Given an array of n integers, count the number of subsets whose elements' product is a square number.

Also count the empty subset with product equal to one.

Input

The first line has an integer n: the size of the array.

The next line has n integers x_1, x_2,\dots, x_n: the contents of the array.

Output

Print one integer: the answer to the problem modulo 10^9 + 7.

Constraints

• 1 \le n \le 5000
• 1 \le x_i \le 5000

Example

Input:

4
2 2 3 6

Output:

4