#include using namespace std; using ll=long long; #define int ll #define rng(i,a,b) for(int i=int(a);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 #ifdef LOCAL #define dmp(x) cerr<<__LINE__<<" "<<#x<<" "< void chmax(t&a,u b){if(a void chmin(t&a,u b){if(b using vc=vector; template using vvc=vc>; using pi=pair; using vi=vc; template ostream& operator<<(ostream& os,const pair& p){ return os<<"{"< ostream& operator<<(ostream& os,const vc& v){ os<<"{"; for(auto e:v)os< void dmpr(ostream&os,const T&t,const Args&... args){ os< ostream& operator<<(ostream&os,const array&a){ return os<(all(a)); } template void print_tuple(ostream&,const T&){ } template void print_tuple(ostream&os,const T&t){ if(i)os<<","; os<(t); print_tuple(os,t); } template ostream& operator<<(ostream&os,const tuple&t){ os<<"{"; print_tuple<0,tuple,Args...>(os,t); return os<<"}"; } template void print(t x,int suc=1){ cout<>i; return i; } vi readvi(int n,int off=0){ vi v(n); rep(i,n)v[i]=read()+off; return v; } template void print(const vector&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 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); } void no(bool ex=true){ #ifdef CAPITAL cout<<"NO"<<"\n"; #else cout<<"No"<<"\n"; #endif if(ex)exit(0); } void possible(bool ex=true){ #ifdef CAPITAL cout<<"POSSIBLE"<<"\n"; #else cout<<"Possible"<<"\n"; #endif if(ex)exit(0); } void impossible(bool ex=true){ #ifdef CAPITAL cout<<"IMPOSSIBLE"<<"\n"; #else cout<<"Impossible"<<"\n"; #endif if(ex)exit(0); } 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; } int mask(int i){ return (int(1)< void mkuni(vc&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 random_device rd; static mt19937_64 gen(rd()); #endif return uniform_int_distribution(l, r)(gen); } template int lwb(const vc&v,const t&a){ return lower_bound(all(v),a)-v.bg; } using uint=unsigned; using ull=unsigned long long; //initfact(); //const uint mod=998244353; //const uint mod=1000000007; //uint mod=1; const uint mod=1012924417; struct mint{ uint v; mint(ll vv=0){s(vv%mod+mod);} mint& s(uint vv){ v=vv>=1; } return res; } mint inv()const{return pow(mod-2);} /*mint inv()const{ int x,y; int g=extgcd(v,mod,x,y); assert(g==1); if(x<0)x+=mod; return mint(x); }*/ friend mint operator+(int x,const mint&y){ return mint(x)+y; } friend mint operator-(int x,const mint&y){ return mint(x)-y; } friend mint operator*(int x,const mint&y){ return mint(x)*y; } friend mint operator/(int x,const mint&y){ return mint(x)/y; } friend ostream& operator<<(ostream&os,const mint&m){ return os<>(istream&is,mint&m){ ll x;is>>x; m=mint(x); return is; } bool operator<(const mint&r)const{return v=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); } #define USE_FMT const mint prim_root=5; /* //in-place fft //size of input must be a power of 2 void inplace_fmt(vector&f,const bool inv){ const int n=f.size(); const mint root=inv?prim_root.inv():prim_root; vc g(n); for(int b=n/2;b>=1;b/=2){ mint w=root.pow((mint::base-1)/(n/b)),p=1; for(int i=0;i&f){ const int n=f.size(); for(int b=n/2;b>=1;b/=2){ for(int i=0;i&f){ const int n=f.size(); for(int b=1;b<=n/2;b*=2){ for(int i=0;i&f,const bool i){ if(!i)broken_fmt(f); else broken_ifmt(f); } vc multiply(vc x,vc y,bool same=false){ int n=x.size()+y.size()-1; int s=1; while(s struct Poly:public vc{ template Poly(Args...args):vc(args...){} Poly(initializer_listinit):vc(all(init)){} int size()const{ return vc::size(); } void