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: 10⁹ + 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 ≤ A_i ≤ 10³