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) {

		final int Amax = 1000001;
		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);
		
		int[] cnt = new int[Amax];
		
		for (int x : A) {
			if(cnt[x] != 0) {
				cnt[x] =2;
				continue;
			}
			for(int i = x; i < Amax; i+= x ) {
				cnt[i] += 1;
			}			
		}
		int ans = 0;
		for(int x: A) {
			if(cnt[x] == 1)
				ans++;
		}
		System.out.println(ans);
		sc.close();
	}
}
