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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;

static class Program
{
    static void Main()
    {
        var nm = Console.ReadLine().Split(" ").Select(int.Parse).ToArray();
        var (n, m) = (nm[0], nm[1]);
        var friendPairs = Enumerable.Range(1, m)
            .Select((i) => Console.ReadLine().Split(" ").Select(s => int.Parse(s) - 1).ToArray());

        var unionFind = new UnionFind(n);
        foreach (var friendPair in friendPairs)
        {
            unionFind.Unite(friendPair[0], friendPair[1]);
        }

        var answer = Enumerable.Range(0, n).Max(i => unionFind.Size(i));

        Console.WriteLine(answer);
    }
}

public class UnionFind
{
    public int[] Parent { get; set; }
    public UnionFind(int n)
    {
        Parent = Enumerable.Repeat(-1, n).ToArray();
    }

    public int Root(int x)
    {
        if (Parent[x] < 0)
        {
            return x;
        }

        Parent[x] = Root(Parent[x]);

        return Parent[x];
    }

    public void Unite(int x, int y)
    {
        if (!Same(x, y))
        {
            Parent[Root(y)] += Parent[Root(x)];
            Parent[Root(x)] = Root(y);
        }
    }

    public bool Same(int x, int y)
    {
        return Root(x) == Root(y);
    }

    public int Size(int x)
    {
        return -Parent[Root(x)];
    }
}