#include <iostream>
#include <vector>
#include<list>
#include <algorithm>
#include <string>
#include <math.h>
#include<map>
#include <utility>
#include <cstring>
#include<queue>
using namespace std;
#define REP(i,k,n) for(int i=k;i<n;i++)
 
#define INF 1844674407370955161
typedef long long int ll;
#define SIZE_OF_ARRAY(array) (sizeof(array)/sizeof(array[0]))
#define MOD 1000000007

template<typename T>
int vector_finder(std::vector<T> vec, T number) {
  auto itr = std::find(vec.begin(), vec.end(), number);
  size_t index = std::distance( vec.begin(), itr );
  if (index != vec.size()) { // 発見できたとき
    return 1;
  }
  else { // 発見できなかったとき
    return 0;
  }
}

template<typename T>
T gcd(T a,T b){
	if(b>0){
		return gcd(b, a % b);
	}else{
		return a;
	}
}

template<typename T>
T lcm(T a,T b){
	T g = gcd(a, b);
	return a /g* b ;
}

void clear( std::queue<pair<int,int> > &q )
{
   std::queue<pair<int,int> > empty;
   std::swap( q, empty );
}
bool IsPrime(int num)
{
    if (num < 2) return false;
    else if (num == 2) return true;
    else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

    double sqrtNum = sqrt(num);
    for (int i = 3; i <= sqrtNum; i += 2)
    {
        if (num % i == 0)
        {
            // 素数ではない
            return false;
        }
    }

    // 素数である
    return true;
}
template<typename T>
int  GetDigit(T num){
    int digit=0;
    while(num!=0){
        num /= 10;
        digit++;
    }
    return digit;
}

template<typename T>
std::vector<T> enum_div(T n)//nの約数を列挙
{
	std::vector<T> ret;
	for(T i=1 ; i*i<=n ; ++i)
	{
		if(n%i == 0)
		{
			ret.push_back(i);
			if(i!=1 && i*i!=n)
			{
				ret.push_back(n/i);
			}
		}
	}
	return ret;
}


class DisjointSet{
    public:
        vector<int> rank, p;

        DisjointSet(){
        }

        DisjointSet(int size){
            rank.resize(size, 0);
            p.resize(size, 0);
            for (int i = 0; i < size;i++){
                makeSet(i);
            }
        }
        void makeSet(int x){
            p[x] = x;
            rank[x] = 0;
        }

        bool same(int x,int y){
            return findSet(x) == findSet(y);
        }
        void unite(int x,int y){
            link(findSet(x), findSet(y));
        }
        void link(int x,int y){
            if(rank[x]>rank[y]){
                p[y] = x;
            }else{
                p[x] = y;
                if(rank[x]==rank[y]){
                    rank[y]++;
                }
            }
        }
        int findSet(int x){
            if(x!=p[x]){
                p[x] = findSet(p[x]);
            }
            return p[x];
        }
};

int N,M;

vector<vector<int> > lp;
int p[10];
ll ans=0;
void dfs(int d,vector<int> o){
    if(d==N){
        bool flag=true;
        REP(i,0,M){
            
            if((o[i]%2)!=p[i]){
                flag=false;
            }
        }
        
        if(flag){
            ans++;
        }
    }else{
        dfs(d+1,o);
        vector<int> oo(o);
        REP(i,0,lp[d].size()){
            oo[lp[d][i]]++;
        }
        dfs(d+1,oo);
    }
}
int main()
{
    
    cin>>N>>M;
    lp.resize(N);
    REP(i,0,M){
        int k;
        cin>>k;
        REP(j,0,k){
        int s;
        cin>>s;
        s--;
        lp[s].push_back(i);
        }
    }
    REP(i,0,M){
        cin>>p[i];
    }
    vector<int> o(M);
    REP(i,0,M){
        o[i]=0;
    }
    dfs(0,o);
    cout<<ans<<endl;

}

Measured memory_bytes: 256