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.*;

class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        int n=Integer.parseInt(bu.readLine()),a[]=new int[n],fac[]=new int[1000001],i,c=0;
        String s[]=bu.readLine().split(" ");
        HashMap<Integer,Integer> hm=new HashMap<>();
        for(i=0;i<n;i++)
        {
            a[i]=Integer.parseInt(s[i]);
            fac[a[i]]++;
            hm.put(a[i],hm.getOrDefault(a[i],0)+1);
        }
        if(a.length==1) {System.out.print(1); return;}

        ArrayList<Integer> al=new ArrayList<>();
        for(i=0;i<n;i++)
        if(hm.get(a[i])==1) al.add(a[i]);

        for(i=0;i<al.size();i++)
        {
            int j,fl=0,k=al.get(i);
            if(fac[k]>1 || (k!=1 && fac[1]>0)) continue;
            for(j=2;j*j<=k;j++)
            if(k%j==0)
            {
                if(fac[j]>0) {fl=1; break;}
                if(fac[k/j]>0) {fl=1; break;}
            }
            if(fl==0) c++;
        }
        System.out.print(c);
    }
}
