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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        var N = scanner.nextInt();
        var A = new LinkedList<Integer>();
        for(int i=0; i<N; i++)
            A.add(scanner.nextInt());

        A.sort(Comparator.naturalOrder());
        var numP = 0;
        while(A.size()!=0) {
            int p = A.getFirst();
            A.remove(0);
            System.out.println("p: " + p);
            System.out.println("A: " + A);

            boolean isPExistInRemains = false;
            for(Iterator<Integer> ite = A.iterator(); ite.hasNext(); ) {
                int next = ite.next();
                if(next % p == 0) ite.remove();
                if(next == p) isPExistInRemains = true;
            }
            if(!isPExistInRemains) numP++;
        }
        System.out.println(numP);
    }
}