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.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner scan = new Scanner(System.in);

		int N = scan.nextInt();
		boolean[] A = new boolean[1000001];
		int a;
		int ans = 0;
		ArrayList<Integer> rep = new ArrayList<Integer>();
		for (int i = 1; i <= N; i++) {
			a = scan.nextInt();
			if (A[a]) {
				rep.add(a);
			}
			A[a] = true;
		}

		for (int i = 1; i < 1000001; i++) {
			if (A[i]) {
				for (int j = 2; i*j < 1000001; j++) {
					A[i*j] = false;
				}
			}
		}

		for (int i = 0; i < rep.size(); i++) {
			A[rep.get(i)] = false;
		}

		for (int i = 1; i < 1000001; i++) {
			if(A[i]) ans++;
		}

		System.out.println(ans);

	}

}