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._

object Main extends App {
  private val MAX = 1_000_000

  val n = readInt
  val A = readLine.split(" ").map(_.toInt)
  val v = Array.fill(MAX + 10)(0)

  A.foreach { Ai =>
    if (v(Ai) > 0) {
      v(Ai) = 2
    } else {
      for (step <- Ai to MAX by Ai) {
        v(step) += 1
      }
    }
  }

  val ans = A.count { Ai => v(Ai) == 1 }
  println(ans)
}