using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            new ABC128().SolveC(new ConsoleInput(Console.In, ' '));
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
  class ABC128
    {
      public void SolveC(ConsoleInput cin)
        {
            var n = cin.ReadInt;
            var m = cin.ReadInt;
            var S = new List<int[]>();
            for (int k = 0; k < m; k++)
            {
                int m_k = cin.ReadInt;
                S.Add(cin.ReadIntArray(m_k));
            }
            var P = cin.ReadIntArray(m);
            var lamp = new int[m];
            int count = 0;
            int countOfOnSwitch = 0;
            for (int bit = 0; bit < 1 << n; bit++) //全スイッチ状態ループ
            {
                for (int k = 0; k < m; k++) //各ランプのループ
                {
                    foreach (int s in S[k])
                    {
                        if ((bit & (1 << s - 1)) != 0)
                        {
                            countOfOnSwitch++;
                        }
                    }
                    if (countOfOnSwitch % 2 == P[k])
                    {
                        lamp[k] = 1;
                    }
                    else
                    {
                        lamp[k] = 0;
                    }
                }
                if (lamp.Sum() == m)
                {
                    count++;
                }
                countOfOnSwitch = 0;
            }
            /*
            WriteLine($"{n} {m}");
            for (int i = 0; i < m; i++)
            {
                foreach (int k in S[i]) { Write($"{k} "); }
                WriteLine();
            }
            foreach (int p in P) { Write($"{p} "); }
            WriteLine();
            */
            WriteLine(count);
            ReadLine();
        }
    }
}
