Problem Statement

You are given a matrix $A$ with $H$ rows and $W$ columns. The element in row $i$ and column $j$ of this matrix is denoted by $A_{i,j}$.

You may perform the following operations any number of times, $0$ or more, in any order.

• Choose the $i$-th row of the matrix $A$. Then, among the elements in the $i$-th row of $A$, all elements equal to the maximum value of the elements in the $i$-th row of $A$ are set to $0$.
• Choose the $j$-th column of the matrix $A$. Then, among the elements in the $j$-th column of $A$, all elements equal to the maximum value of the elements in the $j$-th column of $A$ are set to $0$.

Your goal is to make all elements of the matrix $A$ equal to $0$. Find the minimum number of operations required to achieve the goal.

Input

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

Constraints

Output

Output the minimum number of operations required as an integer. Print a newline at the end.

Sample

3 3
2 0 3
0 3 3
1 1 1

4

7 6
19 26 0 10 27 7
10 5 0 4 6 29
9 26 21 12 30 29
23 4 25 2 13 8
16 7 28 12 6 21
8 17 13 21 3 26
27 3 12 9 7 19

36