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.*;
public class Main{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
	    int[] arr = new int[n];
	    int flag =0;
	    for(int i=0;i<n;i++){
	    	arr[i]=sc.nextInt();
	    }
	    	Arrays.sort(arr);
	    	boolean[] vis = new boolean[arr[n-1]+1];
	    	Arrays.fill(vis,true);
	    	int[] count = new int[arr[n-1]+1];
	    	for(int i=0;i<n;i++){
	    		count[arr[i]]++;
	    	}
	    	for(int i=0;i<n;i++){
	    		if(vis[arr[i]]==true){
	    			for(int j=2*arr[i];j<=arr[n-1];j+=arr[i]){
	    				//System.out.println(j);
	    				vis[j]=false;
	    			}
	    		}
	    	}
	    	int ans=0;
	    	for(int i=0;i<n;i++){
	    		if(vis[arr[i]]==true && count[arr[i]]==1){
	    			ans++;
	    		}
	    	}
	    	System.out.println(ans);

	}
	
}