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;
int f[1 << 20];
int pow(int a, int b, int mod) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = (1ll * ans * a) % mod;
    a = (1ll * a * a) % mod;
    b /= 2;
  }
  return ans;
}
int c[1 << 20];
int cnt[1 << 20];
int st[1 << 20];
int dr[1 << 20];
int fin[1 << 20];
int main(void) {
  int n;
  cin >> n;
  f[0] = c[0] = 1;
  for (int i = 1; i <= 1e6; ++i)
    f[i] = (f[i - 1] * 1ll * i) % mod, c[i] = pow(f[i], mod - 2, mod);
  long long ans = 1;
  while (n--) {
    int p;
    cin >> p;
    ++cnt[p];
  }
  n = 2e5;
  st[1] = dr[n + 1] = 1;
  for (int i = 2; i <= n; ++i)
    st[i] = (1ll * st[i - 1] * (cnt[i] + 1)) % (mod - 1);
  for (int i = n; i; --i) dr[i] = (1ll * dr[i + 1] * (cnt[i] + 1)) % (mod - 1);
  for (int i = 1; i <= n; ++i)
    if (cnt[i]) {
      int our = (1ll * cnt[i] * (cnt[i] + 1) / 2) % (mod - 1);
      fin[i] = (1ll * our * st[i - 1]) % (mod - 1);
      fin[i] = (1ll * fin[i] * dr[i + 1]) % (mod - 1);
    }
  for (int i = 1; i <= n; ++i) ans = (1ll * ans * pow(i, fin[i], mod)) % mod;
  return cout << ans << '\n', 0;
}
