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
#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int main(){
  int n;
  cin>>n;
  vector<int> a(n+1);
  for(int i=0;i<n;i++) cin>>a[i];
  sort(a.begin(),a.end()-1);
  vector<int> used(1000011);
  int ans=0;
  for(int i=0;i<n;i++){
    if(used[a[i]]==0) {
      if(a[i]!=a[i+1]) ans++;
  	  for(int j=1;j*a[i]<1000010;j++) used[j*a[i]]=1;
    }
  }
  cout<<ans;
}
