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.IOException;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;

public class Main {
    private static final StringBuilder builder = new StringBuilder();
    public static void main(String[] args) {
        int n = readInt(), m = readInt();
        HashMap<Integer, Integer> map = new HashMap<>(n);
        for (int i = 1; i <= n; i++) {
            map.put(i, -1);
        }

        int number = 0;
        for (int i = 0; i < m; i++) {
            int a = readInt(), b = readInt();
            if (a > b) {
                int tmp = a;
                a = b;
                b = tmp;
            }

            int ag = map.get(a);
            int bg = map.get(b);
            if (ag >= 0) {
                map.put(b, ag);
            } else if (bg >= 0) {
                map.put(a, bg);
            } else {
                map.put(a, number);
                map.put(b, number);
                number++;
            }
        }

        HashMap<Integer, Integer> countMap = new HashMap<>(number);
        map.forEach((i, g) -> {
            if (g == -1) {
                return;
            }

            int count = countMap.getOrDefault(g, 0);
            countMap.put(g, count + 1);
        });

        System.out.print(countMap.values().stream().mapToInt(v -> v).max().orElse(n));
    }

    private static void read() {
        builder.setLength(0);
        while (true) {
            try {
                int b = System.in.read();
                if (b == ' ' || b == '\n' || b == -1) {
                    break;
                } else {
                    builder.appendCodePoint(b);
                }
            } catch (IOException e) {
                break;
            }
        }
    }

    private static int readInt() {
        read();
        return Integer.parseInt(builder.toString());
    }

    private static int readInt(int radix) {
        read();
        return Integer.parseInt(builder.toString(), radix);
    }

    private static long readLong() {
        read();
        return Long.parseLong(builder.toString());
    }

    private static long readLong(int radix) {
        read();
        return Long.parseLong(builder.toString(), radix);
    }

    private static BigInteger readBigInteger() {
        read();
        return new BigInteger(builder.toString());
    }

    private static BigInteger readBigInteger(int radix) {
        read();
        return new BigInteger(builder.toString(), radix);
    }

    private static double readDouble() {
        read();
        return Double.parseDouble(builder.toString());
    }

    private static BigDecimal readBigDecimal() {
        read();
        return new BigDecimal(builder.toString());
    }

    private static float readFloat() {
        read();
        return Float.parseFloat(builder.toString());
    }

    private static void skipLine() {
        while (true) {
            try {
                int b = System.in.read();
                if (b == '\n' || b == -1) {
                    break;
                }
            } catch (IOException e) {
                break;
            }
        }
    }

    private static void skip() {
        while (true) {
            try {
                int b = System.in.read();
                if (b == ' ' || b == '\n' || b == -1) break;
            } catch (IOException e) {
                break;
            }
        }
    }

}