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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt(), a[] = new int[n], factors[] = new int[1000001];
		for (int i = 0; i < n; i++)
			a[i] = sc.nextInt();
		Arrays.sort(a);
		int m = a[n - 1];
		boolean sieve[] = new boolean[m + 1];
		for (int i = 0; i < m + 1; i++)
			sieve[i] = true;
		for (int i = 0; i < n; i++)
			if (sieve[a[i]])
				for (int j = a[i] * 2; j < m + 1; j = j + a[i])
					sieve[j] = false;
		int ans = 0;
		for (int i = 0; i < n; i++) {
			if (i > 0 && a[i] == a[i - 1])
				continue;
			if (i < n - 1 && a[i] == a[i + 1])
				continue;
			if (sieve[a[i]])
				++ans;
		}
		System.out.println(ans);
	}
}
