#define _USE_MATH_DEFINES #include using namespace std; //template #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(a);i>(b);i--) #define ALL(v) (v).begin(),(v).end() typedef long long int ll; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12; string to_str(ll x){string res; while(x)res+=('0'+(x%10)),x/=10; reverse(ALL(res)); return res;} template inline bool chmax(T& a,T b){ if(a inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; } //template end templatestruct mint { static int get_mod(){return mod;} int val; int inv() const{ int tmp,a=val,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; } mint():val(0){} mint(ll x):val(x>=0?x%mod:mod+(x%mod)){} mint pow(ll t){mint res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;}return res;} mint& operator+=(const mint& x){if((val+=x.val)>=mod)val-=mod;return *this;} mint& operator-=(const mint& x){if((val+=mod-x.val)>=mod)val-=mod; return *this;} mint& operator*=(const mint& x){val=(ll)val*x.val%mod; return *this;} mint& operator/=(const mint& x){val=(ll)val*x.inv()%mod; return *this;} mint operator+(const mint& x)const{return mint(*this)+=x;} mint operator-(const mint& x)const{return mint(*this)-=x;} mint operator*(const mint& x)const{return mint(*this)*=x;} mint operator/(const mint& x)const{return mint(*this)/=x;} bool operator==(const mint& x)const{return val==x.val;} bool operator!=(const mint& x)const{return val!=x.val;} }; using Mint=mint<1012924417>; struct factorial { vector Fact, Finv; public: factorial(int maxx){ Fact.resize(maxx+1),Finv.resize(maxx+1); Fact[0]=Mint(1); rep(i,0,maxx)Fact[i+1]=Fact[i]*(i+1); Finv[maxx]=Mint(1)/Fact[maxx]; rrep(i,maxx,0)Finv[i-1]=Finv[i]*i; } Mint fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];} Mint nPr(int n,int r){if(n<0||n rt,irt; void init(int lg=20){ while(prt.pow((Mint::get_mod()-1)>>1)==1)prt+=1; rt.resize(1<>w; Mint g=prt.pow(t),ig=g.inv(); rep(i,0,mask){ rt[mask+i+1]=rt[mask+i]*g; irt[mask+i+1]=irt[mask+i]*ig; } } } struct FPS{ vector f; FPS():f({1}){} FPS(int _n):f(_n){} Mint& operator[](const int i){return f[i];} FPS inv()const{ assert(f[0]!=0); int n=f.size(); FPS res(n); res.f[0]=f[0].inv(); for(int k=1;k>1;i;i>>=1){ for(int j=0;jFPS operator*(T t)const{return FPS(*this)*=t;} FPS operator/(const FPS& g)const{return FPS(*this)/=g;} templateFPS operator/(T t)const{return FPS(*this)/=t;} FPS& operator+=(FPS g){ int m=max(f.size(),g.f.size()); if(f.size()!=g.f.size()){ if(m==f.size())g.f.resize(m); else f.resize(m); } rep(i,0,m)f[i]+=g[i]; return *this; } FPS& operator-=(FPS g){ int m=max(f.size(),g.f.size()); if(f.size()!=g.f.size()){ if(m==f.size())g.f.resize(m); else f.resize(m); } rep(i,0,m)f[i]-=g[i]; return *this; } FPS& operator*=(FPS g){ int n=1; while(nFPS& operator*=(T t){ for(auto&x:f)x*=t; return *this; } FPS& operator/=(FPS g){*this*=g.inv(); return *this;} templateFPS& operator/=(T t){ for(auto&x:f)x/=t; return *this; } FPS sqrt(){ int n=f.size(); FPS res(1); res[0]=1; for(int k=1;k pre; for(int k=n;k;k>>=1){ FPS g=d; g.f.resize(k); g.ntt(); pre.push_back(g); } auto dfs=[&](auto dfs,int l,int r,int dep)->void{ if(r-l==1){if(l>0)res[l]/=l; return;} int m=(l+r)>>1; dfs(dfs,l,m,dep+1); FPS g(r-l); rep(i,0,m-l)g[i]=res[l+i]; g.ntt(); rep(i,0,r-l)g[i]*=pre[dep][i]; g.ntt(1); rep(i,m,r)res[i]+=g[i-l-1]; dfs(dfs,m,r,dep+1); }; res[0]=1; dfs(dfs,0,n,0); res.f.resize(m); return res; } }; //need to initialize factorial fact(400010); Mint pre[200020]; int main(){ init(); int n; scanf("%d",&n); pre[0]=1; rep(i,0,200010)pre[i+1]=pre[i]*2; FPS b(n+10); b[0]=1; rep(i,1,n+10)b[i]=b[i-1]/(i+1); b=b.inv(); rep(i,1,n+10)b[i]*=fact.fact(i); FPS tanf(n+10),cosf(n+10); rep(i,1,(n+9)/2+1){ tanf[i*2-1]=pre[i*2]*(pre[i*2]-1)*b[i*2]/fact.fact(i*2); if(i%2==0)tanf[i*2-1]*=-1; } rep(i,0,(n+9)/2+1){ cosf[i*2]=fact.fact(i*2).inv(); if(i&1)cosf[i*2]*=-1; } FPS res=tanf+cosf.inv(); res[n]*=fact.fact(n)*2; printf("%d\n",res[n].val); return 0; }