using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;

partial class Solver
{
    int PopCount(ulong x)
    {
        x = (x & 0x5555555555555555UL) + ((x >> 1) & 0x5555555555555555UL);
        x = (x & 0x3333333333333333UL) + ((x >> 2) & 0x3333333333333333UL);
        x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0fUL;
        x = x + (x >> 8);
        x = x + (x >> 16);
        x = x + (x >> 32);
        return (int)(x & 0x7FLU);
    }

    public void Run()
    {
        var N = ni();
        var M = ni();
        var F = new int[M];
        for (int i = 0; i < M; i++)
        {
            var k = ni();
            var f = 0;
            for (int j = 0; j < k; j++)
            {
                var s = ni() - 1;
                f |= (1 << s);
            }
            F[i] = f;
        }
        var p = ni(M);
        int ans = 0;
        for (int bit = 0; bit < (1 << N); bit++)
        {
            bool ok = true;
            for (int i = 0; i < M; i++)
            {
                if (PopCount((ulong)(bit & F[i])) % 2 != p[i])
                {
                    ok = false;
                    break;
                }
            }
            if (ok) ans++;
        }
        cout.WriteLine(ans);
    }
}


// PREWRITEN CODE BEGINS FROM HERE
partial class Solver : Scanner
{
    public static void Main(string[] args)
    {
        new Solver(Console.In, Console.Out).Run();
    }

    TextReader cin;
    TextWriter cout;

    public Solver(TextReader reader, TextWriter writer)
        : base(reader)
    {
        this.cin = reader;
        this.cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer)
    {
    }

    public int ni() { return NextInt(); }
    public int[] ni(int n) { return NextIntArray(n); }
    public long nl() { return NextLong(); }
    public long[] nl(int n) { return NextLongArray(n); }
    public double nd() { return NextDouble(); }
    public string ns() { return Next(); }
}

public class Scanner
{
    private TextReader Reader;
    private Queue<String> TokenQueue = new Queue<string>();
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    public Scanner()
        : this(Console.In)
    {
    }

    public Scanner(TextReader reader)
    {
        this.Reader = reader;
    }

    public int NextInt() { return Int32.Parse(Next(), ci); }
    public long NextLong() { return Int64.Parse(Next(), ci); }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size)
    {
        var array = new string[size];
        for (int i = 0; i < size; i++) array[i] = Next();
        return array;
    }
    public int[] NextIntArray(int size)
    {
        var array = new int[size];
        for (int i = 0; i < size; i++) array[i] = NextInt();
        return array;
    }

    public long[] NextLongArray(int size)
    {
        var array = new long[size];
        for (int i = 0; i < size; i++) array[i] = NextLong();
        return array;
    }

    public String Next()
    {
        if (TokenQueue.Count == 0)
        {
            if (!StockTokens()) throw new InvalidOperationException();
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext()
    {
        if (TokenQueue.Count > 0)
            return true;
        return StockTokens();
    }

    private bool StockTokens()
    {
        while (true)
        {
            var line = Reader.ReadLine();
            if (line == null) return false;
            var tokens = line.Trim().Split(" ".ToCharArray(), StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) continue;
            foreach (var token in tokens)
                TokenQueue.Enqueue(token);
            return true;
        }
    }
}


Measured memory_bytes: 13268