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
  $n = trim(fgets(STDIN));
  $a = explode(" ", trim(fgets(STDIN)));
  $b = array_fill(0,$n,$a[0]);
  if($a == $b){
      echo "0";
      exit;
  }
  $count=0;
  for($i=0; $i<$n; $i++){
      $flag = true;
      for($j=$i+1; $j<$n; $j++){
          if($a[$i]%$a[$j] == 0 || $a[$j]%$a[$i] == 0){
              $flag = false;
          }
      }
      if($flag){
          $count++;
      }
  }
  echo $count;