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;
import java.util.Arrays;

class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] A = new int[N];
		for (int i = 0; i < N; i++) A[i] = sc.nextInt();
		Arrays.sort(A);
		boolean[] ng = new boolean[A[N - 1] + 1];
		int count = 0;
		for (int i = 0; i < N; i++) {
			if (!ng[A[i]]) {
				if (!(i + 1 < N && A[i + 1] == A[i])) count++;
				for (int j = A[i]; j <= A[N - 1]; j += A[i]) ng[j] = true;
			}
		}
		System.out.println(count);
	}
}
