Problem Statement

You are given a matrix $A$ with $H$ rows and $W$ columns.

Initially, the element in the $i$-th row and $j$-th column of the matrix $A$ is $A_{i,j}$. Here, $A_{i,j}$ is 0 or 1.

You may repeat any of the following operations, in any order and any number of times, until the matrix $A$ becomes an empty matrix.

• Operation $1$: Choose one row whose values are all the same, and delete that row.
• Operation $2$: Choose one column whose values are all the same, and delete that column.
• Operation $3$: Choose one row and delete it.

Find the minimum possible number of times operation $3$ is performed before the matrix $A$ becomes an empty matrix.

Input

$H\ W$
$A_{1,1}A_{1,2}\dots A_{1,W}$
$A_{1,1}A_{1,2}\dots A_{2,W}$
$\vdots$
$A_{H,1}A_{H,2}\dots A_{H,W}$

• $1 \le H,W \le 500$
• $A_{i,j}$ is 0 or 1

Output

Output the minimum possible number of times operation $3$ is performed. Print a newline at the end.

Sample

4 3
101
111
010
010

1

101 -> 111 -> 010 -> 10 -> 0 -> (空)
111    010    010    10    0
010    010
010    
                

4 4
1111
1000
1011
1010

0