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;

namespace ABC128
{
    class C
    {
        static void Main(string[] args)
        {
            int[] a = Console.ReadLine().Split(' ').Select(cc => int.Parse(cc)).ToArray();
            int N = a[0], M = a[1];
            List<int[]> list = new List<int[]>();
            for (int i = 0; i < M; i++)
            {
                int[] b = Console.ReadLine().Split(' ').Select(cc => int.Parse(cc)).ToArray();
                list.Add(b);
            }
            int[] p = Console.ReadLine().Split(' ').Select(cc => int.Parse(cc)).ToArray();

            int counter = 0;
            int ns = (int)Math.Pow(2, N);
            for (int i = 0; i < ns; i++)
            {
                int x = i;
                bool[] onoff = new bool[N];
                for (int j = 0; j < N;j++)
                {
                    onoff[j] = x % 2 == 1;
                    x /= 2;
                }

                for (int j = 0; j < M; j++)
                {
                    int[] s = list[j];
                    {
                        int numOn = 0;
                        for (int k = 0; k < s[0]; k++)
                        {
                            int sw = s[k + 1];
                            if (onoff[sw-1]) numOn++; ;
                        }
                        if (numOn % 2 != p[j])
                        {
                            goto label1;
                        }
                    }
                }
                counter++;
            label1:;
            }

            Console.WriteLine(counter);

        }
    }
}