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;

class Program
{
    static void Main(string[] args)
    {
        int retValue = 0;
        int n = int.Parse(Console.ReadLine());
        var listP = new List<int>();

        // スペース区切りの整数の入力
        string[] input = Console.ReadLine().Split(' ');
        for (int i = 0; i < n; i++)
        {
            listP.Add(int.Parse(input[i]));
        }

        for (int i = 0; i < (n - 2); i++)
        {
            int p1 = listP[i];
            int p2 = listP[i + 1];
            int p3 = listP[i + 2];

            if ((p1 < p2 && p2 < p3) || (p1 > p2 && p2 > p3))
            {
                retValue++;
            }
        }


        //出力
        Console.WriteLine(retValue);

    }
}