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>
uint64_t MOD = 1000000007, s = 1, d = 1;
uint64_t M(uint64_t n, uint64_t k) {
  return k == 0       ? 1
         : k == 1     ? n % MOD
         : k % 2 == 0 ? M(n * n % MOD, k / 2)
                      : n * M(n, k - 1) % MOD;
}
int main() {
  std::ios_base::sync_with_stdio(false);
  int m;
  std::cin >> m;
  std::map<uint64_t, uint64_t> factors;
  for (int p; std::cin >> p; ++factors[p])
    ;
  for (auto pk : factors) {
    auto p = pk.first;
    auto k = pk.second;
    s = M(s, k + 1) * M(M(p, -~k * k / 2), d) % MOD;
    d = d * -~k % ~-MOD;
  }
  std::cout << s;
}
