#include <iostream>
using namespace std;
#include <vector>
#include <set>
int main(){
int n;
  cin >> n;
  multiset<int> A;
  int amax = 0;
  for(int i = 0; i < n; i++){
   int a;
   cin >> a;
   A.insert(a);
   if(a>amax)amax = a;
  }
 vector<bool> dp(amax+2,true);
  int ans  = 0;
  for(auto j:A){
    if(dp[j]==true&&A.count(j)==1)ans++;
    for(int i = j; i <= amax; i+=j){
	  dp[i] = false;
 
    }
  }
  cout << ans << endl;
}
### Prompt

Develop a solution in cpp 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 <iostream>
using namespace std;
#include <vector>
#include <set>
int main(){
int n;
  cin >> n;
  multiset<int> A;
  int amax = 0;
  for(int i = 0; i < n; i++){
   int a;
   cin >> a;
   A.insert(a);
   if(a>amax)amax = a;
  }
 vector<bool> dp(amax+2,true);
  int ans  = 0;
  for(auto j:A){
    if(dp[j]==true&&A.count(j)==1)ans++;
    for(int i = j; i <= amax; i+=j){
	  dp[i] = false;
 
    }
  }
  cout << ans << endl;
}
```