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;

signed main(){
  int n;cin>>n;
  map<int,int>m;
  while(n--){
    int a;cin>>a;
    m[a]++;
  }
  int ans=0;
  for(auto p:m){
    int v=p.first,c=p.second;
    if(!c)continue;
    ans+=c==1;
    for(int i=2*v;i<1e6+1;i+=v)if(m.count(i))m[i]=0;
  }
  cout<<ans<<endl;
}
