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 Perl (5.26.1) (judge verdict: Time Limit Exceeded)

use strict;
use warnings;
use utf8;

use Data::Dumper;
use feature qw(say);

my $n = <STDIN>;
chomp $n;

my $input = <STDIN>;
chomp $input;
my $array = [split / /, $input];
my $count = 0;

for (my $i = 0; $i < scalar @$array; $i++) {
    my $is_divided = 0;
    for (my $divide_index = 0; $divide_index < scalar @$array; $divide_index++) {
        if ($i == $divide_index) {
            next;
        } else {
            my $num = $array->[$i];
            my $seperator = $array->[$divide_index];
            $is_divided = 1 if $num % $seperator == 0;
        }
    }
    $count++ unless $is_divided;
}
say $count;