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;
  vector<int> a(n);
  for(int i=0;i<n;i++)cin>>a[i];
  sort(a.begin(),a.end());
  vector<int> cnt(a[n-1]+1);
  for(int i=0;i<n;i++){
    for(int j=a[i];j<cnt.size();j+=a[i]){
      cnt[j]++;
    }
  }
  int ans=0;
  for(int i=0;i<n;i++){
    if(cnt[a[i]]==1)ans++;
  }
  cout<<ans<<endl;
  return 0;
}