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5425: Special Matrices

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：
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题目描述

F. Special Matrices
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
An n×n square matrix is special, if:
  • it is binary, that is, each cell contains either a 0, or a 1;
  • the number of ones in each row and column equals 2.
You are given n and the first m rows of the matrix. Print the number of special n×n matrices, such that the first m rows coincide with the given ones.
As the required value can be rather large, print the remainder after dividing the value by the given number mod.
Input
The first line of the input contains three integers n, m, mod (2≤n≤500, 0≤m≤n, 2≤mod≤109). Then m lines follow, each of them contains n characters − the first rows of the required special matrices. Each of these lines contains exactly two characters '1', the rest characters are '0'. Each column of the given m×n table contains at most two numbers one.
Output
Print the remainder after dividing the required value by number mod.
Examples
Input 
3 1 1000
011
Output 
2
Input 
4 4 100500
0110
1010
0101
1001
Output 
1
Note
For the first test the required matrices are: 
011
101
110

011
110
101
In the second test the required matrix is already fully given, so the answer is 1.

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