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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        var nm = Input.ar;
        var parent = new int[nm[1]];
        var uf = new UnionFind<int>();
        Enumerable.Range(1, nm[0]).ToList().ForEach(v => uf.MakeSet(v));
        for(var i = 0; i < nm[0]; i++)
        {
            var lang = Input.ar;
            for (var k = 1; k <= lang[0]; k++)
                if (parent[lang[k] - 1] == 0)
                    parent[lang[k] - 1] = i + 1;
                else uf.Union(i + 1, parent[lang[k] - 1]);
        }
        var isA = true;
        for (var i = 2; i <= nm[0]; i++)
            if (isA)
                isA = uf.IsSame(1, i);
            else break;
        WriteLine(isA ? "YES" : "NO");
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public  static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static int[][] twodim(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] twodimL(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class UnionFind<T>
{
    private class Vertex
    {
        public T Key { get; set; }
        public Vertex Parent { get; set; }
        public int Rank { get; set; }
        public Vertex(T key) : this(key, null, 0)
        {

        }
        public Vertex(T key, Vertex Parent, int rank)
        {
            this.Key = key;
            this.Parent = Parent;
            this.Rank = rank;
        }
    }
    private readonly Dictionary<T, Vertex> dics;
    private readonly Vertex NIL;

    public int Count { get; private set; }

    public UnionFind()
    {
        NIL = new Vertex(default(T));
        dics = new Dictionary<T, Vertex>();
    }
    
    public T parent(T key)
        => FindSet(dics[key].Parent).Key;
    
    public bool IsSame(T key1, T key2)
    {
        if (!dics.ContainsKey(key1) || !dics.ContainsKey(key2))
            return false;
        return ReferenceEquals(FindSet(dics[key1]),FindSet(dics[key2]));
    }

    public bool MakeSet(T key)
    {
        if (dics.ContainsKey(key))
            return false;
        dics[key] = new Vertex(key, NIL, 0);
        dics[key].Parent = dics[key];
        Count++;
        return true;
    }

    public bool Union(T key1, T key2)
    {
        if (!dics.ContainsKey(key1) || !dics.ContainsKey(key2))
            return false;
        if (IsSame(key1, key2)) return false;
        Link(FindSet(dics[key1]), FindSet(dics[key2]));
        Count--;
        return true;
    }

    private void Link(Vertex vex1, Vertex vex2)
    {
        if (vex1.Rank > vex2.Rank)
        {
            vex2.Parent = vex1;
        }
        else
        {
            vex1.Parent = vex2;
            if (vex1.Rank == vex2.Rank)
                vex2.Rank++;
        }
    }

    private Vertex FindSet(Vertex vex)
    {
        if (!ReferenceEquals(vex.Parent, vex))
            vex.Parent = FindSet(vex.Parent);
        return vex.Parent;
    }
}