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.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();

        int M = sc.nextInt();

        int[][] info = new int[M][2];

        for (int i = 0; i < M; i++) {
            info[i][0] = sc.nextInt();
            info[i][1] = sc.nextInt();
        }

        HashMap<Integer, Set<Integer>> map = new HashMap<>();

        for (int i = 0; i < M; i++) {

            Set<Integer> set = map.getOrDefault(info[i][0], new HashSet<>());
            set.add(info[i][1]);
            map.put(info[i][0], set);

            Set<Integer> set2 = map.getOrDefault(info[i][1], new HashSet<>());
            set2.add(info[i][0]);
            map.put(info[i][1], set2);
        }

        int size = 0;
        for (int key : map.keySet()) {

            if (map.get(key).size() > size) {
                size = map.get(key).size();
            }
        }
        System.out.println(size + 1);
    }
}