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;
using System.Linq;

namespace debug
{
    public static partial class Program
    {
        public static void Main()
        {
            n = Console.ReadLine().ToLong();
            var pis = Console.ReadLine().ArrayLongs();

            long cnt = 0;
            for (int i1 = 1; i1 < n - 1; i1++)
            {
                var list = new List<long>();
                list.Add(pis[i1 - 1]);
                list.Add(pis[i1]);
                list.Add(pis[i1 + 1]);
                list.Sort();
                if (list[1] == pis[i1])
                {
                    cnt++;
                }
            }

            Console.WriteLine(cnt);
        }
    }

    public static partial class Program
    {
        //テンプレここから
        public static long 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;
        public static long GCD(long aaa, long bbb) => bbb == 0 ? aaa : GCD(bbb, aaa % bbb);
        public static long LCM(long aaa, long bbb) => aaa * bbb / GCD(aaa, bbb);
        public static long ToLong(this double ddd) => (long) ddd;
        public static long ToLong(this string str) => long.Parse(str);
        public static long[] ToLong(this IEnumerable<string> strs) => strs.Select(x => x.ToLong()).ToArray();
        public static long[] ArrayLongs(this string str, char opr = ' ') => str.Split(opr).ToLong();
        public static long Diff(long aaa, long bbb) => Math.Abs(Math.Max(aaa, bbb) - Math.Min(aaa, bbb));
        public static long Sign(this long iii) => Math.Sign(iii);
        public static bool IsEven(this long iii) => iii % 2 == 0;
        public static readonly int[] Dx = {0, -1, 0, 1};
        public static readonly int[] Dy = {-1, 0, 1, 0};
        public const int MOD = 1000000007;
        public const string alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
        public const string ALPHABET = "abcdefghijklmnopqrstuvwxyz";
        public static long ToLong(this char ccc) => ccc.ToString().ToLong();
        public static string Join(this IEnumerable<string> array, string sep = "") => string.Join(sep, array);
        public static string Join(this IEnumerable<char> array, string sep = "") => string.Join(sep, array);
        public static string JoinToStr(this IEnumerable<long> array, string sep = "")
            => array.Select(xxx => xxx.ToString()).Join(sep);
        //テンプレここまで
    }
}