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;
#define rep(i,n) for(int i=0;i<n;++i)
long long N,R,M=1e6,a,k,Inf=(1ULL<<62),p=Inf;

int main() {
    cin >> N;
    vector<int> A(N);
    rep(i,N) cin >> A[i];
    sort(begin(A),end(A));
    vector<bool> d(M+1);
    rep(i,N){
        a=A[i];
        if(p==a) { d[a]=1; continue; }
        p=a;
        for(k=2;a*k<=M;++k) d[a*k]=1;
    }
    rep(i,N) R+=!d[A[i]];
    cout << R;
}