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;
typedef long long ll;

int main(){
  ll ans=0;
  ll n,i,j,a,c;
  ll b[1000001]={0};
  cin >> n;
  for(i=0;i<n;i++){
    cin >> a;
    if(b[a]==2){
      b[a]=1;
      ans-=1;
    }
    if(b[a]==0){
      ans+=1;
      b[a]=2;
      for(j=2;j*a<=1000000;j++){
        if(b[j*a]==2){
          ans-=1;
        }
        b[j*a]=1;
      }
    }
  }
  cout << ans;
}