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 }
  
  for (i in 0 until a.size) {
    if(!boolArr[i]) continue
    for (j in i+1 until a.size) {
      if(boolArr[i] && a[j] == a[i]) boolArr[i] = false
      if(!boolArr[j]) continue
      if(a[j] % a[i] == 0) boolArr[j] = false
    }
  }
  
  println(boolArr.filter { bool -> bool }.size)
    
}