#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end())
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v,x) lower_bound(ALL(v),(x))-(v).begin()
#define UB(v,x) upper_bound(ALL(v),(x))-(v).begin()

using ll=long long int;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<typename T,typename U>T ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);}
template<typename T,typename U>T floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);}
template<typename T>int popcnt(T x){return __builtin_popcountll(x);}
template<typename T>int topbit(T x){return (x==0?-1:63-__builtin_clzll(x));}
template<typename T>int lowbit(T x){return (x==0?-1:__builtin_ctzll(x));}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>

class FastIO{
    static constexpr int L=1<<16;
    char rdbuf[L];
    int rdLeft=0,rdRight=0;
    inline void reload(){
        int len=rdRight-rdLeft;
        memmove(rdbuf,rdbuf+rdLeft,len);
        rdLeft=0,rdRight=len;
        rdRight+=fread(rdbuf+len,1,L-len,stdin);
    }
    inline bool skip(){
        for(;;){
            while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
            if(rdLeft==rdRight){
                reload();
                if(rdLeft==rdRight)return false;
            }
            else break;
        }
        return true;
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    inline bool _read(__int128_t& x){
        if(!skip())return false;
        if(rdLeft+40>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    inline bool _read(__uint128_t& x){
        if(!skip())return false;
        if(rdLeft+40>=rdRight)reload();
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        return true;
    }
    template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        if(rdbuf[rdLeft]!='.')return true;
        rdLeft++;
        T base=.1;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x+=base*(rdbuf[rdLeft++]^48);
            base*=.1;
        }
        if(neg)x=-x;
        return true;
    }
    inline bool _read(char& x){
        if(!skip())return false;
        if(rdLeft+1>=rdRight)reload();
        x=rdbuf[rdLeft++];
        return true;
    }
    inline bool _read(string& x){
        if(!skip())return false;
        for(;;){
            int pos=rdLeft;
            while(pos<rdRight and rdbuf[pos]>' ')pos++;
            x.append(rdbuf+rdLeft,pos-rdLeft);
            if(rdLeft==pos)break;
            rdLeft=pos;
            if(rdLeft==rdRight)reload();
            else break;
        }
        return true;
    }
    template<typename T>inline bool _read(vector<T>& v){
        for(auto& x:v){
            if(!_read(x))return false;
        }
        return true;
    }

    char wtbuf[L],tmp[50];
    int wtRight=0;
    inline void flush(){
        fwrite(wtbuf,1,wtRight,stdout);
        wtRight=0;
    }
    inline void _write(const char& x){
        if(wtRight>L-32)flush();
        wtbuf[wtRight++]=x;
    }
    inline void _write(const string& x){
        for(auto& c:x)_write(c);
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
        if(wtRight>L-32)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
                switch (sizeof(x)) {
                case 2: _write("32768"); return;
                case 4: _write("2147483648"); return;
                case 8: _write("9223372036854775808"); return;
                }
            }
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(__int128_t x){
        if(wtRight>L-40)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(__uint128_t x){
        if(wtRight>L-40)flush();
        if(x==0){
            _write('0');
            return;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    template<typename T>inline void _write(const vector<T>& v){
        rep(i,0,v.size()){
            if(i)_write(' ');
            _write(v[i]);
        }
    }
public:
    FastIO(){}
    ~FastIO(){flush();}
    inline void read(){}
    template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
        assert(_read(head));
        read(tail...); 
    }
    template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
    template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
        if(space)_write(' ');
        _write(head);
        write<ln,true>(tail...); 
    }
};

/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"

