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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) throws IOException {
		new Main().solve();
	}

	private void solve() throws IOException {
		try {
			//			solveA();
			//			solveB();
			solveC();
			//			solveD();
			//			 solveE();
			//			 solveF();
		} finally {
			if (in != null) {
				in.close();
			}
			if (out != null) {
				out.flush();
				out.close();
			}
		}

	}

	private void solveA() {

		out.println((nextInt() * 3 + nextInt()) / 2);
	}

	private void solveB() {
		int n = nextInt();
		String[][] s = new String[n][3];

		for (int i = 0; i < n; i++) {
			s[i][0] = next();
			s[i][1] = next();
			s[i][2] = Integer.toString(i + 1);
		}
		Arrays.sort(s,
				(x, y) -> {
					if (x[0].compareTo(y[0]) < 0) {
						return -1;
					} else if (x[0].compareTo(y[0]) > 0) {
						return 1;
					} else {
						return -Integer.compare(Integer.parseInt(x[1]), Integer.parseInt(y[1]));
					}
				});

		for (int i = 0; i < s.length; i++) {
			out.println(s[i][2]);
		}
	}

	private void solveC() {
		int n = nextInt();
		int m = nextInt();
		int[] k = new int[m];

		List<List<Integer>> s = new ArrayList<List<Integer>>();
		for (int i = 0; i < k.length; i++) {
			k[i] = nextInt();
			List<Integer> temp = new ArrayList<Integer>();
			for (int j = 0; j < k[i]; j++) {
				temp.add(nextInt());
			}
			s.add(temp);
		}
		int[] p = IntStream.range(0, m).map(i -> nextInt()).toArray();

		long res = 0;
		for (int i = 0; i < 1 << n; i++) {
			boolean isResult = true;
			for (int j = 0; j < m; j++) {
				List<Integer> sList = s.get(j);
				int compareBase = p[j];
				int compare = 0;
				for (Integer buttonNum : sList) {
					if ((i & (1 << (buttonNum - 1))) >= 1) {
						compare++;
					}
				}
				if (compareBase != compare % 2) {
					isResult = false;
					break;
				}
			}
			if (isResult) {
				res++;
			}

		}

		out.println(res);
	}

	//組み合わせの数nCrを計算
	int calcNumOfCombination(int n, int r) {
		int num = 1;
		for (int i = 1; i <= r; i++) {
			num = num * (n - i + 1) / i;
		}
		return num;
	}

	private void solveD() {
		int n = nextInt();
		int k = nextInt();
		ArrayDeque<Integer> wk = new ArrayDeque<Integer>();
		for (int i = 0; i < n; i++) {
			wk.addLast(nextInt());
		}
		out.println(deq(wk, 0, k, 0, new ArrayList<Integer>()));
	}

	private int deq(ArrayDeque<Integer> wk, int currentK, int k, int total, List<Integer> temochi) {
		if (currentK >= k) {
			return total;
		}
		temochi.add(wk.removeFirst());
		int val1 = deq(wk, currentK + 1, k, total + wk.removeLast(), temochi);
		temochi.remove(temochi.size() - 1);
		temochi.add(wk.removeFirst());
		int val2 = deq(wk, currentK + 1, k, total + wk.removeFirst(), temochi);
		temochi.remove(temochi.size() - 1);
		temochi.add(wk.removeFirst());
		Collections.sort(temochi);
		wk.addFirst(temochi.get(0));
		int val3 = deq(wk, currentK + 1, k, total, temochi);
		temochi.add(0, wk.removeFirst());
		Collections.sort(temochi);
		wk.addLast(temochi.get(0));
		int val4 = deq(wk, currentK + 1, k, total + wk.removeFirst(), temochi);
		temochi.add(0, wk.removeFirst());
		return Integer.max(Integer.max(val1, val2), Integer.max(val3, val4));
	}

	private void solveE() {
		int n = nextInt();

		out.println("");
	}

	private void solveF() {
		int n = nextInt();

		out.println("");
	}

	private final PrintWriter out = new PrintWriter(System.out);
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
}