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 {
    private static final int MOD = 1_000_000_007;
    private static final String YES = "Yes";
    private static final String NO = "No";

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

        int N = sc.nextInt();
        int[] A = new int[N];
        for (int i=0; i<N; i++) {
            A[i] = sc.nextInt();
        }

        System.out.println(solve(N, A));
    }

    private static int solve(int N, int[] A) {
        Arrays.sort(A);
        List<Integer> ans = new ArrayList();
        if (A[0] == A[N-1]) return 0;

        check: for (int i=0; i<N; i++) {
            for (int j=0; j<ans.size(); j++) {
                if (A[i]%ans.get(j) == 0) {
                    continue check;
                }
            }

            ans.add(A[i]);
        }

        return ans.size();
    }
}