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;

namespace ConsoleApp3
{
    internal class Class2
    {
        private static void Main(string[] args)
        {
            var nm = Console.ReadLine().Split(" ").Select(int.Parse).ToArray();
            var n = nm[0];
            var m = nm[1];

            var lookup = Hoge(m).Distinct().ToLookup(x => x.Item1, x => x.Item2);
            var list = new HashSet<HashSet<long>>();
            var list2 = new HashSet<long>();

            foreach (var tomo in lookup.Select(x => x.Key))
            {
                if (list2.Contains(tomo))
                {
                    continue;
                }

                var newSet = new HashSet<long>();
                list.Add(newSet);

                Ho(list2, list, lookup, newSet, tomo);
            }

            try
            {
                Console.WriteLine(list.DefaultIfEmpty(new HashSet<long>(Enumerable.Range(1, n).Cast<long>())).Max(x => x.LongCount()));
            }
            catch
            {
                Console.WriteLine("?");
            }
        }

        private static void Ho(HashSet<long> list2, HashSet<HashSet<long>> list, ILookup<long, long> lookup, HashSet<long> currentHashSet, long tomo)
        {
            if (list2.Contains(tomo))
            {
                return;
            }

            currentHashSet.Add(tomo);
            list2.Add(tomo);

            foreach (var nextTomo in lookup[tomo].Where(x => !list2.Contains(x)))
            {
                Ho(list2, list, lookup, currentHashSet, nextTomo);
            }
        }

        private static IReadOnlyList<(long, long)> Hoge(int m)
        {
            return Enumerable.Range(0, m)
                .SelectMany(_ =>
                {
                    var ab = Console.ReadLine().Split(" ").Select(long.Parse).ToArray();
                    var a = ab[0];
                    var b = ab[1];

                    return new List<(long, long)> { (a, b), (b, a), };
                })
                .ToArray();
        }
    }
}