import java.util.*; import java.io.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		solve();flush();
	}
	//Don't have to see. end------------------------------------------
	static void solve(){//Here is the main function
	ArrayList<Integer> one = nextIntArray();
	int N = one.get(0);
	int M = one.get(1);
	
	Node[] connect = new Node[M];
	for(int i = 0; i < M; i++){
		ArrayList<Integer> tmp = nextIntArray();
		int connectCount = tmp.get(0);
		tmp.remove(0);
		connect[i] = new Node(i, tmp, connectCount);
	}
	ArrayList<Integer> onlist = nextIntArray();
	int output = 0;
	for(int i = 0; i < (1 << N); i++){
		ArrayList<Integer> select = new ArrayList<Integer>();
		for(int j = 0; j < N; j++){
			if((i & (1 << j)) != 0){
				//選ぶ(j番目のスイッチをON)
				select.add(j);
			}
		}
		int onCount = 0;//すべての電球がON
			for(int k = 0; k < M; k++){
				int switchCount = 0;
				for(int l = 0; l < connect[k].count; l++){
					if(select.contains(connect[k].list.get(l) - 1)){
						switchCount++;//つながってるスイッチがON
					}
				}
				if(switchCount % 2 == onlist.get(k)){
					onCount++;//電球を1個ON
				}
			}
		if(onCount == M){
			output++;
		}
	}
	myout(output);
	}
	//Method addition frame start

static class Node{
  int no;
  ArrayList<Integer> list;
  int count;
  Node(int no, ArrayList<Integer> list, int count){
    this.no = no;
    this.list = list;
    this.count = count;
  }
}

	//Method addition frame end
}


Measured memory_bytes: 34596