Binary Matrix

You are given a matrix of size $r \times c$. Every entry of the matrix is $0$ or $1$. In one operation you may flip a single entry: a $0$ becomes $1$, and a $1$ becomes $0$. By performing this operation any number of times, you want to obtain a matrix that satisfies both of the following conditions.

1. Every row contains the same number of $1$s.
2. Every column contains the same number of $1$s.

Compute the minimum number of operations needed to turn the given matrix into a matrix that satisfies both conditions.

The first line contains the number of test cases $T$ ($T \le 1000$).

For each test case, the first line contains two integers $r$ and $c$ ($1 \le r, c \le 40$), where $r$ is the number of rows and $c$ is the number of columns. Each of the next $r$ lines contains $c$ digits with no spaces, describing one row of the matrix.

For each test case, print one line in the form Case #: R, where # is the test case number (starting from $1$) and R is the minimum number of operations needed to transform the given matrix into one that satisfies the conditions. If it is impossible, print $-1$ instead of R.