The Monk wants to teach all its disciples a lesson about patience, since they are always in a hurry to do something crazy. To teach them this, he gives them a list of N numbers, which may or may not be distinct. The students are supposed to solve a simple Mathematical equation based on the array of these N numbers.
g(x) - GCD (a[ 0 ], a[ 1 ], a[ 2 ]... a[n-1] )
f(x) - (a[ 0 ] * a[ 1 ] * a[ 2 ]... * a[n-1] )

The value of the MonkQuotient is: 10^9 + 7.

The equation to be solved is: ( f(x)^g(x) ) % MonkQuotient

Input constraints:
The first line of input will contain an integer — N. The next line will contain N integers denoting the elements of the list. 

Output constraints:
Print the required answer of the equation.

Constraints:
1 ≤ N ≤ 50 
1 ≤ Ai ≤ 10^3

SAMPLE INPUT
2
2 6

SAMPLE OUTPUT
144

Explanation

Here we can see that the product of the elements of array is 12 and the GCD of the array comes out to be 2 .
Thus the answer would be 12^2 which is 144.
'''
# Read input from stdin and provide input before running code

name = raw_input('What is your name?\n')
print 'Hi, %s.' % name
'''
def gcd_reduce(a,b):
	while a:
		a, b = b%a, a
	return b

def gcd(nums):
	return reduce(gcd_reduce, nums)	

def product(nums):
	val = 1
	for x in nums:
		val *= x
	return val

monk_q = (10**9) +7
length = input()
nums = [int(x) for x in raw_input().split()]

print (product(nums)**gcd(nums)) % monk_q