#include using namespace std; #if __has_include() #include using namespace atcoder; templateistream &operator>>(istream &is,static_modint &a){long long b;is>>b;a=b;return is;} istream &operator>>(istream &is,modint &a){long long b;cin>>b;a=b;return is;} #endif using ll=long long; using ull=unsigned long long; using P=pair; templateusing minque=priority_queue,greater>; templatebool chmax(T &a,const T &b){return (abool chmin(T &a,const T &b){return (a>b?(a=b,true):false);} templateistream &operator>>(istream &is,pair&p){is>>p.first>>p.second;return is;} templateistream &operator>>(istream &is,vector &a){for(auto &i:a)is>>i;return is;} templatevoid operator++(pair&a,int n){a.first++,a.second++;} templatevoid operator--(pair&a,int n){a.first--,a.second--;} templatevoid operator++(vector&a,int n){for(auto &i:a)i++;} templatevoid operator--(vector&a,int n){for(auto &i:a)i--;} #define reps(i,a,n) for(int i=(a);i<(n);i++) #define rep(i,n) reps(i,0,n) #define all(x) x.begin(),x.end() #define pcnt(x) __builtin_popcount(x) ll myceil(ll a,ll b){return (a+b-1)/b;} template auto vec(const int (&d)[n],const T &init=T()){ if constexpr (id(d,init)); else return init; } #ifdef LOCAL #include "debug.h" #else #define debug(...) static_cast(0) #define debugg(...) static_cast(0) templateostream &operator<<(ostream &os,const pair&p){os<>testcase; for(int i=0;i vector>matrix_mul(const vector>&a,const vector>&b){ assert(a[0].size()==b.size()); vector>ret(a.size(),vector(b[0].size(),0)); rep(i,a.size())rep(j,b.size())rep(k,b[0].size())ret[i][k]+=a[i][j]*b[j][k]; return ret; } template vector>matrix_pow(vector>a,ll k){ assert(a.size()==a[0].size()); vector>ret(a.size(),vector(a.size(),0)); rep(i,a.size())ret[i][i]=1; while(k){ if(k&1)ret=matrix_mul(ret,a); a=matrix_mul(a,a); k>>=1; } return ret; } template T matrix_det(vector>a){ assert(a.size()==a[0].size()); int n=a.size(); T ret=1; rep(i,n){ int id=-1; reps(j,i,n){ if(a[j][i]!=0){ id=j; break; } } if(id==-1)return 0; if(i!=id){ ret*=-1; swap(a[i],a[id]); } ret*=a[i][i]; T inv=a[i][i].inv(); rep(j,n)a[i][j]*=inv; reps(j,i+1,n){ T x=a[j][i]; rep(k,n)a[j][k]-=a[i][k]*x; } } return ret; } template vector>matrix_inv(vector>a){ assert(a.size()==a[0].size()); int n=a.size(); vector>ret(n,vector(n,0)); rep(i,n)ret[i][i]=1; rep(i,n){ int id=-1; reps(j,i,n){ if(a[j][i]!=0){ id=j; break; } } if(id==-1)return vector>(n,vector(n,0)); if(i!=id){ swap(a[i],a[id]); swap(ret[i],ret[id]); } T inv=a[i][i].inv(); rep(j,n){ a[i][j]*=inv; ret[i][j]*=inv; } rep(j,n)if(i!=j){ T x=a[j][i]; rep(k,n){ a[j][k]-=a[i][k]*x; ret[j][k]-=ret[i][k]*x; } } } return ret; } template void matrix_hessenberg(vector>&a){ assert(a.size()==a[0].size()); int n=a.size(); rep(i,n-2){ int id=-1; reps(j,i+1,n){ if(a[j][i]!=0){ id=j; break; } } if(id==-1)continue; swap(a[i+1],a[id]); rep(j,n)swap(a[j][i+1],a[j][id]); T inv=a[i+1][i].inv(); reps(j,i+2,n){ T x=a[j][i]*inv; rep(k,n)a[j][k]-=a[i+1][k]*x; rep(k,n)a[k][i+1]+=a[k][j]*x; } } } //det(xI-a) template vectormatrix_charpoly(vector>a){ matrix_hessenberg(a); int n=a.size(); vector>ret(n+1); ret[0]={1}; rep(i,n){ ret[i+1].resize(i+2,0); rep(j,i+1)ret[i+1][j+1]+=ret[i][j]; rep(j,i+1)ret[i+1][j]-=ret[i][j]*a[i][i]; T b=1; for(int j=i-1;j>=0;j--){ b*=a[j+1][j]; T c=-a[j][i]*b; rep(k,j+1)ret[i+1][k]+=c*ret[j][k]; } } return ret[n]; } //det(a+xb) template vectormatrix_detpoly(vector>a,vector>b){ assert(a.size()==a[0].size()); assert(b.size()==b[0].size()); assert(a.size()==b.size()); int n=a.size(); int cx=0; T ab=1; rep(i,n){ int id=-1; reps(j,i,n){ if(b[j][i]!=0){ id=j; break; } } if(id==-1){ if(++cx>n)return vector(n+1,0); rep(j,n){ T v=b[j][i]; b[j][i]=0; rep(k,n)a[k][i]-=v*a[k][j]; } rep(j,n)swap(a[j][i],b[j][i]); i--; continue; } if(i!=id){ swap(a[i],a[id]); swap(b[i],b[id]); ab*=-1; } ab*=b[i][i]; T inv=b[i][i].inv(); rep(j,n){ a[i][j]*=inv; b[i][j]*=inv; } rep(j,n)if(i!=j){ T v=b[j][i]; rep(k,n){ a[j][k]-=a[i][k]*v; b[j][k]-=b[i][k]*v; } } } rep(i,n)rep(j,n)a[i][j]*=-1; vector poly=matrix_charpoly(a); rep(i,n+1)poly[i]*=ab; poly.erase(poly.begin(),poly.begin()+cx); poly.resize(n+1,0); return poly; } using mint=modint998244353; void SOLVE(){ int n; cin>>n; auto a=vec({n,n}),b=vec({n,n}); cin>>a>>b; vectorc=matrix_detpoly(a,b); rep(i,n+1)cout<