using System;
using System.Collections.Generic;
using System.IO;
using System.Text;

namespace Contest
{
    struct R
    {
        public string S;
        public int P;
        public int Index;
        public R(string s, int p, int i)
        {
            S = s;
            P = p;
            Index = i;
        }
    }
    class Program
    {
        public void Solve()
        {
            var sc = new Scanner();
            int N = sc.NextInt();
            int M = sc.NextInt();
            List<int>[] s = new List<int>[N];
            for (int i = 0; i < N; i++)
            {
                s[i] = new List<int>();
            }
            for (int i = 0; i < M; i++)
            {
                int k = sc.NextInt();
                for (int j = 0; j < k; j++)
                {
                    s[sc.NextInt() - 1].Add(i);
                }
            }

            int[] p = sc.IntArray();

            int loop = 1 << N;
            int ans = 0;
            for (int i = 0; i < loop; i++)
            {
                int cp = i;
                int[]c = new int[M];
                for (int j = 0; j < N; j++)
                {
                    if (cp % 2 == 1)
                    {
                        foreach (var i1 in s[j])
                        {
                            c[i1]++;
                        }
                    }

                    cp /= 2;
                }

                bool flag = true;
                for (int j = 0; j < M; j++)
                {
                    if (p[j] != c[j] % 2)
                    {
                        flag = false;
                        break;
                    }
                }

                if (flag)
                {
                    ans++;
                }
            }
            Console.WriteLine(ans);
        }
        static void Main() => new Program().Solve();
    }
}

class Scanner
{
    public Scanner()
    {
        _stream = new StreamReader(Console.OpenStandardInput());
        _pos = 0;
        _line = new string[0];
        _separator = ' ';
    }
    private char _separator;
    private StreamReader _stream;
    private int _pos;
    private string[] _line;
    #region get a element
    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = _stream.ReadLine().Split(_separator);
            _pos = 0;
        }
        return _line[_pos++];
    }
    public int NextInt()
    {
        return int.Parse(Next());
    }
    public long NextLong()
    {
        return long.Parse(Next());
    }
    public double NextDouble()
    {
        return double.Parse(Next());
    }
    #endregion
    #region convert array
    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }
    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }
    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }
    #endregion
    #region get array
    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = _stream.ReadLine().Split(_separator);
        _pos = _line.Length;
        return _line;
    }
    public int[] IntArray()
    {
        return ToIntArray(Array());
    }
    public long[] LongArray()
    {
        return ToLongArray(Array());
    }
    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }
    #endregion
}

Measured memory_bytes: 13268