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.ArrayDeque;
    import java.util.ArrayList;
    import java.util.Arrays;
    import java.util.Deque;
    import java.util.List;
    import java.util.Scanner;

    //
    public class Main {

        public static void main(String[] args) {
            Scanner sc = new Scanner(System.in);
            int N = sc.nextInt();
            int M = sc.nextInt();
            int cnt = 0;
            int count = 0;
            int ans = 0;
            int input[][]=new int[M+1][N+1];
            int input_p[]=new int[M+1];

            for(int i=1;i<=M;i++){
                int K = sc.nextInt();
                input[i][0]= K;
                for(int j=1;j<=K;j++){
                    input[i][j]=sc.nextInt();
                }
            }

            for(int k=1;k<=M;k++){
                input_p[k]=sc.nextInt();
            }



            for(int bit=0;bit<(1<<N);bit++){
                count=0;
                for(int i=1;i<=M;i++){
                    cnt=0;
                    for(int j=1;j<=input[i][0];j++){
                        if(((((1<<(input[i][j]-1))&bit)>>(input[i][j]-1)))==1){
                        cnt=cnt+1;
                        }
                    }
                    if(input_p[i]==cnt%2){
                        count=count+1;
                    }
                }
                if(count==M){
                    ans=ans+1;
                }
            }
        System.out.println(ans);
        }
    }