#line 2 "library/Math/modint.hpp"

template<int mod=1000000007>struct fp {
    int v;
    static constexpr int get_mod(){return mod;}
    int inv() const{
        int tmp,a=v,b=mod,x=1,y=0;
        while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
        if(x<0){x+=mod;} return x;
    }
    fp(ll x=0){init(x%mod+mod);}
    fp& init(ll x){v=(x<mod?x:x-mod); return *this;}
    fp operator-()const{return fp()-*this;}
    fp pow(ll t){assert(t>=0); fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
    fp& operator+=(const fp& x){return init(v+x.v);}
    fp& operator-=(const fp& x){return init(v+mod-x.v);}
    fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
    fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
    fp operator+(const fp& x)const{return fp(*this)+=x;}
    fp operator-(const fp& x)const{return fp(*this)-=x;}
    fp operator*(const fp& x)const{return fp(*this)*=x;}
    fp operator/(const fp& x)const{return fp(*this)/=x;}
    bool operator==(const fp& x)const{return v==x.v;}
    bool operator!=(const fp& x)const{return v!=x.v;}
    friend istream& operator>>(istream& is,fp& x){return is>>x.v;}
    friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}
};

/**
 * @brief Modint
 */
#line 2 "library/Convolution/ntt.hpp"

template<typename T,unsigned p=3>struct NTT{
    vector<T> rt,irt;
    NTT(int lg=21){
        unsigned m=T::get_mod()-1; T prt=p;
        rt.resize(lg); irt.resize(lg);
        rep(k,0,lg){
            rt[k]=-prt.pow(m>>(k+2));
            irt[k]=rt[k].inv();
        }
    }
    void ntt(vector<T>& f,bool inv=0){
        int n=f.size();
        if(inv){
            for(int m=1;m<n;m<<=1){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j];
                        f[i]=x+y; f[j]=(x-y)*w;
                    } w*=irt[__builtin_ctz(++t)];
                }
             } T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
        }else{
            for(int m=n;m>>=1;){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j]*w;
                        f[i]=x+y; f[j]=x-y;
                    } w*=rt[__builtin_ctz(++t)];
                }
            }
         }
    }
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m); rep(i,0,b.size())c[i]=b[i];
            ntt(c); rep(i,0,m)res[i]*=c[i];
        } ntt(res,1); res.resize(n); return res;
    }
};

/**
 * @brief Number Theoretic Transform
 */
#line 2 "library/FPS/fps.hpp"

