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: Wrong Answer)

object methods {
  def solver(): Unit = {

    val tempList: Seq[Seq[String]] = {
      for (line <- io.Source.stdin.getLines()) yield {
        line.split(' ').toSeq
      }
    }.toSeq
    val N: Int = tempList(0)(0).toInt
    val numList: Seq[Int] = tempList(1).map(_.toInt)

    //一旦愚直にやってみるO(N*(N-1))
    var allCounter: Int = 0
    numList.zipWithIndex.foreach{v =>
      var i: Int = 0
      var counter: Int = 0
      while(i < N){//iが自分自身のインデックス以外で、割り切れなかったとき
        if(i != v._2 && v._1 % numList(i) != 0) counter += 1
        //任意の値で割り切れなかったとき、counterはN-1になるはず
        if(counter == N-1) allCounter += 1
        i += 1
      }
    }

    println(allCounter)
  }
}

object Main extends App {
  methods.solver()
}