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: Time Limit Exceeded)

object Main extends App {
  val inputs: Seq[String] = scala.io.Source.stdin.getLines().toList
  // val inputs = Seq("4", "5 5 5 5")
  // val inputs = Seq("10", "33 18 45 28 8 19 89 86 2 4")

  val n = inputs(0).toInt
  val nums = inputs(1).split(" ").map(_.toInt)
  // val inputs = Seq("100 0", "")
  println(solve(n, nums))

  def solve(n: Int, nums: Seq[Int]): Int = {
    val sortedNums = nums.sorted
    var divSeq = sortedNums
    val results = scala.collection.mutable.Seq.fill(n)(true)

    (0 until n).foreach { i =>
      // 約分されたものはスキップ
      if(results(i)) {
        val div = divSeq(i)
        (i + 1 until n).foreach { j =>
          if (sortedNums(j) % div == 0) {
            results.update(j, false)
          }

          if (sortedNums(i) == sortedNums(j)) {
            results.update(i, false)
          }
        }

        if(divSeq.tail.isEmpty) {
          return results.filter(v => v).size
        }
      }
    }

    return results.filter(v => v).size
  }
}