A year ago on the bench in public park Leha found an array of n numbers. Leha believes that permutation p is right if for all 1 ≤ i < n condition, that a_{p_i}·a_{p_i + 1} is not perfect square, holds. Leha wants to find number of right permutations modulo 10⁹ + 7.

Input

First line of input data contains single integer n (1 ≤ n ≤ 300) — length of the array.

Next line contains n integers a₁, a₂, ... , a_n (1 ≤ a_i ≤ 10⁹) — found array.

Output

Output single integer — number of right permutations modulo 10⁹ + 7.

Note

For first example:

[1, 2, 4] — right permutation, because 2 and 8 are not perfect squares.

[1, 4, 2] — wrong permutation, because 4 is square of 2.

[2, 1, 4] — wrong permutation, because 4 is square of 2.

[2, 4, 1] — wrong permutation, because 4 is square of 2.

[4, 1, 2] — wrong permutation, because 4 is square of 2.

[4, 2, 1] — right permutation, because 8 and 2 are not perfect squares.

On the Bench

Examples