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
{
    public class Program
    {
        public 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 s = new List<int>[M];
            for (int i = 0; i < M; i++)
            {
                k[i] = cin.ReadInt;
                s[i] = new List<int>();
                for (int j = 0; j < k[i]; j++)
                {
                    s[i].Add(cin.ReadInt);
                }
            }
            var p = cin.ReadIntArray(M);
            Dfs(N, M, s, p, 0, new int[N]);
            Console.WriteLine(count);
        }

        static int count = 0;
        static void Dfs(int N, int M, List<int>[] s, int[] p, int index, int[] state)
        {
            if (index == N)
            {
                var ok = true;
                for (int i = 0; i < M; i++)
                {
                    var sum = 0;
                    foreach (var j in s[i])
                    {
                        sum += state[j - 1];
                    }
                    if (sum % 2 != p[i])
                    {
                        ok = false;
                        break;
                    }
                }
                if (ok)
                {
                    count++;
                }
            }
            else
            {
                var nextState1 = new int[N];
                Array.Copy(state, 0, nextState1, 0, N);
                nextState1[index] = 1;
                var nextState2 = new int[N];
                Array.Copy(state, 0, nextState2, 0, N);
                nextState2[index] = 0;
                Dfs(N, M, s, p, index + 1, nextState1);
                Dfs(N, M, s, p, index + 1, nextState2);
            }
        }
    }

    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