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 OCaml (4.10.0) (judge verdict: Accepted)

let () = Scanf.scanf "%d\n" @@ fun n ->
  let as_ = Array.make 1000001 0 in
  for i = 0 to n - 1 do
    Scanf.scanf "%d " @@ fun a ->
      as_.(a) <- 1 + as_.(a)
  done;
  let dp = Array.make 1000001 1 in
  for a = 0 to 1000000 do
    if as_.(a) <> 1 then dp.(a) <- 0;
    if 0 < as_.(a) then
      let rec mark i =
        if i <= 1000000 then
          (as_.(i) <- 0; mark (i + a)) in
      mark (2 * a)
  done;
  Printf.printf "%d\n" @@
  Array.fold_left ( + ) 0 dp