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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class Program
{
    static void Main(string[] args)
    {
        new Program().Solve();
    }

    void Solve()
    {
        Scanner cin = new Scanner();
        int n = cin.NextInt();
        int m = cin.NextInt();
        List<int>[] s = new List<int>[m];
        int[] p = new int[m];

        for (int i = 0; i < m; i++)
        {
            int k = cin.NextInt();
            s[i] = new List<int>();
            for (int j = 0; j < k; j++)
            {
                s[i].Add(cin.NextInt() - 1);
            }
        }
        for (int i = 0; i < m; i++)
        {
            p[i] = cin.NextInt();
        }

        int ans = 0;
        for (int i = 0; i < Math.Pow(2, n); i++)
        {
            bool ok = true;
            for (int j = 0; j < m; j++)
            {
                var patterns = s[j];
                int count = 0;
                foreach (var pattern in patterns)
                {
                    if ((i >> pattern & 1) == 1)
                    {
                        count++;
                    }

                }
                if (count % 2 != p[j] % 2)
                {
                    ok = false;
                }
            }
            if (ok)
            {
                ans++;
            }
        }

        Console.WriteLine(ans);
    }
}

class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string Next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return Next();
        i = 0;
        return s[i++];
    }

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

    public char[] ArrayChar()
    {
        return Next().ToCharArray();
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextInt() + add;
        }
        return Array;
    }

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

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextLong() + add;
        }
        return Array;
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextDouble() + add;
        }
        return Array;
    }
}