# [USACO08NOV]守护农场Guarding the Farm

## 题目描述

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 <= 700) rows and M (1 < M <= 700) columns. Each member of the matrix is an altitude H\_ij (0 <= H\_ij <= 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.

## 输入输出格式

### 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

## 输入输出样例

### 输入样例 #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
``````

### 输出样例 #1

``````3
``````

## 说明

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.