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 System.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N, M;
        public long MOD = 1000000007;

        public void Run()
        {
            {
                var line = Input.ReadIntArray();
                N = line[0];
                M = line[1];
            }

            var uf = new UnionFind(N + M);

            for (int i = 0; i < N; i++)
            {
                var line = Input.ReadIntArray();
                for (int j = 1; j < line.Length; j++)
                {
                    uf.Unite(i, N + line[j] - 1);
                }
            }

            for (int i = 1; i < N; i++)
            {
                if (!uf.Same(0, i))
                {
                    Console.WriteLine("NO");
                    return;
                }
            }

            Console.WriteLine("YES");
        }


    }

    // libs ----------
    class UnionFind
    {
        public List<int> Par;
        public List<int> Sizes;

        public UnionFind(int n)
        {
            Par = new List<int>();
            Sizes = new List<int>();
            for (int i = 0; i < n; i++)
            {
                Par.Add(i);
                Sizes.Add(1);
            }
        }

        public int Find(int x)
        {
            if (x == Par[x]) return x;
            Par[x] = Find(Par[x]);
            return Par[x];
        }

        public void Unite(int x, int y)
        {
            x = Find(x);
            y = Find(y);
            if (x == y) return;

            if (Sizes[x] < Sizes[y])
            {
                // swap
                int temp = x;
                x = y;
                y = temp;
            }

            Par[y] = x;
            Sizes[x] += Sizes[y];
            Sizes[y] = 0;
        }

        public bool Same(int x, int y)
        {
            return Find(x) == Find(y);
        }

        public int Size(int x)
        {
            return Sizes[Find(x)];
        }
    }

    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}