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: Accepted)

import java.util.*

// https://atcoder.jp/contests/abc170/tasks/abc170_d

fun main() {
    abc170d()
}

fun abc170d() {
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(" ").map { it.toInt() }
    val sorted = a.sorted()
    val max = a.max()!!
    val primes = BooleanArray(max + 1) { false }
    for (i in sorted) {
        if (primes[i]) continue
        var j = 2
        while (i * j <= max) {
            primes[i * j] = true
            j++
        }
    }
    val orig = mutableSetOf<Int>()
    val dup = mutableSetOf<Int>()
    for (i in sorted) {
        if (i in orig) dup.add(i)
        if (!primes[i]) orig.add(i)
    }
    println(orig.count() - dup.count())
}