#include<bits/stdc++.h>
using namespace std;
int main(){
  int n;
  cin>>n;
  map<int,int> b;
  map<int,bool> f;
  int m=0;
  for(int _=0;_<n;_++){
    int a;
    cin>>a;
    b[a]++;
    f[a]=1;
    m=max(a,m);
  }
  for(auto a:b){
    if(a.second>1)
      f[a.first]=0;
    for(int i=2;a.first*i<=m;i++)
      if(b.count(a.first*i))
        f[a.first*i]=0;
  }
  int c=0;
  for(auto a:f)
    c+=(a.second?1:0);
  cout<<c<<endl;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

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

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
int main(){
  int n;
  cin>>n;
  map<int,int> b;
  map<int,bool> f;
  int m=0;
  for(int _=0;_<n;_++){
    int a;
    cin>>a;
    b[a]++;
    f[a]=1;
    m=max(a,m);
  }
  for(auto a:b){
    if(a.second>1)
      f[a.first]=0;
    for(int i=2;a.first*i<=m;i++)
      if(b.count(a.first*i))
        f[a.first*i]=0;
  }
  int c=0;
  for(auto a:f)
    c+=(a.second?1:0);
  cout<<c<<endl;
}
```