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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.util.Scanner

object Main extends App {

  val sc = new Scanner(System.in)

  val n = sc.nextInt
  val al = Vector.fill(n)(sc.nextInt)

  val res = loop(al).length
  println(res)


  def loop(list: Vector[Int]): Vector[Vector[Int]] = {
    val (res1, res2, _) =
      list.tail.foldLeft( (Vector.empty[Vector[Int]], Vector(list.head), list.head) ){ case ( (acc , stack, pre), now) =>
        if(stack.length == 1) (acc, stack :+ now, now)
        else {
          val booby = stack.init.last
          if(
            booby <= pre && pre <= now ||
            booby >= pre && pre >= now
          ) (acc, stack :+ now, now)
          else ( acc :+ stack, Vector(now), now )
        }
      }

    res1 :+ res2
  }
}