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: Accepted)

my $n = <>;
my @sorted_a = sort { $a <=> $b } glob <>;

my @memo = ();

my %counter = ();
for my $cursor (@sorted_a) {
    ++$counter{$cursor};
    if($memo[$cursor] eq 'No') {
        next;
    }
    my $i = 2*$cursor;
    while($sorted_a[$n-1] >= $i) {
        $memo[$i] = 'No';
        $i += $cursor
    }
}

my $ans = grep { $memo[$_] ne 'No' && $counter{$_} == 1 } keys %counter;
print $ans;