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: Runtime Error)

# util functions

# debug
$debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if $debugFlag

def pd(str)
  p str if $debugFlag
end

# input
inputs = []
lc = 0
l = $stdin.gets
while l = $stdin.gets do
  if false
    inputs << l.chomp.split(" ").map(&:to_s)
  else
    inputs << l.chomp.split(" ").map(&:to_i)
  end
  lc += 1
end

# input check
if $debugFlag
  p "--- INPUT (begin) ---"
  inputs.each do |l_i|
    p l_i
  end
  p "--- INPUT (end) ---"
  print "\n"
end

# body

seq = inputs[0]
nseq = []
pre = nil
seq.length.times do |i|
  nseq << seq[i] if seq[i] != pre
  pre = seq[i]
end

pd "nseq: #{nseq}"

def proc( arr )
  if arr.size == 1
    return 1
  end
  
  mono_incr = (arr[0] < arr[1])

  idx = 0
  idx_max = arr.size - 1
  while idx < idx_max do
    if (( mono_incr and arr[idx] < arr[idx + 1]) or ( !mono_incr and arr[idx] > arr[idx + 1]))
      idx += 1
    else
      break
    end
  end

  if idx == idx_max
    return 1
  else
    return 1 + proc( arr[idx + 1..-1] )
  end
end

puts proc( nseq )