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)

import java.util.ArrayDeque;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.function.Function;

public class Main {

	public static void main(String[] args) {
		new Main().run();
	}

	int n;
	int m;

	public void run() {
		Scanner sc = new Scanner(System.in);

		n = sc.nextInt();
		m = sc.nextInt();

	    Map<Integer,Set<Integer>> map = new HashMap<>();
	    int max=0;
		for( int i=0; i< m ; i++ ) {
			Function<? super Integer, ? extends Set<Integer>> createSetIfNull = (v)->{ 
				Set<Integer> s = new HashSet<>();
				s.add(v);
				return s;
			};
			int a = sc.nextInt();
			Set<Integer> r = map.computeIfAbsent(a, createSetIfNull);
			int b = sc.nextInt();
			Set<Integer> l = map.computeIfAbsent(b, createSetIfNull);
			
			r.addAll(l);
			map.put(a, r);
			map.put(b, r);
			
			if( max < r.size() ) {
				max = r.size();
			}
		}
		
		System.out.println(max);
		
		
		
	}
}