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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
const int N=15;
struct node
{
    int a[N];
    int k;
}b[N];
int s[N];
int n,m;
int judge(int p)
{
    //printf("p=%d\n",p);
    int tmp[N];
    memset(tmp,0,sizeof(tmp));
    int j=1;
    while(p>0)
    {
        tmp[j]=p%2;
        p=p/2;
        j++;
    }
    /*
    for(int i=1;i<=n;i++)
        printf("%d ",tmp[i]);
    printf("\n");
    */
    int flag=0;
    for(int i=1;i<=m;i++)
    {
        int cou=0;
        for(int j=1;j<=b[i].k;j++)
        {
            //printf("+ %d %d %d\n",b[i].a[j],tmp[b[i].a[j]],s[i]);
            if(tmp[b[i].a[j]]==1)
            {
                cou++;
            }
        }
        if(cou%2==s[i])
            flag++;
    }
    if(flag==m)
        return 1;
    else
        return 0;
    //return flag;
}
int main()
{

    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++)
    {
        scanf("%d",&b[i].k);
        for(int j=1;j<=b[i].k;j++)
            scanf("%d",&b[i].a[j]);
    }


    for(int i=1;i<=m;i++)
        scanf("%d",&s[i]);
    int p=pow(2,n);
    int ans=0;
    for(int i=0;i<=p-1;i++)
    {
        int tmp=judge(i);
        ans+=tmp;
    }
    printf("%d\n",ans);
    //cout << "Hello world!" << endl;
    return 0;
}