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.io.*;
import java.util.*;
public class Main{
	public static void main(String args[]) throws IOException{
               BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));	
		int N = Integer.parseInt(reader.readLine());
		int[] list = Arrays.stream(reader.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
		Arrays.sort(list);
		int cnt = 0;
		int[] Seive_mod = new int[list[N-1]+1];
		for(int i=0;i<N;i++){
			for(int j = list[i];j<Seive_mod.length;j=j+list[i]){
				Seive_mod[j]+=1;
			}	
		}
		for(int i = 0;i<N;i++){
			if(Seive_mod[list[i]]==1) cnt++;
		}
		System.out.println(cnt);		
	}
}
