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

int a[222222],b[1111111];
int main(){
int n,c=0;
cin>>n;
for(int i=0;i<n;i++)
cin>>a[i];
sort(a,a+n);
for(int i=0;i<n;i++){
    if(b[a[i]]>1) c--,b[a[i]]--;
    if(b[a[i]]) continue;
    for(int j=a[i];j<1111111;j+=a[i])
    b[j]=1;
    b[a[i]]++;
    c++;
}
cout<<c<<endl;
return 0;
}

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

int a[222222],b[1111111];
int main(){
int n,c=0;
cin>>n;
for(int i=0;i<n;i++)
cin>>a[i];
sort(a,a+n);
for(int i=0;i<n;i++){
    if(b[a[i]]>1) c--,b[a[i]]--;
    if(b[a[i]]) continue;
    for(int j=a[i];j<1111111;j+=a[i])
    b[j]=1;
    b[a[i]]++;
    c++;
}
cout<<c<<endl;
return 0;
}

```