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.*;

class Graph
{
	int v;
	Set<Integer> adj[];
	int count = 0;

	Graph(int n)
	{
		v = n;

		adj = new HashSet[n];

		for(int i = 0 ; i < n ; i++)
			adj[i] = new HashSet<Integer>(); 
	}
	void addEdge(int u,int v)
	{
		adj[u].add(v);
		adj[v].add(u);
	}
	int conn()
	{
		int res = -1;
		boolean visited[] = new boolean[v];
		for(int i = 0; i < v ; i++)
		{
			if(!visited[i])
			{
				dfs(i,visited);
				if(count > res)
					res = count;
				count = 0;
			}
		}
		return res;

	}
	void dfs(int cur,boolean visited[])
	{
		visited[cur] = true;
		count++;

		for(int k : adj[cur])
		{
			if(!visited[k])
				dfs(k,visited);
		}
	}

}
public class Main
{
	public static void main(String args[])
	{
		Scanner kb = new Scanner(System.in);

		int n = kb.nextInt();

		Graph G = new Graph(n);

		int m = kb.nextInt();

		while(m-- > 0)
		{
			int a = kb.nextInt();
			int b = kb.nextInt();

			G.addEdge(a-1,b-1);
		}
		System.out.println(G.conn());

	}
}