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.*

fun main(args:Array<String>) {
    val N = 1000000
    val sc = Scanner(System.`in`)
    val n = sc.nextInt()
    val a = (0 until n).map { sc.next().toInt() }
    val ac = a.groupBy { it }.toSortedMap()
    val erato : MutableList<Boolean> = MutableList(N+1) { false }
    var ans = 0
    ac.forEach {
        if (it.value.size == 1 && !erato[it.key]) ans += 1
        for (i in it.key..N step it.key) erato[i] = true
    }

    println(ans)

}