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;
class Program
{
	static void Main(string[] args)
	{
		int a = int.Parse(Console.ReadLine());
		string[] input2 = Console.ReadLine().Split(' ');
      	int[] input = new int[a];
      	int status = 0;
      	for(int j = 0; j < a; j++){
        	input[j] =int.Parse(input2[j]);
        }
      	
		for(int i = 0; i < a-2; i++){
          if(input[i] < input[i+1]){
            if(input[i+1] < input[i+2]){
              status++;
            }
          }
          
          if(input[i] > input[i+1]){
            if(input[i+1] > input[i+2]){
              status++;
            }
          }
        }
      	
      	Console.WriteLine(status);
	}
}