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: Runtime Error)

import java.util.*;

class Main {
    final Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        new Main().run();
    }

    private int n;
    private int[] a;

    private void run() {
        n = sc.nextInt();
        a = new int[n+1];
        a[n] = 200001;

        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }

        boolean[] check = new boolean[200001];
        Arrays.sort(a);
        Arrays.fill(check, true);

        int ans = 0;
        for (int i = 0; i < n; i++) {
            if (a[i + 1] != a[i] && check[a[i]]) {
                ans++;
            }

            for (int j = a[i]; j <= a[n - 1]; j += a[i]) {
                check[j] = false;
            }
        }

        System.out.println(ans);
    }
}