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(void){
    int n;
    int cnt = 0;
    int c2 = 0;
    cin >> n;
    vector<int> v(n);
    for(int i=0;i<n;i++)cin >> v[i];
    sort(v.begin(),v.end());
    int max = v[n-1];
    vector<bool> b(max+1,true);
    for(int x:v){
        if(b[x]){
            if(v[c2] != v[c2+1])cnt++;
            for(int i=1;i<max/x+1;i++)b[i*x] = false;
        }
        c2++;
    }
    cout << cnt << endl;
}
