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: Runtime Error)

import java.util.Scanner;
import java.util.InputMismatchException;

public class Main{
	public static void main(String[] args){
		Scanner scanner = new Scanner(System.in);
		String inputN = scanner.nextLine();
		
		scanner = new Scanner(System.in);
		String inputP = scanner.nextLine();
		String[] pStr = inputP.split(" ", 0);
		
		int n = Integer.parseInt(inputN);
		int pInt[] = new int[n];
		for(int i=0;i<n;i++){
			pInt[i] = Integer.parseInt(pStr[i]);
		}
		
		int iCount = 0;
		
		for(int i=0;i+2<n;i++){
			if(pInt[i] > pInt[i+1] && pInt[i+1] > pInt[i+2]){
				iCount++;
			} else if(pInt[i] < pInt[i+1] && pInt[i+1] < pInt[i+2]){
				iCount++;
			}
		}
		
		System.out.println(iCount);
	}
}