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.io.*;
import java.util.*;

public class Main {
    static ArrayList<HashSet<Integer>> graph;
    static HashSet<Integer>components;
    static int cnt;
    static boolean[]visited;
    public static void dfs(int vertex){
        if (visited[vertex])return;
        components.add(vertex);
        visited[vertex] = true;
        for (int nbr:graph.get(vertex))
            dfs(nbr);
    }
    public static void main(String[] args) throws Exception {
        BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb = new StringBuilder();
        String [] inp = buffer.readLine().split(" ");
        int n = Integer.parseInt(inp[0]), m = Integer.parseInt(inp[1]);
        graph = new ArrayList<>();
        for (int pos = 0; pos < n; pos++) {
            graph.add(new HashSet<>());
        }
        visited = new boolean[n];
        for (int pos = 0; pos < m; pos++) {
            inp = buffer.readLine().split(" ");
            int a = Integer.parseInt(inp[0]), b = Integer.parseInt(inp[1]);
            a--;b--;
            graph.get(a).add(b);
            graph.get(b).add(a);
        }
        components = new HashSet<>();
        int ans = Integer.MIN_VALUE;
        for (int pos = 0; pos < n; pos++) {
            if (graph.get(pos).size()==0)continue;
            if (!visited[pos]) {
                components.clear();
                dfs(pos);
                ans = Math.max(ans, components.size());
            }
        }
        System.out.println(ans);
    }
}