Problem:
Score : 200 points

Problem Statement

We have a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n}.

Print the number of elements p_i (1 < i < n) that satisfy the following condition:

p_i is the second smallest number among the three numbers p_{i - 1}, p_i, and p_{i + 1}.

Constraints

All values in input are integers.

3 \leq n \leq 20

p is a permutation of {1,\ 2,\ ...,\ n}.

Input

Input is given from Standard Input in the following format:

n
p_1 p_2 ... p_n

Output

Print the number of elements p_i (1 < i < n) that satisfy the condition.

Sample Input 1

5
1 3 5 4 2

Sample Output 1

2

p_2 = 3 is the second smallest number among p_1 = 1, p_2 = 3, and p_3 = 5. Also, p_4 = 4 is the second smallest number among p_3 = 5, p_4 = 4, and p_5 = 2. These two elements satisfy the condition.

Sample Input 2

9
9 6 3 2 5 8 7 4 1

Sample Output 2

5

Solution in Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.*;
 
public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
	    int[] number = new int[N];
	    int count = 0;

	    for(int i=0; i<N; i++){
	      number[i] = sc.nextInt();
	    }
	    for(int i=1; i<N-1; i++){
	      if((number[i-1]<=number[i])&&(number[i]<=number[i+1])){
	        count++;
	      }else if((number[i+1]<=number[i])&&(number[i]<=number[i-1])){
	        count++;
	      }
	    }
	    System.out.println(count);
	}

}