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: Wrong Answer)

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

class Program {
    static void Main(string[] args) {
        //入力
        string X = Console.ReadLine();
        int N = int.Parse(X.Split(' ')[0]);
        int M = int.Parse(X.Split(' ')[1]);

        int[] k = new int[M];
        int[][] s = new int[M][];

        for (int i = 0; i < M; i++) {
            string x = Console.ReadLine();
            k[i] = int.Parse(x.Split(' ')[0]);
            s[i] = new int[k[i]];
            for (int j = 0; j < k[i]; j++) {
                s[i][j] = int.Parse(x.Split(' ')[j + 1]) - 1;  //スイッチの番号はゼロスタートにする
            }
        }

        var p_list = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        int p = 0;
        for (int i = 0; i < M; i++) {
            p |= p_list[i] << i;
        }

        int[] A = new int[(int)Math.Pow(2, N)];

        for (int i = 0; i < M; i++) {
            for (int j = 0; j < k[i]; j++) {
                A[s[i][j]] |= 1 << i;
            }
        }

        int ans = 0;

        for (int i = 0; i < (1 << N); i++) {
            int t = 0;
            for (int j = 0; j < N; j++) {
                if ((i >> j & 1) == 1) {
                    t ^= A[i];
                }
            }

            if (t == p) {
                ans++;
            }
        }

        Console.WriteLine(ans);
    }
}