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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

/*
    Author: @__goku__
    ssrivastava990@gmail.com

                   `\-.   `
                      \ `.  `
                       \  \ |
              __.._    |   \.       S O N - G O K U
       ..---~~     ~ . |    Y
         ~-.          `|    |
            `.               `~~--.
              \                    ~.
               \                     \__. . -- -  .
         .-~~~~~      ,    ,            ~~~~~~---...._
      .-~___        ,'/  ,'/ ,'\          __...---~~~
            ~-.    /._\_( ,(/_. 7,-.    ~~---...__
           _...>-  P""6=`_/"6"~   6)    ___...--~~~
            ~~--._ \`--') `---'   9'  _..--~~~
                  ~\ ~~/_  ~~~   /`-.--~~
                    `.  ---    .'   \_
                      `. " _.-'     | ~-.,-------._
                  ..._../~~   ./       .-'    .-~~~-.
            ,--~~~ ,'...\` _./.----~~.'/    /'       `-
        _.-(      |\    `/~ _____..-' /    /      _.-~~`.
       /   |     /. ^---~~~~       ' /    /     ,'  ~.   \
      (    /    (  .           _ ' /'    /    ,/      \   )
      (`. |     `\   - - - - ~   /'      (   /         .  |
       \.\|       \            /'        \  |`.           /
       /.'\\      `\         /'           ~-\         .  /\
      /,   (        `\     /'                `.___..-      \
     | |    \         `\_/'                  //      \.     |
     | |     |                 _Seal_      /' |       |     |
 */

import java.io.*;
import java.util.*;

public class Main
{
    static PrintWriter out = new PrintWriter((System.out));

    public static void main(String args[]) throws IOException
    {
        Kioken sc = new Kioken();
        int n=sc.nextInt();
        int m=sc.nextInt();
        int parent[]=new int[n];
        for (int x = 0; x < n; x++)
        {
            parent[x]=x;
        }
        for (int x = 0; x < m; x++)
        {
            int a=sc.nextInt()-1;
            int b=sc.nextInt()-1;
            fusion(parent,Math.min(a,b),Math.max(a,b));
        }
        HashMap<Integer,Integer> set=new HashMap<>();
        int max=0;
        for (int x = 0; x < n; x++)
        {
            int d=1;
            if(set.containsKey(parent[x]))
            {
                d+=set.get(parent[x]);
            }
            if(d>max)
            {
                max=d;
            }
            set.put(parent[x],d);
        }
        out.println(max);
        out.close();
    }

    public static void fusion(int[] parent,int a,int b)
    {
        int x=kamehamaha(parent,a);
        int y=kamehamaha(parent,b);
        parent[y]=x;
    }

    private static int kamehamaha(int[] parent, int a)
    {
        if(parent[a]!=a)
        {
            return kamehamaha(parent,parent[a]);
        }
        return a;
    }


    public static int lower_bound(ArrayList<Integer> ar, int k)
    {
        int s = 0, e = ar.size();
        while (s != e)
        {
            int mid = s + e >> 1;
            if (ar.get(mid) <= k)
            {
                s = mid + 1;
            }
            else
            {
                e = mid;
            }
        }
        return Math.abs(s) - 1;
    }

    public static int upper_bound(ArrayList<Integer> ar, int k)
    {
        int s = 0;
        int e = ar.size();
        while (s != e)
        {
            int mid = s + e >> 1;
            if (ar.get(mid) < k)
            {
                s = mid + 1;
            }
            else
            {
                e = mid;
            }
        }
        if (s == ar.size())
        {
            return -1;
        }
        return s;
    }

    static class Kioken
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        public String next()
        {
            while (!st.hasMoreTokens())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (Exception e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt()
        {
            return Integer.parseInt(next());
        }

        public long nextLong()
        {
            return Long.parseLong(next());
        }

        public double nextDouble()
        {
            return Double.parseDouble(next());
        }

        public String nextLine()
        {
            try
            {
                return br.readLine();
            }
            catch (Exception e)
            {
                e.printStackTrace();
            }
            return null;
        }

        public boolean hasNext()
        {
            String next = null;
            try
            {
                next = br.readLine();
            }
            catch (Exception e)
            {
            }
            if (next == null || next.length() == 0)
            {
                return false;
            }
            st = new StringTokenizer(next);
            return true;
        }
    }
}