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)

require 'pp'

# 入力値を数値で返却する
def gets_i()
  gets.chomp.to_i
end

# 空白区切の入力値を数値の配列で返却する
def gets_i_list()
  gets.chomp.split(" ").map(&:to_i)
end

N = gets_i
a_list = gets_i_list

count = 0
type = 0

a_list.each_with_index do |a, i|
  next_a = a_list[i+1]
  break if next_a.nil?
  case type
  when 0
    type = next_a <=> a
  when -1
    # 減少
    if next_a <= a
      next
    else
      count += 1
      type = 0
    end
  when 1
    # 増加
    if next_a >= a
      next
    else
      count += 1
      type = 0
    end
  end
end

puts count + 1