Square Subsets

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