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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public final class Main {

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int n = in.nextInt();
        in.nextLine();
        final int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
        }
        Arrays.sort(arr);
        final int max = arr[n - 1];
        final boolean[] sieve = new boolean[max + 1];
        Arrays.fill(sieve, true);
        for (int num : arr) {
            for (int p = 2 * num; p <= max; p += num) {
                sieve[p] = false;
            }
        }
        final Set<Integer> res = new HashSet<>();
        final Set<Integer> remove = new HashSet<>();
        for (int num : arr) {
            if (sieve[num]) {
                if (!res.add(num)) {
                    remove.add(num);
                }
            }
        }
        System.out.println(res.size() - remove.size());
    }
}
