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.

Examples

Input

2 2
2 1 2
1 2
0 1


Output

1


Input

2 3
2 1 2
1 1
1 2
0 0 1


Output

0


Input

5 2
3 1 2 5
2 2 3
1 0


Output

8
import java.util.Arrays;
import java.util.Scanner;
import java.util.Set;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt(), m = scanner.nextInt();
			@SuppressWarnings("unchecked")
			Set<Integer>[] sets = new Set[m];
			IntStream.range(0, m).forEach(i -> {
				int k = scanner.nextInt();
				sets[i] = IntStream.range(0, k).map(j -> scanner.nextInt()).boxed().collect(Collectors.toSet());
			});
			int[] p = IntStream.range(0, m).map(i -> scanner.nextInt()).toArray();
			int[] counts = new int[m];
			System.out.println(IntStream.range(0, 1 << n).filter(i -> {
				Arrays.fill(counts, 0);
				IntStream.range(0, n).filter(j -> (i & (1 << j)) > 0).forEach(j -> {
					IntStream.range(0, m).forEach(k -> counts[k] += sets[k].contains(j + 1) ? 1 : 0);
				});
				return m == IntStream.range(0, m).filter(j -> p[j] == (1 & counts[j])).count();
			}).count());
		}
	}
}
