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.*;
import java.math.*;
import java.util.*;

public class Main {
    FastScanner sc;
    PrintWriter p;

    static boolean visited[];
    static ArrayList<ArrayList<Integer>> adj;

    int dfs(int start) {
        int count = 1;
        visited[start] = true;
        for(int i : adj.get(start)) {
            if(!visited[i])
                count += dfs(i);
        }
        return count;
    }

    void solve() {
        int N = sc.nextInt();
        int M = sc.nextInt();
        adj = new ArrayList<>();
        visited = new boolean[N + 1];

        for(int i = 0; i <= N; i++)
            adj.add(i, new ArrayList<>());

        for(int i = 0; i < M; i++) {
            int u = sc.nextInt();
            int v = sc.nextInt();
            adj.get(u).add(v);
            adj.get(v).add(u);
        }

        int ans = 0;
        for(int i = 1; i <= N; i++) {
            if(!visited[i])
                ans = Math.max(ans, dfs(i));
        }
        p.println(ans);
    }

    void run() {
        try {
            sc = new FastScanner(new File("Friends.in"));
            p = new PrintWriter(new File("Friends.out"));

            solve();

            p.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        sc = new FastScanner(System.in);
        p = new PrintWriter(System.out);

        solve();

        p.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

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

        int[] nextIntArray(int N) {
            int[] A = new int[N];
            for (int i = 0; i < N; i++) {
                A[i] = sc.nextInt();
            }
            return A;
        }

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

        long[] nextLongArray(int N) {
            long[] A = new long[N];
            for (int i = 0; i < N; i++) {
                A[i] = sc.nextLong();
            }
            return A;
        }

        BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

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

        double[] nextDoubleArray(int N) {
            double[] A = new double[N];
            for (int i = 0; i < N; i++) {
                A[i] = sc.nextDouble();
            }
            return A;
        }

    }

    public static void main(String[] args) {
        new Main().runIO();
    }
}