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.*;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.next());
		int m = Integer.parseInt(sc.next());
		int friends[];
		friends = new int[n + 1];

		// 入力を配列に持つ
		String line[];
		line = new String[m];
		for (int i = 0; i < m; i++) {
			int a = Integer.parseInt(sc.next());
			int b = Integer.parseInt(sc.next());
			line[i] = Math.min(a, b) + "_" + Math.max(a, b);
		}
		Arrays.sort(line);

		// 確認用
//		for (int i = 0; i < m; i++) {
//			System.out.println(line[i]);
//		}

		// friends[77]には出席番号77番の人の友達の数が入る
		for (int i = 0; i < m; i++) {

			// 不要な情報であればスキップ
			if (i != 0 && line[i].equals(line[i - 1])) {
				continue;
			}

			friends[Integer.valueOf(line[i].split("_")[0])]++;
			friends[Integer.valueOf(line[i].split("_")[1])]++;
		}

		// 確認用
//		for (int i = 1; i < n + 1; i++) {
//			System.out.println(i + " " + friends[i]);
//		}

		// 最も友達が多い人は、何人友達がいるか？
		int best = 0;
		for (int i = 1; i < n + 1; i++) {
			if (best < friends[i]) {
				best = friends[i];
			}
		}

		// 最も友達が多い人の、友達の数が500人だったら、501グループに分断する
		System.out.println(best + 1);

	}
}