Problem2602--Special Matrices

2602: Special Matrices

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

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.

Source/Category

 
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