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 n, m, k[10], s[10][10], i, p[10], j, ans=0, max=-1, cnt[10]={0};
    int f[10]={0};
    scanf("%d%d", &n, &m);
    for(i=0;i<n;i++){
        scanf("%d", &k[i]);
        for(j=0;j<k[i];j++){
            scanf("%d", &s[i][j]);
        }
    }
    for(i=0;i<n;i++){
        scanf("%d", &p[i]);
    }
    for(f[0]=0;f[0]<=1;f[0]++){
        for(f[1]=0;f[1]<=1;f[1]++){
            for(f[2]=0;f[2]<=1;f[2]++){
                for(f[3]=0;f[3]<=1;f[3]++){
                    for(f[4]=0;f[4]<=1;f[4]++){
                        for(f[5]=0;f[5]<=1;f[5]++){
                            for(f[6]=0;f[6]<=1;f[6]++){
                                for(f[7]=0;f[7]<=1;f[7]++){
                                    for(f[8]=0;f[8]<=1;f[8]++){
                                        for(f[9]=0;f[9]<=1;f[9]++){
                                            for(i=0;i<m;i++){
                                                for(j=0;j<k[i];j++){
                                                    if(f[s[i][j]]==1) cnt[i]++;
                                                    
                                                }
                                                if(cnt[i]%2==p[i]) ans++;
                                            }
                                            if(ans==n) max++;
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }
    printf("%d\n", max);
        
    
            
    
    
    return 0;
}