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: Wrong Answer)

import scala.util.control.Breaks

object Main extends App {
  val n = scala.io.StdIn.readInt()
  val aInput = scala.io.StdIn.readLine()
  val aArray =  aInput.split(" ").map(_.toInt).toVector.sorted

  var result = 0

  aArray.zipWithIndex.foreach { a =>
    val b = new Breaks
    b.breakable {
      (0 to n - 1).foreach { i =>
        if (a._2 != i) {
          val bunbo = aArray(i)
          if (a._1 < bunbo) {
            b.break()
          } else if (a._1 % bunbo == 0) {
            result = result + 1
            b.break()
          } else if (a._1 / 2 + 1 < bunbo) {
            b.break()
          }
        }
      }
    }
  }
  println(n - result)

}