結果

問題 No.1504 ヌメロニム
ユーザー maroon_kuri
提出日時 2021-05-07 21:31:06
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 223 ms / 2,000 ms
コード長 17,364 bytes
コンパイル時間 3,046 ms
コンパイル使用メモリ 223,380 KB
最終ジャッジ日時 2025-01-21 08:01:58
ジャッジサーバーID
（参考情報） 		judge2 / judge6
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ファイルパターン 結果
other AC * 61
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#include <bits/stdc++.h>
using namespace std;
using ll=long long;
#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
    return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
    os<<"{";
    for(auto e:v)os<<e<<",";
    return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
    os<<t<<" ";
    dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
    return os<<vc<t>(all(a));
}
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
    if(i)os<<",";
    os<<get<i>(t);
    print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
    os<<"{";
    print_tuple<0,tuple<Args...>,Args...>(os,t);
    return os<<"}";
}
template<class t>
void print(t x,int suc=1){
    cout<<x;
    if(suc==1)
        cout<<"\n";
    if(suc==2)
        cout<<" ";
}
ll read(){
    ll i;
    cin>>i;
    return i;
}
vi readvi(int n,int off=0){
    vi v(n);
    rep(i,n)v[i]=read()+off;
    return v;
}
pi readpi(int off=0){
    int a,b;cin>>a>>b;
    return pi(a+off,b+off);
}
template<class t,class u>
void print(const pair<t,u>&p,int suc=1){
    print(p.a,2);
    print(p.b,suc);
}
template<class T>
void print(const vector<T>&v,int suc=1){
    rep(i,v.size())
        print(v[i],i==int(v.size())-1?suc:2);
}
string readString(){
    string s;
    cin>>s;
    return s;
}
template<class T>
T sq(const T& t){
    return t*t;
}
//#define CAPITAL
void yes(bool ex=true){
    #ifdef CAPITAL
    cout<<"YES"<<"\n";
    #else
    cout<<"Yes"<<"\n";
    #endif
    if(ex)exit(0);
    #ifdef LOCAL
    cout.flush();
    #endif
}
void no(bool ex=true){
    #ifdef CAPITAL
    cout<<"NO"<<"\n";
    #else
    cout<<"No"<<"\n";
    #endif
    if(ex)exit(0);
    #ifdef LOCAL
    cout.flush();
    #endif
}
void possible(bool ex=true){
    #ifdef CAPITAL
    cout<<"POSSIBLE"<<"\n";
    #else
    cout<<"Possible"<<"\n";
    #endif
    if(ex)exit(0);
    #ifdef LOCAL
    cout.flush();
    #endif
}
void impossible(bool ex=true){
    #ifdef CAPITAL
    cout<<"IMPOSSIBLE"<<"\n";
    #else
    cout<<"Impossible"<<"\n";
    #endif
    if(ex)exit(0);
    #ifdef LOCAL
    cout.flush();
    #endif
}
constexpr ll ten(int n){
    return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int topbit(signed t){
    return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
    return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
    return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
    return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
    return __builtin_popcount(t);
}
int popcount(ll t){
    return __builtin_popcountll(t);
}
bool ispow2(int i){
    return i&&(i&-i)==i;
}
ll mask(int i){
    return (ll(1)<<i)-1;
}
bool inc(int a,int b,int c){
    return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
    sort(all(v));
    v.erase(unique(all(v)),v.ed);
}
ll rand_int(ll l, ll r) { //[l, r]
    #ifdef LOCAL
    static mt19937_64 gen;
    #else
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}
template<class t>
void myshuffle(vc<t>&a){
    rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}
template<class t>
int lwb(const vc<t>&v,const t&a){
    return lower_bound(all(v),a)-v.bg;
}
vvc<int> readGraph(int n,int m){
    vvc<int> g(n);
    rep(i,m){
        int a,b;
        cin>>a>>b;
        //sc.read(a,b);
        a--;b--;
        g[a].pb(b);
        g[b].pb(a);
    }
    return g;
}
vvc<int> readTree(int n){
    return readGraph(n,n-1);
}
//mint107 は verify してねえ
//#define DYNAMIC_MOD
struct modinfo{uint mod,root;
