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.Collections;
using System.Linq;
using System.Numerics;




namespace contest
{

    class contest
    {


        static void Main(string[] args)
        {


            
            var num = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int n = num[0];
            int m = num[1];
            var person = new int[n][];
            var dic = new Dictionary<int, SortedSet<int>>();
            var lang = new SortedSet<int>[m+1];
            for (int i = 0; i < m; i++) lang[i + 1] = new SortedSet<int>();
            for (int i=0; i< n; i++)
            {
                person[i] = Console.ReadLine().Split().Select(int.Parse).ToArray();
                dic[i + 1] = new SortedSet<int>();
                //for (int j = 1; j <= person[i][0]; j++)
                //{
                //    dic[i + 1].Add(person[i][j]);
                //    lang[person[i][j]].Add(i + 1);
                //}

            }

            Array.Sort(person, (a, b) =>   a[0] - b[0]);
            for (int i = 0; i < n; i++)
            {
               
                for (int j = 1; j <= person[i][0]; j++)
                {
                    dic[i + 1].Add(person[i][j]);
                    lang[person[i][j]].Add(i + 1);
                }

            }

            //var memo = new UnionFind(n);
            var memoP = new bool[n+1];
            var memoL = new bool[m + 1];
            memoP[0] = true;
            memoL[0] = true;

            int count = 0;
            int need = (n * (n + 1) / 2);

            bool ll = true;
            var queP = new Queue<int>();
            var queL = new Queue<int>();
            for(int i=1; i<person[0].Length; i++)
            {
                queL.Enqueue(person[0][i]);
                memoL[person[0][i]] = true;
            }
            count += 1;
            memoP[1] = true;

            while(queL.Count()>0 || queP.Count()>0)
            {
                if(ll)
                {
                    if (queL.Count() > 0)
                    {
                        int cur = queL.Dequeue();

                        foreach (var item in lang[cur])
                        {
                            if (!memoP[item])
                            {
                                queP.Enqueue(item);
                                memoP[item] = true;
                                count += item;
                            }

                        }
                    }

                    ll = false;
                }
                else
                {
                    if (queP.Count() > 0)
                    {
                        int cur = queP.Dequeue();

                        foreach (var item in dic[cur])
                        {
                            if (!memoL[item])
                            {
                                queL.Enqueue(item);
                                memoL[item] = true;

                            }

                        }
                    }


                    ll = true;

                    if (count == need) break;
                }

               

            }



            if (count == need) Console.WriteLine("YES");
            else Console.WriteLine("NO");
           
			
           
        }

      
    }

   
}