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)

public class Main {
	public static void main(String[] args) {
		java.util.Scanner s = new java.util.Scanner(System.in);
		int a[] = new int[s.nextInt()];
		for(int i=0;i<a.length;i++) {
			a[i]=s.nextInt();
		}
		System.out.println(calc(a));
	}
	public static int calc(int a[]) {
		int count=0;
		for(int i=0;i<a.length-2;i++) {
			if((a[i]<a[i+1] && a[i+1]<a[i+2])||
					(a[i]>a[i+1] && a[i+1]>a[i+2])){
				count++;
			}
		}
		return count;
	}
}