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.List;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        List<Integer> p = new ArrayList<>();
        int[] yaku = new int[1000005];
        Arrays.fill(yaku, 0);

        for (int i = 0; i < N; i++) {
            int pi = sc.nextInt();
            p.add(pi);

            if (yaku[pi] != 0) {
                yaku[pi] = 2;
                continue;
            }
            for (int j = pi; j < 1000005; j += pi) {
                yaku[j]++;
            }
        }
        sc.close();

        int count = 0;
        for (int i = 0; i < N; i++) {
            if (yaku[p.get(i)] == 1) {
                count++;
            }
        }

        System.out.println(count);
    }
}
