Problem:
Score : 400 points

Problem Statement

On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.

For CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.

The i-th (1≦i≦N) participant can speak K_i languages numbered L_{i,1}, L_{i,2}, ..., L_{i,{}K_i}.

Two participants A and B can communicate with each other if and only if one of the following conditions is satisfied:

There exists a language that both A and B can speak.

There exists a participant X that both A and B can communicate with.

Determine whether all N participants can communicate with all other participants.

Constraints

2≦N≦10^5

1≦M≦10^5

1≦K_i≦M

(The sum of all K_i)≦10^5

1≦L_{i,j}≦M

L_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.

Partial Score

200 points will be awarded for passing the test set satisfying the following: N≦1000, M≦1000 and (The sum of all K_i)≦1000.

Additional 200 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N M
K_1 L_{1,1} L_{1,2} ... L_{1,{}K_1}
K_2 L_{2,1} L_{2,2} ... L_{2,{}K_2}
:
K_N L_{N,1} L_{N,2} ... L_{N,{}K_N}

Output

If all N participants can communicate with all other participants, print YES. Otherwise, print NO.

Sample Input 1

4 6
3 1 2 3
2 4 2
2 4 6
1 6

Sample Output 1

YES

Any two participants can communicate with each other, as follows:

Participants 1 and 2: both can speak language 2.

Participants 2 and 3: both can speak language 4.

Participants 1 and 3: both can communicate with participant 2.

Participants 3 and 4: both can speak language 6.

Participants 2 and 4: both can communicate with participant 3.

Participants 1 and 4: both can communicate with participant 2.

Note that there can be languages spoken by no participant.

Sample Input 2

4 4
2 1 2
2 1 2
1 3
2 4 3

Sample Output 2

NO

For example, participants 1 and 3 cannot communicate with each other.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

class Program
{
    public void Proc()
    {
        Reader.IsDebug = false;
        int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();

        int hitoCount = inpt[0];
        int gengoCount = inpt[1];

        this.hitoList = new Hito[hitoCount];
        for (int i = 0; i < hitoCount; i++)
        {
            this.hitoList[i] = new Hito(i);
            inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).Skip(1).ToArray();

            hitoList[i] = new Hito(i);
            Dictionary<int, bool> grp = new Dictionary<int, bool>();
            if (i > 0)
            {
                foreach (int gengo in inpt)
                {
                    if (!GengoHito.ContainsKey(gengo))
                    {
                        continue;
                    }
                    GengoHito[gengo].Keys.ToList().ForEach(a => { grp[hitoList[a].Root.ID] = true; });
                }
            }

            if (grp.Count >= 1)
            {
                int[] grpList = grp.Keys.ToArray();

                hitoList[grpList[0]].AddItem(hitoList[i]);

                for (int j = 1; j < grpList.Length; j++)
                {
                    hitoList[grpList[0]].AddItem(hitoList[grpList[j]]);
                }

            }


            inpt.ToList().ForEach(a =>
            {
                if (!GengoHito.ContainsKey(a))
                {
                    GengoHito.Add(a, new Dictionary<int, bool>());
                }
                GengoHito[a].Add(i, true);
            });
        }
        Console.WriteLine(hitoList.Any(a => a.Root.ID != 0)?"NO":"YES");

    }

    public Dictionary<int, Dictionary<int, bool>> GengoHito = new Dictionary<int, Dictionary<int, bool>>();
    public Hito[] hitoList = null;
    public class Hito
    {
        public Hito Parent;
        public Hito Root;
        public int ID;

        public List<Hito> Items = new List<Hito>();
        public Hito(int id)
        {
            this.ID = id;
            this.Parent = this;
            this.Root = this;
        }

        public void AddItem(Hito cld)
        {
            cld.Parent = this;
            cld.RefreshRoot(this.Root);
        }

        private void RefreshRoot(Hito newRoot)
        {
            this.Root = newRoot;
            this.Items.ForEach(a => a.RefreshRoot(newRoot));
        }
    }

    public class Reader
    {
        public static bool IsDebug = true;
        private static String PlainInput = @"



4 4
2 1 2
2 1 2
1 3
2 4 3


";
        private static System.IO.StringReader Sr = null;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (Sr == null)
                {
                    Sr = new System.IO.StringReader(PlainInput.Trim());
                }
                return Sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
    }
    static void Main()
    {
        Program prg = new Program();
        prg.Proc();
    }
}