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;
void solve(){
  vector<int>count(1000005);
  int n;
  cin>>n;
  for(int i=0;i<n;i++){
    int k;
    cin>>k;
    count[k]++;
  }
  int ans=0;
  vector<int>vis(1000005,0);
  for(int i=1;i<=1000000;i++){
    if(count[i]==0||vis[i])
      continue;
    if(count[i]==1&&!vis[i])
      ans++;
    for(int j=i;j<=1000000;j+=i)
      vis[j]=1;
  }
  cout<<ans;
}
    
int main(){
  solve();
  return 0;
}
  