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: Runtime Error)


#include <stdio.h>
#include <math.h>

int bit[11];

void bitplus(int[]);

int main(){
    int N, M, K[10], S[10][10], P[10];
    int i, j, k, sum, cnt, ans, bitn;

    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<10; i++){
        bit[i] = 0;
    }

    bitn = pow(2, N);
    
    for(i=0; i<bitn; i++){
        cnt=0;

        for(j=0; j<M; j++){
            sum=0;
            for(k=0; k<K[j]; k++){
                if(bit[K[k]-1] == 1)
                    sum++;
            }

            if(sum % 2 == P[j])
                cnt++;
        }
        
        if(cnt == M)
            ans++;

        bitplus(bit);
    }

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

    return 0;
}

void bitplus(int a[]){
    int i;

    a[0] += 1;
    for(i=0; i<10; i++){
        if(a[i] == 2){
            a[i] = 0;
            a[i+1] += 1;
        }
    }
}