推導不多說了 在很久之前就寫過了
觀察柿子

#include<cstdio>
#include<cstdlib>
#include<algorithm>
using namespace std;
typedef long long ll;

const int N=400005;
const int
 
 P=998244353;
const int G=3;

inline int Pow(ll a,int b){
  ll ret=1; for (;b;b>>=1,a=a*a%P) if (b&1) ret=ret*a%P; return (int)ret;
}
inline int Inv(int a){
  return Pow(a,P-2);
}

int num;
int w[2][N];
inline void Pre(int n){
  num=n;
  int g=Pow(G,(P-1)/num),invg=Inv(g);
  w[0][0]=w[1][0]=1;
  for
 
 (int i=1;i<num;i++)
    w[0][i]=(ll)w[0][i-1]*invg%P,w[1][i]=(ll)w[1][i-1]*g%P;
}
int R[N];
inline void FFT(int *a,int n,int r){
  for (int i=0;i<n;i++) if (i<R[i]) swap(a[i],a[R[i]]);
  for (int i=1;i<n;i<<=1)
    for (int j=0;j<n;j+=(i<<1))
      for (int k=0;k<i;k++){
    ll x
 
=a[j+k],y=(ll)w[r][num/(i<<1)*k]*a[j+i+k]%P;
    a[j+k]=(x+y)%P; a[j+i+k]=(x+P-y)%P;
      }
  if (!r) for (int i=0,inv=Pow(n,P-2);i<n;i++) a[i]=(ll)a[i]*inv%P;
}

inline void GetInv(int *a,int *b,int n){
  static int tmp[N];
  if (n==1) return void(b[0]=Inv(a[0]));
  GetInv(a,b,n>>1);
  for (int i=0;i<n;i++) tmp[i]=a[i],tmp[n+i]=0;
  int L=0; while (!(n>>L&1)) L++;
  for (int i=1;i<(n<<1);i++) R[i]=(R[i>>1]>>1)|((i&1)<<L);
  FFT(tmp,n<<1,1); FFT(b,n<<1,1);
  for (int i=0;i<(n<<1);i++)
    tmp[i]=(ll)b[i]*(2+P-(ll)tmp[i]*b[i]%P)%P;
  FFT(tmp,n<<1,0);
  for (int i=0;i<n;i++) b[i]=tmp[i],b[n+i]=0;
}

int n,m;
ll inv[N];
int a[N],b[N];

int main(){
  freopen("t.in","r",stdin);
  freopen("t.out","w",stdout);
  scanf("%d",&n);
  for (m=1;m<=n;m<<=1); Pre(m<<1);
  inv[1]=1; for (int i=2;i<=n;i++) inv[i]=(P-P/i)*inv[P%i]%P;
  inv[0]=1; for (int i=1;i<=n;i++) (inv[i]*=inv[i-1])%=P;
  a[0]=1; for (int i=1;i<=n;i++) a[i]=((P-inv[i])<<1)%P;  
  GetInv(a,b,m);
  int ans=b[n];  
  for (int i=n;i;i--) ans=((ll)ans*i+b[i-1])%P;
  printf("%d\n",ans);
  return 0;
}