#ifdef DYNAMIC_MOD
constexpr modinfo(uint m,uint r):mod(m),root(r),im(0){set_mod(m);}
ull im;
constexpr void set_mod(uint m){
    mod=m;
    im=ull(-1)/m+1;
}
uint product(uint a,uint b)const{
    ull z=ull(a)*b;
    uint x=((unsigned __int128)z*im)>>64;
    uint v=uint(z)-x*mod;
    return v<mod?v:v+mod;
}
#endif
};
template<modinfo const&ref>
struct modular{
    static constexpr uint const &mod=ref.mod;
    static modular root(){return modular(ref.root);}
    uint v;
    //modular(initializer_list<uint>ls):v(*ls.bg){}
    modular(ll vv=0){s(vv%mod+mod);}
    modular& s(uint vv){
        v=vv<mod?vv:vv-mod;
        return *this;
    }
    modular operator-()const{return modular()-*this;}
    modular& operator+=(const modular&rhs){return s(v+rhs.v);}
    modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
    modular&operator*=(const modular&rhs){
        #ifndef DYNAMIC_MOD
        v=ull(v)*rhs.v%mod;
        #else
        v=ref.product(v,rhs.v);
        #endif
        return *this;
    }
    modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
    modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
    modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
    modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
    modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
    modular pow(ll n)const{
        modular res(1),x(*this);
        while(n){
            if(n&1)res*=x;
            x*=x;
            n>>=1;
        }
        return res;
    }
    modular inv()const{return pow(mod-2);}
    /*modular inv()const{
        int x,y;
        int g=extgcd<ll>(v,mod,x,y);
        assert(g==1);
        if(x<0)x+=mod;
        return modular(x);
    }*/
    friend modular operator+(int x,const modular&y){
        return modular(x)+y;
    }
    friend modular operator-(int x,const modular&y){
        return modular(x)-y;
    }
    friend modular operator*(int x,const modular&y){
        return modular(x)*y;
    }
    friend modular operator/(int x,const modular&y){
        return modular(x)/y;
    }
    friend ostream& operator<<(ostream&os,const modular&m){
        return os<<m.v;
    }
    friend istream& operator>>(istream&is,modular&m){
        ll x;is>>x;
        m=modular(x);
        return is;
    }
    bool operator<(const modular&r)const{return v<r.v;}
    bool operator==(const modular&r)const{return v==r.v;}
    bool operator!=(const modular&r)const{return v!=r.v;}
    explicit operator bool()const{
        return v;
    }
};
#ifndef DYNAMIC_MOD
extern constexpr modinfo base{998244353,3};
//extern constexpr modinfo base{1000000007,0};
//modinfo base{1,0};
#ifdef USE_GOOD_MOD
static_assert(base.mod==998244353);
#endif
#else
modinfo base(1,0);
extern constexpr modinfo base107(1000000007,0);
using mint107=modular<base107>;
#endif
using mint=modular<base>;
const int vmax=(1<<21)+10;
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
    fact[0]=1;
    rng(i,1,vmax){
        fact[i]=fact[i-1]*i;
    }
    finv[vmax-1]=fact[vmax-1].inv();
    for(int i=vmax-2;i>=0;i--){
        finv[i]=finv[i+1]*(i+1);
    }
    for(int i=vmax-1;i>=1;i--){
        invs[i]=finv[i]*fact[i-1];
    }
}
mint choose(int n,int k){
    return fact[n]*finv[n-k]*finv[k];
}
mint binom(int a,int b){
    return fact[a+b]*finv[a]*finv[b];
}
mint catalan(int n){
    return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}
/*
const int vmax=110;
mint binbuf[vmax][vmax];
mint choose(int n,int k){
    return binbuf[n-k][k];
}
mint binom(int a,int b){
    return binbuf[a][b];
}
void initfact(){
    binbuf[0][0]=1;
    rep(i,vmax)rep(j,vmax){
        if(i)binbuf[i][j]+=binbuf[i-1][j];
        if(j)binbuf[i][j]+=binbuf[i][j-1];
    }
}
*/
#define USE_GOOD_MOD
//size of input must be a power of 2
//output of forward fmt is bit-reversed
//output elements are in the range [0,mod*4)
