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: Wrong Answer)

=begin
  1, Ai - A(i+i) を算出
  2, 前回の Ai - A(i+1)と
  2.1, 一致していればそのまま
  2.2, 不一致なら Ai までカットして ans(配列) に入れる
=end

n = gets.to_i
A = gets.split.map(&:to_i)
j = 0
old = 0
ans = []

n.times do |i|
  if i+1 == n
    ans << A.slice(j..i)
    break
  end
  pm = A[i] - A[i+1]
  old = pm if old == 0
  unless old == pm && pm >= -1 && pm <= 1
    old = 0
    ans << A.slice(j..i)
    j = i + 1
  end
end

puts ans.length