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)

gets
xs = gets.chomp.split.map(&:to_i)

count = 0
state = :none
before_x = :none
xs.each do |x|
    if state == :none
        state = :mono_decreasing_and_mono_increasing
        count = count + 1
    elsif state == :mono_decreasing_and_mono_increasing
        if x > before_x
            state = :mono_increasing
        elsif x < before_x
            state = :mono_decreasing
        else
            state = :mono_decreasing_and_mono_increasing
        end
    elsif state == :mono_increasing
        if x < before_x
            state = :mono_decreasing_and_mono_increasing
            count = count + 1
        end
    elsif state == :mono_decreasing
        if x > before_x
            state = :mono_decreasing_and_mono_increasing
            count = count + 1
        end
    end

    before_x = x
end

puts count