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: Runtime Error)

import java.util.Scanner;

public class Main {

	static int MOD = 1000000007;

	public static void main(String[] args) {
		exec_1_1();

	}

	public static void exec_1_1() {

		try(var sc = new Scanner(System.in)) {

			int N = sc.nextInt();

			int M = sc.nextInt();

			int[] f = new int[N];


			for(int i=0; i<N; i++) f[i]=-1;

			for(int i=0; i<M; i++) {
				int a = sc.nextInt()-1;
				int b = sc.nextInt()-1;

				if(f[a]>-1&&f[b]<0) {
					int swap = a;
					b = a;
					a = swap;
				}

				int rIdx = rootIdx(f, a);
				if(rIdx==rootIdx(f, b)) continue ;

				f[rIdx] += rootVal(f, b);
				f[b] = rIdx;
			}

			int min = 0;

			for(int i=0; i<N; i++) min = Math.min(min, f[i]);

			System.out.println(min*-1);
		}
	}


	public static int rootVal(int[] f, int x) {

		if(f[x]<0)return f[x];

		return rootVal(f, f[x]);

	}

	public static int rootIdx(int[] f, int x) {

		if(f[x]<0)return x;

		return rootIdx(f, f[x]);

	}
}