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 scala.io.StdIn._
import scala.math._

object Main extends App with StdInHelper {
  val n = readInt
  val as = readInts

  val maxA = as.max
  val dp = scala.collection.mutable.Map[Int, Int]().withDefaultValue(0)

  for (a <- as) {
    for (i <- a to maxA by a) {
      dp(i) += 1
    }
  }

  var res = 0

  for (a <- as) {
    if (dp(a) == 1) res += 1
  }

  println(res)
}

trait StdInHelper {
  def readStrings = {
    val l = readLine
    if (l == "") Array.empty[String]
    else l.split(" ")
  }
  def readInts = readStrings.map(_.toInt)
  def readLongs = readStrings.map(_.toLong)
  def readDoubles = readStrings.map(_.toDouble)
  def readBigInts = readStrings.map(BigInt.apply(_))
  def readBigDecimals = readStrings.map(BigDecimal.apply(_))
}