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) {
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());
		int M = Integer.parseInt(sc.next());
		int[] K = new int[M];
		int[] P = new int[M];
		int[][] S = new int[M][];
		int answer = 0;
		for(int i = 0; i < M; i++) {
			K[i] = Integer.parseInt(sc.next());
			S[i] = new int[K[i]];
			for(int j = 0; j < K[i]; j++) {
				S[i][j] = Integer.parseInt(sc.next());
			}
		}
		for(int i = 0; i < M; i++) {
			P[i] = Integer.parseInt(sc.next());
		}
		sc.close();

		//ビット全探索
		for(int i = 0; i < Math.pow(2, N); i++) {
			boolean check = true;
			for(int j = 0; j < M; j++) {
				int count = 0;
				//各スイッチが点灯しているかどうか確認
				for(int k = 0; k < K[j]; k++) {
					if((1 & i >> S[j][k]  - 1) == 1) count++;
				}
				//2で割った余りが一致するかどうか確認
				if(count % 2 != P[j]) {
					 check = false;
				}
			}
			if(check) {
				answer++;
			}
		}
		System.out.println(answer);
	}

}