Description: 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 api·api + 1 is not perfect square, holds. Leha wants to find number of right permutations modulo 109 + 7. Input Format: First line of input data contains single integer n (1 ≤ n ≤ 300) — length of the array. Next line contains n integers a1, a2, ... , an (1 ≤ ai ≤ 109) — found array. Output Format: 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.