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 Scala (2.13.1) (judge verdict: Time Limit Exceeded)

import java.util.Scanner

import scala.annotation.tailrec

object Main extends App {
  val sc = new Scanner(System.in)
  val N = sc.nextInt
  val As = Vector.fill(N)(sc.nextInt).sorted

  @tailrec def loop(done: Seq[Int], queue: Seq[Int], count: Int): Int = queue match {
    case first +: second +: rest =>
      if (done.exists(first % _ == 0)) {
        loop(done, second +: rest, count)
      } else if (second == first) {
        loop(first +: done, second +: rest, count)
      } else {
        loop(first +: done, second +: rest, count + 1)
      }
    case first +: rest =>
      if (done.exists(first % _ == 0)) {
        loop(done, rest, count)
      } else {
        loop(first +: done, rest, count + 1)
      }
    case _ => count
  }

  val ans = loop(Seq.empty[Int], As, 0)
  println(ans)
}