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;
using CS=System.Runtime.CompilerServices;
//using System.Diagnostics;
using static System.Math;
using ll=System.Int64;
using static Contest_D.Lib_IO;
using static Contest_D.Lib_Minifunc;


namespace Contest_D {

public static class Entry
{

	public static void Main() {
		checked{
			long n, m;
			Lib_IO.rm(out n, out m);
			P<ll,ll>[] ab;
			rl(m,out ab);

			UnionFind uf = new UnionFind(n);
			foreach (var e in ab)
			{
				uf.Unite(e.A-1,e.B-1);
			}

			long ans = 0;
			foreach (var e in uf.AllSizes())
			{
				chmax(ref ans, e.Value);
			}



			Lib_IO.wm(ans);
		}
	}

public class UnionFind {
	private long[] data;

	public UnionFind(long size) {
		data = new long[size];
		for (int i = 0; i < size; i++) data[i] = -1;
	}
	public bool Unite(long x, long y) {
		x = Find(x);
		y = Find(y);

		if (x != y) {
			if (data[y] < data[x]) { var t = y; y = x; x = t; }
			data[x] += data[y];
			data[y] = x;
		}
		return x != y;
	}
	public bool IsSameGroup(long x, long y) { return Find(x) == Find(y); }
	public long Find(long x) { return data[x] < 0 ? x : data[x] = Find(data[x]); }
	public long Size(long x) { return -data[Find(x)]; }
	public Dictionary<long,long> AllSizes(){
		var ret = new Dictionary<long, long>();
		for (int i = 0; i < data.Length; i++)  if(data[i]<0) ret[i] = -data[i];
		return ret;
	}
}













}



#region BaseModule


public static class Lib_Minifunc{
	public const long MOD1 = 1000000007; // 10^9+7
	public const double EPS1 = 1e-8;
	public const long INF1 = 1000000000000000;  // 10^15
	[CS.MethodImpl(256)] public static void swap1<T>(ref T a,ref T b) { T t = a; a = b; b = t; }
	[CS.MethodImpl(256)] public static void swap2<T>(ref T a,ref T b) where T : IComparable { if (a.CompareTo(b)==1) swap1(ref a, ref b); }  // b の方が小さければ交換

