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| #include<cstdio> #include<cstring> #include<algorithm> #include<iostream> #include<queue> #include<map> #include<stack> #include<cmath> #include<set> #include<bitset> #include<complex> #include<cstdlib> #include<assert.h> #define inc(i,l,r) for(int i=l;i<=r;i++) #define dec(i,l,r) for(int i=l;i>=r;i--) #define link(x) for(edge *j=h[x];j;j=j->next) #define mem(a) memset(a,0,sizeof(a)) #define ll long long #define eps 1e-8 #define succ(x) (1<<x) #define lowbit(x) (x&(-x)) #define mid (x+y>>1) #define sqr(x) ((x)*(x)) #define NM 270005 #define nm 100005 const double pi=acos(-1); const ll inf=998244353; using namespace std; ll read(){ ll x=0,f=1;char ch=getchar(); while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();} while(isdigit(ch))x=x*10+ch-'0',ch=getchar(); return f*x; }
int n; ll a[NM],b[NM],inv[NM],invp[NM],p[NM],ans;
int lim,bit,rev[NM],W[NM],w[NM],invn;
inline void reduce(ll&x){x+=x>>63&inf;} ll qpow(ll x,ll t){ ll s=1; for(;t;t>>=1,x=x*x%inf)if(t&1)s=s*x%inf; return s; } void init(int m){ for(lim=1,bit=0;lim<m;lim<<=1)bit++;invn=qpow(lim,inf-2); inc(i,0,lim-1)rev[i]=(rev[i>>1]>>1)|((i&1)<<(bit-1)); ll t=qpow(3,(inf-1)/lim);W[0]=1; inc(i,1,lim)W[i]=W[i-1]*t%inf; } void fft(ll*a,int f=0){ int n=lim; inc(i,1,n-1)if(i<rev[i])swap(a[i],a[rev[i]]); for(int k=1;k<n;k<<=1){ int t=n/k>>1; for(int i=0,j=0;i<k;i++,j+=t)w[i]=W[f?n-j:j]; for(int i=0;i<n;i+=k<<1) for(int j=0;j<k;j++){ ll x=a[i+j],y=w[j]*a[i+j+k]%inf; reduce(a[i+j]=x+y-inf);reduce(a[i+j+k]=x-y); } } if(f)inc(i,0,n-1)a[i]=a[i]*invn%inf; }
int main(){ n=read(); p[0]=p[1]=invp[0]=invp[1]=inv[1]=1; inc(i,2,n)p[i]=p[i-1]*i%inf,inv[i]=inv[inf%i]*(inf-inf/i)%inf,invp[i]=invp[i-1]*inv[i]%inf; inc(i,0,n)if(i&1)a[i]=inf-invp[i];else a[i]=invp[i]; b[0]=1;b[1]=n+1;inc(i,2,n)b[i]=(qpow(i,n+1)-1+inf)%inf*inv[i-1]%inf*invp[i]%inf; init(n+n+1); fft(a);fft(b); inc(i,0,lim-1)a[i]=a[i]*b[i]%inf; fft(a,1); inc(i,0,n)ans+=qpow(2,i)*p[i]%inf*a[i]%inf,ans%=inf; printf("%lld\n",ans); return 0; }
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