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 CodeForces.Round338;

import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Map;
import java.util.StringTokenizer;
import java.util.TreeMap;

/**
 * Created by ilya on 09.01.16.
 */

public class D615 {
    static final long MOD = (long) (1e9 + 7);

    public static void main(String[] args) {
        sc sc = new sc();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int m = sc.nextInt();
        TreeMap<Long, Long> map = new TreeMap<>();
        for (int i = 0; i < m; i++) {
            long a = sc.nextLong();
            if (map.containsKey(a)) map.put(a, map.get(a) + 1);
            else map.put(a, 1l);
        }
        long d = 1l;
        long ans = 1l;
        for (Map.Entry<Long, Long> x : map.entrySet()) {
            long fp = binPow(x.getKey(), (x.getValue() + 1) * x.getValue() / 2);
            ans = binPow(ans, (x.getValue() + 1)) * binPow(fp, d) % MOD;
            d = d * (x.getValue() + 1) % (MOD - 1);
        }
        out.println(ans);
        out.close();
    }

    public static long binPow(long a, long q){
        a %= MOD;
        if (q == 0) return 1;
        return ((q % 2 == 1 ? a : 1) * binPow(a * a, q / 2)) % MOD;
    }

    public static class sc {
        BufferedReader br;
        StringTokenizer st;

        public sc() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        Integer nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}

