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.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		var sc = new Scanner(System.in);
		var n = sc.nextInt();
		var a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		sc.close();
		Arrays.sort(a);

		var sameSet = new HashSet<Integer>();
		for (int i = 0; i < a.length - 1; i++) {
			if (a[i] == a[i + 1]) {
				sameSet.add(a[i]);
			}
		}

		var result = 0;
		var set = new HashSet<Integer>();
		for (int i = 0; i < a.length; i++) {
			if (!sameSet.contains(a[i])) {
				var divisors = getDivisors(a[i]);
				var check = true;
				for (int j = 0; j < divisors.size(); j++) {
					if (set.contains(divisors.get(j))) {
						check = false;
						break;
					}
				}
				if (check) {
					result++;
				}
			}
			set.add(a[i]);
		}

		System.out.println(result);
	}

	public static List<Integer> getDivisors(int n) {
		var list = new ArrayList<Integer>();
		for (var i = 1; i < (int)Math.sqrt(n) + 1; i++) {
			if (n % i == 0) {
				list.add(i);
				var divisor = n / i;
				if (divisor != i) {
					list.add(divisor);
				}
			}
		}

		Collections.sort(list);
		return list;
	}
}
