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;
const ll MAX=1001000;
int main(){
  ll N;
  cin>>N;
  vector<ll>A(N);
  for(ll i=0;i<N;i++)cin>>A[i];
  vector<ll>D(MAX,0);
  for(auto a:A){
    if(D[a]!=0){
      D[a]=2;
      continue;
    }
    for(ll i=a;i<=MAX;i+=a){
      D[i]++;
    }
  }
  ll cnt=0;
  for(auto a:A){
    if(D[a]==1)cnt++;
  }
  cout<<cnt<<endl;
}