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.io.*;
import java.util.*;

/**
 * @auther chao
 * @date 15/12/30
 */
public class MainApp {
    static final long MOD = 1000000007l;
    static final int MAX = 200001;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int m = in.nextInt();
        long[] a = new long[MAX];
        for (int i = 0; i < m ;i++) {
            a[in.nextInt()]++;
        }
        long[] pre = new long[MAX];
        long[] suf = new long[MAX];

        pre[0] = 1;
        for (int i = 1; i < MAX; i++) {
            pre[i] = (pre[i-1] * (a[i] + 1)) % (MOD - 1);
        }
        suf[MAX - 1] = 1;
        for (int i = MAX - 2; i >= 0; i--) {
            suf[i] = (suf[i+1] * (a[i] + 1) ) % (MOD - 1);
        }

        long ans = 1;
        for (int i = 2; i < MAX - 1; i++) {
            if (a[i] == 0)  continue;
            long p = (a[i] * (a[i] + 1) / 2) % (MOD - 1);
            p = (p * suf[i+1]) % (MOD - 1);
            p = (p * pre[i-1]) % (MOD - 1);
            ans = (ans * getPow(i, p)) % 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;
    }
}