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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include<stdio.h>
#include <string.h>
int beki(int a,int b)
{
  int i;
  int c = 1;
  for(i=0;i<b;i++){
    c=c*a;
  }
  return(c);
}
int on(int q[10],int s[],int k)
{
  int a,i;
  for(i=0;i<k;i++){
    a=a*q[s[k]];
  }
  return(a);
}
int main(void)
{
  int n,m;
  int k[10];
  int s[10][10];
  int i,j,l;
  int p[10];
  int a=0;
  int b;
  int c =0;
  int q[10];
  
  scanf("%d %d",&n,&m);
  
  for(i=0;i<m;i++);{
    scanf("%d",&k[i]);
    for(j=0;j<k[i];j++){
      scanf("%d",&s[i][j]);
    }
  }
  for(i=0;i<m;i++){
    scanf("%d",&p[i]);
  }
  for(i=0;i<beki(2,n);i++){
    b = i;
    for(j=0;j<n;j++){
      q[j] = b / beki(2,n-j-1);
      b=b-beki(2,n-j-1)* q[j];
    }
    for(l=0;l<m;l++){
      if(on(q,s[i],k)==1)
        c++;
      else break;
    }
    if(c==m)
      a++;
  }
  printf("%d",a);
     return 0;
}