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

public class AtCoderA
{
    static void Main()
    {
        var sc = new Scanner();

        int n = sc.NextInt();
        int m = sc.NextInt();

        UnionFind uf = new UnionFind(n);

        for (int i = 0; i < m; i++)
        {
            int a = sc.NextInt() - 1;
            int b = sc.NextInt() - 1;
            uf.Unite(a, b);
        }

        long answer = 0;

        for (int i = 0; i < n; i++)
        {
            answer = Math.Max(answer, uf.GetSize(i));
        }

        Console.WriteLine(answer);
    }

    // 木の併合
    class UnionFind
    {
        private readonly int[] parents;
        private readonly int[] sizes;

        public UnionFind(int count)
        {
            parents = new int[count + 1];
            sizes = new int[count + 1];
            for (int i = 0; i < count + 1; i++)
            {
                parents[i] = i;
                sizes[i] = 1;
            }
        }

        // TreeのNode数の取得
        public int GetSize(int branch)
        {
            return sizes[GetRoot(branch)];
        }

        // Treeの併合、Node数の合算
        public void Unite(int x, int y)
        {
            int rootX = GetRoot(x);
            int rootY = GetRoot(y);
            if (rootX == rootY) return;
            sizes[rootX] += sizes[rootY];
            parents[rootY] = rootX;
        }

        // 同じTreeに含まれるか
        public bool IsSameRoot(int x, int y)
        {
            return GetRoot(x) == GetRoot(y);
        }

        // Rootの取得
        public int GetRoot(int n)
        {
            if (parents[n] == n)
            {
                return n;
            }
            else
            {
                return parents[n] = GetRoot(parents[n]);
            }
        }
    }

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}