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.Linq;

public class Test
{
	public static void Main()
	{
		// your code goes here
		
		int n = int.Parse(Console.ReadLine());
		var p = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
		int counter = 0;
		int a = 0;
		int b = 0;
		int c = 0;
		
		for(int i=1; i!=n-1;i++){
			a = p[i-1];
			b = p[i];
			c = p[i+1];
			if(a!=c){
				if((a<=b)==(b<=c)){
					counter++;
				}
			}
		}
		
		Console.WriteLine(counter);
		
	}
}