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: Wrong Answer)

<?php
fscanf(STDIN, "%d", $n);
$lineInput = trim(fgets(STDIN));
$A= explode(" ", $lineInput);
if(in_array(1,$A)){
    echo 0;
}else{
    if(count($a) == 1){
        echo 1;
    }else{
        
        $arr = array_unique($A);
        $dubs = array_count_values($A);
        $dubs = array_diff($dubs,array(1));
        rsort($arr);
        $ans = count($arr);
        if($ans > 1){
            for($i=0; $i<count($arr); $i++){
                if(array_key_exists($arr[$i], $dubs)){
                    $ans--;
                    break;
                }
                for($j = count($arr) - 1; $j > $i ; $j--){
                    if($arr[$i] % $arr[$j] == 0){
                        $ans--;
                        break;
                    }
                }
            
            }
        }else{
            if(array_key_exists($arr[0], $dubs)){
                $ans--;
            }
        }
    }
    echo $ans;
}

?>