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.TreeMap;

public class Main {
	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		TreeMap<Integer, Integer>map = new TreeMap<Integer, Integer>();

		for (int i=0; i<n; i++){
			int a = sc.nextInt();
			if (map.containsKey(a)){
				map.put(a, map.get(a)+1);
			} else {
				map.put(a, 1);
			}
		}
		int max = map.lastKey();
		boolean[] b = new boolean[max+1];
		for (int i=0; i<max+1; i++){
			b[i] = true;
		}
		for (int key : map.keySet()){
			if (b[key] == false){
				continue;
			}
			for (int i = 2; i*key <= max; i++){
				b[i*key] = false;
			}
		}
		int ans = 0;
		for (int key : map.keySet()){
			if (map.get(key) == 1 && b[key] == true){
				ans++;
			}
		}
		System.out.println(ans);
	}

}