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;

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);
        boolean[] A = new boolean[a[n-1]+1];
        int count = 0;
        for(int i = 0;i<n;i++){
            if(!A[a[i]]){
                if(!(i+1<n&&a[i+1]==a[i]))count++;
                for(int j = a[i];j<=a[n-1];j+=a[i])A[j]=true;
            }
        }
        System.out.println(count);
	}
}
