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 Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

fun main() {
  val n = readLine()!!.toInt()
  val a = readLine()!!.split(" ").map(String::toInt).toList().sorted()
  
  val boolArr = BooleanArray(a.size) { true }
  
  val aSize = a.size
  for (i in 0 until aSize) {
    if(!boolArr[i]) continue
    
    if(i!=aSize-1 && a[i]==a.last()) {
      for(i in i until aSize) boolArr[i] = false
      break
    }
    if(a[i] > a.last().div(0.5)) break
    
    
      
    for (j in i+1 until aSize) {
      
      if(!boolArr[j]) continue
      
      if(a[j] % a[i] == 0) {
        boolArr[j] = false
        if(boolArr[i] && a[j] == a[i]) {
          boolArr[i] = false
        }
      }
      
      
    }
  }
  
  println(boolArr.filter { bool -> bool }.size)
    
}