Problem:
Score : 300 points

Problem Statement

We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.

Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.

How many combinations of "on" and "off" states of the switches light all the bulbs?

Constraints

1 \leq N, M \leq 10

1 \leq k_i \leq N

1 \leq s_{ij} \leq N

s_{ia} \neq s_{ib} (a \neq b)

p_i is 0 or 1.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M

Output

Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.

Sample Input 1

2 2
2 1 2
1 2
0 1

Sample Output 1

1

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

There are four possible combinations of states of (Switch 1, Switch 2): (on, on), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all the bulbs, so we should print 1.

Sample Input 2

2 3
2 1 2
1 1
1 2
0 0 1

Sample Output 2

0

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an even number of switches that are "on" among the following: Switch 1.

Bulb 3 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

Switch 1 has to be "off" to light Bulb 2 and Switch 2 has to be "on" to light Bulb 3, but then Bulb 1 will not be lighted. Thus, there are no combinations of states of the switches that light all the bulbs, so we should print 0.

Sample Input 3

5 2
3 1 2 5
2 2 3
1 0

Sample Output 3

8

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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

class Program
{
    static void Main()
    {
        var line1 = MyUtil.ReadlongArray();
        int switchCount = (int)line1[0];
        int denkyuCount = (int)line1[1];

        List<long>[] denkyu = new List<long>[line1[1]];

        for (int i = 0; i < line1[1]; i++)
        {
            var input = MyUtil.ReadlongArray().ToList();
            input.RemoveAt(0);
            denkyu[i] = input;
        }

        var target = MyUtil.ReadlongArray();
        int bit = 0;
        int res = 0;

        while (true)
        {
            if (bit.GetBit(switchCount + 1) == 1)
            {
                break;
            }

            int ok = 0;
            for (int i = 0; i < denkyu.Length; i++)
            {
                var count = denkyu[i].Count(sw => bit.GetBit((int)sw) == 1);
                if (count % 2 == target[i])
                {
                    ++ok;
                }
            }

            if (ok == denkyuCount)
            {
                res++;
            }

            bit++;
        }

        WriteLine(res);

        ReadKey();
    }
}


static class MyUtil
{
    public static int GetBit(this int num, int count)
    {
        int mask = (int)Math.Pow(2, count - 1);
        return (num & mask) == 0 ? 0 : 1;
    }

    public static int[] ToBit(this int num)
    {
        const int size = sizeof(int) * 8;
        var array = new int[size];
        for (int i = 0; i < size; i++)
        {
            array[i] = num.GetBit(size - i);
        }
        return array;
    }

    public static long[] ReadlongArray()
    {
        return ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
    }

    /// <summary>
    /// <see cref="IEnumerable{T}"/>の各要素を並べてコンソールに出力します。各要素の間には半角スペースが一つ入ります。
    /// </summary>
    /// <typeparam name="T"></typeparam>
    /// <param name="ts"></param>
    public static void WriteToConsole<T>(this IEnumerable<T> ts)
    {
        StringBuilder stringBuilder = new StringBuilder();
        foreach (T t in ts)
        {
            stringBuilder.Append(t.ToString());
            stringBuilder.Append(" ");
        }
        stringBuilder.Remove(stringBuilder.Length - 1, 1);
        Console.WriteLine(stringBuilder.ToString());
    }

    public static void WriteToDebugConsole<T>(this IEnumerable<T> ts)
    {
        StringBuilder stringBuilder = new StringBuilder();
        foreach (T t in ts)
        {
            stringBuilder.Append(t.ToString());
            stringBuilder.Append(" ");
        }
        stringBuilder.Remove(stringBuilder.Length - 1, 1);
        System.Diagnostics.Debug.WriteLine(stringBuilder.ToString());
    }
}