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. 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 single integer -- number of right permutations modulo 109 + 7. 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.