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.Linq;
using System.Collections.Generic;

namespace agc030_a
{
    class Program
    {
        static void Main(string[] args)
        {
            var text = Console.ReadLine();
            var list = text.Split(' ').ToList().Select(x => int.Parse(x)).ToList();

            var a = list[0];
            var b = list[1];

            var hogelist = new List<hoge>();
            for(int i = 0; i < b; i++){
                text = Console.ReadLine();
                list = text.Split(' ').ToList().Select(x => int.Parse(x)).ToList();

                var item = new hoge();

                item.a = list.Skip(1).ToList();

                hogelist.Add(item);
            }

            text = Console.ReadLine();
            list = text.Split(' ').ToList().Select(x => int.Parse(x)).ToList();

            for(int i = 0; i < list.Count; i++){
                hogelist[i].answer = list[i];
            }

            var pattern = Math.Pow(2, a);

            var sw = new List<int>();
            for(int i = 0; i < a; i++){
                sw.Add(0);
            }

            var allon = 0;
            for(int i = 0; i < pattern; i++){
                var bin = Convert.ToString(i, 2);
                var remain = a - bin.Length;
                if (remain > 0){
                    bin = new string('0', remain) + bin;
                } 

                for (int j = 0; j < a; j++){
                    var onoff = int.Parse(bin.Substring(j, 1));
                    sw[j] = onoff;
                }

                var isFind = false;
                foreach(var item in hogelist){
                    var total = 0;
                    foreach(var lampsw in item.a){
                        total = total + sw[lampsw - 1];
                    }

                    var md = total % 2;

                    if (item.answer != md){
                        isFind = true;
                        break;

                    }

                }

                if (isFind == false){
                    allon++;
                }


            }

            Console.WriteLine(allon);
        }
    }

    class hoge{      
        public List<int> a;

        public int answer;
    }
}