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 br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		int arr[] = new int[n];
		for(int i=0;i<n;i++)
			arr[i] = Integer.parseInt(st.nextToken());
		Arrays.sort(arr);
		int count = 0;
		if(n==1)
		{
			System.out.println("1");
			return;
		}
		if(arr[0]==arr[n-1])
		{
			System.out.println(count);
			return;
		}
		int freq[] = new int[arr[n-1]+1];
		int prim[] = new int[arr[n-1]+1];
		for(int i=0;i<n;i++)
		{
			freq[arr[i]]++;
		}
		for(int i=0;i<n;i++)
		{
			if(prim[arr[i]]==0){
			for(int j=2*arr[i];j<=arr[n-1];j+=arr[i])
			{
				prim[j]=1;
			}
		}
		}
		for(int i=0;i<n;i++)
		{
			if(prim[arr[i]]==0 && freq[arr[i]]==1)
				count++;
		}
		System.out.println(count);

	}
}