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 total=0;
      	int p[]=new int[n];
      
      	for(int t=0;t<n;t++){
        	p[t]= sc.nextInt();
        }
      	
      	for(int k=0;k<n-2;k++){
        	if(p[k]<p[k+1]){
            	if(p[k+1]<p[k+2]){
                	total+=1;
                }
            }else{
            	if(p[k+2]<p[k+1]){
                	total+=1;
                }
            }
        }
      	
      	System.out.println(total);
      
      
    }
}