FJ省队集训DAY4 T1

 1 #include<cstdio>
 2 #include<iostream>
 3 #include<cmath>
 4 #include<cstring>
 5 #include<algorithm>
 6 #define ll long long
 7 const int Mod=1000000009,N=3000;
 8 ll jc[N+10],jcny[N+10],jcnys[N+10],K[N+10],p[N+10],f[N+10];
 9 int read(){
10     int t=0,f=1;char ch=getchar();
11     while (ch<‘0‘||ch>‘9‘){if (ch==‘-‘)f=-1;ch=getchar();}
12     while (‘0‘<=ch&&ch<=‘9‘){t=t*10+ch-‘0‘;ch=getchar();}
13     return t*f;
14 }
15 int Pow(int a,int n){
16     int res=1;
17     while (n){
18         if (n%2) res=((ll)res*a)%Mod;
19         a=((ll)a*a)%Mod;
20         n/=2;
21     }
22     return res;
23 }
24 int main(){
25     jc[0]=1;
26     for (int i=1;i<=3000;i++) jc[i]=(ll)(jc[i-1]*i)%Mod;
27     jcny[3000]=Pow(jc[3000],Mod-2)%Mod;
28     for (int i=2999;i>=0;i--) jcny[i]=(ll)jcny[i+1]*(i+1)%Mod;
29     for (int i=0;i<=3000;i++) jcnys[i]=(ll)jcny[i]*jcny[i]%Mod;
30     for (int i=0;i<=3000;i++)
31      if ((i&1)&&jcny[i]) K[i]=Mod-jcny[i];else K[i]=jcny[i];
32     int n=read();
33     for (int i=1;i<=n;i++) {
34         int x=read();p[x]++;
35     } 
36     f[0]=1;
37     for (int k=1,tot=0;k<=n;k++){
38         if (p[k]==0) continue;
39         tot+=p[k];
40         for (int i=tot;i>=0;i--){
41             f[i]=(ll)f[i]*jcnys[p[k]]%Mod;
42             for (int j=1;j<=p[k]&&j<=i;j++)
43              f[i]=((ll)f[i-j]*K[j]%Mod*jcnys[p[k]-j]+f[i])%Mod;
44         }
45     }
46     ll ans=0;
47     for (int i=0;i<=n;i++)
48      ans=((ll)jc[n-i]*f[i]+ans)%Mod;
49     for (int i=1;i<=n;i++)
50      ans=(ll)ans*jc[p[i]]%Mod;
51     printf("%I64d\n",ans); 
52 }