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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        List<Long> p = new ArrayList<>();
        // Set<Long> p = new HashSet<Long>();
        for (long i = 0; i < N; i++) {
            long pi = sc.nextLong();
            if (!p.contains(pi)) {
                p.add(pi);
            }
        }
        sc.close();
        if (p.size() == 1) {
            System.out.println(0);
            return;
        }

        Collections.sort(p);

        int count = 0;
        for (int i = 0; i < N; i++) {
            boolean flg = true;

            for (int j = 0; j < N; j++) {
                if (i == j) {
                    continue;
                }
                if (p.get(i) % p.get(j) == 0) {
                    flg = false;
                    break;
                }
            }

            if (flg) {
                count++;
            }
        }
        System.out.println(count);
    }
}