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];
        for (int i = 0; i < a.length; i++) {
            a[i] = sc.nextInt();
        }

        Arrays.sort(a);

        int max = a[n-1];

        int[] aa = new int[max + 1];
        Set<Integer> dup = new HashSet<>();
        for (int k : a) {
            if (aa[k] == 0) {
                for (int i = 2 * k; i < max + 1; i = i + k) {
                    aa[i] = 1;
                }
                aa[k] = 1;
                dup.add(k);
            } else {
                if (dup.contains(k)) dup.remove(k);
            }
        }

        System.out.println(dup.size());
    }
}