#include<bits/stdc++.h>
using namespace std;
const int N=1e6+2;
bool mark[N],flag[N];

int main()
{
    int n,i,j,a,ans=0;
    scanf("%d",&n);
    for(i=0; i<n; i++)
    {
        scanf("%d",&a);
        if(mark[a])flag[a]=true;
        mark[a]=true;
    }
    for(i=1; i<N; i++)
    {
        if(mark[i])
        {
            for(j=i+i; j<N; j+=i)mark[j]=false;
            ans+=(flag[i]^1);
        }
    }
    printf("%d\n",ans);
    return 0;
}

### Prompt

Create a solution in cpp for 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;
const int N=1e6+2;
bool mark[N],flag[N];

int main()
{
    int n,i,j,a,ans=0;
    scanf("%d",&n);
    for(i=0; i<n; i++)
    {
        scanf("%d",&a);
        if(mark[a])flag[a]=true;
        mark[a]=true;
    }
    for(i=1; i<N; i++)
    {
        if(mark[i])
        {
            for(j=i+i; j<N; j+=i)mark[j]=false;
            ans+=(flag[i]^1);
        }
    }
    printf("%d\n",ans);
    return 0;
}

```