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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.io.*;
import java.util.Scanner;

class Main{
    public static void main(String args[]){
        int count = 0;
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        String[] a =new String[n];
        int[] b = new int[n];
        try{
            BufferedReader br = new BufferedReader (new InputStreamReader(System.in));
            String str = br.readLine();
                a =str.split(" ");
            for(int j = 0; j<n;j++){
                b[j] = Integer.parseInt(a[j]);
            }
            for(int i = 0;i < n-2;i++){
                if(b[i]<b[i + 1]&& b[i + 1]<b[i + 2]){
                    count++;
                }else if(b[i]>b[i + 1]&&b[i + 1]>b[i + 2]){
                    count++;
                }
            }
            System.out.print(count);
        }catch(IOException e){
        }
    }
}