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: Time Limit Exceeded)



let () = Scanf.scanf "%d\n" @@ fun n -> 
  let array = Array.init n @@ fun _ -> Scanf.scanf " %d" Fun.id in
  let () = Array.sort compare array in
  let dp = Array.make 1000010 true in
  let amax = 1000000 in
  let ans = ref 0 in
  for i=0 to n-1 do
    let a = array.(i) in
    let k = amax/a in
    if dp.(a)
    then
      begin
        if (i=0 || i>0 && array.(i-1) <> a) && (i=n-1 || i<n-1 && array.(i+1) <> a) then ans := !ans + 1
      end;
      for j=1 to k do
        dp.(a*j) <- false
      done
  done;
  Printf.printf "%d\n" !ans