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;
bool Used[1000100];
int X[200200];
int main()
{
  int N;
  cin>>N;
  for(int i=0;i<N;i++)
    cin>>X[i];
  sort(X,X+N);
  int Ans=0;
  for(int i=0;i<N;i++)
    if(!Used[X[i]])
    {
      Ans++;
      if(X[i]==X[i+1])
        Ans--;
      for(int j=X[i];j<=1000000;j+=X[i])
        Used[j]=true;
    }
  cout<<Ans<<endl;
  return 0;
}
