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.util.Scanner;

public class Main {
	public static void main(String[]args) {
		try(Scanner scan = new Scanner(System.in)){		
			int N = scan.nextInt();//スイッチの個数
			int M= scan.nextInt();//ｍ個の電球
			
			int[]k = new int[M];
			int[][]s = new int[M][N];
			
			for(int i = 0;i<M;i++) {
				k[i]  =scan.nextInt();
				for(int j =0;j<k[i];j++) {
					s[i][j] = scan.nextInt();
				}
			}
			int[]p = new int[M];//０or1
			
			for(int i = 0;i<M;i++) {
				p[i] =scan.nextInt();
			}
			
			int[] sw = new int[N];
			int dennkyugatukutouri = 0;
			for(int i = 0;i<(int)Math.pow(2, N);i++) {	
				for(int j = 0;j<N;j++) {
					if((1&i>>j)==1) 
						sw[j] = 1;
					else
						sw[j] = 0;
				}
				
				int hikarukosuu = 0;
				for(int z = 0;z<M;z++) {
					int onkosuu = 0;
					for(int w = 0;w<k[z];w++) {
						if(sw[s[z][w]-1]==1) {
							onkosuu++;
						}
					}
					if(onkosuu%2==p[z]) {
						hikarukosuu++;
					}
				}
				
				if(hikarukosuu==M) {
					dennkyugatukutouri++;
				}
				
				
			}
			
			
			System.out.println(dennkyugatukutouri);
			
			
			
		}
		
		
	}
		
	

}