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 = Integer.parseInt(sc.next());
        int[] a = new int[n];
        for(int i=0; i<n; i++) {
            a[i] = Integer.parseInt(sc.next());
        }
        
        Arrays.sort(a);
        boolean[] boo = new boolean[a[n-1]+1];
        for(int i=0; i<a[n-1]+1; i++) {
            boo[i] = true;
        }
        
        int count = 0;
        for(int i=0; i<n; i++) {
            if(i>0) {
                if(a[i] == a[i-1] && boo[a[i]]) {
                    boo[a[i]] = false;
                    count--;
                    continue;
                }
            }
            if(boo[a[i]] == true) {
                int x = 2;
                while(a[i]*x <= a[n-1]) {
                    boo[a[i]*x] = false;
                    x++;
                }
                count++;
            } 
        }
        System.out.println(count);
    }
}