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.*;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    boolean[] arr = new boolean[1000001];
    boolean[] is = new boolean[1000001];
    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);
    int sum = 0;
    for(int i=0;i<n;i++){
      if(!arr[a[i]] && !is[a[i]]){
       
        //System.out.println(a[i]);
        sum++;
        for(int j=2*a[i];j<1000001;j+=a[i]){
          arr[j] = true;
        }
        is[a[i]] = true;
      }else if(!arr[a[i]] && is[a[i]]){
        arr[a[i]] = true;
        sum--;
      }
    }
    System.out.println(sum);
                    
  }
}