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;
typedef int64_t ll;
int nm[1000001];

int main(){
  int n,cnt=0;
  cin>>n;
  int a[n];
  set<int> s;
  for(int i=0;i<n;i++){
    cin>>a[i];
    s.insert(a[i]);
    nm[a[i]]++;
  }
  vector<bool> era(1e6+1,true);
  int b,c;
  for(auto i:s){
    b=i;c=2*b;
    while(c<=1e6){
      era[c]=false;
      c+=b;
    }
  }
  for(int i=0;i<n;i++){
    if(era[a[i]] && nm[a[i]]==1)cnt++;
  }
  cout<<cnt<<endl;
}
