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;
using static System.Console;

public static class Program
{
    public static void Main()
    {
        var lineNM = ReadLine().Split(' ').Select(int.Parse).ToArray();
        var n = lineNM[0];
        var m = lineNM[1];

        var setList = new List<HashSet<int>>();
        for(int i = 0; i < m; ++i)
        {
            var line = ReadLine().Split(' ');
            var line0 = int.Parse(line[0]);
            var line1 = int.Parse(line[1]);
            bool found0 = false;
            bool setFound = false;
            List<int> foundList = new List<int>();
            for (int j = 0; j < setList.Count && foundList.Count <= 2; ++j)
            {
                if (setList[j].Contains(line0))
                {
                    foundList.Add(j);
                    setFound = true;
                    found0 = true;
                    break;
                }
                else if (setList[j].Contains(line1))
                {
                    foundList.Add(j);
                    setFound = true;
                    break;
                } 
                else
                {
                    continue;
                }
            }
            if (!setFound)
            {
                setList.Add(new HashSet<int>());
                setList[setList.Count - 1].Add(line1);
                setList[setList.Count - 1].Add(line0);
            }
            else
            {
                if(foundList.Count == 1)
                {
                    if (found0)
                    {
                        setList[foundList[0]].Add(line1);
                    }
                    else
                    {
                        setList[foundList[0]].Add(line0);
                    }
                }
                else
                {
                    setList[foundList[0]].IntersectWith(setList[foundList[1]]);
                    setList.RemoveAt(foundList[1]);
                }
            }
        }
        if (setList.Count == 0) WriteLine(n);
        else WriteLine(setList.Select(it => it.Count).Max());
    }
}