Problem:
Score : 400 points

Problem Statement

There are N persons called Person 1 through Person N.

You are given M facts that "Person A_i and Person B_i are friends." The same fact may be given multiple times.

If X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.

Takahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.

At least how many groups does he need to make?

Constraints

2 \leq N \leq 2\times 10^5

0 \leq M \leq 2\times 10^5

1\leq A_i,B_i\leq N

A_i \neq B_i

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
\vdots
A_M B_M

Output

Print the answer.

Sample Input 1

5 3
1 2
3 4
5 1

Sample Output 1

3

Dividing them into three groups such as \{1,3\}, \{2,4\}, and \{5\} achieves the goal.

Sample Input 2

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output 2

4

Sample Input 3

10 4
3 1
4 1
5 9
2 6

Sample Output 3

3

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Security.Cryptography.X509Certificates;
using System.Text;
using System.Threading.Tasks;

namespace D
{
    class Program
    {
        static void Main(string[] args)
        {
            string line = Console.ReadLine();

            string[] strs = line.Split(' ');
            int N = int.Parse(strs[0]);
            int M = int.Parse(strs[1]);

            List<(int, int)> datas = new List<(int, int)>();
            List<HashSet<int>> list = new List<HashSet<int>>();
            for(int i = 0; i < M; i++)
            {
                line = Console.ReadLine();
                strs = line.Split(' ');
                var A = int.Parse(strs[0]);
                var B = int.Parse(strs[1]);
                if (A > B)
                {
                    datas.Add((B, A));
                }
                else
                {
                    datas.Add((A, B));
                }
            }
            datas.Sort((x,y) => {
                if (x.Item1 > y.Item1) return 1;
                if (x.Item1 < y.Item1) return -1;
                if (x.Item2 > y.Item2) return 1;
                if (x.Item2 < y.Item2) return -1;
                return 0;
            });
            bool nolist;
            foreach (var data in datas)
            {
                nolist = true;
                foreach (var nums in list)
                {
                    if (nums.Contains(data.Item1) && nums.Contains(data.Item2))
                    {
                        nolist = false;
                        break;
                    }
                    else if (nums.Contains(data.Item1))
                    {
                        nolist = false;
                        nums.Add(data.Item2);
                        break;
                    }
                    else if (nums.Contains(data.Item2))
                    {
                        nolist = false;
                        nums.Add(data.Item1);
                        break;
                    }
                }
                if (nolist)
                {
                    var nums = new HashSet<int>();
                    nums.Add(data.Item1);
                    nums.Add(data.Item2);
                    list.Add(nums);
                }
            }

            int max = 0;
            foreach(var nums in list)
            {
                if (max < nums.Count) max = nums.Count;
            }
            Console.WriteLine(max);
        }
    }
}