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: Time Limit Exceeded)

using System;

using System.Collections.Generic;

class Program
{
    static void Main(string[] args)
    {
        string a = Console.ReadLine(); //標準入力
        string[] aa = a.Split(' ');

        List<(int, int)> friends = new List<(int, int)>();
        int N = int.Parse(aa[0]);
        int M = int.Parse(aa[1]);

        for (int i = 0; i < M; i++)
        {
            string b = Console.ReadLine(); //標準入力
            string[] bb = b.Split(' ');

            friends.Add((int.Parse(bb[0]), int.Parse(bb[1])));
        }

        List<List<bool>> friendsGroup = new List<List<bool>>();
        for (int i = 0; i < N; i++)
        {
            friendsGroup.Add(new List<bool>());

            for (int j = 0; j < N; j++)
            {
                friendsGroup[i].Add(false);
            }
        }

        for (int i = 0; i < M; i++)
        {
            friendsGroup[friends[i].Item1 - 1][friends[i].Item2 - 1] = true;
            friendsGroup[friends[i].Item2 - 1][friends[i].Item1 - 1] = true;
        }

        List<List<bool>> tempfriendsGroup = friendsGroup;
        bool isSame = false;
        do
        {
            tempfriendsGroup = friendsGroup;
            friendsGroup = resetFriend(friendsGroup, N);
            if (friendsGroup == tempfriendsGroup)
            {
                isSame = true;
            }
        } while (!isSame);


        int maxcount = 0;
        for (int i = 0; i < N; i++)
        {
            int count = 0;
            for (int j = 0; j < N; j++)
            {
                if (friendsGroup[i][j])
                {
                    count++;
                }
            }
            if (maxcount < count)
            {
                maxcount = count;
            }
        }

        Console.WriteLine("{0}", maxcount);

    }

    static List<List<bool>> resetFriend(List<List<bool>> friendGroup,int N)
    {
        for (int i = 0; i <N; i++)
        {
            friendGroup[i][i] = true;

            for (int j = i; j < N; j++)
            {
                if (friendGroup[i][j])
                {
                    for (int k = 0; k < N; k++)
                    {
                        if (friendGroup[i][k])
                        {
                            friendGroup[j][k] = true;
                            friendGroup[k][j] = true;
                        }
                    }
                }
            }
        }
        return friendGroup;

    }

}