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: IndexedSeq[String] = scala.io.Source.stdin.getLines().toIndexedSeq

  val n = inputs(0).toInt
  val nums = inputs(1).split(" ").map(_.toInt)

  println(solve(n, nums))

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

    (0 until n).foreach { i =>
      // 約分されたものはスキップ
      if(results(i)) {
        // 分母
        val div = divSeq(i)

        (i + 1 until n).foreach { j =>
          // 約分されたものはスキップ
          if(results(j)) {
            // 割り切れる人たち
            if (sortedNums(j) % div == 0) {
              results.update(j, false)
            }

            // 同じ数値を持つものは消す.
            if (sortedNums(i) == sortedNums(j)) {
              results.update(i, false)
            }
          }
        }
      }
    }

    var result = 0
    results.foreach { v =>
      if (v) {
        result = result + 1
      }
    }

    return result
  }
}