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.Linq;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices.ComTypes;
using System.Xml.Serialization;

namespace AtCoder
{
    class Program
    {

        const int BiggestMod = 1000000007;

        public static void Main()
        {

            var num = int.Parse(Console.ReadLine());

            var args = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var ans = 0;

            Array.Sort(args);

            if (!args.Any(x => x != args[0])) Console.WriteLine(0);
            else
            {
                for (var i = 0; i < num; i++)
                    if (args[i] != -1)
                    {

                        ans++;

                        for (int j = i; j < num; j++)
                            if (args[j] > args[i])
                                if (args[j] % args[i] == 0)
                                {

                                    args[j] = -1;

                                }

                    }

                Console.WriteLine(ans);

            }
        }

    }

}