A9734. Special Matrices

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 $mod$ .

The first line of the input contains three integers $n$ , $m$ , $mod$ ( $2<=n<=500$ , $0<=m<=n$ , $2<=mod<=10^{9}$ ). 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.

Print the remainder after dividing the required value by number $mod$ .

For the first test the required matrices are:

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