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)

object Main extends App {
  val n = readInt
  val a = readLine.split(" ").map{_.toInt}
  
  if (n <= 2) println(1)
  else {
    //dp[i]; a0～a(i-1)までの最適な分け方
    val dp = Array.fill[Int](n+1)(0)
    //初期条件
    dp(1) = 1
    dp(2) = 1
    var head = 0//区切りの先頭id
    for (i <- 2 to n-1) {
      if (head == i) dp(i+1) = dp(i)
      else {
        if(a(i-2) <= a(i-1) && a(i-1) <= a(i)) dp(i+1) = dp(i)
        else if (a(i-2) >= a(i-1) && a(i-1) >= a(i)) dp(i+1) = dp(i)
        else {
          dp(i+1) = dp(i)+1
          head = i+1
        }
      }
    }
    println(dp(n))
  }
}