ups(int s){ if(size()resize(s,0); } Poly low(int s)const{ return Poly(this->bg,this->bg+min(max(s,int(1)),size())); } Poly rev()const{ auto r=*this; reverse(all(r)); return r; } Poly operator-()const{ Poly res=*this; for(auto&v:res)v=-v; return res; } Poly& operator+=(const Poly&r){ ups(r.size()); rep(i,r.size()) (*this)[i]+=r[i]; return *this; } template Poly& operator+=(T t){ (*this)[0]+=t; return *this; } Poly& operator-=(const Poly&r){ ups(r.size()); rep(i,r.size()) (*this)[i]-=r[i]; return *this; } template Poly& operator-=(T t){ (*this)[0]-=t; return *this; } template Poly& operator*=(T t){ for(auto&v:*this) v*=t; return *this; } Poly& operator*=(const Poly&r){ return *this=multiply(*this,r); } Poly square()const{ return multiply(*this,*this,true); } #ifndef USE_FMT Poly inv(int s)const{ Poly r{D(1)/(*this)[0]}; for(int n=1;n f=low(2*n); f.resize(n*4); inplace_fmt(f,false); rep(i,n*4) r[i]=r[i]*2-r[i]*r[i]*f[i]; inplace_fmt(r,true); r.resize(2*n); } return r.low(s); } #endif template Poly& operator/=(T t){ return *this*=D(1)/D(t); } Poly quotient(const Poly&r,const Poly&rri)const{ int m=r.size(); assert(r[m-1].v); int n=size(); int s=n-m+1; if(s<=0) return {0}; return (rev().low(s)*rri.low(s)).low(s).rev(); } Poly& operator/=(const Poly&r){ return *this=quotient(r,r.rev().inv(max(size()-r.size(),int(0))+1)); } Poly& operator%=(const Poly&r){ *this-=*this/r*r; return *this=low(r.size()-1); } Poly operator+(const Poly&r)const{return Poly(*this)+=r;} template Poly operator+(T t)const{return Poly(*this)+=t;} Poly operator-(const Poly&r)const{return Poly(*this)-=r;} template Poly operator-(T t)const{return Poly(*this)-=t;} template Poly operator*(T t)const{return Poly(*this)*=t;} Poly operator*(const Poly&r)const{return Poly(*this)*=r;} template Poly operator/(T t)const{return Poly(*this)/=t;} Poly operator/(const Poly&r)const{return Poly(*this)/=r;} Poly operator%(const Poly&r)const{return Poly(*this)%=r;} Poly dif()const{ Poly r(max(int(0),size()-1)); rep(i,r.size()) r[i]=(*this)[i+1]*(i+1); return r; } Poly inte()const{ Poly r(size()+1,0); rep(i,size()) r[i+1]=(*this)[i]*invs[i+1]; return r; } //VERIFY: yosupo //opencupXvcIII GP of Peterhof H Poly log(int s)const{ return (low(s).dif()*inv(s-1)).low(s-1).inte(); } //Petrozavodsk 2019w Day1 G //yosupo judge Poly exp(int s)const{ return exp2(s).a; } //2つほしいときはコメントアウトの位置ずらす pair exp2(int s)const{ assert((*this)[0]==mint(0)); Poly f{1},g{1}; for(int n=1;;n*=2){ if(n>=s)break; g=g*2-(g.square()*f).low(n); //if(n>=s)break; Poly q=low(n).dif(); q=q+g*(f.dif()-f*q).low(2*n-1); f=f+(f*(low(2*n)-q.inte())).low(2*n); } return make_pair(f.low(s),g.low(s)); } //CF250 E Poly sqrt(int s)const{ assert((*this)[0]==1); Poly r{1}; for(int n=1;n divide(const Poly&r,const Poly&rri)const{ Poly a=quotient(r,rri); Poly b=*this-a*r; return make_pair(a,b.low(r.size()-1)); } //Yukicoder No.215 Poly pow_mod(int n,const Poly&r)const{ Poly rri=r.rev().inv(r.size()); Poly cur{1},x=*this%r; while(n){ if(n%2) cur=(cur*x).divide(r,rri).b; x=(x*x).divide(r,rri).b; n/=2; } return cur; } D eval(D x)const{ D r=0,w=1; for(auto v:*this){ r+=w*v; w*=x; } return r; } }; signed main(){ cin.tie(0); ios::sync_with_stdio(0); cout<>n; int h=(n-1)/2; Poly f(h+1); rng(i,1,h+1) f[i]=-finv[i*2]*(i%2==1?1:-1); f[0]=1; auto g=f.inv(h+1); dmp(g); mint ans=0; rep(i,h+1){ int len=n-1-i*2; mint w=g[i]*finv[len+1]; if(len/2%2)w=-w; ans+=w; } print(ans*fact[n]*2); }