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.Scanner;

public class Main {
    static int[] data;
    static int[] w;

    static int root(int q) {
        if (data[q] != q) {
            data[q] = root(data[q]);
        }
        return data[q];
    }

    static void union(int p, int q) {
        int rp = root(p);
        int rq = root(q);
        if (w[rp] > w[rq]) {
            data[rq] = rp;
            w[rp] += w[rq];
        } else {
            data[rp] = rq;
            w[rq] += w[rp];
        }
    }

    static boolean find(int p, int q) {
        return root(p) == root(q);
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        data = new int[n];
        w = new int[n];
        for (int i = 0; i < n; i++) {
            data[i] = i;
            w[i] = 1;
        }
        for (int i = 0; i < m; i++) {
            int a = scanner.nextInt();
            int b = scanner.nextInt();
            if (!find(a - 1, b - 1)) union(a - 1, b - 1);
        }
        int ans = 0;
        for (int i = 0; i < n; i++) {
            if (data[i] == i)
                ans = Math.max(ans, w[i]);
        }
        System.out.println(ans);
    }
}