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 Raku (Rakudo 2020.02.1) (judge verdict: Time Limit Exceeded)

my ($,*@a) = words; 
my @dp;
@a = @a>>.Int.sort;
my $max=@a.max;
@dp[$_] = True for 0..$max;
@dp[0] = False;
my $res = 0;
for ^@a -> $i {
  my $n := @a[$i];
  next unless @dp[$n];
  if (@a[$i+1]:exists && @a[$i] == @a[$i+1]) || (@a[$i-1]:exists && @a[$i-1] == @a[$i]) {
  } else {
    $res++;
  }
  my $x=$n+$n;
  while $x <= $max { @dp[$x] = False; $x += $n; }
}
$res.say;