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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Deque;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
 
 
public class Main {
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		Scanner sc = new Scanner(System.in);
		
		int N = Integer.parseInt(sc.next());
		int M = Integer.parseInt(sc.next());
		
		List<int[]> lines = new ArrayList<>();
		
		for(int i=0;i<M;i++){
			int k = Integer.parseInt(sc.next());
			int[] line = new int[k];
			for(int j=0;j<k;j++){
				line[j] = Integer.parseInt(sc.next())-1;
			}
			lines.add(line);
		}
		
		int[] P = new int[M];
		for(int i=0;i<M;i++){
			P[i] = Integer.parseInt(sc.next());
		}
		
		int ans = 0;
		for(int i=0; i<(1<<N);i++){
			boolean flag = true;
			for(int j=0;j<M;j++){
				int on = 0;
				for(int k:lines.get(j)){
					if((1&i>>k)==1)on++;
				}
				if(on%2 != P[j]){
					flag = false;
					break;
				}
			}
			if(flag)ans++;
		}
	
		System.out.println(ans);
		
		
		
	}
	
}