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.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt(), m = scanner.nextInt();
			UnionFindTree uft = new UnionFindTree(n);
			IntStream.range(0, m).forEach(i -> {
				int a = scanner.nextInt() - 1, b = scanner.nextInt() - 1;
				uft.union(a, b);
			});
			Map<Integer, Integer> map = new HashMap<>();
			IntStream.range(0, n).forEach(i -> {
				int root = uft.find(i);
				map.put(root, map.getOrDefault(root, 0) + 1);
			});
			System.out.println(map.values().stream().mapToInt(Integer::intValue).max().getAsInt());
		}
	}

	/**
	 * Union Find Treeの実装<br/>
	 * https://atcoder.jp/contests/abc040/submissions/4708654 を参考に作成
	 */
	private static class UnionFindTree {
		int[] parent;
		int[] count;

		UnionFindTree(int size) {
			parent = new int[size];
			IntStream.range(0, size).forEach(i -> parent[i] = i);
			count = new int[size];
			Arrays.fill(count, 1);
		}

		int find(int x) {
			if (parent[x] == x) {
				return x;
			} else {
				int v = find(parent[x]);
				parent[x] = v;
				return v;
			}
		}

		/**
		 * @param x
		 * @param y
		 * @return xとyがつながっているかどうか
		 */
		@SuppressWarnings("unused")
		boolean same(int x, int y) {
			return find(x) == find(y);
		}

		/**
		 * xとyを結合する
		 * 
		 * @param x
		 * @param y
		 */
		void union(int x, int y) {
			int rootX = find(x);
			int rootY = find(y);
			if (rootX == rootY) {
				return;
			}
			parent[rootX] = rootY;
			parent[x] = rootY;
			count[rootY] += count[rootX];
		}

		/**
		 * @param x
		 * @return xと結ぶ都市の数
		 */
		public int count(int x) {
			return count[find(x)];
		}
	}
}