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: Time Limit Exceeded)

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

		boolean[] dp = new boolean[n];
		Arrays.fill(dp, true);

		int count = 0;
		for (int i = 0; i < n; i++) {

			if (dp[i]) {
				for (int j = i + 1; j < n; j++) {
					if (dp[j]) {
						if (input[i] == input[j])
							dp[i] = dp[j] = false;

						else if (input[j] % input[i] == 0)
							dp[j] = false;
					}
				}
			}

			if (dp[i])
				count++;
		}

		System.out.println(count);
	}
}