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.at(i);
  }
  int m=1000005;
  vector<int>cnt(m);
  for(int x:a){
    if(cnt[x]!=0){
      cnt[x]=2;
      continue;
    }
    for(int i=x;i<m;i+=x){
      cnt[i]++;
    }
  }
  int ans=0;
  for(int x:a){
    if(cnt[x]==1){
      ans++;
    }
  }
  cout << ans << endl;
}
    
