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.*;
public class Main{
	static int count;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		ArrayList<ArrayList<Integer>> graph = new ArrayList<>();
		int n = sc.nextInt();
		for(int i=0;i<n;i++){
			graph.add(new ArrayList<Integer>());
		}
		int m = sc.nextInt();
		for(int i=0;i<m;i++){
			int a = sc.nextInt()-1;
			int b = sc.nextInt()-1;
			graph.get(a).add(b);
			graph.get(b).add(a);
		}
		boolean[] vis = new boolean[n];
		int max=0;
		for(int i=0;i<n;i++){
			if(vis[i]==false){
				count=0;
				dfs(graph,vis,i);
				if(count>max){
					max=count;
				}
			}
		}
		System.out.println(max);

	}
	public static void dfs(ArrayList<ArrayList<Integer>> graph, boolean[] vis,int start){
		vis[start]=true;
        count++;
        for(int i=0;i<graph.get(start).size();i++){
             if(vis[graph.get(start).get(i)]==false){
             	dfs(graph,vis,graph.get(start).get(i));
             }
        }
	}
}