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;

namespace ConsoleApp1
{
    class ABC117D
    {
        // https://atcoder.jp/contests/abc177/tasks/abc177_d
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split();
            int N = Int32.Parse(NM[0]);
            int M = Int32.Parse(NM[1]);

            if (M > 0)
            {
                var hs = new HashSet<int>();
                var ns = new HashSet<(int, int)>();

                var AB = Console.ReadLine().Split();
                int A = Int32.Parse(AB[0]);
                int B = Int32.Parse(AB[1]);

                hs.Add(A);
                hs.Add(B);

                for (int i = 1; i < M; i++)
                {
                    AB = Console.ReadLine().Split();
                    A = Int32.Parse(AB[0]);
                    B = Int32.Parse(AB[1]);

                    if (hs.Contains(A) || hs.Contains(B))
                    {
                        hs.Add(A);
                        hs.Add(B);
                    }
                    else
                    {
                        ns.Add((A, B));
                    }
                }

                var max = hs.Count;
                while (max <= ns.Count)
                {
                    hs = new HashSet<int>();
                    var ns2 = new HashSet<(int, int)>();

                    foreach (var item in ns)
                    {
                        A = item.Item1;
                        B = item.Item2;
                        hs.Add(A);
                        hs.Add(B);
                        break;
                    }
                    foreach (var item in ns)
                    {
                        A = item.Item1;
                        B = item.Item2;

                        if (hs.Contains(A) || hs.Contains(B))
                        {
                            hs.Add(A);
                            hs.Add(B);
                        }
                        else
                        {
                            ns2.Add((A, B));
                        }
                    }

                    max = Math.Max(max, hs.Count);
                    ns = ns2;
                }

                Console.WriteLine(max);
            }
            else
            {
                Console.WriteLine(1);
            }
        }
    }
}