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: Accepted)

using System;
using System.Linq;
using System.Numerics;
using System.Collections;
using System.Collections.Generic;

public class Program {
    static void Main (string[] args) {
        var n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split().Select(x => int.Parse(x)).ToList();
        
        var aa = new List<int>();
        aa.Add(a[0]);
        for (int i = 1; i < n; ++i) {
            if (a[i - 1] != a[i]) { aa.Add(a[i]); }
        }
        
        if (aa.Count == 1) {
            Console.WriteLine(1);
            return;
        }
        
        var cnt = 1;
        var b = aa[1] - aa[0] < 0 ? -1 : 1;
        for (int i = 1; i < aa.Count; ++i) {
            var d = aa[i] - aa[i - 1] < 0 ? -1 : 1;
            if (!(d == b)) {
                cnt += 1;
                if (i < aa.Count-1) { b = aa[i + 1] - aa[i] < 0 ? -1 : 1; }
            } else {
                b = d;
            }
        }
        Console.WriteLine(cnt);
    }
}