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;

object Main extends App {

  val sc = new Scanner(System.in);

  val n = sc.nextInt();
  val as = List.fill(n)(sc.nextInt());

  @scala.annotation.tailrec
  def sub(as1: List[Int], as2: List[Int]): List[Int] = {
    as1 match {
      case Nil => as2;
      case h :: t =>
        val (as1_1, as1_2) = t.partition(_ % h != 0);
        val as2_1 = as2.filter(_ % h != 0);
        if (as1_2.exists(_ == h)) {
          sub(as1_1, as2_1);
        } else {n
          sub(as1_1, h :: as2_1);
        }
    }
  }

  println(sub(as.sorted, Nil).size);
}