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 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DFriends solver = new DFriends();
        solver.solve(1, in, out);
        out.close();
    }

    static class DFriends {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), m = in.nextInt();
            UnionFind uf = new UnionFind(n);
            for (int i = 0; i < m; i++) {
                int a = in.nextInt() - 1, b = in.nextInt() - 1;
                uf.union(a, b);
            }

            int answer = 0;
            for (int i = 0; i < n; i++) {
                answer = Math.max(answer, uf.size(i));
            }

            out.println(answer);
        }

    }

    static class InputReader {
        public final BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }

    static class UnionFind {
        private final int[] __rep;
        private final int[] __size;

        public UnionFind(int n) {
            __rep = new int[n];
            __size = new int[n];
            for (int i = 0; i < n; i++) {
                __rep[i] = i;
                __size[i] = 1;
            }
        }

        public int rep(int x) {
            if (__rep[x] == x) {
                return x;
            }

            int r = rep(__rep[x]);
            __rep[x] = r;
            return r;
        }

        public int size(int x) {
            return __size[rep(x)];
        }

        public boolean union(int x, int y) {
            x = rep(x);
            y = rep(y);

            if (x == y) {
                return false;
            }

            if (size(x) < size(y)) {
                int t = x;
                x = y;
                y = t;
            }

            // now size(x) >= size(y)

            __rep[y] = x;
            __size[x] += __size[y];
            return true;
        }

    }
}