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<bits/stdc++.h>
using namespace std;
int main() {
  int n,i,a,ma=0,ans=0;
  cin>>n;
  map<int,int> m;
  set<int> s;
  for(i=0;i<n;i++){
    cin>>a;
    if(ma<a) ma=a;
    if(m.count(a)) m.at(a)++;
    else m[a]=1;
  }
  for(auto z:m){
    if(!s.count(z.first)){
      if(z.second==1) ans++;
      for(i=1;i*z.first<=ma;i++) s.insert(i*z.first);
    }
  }
  cout<<ans<<endl;
}