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);
    final int N = sc.nextInt();
    int[] a = new int[N];
    for(int i=0;i<N;i++){
      a[i] = sc.nextInt();
    }
    int[] x = new int[1000001];
    for(int i=0;i<N;i++){
      if(x[a[i]] >= 1){
        x[a[i]]++;
        continue;
      }
      for(int j = 1; a[i] * j <= 1000000;j++){
     	x[a[i] * j]++;  //1つ存在すれば1 2つ以上存在すれば2以上なので解に含めない　
      }
    }
    int count = 0;
    for(int i=0;i<N;i++){
      if(x[a[i]] == 1){
        count++;
      }
    }
    System.out.println(count);
  }
}