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 + 1];
        A[N] = 1000001;
        for (int i = 0; i < N; i++) {
            A[i] = sc.nextInt();
        }
        Arrays.sort(A);
        sc.close();

        boolean[] check = new boolean[1000001];
        Arrays.fill(check, true);
        int ans = 0;

        // 小さい順に見ていく
        for (int i = 0; i < N; i++) {
            if (A[i + 1] != A[i] && check[A[i]]) {
                ans++;
            }

            for (int j = A[i]; j <= A[N - 1]; j += A[i]) {
                check[j] = false;
            }
        }

        System.out.println(ans);
    }
}
