Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5

Solution in C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <algorithm>
#include<iostream>
#include<vector>
#include<deque>
#include<queue>
#include<stack>
#include<list>
#include<map>
#include<set>
#include<string>
#include <sstream>
#include<bitset>

#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<limits.h>
const int INF = 0x7fffffff;
using lll = long long;
using ull = unsigned long long;
using namespace std;


int main(){
  lll ii,jj,kk;
  vector<int> ret;
  int n;
  vector<int> a;

  cin >> n;
  a.resize(n);

  for(ii=0;ii<n;ii++){
    cin >> a[ii];
  }

  bool flg=true;
  int cnt=0;

  sort(a.begin(),a.end());
  int start;
  for(ii=0;ii<n;ii++){
    flg=true;
    if(ii != n-1){
      start = ii+1;
    }
    else{
      start = ii;
    }

    for(jj=start;jj>=0;jj--){
      //cout << "ii:" << ii << "jj:" << jj << endl;
      if(ii!=jj){
        if(a[ii] % a[jj] == 0){
          flg = false;
        }
      }
    }
    
    if(flg){
      //cout << a[ii] << endl;
      cnt++;
    }
  }

  cout << cnt << endl;
  
  return 0;
}