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.Linq;

class Program
{
  static void Main(string[] args)
  {
    string[] firstLine = Console.ReadLine().Split(' ');
    //uint N = uint.Parse(firstLine[0]);
    uint M = uint.Parse(firstLine[1]);

    List<List<uint>> members = new List<List<uint>>();

    for (int i = 0; i < M; i++)
    {
      string[] items = Console.ReadLine().Split(' ');

      uint A = uint.Parse(items[0]);
      uint B = uint.Parse(items[1]);

      bool isGroupExist = false;
      foreach (var list in members)
      {
        bool isContainsA = list.Contains(A);
        bool isContainsB = list.Contains(B);

        if(isContainsA && isContainsB)
        {
          isGroupExist = true;
          break;
        }
        else if (isContainsA)
        {
          list.Add(B);
          isGroupExist = true;
          break;
        }
        else if (isContainsB)
        {
          list.Add(A);
          isGroupExist = true;
          break;
        }
      }

      if (!isGroupExist)
      {
        members.Add(new List<uint>());
        members.Last().Add(A);
        members.Last().Add(B);
      }
    }

    int maxGroupNum = 0;
    foreach (var list in members)
    {
      if (list.Count > maxGroupNum)
      {
        maxGroupNum = list.Count;
      }
    }

    Console.WriteLine(maxGroupNum);
    return;
  }
}