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() {
    val n = readLine()!!.toInt()
    if (n == 1) {
        println(1)
        return
    }

    val list = readLine()!!.split(" ").map { it.toInt() }.sorted()
    val mList = list.toMutableList()
    list.toSet()
        .asSequence()
        .filter { x -> list.count { it == x } > 1 }
        .forEach { x -> mList.removeIf { it % x == 0 } }
    var result = 0
    while (mList.isNotEmpty()) {
        val x = mList.removeAt(0)
        mList.removeIf { it % x == 0 }
        result += 1
        if (mList.isEmpty()) {
            break
        } else if (mList.size == 1) {
            result += 1
            break
        }

        if (mList.first() * 2 > mList.last()) {
            result += mList.size
            break
        }
    }

    println(result)
}