Problem Statement

There is a box divided into a grid of cells with $H$ rows and $W$ columns. It contains some strawberries.

The state of the box is represented by $S$. If $S_{x,y} = 1$, the cell in row $x$, column $y$ contains 1 strawberry. If $S_{x,y} = 0$, the cell in row $x$, column $y$ is empty.

Tomoe came up with the following method to distinguish these strawberries.

1. Define $A_{x,y}$ as the sum of $S_{i,j}$ over all pairs of integers $(i,j)$ satisfying $i = x, 1 \le j \le y$.
2. Define $B_{x,y}$ as the sum of $S_{i,j}$ over all pairs of integers $(i,j)$ satisfying $1 \le i \le x, j = y$.
3. If a strawberry exists in the cell in row $x$, column $y$, label that strawberry with the tuple $(A_{x,y},B_{x,y})$.

However, with this method, multiple strawberries may receive the same label, making them indistinguishable from each other. Therefore, she decided to add some strawberries before labeling.

More formally, she performed the operation of setting $S_{x,y} \leftarrow 1$ for some $(x,y)$ with $S_{x,y} = 0$, any number of times (0 or more).

What is the minimum number of strawberries she must add so that, when the labeling is done afterward, all strawberries receive pairwise distinct labels?

Input

$H\ W$
$S_{1,1}\ S_{1,2}\ ...\ S_{1,W}$
$S_{2,1}\ S_{2,2}\ ...\ S_{2,W}$
$\vdots$
$S_{H,1}\ S_{H,2}\ ...\ S_{H,W}$

• All inputs are integers.
• $1 \le H \le 300$
• $1 \le W \le 300$
• $0 \le S_{x,y} \le 1$

Output

Output the answer on 1 line.
Print a newline at the end.

Sample

3 2
1 0
0 1
0 1

1

4 4
0 1 1 1
1 1 1 0
1 0 1 1
1 0 1 0

2

5 5
0 0 1 0 1
0 1 0 1 0
0 0 1 0 1
0 1 0 1 0
0 0 1 0 1

8

1 1
0

0