	[CS.MethodImpl(256)] public static bool chmin<T>(ref T a,T b) where T : IComparable { bool r; if (r = (a.CompareTo(b)== 1)) a = b; return r; }  // b の方が小さければ a を更新
	[CS.MethodImpl(256)] public static bool chmax<T>(ref T a,T b) where T : IComparable { bool r; if (r = (a.CompareTo(b)==-1)) a = b; return r; }  // b の方が大きければ a を更新
	[CS.MethodImpl(256)] public static bool inside(long i,long n) => (0<=i&&i<n);
	[CS.MethodImpl(256)] public static bool inside(long x,long y,long w,long h) => (inside(x,w)&&inside(y,h));
	[CS.MethodImpl(256)] public static T min<T>(params T[] a) where T : IComparable { T m = a[0]; for (int i=1;i<a.Length;i++) chmin(ref m, a[i]); return m; }
	[CS.MethodImpl(256)] public static T max<T>(params T[] a) where T : IComparable { T m = a[0]; for (int i=1;i<a.Length;i++) chmax(ref m, a[i]); return m; }
	[CS.MethodImpl(256)] public static long mod(long a,long m=MOD1) { var v = a%m; return (v<0?(m<0?v-m:v+m):v); }
	[CS.MethodImpl(256)] public static long ceil(long a,long b) => (a%b==0||(a<0&&0<b)||(0<a&&b<0)?a/b:a/b+1);	// 整数商の切り上げ
	[CS.MethodImpl(256)] public static long round(double a) => Convert.ToInt64(a);	// 四捨五入
	public static string YES(bool a) => a?"YES":"NO";
	public static string yes(bool a) => a?"Yes":"No";
	[CS.MethodImpl(256)] public static P<T,U> initp<T,U>(T a,U b) => new P<T,U>(a,b);
	[CS.MethodImpl(256)] public static P<T,U,V> initp<T,U,V>(T a,U b,V c) => new P<T,U,V>(a,b,c);
	[CS.MethodImpl(256)] public static P<T,U,V,W> initp<T,U,V,W>(T a,U b,V c,W d) => new P<T,U,V,W>(a,b,c,d);
	public static T[] initc<T>(long l1) where T : new() { var m = new T[l1]; for (int i=0;i<m.Length;i++) m[i] = new T(); return m; }	// new制約は遅い
	public static int[] range(long s, long c) => Enumerable.Range((int)s,(int)c).ToArray();
	[CS.MethodImpl(256)] public static T[] inita<T>(long l1,T v=default(T)) => Enumerable.Repeat(v,(int)l1).ToArray();
	public static T[][] inita<T>(long l1,long l2,T v=default(T)) { var m = new T[l1][]; for (int i=0;i<m.Length;i++) m[i] = inita(l2,v); return m; }
	public static void shift(this IList<int> l,int o) { for (int i = 0;i<l.Count;i++) l[i]+=o; }
	public static void shift(this IList<long> l,long o) { for (int i = 0;i<l.Count;i++) l[i]+=o; }
	[CS.MethodImpl(256)] public static bool initd<T,U>(this IDictionary<T,U> d, T k, U v=default(U)) { if(d.ContainsKey(k)) { return false; } else { d[k] = v; return true; } }
	public static void sort<T>(this T[] a,int o=1, Comparison<T> f=null) where T : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.CompareTo(y));break;
			case -1: Array.Sort(a,(x,y)=>y.CompareTo(x));break;
			default: break;
		}
	}
	public static void sort<T,U>(this P<T,U>[] a,int o, Comparison<P<T,U>> f=null) where T : IComparable where U : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			default: break;
		}
	}
	public static void sort<T,U,V>(this P<T,U,V>[] a,int o, Comparison<P<T,U,V>> f=null) where T : IComparable where U : IComparable where V : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			case  3: Array.Sort(a,(x,y)=>x.C.CompareTo(y.C));break;
			case -3: Array.Sort(a,(x,y)=>y.C.CompareTo(x.C));break;
			default: break;
		}
	}
	public static void sort<T,U,V,W>(this P<T,U,V,W>[] a,int o, Comparison<P<T,U,V,W>> f=null) where T : IComparable where U : IComparable where V : IComparable where W : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			case  3: Array.Sort(a,(x,y)=>x.C.CompareTo(y.C));break;
			case -3: Array.Sort(a,(x,y)=>y.C.CompareTo(x.C));break;
			case  4: Array.Sort(a,(x,y)=>x.D.CompareTo(y.D));break;
			case -4: Array.Sort(a,(x,y)=>y.D.CompareTo(x.D));break;
			default: break;
		}
	}
}


public struct P<T,U>
{
	public T A; public U B;
	public P(T a,U b) { A = a; B = b; }
	public static implicit operator KeyValuePair<T,U>(P<T,U> a) => new KeyValuePair<T,U>(a.A,a.B);
	public static implicit operator P<T,U>(KeyValuePair<T,U> a) => new P<T,U>(a.Key,a.Value);
}
public struct P<T,U,V>
{
	public T A; public U B; public V C;
	public P(T a,U b,V c) { A = a; B = b; C = c; }
}
public struct P<T,U,V,W>
{
	public T A; public U B; public V C; public W D;
	public P(T a,U b,V c,W d) { A = a; B = b; C = c; D = d; }
}

