int)res.size();i++)res[i]=(*this)[i]*g[i]; return res; } fps pre(int d)const{ fps res(begin(*this),begin(*this)+min((int)this->size(),d)); if((int)res.size()first==0){ g0=it0->second; it0++; } for(int i=this->size()-1;i>=0;i--){ for(auto it=it0;it!=g.end();it++){ auto[j,gj]=*it; if(i+j>=this->size())break; (*this)[i+j]+=(*this)[i]*gj; } (*this)[i]*=g0; } return *this; } fps operator*(const sfps& g)const{return fps(*this)*=g;} fps& operator/=(const sfps& g){ auto it0=g.begin(); assert(it0->first==0&&it0->second!=0); mint g0_inv=it0->second.inv(); it0++; for(int i=0;i<(int)this->size();i++){ (*this)[i]*=g0_inv; for(auto it=it0;it!=g.begin();it++){ auto[j,gj]=*it; if(i+j>=this->size())break; (*this)[i+j]-=(*this)[i]*gj; } } return *this; } fps operator/(const sfps& g)const{return fps(*this)/=g;} fps pow(long long d,const fps& g)const{ fps res={1},pow2=*this; while(d>0){ if(d&1)res=(res*pow2).reminder(g); pow2=(pow2*pow2).reminder(g); d>>=1; } return res; } fps derivative()const{ fps res; for(int i=1;i<(int)this->size();i++)res.push_back((*this)[i]*i); return res; } fps integral()const{ fps res={0}; for(int i=0;i<(int)this->size();i++)res.push_back((*this)[i]/(i+1)); return res; } fps log(int d)const{ return fps(this->derivative()*this->inv(d)).integral().pre(d); } fps exp(int d)const{ fps g={1}; for(int k=1;ksize()&&(*this)[i0]==mint(0))i0++; if(i0==(int)this->size())return fps(d,mint(0)); mint c0=(*this)[i0]; fps fs=(*this>>i0)/c0; if(i0>=(d+k-1)/k)return fps(d,mint(0)); int ds=(int)(d-k*i0); fps gs=fps(mint(k)*fs.log(ds)).exp(ds); fps g=fps(gs*c0.pow(k))<<(int)(k*i0); return g; } friend istream& operator>>(istream& is,fps&f){ for(auto&e:f)cin>>e; return is; } friend ostream& operator<<(ostream& os,const fps& f){ if((int)f.size()==0)os<<0; else{ for(int i=0;i<(int)f.size();i++){ os<; using sfps=vector>; template struct factional_prime{ long long inv_[MAX_N+1]; long long fac_[MAX_N+1]; long long fac_inv_[MAX_N+1]; factional_prime(){ inv_[0]=0;inv_[1]=fac_[0]=fac_[1]=fac_inv_[0]=fac_inv_[1]=1; for(long long i=2;i<=MAX_N;i++){ inv_[i]=((mod-mod/i)*inv_[mod%i])%mod; fac_[i]=(fac_[i-1]*i)%mod; fac_inv_[i]=(fac_inv_[i-1]*inv_[i])%mod; } } long long inv(long long n){ if(n<0)return 0; return inv_[n]; } long long fac(long long n){ if(n<0)return 0; return fac_[n]; } long long finv(long long n){ if(n<0)return 0; return fac_inv_[n]; } long long nCr(long long n,long long r){ if(n fp; signed main(){ int n;cin>>n; vector a(n);for(auto&&e:a)cin>>e; auto prod=[&](auto prod,int l,int r)->fps { if(r-l==1){ return fps({1,a[l]}); }else{ int m=(l+r)/2; return prod(prod,l,m)*prod(prod,m,r); } }; fps f=prod(prod,0,n); mint ans=0; for(int i=0;i<=n;i++){ ans+=f[i]*mint(i).pow(n-i); } cout<