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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;
public class MainClass
{
	public const long Giri = 1000000007;
	public const long DpInf = 99999999999999;
	
	public static void Main(string[] args)
	{
		var p = Input().ToInt();
		var n = p[0];
		var m = p[1];
		
		var u = new UnionFind(n);
		
		for(int i = 0; i < m; i++)
		{
			p = Input().ToInt(-1);
			u.Unite(p[0], p[1]);
		}
		
		var h = new Dictionary<int, int>();
		for(int i = 0; i < n; i++)
		{
			int r = u.Root(i);
			if(!h.ContainsKey(r))
			{
				h.Add(r, 0);
			}
			h[r]++;
		}
		int max = 0;
		foreach(var hr in h.Keys)
		{
			max = Math.Max(max, h[hr]);
		}
		Console.WriteLine(max);
	}
	
	
	
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str, int offset = 0)
	{
		var r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt() + offset;
		return r;
	}
}

public class UnionFind
{
	private int[] par;
	public UnionFind(int n)
	{
		par = new int[n];
		for(int i = 0; i < n; i++)
			par[i] = i;
	}
	public int Root(int x)
	{
		if(par[x] == x) return x;
		return par[x] = Root(par[x]);
	}
	public void Unite(int x, int y)
	{
		int rx = Root(x);
		int ry = Root(y);
		if(rx == ry) return;
		par[rx] = ry;
	}
	public bool InSameTree(int x, int y)
	{
		return Root(x) == Root(y);
	}
}