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)

use strict;
my ($N) = split(/ /,<>);
my $s = <>;chomp $s;
my @dat = split(/ /,$s);
@dat = sort{$a<=>$b}@dat; 
my %DB;
for(my $i=0;$i<=$#dat;$i++){
  #print "$dat[$i]\n";
   my $flag =1;
   if( $dat[$i]==$dat[$i+1] ){ $DB{$dat[$i]}=2;next;}
   if( defined($DB{$dat[$i]})){  $DB{$dat[$i]}=2;next;}
   foreach my $key (sort keys %DB){
      if( $dat[$i]%$key == 0){
        $flag=0;
        last;
      }
   }
   if($flag){
     $DB{$dat[$i]}=1;       
   }
}
my $count =0;
foreach my $key (keys %DB){
    if( $DB{$key} == 1){
        $count++;
    }
}
print "$count";