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();
      
        List<Integer> div = new ArrayList<Integer>();
        for(int i=0;i<N;i++){
          div.add(sc.nextInt());
        }
          
        Collections.sort(div);
      int max = div.get(div.size()-1);
      boolean[] flg = new boolean[max+1]; 
      
      for(int i=0;i<div.size()-1;i++){
        int now = div.get(i);
        if(now == div.get(i+1)){
          flg[now] = true;
        }
        for(int j=now*2;j<max+1;j=j+now){
          flg[j] = true;
        }
      }
      
      int count = 0;
      for(int i=0;i<div.size();i++){
        if(!flg[div.get(i)]){
          count++;
        }
      }
      
      System.out.println(String.valueOf(count));
    }
}