B - Blocks on Grid

Score : $200$ points

Problem Statement

We have a grid with $H$ horizontal rows and $W$ vertical columns. The square at the $i$-th row from the top and $j$-th column from the left has $A_{i, j}$ blocks stacked on it.

At least how many blocks must be removed to make all squares have the same number of blocks?

Constraints

• $1 \leq H,W \leq 100$
• $0\leq A_{i,j} \leq 100$

Input

Input is given from Standard Input in the following format:

$H$ $W$

$A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,W}$

$\vdots$

$A_{H,1}$ $A_{H,2}$ $\ldots$ $A_{H,W}$

Output

Print the minimum number of blocks that must be removed.

2 3
2 2 3
3 2 2

2

Removing $1$ block from the top-right square and $1$ from the bottom-left square makes all squares have $2$ blocks.

3 3
99 99 99
99 0 99
99 99 99

792

3 2
4 4
4 4
4 4

0