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.io.*;
import java.util.*;

class Main {
	static final int M = 2;

	public static void main(String[] args) throws Exception {
		final Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();

		List<Integer>[] ss = new List[m];

		for (int i = 0; i < m; i++) {
			int k = sc.nextInt();
			ss[i] = new ArrayList<>();
			while (k-- > 0) {
				ss[i].add(sc.nextInt());
			}
		}
		int[] ps = new int[m];
		for (int i = 0; i < m; i++) {
			ps[i] = sc.nextInt();
		}

		long count = 0;
		for (int i = 0; i < (1 << n); i++) {
			boolean ok = true;
			for (int j = 0; j < m; j++) {
				int p = 0;
				for (Integer s : ss[j]) {
					if (((i >> (s - 1)) & 1) == 1) {
						p++;
					}
				}
				if (p % 2 != ps[j]) {
					ok = false;
					break;
				}
			}
			if (ok) count++;
		}

		System.out.println(count);
	}
}
