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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Security.AccessControl;
using System.Security.Cryptography;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = ReadLineInt();
            var p = ReadLineIntSpilit();
            var re = 0;

            for (int i = 0; i < n-2; i++) {
                if (p[i] < p[i + 1] && p[i + 1] > p[i + 2] ) re++;
                else if (p[i] > p[i + 1] && p[i + 1] > p[i+2]) re++;
            }

            Console.WriteLine(re);
            ReadLine();
        }

        //メモ

        //アルゴリズム

        //・全探索解

        /*
         * 例 [A, B, C]
         *
         *  A - B, A - C
         *  B - C
         * 
            for (int i = 0; i < n; i++) {
           
                for (int j = i + 1; j < n; j++) {

                    array[i], array[j]

                }
            }
        */

        //配列
        
            //降順
            //var sort = array.OrderBy(x => -x).ToArray();

            //合計値
            //array.Sum();

        //切り捨て

            //double d = Math.Floor(n);

        //切り上げ
       
            //double d = Math.Celling(n);

        //kのn乗
        //(int) Math.Pow(k, n);

        //for文の逆
        //for(int i = array.Length - 1; i >= 0; i--) { }


        /// <summary>
        /// 最大公約数
        /// </summary>
        static int gcd(int a, int b)
        {
            if (a > b) {
                return gcd(b, a);
            }

            while (b != 0) {
                var remainder = a % b;
                a = b;
                b = remainder;
            }

            return a;
        }

        //最小公倍数
        static int lcm(int a, int b) => a * b / gcd(a, b);

        /// <summary>
        /// コンビネーション
        /// </summary>
        static int nCm(int n, int m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * nCm(n - 1, m - 1) / m;
        }

        /// <summary>
        /// 数字配列の重複をカウント
        /// </summary>
        public static int DistinctInt(IEnumerable<int> array)
        {
            var q = array.Distinct().Count();
            return array.Count() - q;
        }

        /// <summary>
        /// 文字配列の重複をカウント
        /// </summary>
        /// <param name="array"></param>
        /// <returns></returns>
        public static int DistinctString(IEnumerable<string> array)
        {
            var q = array.Distinct().Count();
            return array.Count() - q;
        }

        public static string ReadLine() => Console.ReadLine();
        public static int ReadLineInt() => int.Parse(Console.ReadLine());
        public static long ReadLineLongInt() => long.Parse(Console.ReadLine());
        public static string[] ReadLineStringSplit(char a = ' ') => ReadLine().Split(a).ToArray();
        public static int[] ReadLineIntSpilit(char a = ' ') => ReadLine().Split(a).Select(x => int.Parse(x)).ToArray();
        public static long[] ReadLineLongSpilit(char a = ' ') => ReadLine().Split(a).Select(x => long.Parse(x)).ToArray();
        static string[] GetAlphaLowerArray() => new string[] { "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z" };
        static string[] GetAlphaUpperArray() => new string[] { "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z" };
    }
}