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;

vector<int> cnt(1000000);

int main(){
    int n;cin>>n;
    int x;
    for(int i=0;i<n;i++){
        cin>>x;
        cnt[x]++;
    }
    int rj=0;
    for(int i=1;i<=1000000;i++){
        if(cnt[i]){
            if(cnt[i]==1)rj++;
            for(int j=i+i;j<=1000000;j=j+i){
                cnt[j]=0;
            }
        }
    }
    cout <<rj<<endl;
}
