p02988 AtCoder Beginner Contest 132 - Ordinary Number_16996
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.

Examples

Input

5
1 3 5 4 2


Output

2


Input

9
9 6 3 2 5 8 7 4 1


Output

5
import java.util.Scanner;
public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int []a = new int [n];
		int count = 0;
		for(int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		for(int i = 0; i < n - 2; i++) {
			if((a[i+1] > a[i] && a[i+1] < a[i+2]) || (a[i+1] < a[i] && a[i+1] > a[i+2])) {
				count++;
			}
		}
		System.out.println(count);
		
		

	}

}
