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 (2.7.1) (judge verdict: Accepted)

_ = gets
a = gets.chomp.split.map(&:to_i)

res = 0
loop do
  if a.empty?
    break
  elsif a.size <= 1
    res += 1
    break
  end
  
  cur = a.shift
  if cur < a[0]
    while !a.empty? && cur <= a[0]
      cur = a.shift
    end
    res += 1
  elsif cur > a[0]
    while !a.empty? && cur >= a[0]
      cur = a.shift
    end
    res += 1
  end
  
  if a.empty?
    break
  elsif a.size <= 1
    res += 1
    break
  end
  
  cur = a.pop
  if cur < a[-1]
    while !a.empty? && cur <= a[-1]
      cur = a.pop
    end
    res += 1
  elsif cur > a[-1]
    while !a.empty? && cur >= a[-1]
      cur = a.pop
    end
    res += 1
  end
end
puts res