F. Special Matricestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAn 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.InputThe 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.OutputPrint the remainder after dividing the required value by number mod.ExamplesInput3 1 1000011Output2Input4 4 1005000110101001011001Output1NoteFor the first test the required matrices are: 011101110011110101In the second test the required matrix is already fully given, so the answer is 1.
Input3 1 1000011
Output2
['combinatorics', 'dp', '*2100']