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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Set;

public class Main {

    public static long MOD = (long) 1e9 + 7;

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

        int n = inputReader.getNextInt();
        int[] freq = new int[200001];
        long res = 1;
        long divs = 0;

        for(int i = 0; i < n; i++) {
            int x = inputReader.getNextInt();
            freq[x] = freq[x] + 1;
        }

        for(int i = 2; i < 200001; i++) {
            if(freq[i] == 0) {
                continue;
            }

            res = fastExp(res, freq[i]+1, MOD);
            res = (res * fastExp(i, (divs+1) * ((1L * freq[i] * (freq[i]+1) / 2) % (MOD-1)), MOD)) % MOD;

            divs = (divs + (divs + 1) * freq[i]) % (MOD-1);
        }

        out.println(res);

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

    public static long fastExp(long b, long e, long mod) {
        long res = 1;
        while(e > 0) {
            if((e & 1) > 0) {
                res = (res * b) % mod;
            }
            b = (b * b) % mod;
            e = e >> 1;
        }
        return res;
    }

    public static class InputReader {

        static final String SEPARATOR = " ";

        String[] split;
        int head = 0;
        BufferedReader in;

        public InputReader(BufferedReader in) {
            this.in = in;
        }

        private void fillBuffer() throws IOException {
            if(split == null || head >= split.length) {
                head = 0;
                split = in.readLine().split(SEPARATOR);
            }
        }

        public String getNextToken() throws IOException {
            fillBuffer();
            return split[head++];

        }

        public int getNextInt() throws IOException {
            return Integer.parseInt(getNextToken());
        }

        public long getNextLong() throws IOException {
            return Long.parseLong(getNextToken());
        }
    }

    public static <T> String arrayToString(T[] arr) {
        StringBuilder stringBuilder = new StringBuilder();
        for(T x: arr) {
            stringBuilder.append(x + " ");
        }
        return stringBuilder.toString();
    }

}