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;
const int m=1e6;


int main(){
    int n; cin>>n;
    vector<int> a(n);
    for(int &x: a) cin>>x;
    sort(a.begin(),a.end());
    vector<int> cn(m+1,1);
    int ans=0;
    for(int i=0;i<n;i++){
        if(cn[a[i]]==1){
            for(int j=a[i];j<=m;j+=a[i]){
                cn[j]=0;
            }
            if(i<n-1&&a[i]==a[i+1]) continue;
            ans++;
        }
    }
    cout<<ans<<endl;
}