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.FileNotFoundException;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {

		//    	File file = new File("src/in.txt");
		//    	Scanner sc = new Scanner(file);

		Scanner sc = new Scanner(System.in);

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

		int[][] s = new int[M][N];

		for (int i = 0; i < M; i++) {
			int k = sc.nextInt();
			for (int j = 0; j < k; j++) {
				int num = sc.nextInt()-1;
				s[i][num] = 1;
			}
		}

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

		int ans = 0;
		for (int i = 0; i < 1 << N; i++) {
			boolean flg = true;
			// bit全探索の全通りのloop
			int[] A = new int[N];
			for (int j = 0; j < N; j++) {
				if ((1 & i >> j) == 1) {
					A[j] = 1;
				}
			}

			for (int k = 0; k < M; k++) {
				int sum = 0;
				for (int l = 0; l < N; l++) {
					sum = sum + s[k][l] * A[l];
				}
				if (sum%2 != p[k]) {
					flg = false;
				}
			}
			if (flg == true) {
				ans++;
			}
		}
		System.out.println(ans);

	}
}
