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;
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;
        }
        Set<Integer> set = new HashSet<>();
        Set<Integer> set2 = 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);
            if (!set.contains(a)) {
                set.add(a);
            } else {
                set2.add(a);
            }
        }
        boolean[] b = new boolean[max + 1];
        Arrays.fill(b, true);
        Collections.sort(list);
        int ans = 0;
        for (int i = 0; i < n; i++) {
            int a = list.get(i);
            if (!set2.contains(a) && b[a]) {
                ans++;
            }
            for (int j = a; j <= max; j += a) {
                b[j] = false;
            }
        }
        System.out.println(ans);
    }
}