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.*;
import java.io.PrintWriter;
public class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		TreeMap<Integer,Boolean> map=new TreeMap<>();
		for(int i=0; i<n; i++){
			int a=sc.nextInt();
			if(map.containsKey(a)){
				map.put(a,true);
			}else{
				map.put(a,false);
			}
		}
		boolean[] fur=new boolean[1000001];
		int ans=0;
		for(int i:map.keySet()){
			if(!fur[i]){
				int mul=1;
				while(1000000>=i*mul){
					fur[i*mul]=true;
					mul++;
				}
				if(!map.get(i)){
					ans++;
				}
			}
		}
		System.out.println(ans);
	}
}
