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: Accepted)

<?php
list($n) = ints();
$a = ints();
for ($i = 0; $i < $n; ++$i) {
    if (isset($cnt[$a[$i]])) $cnt[$a[$i]]++;
    else $cnt[$a[$i]] = 1;
}
ksort($cnt);
if (isset($cnt[1])) {
    if ($cnt[1] > 1) exit('0');
    else exit('1');
}
$max = max($a);
$isPrime = isPrimeArr($max);
$ans = 0;
foreach ($cnt as $i => $v) {
    if ($v === 1 && $isPrime[$i]) $ans++;
}
echo $ans;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}

function isPrimeArr($max)
{
    global $cnt;
    $arr = array_fill(0, $max + 1, true);
    $arr[0] = false;
    foreach ($cnt as $i => $v) {
        for ($j = 2 * $i; $j <= $max; $j += $i) {
            $arr[$j] = false;
        }
    }
    return $arr;
}