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.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    sc.nextLine();

    ArrayList<Integer> aList = new ArrayList<Integer>();
    for(int i = 0;i < n;i++) {
      aList.add(sc.nextInt());
    }
    Collections.sort(aList);
    int max = Collections.max(aList);
    boolean[] bArray = new boolean[max+1];

    for(int i = 0;i < max+1 ; i++) {
        bArray[i] = true;
    }

    int num = 0;
    for(int i :aList) {
      if(bArray[i]) {
        if(num != n-1 && i == aList.get(num+1)) {
          bArray[i] = false;
        }
        for(int j = i*2;j <= max; j += i) {
          bArray[j] = false;
        }
      }
      num++;
    }

    int cnt = 0;
    for(int i :aList) {
      if(bArray[i]) {
        cnt++;
      }
    }
    System.out.println(cnt);
    }
}
