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;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class MainClass
{
	public static void Main(string[] args)
	{
		int n = int.Parse(Console.ReadLine());
		string[] rt = Input();
		int[] p= new int[n];
		for(int i = 0; i < n; i++)
		{
			p[i]= int.Parse(rt[i]);
		}
		int r=0;
		for(int i = 1; i< n-1;i++)
		{
			int a = p[i-1];
			int b = p[i-0];
			int c = p[i+1];
			int min = Math.Max(a, Math.Max(b, c));
			if(b==min)
				continue;
			
			if(a==min && b>= c)
			{
				r++;
			}
			else if(c==min && b >=a)
			{
				r++;
			}
		}
		Console.WriteLine(r);
	}

	public static string[] Input()
	{
		return Console.ReadLine().Split(' ');
	}

	
	public static int Clamp(int val, int max, int min = 0)
	{
		return Math.Min(max, Math.Max(min, val));
	}

	
}