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.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[] h = new int[n];
      if(n == 1){
        System.out.println(1);
        return;
      }
		for(int i = 0 ; i < n ; i++) {
			h[i] = sc.nextInt();
		}
		Arrays.sort(h);
		int length = h.length;
		boolean[] checked = new boolean[h[n - 1] + 1];
		Arrays.fill(checked, false);
		for(int i = 0 ;  i < h.length ; i++) {

			if(checked[h[i]])
				continue;

			for(int j = h[i] ; j <= h[n - 1] ; j += h[i]) {

				if(h[i] == j) {

					if(i == 0) {
						if(h[i] == h[i + 1])
							checked[j] = true;
					}
					else if(i == h.length - 1) {
						if(h[i] == h[i - 1])
							checked[j] = true;
					}else
						if(h[i] == h[i + 1] || h[i] == h[i - 1])
							checked[j] = true;
				}
              else
                checked[j] = true;
			}
		}
		int count = 0;
		for(int i = 0 ; i < h.length ; i++) {
			if(!checked[h[i]])
				count++;

		}

		System.out.println(count);

	}
}

