On the Bench
题目描述
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.
3
1 2 4
2
7
5 2 4 2 4 1 1
144
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.
题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 63 题。保留原作者与原赛事署名。