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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use v5.18; # strict say state
use warnings;
use List::Util qw(reduce first max min sum0);

chomp (my $n = <STDIN>);
chomp (my @a = split / /, <STDIN>);
my $ans = 0;
my ($cf, $uf, $df) = (1, 1, 1);
for my $i (1..($n-1)) {
  
  if (abs($a[$i]-$a[$i-1])>1) {
    $ans++ if $cf;
  } elsif ($a[$i]>$a[$i-1]) {
    if ($cf==0 && $df) {
      $cf = $uf = $df = 1;
      next;
    } else {
      $uf = 1;
      $df = 0;
    }
    if ($cf) {
      $ans++;
      $cf = 0;
    }
  } elsif ($a[$i]<$a[$i-1]) {
    if ($cf==0 && $uf) {
      $cf = $uf = $df = 1;
      next;
    } else {
      $uf = 0;
      $df = 1;
    }
    if ($cf) {
      $ans++;
      $cf = 0;
    }
  }
}
say $ans+$cf;