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)

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

my $ans = 0;
for my $cursor (0..$#sorted_a) {
    if($cursor != $#sorted_a && $sorted_a[$cursor] == $sorted_a[$cursor+1]) {
        next;
    }
    ++$ans;
    for (0..$cursor-1) {
        if($sorted_a[$cursor] % $sorted_a[$_] == 0) {
            --$ans;
            last;
        }
    }
}

print $ans;