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,Z=0;
  cin>>N;
  vector<int> p(N+1);
  for(int i=0;i<N;i++){
    cin>>p.at(i);
  }
  p.at(N)=2000000;
  vector<int> q(1000002);
  sort(p.begin(), p.end());
  for(int i=0;i<N;i++){
    if(q.at(p.at(i))==0){
      if(p.at(i)!=p.at(i+1)){
        Z++;
      }
      int D=p.at(i);
      while(D<1000002){
        q.at(D)++;
        D+=p.at(i);
      }
    }
  }
  cout<<Z<<endl;
}