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 scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] a = new int[n];
		for(int i = 0;i < n; ++i) a[i] = scan.nextInt();
	
		int[] count = new int[1000001];
		for(int i:a){
			if(count[i] != 0){
				count[i] = 2;
				continue;
			}

			for(int j = i;j <= 1000000; j +=i){
				++count[j];
			}
		}
		int ans = 0;
		for(int i : a){
			ans += (count[i] == 1?1:0);
		}
		System.out.print(ans);
	}
}

