At the start of the matrix game, we have an N x M matrix. Each grid has some balls.
The grid in (i,j) (0 ≤ i < N, 0 ≤ j < M) has A_ij balls.
In each operation you can remove one ball from a grid or add one ball into a grid.
The goal of this game is to make each of the rows has the same number of balls and each of the columns has the same number of balls.
What is the minumun operations you should use?

The first line of the input is T(1≤ T ≤ 100), which stands for the number of test cases you need to solve.
The first line of each test case contains two integers N and M (1 ≤ N,M ≤ 20).
The next N lines describe Aij, each line contains M integers. (0 ≤ Aij ≤ 20).

For each test case, print the case number and the answer.

2
2 3
4 8 5
2 4 6
3 3
1 5 2
3 5 4
2 3 4

Case 1: 7
Case 2: 7

for the first example, the number of balls after operations is

4 6 5

6 4 5