using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class Program
{
    static void Main(string[] args)
    {
        new Program().Solve();
    }

    void Solve()
    {
        Scanner cin = new Scanner();
        int n = cin.NextInt();
        int m = cin.NextInt();
        List<int>[] s = new List<int>[m];
        int[] p = new int[m];

        for (int i = 0; i < m; i++)
        {
            int k = cin.NextInt();
            s[i] = new List<int>();
            for (int j = 0; j < k; j++)
            {
                s[i].Add(cin.NextInt() - 1);
            }
        }
        for (int i = 0; i < m; i++)
        {
            p[i] = cin.NextInt();
        }

        int ans = 0;
        for (int i = 1; i < Math.Pow(2, n); i++)
        {
            bool ok = true;
            foreach (var (patterns, lightIndex) in s.Indexed())
            {
                int count = 0;
                foreach (var pattern in patterns)
                {
                    if((i >> pattern & 1) == 1)
                    {
                        count++;
                    }

                }
                if (count % 2 != p[lightIndex] % 2)
                {
                    ok = false;
                }
            }
            if (ok)
            {
                ans++;
            }
        }

        Console.WriteLine(ans);
    }
}

class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string Next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return Next();
        i = 0;
        return s[i++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public char[] ArrayChar()
    {
        return Next().ToCharArray();
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextInt() + add;
        }
        return Array;
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextLong() + add;
        }
        return Array;
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextDouble() + add;
        }
        return Array;
    }
}

public static partial class TupleEnumerable
{
    public static IEnumerable<(T item, int index)> Indexed<T>(this IEnumerable<T> source)
    {
        if (source == null) throw new ArgumentNullException(nameof(source));

        IEnumerable<(T item, int index)> impl()
        {
            var i = 0;
            foreach (var item in source)
            {
                yield return (item, i);
                ++i;
            }
        }

        return impl();
    }
}