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)

N=gets.to_i
ary=gets.split.map(&:to_i)

pos_prev = 0
count = 0
type = :NONE
1.upto(N-1) do |n|
  case type
  when :NONE
      if ary[n] == ary[pos_prev]
        pos_prev = n
        next
      end
      if ary[n] < ary[pos_prev]
      type = :DEC
    else
      type = :INC
    end
  when :INC
    if ary[n] < ary[pos_prev]
      count += 1
      type = :NONE
    end
  when :DEC
    if ary[pos_prev] < ary[n]
      count += 1
      type = :NONE
    end
  end
  pos_prev = n
end
puts count + 1