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
'''
n=raw_input()
n=int(n)
a=map(int,raw_input().split())
m_a=a[0]
f=1
for j in a:
	f*=j
	if j<=m_a:
		m_a=j

g=0
for k in xrange(1,m_a+1):
	count=0
	for l in a:
		if l%k!=0:
			break
		else:
			count+=1
	if count==len(a):
		g=k
if g==0:
	g=1
print pow(f,g)%(1000000007)