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.