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

public static partial class Program
{
    public static void Main()
    {
        var nm = CRL().ArrayInts();
        var n = nm[0];
        var m = nm[1];

        var k = new int[m];
        var stt = new int[m][];
        for (int i = 0; i < m; i++)
        {
            var inp = CRL().ArrayInts();
            k[i] = inp[0];
            stt[i] = inp.Skip(1).Take(inp.Length - 1).ToArray();
        }

        var pis = CRL().ArrayInts();

        var ans = 0;
        for (int bit = 1; bit <= 1 << n; bit++)
        {
            var cnt = new int[m];
            for (int light = 0; light < n; light++)
            {
                if (((bit >> light) & 1) == 1)
                {
                    for (int query = 0; query < m; query++)
                    {
                        cnt[query] += stt[query].Contains(light + 1) ? 1 : 0;
                    }
                }
            }

            var flag = true;
            for (int i = 0; i < m; i++)
            {
                if (cnt[i] % 2 == pis[i])
                {
                    continue;
                }

                flag = false;
                break;
            }

            if (flag)
            {
                ans++;
            }
        }
        
        CWL(ans);
    }
}

public static partial class Program
{
    //テンプレここから
    public static int Sigma(int n, int next = 1, int val = 0) => next > n ? val : Sigma(n, next + 1, val + next);
    public static long GCD(long a, long b) => b == 0 ? a : GCD(b, a % b);
    public static int GCD(int a, int b) => b == 0 ? a : GCD(b, a % b);
    public static long LCM(long a, long b) => a * b / GCD(a, b);
    public static int LCM(int a, int b) => a * b / GCD(a, b);
    public static string CRL() => Console.ReadLine();
    public static void CWL(object obj) => Console.WriteLine(obj);
    public static int ToInt(this double d) => (int) d;
    public static long ToLong(this double d) => (long) d;
    public static int ToInt(this string str) => int.Parse(str);
    public static long ToLong(this string str) => long.Parse(str);
    public static long[] ToLong(this IEnumerable<string> strs) => strs.Select(x => x.ToLong()).ToArray();
    public static int[] ToInt(this IEnumerable<string> strs) => strs.Select(x => x.ToInt()).ToArray();
    public static long[] ArrayLongs(this string str, char opr = ' ') => str.Split(opr).ToLong();
    public static int[] ArrayInts(this string str, char opr = ' ') => str.Split(opr).ToInt();
    public static long Diff(long a, long b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static int Diff(int a, int b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static long Sign(this long i) => Math.Sign(i);
    public static bool IsEven(this long i) => i % 2 == 0;
    public static bool IsEven(this int i) => i % 2 == 0;
    public static readonly int[] Dx = new[] {0, -1, 0, 1};
    public static readonly int[] Dy = new[] {-1, 0, 1, 0};
    public const int Mod = 1000000007;
    public static string alphabet = "abcdefghijklmnopqrstuvwxyz";
    public static long ToLong(this char c) => c.ToString().ToInt();
    public static long[] Sort(this long[] array) => array.OrderBy(x => x).ToArray();
    public static int[] Sort(this int[] array) => array.OrderBy(x => x).ToArray();
    public static long[] DSort(this long[] array) => array.OrderByDescending(x => x).ToArray();
    public static int[] DSort(this int[] array) => array.OrderByDescending(x => x).ToArray();
    public static string Join(this IEnumerable<string> array, string sep = "") => string.Join(sep, array);
    public static string Join(this IEnumerable<char> array, string sep = "") => string.Join(sep, array);

    public static string JoinToStr(this IEnumerable<int> array, string sep = "")
        => array.Select(x => x.ToString()).Join(sep);

    //テンプレここまで
}

Measured memory_bytes: 17616