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: Accepted)

import java.util.Scanner

import scala.io.StdIn._
object Main extends App {

  def read(): (Int, Array[Int]) = {
    val sc: Scanner = new Scanner(System.in)
    val n = sc.nextInt()
    val arr = Array.fill(n)(sc.nextInt)
    sc.close()
    (n, arr)
  }

  def solve(): Int = {
    val (_, arr) = read()
    val sorted = arr.sorted
    val len = sorted.length
    val maxLen = Math.max(len, sorted(len-1)) + 1
    val cntArr = Array.fill(maxLen)(0)

    sorted.foreach { num =>
      if(cntArr(num) != 0) cntArr(num) = 2
      else (num until maxLen by num).foreach(cntArr(_) += 1)
    }
    sorted.foldLeft(0) { (cnt, num) =>
      if(cntArr(num) == 1) cnt+1 else cnt
    }
  }

  println(solve())

}