#include <bits/stdc++.h>
using namespace std;
 
int main(){
  int N;
  cin >> N;
  vector<int> A(N);
  for (int i = 0; i < N; ++i){
    cin >> A.at(i);
  }
  vector<int> cnt(1000003);
  for (int x : A ){
    if(cnt.at(x)!=0){
      cnt.at(x) = 2;
      continue;
    }
    for (int i = x; i < 1000003; i += x) cnt.at(i) ++;
  }
  int ans = 0;
  for (int x : A){
    if(cnt.at(x)==1) ans ++;
  }
  cout << ans << endl;
  return 0;
}
### Prompt

In Cpp, your task is to solve 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;
  vector<int> A(N);
  for (int i = 0; i < N; ++i){
    cin >> A.at(i);
  }
  vector<int> cnt(1000003);
  for (int x : A ){
    if(cnt.at(x)!=0){
      cnt.at(x) = 2;
      continue;
    }
    for (int i = x; i < 1000003; i += x) cnt.at(i) ++;
  }
  int ans = 0;
  for (int x : A){
    if(cnt.at(x)==1) ans ++;
  }
  cout << ans << endl;
  return 0;
}
```