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();
    long[] a = new long[n];
    for(int i = 0; i < n; i++) {
      a[i] = sc.nextLong();
    }
    Arrays.sort(a);
    int m = (int)a[n - 1];
    int[] b = new int[m + 1];
    int ans = 1;
    if((n > 1) && (a[0] == a[1])) ans = 0;
    for(int i = 0; i < n; i++) {
      if(b[(int)a[i]] == 0) {
        for(int j = (int)(2 * a[i]); j < m + 1; j += ((int)a[i])) {
          if(b[j] == 0) b[j] = 1;
        }
      }
    }
    for(int i = 1; i < n; i++) {
      if(a[i] != a[i - 1]) {
        if(i == (n - 1)) {
          if(b[(int)a[i]] == 0) ans++;
        } else if(a[i] != a[i + 1]) {
          if(b[(int)a[i]] == 0) ans++;
        }
      }
    }
    System.out.println(ans);
  }
}