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 scn = new Scanner(System.in);
        int n = scn.nextInt();
        int[] a = new int[n];
        int[] b = new int[1000001];
        Arrays.fill(b,0);
        int ans = 0;
        for(int i=0;i<n;i++){
            a[i]=scn.nextInt();
        }

        for(int i=0;i<n;i++){
            if(b[a[i]]!=0){
                b[a[i]]=2;
                continue;
            }
            for(int j=a[i];j<1000001;j+=a[i]){
                b[j]++;
            }
        }
        for (int i=0;i<n;i++) {
            if (b[a[i]]==1) ans++;
        }

        System.out.println(ans);
     scn.close();

    }

}