104 lines
2.0 KiB
C++
104 lines
2.0 KiB
C++
#include<cstdio>
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#include<cstdlib>
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#include<cstring>
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#include<cmath>
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#include<iostream>
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#include<algorithm>
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using namespace std;
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typedef long long ll;
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const ll Mod=998244353;
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const ll g=3;
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ll fp(ll a,ll k)
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{
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ll res=1LL;
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while(k>0)
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{
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if(k&1)res=res*a%Mod;
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a=a*a%Mod;
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k>>=1;
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}
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return res;
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}
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ll f[100005],inv[100005];
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void change(ll y[],int len)
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{
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for(int i=1,j=len/2;i<len-1;i++)
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{
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if(i<j)swap(y[i],y[j]);
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int k=len/2;
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while(j>=k)
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{
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j-=k;
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k/=2;
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}
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if(j<k)j+=k;
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}
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}
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void ntt(ll y[],int len,int on)
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{
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change(y,len);
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for(int h=2;h<=len;h<<=1)
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{
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ll wn=fp(g,(Mod-1)/h);
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if(on==-1)wn=fp(wn,Mod-2);
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for(int j=0;j<len;j+=h)
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{
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ll w=1LL;
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for(int k=j;k<j+h/2;k++)
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{
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ll u=y[k];
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ll t=w*y[k+h/2]%Mod;
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y[k]=(u+t)%Mod;
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y[k+h/2]=(u-t+Mod)%Mod;
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w=w*wn%Mod;
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}
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}
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}
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if(on==-1)
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{
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ll t=fp(len,Mod-2);
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for(int i=0;i<len;i++)
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y[i]=y[i]*t%Mod;
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}
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}
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ll dp[100005];
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ll x1[200005],x2[200005];
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void cdq(int l,int r)
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{
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if(l==r)return;
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int m=(l+r)>>1;
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cdq(l,m);
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int len=1;
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while(len<=r-l+1)len<<=1;
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for(int i=0;i<len;i++)
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{
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x1[i]=(l+i<=m ? dp[l+i]*inv[l+i]%Mod : 0);
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x2[i]=(l+i<r ? 1LL*(i+1)*(i+1)%Mod : 0);
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}
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ntt(x1,len,1);
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ntt(x2,len,1);
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for(int i=0;i<len;i++)
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x1[i]=x1[i]*x2[i]%Mod;
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ntt(x1,len,-1);
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for(int i=m+1;i<=r;i++)
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dp[i]=(dp[i]+f[i-1]*x1[i-l-1]%Mod)%Mod;
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cdq(m+1,r);
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}
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void prepare()
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{
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f[0]=1LL;
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for(int i=1;i<=100000;i++)
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f[i]=i*f[i-1]%Mod;
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for(int i=0;i<=100000;i++)
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inv[i]=fp(f[i],Mod-2)%Mod;
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dp[0]=1LL;
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cdq(0,100000);
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}
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int main()
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{
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prepare();
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int n;
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while(scanf("%d",&n)!=EOF)printf("%I64d\n",dp[n]);
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return 0;
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}
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