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.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		List<Integer> list = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			list.add(sc.nextInt());
		}
		Collections.sort(list);
		boolean[] array = new boolean[list.get(list.size() - 1) * 2 + 100];
		for (int i = 0; i < n; i++) {
			int num = list.get(i);
			for (int j = num * 2; j < list.get(list.size() - 1) * 2 + 100; j += num) {
				array[j] = true;
			}
		}
		int count = 0;
		Set<Integer> delList = new HashSet<>();
		for (int i = 0; i < n - 1; i++) {
			if (list.get(i) == list.get(i + 1)) {
				delList.add(list.get(i));
			}
		}
		list.removeAll(delList);
		for (int num : list) {
			if (!array[num]) {
				++count;
			}
		}
		System.out.println(count);
	}
}