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) {
        final Scanner sc = new Scanner(System.in);

        final int N = sc.nextInt();
        final int M = 10000005;

        final int[] a = new int[N];

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

        Arrays.sort(a);

        final int[] cnt = new int[M];

        for (int x : a) {
            if (cnt[x] != 0) {
                cnt[x] = 2;
                continue;
            }
            for (int i = x; i < M; i += x) {
                cnt[i]++;
            }
        }

        int ans = 0;

        for (int x : a) {
            if (cnt[x] == 1) ans++;
        }

        System.out.println(ans);
    }
}
