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);
  $nums = explode(' ', trim(fgets(STDIN)));
  $count = 0;

  for ($i = 0; $i < $n; $i++) {
    for ($j = 0; $j < $n; $j++) {
      if ($nums[$i] == $nums[$j]) {
        break;
      }
      if ($i != $j && $nums[$i] % $nums[$j] == 0) {
        break;
      }
    }
    if ($j == $n) {
      $count++;
    }
  }

  echo $count;