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);
  vector<bool>B(1000001,true);
  vector<int>D(1000001,0);
  for(int i=0;i<N;i++){
    cin>>A[i];
    D[A[i]]++;
    if(B[A[i]]==false||D[A[i]]>1)continue;
    for(int j=2;A[i]*j<=1000000;j++)B[j*A[i]]=false;
  }
  int ans=0;
  for(int i=0;i<N;i++)if(B[A[i]]&&D[A[i]]<2)ans++;
  cout<<ans<<endl;
}