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

namespace Atcoder
{
    public class Program
    {
        static void Main(string[] args)
        {
            var r1 = ReadSplit();
            var n = r1[0].Int();
            var m = r1[1].Int();
            var l = new int[m][];
            var ans = new int[m][];
            for (int i = 0; i < m; i++)
            {
                var r2 = ReadSplit();
                var k = r2[0].Int();
                l[i] = new int[k];
                ans[i] = new int[k];
                for (int j = 0; j < k; j++)
                {
                    l[i][j] = r2[j + 1].Int();
                }
            }
            var s = new int[m];
            var r3 = ReadSplit();
            for (int i = 0; i < m; i++)
            {
                s[i] = r3[i].Int();
            }

            var ansCount = 0;
            for (int i = 0; i < Math.Pow(2, n); i++)
            {
                for (int j = 0; j < m; j++)
                {
                    for (int o = 0; o < ans[j].Length; o++)
                    {
                        ans[j][o] = 0;
                    }
                }
                for (int j = 0; j < n; j++)
                {
                    if ((i >> j & 1) == 1)
                    {
                        On(j + 1, l, ans);
                    }
                }
                var tmp = 0;
                for (int j = 0; j < m; j++)
                {
                    if (ans[j].Sum() % 2 == s[j]) tmp++;
                }
                if (tmp == m)
                {
                    ansCount++;
                }
            }
            WriteRead(ansCount);
        }

        private static void On(int s, int[][] d, int[][] ans)
        {
            for (int i = 0; i < d.Length; i++)
            {
                for (int j = 0; j < d[i].Length; j++)
                {
                    var di = d[i][j];
                    if (di == s)
                    {
                        ans[i][j] = 1;
                    }
                }
            }
        }

        public static string Read()
        {
            return Console.ReadLine();
        }

        public static string[] ReadSplit()
        {
            return Console.ReadLine().Split(' ');
        }

        public static void WriteRead(object str)
        {
            Console.WriteLine(str);
            Read();
        }

        public static void Write(object str)
        {
            Console.WriteLine(str);
        }

        private static bool ChangeMin<T>(ref T a, T b) where T : IComparable
        {
            if (a.CompareTo(b) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        private static bool ChangekMax<T>(ref T a, T b) where T : IComparable
        {
            if (b.CompareTo(a) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }
    }
}


public static class Extentions
{
    public static int Int(this object obj)
    {
        return int.Parse(obj.ToString());
    }

    public static long Long(this object obj)
    {
        return long.Parse(obj.ToString());
    }

    public static decimal Decimal(this object obj)
    {
        return decimal.Parse(obj.ToString());
    }

    public static double Double(this object obj)
    {
        return double.Parse(obj.ToString());
    }

    public static T2 GetValueZero<T1, T2>(this Dictionary<T1, T2> d, T1 key) where T2 : struct
    {
        T2 value;
        if (d.TryGetValue(key, out value))
        {
            return value;
        }
        return new T2();
    }
}



Measured memory_bytes: 13396