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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Pradyumn
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            final int mod = (int) 1e9 + 7;
            final int pmod = mod - 1;
            final int max = 2 * 100000 + 100;

            int m = in.nextInt();

            int a[] = new int[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] = ((a[i] + 1) * pre[i - 1]) % pmod;

            suf[max - 1] = 1;
            for (int i = max - 2; i >= 0; i--)
                suf[i] = ((a[i] + 1) * suf[i + 1]) % pmod;

            long ans = 1;

            for (int i = 2; i + 1 < max; i++) {
                long curr = i;
                long oth = (pre[i - 1] * suf[i + 1]) % pmod;
                for (int j = 1; j <= a[i]; j++) {
                    ans = (ans * NT.powerMod(curr, oth, mod)) % mod;
                    curr = (curr * i) % mod;
                }
            }

            out.println(ans);
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        private static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class NT {
        public static long powerMod(long a, long n, long mod) {
            //    a %= mod;
            long ret = 1;
            int x = 63 - Long.numberOfLeadingZeros(n);
            for (; x >= 0; x--) {
                ret = ret * ret % mod;
                if (n << 63 - x < 0) ret = ret * a % mod;
            }
            return ret;
        }

    }
}

