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);
        int n = sc.nextInt();
        int[] a = new int[n];
        HashMap<Integer, Integer> map = new HashMap<>();
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            int count = map.getOrDefault(a[i], 0);
            map.put(a[i], ++count);
        }

        int size1 = map.getOrDefault(1, 0);
        int count = n;
        for (int i = 0; i < n; i++) {
            if (map.getOrDefault(a[i], 0) > 1) {
                count--;
                continue;
            }
            // 1の時は他に１があれば対象
            if (a[i] == 1 && size1 > 1) {
                count--;
                continue;
            }
            // １以外の時に、１が一つでもあれば対象
            if (a[i] != 1 && size1 > 0) {
                count--;
                continue;
            }

            Set<Integer> div = getDiv(a[i]);
            for (Integer d : div) {
                if (map.containsKey(d)) {
                    count--;
                    break;
                }
            }
        }

        System.out.println(count);
    }

    private static Set<Integer> getDiv(int i) {
        Set<Integer> res = new HashSet<>();
        for (int j = 2; j * j <= i; j++) {
            if (i % j == 0) {
                res.add(j);
                res.add(i / j);
            }
        }

        return res;
    }

}