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;

class Point{
	int[] x;
	Point(int[] a){
	this.x = a;
	}

}


public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int M = sc.nextInt();

		int[][] S = new int[M][N+1];

		for(int i = 0 ; i < M ; i ++){
			int k = sc.nextInt();
			for(int j = 0 ; j < k ; j++){
				S[i][j] = sc.nextInt();
			}
		}

		int[] P = new int[M];
		for(int i = 0 ; i < M ; i++){
			P[i] = sc.nextInt();
		}


		sc.close();

		int aans = (int)Math.pow(2, N);
		String denkyu;
		String ar = "%0" + N + "d";

		int count = 0;
		int a = 0;
		int ans = 0;
		for(int i = 0 ; i < aans ; i++){
			denkyu = String.format(ar ,Integer.parseInt(Integer.toBinaryString(i)));
			//System.out.println(denkyu);



			for(int j = 0 ; j < M ; j++){
				for(int k = 0 ; k < N ; k++){
					if(S[j][k] ==0){
						break;
					}
					//System.out.println("S : " + S[j][k]);
					a += Integer.parseInt(String.valueOf(denkyu).substring(S[j][k]-1,S[j][k]));

					}
				//System.out.println("a : " + a);
				if(a%2 == P[j]){
					count++;
				}
				a = 0;
			}
			//System.out.println(count);
			if(count == M){
				ans++;
			}
			count = 0;
		}
		System.out.println(ans);
	}

}