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)

#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;  // cannot be used in GCJ
using System.Text;
using System.Threading.Tasks;

namespace Contest
{
    public class Program
    {
        public static IO.StreamScanner scanner = new IO.StreamScanner(Console.OpenStandardInput());

        public static void Main()
        {
            var n = scanner.Integer();
            var ps = scanner.ScanLine().Split().Select(v => int.Parse(v)).ToArray();
            IO.Printer.Out.WriteLine(GetAns(n, ps));
            IO.Printer.Out.Flush();
        }

        public static int GetAns(int n, int[] ar)
        {
            var ret = 0;
            for (int i = 1; i < n - 1; i++)
            {
                var wk = new int[] { ar[i - 1], ar[i], ar[i + 1] }.OrderBy(v => v).ToArray();
                if (wk[1] == ar[i]) ret++;
            }

            return ret;
        }
    }
    

#if DEBUG

    [TestClass]
    public class Test
    {
        [TestMethod]
        public void Test1()
        {
            Assert.AreEqual(2, Program.GetAns(5, new int[] { 1, 3, 5, 4, 2 }));
        }

        public static bool IsEq(IEnumerable<IEnumerable<int>> l1, IEnumerable<IEnumerable<int>> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i < l1.Count(); i++)
            {
                if (!IsEq(l1.ElementAt(i), l2.ElementAt(i))) return false;
            }
            return true;
        }

        public static bool IsEq(IEnumerable<int> l1, IEnumerable<int> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for(int i=0; i<l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        public static bool IsEq(IEnumerable<double> l1, IEnumerable<double> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i < l1.Count(); i++)
            {
                if (!IsEq(l1.ElementAt(i), l2.ElementAt(i))) return false;
            }
            return true;
        }

        public static bool IsEq(IEnumerable<bool> l1, IEnumerable<bool> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i < l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        public static bool IsEq(double a, double b)
        {
            return Math.Abs(a - b) < 1E-5;
        }
    }


#endif

    // Used in LeetCode
    public class TreeNode
    {
        public int val;
        public TreeNode left;
        public TreeNode right;
        public TreeNode(int x) { val = x; }
    }

    public static class LeetCode
    {
        public static TreeNode ParseBinaryTree(string str)
        {
            var ar = str.Replace("[", "").Replace("]", "").Split(',');

            var nodes = new List<TreeNode>();
            for (int i = 0; i < ar.Length; i++)
            {
                nodes.Add(ar[i] == "null" ? null : new TreeNode(int.Parse(ar[i])));
                var parent = (i + 1) / 2 - 1;

                // if the node class parent property
                //if(parent >= 0)
                //{
                //    nodes.Last().Parent = nodes[parent];
                //}
            }

            for (int i = 0; i < nodes.Count(); i++)
            {
                var l = (i + 1) * 2 - 1;
                var r = (i + 1) * 2;
                if (l >= 0 && l < nodes.Count() && nodes[i] != null) nodes[i].left = nodes[l];
                if (r >= 0 && r < nodes.Count() && nodes[i] != null) nodes[i].right = nodes[r];
            }

            return nodes.First();
        }

        public static IList<IList<int>> ParseLLI(string str)
        {
            var ret = new List<IList<int>>();

            var split = str.Split(']');
            foreach (var s in split)
            {
                var v = s.Replace(",[", "").Replace(", [", "").Replace("[", "");
                if (string.IsNullOrWhiteSpace(v))
                {
                    ret.Add(new List<int>());
                    continue;
                }
                ret.Add(v.Split(',').Select(i => int.Parse(i)).ToList());
            }

            return (IList<IList<int>>)ret;
        }

        public static IList<int> ParseLI(string str)
        {
            str = str.Replace("[", "").Replace("]", "");
            return str.Split(',').Select(v => int.Parse(v)).ToList();
        }
    }

    namespace IO
    {
        using System.IO;
        using System.Text;
        using System.Globalization;

        public class Printer : StreamWriter
        {
            static Printer()
            {
                Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
            }

            public static Printer Out { get; set; }

            public override IFormatProvider FormatProvider
            {
                get { return CultureInfo.InvariantCulture; }
            }

            public Printer(Stream stream)
                : base(stream, new UTF8Encoding(false, true))
            {
            }

            public Printer(Stream stream, Encoding encoding)
                : base(stream, encoding)
            {
            }

            public void Write<T>(string format, T[] source)
            {
                base.Write(format, source.OfType<object>().ToArray());
            }

            public void WriteLine<T>(string format, T[] source)
            {
                base.WriteLine(format, source.OfType<object>().ToArray());
            }
        }

        public class StreamScanner
        {
            public StreamScanner(Stream stream)
            {
                str = stream;
            }

            public readonly Stream str;
            private readonly byte[] buf = new byte[1024];
            private int len, ptr;
            public bool isEof;

            public bool IsEndOfStream
            {
                get { return isEof; }
            }

            private byte read()
            {
                if (isEof) return 0;
                if (ptr < len) return buf[ptr++];
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
                isEof = true;
                return 0;
            }

            public char Char()
            {
                byte b;
                do b = read(); while ((b < 33 || 126 < b) && !isEof);
                return (char)b;
            }

            public string Scan()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                    sb.Append(b);
                return sb.ToString();
            }

            public string ScanLine()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b != '\n'; b = (char)read())
                    if (b == 0) break;
                    else if (b != '\r') sb.Append(b);
                return sb.ToString();
            }

            public long Long()
            {
                if (isEof) return long.MinValue;
                long ret = 0;
                byte b;
                var ng = false;
                do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
                if (b == 0) return long.MinValue;
                if (b == '-')
                {
                    ng = true;
                    b = read();
                }
                for (; ; b = read())
                {
                    if (b < '0' || '9' < b)
                        return ng ? -ret : ret;
                    ret = ret * 10 + b - '0';
                }
            }

            public int Integer()
            {
                return (isEof) ? int.MinValue : (int)Long();
            }

            public double Double()
            {
                var s = Scan();
                return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
            }

            static T[] enumerate<T>(int n, Func<T> f)
            {
                var a = new T[n];
                for (int i = 0; i < n; ++i) a[i] = f();
                return a;
            }

            public char[] Char(int n)
            {
                return enumerate(n, Char);
            }

            public string[] Scan(int n)
            {
                return enumerate(n, Scan);
            }

            public double[] Double(int n)
            {
                return enumerate(n, Double);
            }

            public int[] Integer(int n)
            {
                return enumerate(n, Integer);
            }

            public long[] Long(int n)
            {
                return enumerate(n, Long);
            }
        }
    }
}