This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("avx2,fma")
#define rep(i,l,r) for (int i = l; i < r; i++)
#define repr(i,r,l) for (int i = r; i >= l; i--)
#define X first
#define Y second
#define pb push_back
#define endl '\n'
#define debug(x) cerr << #x << " : " << x << endl;
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pll;
const long long int N = 2e3+20,mod = 1e9+7,inf = 1e18+10,maxm= (1 << 21);
inline int mkay(int a,int b){
if (a+b >= mod) return a+b-mod;
if (a+b < 0) return a+b+mod;
return a+b;
}
inline int poww(int a,int k){
if (k < 0) return 0;
int z = 1;
while (k){
if (k&1) z = 1ll*z*a%mod;
a = 1ll*a*a%mod;
k >>= 1;
}
return z;
}
bool b[N];
int dp[N],pre[N][N],c[N][N];
int main(){
ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
int n;
cin >> n;
rep(i,0,n){
int x;
cin >> x;
b[x] = 1;
}
int m = n * 2;
rep(i,0,m+1)
c[0][i] = 1;
rep(i,1,m+1)
rep(j,i,m+1)
c[i][j] = mkay(c[i-1][j-1],c[i][j-1]);
dp[0] = 1;
rep(i,1,n+1){
rep(j,1,i+1){
dp[i] = mkay(dp[i],1ll*c[j-1][i-1]*dp[j-1]%mod*dp[i-j]%mod*(i-j+2)%mod);
}
}
int c0 = 0,c1 = 0;
pre[m+1][0] = 1;
repr(i,m,1){
if (b[i]){
rep(j,0,c1+2){
pre[i][j] = pre[i+1][j];
rep(y,1,j+1){
pre[i][j] = mkay(pre[i][j],1ll*pre[i+1][y-1]*dp[j-y]%mod*c[j-y][c1-y+1]%mod*(j-y+2)%mod);
}
}
c1++;
}
else{
rep(j,0,c1+1){
pre[i][j] = 1ll*pre[i+1][j]*max(0,-c0+j)%mod;
}
c0++;
}
}
cout << 1ll*pre[1][n]*poww(poww(2,n),mod-2)%mod;
}
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