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.IO;
using System.Collections.Generic;

namespace _132
{
    class Program
    {
        static void Main(string[] args)
        {
            solve_132B();
        }


        public static void solve_132B()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            string[] test = Console.ReadLine().Split(' ');

            int[] p = Array.ConvertAll(test, int.Parse);
            int count = 0;
            for (int i = 1; i < n; i++)
            {
                if (i < n - 1 && ((p[i] > p[i - 1] && p[i] < p[i + 1]) || (p[i] > p[i + 1] && p[i] < p[i - 1])))
                {
                    count++;
                }
            }

            Console.WriteLine(count);
        }
        public static void solve_132A()
        {
            string a = Console.ReadLine();

            char[] str = a.ToCharArray();

            Array.Sort(str);
            
            string ansewr = "Yes";
            if (str[0] != str[1] || str[2] != str[3] || str[0] == str[2])
            {
                ansewr = "No";
            }

            Console.WriteLine(ansewr);
        }
    }
}