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.IOException;
import java.math.BigInteger;
import java.util.InputMismatchException;

public class Multipliers {
	private static final int MOD = 1000000007;
	
    public static void main(String[] args) {
        FasterScanner sc = new FasterScanner();
        
        int M = sc.nextInt();
        
        int[] freq = new int[200001];
        for (int i = 0; i < M; i++) {
        	int P = sc.nextInt();
        	freq[P]++;
        }
        
        long all = 1;
        long div = 1;
        for (int i = 2; i < freq.length; i++) {
        	long prod = modPow(i, (freq[i] + 1L) * freq[i] / 2, MOD);
        	all = modPow(all, freq[i] + 1, MOD) * modPow(prod, div, MOD);
        	div = (div * (freq[i] + 1)) % (MOD - 1);
        }
        System.out.println(all);
    }
    
    public static long modInv(long d, long m) {
    	return BigInteger.valueOf(d).modInverse(BigInteger.valueOf(m)).longValue();
    }
    
    public static long modPow(long b, long e, long m) {
    	return BigInteger.valueOf(b).modPow(BigInteger.valueOf(e), BigInteger.valueOf(m)).longValue();
    }

	public static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

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

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

		public int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public int[] nextIntArray(int n, int offset) {
			int[] arr = new int[n + offset];
			for (int i = 0; i < n; i++) {
				arr[i + offset] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public long[] nextLongArray(int n, int offset) {
			long[] arr = new long[n + offset];
			for (int i = 0; i < n; i++) {
				arr[i + offset] = nextLong();
			}
			return arr;
		}

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

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}