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 scan = new Scanner(System.in);
    int n = scan.nextInt();
    int[] a = new int[n];


    for (int i=0;i<n;i++){
      a[i] = scan.nextInt();
    }

    Arrays.sort(a);
    int[] b = new int[a[n-1]+1];

    for (int j=0;j<b.length; j++){
      b[j] = 0;
    }

    long sum = 0;

    for (int i=0;i<n;i++){

      int current = a[i];
      for (int j=current;j<=a[n-1];j+=current){
        b[j] += 1;
      }
    }

    for (int i=0;i<n;i++){
      if (b[a[i]] < 2){
        sum += 1;
      }
    }

    System.out.println(sum);

  }

}
