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>
#define rep(i,n) for (int i = 0; i < (n); i++)
using namespace std;
using ll = long long;

int M = 1000005;

int main(){
  int n; cin >>n;
  vector<int> a(n);
  rep(i,n) cin >>a[i];
  vector<int> cnt(M);
  for(int x : a){
    if(cnt[x]!=0){
      cnt[x] = 2;
      continue;
    }
    for(int i = x; i<M; i+=x) cnt[i]++;
  }
  int ans = 0;
  for(int x : a){
    if(cnt[x]==1) ans++;
  }
  cout << ans << endl;
  return 0; 
}