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;
using p=pair<int,int>;
#define int long long
#define rep(i,N) for(int i=0;i<N;++i)

signed main(){
  int N;
  cin>>N;
  vector<int> A(N);
  rep(i,N)cin>>A[i];
  vector<int> Erat(1000001);
  for(int C:A){
    if(Erat[C]!=0){
      Erat[C]=2;
      continue;
    }
    for(int i=C;i<1000001;i+=C)Erat[i]+=1;
  }
  int ans=0;
  for(int C:A){
    if(Erat[C]==1)ans+=1;
  }
  cout<<ans<<endl;
  return 0;
}  