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.security.KeyStore.TrustedCertificateEntry
import java.util
import java.util.regex.Pattern
import java.util.{ArrayList, Collections, Comparator, List => JList}

import scala.collection.immutable.TreeMap
import scala.math._
import scala.collection.mutable
import scala.collection.mutable.{ArrayBuffer, ListBuffer}
import scala.util.{Failure, Success, Try}

object Main{
  val LINE_SEPARATOR = "\n"
  def main(args: Array[String]): Unit = {
    if (sys.env.getOrElse("TEST", "")=="1"){
      println(test());
    }else{
      val input=io.Source.stdin.getLines().mkString(LINE_SEPARATOR);
      println(solve(input).trim());
    }
  }

  def init (nRows: Int, nCols: Int, default: Int) = Array.tabulate(nRows,nCols)( (x,y) =>  default)

  def sortIgnoreCase1(list: JList[String]): JList[String] = {
    val r = new ArrayList[String](list)
    Collections.sort(r, new Comparator[String] {
      override def compare(o1: String, o2: String): Int = o1.compareToIgnoreCase(o2)
    })
    r
  }

  def solve(input: String): String = {
    val n = input.split(LINE_SEPARATOR).head.toInt
    val a = input.split(LINE_SEPARATOR).tail.head.split(" ").map(_.toInt).sorted
    val res = (0 to pow(10, 6).toInt).map(_ => 0).toArray
    a.foreach{ai =>
      if (res(ai) == 0) {
        (ai to pow(10, 6).toInt by ai).foreach{aix =>
          res(aix) += 1
        }
      } else {
        res(ai) += 1
      }
    }
    a.map(res(_) == 1).count(b => b).toString
  }

  def medianCalculator(seq: Seq[Long]): Long = {
    //In order if you are not sure that 'seq' is sorted
    val sortedSeq = seq.sortWith(_ < _)

    if (seq.size % 2 == 1) sortedSeq(sortedSeq.size / 2)
    else {
      val (up, down) = sortedSeq.splitAt(seq.size / 2)
      (up.last + down.head) / 2
    }
  }

  def factorize(x: Long): List[Long] = {
    def foo(x: Long, a: Long = 2, list: List[Long] = Nil): List[Long] = a*a > x match {
      case false if x % a == 0 => foo(x / a, a    , a :: list)
      case false               => foo(x    , a + 1, list)
      case true                => x :: list
    }
    foo(x)
  }

  def divisors(n: Int): Vector[Int] = {
    val halfList = (1 to sqrt(n).toInt).toVector.filter(n % _ == 0).map(_.toInt)
    val reversedList = if (sqrt(n).floor == sqrt(n)) halfList.reverse.tail.map(n/_) else halfList.reverse.map(n/_)
    halfList ++ reversedList
  }

  def gcd(m: Long, n: Long): Long = n match {
    case 0 => m
    case _ => gcd(n, m % n)
  }
  def lcm(a: Long, b: Long): Long = a * b / gcd(a, b)

  val tests=List(
    """5
      |24 11 8 3 16""".stripMargin -> """3
                                            |
                                          |
                               |
                                     |
                                   |
                                 |""".stripMargin
    ,
    """4
      |5 5 5 5""".stripMargin -> """0
                                       |
                                          |
                                 |""".stripMargin,
    """10
      |33 18 45 28 8 19 89 86 2 4""".stripMargin -> """5
                                |""".stripMargin
  )

  def test():String= {
    return tests.map{case (i,o)=>(i.trim(),o.trim())}
      .zipWithIndex.map{
      case ((input,outputExpect),i)=>{
        val output=solve(input).trim();
        s"test${i+1}:"+(if(output==outputExpect){
          "Passed"
        }else{
          s"Failed\nexpect:\n${outputExpect}\noutput:\n${output}"
        })
      }}
      .mkString("\n");
  }
}