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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

//created by Whiplash99
import java.io.*;
import java.util.*;
public class Main
{
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        N=Integer.parseInt(br.readLine().trim());
        String s[]=br.readLine().trim().split(" ");
        int a[]=new int[N];
        for(i=0;i<N;i++) a[i]=Integer.parseInt(s[i]);

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