template<typename T>struct Poly:vector<T>{
    Poly(int n=0){this->assign(n,T());}
    Poly(const initializer_list<T> f):vector<T>::vector(f){}
    Poly(const vector<T>& f){this->assign(ALL(f));}
    T eval(const T& x){
        T res;
        for(int i=this->size()-1;i>=0;i--)res*=x,res+=this->at(i);
        return res;
    }
    Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
    void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
    Poly operator>>(int sz)const{
        if((int)this->size()<=sz)return {};
        Poly ret(*this);
        ret.erase(ret.begin(),ret.begin()+sz);
        return ret;
    }
    Poly operator<<(int sz)const{
        Poly ret(*this);
        ret.insert(ret.begin(),sz,T(0));
        return ret;
    }
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0)const{
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m);
        rep(i,0,a.size())res[i]=a[i];
        NTT(res,0);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m);
            rep(i,0,b.size())c[i]=b[i];
            NTT(c,0);
            rep(i,0,m)res[i]*=c[i];
        }
        NTT(res,1);
        res.resize(n);
        return res;
    }
    Poly square()const{return Poly(mult(*this,*this,1));}
    Poly operator-()const{return Poly()-*this;}
    Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
    Poly operator+(const T& g)const{return Poly(*this)+=g;}
    Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
    Poly operator-(const T& g)const{return Poly(*this)-=g;}
    Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
    Poly operator*(const T& g)const{return Poly(*this)*=g;}
    Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
    Poly operator/(const T& g)const{return Poly(*this)/=g;}
    Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
    pair<Poly,Poly> divmod(const Poly& g)const{
        Poly q=*this/g,r=*this-g*q;
        r.shrink();
        return {q,r};
    }
    Poly& operator+=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]+=g[i];} return *this;
    }
    Poly& operator+=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]+=g; return *this;
    }
    Poly& operator-=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]-=g[i];} return *this;
    }
    Poly& operator-=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]-=g; return *this;
    }
    Poly& operator*=(const Poly& g){
        *this=mult(*this,g,0);
        return *this;
    }
    Poly& operator*=(const T& g){
        rep(i,0,this->size())(*this)[i]*=g;
        return *this;
    }
    Poly& operator/=(const Poly& g){
        if(g.size()>this->size()){
            this->clear(); return *this;
        }
        Poly g2=g;
        reverse(ALL(*this));
        reverse(ALL(g2));
        int n=this->size()-g2.size()+1;
        this->resize(n); g2.resize(n);
        *this*=g2.inv(); this->resize(n); 
        reverse(ALL(*this));
        shrink();
        return *this;
    }
    Poly& operator/=(const T& g){
        rep(i,0,this->size())(*this)[i]/=g;
        return *this;
    }
    Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;}
    Poly diff()const{
        Poly res(this->size()-1);
        rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
        return res;
    }
    Poly inte()const{
        Poly res(this->size()+1);
        for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]/i;
        return res;
    }
    Poly log()const{
        assert(this->front()==1); const int n=this->size();
        Poly res=diff()*inv(); res=res.inte(); 
        res.resize(n); return res;
    }
    Poly shift(const int& c)const{
        const int n=this->size();
        Poly res=*this,g(n); g[0]=1; rep(i,1,n)g[i]=g[i-1]*c/i;
        vector<T> fact(n,1);
        rep(i,0,n){
            if(i)fact[i]=fact[i-1]*i;
            res[i]*=fact[i];
        }
        res=res.rev();
        res*=g;
        res.resize(n);
        res=res.rev();
        rep(i,0,n)res[i]/=fact[i];
        return res;
    }
    Poly inv()const{
        const int n=this->size();
        Poly res(1); res.front()=T(1)/this->front();
        for(int k=1;k<n;k<<=1){
            Poly f(k*2),g(k*2);
            rep(i,0,min(n,k*2))f[i]=(*this)[i];
            rep(i,0,k)g[i]=res[i];
            NTT(f,0);
            NTT(g,0);
            rep(i,0,k*2)f[i]*=g[i];
            NTT(f,1);
            rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
            NTT(f,0);
            rep(i,0,k*2)f[i]*=g[i];
            NTT(f,1);
            rep(i,0,k)f[i]=res[i];
            swap(res,f);
        } res.resize(n); return res;
    }
    Poly exp()const{
        const int n=this->size();
        if(n==1)return Poly({T(1)});
        Poly b(2),c(1),z1,z2(2);
        b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1];
        for(int k=2;k<n;k<<=1){
            Poly y=b;
            y.resize(k*2);
            NTT(y,0);
            z1=z2;
            Poly z(k);
            rep(i,0,k)z[i]=y[i]*z1[i];
            NTT(z,1);
            rep(i,0,k>>1)z[i]=0;
            NTT(z,0);
            rep(i,0,k)z[i]*=-z1[i];
            NTT(z,1);
            c.insert(c.end(),z.begin()+(k>>1),z.end());
            z2=c;
            z2.resize(k*2);
            NTT(z2,0);
            Poly x=*this;
            x.resize(k);
            x=x.diff();x.resize(k);
            NTT(x,0);
            rep(i,0,k)x[i]*=y[i];
            NTT(x,1);
            Poly bb=b.diff();
            rep(i,0,k-1)x[i]-=bb[i];
            x.resize(k*2);
            rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;}
            NTT(x,0);
            rep(i,0,k*2)x[i]*=z2[i];
            NTT(x,1);
            x.pop_back();
            x=x.inte();
            rep(i,k,min(n,k*2))x[i]+=(*this)[i];
            rep(i,0,k)x[i]=0;
            NTT(x,0);
            rep(i,0,k*2)x[i]*=y[i];
            NTT(x,1);
            b.insert(b.end(),x.begin()+k,x.end());
        } b.resize(n); return b;
    }
    Poly pow(ll t){
        if(t==0){
            Poly res(this->size()); res[0]=1;
            return res;
        }
        int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
        Poly res(n); if(__int128_t(t)*k>=n)return res;
        n-=t*k; Poly g(n); T c=(*this)[k],ic=c.inv();
        rep(i,0,n)g[i]=(*this)[i+k]*ic;
        g=g.log(); for(auto& x:g)x*=t; g=g.exp();
        c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
    }
    void NTT(vector<T>& a,bool inv)const;
};

