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

namespace AtCorder
{
    class Program
    {
        static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }
        public void Solve(ConsoleInput cin)
        {
            var N = cin.ReadInt;
            var M = cin.ReadInt;
            var k = new int[M];
            var X = new List<int[]>(M);
            var ans = 0;
            for(int i = 0; i < M; i++)
            {
                k[i] = cin.ReadInt;
                var s = new int[k[i]];
                for(int j = 0; j < k[i]; j++)
                {
                    s[j] = cin.ReadInt;
                }
                X.Add(s);
            }
            var P = cin.ReadIntArray(M);
            for(int i = 0; i < Pow(2, N); i++)
            {
                var isrow = 0;
                var tmp = int.Parse(Convert.ToString(i, 2)).ToString("0000000000");
                for(int j = 0; j < M; j++)
                {
                    var ison = 0;
                    for(int t = 0; t < k[j]; t++)
                    {
                        var index = X[j][t] - 1;
                        if(tmp[9-index] == '1')
                        {
                            ison++;
                        }
                    }

                    if(ison % 2 == P[j])
                    {
                        isrow++;
                    }
                    else
                    {
                        break;
                    }
                }
                if(isrow == M)
                {
                    ans++;
                }
            }
            WriteLine(ans);
        }
    }

    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; }
    }
}


Measured memory_bytes: 13396