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 scanner = new Scanner(System.in);

        var N = scanner.nextInt();
        var A = new TreeSet<Integer>();
        var duplicated = new TreeSet<Integer>();
        for(int i=0; i<N; i++) {
            var A_i =  scanner.nextInt();
            if(!A.add(A_i)) duplicated.add(A_i);
        }

        var A_MAX = A.last();
        var isPTable = new boolean[A_MAX+1];
        Arrays.fill(isPTable, true);

        for (Integer value : A) {
            if(!isPTable[value]) continue;
            if(duplicated.contains(value)) isPTable[value] = false;

            for(int i=2; ; i++) {
                var multiple = value*i;
                if(multiple > A_MAX) break;
                isPTable[multiple] = false;
            }
        }
        System.out.println(A.stream().filter(value -> isPTable[value]).count());
    }
}