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

int main(){
  int N; cin >> N;
  multiset<int> A;
  int Amax=0;
  for(int i=0; i<N; i++){
    int d; cin >> d;
    A.insert(d);
    if(Amax<d) Amax=d;
  }
  
  int icount=0;
  while(!A.empty()){
    int af=*A.begin();
    if(A.count(af)==1) icount++;
    for(int d=af; d<=Amax; d+=af){
      A.erase(d);
    }
  }
  cout << icount << endl;
}
### Prompt

Create a solution in cpp for the following problem:

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;
  multiset<int> A;
  int Amax=0;
  for(int i=0; i<N; i++){
    int d; cin >> d;
    A.insert(d);
    if(Amax<d) Amax=d;
  }
  
  int icount=0;
  while(!A.empty()){
    int af=*A.begin();
    if(A.count(af)==1) icount++;
    for(int d=af; d<=Amax; d+=af){
      A.erase(d);
    }
  }
  cout << icount << endl;
}
```