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)

import java.util.ArrayDeque

//

fun main() {
    abc170d()
}

fun abc170d() {
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(" ").map { it.toInt() }
    val unique = a.toSet()
    val sortedUnique = unique.sorted()
    val queue = ArrayDeque(sortedUnique)
    val itemCount = a.groupingBy { it }.eachCount()
    var count = 0
    while (queue.isNotEmpty()) {
        val t = queue.poll()
        if (itemCount[t] == 1) count++
        val size = queue.size
        repeat(size) {
            val j = queue.poll()
            if (j % t != 0) {
                queue.add(j)
            }
        }
    }
    println(count)
}