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 mod = 1e9 + 7;
const int maxn = 200000;
int a[200010];
long long pre[maxn + 10];
long long nxt[maxn + 10];
long long z[maxn + 10];
long long fastmod(long long x, int k) {
  long long ans = 1;
  while (k) {
    if (k % 2 == 1) ans = ans * x % mod;
    x = x * x % mod;
    k >>= 1;
  }
  return ans;
}
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    a[x]++;
  }
  pre[1] = 1, nxt[maxn + 1] = 1;
  for (int i = 2; i <= maxn; i++)
    pre[i] = pre[i - 1] * (a[i - 1] + 1) % (mod - 1);
  for (int i = maxn; i >= 2; i--)
    nxt[i] = nxt[i + 1] * (a[i + 1] + 1) % (mod - 1);
  for (int i = 2; i <= maxn; i++) {
    z[i] =
        pre[i] * nxt[i] % (mod - 1) * (1ll * a[i] * (a[i] + 1) / 2 % (mod - 1));
    z[i] = z[i] % (mod - 1);
  }
  long long ans = 1;
  for (int i = 2; i <= maxn; i++)
    if (a[i]) ans = (ans * fastmod(i, z[i])) % mod;
  cout << ans << endl;
  return 0;
}
