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: Wrong Answer)

import java.util.*; 
 
public class Main{
  
  public static void main (String [] args){
    Scanner scanner = new Scanner(System.in);     
    int num1 = scanner.nextInt();
    
    int a [ ] = new int [num1];
    
    int t = 0;
    
    for(int i = 1; i < a.length-1; i++) {
      a[i]=scanner.nextInt();
      
      if((a[i-1] < a[i]) && (a[i] < a[i+1])){
        t++;  
      
      } else if ((a[i-1] > a[i]) && (a[i] > a[i+1])) {
        t++;
       
      }
    }
    System.out.println(t);    
  }
  
}