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: Runtime Error)

import java.io.*;
import java.util.*;
public class Main {
 public static void main(String[] args) throws Exception {
  Scanner file = new Scanner(System.in);
  int n = file.nextInt();
  int m = file.nextInt();
  int[][] a = new int[m][];
  for (int i = 0; i < m; i++) {
   int k = file.nextInt();
   a[i] = new int[k];
   for (int j = 0; j < k; j++) {
    a[i][j] = file.nextInt() - 1; 
   }
  }
  int[] b = new int[n];
  for (int i = 0; i < n; i++) b[i] = file.nextInt();
  int tot = 0;
  for (int i = 0; i < (1 << n); i++) {
   int count = 0;
   int[] c = new int[n];
   for (int j = 0; j < (1 << n); j <<= 1) {
    if ((j & i) > 0) c[(int) (Math.log(j) / Math.log(2))] = 1; 
   }
   int[] d = new int[m];
   for (int j = 0; j < m; j++) {
    int t = 0;
    for (int k = 0; k < a[j].length; k++) {
     if (c[a[j][k]] == 1) t++; 
    }
    t %= 2;
    if (t == b[j]) count++;
   }
   if (count == m) tot++;
  }
  System.out.println(tot);
  file.close();
  System.exit(0);
 }
}