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

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

    Scanner cin;

    public Program() { }

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

    void Calc()
    {
        cin = new Scanner();

        int N = cin.nextInt();
        int M = cin.nextInt();

        //int[] Switches = new int[N + 1];
        int[] Bulbs = new int[M + 1];

        int[][] S = new int[M + 1][];

        for (int i = 1; i <= M; ++i)
        {
            int K = cin.nextInt();
            int[] s = new int[K + 1];

            for (int j = 1; j <= K; ++j)
            {
                s[j] = cin.nextInt();
            }

            S[i] = s;
        }

        int[] P = new int[M + 1];

        for (int i = 1; i <= M; ++i)
        {
            P[i] = cin.nextInt();
        }

        int switchKumiCount = (1 << N);
        int[] swichKumi = new int[switchKumiCount];

        int ansCount = 0;

        for (int i = 0; i < swichKumi.Length; ++i)
        {
            int bulbCount = 0;

            // スイッチN個のon/offの組み合わせを全て調べる
            for (int j = 1; j <= M; ++j)
            {
                // kの行を調べる
                int onCount = 0;

                for (int l = 0; l < S[j].Length; ++l)
                {
                    // 電球がonになるためのスイッチの番号（０始まりにする）
                    int switchIndex = S[j][l] - 1;
                    bool flag = ((i & (1 << switchIndex)) != 0);
                    if (flag) { ++onCount; }
                }

                if ((onCount & 1) == P[j])
                {
                    ++bulbCount;
                }
            }

            if (bulbCount == M)
            {
                ++ansCount;
            }
        }

        WriteLine(ansCount);
    }
}

public static class StringExtension
{
    public static char GetChar1(this string str, int indexOneBase)
    {
        return str[indexOneBase - 1];
    }
}

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 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;
    }
}


Measured memory_bytes: 13268