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;

namespace cs
{
    public class Program
    {
        public static void Main(string[] args)
        {
            
            var N = int.Parse(Console.ReadLine());
            var input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);

            int Cnt = 0;


            for(int i = 1; i < N-1; i++){
                if(input[i-1] <= input[i] && input[i] < input[i+1]) Cnt++;
                else if(input[i - 1] > input[i] && input[i] >= input[i+1]) Cnt++;


            }
            
            Console.WriteLine(Cnt);
            
/*
            Console.WriteLine();
            Console.WriteLine("続行するにはアレ");*/
            //Console.ReadKey();
           
        }

        public static long GCD(long n, long m){
            
            if(m % n == 0) return n;
            else return GCD(m%n, n);

        }

        public static long LCD(long n, long m){

            return m * n / GCD(n,m);
        }
    }
}