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.Scanner;

class UnionFind {
    int[] parent;

    UnionFind(int n) {
        parent = new int[n];
        Arrays.fill(parent, -1);
    }

    int find(int x) {
        if (parent[x] < 0) {
            return x;
        } else {
            parent[x] = find(parent[x]);
            return parent[x];
        }
    }

    void unite(int x, int y) {
        int rootX = find(x);
        int rootY = find(y);
        if (rootX == rootY) {
            return;
        }

        if (parent[rootX] > parent[rootY]) {
            int temp = rootX;
            rootX = rootY;
            rootY = temp;
        }
        parent[rootX] += parent[rootY];
        parent[rootY] = rootX;
    }

}


public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = nextInt(scanner);
        int m = nextInt(scanner);
        UnionFind unionFind = new UnionFind(n);
        for (int i = 0; i < m; i++) {
            unionFind.unite(nextInt(scanner) - 1, nextInt(scanner) - 1);
        }
        System.out.println(Math.abs(Arrays.stream(unionFind.parent).min().orElse(0)));
    }

    private static int nextInt(Scanner scanner) {
        return Integer.parseInt(scanner.next());
    }

    private static long nextLong(Scanner scanner) {
        return Long.parseLong(scanner.next());
    }

    private static float nextFloat(Scanner scanner) {
        return Float.parseFloat(scanner.next());
    }

    private static double nextDouble(Scanner scanner) {
        return Double.parseDouble(scanner.next());
    }


}