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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        CP sc = new CP();
        int n = sc.nextInt(), m = sc.nextInt();
        ArrayList<ArrayList<Integer>> adj = new ArrayList<>();
        for (int i = 0; i < n; i++)
            adj.add(new ArrayList<>());
        for (int i = 0; i < m; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            adj.get(u).add(v);
            adj.get(v).add(u);
        }
        boolean[] visited = new boolean[n];
        int max = Integer.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            if (!visited[i]) {
                c = 0;
                DFS(adj, visited, i);
                if (max < c)
                    max = c;
            }
        }
        System.out.println(max + 1);
    }

    static int c;

    static void DFS(ArrayList<ArrayList<Integer>> adj, boolean[] visited, int s) {
        visited[s] = true;
        for (int u : adj.get(s))
            if (!visited[u]) {
                c++;
                DFS(adj, visited, u);
            }
    }

    /*****************************************************************************/
    static class CP {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        public CP() {
            bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        }

        int nextInt() {
            return Integer.parseInt(NNNN());
        }

        long nextLong() {
            return Long.parseLong(NNNN());
        }

        double nextDouble() {
            return Double.parseDouble(NNNN());
        }

        String NNNN() {
            while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        String nextLine() {
            String spl = "";
            try {
                spl = bufferedReader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return spl;
        }
    }
    /*****************************************************************************/
}