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() {
    abc170d()
}

fun abc170d() {
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(" ").map { it.toInt() }
    val unique = a.toSet()
    val sortedUnique = unique.sorted()
    val itemCount = a.groupingBy { it }.eachCount()
    var count = 0
    for (i in sortedUnique.lastIndex downTo 0) {
        if (itemCount[sortedUnique[i]] != 1) continue
        var found = false
        for (j in 0 until i) {
            if (sortedUnique[i] % sortedUnique[j] == 0) {
                found = true
                break
            }
        }
        if (!found) count += itemCount[sortedUnique[i]]!!
    }
    println(count)
}