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
#include<bits/stdc++.h>
using namespace std;

int main()
{
 int n;
 int m=1000005;
 cin>>n;
vector<int> hash(m,0);
 
 vector<int> arr(n);
 for(int i=0;i<n;i++)
 {
     cin>>arr[i];
     if(hash[arr[i]]>1)
     continue;
     else
     {
         for(int j=arr[i];j<=m;j+=arr[i])
         {
             hash[j]++;
         }
     }
}
 int count=0;
 for(int i =0;i<n;i++)
 {
     if(hash[arr[i]]==1)
     count++;
 }
 
 
 cout<<count<<endl;
 
 
}
