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.HashMap;
import java.util.Scanner;

public class Main {
	
	public static void main(String[] args) {
		
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int a[] = new int[n];
		
		HashMap<Integer,Integer> h = new HashMap<>();
		for(int i=0;i<n;i++)
		{
			a[i] = s.nextInt();
			if(h.containsKey(a[i]))
			h.put(a[i],h.get(a[i])+1);
			else
			h.put(a[i],1);
		}
		
		int ctr = 0;
		for(int i=0;i<n;i++) {
			int k = a[i];
			if(k==1) {
				if(h.get(1)>1) {
					ctr++;
				}
			}
			else if(h.get(a[i])>1 || h.containsKey(1)) {
				ctr++;
			}
			else {
				for(int j=2;j*j<=k;j++) {
					if(k%j==0) {
						if(h.containsKey(j) || h.containsKey(k/j)) {
							ctr++;
							break;
						}
					}
				}
			}
			
		}
		System.out.println(n-ctr);
		
	}
}