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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

	public static void main (String[] args) {

		Scanner sc = new Scanner (System.in);
		
		int N = sc.nextInt();
		
		int[] list = new int [N];
		
		for (int index=0; index<N; index++){
		    list[index]=sc.nextInt();
		}

        int count = 0;
        
		for (int index=1; index<N-1; index++){
		    if (list[index]<list[index+1]&&list[index]>list[index-1]){
		        count++;
		    } else if (list[index]>list[index+1]&&list[index]<list[index-1]){
		        count ++;
		    }
		}
		
		System.out.println(count);

		sc.close();
	}
}