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);
$list = fscanf(STDIN, str_repeat("%d", $N));
sort($list);
$bai_list  = [];
$same_list = [];
$ans = 0;
if($list[0] === 1){
    echo 0;
    exit;
}
foreach($list as $value){
    if(isset($same_list[$value])){
        if($same_list[$value] == 1){
            $ans--;
            $same_list[$value] = 2;
        }
    }elseif(!isset($bai_list[$value])){
        $no = $value;
        while($no < 1000000){
            $bai_list[$no] = 1;
            $no += $value;
        }
        $bai_list[$no] = 1;
        $same_list[$value] = 1;
        $ans++;
    }else{
        $same_list[$value] = 2;
    }
}

echo $ans;