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;
using ll =long long;
#define all(v) v.begin(),v.end()
 
int main() {
  ll N;
  cin>>N;
  vector<ll> A(N);
  for(ll i=0;i<N;i++) {
cin>>A[i];
  }
  sort(all(A));
  vector<ll> note(A.back());
  
  for(ll i=0;i<N;i++) {
ll count=1;
    while(A[i]*count<=A.back()) {
note[A[i]*count-1]++;
    count++;
    }
  }
  
  ll ans=0;
  for(ll i=0;i<N;i++) {
if(note[A[i]-1]==1) {
ans++;
}
  }
  
  cout<<ans<<endl;
}