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
A = gets.split.map(&:to_i)

def gte(start)
  current = A[start]
  (start...N).each do |i|
    next_v = A[i]
    if next_v < current
      return i
    end
    current = next_v
  end
  return N
end

def lte(start)
  current = A[start]
  (start...N).each do |i|
    next_v = A[i]
    if A[i] > current
      return i
    end
    current = next_v
  end
  return N
end


ans = 0
i = 0
while i < N
  i = [gte(i), lte(i)].max
  ans += 1
end
puts ans