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.*;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		int n = Integer.parseInt(in.readLine());
		int[] p = new int[n];
		String[] tokens = in.readLine().split(" ");
		for (int i = 0; i < n; ++i) {
			p[i] = Integer.parseInt(tokens[i]);
		}
		long count = 0;
		for (int i = 1; i + 1 < n; ++i) {
			if (check(p, i - 1, i, i + 1)) {
				++count;
			}
		}

		System.out.println(count);
		in.close();
	}

	static boolean check(int[] p, int i, int j, int k) {
		if (p[i] < p[j] && p[j] < p[k]) {
			return true;
		} else if (p[i] > p[j] && p[j] > p[k]) {
			return true;
		} else {
			return false;
		}
	}

}