A16432 | Matrix Problem

You are given a matrix $a$ , consisting of $n$ rows by $m$ columns. Each element of the matrix is equal to $0$ or $1$ .

You can perform the following operation any number of times (possibly zero): choose an element of the matrix and replace it with either $0$ or $1$ .

You are also given two arrays $A$ and $B$ (of length $n$ and $m$ respectively). After you perform the operations, the matrix should satisfy the following conditions:

1. the number of ones in the $i$ -th row of the matrix should be exactly $A_i$ for every $i \in [1, n]$ .
2. the number of ones in the $j$ -th column of the matrix should be exactly $B_j$ for every $j \in [1, m]$ .

Calculate the minimum number of operations you have to perform.

The first line contains two integers $n$ and $m$ ( $2 \le n, m \le 50$ ).

Then $n$ lines follow. The $i$ -th of them contains $m$ integers $a_{i,1}, a_{i,2}, \dots, a_{i,m}$ ( $0 \le a_{i,j} \le 1$ ).

The next line contains $n$ integers $A_1, A_2, \dots, A_n$ ( $0\le A_i\le m$ ).

The next line contains $m$ integers $B_1, B_2, \dots, B_m$ ( $0\le B_i\le n$ ).

Print one integer — the minimum number of operations you have to perform, or -1 if it is impossible.