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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		final int c = 1000005;

		int n = sc.nextInt();
		int[] a = new int[n];
		int[] cnt = new int[c];

		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(sc.next());

			if (cnt[a[i]] != 0) {
				cnt[a[i]] = 2;
				continue;
			}
			for (int j = a[i]; j < c; j += a[i]) {
				cnt[j]++;
			}
		}

		int ans = 0;
		for (int i = 0; i < n; i++) {
			if (cnt[a[i]] == 1)
				ans++;
		}

		System.out.println(ans);

	}

}
