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: Accepted)

n = gets.to_i
as = gets.split.map(&:to_i)

state = 0
ans = 1
bef = nil
as.each do |a|
  if state == 1
    if bef < a
      ans += 1
      state = 0
    end
  elsif state == 2
    if bef > a
      ans += 1
      state = 0
    end
  elsif bef != nil
    state =
      if bef < a
        2
      elsif bef > a
        1
      end
  end

  bef = a
end
puts ans