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));
$nums =  explode(" ", trim(fgets(STDIN)));
sort($nums);
$ans =  0;
foreach ($nums as $key => $value) {
	$flg =false;
	for($i=0; $i<$key; $i++){
		if($num[$i] > $value/2){
			break;
		}
		if($value % $nums[$i] == 0){
			$flg = true;
			break;
		}
	}
	if($flg===false && $nums[$key]!=$nums[$key+1]){ $ans +=1;}
}

echo $ans."\n";