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; int a[n]; 
  unordered_map<int,int> a1,a2,a3;
  for(int i=0;i<n;i++){ cin>>a[i];a1[a[i]]++; }
  sort(a,a+n);
  for(int i=0;i<n;i++){
    if(!a2[a[i]]){
    for(int j=a[i];j<=1e6;j+=a[i]){
      a3[j]+=a1[a[i]];
    }
      a2[a[i]]=1;
    }
  }
  int cnt=0;
  for(int i=0;i<n;i++){
    if(a3[a[i]]==1){ cnt++;}
  }
  cout<<cnt<<endl;
}