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.
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class CodeForces
{
    static long MOD = 1000000007;
    
    static long expo(long a, long q){
        a %= MOD;
        if (q == 0) return 1;
        return ((q % 2 == 1 ? a : 1) * expo(a * a, q / 2)) % MOD;
    }
    public static void main (String[] args) throws java.lang.Exception
    {
        // your code goes here
        Scanner sc = new Scanner(System.in);
        
        int m = sc.nextInt();
        Map<Integer, Integer> M = new HashMap<Integer, Integer>();
        
        for (int i = 0; i < m; ++i){
            int a = sc.nextInt();
            if (M.containsKey(a)){
                M.put(a, M.get(a) + 1);
            }
            else{
                //System.out.println(a);
                M.put(a, 1);
            }
        }
        
        long d = 1;
        long ans = 1;
        for (Map.Entry<Integer, Integer> entry: M.entrySet()){
            long v = (long)entry.getValue();
            long fp = expo(entry.getKey(), v * (v + 1) / 2);
            ans = (expo(ans, (v + 1)) * expo(fp, d) ) % MOD;
            d = (d * (v+1)) % (MOD - 1);
        }
        
        System.out.println(ans);
        
        sc.close();
    }
}