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: Runtime Error)

object Main extends App {
  val in = new java.util.Scanner(System.in)
  val N = in.nextInt
  val As = List.fill(N)(in.nextInt).sorted
  val dividable = new Array[Boolean](1_000_001)

  def count(l: List[Int], c: Int): Int = l match {
    case Nil => c
    case x :: xs =>
      if (dividable(x)) count(xs, c)
      else {
        (x to 1_000_001 by x).foreach {i => dividable(i) = true}
        count(xs, c + (if (xs.headOption == Some(x)) 0 else 1))
      }
  }

  println(count(As, 0))
}