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;cin>>N;map<int,int>M;
  for(int i=0;i<=1000000;i++)
    M[i]=0;
  set<int>S;
  for(int i=0;i<N;i++){
  int a;cin>>a;
    M.at(a)++;
    S.insert(a);
  }for(int i=1;i<=1000000;i++){
  if(S.count(i))
    for(int j=2;j*i<=1000000;j++)
      if(S.count(i*j))S.erase(i*j);
  }int ans=0;
  for(auto x:S){
  if(M.at(x)==1)ans++;
  }cout<<ans<<endl;
  return 0;
}