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 c[1000005];
int main(){
    int n;
    cin >> n;
    int a[n+1];
    for(int i=0;i<n;i++)cin >> a[i];
    sort(a,a+n);
    int ans=0;
    for(int i=0;i<n;i++){
        for(int j=a[i];j<=a[n-1];j+=a[i])c[j]++;
    }
    for(int i=0;i<n;i++)if(c[a[i]]==1)ans++;
    cout << ans << endl;
}
