# 往届 ACM 队训练题 (参考)

1043. Guarding the Farm

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 $N$ ($1 < N \le 700$) rows and $M$ ($1 < M \le 700$) 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 xclusively 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 $1$.

### 输入格式

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

### 输出格式

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

### 样例

Input
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
3


### 提示

OUTPUT DETAILS:

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.