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();
		int[] A = new int[n];
		Arrays.setAll(A, i -> sc.nextInt());
		Arrays.sort(A);
		boolean[] dp = new boolean[1000001];
		for (int i = 1; i < n; i++) {
			if (A[i] == A[i - 1]) {
				if (!dp[A[i]]) {
					for (int j = A[i]; j < 1000001; j += A[i]) {
						dp[j] = true;
					}
				}
			}
		}
		long ans = 0;
		for (int i = 0; i < n; i++) {
			if (!dp[A[i]]) {
				ans++;
				for (int j = A[i]; j < 1000001; j += A[i]) {
					dp[j] = true;
				}
			}
		}
		System.out.println(ans);
	}

}
