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;
    map<int,int> m;
    
    int a;
    for(int i=0; i<n; i++){
        cin>>a;
        m[a]++;
    }
    
    vector<int> b(1000001,0);
    int ans = 0;
    for(auto p : m){
        int x = p.first;
        int c = p.second;
        for(int i=x; i<=1000000; i+=x){
            b[i] += c;
        }
        if(b[x]==1)ans++;
    }
    
    cout << ans << endl;
    return 0;
}
