Problem1513--On the Bench

1513: On the Bench

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

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.

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