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: Accepted)

#!/usr/bin/perl
use POSIX qw(floor);

my ($n) = map { $_ - 0 } split(/\s+/,<STDIN>);
my @A = map { $_ - 0 } split(/\s+/,<STDIN>);

if( $n == 1 ){
  print "1\n";
  exit(0);
}

my %ka = ();
for(my $i=0;$i<$n;$i++){
  $ka{$A[$i]} ++;
}

my @f = ();
$#f = 1000000;

if( $ka{'1'} > 1 ){
  print "0\n";
  exit(0);
}
if( $ka{'1'} == 1 ){
  print "1\n";
  exit(0);
}

my @ka1 = sort { $a <=> $b } map { $_ - 0 } keys %ka;

my $tot = $n;
for(my $i=0;$i<=$#ka1;$i++){
  my $ka2 = $ka1[$i] - 0;
  if( $f[$ka2] ){
    $tot -= $ka{$ka2};
    next;
  }
  if( $ka{$ka2} > 1 ){
    $tot -= $ka{$ka2};
  }
  my $j = 2;
  while( $ka2 * $j <= 1000000 ){
    $f[$ka2 * $j] = 1;
    $j++;
  }
}
print "$tot\n";

exit(0);