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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
$n=trim(fgets(STDIN));
if($n==1){
  echo 1;
  exit;
}
$a=explode(" ",trim(fgets(STDIN)));
sort($a);
$ans=0;
$b=array();
$i=0;
while($i<count($a)){
  $j=1;
  $e=0;
  while($j<count($a)){
    if($a[$j]%$a[0]!=0){
      $b[]=$a[$j];
    }else{
      if($a[$j]==$a[0]){
        ++$e;
      }
    }
    ++$j;
  }
  if($e==0){
    ++$ans;
  }
  if(isset($b)){
    $a=$b;
    unset($b);
  }else{
    break;
  }
}
echo $ans;