ZUFEOJ Home ProblemSet Source/Category Contest Status Ranklist F.A.Qs
Login Register

4083: On the Bench

内存限制：256 MB 时间限制：2 S
题面：传统 评测方式：文本比较 上传者：
提交：1 通过：1
提交提交记录统计Web Board

题目描述

C. On the Bench
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
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
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
Output single integer − number of right permutations modulo 109+7.
Examples
Input 
3
1 2 4
Output 
2
Input 
7
5 2 4 2 4 1 1
Output 
144
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.

输入样例 复制

输出样例 复制

分类标签