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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

public class Hello
{
	public static void Main()
	{
		var n = int.Parse(Console.ReadLine().Trim());
		string[] line = Console.ReadLine().Trim().Split(' ');
		var a = Array.ConvertAll(line, int.Parse);
		var count = 0;
		for (int i = 1; i <= n - 2; i++)
			if (check(a[i - 1], a[i], a[i + 1])) count++;
		Console.WriteLine(count);
	}
	static bool check(int a, int b, int c)
	{
		var t = new int[3];
		t[0] = a; t[1] = b; t[2] = c;
		Array.Sort(t);
		return t[1] == b;
	}
}