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.Scanner;
import java.util.Arrays;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);

    int n = sc.nextInt();
    int[] a = new int[n];
    for (int i = 0; i < n; i++) {
      a[i] = sc.nextInt();
    }
    Arrays.sort(a);

    int[] ctr = new int[1000001];

    for (int i = 0; i < n; i++) {
      for (int j = a[i]; j <= 1000000; j += a[i]) {
        if (j == a[i] && ctr[j] != 0) {
          ctr[j]++; break;
        }
        ctr[j]++;
      }
    }

    int result = 0;
    for (int i : a) {
      if (ctr[i] == 1) result++;
    }

    System.out.println(result);
  }
}
