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 string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("5");
            WillReturn.Add("1 3 5 4 2");
            //2
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("9");
            WillReturn.Add("9 6 3 2 5 8 7 4 1");
            //5
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        int[] PArr = InputList[1].Split(' ').Select(X => int.Parse(X)).ToArray();

        int Answer = 0;
        int UB = PArr.GetUpperBound(0);
        for (int I = 0; I <= UB; I++) {
            var PList = new List<int>();
            for (int J = I; J <= I + 2 && J <= UB; J++) {
                PList.Add(PArr[J]);
            }
            if (PList.Count == 3) {
                if (PList[0] < PList[1] && PList[1] < PList[2]) {
                    Answer++;
                }
                else if (PList[0] > PList[1] && PList[1] > PList[2]) {
                    Answer++;
                }
            }
        }
        Console.WriteLine(Answer);
    }
}