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.*;
public class Main {

  public static void main (String[] args) {

    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int[] p = new int[n];

    for (int i = 0; i < n; i++) {
      p[i] = sc.nextInt();
    }
    sc.close();

    int count = 0;
    
    for(int i=1; i<n-1; i++){
      int p1 = p[i-1];
      int p2 = p[i];
      int p3 = p[i+1];
      if ((p1 < p2) && (p2 < p3)){
        count++;
      } else if ((p3 < p2) && (p2 < p1)) {
        count++;
      }
    }

    System.out.println(count);

  }
  
}