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

class Program
{
    public static cp alg;
    public static int[] P;
    public static int[][] KS;
    public static int N;
    public static int M;
    public static double num = 0;
    static void Main(string[] args)
    {
        alg = new cp();

        var temp = alg.inputSplitInt();
        N = temp[0];
        M = temp[1];
        KS = alg.inputJaggedArrayInt(M);
        P = alg.inputSplitInt();
        int ans = 0;
        for (int a = 0; a < (1 << N); a++)
        {
            var bit = new List<int>();
            for (int b = 0; b < N; b++)
            {
                if ((a & (1 << b)) > 0)
                {
                    bit.Insert(0, 1);
                }
                else
                {
                    bit.Insert(0, 0);
                }
            }
            bool f = true;
            for (int b = 0; b < M; b++)
            {
                int onCount = 0;
                for (int c = 0; c < KS[b][0]; c++)
                {
                    int index = KS[b][c + 1] - 1;
                    if (bit[index] == 1)
                    {
                        onCount++;
                    }
                }
                if (onCount % 2 != P[b])
                {
                    f = false;
                }
            }
            if (f)
            {
                ans++;
            }
        }
        WriteLine(ans);
    }
}

class cp
{

    public cp()
    {
    }
    public int GCD(int a, int b)
    {
        return a % b == 0 ? b : GCD(b, a % b);
    }
    public int LCM(int a, int b)
    {
        return a * b / GCD(a, b);
    }
    public int countChar(string s, string key)
    {
        return (s.Length - s.Replace(key, "").Length);
    }
    public string Yn(bool f)
    {
        if (f)
        {
            return "Yes";
        }
        else
        {
            return "No";
        }
    }
    public string YN(bool f)
    {
        if (f)
        {
            return "YES";
        }
        else
        {
            return "NO";
        }
    }
    public string yn(bool f)
    {
        if (f)
        {
            return "yes";
        }
        else
        {
            return "no";
        }
    }
    public void inputSkip()
    {
        ReadLine();
        return;
    }
    public string inputString()
    {
        return ReadLine();
    }
    public string[] inputSplitString()
    {
        return ReadLine().Split();
    }
    public string[] inputLinesString(int len)
    {
        var arr = new string[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine();
        }
        return arr;
    }
    public string[][] inputJaggedArrayString(int len)
    {
        var arr = new string[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split();
        }
        return arr;
    }
    public int inputInt()
    {
        return int.Parse(ReadLine());
    }
    public int[] inputSplitInt()
    {
        return ReadLine().Split().Select(i => int.Parse(i)).ToArray();
    }
    public int[] inputLinesInt(int len)
    {
        var arr = new int[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = int.Parse(ReadLine());
        }
        return arr;
    }
    public int[][] inputJaggedArrayInt(int len)
    {
        var arr = new int[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => int.Parse(i)).ToArray();
        }
        return arr;
    }
    public long inputLong()
    {
        return long.Parse(ReadLine());
    }
    public long[] inputSplitLong()
    {
        return ReadLine().Split().Select(i => long.Parse(i)).ToArray();
    }
    public long[] inputLinesLong(long len)
    {
        var arr = new long[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = long.Parse(ReadLine());
        }
        return arr;
    }
    public long[][] inputJaggedArrayLong(int len)
    {
        var arr = new long[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => long.Parse(i)).ToArray();
        }
        return arr;
    }
    public double inputDouble()
    {
        return double.Parse(ReadLine());
    }
    public double[] inputSplitDouble()
    {
        return ReadLine().Split().Select(i => double.Parse(i)).ToArray();
    }
    public double[] inputLinesDouble(int len)
    {
        var arr = new double[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = double.Parse(ReadLine());
        }
        return arr;
    }
    public double[][] inputJaggedArrayDouble(int len)
    {
        var arr = new double[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => double.Parse(i)).ToArray();
        }
        return arr;
    }
}