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: Accepted)

import java.util.ArrayList;
import java.util.HashSet;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn=new Scanner(System.in);
		int n=scn.nextInt();
		int m =scn.nextInt();
		ArrayList<ArrayList<Integer>> al=new ArrayList<>();
		for(int i=0;i<n;i++){
			ArrayList<Integer>al1=new ArrayList<>();
			al.add(al1);
		}
		HashSet<String> hs =new HashSet<>();
		for(int i=0;i<m;i++){
			int val1= scn.nextInt();
			int val2 =scn.nextInt();
		     String s1=val1+"#"+val2;
		     String s2=val2+"#"+val1;
		     if(hs.contains(s1)|| hs.contains(s2)){
		    	 continue;
		     }
		     hs.add(s1);
		     al.get(val1-1).add(val2-1);
		     al.get(val2-1).add(val1-1);
		     
		}
		int max=0;
		HashSet<Integer>hs1=new HashSet<>();
		for(int i=0;i<n;i++){
			cnt=0;
		     dfs(i,al,hs1);
		     max=Math.max(cnt, max);
		}
		 System.out.println(max);

	}
	static int cnt=0;
	public static void dfs(int s, ArrayList<ArrayList<Integer>>al , HashSet<Integer> hs){
		if(hs.contains(s)){
			return ;
		}
		hs.add(s);
		cnt++;
		
		for(int val : al.get(s)){
			dfs(val,al,hs);
		}
	}

}