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 $not_divided_array = [];
my $candidate_array = [sort { $a <=> $b } @$array];

while (1) {
    my $candidate = $candidate_array->[0];
    last unless $candidate;

    my $new_candidate_array = [];

    my $has_same = 0;
    for (my $i = 1; $i < scalar @$candidate_array; $i++) {
        my $divided = $candidate_array->[$i];
        if ($divided == $candidate) {
            $has_same = 1;
        } else {
            unless ($divided % $candidate == 0) {
                push @$new_candidate_array, $divided;
            }
        }
    }
    $candidate_array = $new_candidate_array;

    push @$not_divided_array, $candidate unless $has_same;
}
say scalar @$not_divided_array;