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 unsigned long long MOD9 = 1e9 + 7;
unsigned long long ModPow(unsigned long long a, unsigned long long b,
                          unsigned long long mod) {
  a %= mod;
  if (!b) return 1;
  return (b % 2 ? a : 1) * ModPow(a * a, b / 2, mod) % mod;
}
map<unsigned long long, unsigned long long> m;
int main() {
  unsigned long long n, a, res = 1, f, d = 1;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a;
    m[a]++;
  }
  for (auto x : m) {
    f = ModPow(x.first, x.second * (x.second + 1) / 2, MOD9);
    res = ModPow(res, x.second + 1, MOD9) * ModPow(f, d, MOD9) % MOD9;
    d = (d * (x.second + 1)) % (MOD9 - 1);
  }
  cout << res;
  return 0;
}
