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.Arrays;
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(0);
            return;
        }

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

        Arrays.sort(a);
        int count = n;
        if(a[0] == a[1]){count--;}
        for(int i = n-1; i >= 0; i--){
            int half = a[i] / 2;
            for(int j = 0; j <= i-1; j++){
                if(a[i] == a[j]){
                    count--;
                    break;
                }
                if(a[j] > half){
                    break;
                }
                if(a[i] % a[j] == 0){
                    count--;
                    break;
                }
            }
        }
        System.out.println(count);
    }
}