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.
def gcd(a,b):
	if(b==0):
		return a
	else:
		return gcd(b,a%b)

def f(x):
	g = x[0]
	for a in x:
		g = gcd(g,a)
	return g

def g(x):
	r = 1
	for a in x:
		r*=a
	return r
	
monkQuo = 10**9 + 7
tc = input()
l = list(map(int,raw_input().split()))
print (g(l)**f(l))%monkQuo