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.lang.*;

public class Main{
    public static void main(String[]args){
        Scanner sc = new Scanner(System.in);
        int N=sc.nextInt();
        int ans=0;
        int p[]=new int[1000001];
        int a[]=new int[N];
        for(int i=0; i<N; i++){
            a[i]=sc.nextInt();
        }
        Arrays.sort(a);
        for(int i=0; i<N; i++){
            if(p[a[i]]<2){
                for(int j=1; a[i]*j<a[N-1]+1; j++){
                    p[a[i]*j]++;
                }
            }
        }
        for(int i=0; i<N; i++){
            if(p[a[i]]<2){
                ans++;
            }
        }
        System.out.println(ans);
    }
}