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: Wrong Answer)

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

namespace atcoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var buffer = Console.ReadLine().Split();
            var N = int.Parse(buffer[0]);
            var M = int.Parse(buffer[1]);

            Dictionary<string, string>[] list = new Dictionary<string, string>[N];
            for (int i = 0; i < N; i++) list[i] = new Dictionary<string, string>();
            for (int i = 0; i < M; i++)
            {
                buffer = Console.ReadLine().Split();
                var a = int.Parse(buffer[0]) - 1;
                var b = int.Parse(buffer[1]) - 1;
                list[a][buffer[1]] = "";
                list[b][buffer[0]] = "";
            }

            int max = int.MinValue;
            foreach (var v in list)
            {
                if (v.Keys.Count == 0) continue;
                max = v.Keys.Count > max ? v.Keys.Count : max;
            }

            Console.WriteLine(max + 1);
        }
    }
}