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() {
  map<int, int> mp;
int n;
  cin>>n;
  vector<int> v(n);
  for(int i=0; i<n; i++)cin>>v[i],mp[v[i]]++;
  int ans = 0;
  for(int i = 0; i<n; i++){
    int f = 1;
    mp[v[i]]--;
    for(int j = 1; j*j<=v[i]; j++) {
      if(v[i]%j == 0 and (mp[j] or mp[v[i]/j])){
        f = 0;
        break;
      }
      
    } 
    mp[v[i]]++;
    ans += f;
  } 
  cout<<ans<<endl;
  return 0;
} 