#include<iostream>
#include<vector>
using namespace std;

int main(){
    int n;
    cin>>n;
    vector<int> a(n), cnt(1000001);
    for(int i=0;i<n;i++){
        cin>>a[i];
        ++cnt[a[i]];
    }
    for(int i=1000000;i>=1;i--){
        for(int j=2*i;j<=1000000;j+=i){
            cnt[j]+=cnt[i];
        }
    }
    int ans=0;
    for(int i=0;i<n;i++){
        if(cnt[a[i]]==1)++ans;
    }
    cout<<ans<<endl;
    return 0;
}
### Prompt

Your challenge is to write a CPP solution to 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<iostream>
#include<vector>
using namespace std;

int main(){
    int n;
    cin>>n;
    vector<int> a(n), cnt(1000001);
    for(int i=0;i<n;i++){
        cin>>a[i];
        ++cnt[a[i]];
    }
    for(int i=1000000;i>=1;i--){
        for(int j=2*i;j<=1000000;j+=i){
            cnt[j]+=cnt[i];
        }
    }
    int ans=0;
    for(int i=0;i<n;i++){
        if(cnt[a[i]]==1)++ans;
    }
    cout<<ans<<endl;
    return 0;
}
```