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,a,ans = 0;
    cin >> n;
    vector<int> num(1000001,0);
    for(int i = 0;i < n;i++){
        cin >> a;
        num[a]++;
    }
    for(int i = 1;i<= 1000000;i++){
        if(num[i] >= 1){
            if(num[i] == 1)ans++;
            for(int j = i;j <= 1000000;j += i){
                num[j] = 0;
            }
        }
    }
    cout << ans << endl;
}
