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.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		int[] s=sc.Ia;
		int[] a=new int[s[1]];
		for(int i = 0;i<s[1];i++) {
			int[] e=sc.Ia;
			for(int j = 1;j<e.Length;j++) {
				a[i]|=1<<(e[j]-1);
			}
		}
		int[] p=sc.Ia;
		int ans=0;
		for(int i = 0;i<(1<<s[0]);i++) {
			int q=0;
			for(int j = 0;j<s[1];j++) {
				if(bits(a[j]&i)%2==p[j]){q++;}
				else{break;}
			}
			if(q==s[1]){ans++;}
		}
		Console.WriteLine("{0}",ans);
	}
	static int bits(long bits){
		bits=(bits&0x55555555)+(bits>>1&0x55555555);
		bits=(bits&0x33333333)+(bits>>2&0x33333333);
		bits=(bits&0x0f0f0f0f)+(bits>>4&0x0f0f0f0f);
		bits=(bits&0x00ff00ff)+(bits>>8&0x00ff00ff);
		return (int)((bits&0x0000ffff)+(bits>>16&0x0000ffff));
	}
}

public class Sc{
	private string[] a;
	private int n=-1,m=0;
	public int I{get{if(n==-1||n==a.Length-1){n=-1;a=Console.ReadLine().Split();}n++;return int.Parse(a[n]);}}
	public long L{get{if(n==-1||n==a.Length-1){n=-1;a=Console.ReadLine().Split();}n++;return long.Parse(a[n]);}}
	public double D{get{if(n==-1||n==a.Length-1){n=-1;a=Console.ReadLine().Split();}n++;return double.Parse(a[n]);}}
	public string S{get{if(n==-1||n==a.Length-1){n=-1;a=Console.ReadLine().Split();}n++;return a[n];}}
	public string Sz{get{return Console.ReadLine();}}
	public int[] Ia{get{if(n!=-1&&n!=a.Length-1){m=n;n=-1;return Array.ConvertAll(a.Skip(m+1).ToArray(),int.Parse);}return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public int[] Ia2(int b){return Array.ConvertAll((((b&1)!=0?"0 ":"")+Console.ReadLine()+((b&2)!=0?" 0":"")).Split(),int.Parse);}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public string[] Sa2{get{return (Console.ReadLine()+" 0").Split();}}
}