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) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] minfactor = new int[1000001];
        boolean[] ng = new boolean[1000001];
        for (int i = 0; i < n; i++) {
            int num = sc.nextInt();
            if (minfactor[num] == 0) {
                minfactor[num] = num;
            } else {
                ng[num] = true;
            }
        }
        
        int ans = 0;
        for (int i = 1; i < 1000001; i++) {
            if (minfactor[i] == i) {
                if (!ng[i]) ans ++;
                
                for (int j = i; j < 1000001; j += i) {
                    minfactor[j] = i;
                }
            }
        }
        System.out.println(ans);
    }
}
