SOLVE

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The Confused Monk

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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 ≤ **A _{i}** ≤ 10

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.

Time Limit:
2.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

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