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) {
    
        var sc = new Scanner(System.in);
    
        int n = Integer.parseInt(sc.next());
        var a = new int[n];
        var b = new boolean[1000001];
        var set1 = new HashSet<Integer>();
        var set2 = new HashSet<Integer>();
        for(int i = 0; i < n; i++){
            a[i] = Integer.parseInt(sc.next());
            set1.add(a[i]);
            if(b[a[i]]){
                set2.add(a[i]);
            }else{
                b[a[i]] = true;
            }
        }
        for(int i : set2){
            b[i] = false;
        }
        
        for(int i : set1){
            int x = i+i;
            while(x <= 1000000){
                b[x] = false;
                x += i;
            }
        }
        int ans = 0;
        for(int i = 1; i <= 1000000; i++){
            if(b[i]) ans++;
        }
        System.out.println(ans);
    }
}