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 <iostream>
#include <cstdio>
#include <algorithm>
#include <string.h>
using namespace std;
#define endl '\n'
#define pi pair<int, int>
#define f first
#define s second
#define ll long long
const int mod = 1000000007;
const int maxn = 603;
int n;
bool a[2 * maxn];
int p[maxn], dp[maxn], dp2[maxn];
int c[maxn][maxn], f[maxn][maxn];
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
cin >> n;
for(int i = 0; i < n; i++){
int x;
cin >> x;
a[x] = 1;
}
f[0][0] = c[0][0] = 1;
for(int i = 0; i < n; i++)
for(int j = i; j <= 2 * i && j < n; j++){
(f[i + 1][j + 2] += f[i][j]) %= mod;
(f[i + 1][j + 1] += 2 * f[i][j] % mod) %= mod;
(f[i + 1][j] += f[i][j]) %= mod;
}
for(int i = 0, j = 1; i < n; i++){
p[i] = (ll)f[i][i] * j % mod * (i + 2) % mod;
j = (ll)j * (i + 1);
for(int k = 0; k <= i; k++){
(c[i + 1][k] += c[i][k]) %= mod;
(c[i + 1][k + 1] += c[i][k]) %= mod;
}
}
dp[0] = 1;
for(int i = 2 * n, x = 0, y = 0; i > 0 && y <= x; i--){
if(a[i]){
memcpy(dp2 + y, dp + y, (x - y + 1) * sizeof(int));
for(int j = y; j <= x; j++)
for(int k = j; k <= x; k++){
(dp[k + 1] += (ll)dp2[j] * c[x - j][k - j] % mod * p[k - j] % mod) %= mod;
}
x++;
}else{
for(int j = y; j <= x; j++) dp[j] = (ll)dp[j] * (j - y) % mod;
y++;
}
}
int ret = dp[n];
for(int i = n, j = (mod + 1) / 2; i; i >>= 1){
if(i & 1) ret = (ll)ret * j % mod;
j = (ll)j * j % mod;
}
cout << ret << endl;
return 0;
}
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