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;
  unordered_map<int,int>mp;
  int arr[n],sieve[1000001]={0};
  for(int i=0;i<n;i++){
   cin>>arr[i];++mp[arr[i]];}
   for(auto i : mp) {
       for(int j=i.first*2;j<=1000001;j+=i.first) {
           sieve[j]=1;
       }
   }
   int ans=0;
   for(int i=0;i<n;i++) {
       if(sieve[arr[i]]==0&&mp[arr[i]]==1)
       ans++;
   }
   cout<<ans;
	return 0; 
} 
