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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;


int main(){
    int n;
    scanf("%d",&n);
    vector <int> l(n);
    for (int i=0;i<n;i++) {
        scanf("%d",&l[i]);
    }
    sort(l.begin(),l.end());
    int count=0;
    int b=0;
    for (int i =0;i<n;i++){
        count++;
        for (int j=b;j<i;j++){
            if(l[i] % l[j]==0){
                swap(l[i],l[b]);
                b++;
                break;
            }
        }
    }
    printf("%d\n",count);
    return 0;
}