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 double eps = 1E-9;
const double Exp = 2.718281828459045;
const double pi = 3.14159;
const double E = 2.7182818284590452354;
const int Max_Bit = 63;
const int INF = 2000000000;
const long long LINF = 1000000000000000007ll;
const int MOD = 1000000007;
const int NMAX = 200005;
const int MMAX = 100000;
const int base = 1000 * 1000 * 1000;
int deg[NMAX];
int main() {
  int m;
  cin >> m;
  for (int i = 1; i <= m; i++) {
    int p;
    cin >> p;
    deg[p]++;
  }
  int flag = 0;
  for (int i = 1; i < NMAX; i++)
    if (deg[i] > 0 && (deg[i] & 1)) flag = 1;
  long long totalsum = 1;
  if (flag == 1) {
    for (int i = 1; i < NMAX; i++) {
      for (int j = 1; j <= deg[i]; j++) {
        totalsum *= i;
        if (totalsum >= MOD) totalsum %= MOD;
      }
    }
    for (int i = 1; i < NMAX; i++) deg[i]++;
    for (int i = 1; i < NMAX; i++) {
      long long cursum = totalsum;
      if (flag && deg[i] > 0 && deg[i] % 2 == 0) {
        deg[i] >>= 1;
        flag = 0;
      }
      for (int j = 1; j <= deg[i] - 1; j++) {
        totalsum *= cursum;
        if (totalsum >= MOD) totalsum %= MOD;
      }
    }
    cout << totalsum << endl;
  } else {
    for (int i = 1; i < NMAX; i++) {
      for (int j = 1; j <= (deg[i] >> 1); j++) {
        totalsum *= i;
        if (totalsum >= MOD) totalsum %= MOD;
      }
    }
    for (int i = 1; i < NMAX; i++) deg[i]++;
    for (int i = 1; i < NMAX; i++) {
      long long cursum = totalsum;
      for (int j = 1; j <= deg[i] - 1; j++) {
        totalsum *= cursum;
        if (totalsum >= MOD) totalsum %= MOD;
      }
    }
    cout << totalsum << endl;
  }
  return 0;
}
