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.math.BigInteger;
import java.util.*;
import java.util.function.BiFunction;
import java.util.function.Function;
import java.util.stream.Collectors;

public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int m = sc.nextInt();
    if (m == 0) {
      System.out.println(1);
      return;
    }
    Map<Integer, UnionFind<Integer>> friendSetMap = new HashMap<>();
    for (int i = 1; i <= n; i++) {
      friendSetMap.put(i, new UnionFind<>(1));
    }
    for (int i = 0; i < m; i++) {
      int a = sc.nextInt();
      int b = sc.nextInt();
      UnionFind.union(friendSetMap.get(a), friendSetMap.get(b), Integer::sum);
    }
    int result = 0;
    for (int i = 1; i <= n; i++) {
      Integer value = friendSetMap.get(i).getRoot().getValue();
      if (value > result) {
        result = value;
      }
    }
    System.out.println(result);
  }
}

class UnionFind<T> {
  UnionFind<T> parent;
  private T value;

  public UnionFind(T value) {
    this.value = value;
  }

  public static <S> void union(UnionFind<S> a, UnionFind<S> b, BiFunction<S, S, S> unionMap) {
    UnionFind<S> aRoot = a.getRoot();
    UnionFind<S> bRoot = b.getRoot();
    if (aRoot != bRoot) {
      bRoot.parent = aRoot;
      aRoot.value = unionMap.apply(aRoot.getValue(), bRoot.getValue());
    }
  }

  public T getValue() {
    return value;
  }

  public UnionFind<T> getRoot() {
    if (parent == null) {
      return this;
    }
    UnionFind<T> root = parent.getRoot();
    parent = root;
    return root;
  }
}