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.

INPUT:
* 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

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

Input:
Output: