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 n,N=1e6;
int main()
{
    vector<int> v(N);
    cin>>n;
    int x;
    while(n--)
    {
        cin>>x;
        v[x]++;
    }
    
    int ans=0;
    for(int i=1;i<=N;i++)
    {
        if(v[i])
        {
           if(v[i]==1)ans++;
            
            for(int j=i+i;j<=N;j+=i)
            {
                v[j]=0;
            }
            
        }
        
    }
    cout<<ans<<endl;
    
}
