CF489F Special Matrices
Description
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 Format
The first line of the input contains three integers $ n $ , $ m $ , $ mod $ ( $ 2
Output Format
Print the remainder after dividing the required value by number $ mod $ .
Explanation/Hint
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.
011
101
110
011
110
101
`In the second test the required matrix is already fully given, so the answer is 1.