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.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner sc = new Scanner(System.in);
		int N, M;
		N = sc.nextInt();
		M = sc.nextInt();

		int[] a = new int[N];
		for (int i = 0; i < M; i++) {
			int K;
			K = sc.nextInt();
			for (int j = 0; j < K; j++) {
				int S;
				S = sc.nextInt();
				S--;
				a[S] |= 1 << i;		//1を左にiビットシフト
			}
		}

		int p = 0;
		for (int i = 0; i < M; i++) {
			int x;
			x = sc.nextInt();
			p |= x << i;
		}

		int t = 0;
		int ans = 0;
		for (int s = 0; s < (1 << N); s++) {	//s < (1 << N); ... 1 << N(N = 3だとすると) 000から111まで回す。
			t = 0;
			for (int i = 0; i < N; i++) {
				if ((s >> i & 1) == 1) {	//iビット目が立っているかを判定
					t ^= a[i];
				}
			}
			if (t == p) {
				ans++;
			}
		}

		System.out.println(ans);
	}
}