/**
 * @brief Formal Power Series (NTT-friendly mod)
 */
#line 7 "sol.cpp"
using Fp=fp<998244353>;
NTT<Fp,3> ntt;
template<>void Poly<Fp>::NTT(vector<Fp>& v,bool inv)const{return ntt.ntt(v,inv);}

#line 2 "library/Math/matrix.hpp"

template<class T>struct Matrix{
    int h,w; vector<vector<T>> val; T det;
    Matrix(){}
    Matrix(int n):h(n),w(n),val(vector<vector<T>>(n,vector<T>(n))){}
    Matrix(int n,int m):h(n),w(m),val(vector<vector<T>>(n,vector<T>(m))){}
    vector<T>& operator[](const int i){return val[i];}
    Matrix& operator+=(const Matrix& m){
        assert(h==m.h and w==m.w);
        rep(i,0,h)rep(j,0,w)val[i][j]+=m.val[i][j];
        return *this;
    }
    Matrix& operator-=(const Matrix& m){
        assert(h==m.h and w==m.w);
        rep(i,0,h)rep(j,0,w)val[i][j]-=m.val[i][j];
        return *this;
    }
    Matrix& operator*=(const Matrix& m){
        assert(w==m.h);
        Matrix<T> res(h,m.w);
        rep(i,0,h)rep(j,0,m.w)rep(k,0,w)res.val[i][j]+=val[i][k]*m.val[k][j];
        *this=res; return *this;
    }
    Matrix operator+(const Matrix& m)const{return Matrix(*this)+=m;}
    Matrix operator-(const Matrix& m)const{return Matrix(*this)-=m;}
    Matrix operator*(const Matrix& m)const{return Matrix(*this)*=m;}
    Matrix pow(ll k){
        Matrix<T> res(h,h),c=*this; rep(i,0,h)res.val[i][i]=1;
        while(k){if(k&1)res*=c; c*=c; k>>=1;} return res;
    }
    vector<int> gauss(int c=-1){
        if(val.empty())return {};
        if(c==-1)c=w;
        int cur=0; vector<int> res; det=1;
        rep(i,0,c){
            if(cur==h)break;
            rep(j,cur,h)if(val[j][i]!=0){
                swap(val[cur],val[j]);
                if(cur!=j)det*=-1;
                break;
            }
            det*=val[cur][i];
            if(val[cur][i]==0)continue;
            rep(j,0,h)if(j!=cur){
                T z=val[j][i]/val[cur][i];
                rep(k,i,w)val[j][k]-=val[cur][k]*z;
            }
            res.push_back(i);
            cur++;
        }
        return res;
    }
    Matrix inv(){
        assert(h==w);
        Matrix base(h,h*2),res(h,h);
        rep(i,0,h)rep(j,0,h)base[i][j]=val[i][j];
        rep(i,0,h)base[i][h+i]=1;
        base.gauss(h);
        det=base.det;
        rep(i,0,h)rep(j,0,h)res[i][j]=base[i][h+j]/base[i][i];
        return res;
    }
    bool operator==(const Matrix& m){
        assert(h==m.h and w==m.w);
        rep(i,0,h)rep(j,0,w)if(val[i][j]!=m.val[i][j])return false;
        return true;
    }
    bool operator!=(const Matrix& m){
        assert(h==m.h and w==m.w);
        rep(i,0,h)rep(j,0,w)if(val[i][j]==m.val[i][j])return false;
        return true;
    }
    friend istream& operator>>(istream& is,Matrix& m){
        rep(i,0,m.h)rep(j,0,m.w)is>>m[i][j];
        return is;
    }
    friend ostream& operator<<(ostream& os,Matrix& m){
        rep(i,0,m.h){
            rep(j,0,m.w)os<<m[i][j]<<(j==m.w-1 and i!=m.h-1?'\n':' ');
        }
        return os;
    }
};

