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)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);

        scanner.nextLine();

        final String[] sp = scanner.nextLine().split(" ");
        final int[] nums = Arrays.stream(sp).mapToInt(Integer::parseInt).toArray();

        int count = 0;
        for (int i = 0; i < nums.length - 2; i++) {
            int p0 = nums[i];
            int p1 = nums[i + 1];
            int p2 = nums[i + 2];

            if (Math.max(Math.max(p0, p1), p2) != p1 && Math.min(Math.min(p0, p1), p2) != p1) {
                count++;
            }
        }

        System.out.println(count);
    }
}