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);
$a_list = explode(' ', trim(fgets(STDIN)));
sort($a_list);

$answer = 0;
for ($i = 0; $i < $n; ++$i) {
    for ($j = 0; $j < $i; ++$j) {
        if ($i === $j) {
            continue;
        }
        if ($a_list[$i] % $a_list[$j] === 0) {
            continue 2;
        }
    }

    ++$answer;
}

echo $answer;