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 static System.Console;
using static System.Math;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace TemplateAlgorithm
{
    class Program
    {
        public const long Inf = (long)1e18;
        public const double eps = 1e-6;
        public const string alfa = "abcdefghijklmnopqrstuvwxyz";
        public const string ALFA = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
        public const int MOD = 1000000007;


        static void Main(string[] args)
        {
            int n = IO.ReadInt();
            var a  = IO.ReadIntArr();

            int count = 0;
            for (var i = 1; i < n-1; i++)
            {
                if (a[i - 1] < a[i] && a[i] < a[i + 1]) count++;
                else if (a[i - 1] > a[i] && a[i] > a[i + 1]) count++;
            }
            WriteLine(count);
        }

        static int ToInt(char c) => c - '0';

        #region MIN,MAX

        /// <summary>
        /// 最大値を返す
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="vals"></param>
        /// <returns></returns>
        public static T MaxValue<T>(params T[] vals) => vals.Max();

        /// <summary>
        /// 最小値を返す
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="vals"></param>
        /// <returns></returns>
        public static T MinValue<T>(params T[] vals) => vals.Min();
        #endregion
    }

    #region IO

    /// <summary>
    /// IO
    /// </summary>
    public class IO
    {
        public static string ReadStr(bool isTrim = false) => (isTrim) ? ReadLine().Trim() : ReadLine();
        public static int ReadInt() => int.Parse(ReadStr());

        public static long ReadLong() => long.Parse(ReadStr());

        public static decimal ReadDecimal() => decimal.Parse(ReadStr());
        public static double ReadDouble() => double.Parse(ReadStr());
        public static string[] ReadStrArr(char separator = ' ') => ReadLine().Split(separator);
        public static int[] ReadIntArr() => Array.ConvertAll(ReadStrArr(), int.Parse);
        public static long[] ReadLongArr() => Array.ConvertAll(ReadStrArr(), long.Parse);

        public static decimal[] ReadDecimalArr() => Array.ConvertAll(ReadStrArr(), decimal.Parse);
        public static double[] ReadDoubleArr() => Array.ConvertAll(ReadStrArr(), double.Parse);

        public static void Cout<T>(T value) => WriteLine(value);
        public static void CoutJoin<T>(T[] values, string separator = " ") => Cout(string.Join(separator, values));
    }

    #endregion    
}