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;
    vector<int> A(N);
    for(int i=0; i<N; i++) cin >> A[i];
    sort(A.begin(), A.end());

    const int MX = 1e6;
    bitset<MX+1> ng;
    int ans = 0;
    for(int i=0; i<N; i++){
        if(!ng[A[i]]){
            if(i==N-1 || A[i] != A[i+1]) ans++;
            for(int j=A[i]; j<=MX; j+=A[i]) ng[j] = 1;
        }
    }

    cout << ans << endl;
    return 0;
}
