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)

fun intList() = readLine()?.split(" ")?.map(String::toInt) ?: TODO()
fun main(args: Array<String>) {
    val n = readLine()?.toInt() ?: return
    val a = intList().sorted()
    val max = a.last()
    val flags = Array(max + 1) { true }
    val proceed = hashMapOf<Int, Boolean>()
    a.forEach { i ->
        var v = if (proceed[i] == true) {
            i
        } else {
            i + i
        }
        proceed[i] = true
        while (v <= max) {
            flags[v] = false
            v += i
        }
    }
    println(a.count { flags[it] }.toString())
}