/**
 * @brief Matrix
 */
#line 2 "library/Math/charpoly.hpp"

template<typename T>vector<T> CharPoly(Matrix<T> a){
    // to Hessenberg
    //reference:http://www.oishi.info.waseda.ac.jp/~samukawa/eigvieta.pdf
    int n=a.h;
    rep(s,0,n-2){
        rep(j,s+1,n)if(a[j][s]!=0){
            swap(a[j],a[s+1]);
            rep(i,0,n)swap(a[i][j],a[i][s+1]);
            break;
        }
        if(a[s+1][s]==0)continue;
        T X=T(1)/a[s+1][s];
        rep(i,s+2,n){
            T base=a[i][s]*X;
            rep(j,0,n)a[i][j]-=a[s+1][j]*base;
            rep(j,0,n)a[j][s+1]+=a[j][i]*base;
        }
    }
    vector dp(n+1,vector<T>(n+1));
    dp[0][0]=1;
    rep(i,0,n){
        rep(k,0,i+1){
            dp[i+1][k+1]+=dp[i][k];
            dp[i+1][k]-=dp[i][k]*a[i][i];
        }
        T prod=1;
        for(int j=i-1;j>=0;j--){
            prod*=a[j+1][j];
            T base=prod*a[j][i];
            rep(k,0,i+1)dp[i+1][k]-=dp[j][k]*base;
        }
    }
    return dp[n];
}

/**
 * @brief Characteristic Polynomial
*/
#line 2 "library/Utility/random.hpp"

struct Random{
    random_device rnd;
    unsigned x=123456789,y=362436069,z=521288629,w=rnd();
    Random(){}
    unsigned get(){
        unsigned t=x^(x<<11);
        x=y,y=z,z=w;
        return w=(w^(w<<19))^(t^(t>>8));
    }
    unsigned get(unsigned L){
        return get()%(L+1);
    }
    template<typename T>T get(T L,T R){
        return get(R-L)+L;
    }
    double uniform(){
        return double(get())/UINT_MAX;
    }
    string str(int n){
        string ret;
        rep(i,0,n)ret+=get('a','z');
        return ret;
    }
    template<typename Iter>void shuffle(Iter first,Iter last){
        if(first==last)return;
        int len=1;
        for(auto it=first+1;it!=last;it++){
            len++;
            int j=get(0,len-1);
            if(j!=len-1)iter_swap(it,first+j);
        }
    }
    template<typename T>vector<T> select(int n,T L,T R){
        set<T> ret;
        while(ret.size()<n)ret.insert(get(L,R));
        return {ALL(ret)};
    }
};

/**
 * @brief Random
 */
#line 14 "sol.cpp"

template<typename T>vector<T> det_ApBx(Matrix<T> a,Matrix<T> b){
    Random gen;
    int n=a.h;
    Poly<T> f(n+1);
    T ran=gen.get();
    rep(i,0,n)rep(j,0,n)a[i][j]+=b[i][j]*ran;
    auto ainv=a.inv();
    if(a.det==0)return f;
    b*=ainv;
    rep(i,0,n)rep(j,0,n)b[i][j]=-b[i][j];
    f=CharPoly(b);
    reverse(ALL(f));
    for(auto& x:f)x*=a.det;
    return f.shift((-ran).v);
}

FastIO io;
int main(){
    int n;
    io.read(n);
    Matrix<Fp> a(n,n),b(n,n);
    rep(i,0,n)rep(j,0,n)io.read(a[i][j].v);
    rep(i,0,n)rep(j,0,n)io.read(b[i][j].v);
    
    auto ret=det_ApBx(a,b);
    rep(i,0,n+1)io.write(ret[i].v);
    return 0;
}