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.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class Main {


    public static void main(String[] args) throws Exception {
        Reader in = new Reader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

        long mod = 1000000007;

        int m = in.nextInt();
        int n = 0;
        int[] p = new int[m];
        int[] count = new int[m];
        for (int i = 0; i < m; i++) {
            p[i] = in.nextInt();
        }
        Arrays.sort(p);
        count[0] = 1;
        for (int i = 1; i < m; i++) {
            if (p[i] == p[n]) {
                count[n]++;
            } else {
                n++;
                p[n] = p[i];
                count[n] = 1;
            }
        }

        long sum = 1;
        for (int i = 0; i <= n; i++) {
            sum = (sum * (1 + count[i])) % (2 * mod - 2);
        }

        long ans = 1;
        for (int i = 0; i <= n; i++) {
            int key = p[i];
            int value = count[i];

            ans = (ans * pow(key, (value * sum) / 2, mod)) % mod;
        }

        out.println(ans);

        out.flush();
        in.close();
        out.close();
    }

    private static long pow(long a, long b, long mod) {
        long ans = 1;
        long base = a;
        while (b != 0) {
            if ((b & 1) != 0) {
                ans = (ans * base) % mod;
            }
            base = (base * base) % mod;
            b >>= 1;
        }
        return ans;
    }

    static class Reader {
        BufferedReader reader;
        StringTokenizer st;

        Reader(InputStreamReader stream) {
            reader = new BufferedReader(stream);
            st = null;
        }

        void close() throws IOException {
            reader.close();
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

        String nextLine() throws IOException {
            return reader.readLine();
        }

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

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

    }
}