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)

def f(a)
  count = 1
  greaterp = nil
  a.inject{|r, n|
    next r if r == n
    if greaterp.nil?
      greaterp = r > n
    end
    # p [greaterp, r, n, count]
    if greaterp
      if r < n
        greaterp = nil
        count += 1
      end
    else
      if r > n
        greaterp = nil
        count += 1
      end
    end
    n
  }
  count
end

N = gets.to_i
A = gets.split.map(&:to_i)
puts f(A)