Problem:
Score : 300 points

Problem Statement

You are given an array A of length N.
Your task is to divide it into several contiguous subarrays.
Here, all subarrays obtained must be sorted in either non-decreasing or non-increasing order.
At least how many subarrays do you need to divide A into?

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Each A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible number of subarrays after division of A.

Sample Input 1

6
1 2 3 2 2 1

Sample Output 1

2

One optimal solution is to divide the array into [1,2,3] and [2,2,1].

Sample Input 2

9
1 2 1 2 1 2 1 2 1

Sample Output 2

5

Sample Input 3

7
1 2 3 2 1 999999999 1000000000

Sample Output 3

3

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;
using System.Diagnostics;
using System.Text;

public class Program{
    public static void Main(){
        var watch = new Stopwatch();
        watch.Start();
        var isTest = false;
        var stream = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
        Console.SetOut(stream);
        TextReader reader;
        string filename="";
        if(filename.Length!=0){
            reader = new StreamReader(filename);
        }else{
            reader = Console.In;
        }

        var n = int.Parse(reader.ReadLine());
        //頭からなめていくしかないよね
        var a = reader.ReadLine().Split().Select(int.Parse).ToArray();
        Queue<int> lis = new Queue<int>();
        int count = 1;
        for(int i=0; i<n; i++){
            if(lis.Count()!=2){
                lis.Enqueue(a[i]);
            }else{
                int[] vector = lis.ToArray();
                //負なら単調増加、正なら単調減少 差がゼロなら無視
                var dif = vector[0]-vector[1];
                if(dif!=0){
                    
                    if( (dif<0 && (vector[1]>a[i])) || (dif>0 && (vector[1]<a[i])) ){
                        lis.Clear();
                        count++;
                    }
                    //Console.WriteLine($"vector[1] = {vector[1]}");
                    //Console.WriteLine($"a[{i}] = {a[i]}");
                }
                lis.Enqueue(a[i]);
                if(lis.Count>2)lis.Dequeue();
            }
        }
        Console.WriteLine(count);

        watch.Stop();
        if(isTest){
            Console.WriteLine($"実行時間{watch.ElapsedMilliseconds}ミリ秒");
        }
        Console.Out.Flush();
    }
}