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: Wrong Answer)

fun main() {
    val N = readLine()!!.toInt()
    val A = readLine()!!.split(" ").map { it.toInt() }.sorted()

    if (N == 1) {
        println(0)
        return
    }

    val a = mutableListOf<Int>()
    val b = mutableListOf<Int>()
    a.add(A[0])
    var flag2 = A[0] == 2
    for (i in 1 until N) {
        if (A[i] == 2) flag2 = true
        if (a.all { A[i] % it != 0 }) {
            a.add(A[i])
        } else if (a.contains(A[i])) {
            b.add(A[i])
        }
    }
    println(a.count { !b.contains(it) })
}