using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Sandbox
{
    class Program
    {
        static void Main(string[] args)
        {
            var scanner = new Scanner();
            var n = scanner.GetNextAsInt();
            var m = scanner.GetNextAsInt();

            var ss = new List<int>[m];

            for (var i = 0; i < m; i++)
            {
                var si = scanner.ToIntArrayFromNextLine();
                ss[i] = si.Skip(1).Select(j => j - 1).ToList();
            }

            var p = scanner.ToIntArrayFromNextLine();

            var patternNum = Math.Pow(2, n);
            var count = 0;

            for (var pattern = 0; pattern < patternNum; pattern++)
            {
                var onHash = new HashSet<int>();
                for (var ni = 0; ni < n; ni++)
                {
                    if ((pattern & (01 << ni)) != 0)
                    {
                        onHash.Add(ni);
                    }
                }

                var isok = true;

                for (var mi = 0; mi < m; mi++)
                {
                    var si = ss[mi];
                    var onNum = 0;
                    foreach (var sii in si)
                    {
                        if (onHash.Contains(sii))
                        {
                            onNum++;
                        }
                    }

                    if (onNum % 2 != p[mi])
                    {
                        isok = false;
                        break;
                    }
                }

                if (isok)
                {
                    count++;
                }
            }
            Console.WriteLine(count);
        }
    }

    #region String Scanner
    public class Scanner
    {
        private const char Separator = ' ';
        private readonly StreamReader _Stream = new StreamReader(Console.OpenStandardInput());
        private int _Pos;
        private string[] _Line = new string[0];

        #region get a element
        public string GetNext()
        {
            // ReSharper disable once InvertIf
            if (this._Pos >= this._Line.Length)
            {
                // ReSharper disable once PossibleNullReferenceException
                this._Line = this._Stream.ReadLine().Split(Separator);
                this._Pos = 0;
            }
            return this._Line[this._Pos++];
        }
        public int GetNextAsInt()
        {
            return int.Parse(this.GetNext());
        }
        public long GetNextAsLong()
        {
            return long.Parse(this.GetNext());
        }
        public double GetNextAsDouble()
        {
            return double.Parse(this.GetNext());
        }
        #endregion

        #region get array
        public string[] ToArrayFromNextLine()
        {
            if (this._Pos >= this._Line.Length)
            {
                // ReSharper disable once PossibleNullReferenceException
                this._Line = this._Stream.ReadLine().Split(Separator);
            }

            this._Pos = this._Line.Length;
            return this._Line;
        }
        public int[] ToIntArrayFromNextLine()
        {
            return ToIntArray(this.ToArrayFromNextLine());
        }
        public long[] ToLongArrayFromNextLine()
        {
            return ToLongArray(this.ToArrayFromNextLine());
        }
        public double[] ToDoubleArrayFromNextLine()
        {
            return ToDoubleArray(this.ToArrayFromNextLine());
        }
        #endregion

        #region convert array
        private static int[] ToIntArray(string[] array)
        {
            var result = new int[array.Length];
            for (var i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }
            return result;
        }
        private static long[] ToLongArray(string[] array)
        {
            var result = new long[array.Length];
            for (var i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }
            return result;
        }
        private static double[] ToDoubleArray(string[] array)
        {
            var result = new double[array.Length];
            for (var i = 0; i < array.Length; i++)
            {
                result[i] = double.Parse(array[i]);
            }
            return result;
        }
        #endregion
    }
    #endregion
}


Measured memory_bytes: 13652