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;
using System.Linq;
using System.Collections.Generic;

public class Program
{
    public static void Main()
    {
        Console.ReadLine();
        var aList = Console.ReadLine().Split(" ").Select(int.Parse).ToList();
        aList.Sort();

        var duplicatedPenalty = 0;

        for (var i = 0; i < aList.Count; i++)
        {
            for (var j = 0; j < i; j++)
            {
                if (aList[i] % aList[j] == 0)
                {
                    aList.RemoveAt(i);
                    i--;
                    break;
                }
            }

            if(i < aList.Count - 1)
            {
                if(aList[i] == aList[i+1])
                {
                    duplicatedPenalty++;
                }
            }
        }

        Console.WriteLine(aList.Count - duplicatedPenalty);

    }
}