Ayrat has number n, represented as it's prime factorization pi of size m, i.e. n = p1·p2·...·pm. Ayrat got secret information that that the product of all divisors of n taken modulo 109 + 7 is the password to the secret data base. Now he wants to calculate this value.

Input

The first line of the input contains a single integer m (1 ≤ m ≤ 200 000) — the number of primes in factorization of n. 

The second line contains m primes numbers pi (2 ≤ pi ≤ 200 000).

Output

Print one integer — the product of all divisors of n modulo 109 + 7.

Examples

Input

2
2 3


Output

36


Input

3
2 3 2


Output

1728

Note

In the first sample n = 2·3 = 6. The divisors of 6 are 1, 2, 3 and 6, their product is equal to 1·2·3·6 = 36.

In the second sample 2·3·2 = 12. The divisors of 12 are 1, 2, 3, 4, 6 and 12. 1·2·3·4·6·12 = 1728.
#include <bits/stdc++.h>
using namespace std;
const int M = 200001;
const long long int MOD = 1000000007;
long long int N = 1, c[M], i, j, N2, m;
bool flag;
int main() {
  cin >> m;
  fill(c, c + M, 1);
  while (m--) {
    int p;
    cin >> p;
    c[p]++;
    N *= p, N %= MOD;
  }
  for (i = 1; i < M; i++)
    if (c[i] % 2 == 0) {
      c[i] /= 2;
      flag = true;
      break;
    }
  if (!flag) {
    N = 1;
    for (i = 1; i < M; i++)
      for (j = 1; j * 2 < c[i]; j++) N *= i, N %= MOD;
  }
  for (i = 1; i < M; i++) {
    N2 = N;
    for (j = 1; j < c[i]; j++) N *= N2, N %= MOD;
  }
  cout << N << endl;
}