//input of inverse fmt should be bit-reversed
template<class mint>
void inplace_fmt(const int n,mint*const f,bool inv){
    static constexpr uint mod=mint::mod;
    static constexpr uint mod2=mod*2;
    static constexpr int L=30;
    static mint g[L],ig[L],p2[L];
    if(g[0].v==0){
        rep(i,L){
            mint w=-mint::root().pow(((mod-1)>>(i+2))*3);
            g[i]=w;
            ig[i]=w.inv();
            p2[i]=mint(1<<i).inv();
        }
    }
    if(!inv){
        int b=n;
        if(b>>=1){//input:[0,mod)
            rep(i,b){
                uint x=f[i+b].v;
                f[i+b].v=f[i].v+mod-x;
                f[i].v+=x;
            }
        }
        if(b>>=1){//input:[0,mod*2)
            mint p=1;
            for(int i=0,k=0;i<n;i+=b*2){
                rng(j,i,i+b){
                    uint x=(f[j+b]*p).v;
                    f[j+b].v=f[j].v+mod-x;
                    f[j].v+=x;
                }
                p*=g[__builtin_ctz(++k)];
            }
        }
        while(b){
            if(b>>=1){//input:[0,mod*3)
                mint p=1;
                for(int i=0,k=0;i<n;i+=b*2){
                    rng(j,i,i+b){
                        uint x=(f[j+b]*p).v;
                        f[j+b].v=f[j].v+mod-x;
                        f[j].v+=x;
                    }
                    p*=g[__builtin_ctz(++k)];
                }
            }
            if(b>>=1){//input:[0,mod*4)
                mint p=1;
                for(int i=0,k=0;i<n;i+=b*2){
                    rng(j,i,i+b){
                        uint x=(f[j+b]*p).v;
                        f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
                        f[j+b].v=f[j].v+mod-x;
                        f[j].v+=x;
                    }
                    p*=g[__builtin_ctz(++k)];
                }
            }
        }
    }else{
        int b=1;
        if(b<n/2){//input:[0,mod)
            mint p=1;
            for(int i=0,k=0;i<n;i+=b*2){
                rng(j,i,i+b){
                    ull x=f[j].v+mod-f[j+b].v;
                    f[j].v+=f[j+b].v;
                    f[j+b].v=x*p.v%mod;
                }
                p*=ig[__builtin_ctz(++k)];
            }
            b<<=1;
        }
        for(;b<n/2;b<<=1){
            mint p=1;
            for(int i=0,k=0;i<n;i+=b*2){
                rng(j,i,i+b/2){//input:[0,mod*2)
                    ull x=f[j].v+mod2-f[j+b].v;
                    f[j].v+=f[j+b].v;
                    f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;
                    f[j+b].v=x*p.v%mod;
                }
                rng(j,i+b/2,i+b){//input:[0,mod)
                    ull x=f[j].v+mod-f[j+b].v;
                    f[j].v+=f[j+b].v;
                    f[j+b].v=x*p.v%mod;
                }
                p*=ig[__builtin_ctz(++k)];
            }
        }
        if(b<n){//input:[0,mod*2)
            rep(i,b){
                uint x=f[i+b].v;
                f[i+b].v=f[i].v+mod2-x;
                f[i].v+=x;
            }
        }
        mint z=p2[__lg(n)];
        rep(i,n)f[i]*=z;
    }
}
template<class mint>
void inplace_fmt(vector<mint>&f,bool inv){
    inplace_fmt(si(f),f.data(),inv);
}
//size of input must be a power of 2
//output elements are in the range [0,mod*4)
template<class mint>
void half_fmt(const int n,mint*const f){
    static constexpr uint mod=mint::mod;
    static constexpr uint mod2=mod*2;
    static const int L=30;
    static mint g[L],h[L];
    if(g[0].v==0){
        rep(i,L){
            g[i]=-mint::root().pow(((mod-1)>>(i+2))*3);
            h[i]=mint::root().pow((mod-1)>>(i+2));
        }
    }
    int b=n;
    int lv=0;
    if(b>>=1){//input:[0,mod)
        mint p=h[lv++];
        for(int i=0,k=0;i<n;i+=b*2){
            rng(j,i,i+b){
                uint x=(f[j+b]*p).v;
                f[j+b].v=f[j].v+mod-x;
