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.chomp.to_i
arr = gets.chomp.split(" ").map(&:to_i)
newArr = []

# 増加 or 減少
isUp = false
isDown = false

count = 1

(arr.size-1).times do |id|
  chk = arr[id+1] - arr[id]
#  puts %(id : #{id} #{arr[id]} , #{arr[id+1]})

  if isUp
    if chk == 1 || chk == 0
      newArr << arr[id]
    else
      isUp = false
      count += 1
      newArr << arr[id]
      newArr << "|"
      next
    end
  end

  if isDown
    if chk == -1 || chk == 0
      newArr << arr[id]
    else
      isDown = false
      count += 1
      newArr << arr[id]
      newArr << "|"
      next
    end
  end

  if isDown == false && isUp == false
    newArr << arr[id]
    case chk
      when 1
        isUp = true
        isDown = false
      when -1
        isDown = true
        isUp = false
      when 0
      else
        isUp = false
        isDown = false
        count += 1
        newArr << "|"
    end
  end

#  puts %(chk:#{chk})
#  puts %(isUp:#{isUp}, isDown:#{isDown})
#  puts count

end

#p newArr
puts count