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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(void) {
  int i,j,k,ans=0;

  int n,m;
  scanf("%d%d", &n, &m);

  int num[11]={},switch_num,s[11][11]={};
  for(i=1;i<=m;i++){
    scanf("%d", &num[i]);
    for(j=0;j<num[i];j++){
      scanf("%d", &switch_num);
      for(k=0;;k++){
        if(s[switch_num][k]==0){
          s[switch_num][k]=i;
          break;
        }
      }
    }
  }

  int p[11]={};
  for(i=1;i<=m;i++){
    scanf("%d", &p[i]);
  }

  int lamp[11]={},on[12]={},lamp_num=0,flag=0;
  while(1){//for(i=1;i<=n;i++){printf("%d ", on[i]);}printf("\n");
    flag=0;
    for(i=1;i<=m;i++){
      lamp[i]=0;
    }

    for(i=1;i<=m;i++){
      if(on[i]==1){
        for(j=0;;j++){
          lamp_num=s[i][j];
          if(lamp_num==0){
            break;
          }
          lamp[lamp_num]=(lamp[lamp_num]+1)%2;
        }
      }
    }

    for(i=1;i<=m;i++){
      if(lamp[i]!=p[i]){
        flag=1;
        break;
      }
    }
    if(flag==0){
      ans++;
      //for(i=1;i<=m;i++){printf("%d ", lamp[i]);}printf("\n");
    }

    on[1]++;
    for(i=1;;i++){
      if(on[i]==2){
        on[i]=0;
        on[i+1]++;
      }else{
        break;
      }
    }
    if(on[n+1]==1){
      break;
    }
  }

  printf("%d\n", ans);

  return 0;
}