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;
#define ll long long

int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ll n;
  cin>>n;
  vector<ll>a(1000002);
  for(ll i=0;i<n;i++){
    ll val;
    cin>>val;
    a[val]++;
  }
  
  ll ans=0;
  for(ll i=1;i<=1e6;i++){
    if(a[i]>0){
    	if(a[i]==1){
    		ans+=a[i];
		}
      for(ll j=2*i;j<=1e6;j+=i){
        a[j]=0;
      }
    }
  }
  cout<<ans;
  return 0;
}