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
//package atcoder;

import java.util.*;

public class Main {

    public static void main(String[] args) {
        final Scanner in = new Scanner(System.in);
        final int N = in.nextInt();
        final int[] A = new int[N + 1];
        final Set<Integer> idx = new HashSet<>(N);
        final Map<Integer, List<Integer>> As = new HashMap<>(N);
        int max = Integer.MIN_VALUE;
        for (int i = 1; i <= N; ++i) {
            A[i] = in.nextInt();
            max = Math.max(max, A[i]);
            if (!As.containsKey(A[i])) {
                As.put(A[i], new ArrayList<>());
            }
            As.get(A[i]).add(i);
            idx.add(i);
        }

        int i = 1;
        while (i <= N && !idx.isEmpty()) {
            int value = A[i];
            while (value <= max) {
                if (As.containsKey(value)) {
                    for (int j : As.get(value)) {
                        if (j != i) {
                            idx.remove(j);
                        }
                    }
                }
                value += A[i];
            }
            ++i;
        }

        System.out.println(idx.size());
    }
}
