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

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    if(n == 1) {
      System.out.println(1);
    }else {
      sc.nextLine();
      String[] str = sc.nextLine().split(" ");

      ArrayList<Integer> aList = new ArrayList<Integer>();
      for(int i = 0;i < n;i++) {
        aList.add(Integer.parseInt(str[i]));
      }
      Collections.sort(aList);

      if(aList.contains(1)) {
        if(aList.get(1) != 1) {
          System.out.println(1);
        }else {
          System.out.println(0);
        }
      }else {
        int max = Collections.max(aList);
        boolean[] bArray = new boolean[max+1];
        int cnt = 0;

        for(int i = 0;i < max+1 ; i++) {
          if(aList.contains(i)) {
            bArray[i] = true;
            cnt++;
          }else {
            bArray[i] = false;
          }
        }

        for(int i = 1;i < n;i++) {
          if(bArray[aList.get(i)]) {
            for(int j = 0;j < i;j++) {
              if(aList.get(i) % aList.get(j) == 0) {
                int c = 1;
                for(int k = aList.get(i);k <= max; k = c * aList.get(i)) {
                  if(aList.contains(k)) {
                    bArray[k] = false;
                    cnt--;
                  }
                  c++;
                }
                break;
              }
              if(aList.get(i) / aList.get(j) <= 2) {
                break;
              }
            }
          }
        }
        System.out.println(cnt);
        }
      }

  }
}