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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
class Program
{
	static void Main()
	{
        int a = int.Parse(Console.ReadLine());
        if(a == 1)
        {
            Console.WriteLine(0);
            return;
        }

        string[] b = Console.ReadLine().Split(' ');
        int[] c = Array.ConvertAll(b, int.Parse);

        Array.Sort(c);

        int r = 0;
        bool d = false;

        for(int i=0; i<c.Length; i++)
        {
            if(i == 0)
            {
                if(c[i] == c[i+1])
                {
                    continue;
                }
                else
                {
                    r += 1;
                }
            }
            else if(i == c.Length-1)
            {
                if(c[i] == c[i-1])
                {
                    continue;
                }
                else
                {
                    d = false;
                    for(int j=0; j<i; j++)
                    {
                        if(c[i] % c[j] == 0)
                        {
                            d = true;
                            break;
                        }
                    }
                    if(!d)
                    {
                        r += 1;
                    }
                }
            }
            else
            {
                if((c[i] == c[i-1]) || (c[i] == c[i+1]))
                {
                    continue;
                }
                else
                {
                    d = false;
                    for(int j=0; j<i; j++)
                    {
                        if(c[i] % c[j] == 0)
                        {
                            d = true;
                            break;
                        }
                    }
                    if(!d)
                    {
                        r += 1;
                    }
                }
            }
        }
        Console.WriteLine(r);
	}
}