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.HashSet;
import java.util.Scanner;


	public class Main {
		
		

		public static void main(String[] args) {

			Scanner sc = new Scanner(System.in);
	        
			int n = sc.nextInt();
			int[] a = new int[n];
			HashSet<Integer> h = new HashSet<Integer>();
			
			for(int i=0;i<n;i++) {
				a[i] = sc.nextInt();
			}
			
			Arrays.sort(a);
			int ret = n;
			
			for(int i=0;i<n;i++) {
				if(i<n-1) {
					if((a[i]==a[i+1])) {
						ret--;
						for(int j=1;j*a[i]<=a[n-1];j++) {
							h.add(j*a[i]);
						}
						continue;
					}
				}
				
				
				if(!h.contains(a[i])) {
					for(int j=1;j*a[i]<=a[n-1];j++) {
						h.add(j*a[i]);
					}
				}else {
					ret--;
				}
			}
			
			
			System.out.println(ret);
		}
	}
