Mountain Valleys

Problem Description

There is a mountainous area, which can be viewed as a grid with $N$ rows and $M$ columns. The altitude at row $i$, column $j$ is $h_{i,j}$.

If a cell's altitude is not greater than the altitude of all of its neighboring cells (neighbors include up, down, left, right, and the four diagonals — up to $8$ directions in total), then the cell is called a valley.

Count how many valleys there are in the mountainous area.

Input Format

The first line contains $2$ integers $N, M$, the size of the mountainous area.

The following $N$ lines each contain $M$ integers $h_{i,1}, h_{i,2}, \dots, h_{i,M}$, the altitudes.

Output Format

Output $1$ line containing $1$ integer $C$, the number of valleys.

Sample Input

3 5
7 6 6 7 9
6 5 6 7 6
6 5 7 8 9

Sample Output

3

Sample Explanation

In the given $3 \times 5$ grid, there are $3$ valleys in total, located at positions $(2,2)$ (altitude $5$), $(3,2)$ (altitude $5$), and $(2,5)$ (altitude $6$). Each of these positions has an altitude not greater than that of its surrounding cells (up to $8$ neighbors).

Constraints

$1 \le N, M \le 100$ and $1 \le h_{i,j} \le 10^5$ are guaranteed.