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.Text;
using System.Collections.Generic;
using System.Linq;
using System.IO;

namespace AtCoder.XXX.D
{ 
    public class Program
    {
        public static void Main(string[] args)
        {
            var n = int.Parse(r());
            var datas = cr();
            var cnt = 0;
            for(var i = 0; i < n;i++)
			{
                for(var j = 0; j < n;j++)
				{
                    if (datas[i] == int.MaxValue)
                    {
                        break;
                    }
if(datas.Count(x=>x == datas[i]) > 1)
					{
                        cnt++;
                        break;
					}

                    if(i == j) 
					{
                        continue;
					}
                    if (datas[i] % datas[j] == 0)
                    {
                        datas[i] = int.MaxValue;
                        cnt++;
                    }
                }
			}
            P(n-cnt);
        }

        private static StreamReader sr;
        public static int[] Ecr()
        {
            if (sr == null)
            {
                sr = new StreamReader("input.txt", Encoding.GetEncoding("UTF-8"));
            }
            return sr.ReadLine().Split().Select(int.Parse).ToArray();
        }
        public static  int[] cr()
        {
            return Console.ReadLine().Split().Select(int.Parse).ToArray();
        }
        public static string Er()
        {
            if (sr == null)
            {
                sr = new StreamReader("input.txt", Encoding.GetEncoding("UTF-8"));
            }
            return sr.ReadLine();
        }
        public static string r()
        {
            return Console.ReadLine();
        }
        public static int cri()
        {
            return int.Parse(Console.ReadLine());
        }
        public static void P(string str)
        {
            Console.WriteLine(str);
        }
        public static void P(int num)
        {
            P(num.ToString());
        }
    }
}