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 System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
public class ABC
{
    public static void Main()
    {
        int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int N = x[0];
        int M = x[1];
        string[] readk = new string[M];
        for (int i = 0; i < M; i++)
        {
            readk[i] = Console.ReadLine();
        }
        int[] readp = Console.ReadLine().Split().Select(int.Parse).ToArray();

        light[] lights = new light[M];
        string switches = "";
        string lastStatus = "";

        for (int i = 0; i < M; i++)
        {
            lights[i] = new light(N, readk[i]);
            lights[i].residue =readp[i];
        }
        for (int i = 0; i < N; i++)
        {
            switches += "0";
            lastStatus += "1";
        }

        int output = 0;
        for (int i = 0; i <= 2048; i++)
        {
            

            bool breakflag = false;
            for (int j = 0; j < M; j++)
            {
                lights[j].changeStatus(switches);
                if (lights[j].on == false)
                {
                    breakflag = true;
                    break;
                }
            }
            if (breakflag == false)
            {
                output++;
            }


            if (lastStatus == switches) break;
            switches = next(switches);
        }
        Console.WriteLine(output);


    }

    public static string next(string now)
    {
        string output = "";
        output = now;

        if (now[output.Length-1] == '0')
        {
            output = now.Substring(0, output.Length-1) + "1";
            return output;

        }
        else
        {
            return next(now.Substring(0, output.Length - 1)) + "0";

        }

        
        

    }

    
}

public class light
{
    public bool on;
    public int[] rule;
    public int[] input;
    public int residue;
    public light()
    {

    }
    public light(int N,string read)
    {
        var split = read.Split();
        this.rule = new int[N];
        for (int i = 1; i < split.Length; i++)
        {
            int value = int.Parse(split[i]);
            this.rule[value-1] = 1;
        }


    }

    public bool changeStatus(string input)
    {

        int sum = 0;
        int N = input.Length;
        int[] intinput = new int[N];
        for (int i = 0; i < N; i++)
        {
            intinput[i] = int.Parse(input[i].ToString());
        }

        for (int i = 0; i < N; i++)
        {
            sum += intinput[i] * this.rule[i];
        }
        if (sum % 2 == this.residue)
        {
            this.on = true;
        }
        else
            this.on = false;
        return this.on;

    }
}