                f[j].v+=x;
            }
            p*=g[__builtin_ctz(++k)];
        }
    }
    if(b>>=1){//input:[0,mod*2)
        mint p=h[lv++];
        for(int i=0,k=0;i<n;i+=b*2){
            rng(j,i,i+b){
                uint x=(f[j+b]*p).v;
                f[j+b].v=f[j].v+mod-x;
                f[j].v+=x;
            }
            p*=g[__builtin_ctz(++k)];
        }
    }
    while(b){
        if(b>>=1){//input:[0,mod*3)
            mint p=h[lv++];
            for(int i=0,k=0;i<n;i+=b*2){
                rng(j,i,i+b){
                    uint x=(f[j+b]*p).v;
                    f[j+b].v=f[j].v+mod-x;
                    f[j].v+=x;
                }
                p*=g[__builtin_ctz(++k)];
            }
        }
        if(b>>=1){//input:[0,mod*4)
            mint p=h[lv++];
            for(int i=0,k=0;i<n;i+=b*2){
                rng(j,i,i+b){
                    uint x=(f[j+b]*p).v;
                    f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
                    f[j+b].v=f[j].v+mod-x;
                    f[j].v+=x;
                }
                p*=g[__builtin_ctz(++k)];
            }
        }
    }
}
template<class mint>
void half_fmt(vector<mint>&f){
    half_fmt(si(f),f.data());
}
#ifdef USE_GOOD_MOD
template<class mint>
vc<mint> multiply(vc<mint> x,const vc<mint>&y,bool same=false){
    int n=si(x)+si(y)-1;
    int s=1;
    while(s<n)s*=2;
    x.resize(s);inplace_fmt(x,false);
    if(!same){
        vc<mint> z(s);
        rep(i,si(y))z[i]=y[i];
        inplace_fmt(z,false);
        rep(i,s)x[i]*=z[i];
    }else{
        rep(i,s)x[i]*=x[i];
    }
    inplace_fmt(x,true);x.resize(n);
    return x;
}
template<class mint>
vc<mint> multiply_givenlength(vc<mint> x,const vc<mint>&y,bool same=false){
    int s=si(x);
    assert(ispow2(s));
    assert(si(y));
    x.resize(s);inplace_fmt(x,false);
    if(!same){
        vc<mint> z(s);
        rep(i,si(y))z[i]=y[i];
        inplace_fmt(z,false);
        rep(i,s)x[i]*=z[i];
    }else{
        rep(i,s)x[i]*=x[i];
    }
    inplace_fmt(x,true);
    return x;
}
#else
//59501818244292734739283969-1=5.95*10^25 までの値を正しく計算
//最終的な列の大きさが 2^24 までなら動く
//最終的な列の大きさが 2^20 以下のときは，下の 3 つの素数を使ったほうが速い（は？）
//VERIFY: yosupo
//Yukicoder No980 (same=true)
namespace arbitrary_convolution{
    constexpr modinfo base0{167772161,3};//2^25 * 5 + 1
    constexpr modinfo base1{469762049,3};//2^26 * 7 + 1
    constexpr modinfo base2{754974721,11};//2^24 * 45 + 1
    //extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
    //extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
    //extern constexpr modinfo base2{1053818881,7};//2^20 * 1005 + 1
    using mint0=modular<base0>;
    using mint1=modular<base1>;
    using mint2=modular<base2>;
    template<class t,class mint>
    vc<t> sub(const vc<mint>&x,const vc<mint>&y,bool same=false){
        int n=si(x)+si(y)-1;
        int s=1;
        while(s<n)s*=2;
        vc<t> z(s);rep(i,si(x))z[i]=x[i].v;
        inplace_fmt(z,false);
        if(!same){
            vc<t> w(s);rep(i,si(y))w[i]=y[i].v;
            inplace_fmt(w,false);
            rep(i,s)z[i]*=w[i];
        }else{
            rep(i,s)z[i]*=z[i];
        }
        inplace_fmt(z,true);z.resize(n);
        return z;
    }
    template<class mint>
    vc<mint> multiply(const vc<mint>&x,const vc<mint>&y,bool same=false){
        auto d0=sub<mint0>(x,y,same);
        auto d1=sub<mint1>(x,y,same);
        auto d2=sub<mint2>(x,y,same);
        int n=si(d0);
        vc<mint> res(n);
        static const mint1 r01=mint1(mint0::mod).inv();
        static const mint2 r02=mint2(mint0::mod).inv();
        static const mint2 r12=mint2(mint1::mod).inv();
        static const mint2 r02r12=r02*r12;
        static const mint w1=mint(mint0::mod);
        static const mint w2=w1*mint(mint1::mod);
        rep(i,n){
