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)

import java.util.Scanner

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

  var x = Array.fill(N)(false)
  if (A(0) == A(1)) x(0) = true
  for (i <- 1 until N) {
    @scala.annotation.tailrec
    def loop(j: Int = 0): Unit = {
      if (A(i) % A(j) == 0) x(i) = true
      if (j + 1 < i) loop(j + 1)
    }

    loop()
  }
  println(x.count(!_))
}