# #1619. [Usaco2008 Nov]Guarding the Farm 保卫牧场

#### 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

#### 样例输入

``````
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

``````

#### 样例输出

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

#### 数据范围与提示

三个山丘分别是：左上角的高度为4的方格，右上角的高度为1的方格，还有最后一行中高度为2的方格．