#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
int b[(int) 1e6+7]={};
int  main(){
    int n,ans=0;
    cin >> n;
    int a[n];
    rep(i,n) cin >> a[i];
    for(int i=0;i<n;i++){
        if(b[a[i]]!=0){
            b[a[i]]=2;
            continue;
        } 
        
        for(int j=a[i];j<=1e6;j+=a[i]) b[j]++;
    }
    rep(i,n){
        if(b[a[i]]==1) ans++;
    }
    cout << ans << 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;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
int b[(int) 1e6+7]={};
int  main(){
    int n,ans=0;
    cin >> n;
    int a[n];
    rep(i,n) cin >> a[i];
    for(int i=0;i<n;i++){
        if(b[a[i]]!=0){
            b[a[i]]=2;
            continue;
        } 
        
        for(int j=a[i];j<=1e6;j+=a[i]) b[j]++;
    }
    rep(i,n){
        if(b[a[i]]==1) ans++;
    }
    cout << ans << endl;
}
```