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.

Examples

Input

5
24 11 8 3 16


Output

3


Input

4
5 5 5 5


Output

0


Input

10
33 18 45 28 8 19 89 86 2 4


Output

5
import java.util.Scanner;
import java.util.stream.Stream;

public class Main {

	public static void main(String[] args) {
		try(Scanner scanner = new Scanner(System.in)) {
			String data1 = scanner.nextLine();
			String data2 = scanner.nextLine();

			String[] data2Array = data2.split(" ");
			int[] a = Stream.of(data2Array).mapToInt(Integer::parseInt).toArray();

			int[] array = new int[10000005];
			for (int x : a) {
				if (array[x] != 0) {
					array[x] = 2;
					continue;
				}
				for (int i = x; i < 10000005; i += x) {
					array[i]++;
				}
			}

			int ans = 0;
			for (int x : a) {
				if (array[x] == 1) {
					ans++;
				}
			}
			System.out.println(ans);
		}
	}
}