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 Ruby (2.3.3) (judge verdict: Wrong Answer)

  n = gets.to_i
  a = gets.chomp.split(" ").map(&:to_i)
  r = 0
  sa_value = []
  skip = 0
  (n-1).times do |i|
    sa_value[i] = a[i+1]-a[i]
  end
  (n-2).times do |i|
    if skip == 1
      skip = 0
      next
    else
      if sa_value[i] == 0
        next
      elsif sa_value[i+1] == 0
        next
      else
        if sa_value[i] == sa_value[i+1]
          next
        else
          r += 1
          skip = 1
        end
      end
    end
  end
  puts r+1