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 sys
import math
import itertools
from collections import defaultdict

m = int(sys.stdin.readline().rstrip())
divs = map(int,sys.stdin.readline().rstrip().split())

d = defaultdict(lambda: 0)
number = 1
for divi in divs:
	d[divi] += 1
	number *= divi
	number %= (10**9 + 7)

tot = 1
for k,v in d.items():
	tot *= (v+1)
	#print k, v, tot

isperf = False

if tot%2 == 1:
	isperf = True
	#tot -= 1
	sqrt = 1;
	for k,v in d.items():
		sqrt *= pow(k, (v/2), (10**9 + 7))
		sqrt %= (10**9 + 7)
	tot /=2
else:
	tot /=2

#tot %= (10**9 + 7)


ans = pow(number, tot, (10**9 + 7))

if isperf:
	ans *= sqrt
	ans %= (10**9 + 7)

print ans

