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

class Main{
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		HashSet<Integer> hs = new HashSet<>();
		ArrayList<HashSet<Integer>> groups = new ArrayList<>();
		for(int i=1;i<=n;i++)
			hs.add(i);
		for(int i=0;i<m;i++){
			int a = sc.nextInt();
			int b = sc.nextInt();
			if (hs.contains(a)){
				boolean added = false;
				hs.remove(a);
				for(int j=0;j<groups.size();j++){
					if (groups.get(j).contains(b)){
						groups.get(j).add(a);
						added = true;
					}
				}
				if (!added){
					HashSet<Integer> hs2 = new HashSet<Integer>();
					hs2.add(a);
					groups.add(hs2);
				}
			}
			if (hs.contains(b)){
				boolean added = false;
				for(int j=0;j<groups.size();j++){
					if(groups.get(j).contains(a)){
						groups.get(j).add(b);
						added = true;
					}
				}
				if (!added){
					HashSet<Integer> hs2 = new HashSet<Integer>();
					hs2.add(a);
					groups.add(hs2);
				}
			}
		}
		int max = 0;
		for(int i=0;i<groups.size();i++){
			if (max < groups.get(i).size())
				max = groups.get(i).size();
		}
		System.out.println(max);
		sc.close();
	}
}