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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.InputStreamReader
import java.io.BufferedReader

fun main(args: Array<String>) {
  val br = BufferedReader(InputStreamReader(System.`in`))

  val n = br.readLine().toInt()
  val seq = br.readLine().split(" ").map { it.toInt() }.toIntArray()

  tailrec fun rec(acc: Int, pre: Int, i: Int, sign: Int): Int {
    return when {
      i == n -> acc
      pre == seq[i] && sign == 0 -> rec(acc, seq[i], i+1, 0)
      pre < seq[i] && sign == 0 -> rec(acc, seq[i], i+1, 1)
      pre > seq[i] && sign == 0 -> rec(acc, seq[i], i+1, -1)
      pre <= seq[i] && sign > 0 -> rec(acc, seq[i], i+1, 1)
      pre >= seq[i] && sign < 0 -> rec(acc, seq[i], i+1, -1)
      else -> rec(acc+1, seq[i], i+1, 0)
    }
  }

  val ans = rec(1, seq[0], 1, 0)
  println(ans)
}