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[] a = new int[n];
        for(int i=0 ;i<n; i++) {
            a[i] = sc.nextInt();
        }
        Arrays.sort(a);
        boolean[] b = new boolean[1000001];
 
        int res = 0;
        for(int i=0; i<n; i++) {
            int num = a[i];
            if(!b[num] && !(i<n-1 && num == a[i+1])) res++;
            if(!b[num]) {
                for(int j = num; j<=1000000; j+=num) {
                    b[j] = true;
                }
            }
        }
        System.out.println(res);
    }
}