public static class Lib_IO
{
	class Prt : System.IO.StreamWriter
	{
		public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
		public Prt(System.IO.Stream s) : base(s,new UTF8Encoding(false,true)) {}
		public Prt(System.IO.Stream s,Encoding e) : base(s,e) {}
	}
	static Prt sw = new Prt(Console.OpenStandardOutput());
	static char[] sp = new char[] {' '};
	[CS.MethodImpl(256)] static bool eq<T,U>() => typeof(T).Equals(typeof(U));
	[CS.MethodImpl(256)] static T ct<T,U>(U a) => (T)Convert.ChangeType(a,typeof(T));
	[CS.MethodImpl(256)] static T cv<T>(string s) =>
		eq<T,int>()	? ct<T,int>(int.Parse(s))
	  : eq<T,long>()   ? ct<T,long>(long.Parse(s))
	  : eq<T,double>() ? ct<T,double>(double.Parse(s,System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T,char>()   ? ct<T,char>(s[0])
					   : ct<T,string>(s);
	public static string[] rm<T>(out T a) {
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(z[0]);
		return z;
	}
	public static string[] rm<T,U>(out T a,out U b) {
		var z = rm<T>(out a); 
		b = cv<U>(z[1]);
		return z;
	}
	public static string[] rm<T,U,V>(out T a,out U b,out V c) {
		var z = rm<T,U>(out a,out b); 
		c = cv<V>(z[2]);
		return z;
	}
	public static string[] rm<T,U,V,W>(out T a,out U b,out V c,out W d) {
		var z = rm<T,U,V>(out a,out b,out c); 
		d = cv<W>(z[3]);
		return z;
	}
	public static string[] rm<T,U,V,W,X>(out T a,out U b,out V c,out W d,out X e) {
		var z = rm<T,U,V,W>(out a,out b,out c,out d); 
		e = cv<X>(z[4]);
		return z;
	}
	public static string[] rm<T,U,V,W,X,Y>(out T a,out U b,out V c,out W d,out X e,out Y f) {
		var z = rm<T,U,V,W,X>(out a,out b,out c,out d,out e); 
		f = cv<Y>(z[5]);
		return z;
	}
	public static string[] ra<T>(out T[] a) {		
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries);
		a = new T[z.Length];
		for(int i=0;i<a.Length;i++) a[i] = cv<T>(z[i]);
		return z;
	}
	public static string[][] rl<T>(long n,out T[] a) {
		a = new T[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = rm(out a[i]);
		return y;
	}
	public static string[][] rl<T,U>(long n,out P<T,U>[] a) {
		a = new P<T,U>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p;
			y[i] = rm(out o,out p);
			a[i] = new P<T,U>(o,p);
		}
		return y;
	}
	public static string[][] rl<T,U,V>(long n,out P<T,U,V>[] a) {
		a = new P<T,U,V>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q;
			y[i] = rm(out o,out p,out q);
			a[i] = new P<T,U,V>(o,p,q);
		}
		return y;
	}
	public static string[][] rl<T,U,V,W>(long n,out P<T,U,V,W>[] a) {
		a = new P<T,U,V,W>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q; W r;
			y[i] = rm(out o,out p,out q,out r);
			a[i] = new P<T,U,V,W>(o,p,q,r);
		}
		return y;
	}
	public static string[][] rx<T>(long n,out T[][] a) {
		a = new T[n][];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = ra(out a[i]);
		return y;
	}

	static void wwp(Action act){
		sw.AutoFlush = false;
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	[CS.MethodImpl(256)] static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void wm(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length-1;i++) Console.Write(wfm(a[i].GetType())+" ",a[i]);
			Console.WriteLine(wfm(a[a.Length-1].GetType()),a[a.Length-1]);
		});
	}
	public static void wa<T>(IList<T> a) { wxa(new IList<T>[]{a}, " "); }
	public static void wl<T>(IList<T> a) {
		wwp(()=>{
			var f = wfm(typeof(T));
			if(a.Count==0){
				Console.WriteLine();
			}else{
				foreach(T x in a) Console.WriteLine(f,x);
			}
		});
	}
	static void wxa<T>(IList<IList<T>> a, string s) {
		wwp(()=>{
			var f = wfm(typeof(T));
			var g = f + s;
			foreach(var b in a) {
				if(b.Count==0){
					Console.WriteLine();
				}else{
					for(int i=0;i<b.Count-1;i++) Console.Write(g,b[i]);
					Console.WriteLine(f,b[b.Count-1]);
				}
			}
		});
	}
	public static void wx<T>(IList<IList<T>> a) { wxa(a, " "); }
	public static void wg<T>(IList<IList<T>> a) { wxa(a, ""); }
}

#endregion



}