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.

import java.util.*;

public class saisumit {
    static long MOD = 1000000007l;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long m = in.nextInt();
        Map<Long, Integer> map = new HashMap<>();
        int index = 0;
        long[] val = new long[200000];
        long[] num = new long[200000];
        for (int i = 0; i < m ;i++) {
            long x = in.nextLong();
            if (map.containsKey(x)) {
                num[map.get(x)]++;
            } else {
                num[index] = 1;
                val[index] = x;
                map.put(x, index);
                index++;
            }
        }
        int n = index;
        int pOdd = -1;
        for (int i = 0; i < n; i++) {
            if (num[i] % 2 == 1) {
                pOdd = i;
                break;
            }
        }
        if (pOdd == -1) {
            long pow = 1;
            for (int i = 0; i < n; i++) {
                pow = (pow * (num[i] + 1)) % (MOD - 1);
            }

            long ans = 1;
            for (int i = 0; i < n; i++) {
                ans = (ans * getPow(val[i], (pow * num[i]/2) % (MOD - 1))) % MOD;
            }
            System.out.println(ans);
        } else {
            long pow = (num[pOdd] + 1)/2;
            for (int i = 0; i < n; i++) {
                if (i == pOdd) continue;
                pow = (pow * (num[i] + 1)) % (MOD - 1);
            }
            long ans = 1;
            for (int i = 0; i < n; i++) {
                ans = (ans * getPow(val[i], (pow * num[i]) % (MOD - 1))) % MOD;
            }
            System.out.println(ans);
        }
    }

    private static long getPow(long x, long y) {
        if (y == 0) {
            return 1;
        }
        long res = getPow(x, y/2);
        res = (res*res) %MOD;
        if (y %2 == 1) {
            res = (res * x) %MOD;
        }
        return res;
    }
}