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.Arrays;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int answer = 0;
    int[] a = new int[n];
    for(int i = 0; i < n; i++){
      a[i] = sc.nextInt();
    }
    Arrays.sort(a);
    int amax = a[n-1];
    boolean[] isNotPrime = new boolean[amax + 1];
    Arrays.fill(isNotPrime, true);
    for(int i = 0; i < n; i++){
      int div = a[i];
      if(i > 0 && a[i-1] == div) {
        isNotPrime[div] = false;
        continue;
      }
      for(int j = 2; j * div <= amax; j++){
        isNotPrime[j * div] = false;
      }
    }
    for(int i = 0; i < n; i++){
      if(isNotPrime[a[i]] == true) answer++;
    }
    System.out.println(answer);
  }
}