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)

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
    val max = sortedNums(sortedNums.size - 1)
    var divSeq = sortedNums
    // 不要な配列が増えるが、添字で直接処理できるように入力の最大値分のデータを用意
    val results = scala.collection.mutable.IndexedSeq.fill(max + 1)(0)

    (1 to n).foreach { i =>
      // 分母
      val div = divSeq(i-1)

      // <= 1にしてelseなしでも良い
      if(results(div) == 0) {
        Range.inclusive(div, max, div).foreach { j =>
          results.update(j, results(j) + 1)
        }
      } else {
        results.update(div, 2)
      }
    }

    // 入力に関係ない範囲を無視するためにsortedNumsのデータでアクセスしてチェック
    var result = 0
    sortedNums.foreach { v =>
      if (results(v) == 1) {
        result = result + 1
      }
    }
    return result
  }
}