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;

public class CSharp
{
    public static void Main()
    {
        Kyopuro chokudai = new Kyopuro();
        chokudai.AtCoder();
    }
}

public class Kyopuro
{

    int n;
    int[] p;

    public void AtCoder()
    {
        string[] input;
        n = int.Parse(Console.ReadLine());
        input = Console.ReadLine().Split(' ');
        p = new int[n];
        for(int i=0; i<n; i++)
        {
            p[i] = int.Parse(input[i]);
        }
        var x = new List<int>();
        int ans = 0;
        for(int i=1; i<n-1; i++)
        {
            x = new List<int>();
            x.Add(p[i - 1]);
            x.Add(p[i]);
            x.Add(p[i + 1]);
            x.Sort();
            if (x[1] == p[i]) ans++;
        }
        
        Console.WriteLine(ans);
        
    }
    public static void DebugWL(object x) { System.Diagnostics.Debug.WriteLine(x); }
}