The farm has many hills upon which Farmer John would like to place guards to ensure the safety of his valuable milk-cows.

He wonders how many guards he will need if he wishes to put one on top of each hill. He has a map supplied as a matrix of integers; the matrix has $N$ $(1 \lt N \le 700)$ rows and $M$ $(1 \lt M \le 700)$ columns. Each member of the matrix is an altitude $H_{ij}$ $(0 \le H_{ij} \le 10,000)$. Help him determine the number of hilltops on the map.

A hilltop is one or more adjacent matrix elements of the same value surrounded exclusively by either the edge of the map or elements with a lower (smaller) altitude. Two different elements are adjacent if the magnitude of difference in their $X$ coordinates is no greater than 1 and the magnitude of differences in their $Y$ coordinates is also no greater than 1.

Input

• Line 1: Two space-separated integers: $N$ and $M$
• Lines $2,\ldots,N+1$: Line $i+1$ describes row $i$ of the matrix with $M$ space-separated integers: $H_{ij}$

Output

• Line 1: A single integer that specifies the number of hilltops

Examples

Input 1

8 7
4 3 2 2 1 0 1
3 3 3 2 1 0 1
2 2 2 2 1 0 0
2 1 1 1 1 0 0
1 1 0 0 0 1 0
0 0 0 1 1 1 0
0 1 2 2 1 1 0
0 1 1 1 2 1 0

Output 1

3

There are three peaks: The one with height 4 on the left top, one of the points with height 2 at the bottom part, and one of the points with height 1 on the right top corner.

Problem credits: Fatih Gelgi, 2008