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 sc = new Scanner(System.in);
    int n = Integer.parseInt(sc.nextLine());
    String str = sc.nextLine();
    List<String> strList = Arrays.asList(str.split(" "));
    List<List<Integer>> list = new ArrayList<List<Integer>>();
    for(int i = 0; i < n - 2; i++){
      	List<Integer> tmp = new ArrayList<Integer>();
      	tmp.add(Integer.parseInt(strList.get(i)));
      	tmp.add(Integer.parseInt(strList.get(i+1)));
      	tmp.add(Integer.parseInt(strList.get(i+2)));
      	list.add(tmp);
    }
    int count = 0;
    for(int i = 0; i < list.size(); i++){
      List<Integer> tmp = list.get(i);
      if(test(tmp, tmp.get(2)) == true){
        count++;
      }
    }
    System.out.print(count);
  }
  public static boolean test(List<Integer> list, int secondElem){
  	boolean ret = false;
    Collections.sort(list);
    if(list.get(1) == secondElem){
      if(list.get(1) != list.get(0) && list.get(1) != list.get(2)){
	    ret = true;
      }
    }
    return ret;
  }
}