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 Atcoder;
using System;
using System.Collections.Generic;
using System.ComponentModel.Design;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var ps = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

            int ret = 0;
            for (int i = 0; i < ps.Length -2; i++)
            {
                if (ps[i] < ps[i + 1] && ps[i + 1] < ps[i + 2] ||
                    ps[i] > ps[i + 1] && ps[i + 1] > ps[i + 2])
                {
                    ret++;
                }
            }
            Console.WriteLine(ret);
        }
        //static void Main(string[] args)
        //{
        //    var temp = new Atcoder.ABC130.D();
        //    temp.Run();
        //}

    }
}