BNMT - Binary Matrix

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You are given a matrix of size r x c. Each of the elements can be either 0 or 1.  In each operation you can flip any element of this matrix, i.e. convert 0 to 1 or convert 1 to 0. Your goal is to convert the matrix such that -

1. Each of the rows will have the same number of 1s and
2. Each of the columns will have the same number of 1s.

What is the minimum number of operations required to achieve this?

Input

Input starts with a positive integer T (~1000) which indicates the number of inputs.

Each case starts with two integers m and n (1 <= r, c <= 40), here r is the number of rows and c is the number of columns of the matrix. Each of the next m lines will have n integers each, either 0 or 1.

Output

For each test case, output `“Case #: R”` in a single line, where `#` will be replaced by case number and R will be replaced by the minimum number of steps required to achieve the target matrix. Replace R by `-1` if it is not possible to reach target matrix.

Example

Sample Input:

```3
2 3
111
111
3 3
011
011
011
2 3
001
000```

Sample Output:

```Case 1: 0
Case 2: 3
Case 3: 1```