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.Linq;
using System.Collections.Generic;
using System;

public class UnionFind
{
    private int[] data;
    public UnionFind(int size)
    {
        data = new int[size];
        for (int i = 0; i < size; i++) data[i] = -1;
    }
    public bool Unite(int x, int y)
    {
        x = Root(x);
        y = Root(y);
        if (x != y)
        {
            if (data[y] < data[x])
            {
                var tmp = y;
                y = x;
                x = tmp;
            }
            data[x] += data[y];
            data[y] = x;
        }
        return x != y;
    }
    public bool IsSameGroup(int x, int y) => Root(x) == Root(y);
    public int Root(int x) => data[x] < 0 ? x : data[x] = Root(data[x]);
    public int getMem(int x) => -data[Root(x)];
}


public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var m = int.Parse(line[1]);
        var uf = new UnionFind(n);
        for (int i = 0; i < m; i++)
        {
            line = Console.ReadLine().Trim().Split(' ');
            uf.Unite(int.Parse(line[0]) - 1, int.Parse(line[1]) - 1);
        }
        var d = new Dictionary<int, int>();
        for (int i = 0; i < n; i++)
        {
            var r = uf.Root(i);
            if (d.ContainsKey(r)) d[r]++;
            else d[r] = 1;
        }
        getAns(d);
    }
    static void getAns(Dictionary<int, int> d)
    {
        var d2 = new List<int>();
        foreach (var x in d) d2.Add(x.Value);
        var a = d2.Distinct().OrderBy(x => x).ToArray();
        var aL = a.Length;
        var ans = a[0];
        for (int i = 1; i < aL; i++)
            ans += a[i] - a[i - 1];
        Console.WriteLine(ans);
    }
}