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.split.map(&:to_i)

b, c, f=a[0], 0, -1
(1...n).each do |i|
  e=a[i]
  if f==-1 # ?
    if b<e
      f=0
    elsif b>e
      f=1
    else
      f=-1
    end
  elsif f==0 # increasing
    if b<=e
      #
    else
      f=-1
      c+=1
    end
  elsif f==1 # dec
    if b>e
      #
    else
      f=-1
      c+=1
    end
  else # yabai
    #
  end
  b=e
end

puts c+1