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 ConsoleApp87 {
    class Program {
        static void Main(string[] args) {
            var st = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = st[0];
            int M = st[1];

            var k = new int[M];

            var s = new int[M][];
            for (int i = 0; i < M; i++) {
                var x = Console.ReadLine().Split().Select(int.Parse).ToArray();
                k[i] = x[0];
                s[i] = new int[k[i]];
                for (int j = 0; j < k[i]; j++) {
                    s[i][j] = x[j + 1] - 1;
                }
            }

            var p = Console.ReadLine().Split().Select(int.Parse).ToArray();

            int ans = 0;
            int cnt = 0;

            for (int bit = 0; bit < (1 << N); bit++) {
                for (int lb = 0; lb < M; lb++) {
                    cnt = 0;
                    foreach(var element in s[lb]) {
                        if ((bit & (1 << element)) != 0) {
                            cnt++;
                        }
                    }

                    if (cnt % 2 == p[lb]) {
                        //OKなので何もせずスルーする
                    } else {
                        goto skip;
                    }
                }
                ans++;

                skip:;
            }

            Console.WriteLine(ans);
        }
    }
}