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.
# -*- coding: utf-8 -*-
import sys,copy,math,heapq,itertools as it,fractions,re,bisect,collections as coll
import random
mod = 10**9+7

n = int(raw_input())
d = [0]*200001 
p = map(int, raw_input().split())
sp = set(p)

for pi in p:
    d[pi] += 1

ls = coll.defaultdict(list)
for pi in sp:
    ls[d[pi]].append(pi)

s = 1
for pi in sp:
    s *= d[pi] + 1

ans = 1
for k, ele in ls.iteritems():
    val = 1
    for pi in ele:
        val = (val * pi) % mod
    ans = (ans * pow(pow(val, s/(k + 1), mod), d[pi]*(d[pi] + 1)/2, mod)) % mod

print ans