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.Text;
using System.Threading;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionD
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            // 文字列の入力
            string s = Console.ReadLine();


            // 整数配列の入力
            var ary = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
            Array.Sort(ary);
            ary = ary.Concat(new int[] { 0 }).ToArray();
            int samecount = 0;
            bool sameflag = false;
            for (int i = 0; i < ary.Length -1 ; i++)
            {
                sameflag = false;
                int cursor = i+1;
                if (ary[i] == 0) break;
                for (int j = i+1; j < ary.Length; j++)
                {
                    if (ary[j] == 0)
                    {
                        ary[cursor] = 0;
                        break;
                    }
                    if (ary[j] % ary[i] == 0)
                    {
                        if (ary[j] == ary[i]) sameflag = true;
                        continue;
                    }
                    else
                    {
                        ary[cursor++] = ary[j];
                    }


                }
                if (sameflag) samecount++;
            }


            int count = Array.IndexOf(ary, 0);

            Console.WriteLine(count - samecount);

            Console.Out.Flush();
        }
    }
}