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.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

public class Main {

    public static final int MOD = 1000000007;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        if (n == 1) {
            System.out.println(1);
            return;
        }
        Map<Integer, Integer> map = new HashMap<>();
        Set<Integer> set3 = new HashSet<>();
        List<Integer> list = new ArrayList<>();
        int max = 0;
        for (int i = 0; i < n; i++) {
            int a = Integer.parseInt(sc.next());
            max = Math.max(max, a);
            list.add(a);
            map.merge(a, 1, Integer::sum);
        }
        Collections.sort(list);
        for (int i = 1; i <= max; i++) {
            set3.add(i);
        }
        int ans = 0;
        for (int a : list) {
            if (map.get(a) == 1 && set3.contains(a)) {
                ans++;
            }
            int idx = 1;
            while (a * idx <= max) {
                set3.remove(a * idx);
                idx++;
            }
        }
        System.out.println(ans);
    }
}