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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;

namespace AtCoder170
{
    class ProgramD
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());

            var input2 = Console.ReadLine();
            var inputList2 = input2.Split(" ").Select(int.Parse).ToArray();

            var dic = new Dictionary<int, bool>();

            for (var idx = 0; idx < N; idx++)
            {
                if (dic.ContainsKey(inputList2[idx]))
                {
                    continue;
                }

                var flg = true;
                for (var idx2 = 0; idx2 < idx; idx2++)
                {
                    if (inputList2[idx] < inputList2[idx2]) continue;
                    if (inputList2[idx] % inputList2[idx2] == 0)
                    {
                        flg = false;
                        break;
                    };

                }

                if (flg)
                {
                    for (var idx2 = idx + 1; idx2 < N; idx2++)
                    {
                        if (inputList2[idx] < inputList2[idx2]) continue;
                        if (inputList2[idx] % inputList2[idx2] == 0)
                        {
                            flg = false;
                            break;
                        };

                    }
                }

                dic.Add(inputList2[idx], flg);
            }

            Console.WriteLine(dic.Count(d => d.Value));
        }
    }
}