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
An = gets.split.map(&:to_i).first(N)
count = 0

while An.size > 0 do
  prev_num, next_num = An.shift(2)
  break count += 1 unless next_num

  loop do
    if prev_num < next_num
      break count += 1 if An.size.zero? || next_num > An.first
      prev_num = next_num
      next_num = An.shift
    else
      break count += 1 if An.size.zero? || next_num < An.first
      prev_num = next_num
      next_num = An.shift
    end
  end
end

puts count