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(void){
  int t=0,k,n,cnt=0; cin>>n;
  multiset<int> a;
  for(int i=0; i<n; ++i){ cin>>k; a.insert(k); t=max(t,k);}
  vector<int> b(t+1,0);
  for(auto itr=a.begin(); itr!=a.end();){
    cnt=a.count(*itr);
    for(int i=1; i*(*itr)<=t; ++i) b[i*(*itr)]+=cnt;
    while(cnt--) ++itr;
  }
  int res=0;
  for(auto itr=a.begin(); itr!=a.end(); ++itr) if(b[*itr]==1) ++res;
  cout<<res;
  return 0;
}