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_ = 200500;
const long long MOD = (long long)1e9 + 7;
int M;
map<int, int> D;
long long power(long long a, long long b) {
  long long ret = 1;
  while (b > 0) {
    if (b & 1) ret = (ret * a) % MOD;
    a = (a * a) % MOD;
    b >>= 1;
  }
  return ret;
}
int main() {
  scanf("%d", &M);
  while (M--) {
    int p;
    scanf("%d", &p);
    ++D[p];
  }
  long long ans = 1, num = 1;
  for (auto x : D) {
    int p = x.first, q = x.second;
    long long s = 1, t = 1;
    for (int i = 0; i <= q; i++) {
      s = (s * t) % MOD;
      t = (t * p) % MOD;
    }
    ans = (power(ans, q + 1) * power(s, num)) % MOD;
    num = (num * (q + 1)) % (MOD - 1);
  }
  printf("%lld\n", ans);
  return 0;
}
