/*
csc -debug C.cs && mono --debug C.exe <<< "2 2
2 1 2
1 2
0 1"
*/

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

public class HelloWorld {
    public static void SolveCodeForces() {
        var N = cin.NextInt();
        var M = cin.NextInt();

        var masks = new int[M];
        for (var i = 0; i < M; i++) {
            var mask = 0;
            var switches = cin.IntArray();
            for (var j = 1; j < switches.Length; j++) {
                mask |= 1 << (switches[j] - 1);
            }
            masks[i] = mask;
// System.Console.WriteLine(new {i, mask});
        }

        var P = cin.IntArray();

        var ans = 0;

        var max = Math.Pow(2, N);
        for (var i = 0; i < max; i++) {

            var ok = true;
            for (var j = 0; j < masks.Length; j++) {
                var res = i & masks[j];
                var cnt = CountBits(res);
                if (cnt % 2 != P[j]) {
                    ok = false;
                    break;
                }
            }

            if (ok) ans++;

        }

        System.Console.WriteLine(ans);
    }

    public static int CountBits(int value) {
        int count = 0;
        while (value != 0) {
            count++;
            value &= value - 1;
        }
        return count;
    }

    static Scanner cin = new Scanner();
    static StringBuilder cout = new StringBuilder();

    static public void Main () {
        SolveCodeForces();
        // IncreaseStack(SolveCodeForces);
        // System.Console.Write(cout.ToString());
    }

    public static void IncreaseStack(ThreadStart action, int stackSize = 128000000)
    {
        var thread = new Thread(action, stackSize);
        thread.Start();
        thread.Join();
    }
}

public static class Helpers {
    public static T[] CreateArray<T>(int length, Func<int, T> itemCreate) {
        var result = new T[length];
        for (var i = 0; i < result.Length; i++)
            result[i] = itemCreate(i);
        return result;
    }
}

public class Scanner
{
    private string[] line = new string[0];
    private int index = 0;

    public string Next() {
        if (line.Length <= index) {
            line = Console.ReadLine().Split(' ');
            index = 0;
        }
        var res = line[index];
        index++;
        return res;
    }

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

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

    public ulong NextUlong() {
        return ulong.Parse(Next());
    }

    public string[] Array() {
        line = Console.ReadLine().Split(' ');
        index = line.Length;
        return line;
    }

    public int[] IntArray(int emptyPrefixLen = 0) {
        var array = Array();
        var result = new int[emptyPrefixLen + array.Length];
        for (int i = 0; i < array.Length; i++)
            result[emptyPrefixLen + i] = int.Parse(array[i]);
        return result;
    }

    public long[] LongArray() {
        var array = Array();
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
            result[i] = long.Parse(array[i]);
        return result;
    }

    public ulong[] UlongArray() {
        var array = Array();
        var result = new ulong[array.Length];
        for (int i = 0; i < array.Length; i++)
            result[i] = ulong.Parse(array[i]);
        return result;
    }
}

Measured memory_bytes: 13140