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.*;

class Main {
	static Scanner sc;
	static int n, m;
	static ArrayList<Integer>[] targets;
	static int[] constraints;
	static Boolean[] states;
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		n = sc.nextInt();
		m = sc.nextInt();

		targets = new ArrayList[m];
		for (int i = 0; i < m; i++) {
			int k = sc.nextInt();
			ArrayList<Integer> target = new ArrayList<Integer>();
			for (int j = 0; j < k; j++) {
				target.add(sc.nextInt() - 1);
			}
			targets[i] = target;
		}
		constraints = new int[m];
		for (int i = 0; i < m; i++) {
			constraints[i] = sc.nextInt();
		}

		states = new Boolean[n];
		int ans = dfs(0);
		System.out.println(ans);
	}

	public static int dfs(int index) {
		if (index == n) {
			if (check()) {
				return 1;
			} else {
				return 0;
			}
		}

		int sum = 0;
		states[index] = false;
		sum += dfs(index + 1);
		states[index] = true;
		sum += dfs(index + 1);
		return sum;
	}

	public static Boolean check() {
		for (int i = 0; i < m; i++) {
			int count = 0;
			for (int j = 0; j < targets[i].size(); j++) {
				if (states[targets[i].get(j)]) {
					count++;
				}
			}
			if (count % 2 != constraints[i]) {
				return false;
			}
		}
		return true;
	}
}
