Problem:
Score : 400 points

Problem Statement

Given is a number sequence A of length N.

Find the number of integers i \left(1 \leq i \leq N\right) with the following property:

For every integer j \left(1 \leq j \leq N\right) such that i \neq j , A_j does not divide A_i.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5

Solution in Perl (5.26.1) (judge verdict: Time Limit Exceeded)

my $N = 0;
my $cnt = 0;
while(<STDIN>)
{
  chomp $_;
  my @cols = split(" ", $_);
  if($cnt == 0) {
    $N = $cols[0];
    $cnt++;
  }elsif($cnt == 1) {
    my $num = $N;
    my %dup;
    foreach my $val (@cols) {
      if( exists($dup{$val}) ) {
        $dup{$val} += 1;
      }else {
        $dup{$val} = 1;
      }
    }
    my @nrs = keys(%dup);
    my @neos = sort {$b <=> $a} @nrs;
    my $neo_num = @neos;
    for(my $i=0; $i < $neo_num; $i++) {
      my $val = $neos[$i];
      if($dup{$val} > 1) {
        $num = $num - $dup{$val};
      }elsif($i == ($neo_num-1)) {
      }else {
        for(my $j=($i+1); $j < $neo_num; $j++) {
          my $cur = $val % $neos[$j];
          if( $cur == 0 ) {
            $num--;
            last;
          }
        }
      }
    }
    print $num;
  }
}