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 < (int)(n); i++)
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;

int main(){
  int n;
  cin >> n;
  vi a(n);
  rep(i,n) cin >> a[i];
  sort(a.rbegin(),a.rend());
  int len = a[0]+1;
  vi cnt(len+1);
  rep(i,n){
    for(int j=a[i]; j<=len; j+=a[i]) cnt[j]++;
  }
  int ans = 0;
  rep(i,n){
    if(cnt[a[i]] == 1) ans++;
  }
  cout << ans << endl;
}
