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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {

	static Scanner sc = new Scanner(System.in);

	static class FastScanner {
		private final InputStream in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;

		public FastScanner(InputStream source) {
			in = source;
		}

		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;
		}

		public boolean hasNext() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr]))
				ptr++;
			return hasNextByte();
		}

		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();
			}
		}

		public int nextInt() {
			long nl = nextLong();
			if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
				throw new NumberFormatException();
			return (int) nl;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}
	}

	/**
	 * Compute n! mod. p, (n!)^(-1) mod.p
	 *
	 * @param fac[]
	 *            : n! mod. p
	 * @param finv[]
	 *            : (n!)^(-1) mod. p
	 * @param MAX
	 *            :
	 * @param MOD
	 *            :
	 */

	static void hz_COMinit(long fac[], long finv[], long inv[], final int MAX, final long MOD) {
		fac[0] = fac[1] = 1L;
		finv[0] = finv[1] = 1L;
		inv[1] = 1L;
		for (int i = 2; i < MAX; i++) {
			fac[i] = fac[i - 1] * i % MOD;
			inv[i] = MOD - inv[(int) (MOD % i)] * (MOD / i) % MOD;
			finv[i] = finv[i - 1] * inv[i] % MOD;
		}
	}
	/*
	 * static void hz_COMinit(long fac[], long finv[], long inv[],final int MAX,
	 * final long MOD) { fac[0] = fac[1] = 1L; finv[0] = finv[1] = 1L; inv[1] =
	 * 1L; for (int i = 2; i < MAX; i++){ fac[i] = (BigInteger.valueOf(fac[i -
	 * 1]).multiply(BigInteger.valueOf(i)).mod(BigInteger.valueOf(MOD))).
	 * longValue(); inv[i] =
	 * (BigInteger.valueOf(MOD).subtract(BigInteger.valueOf(inv[(int)(MOD%i)]).
	 * multiply(BigInteger.valueOf(MOD/i)).mod(BigInteger.valueOf(MOD)))).
	 * longValue(); finv[i] = (BigInteger.valueOf(finv[i -
	 * 1]).multiply(BigInteger.valueOf(inv[i])).mod(BigInteger.valueOf(MOD))).
	 * longValue(); } }
	 */

	/**
	 * @Compute nCk(二項係数計算) mod. p
	 * @param fac[]
	 *            : n! mod. p
	 * @param finv[]
	 *            : (n!)^(-1) mod. p
	 * @return :nCk(二項係数計算) mod. p
	 */
	static long hz_COM(long fac[], long finv[], int n, int k, final long MOD) {
		if (n < k)
			return 0;
		if (n < 0 || k < 0)
			return 0;
		return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
	}
	/*
	 * static long hz_COM(long fac[],long finv[], int n, int k, final long MOD){
	 * if (n < k) return 0; if (n < 0 || k < 0) return 0; return
	 * BigInteger.valueOf(fac[n]) .multiply(BigInteger.valueOf(finv[k])
	 * .multiply(BigInteger.valueOf(finv[n - k])) .mod(BigInteger.valueOf(MOD))
	 * ) .mod(BigInteger.valueOf(MOD)).longValue(); }
	 */

	static int hz_swap(int a, int b) {
		if (a >= b)
			return a;
		else
			return b;
	}

	static long hz_swap(long a, long b) {
		if (a >= b)
			return a;
		else
			return b;
	}

	// mod上での差分
	static long hz_modSub(long a, long b, long mod) {
		long v = a - b;
		if (v < 0)
			v += mod;
		return v % mod;
	}

	// mod上での割算
	static long hz_modDiv(long a, long b, long mod) {
		return (a % mod) * hz_modInv(b, mod) % mod;
	}

	// 逆元
	static long hz_modInv(long a, long mod) {
		return hz_modPow(a, mod - 2L, mod);
	}

	// mod上での累乗
	static long hz_modPow(long n, long k, long mod) {

		long result = 1L;

		// k を右シフトしつつ n を 2 乗していく
		while (k > 0L) {
			// k の最下ビットが 1 なら、今の n を答えに掛ける
			if ((k & 1L) == 1L)
				result = (result * n) % mod;
			n = n * n % mod;
			k >>= 1L;
		}

		return result;
	}

	// Union Find Tree
	static class HZ_UF {

		public int[] par;
		public int[] rank;

		public HZ_UF(int n) {
			this.par = new int[n + 1];
			this.rank = new int[n + 1];

			Arrays.fill(par, -1);
			Arrays.fill(rank, 0);
		}

		public void unite(int x, int y) {
			link(root(x), root(y));
		}

		public boolean link(int x, int y) {
			if (x == y)
				return false;
			if (rank[x] > rank[y]) {
				par[x] += par[y];
				par[y] = x;
			} else {
				par[y] += par[x];
				par[x] = y;
				if (rank[x] == rank[y])
					rank[y]++;
			}
			return true;
		}

		public boolean isSame(int x, int y) {
			return root(x) == root(y);
		}

		public int root(int x) {
			if (par[x] < 0)
				return x;
			else
				return x = root(par[x]);
		}

		public int size(int x) {
			return -par[root(x)];
		}
	}

	public static void main(String[] args) {

		solve_abc128_c();
	}
  
  	public static void solve_abc128_c() {

		FastScanner sc = new FastScanner(System.in);
		
		int n = sc.nextInt();
		int m = sc.nextInt();
		
		int[] k = new int[m+1];
		boolean[][] s = new boolean[m+1][n+1];
		
		for(int i=0;i<=m;i++) Arrays.fill(s[i], false);
		for(int i=1;i<=m;i++){
			k[i] = sc.nextInt();
			for(int j=1;j<=k[i];j++){
				s[i][sc.nextInt()] = true;
			}
		}
		
		int[] p = new int[m+1];
		for(int i=1;i<=m;i++) p[i] = sc.nextInt();
		
		int ans = 0;
		boolean[] b = new boolean[n+1];
		
		ans += solve_abc128_c_dfs(1, n, m, s, p, b, true);
		ans += solve_abc128_c_dfs(1, n, m, s, p, b, false);
		
		System.out.println(ans);
	}
	
	//b:swich(idx si) is on/off
	public static int solve_abc128_c_dfs(int si, int n, int m, boolean[][] s, int[] p, boolean[] b, boolean bi) {

		b[si] = bi;
		
		if(si == n){
			int ans = 1;
			for(int i=1;i<=m;i++){
				int sum = 0;
				for(int j=1;j<=n;j++){
					if(s[i][j] && b[j]) sum++;
				}
				if(sum % 2 != p[i]){
					ans = 0;
					break;
				}
			}
			return ans;
		}
		
		int ans = 0;
		ans += solve_abc128_c_dfs(si + 1, n, m, s, p, b, true);
		ans += solve_abc128_c_dfs(si + 1, n, m, s, p, b, false);
		return ans;
	}
}