            ull a=d0[i].v;
            ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;
            ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;
            res[i].v=(a+b*w1.v+c*w2.v)%mint::mod;
        }
        return res;
    }
    template<class t,class mint>
    vc<t> sub_givenlength(const vc<mint>&x,const vc<mint>&y,bool same=false){
        int s=si(x);
        assert(ispow2(s));
        assert(si(y)==s);
        vc<t> z(s);rep(i,si(x))z[i]=x[i].v;
        inplace_fmt(z,false);
        if(!same){
            vc<t> w(s);rep(i,si(y))w[i]=y[i].v;
            inplace_fmt(w,false);
            rep(i,s)z[i]*=w[i];
        }else{
            rep(i,s)z[i]*=z[i];
        }
        inplace_fmt(z,true);
        return z;
    }
    template<class mint>
    vc<mint> multiply_givenlength(const vc<mint>&x,const vc<mint>&y,bool same=false){
        auto d0=sub_givenlength<mint0>(x,y,same);
        auto d1=sub_givenlength<mint1>(x,y,same);
        auto d2=sub_givenlength<mint2>(x,y,same);
        int n=si(d0);
        vc<mint> res(n);
        static const mint1 r01=mint1(mint0::mod).inv();
        static const mint2 r02=mint2(mint0::mod).inv();
        static const mint2 r12=mint2(mint1::mod).inv();
        static const mint2 r02r12=r02*r12;
        static const mint w1=mint(mint0::mod);
        static const mint w2=w1*mint(mint1::mod);
        rep(i,n){
            ull a=d0[i].v;
            ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;
            ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;
            res[i].v=(a+b*w1.v+c*w2.v)%mint::mod;
        }
        return res;
    }
}
using arbitrary_convolution::multiply;
using arbitrary_convolution::multiply_givenlength;
#endif
namespace integer_convolution{
    extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
    extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
    using mint0=modular<base0>;
    using mint1=modular<base1>;
    template<class t>
    vc<t> sub(const vi&x,const vi&y,bool same=false){
        int n=si(x)+si(y)-1;
        int s=1;
        while(s<n)s*=2;
        vc<t> z(s);rep(i,si(x))z[i]=x[i];
        inplace_fmt(z,false);
        if(!same){
            vc<t> w(s);rep(i,si(y))w[i]=y[i];
            inplace_fmt(w,false);
            rep(i,s)z[i]*=w[i];
        }else{
            rep(i,s)z[i]*=z[i];
        }
        inplace_fmt(z,true);z.resize(n);
        return z;
    }
    vi multiply(const vi&x,const vi&y,bool same=false){
        auto d0=sub<mint0>(x,y,same);
        auto d1=sub<mint1>(x,y,same);
        const mint1 r=mint1(mint0::mod).inv();
        int n=si(d0);
        vi res(n);
        rep(i,n){
            res[i]=d0[i].v+(r*(d1[i]-d0[i].v)).v*(ull)mint0::mod;
        }
        return res;
    }
}
//最大で 1<<mx のサイズの fft が登場！
template<class mint>
vc<mint> large_convolution(const vc<mint>&a,const vc<mint>&b,int mx){
    int n=si(a),m=si(b);
    vc<mint> c(n+m-1);
    int len=1<<(mx-1);
    for(int i=0;i<n;i+=len){
        for(int j=0;j<n;j+=len){
            int x=min(len,n-i),y=min(len,m-j);
            auto d=multiply(vc<mint>(a.bg+i,a.bg+i+x),vc<mint>(b.bg+j,b.bg+j+y));
            rep(k,si(d))
                c[i+j+k]+=d[k];
        }
    }
    return c;
}
void slv(){
    int n;cin>>n;
    string s;cin>>s;
    vc<mint> a(n),b(n);
    rep(i,n)if(s[i]=='i')a[i]=1;
    else b[n-1-i]=1;
    auto c=multiply(a,b);
    c.resize(n-1);
    rep(i,n-1)c[i]*=fact[n-2-i];
    vc<mint> d(n-1);
    rep(i,n-1)d[i]=finv[i];
    auto e=multiply(c,d);
    e.resize(n-1);
    reverse(all(e));
    rep(i,n-1)e[i]*=finv[i];
    int ans=0;
    rep(i,n-1)ans^=e[i].v;
    print(ans);
}
signed main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout<<fixed<<setprecision(20);
    
    initfact();
    //int t;cin>>t;rep(_,t)
    slv();
}
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