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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		int[][] switches = new int[m][];
		int[] p = new int[m];

		int Allptr = (int) Math.pow(2, n);
		boolean[] light = new boolean[Allptr];
		Arrays.fill(light, true);

		for ( int i = 0; i < m; i++ ) {
			int k = in.nextInt();
			int[] s = new int[k];
			for ( int j = 0; j < k; j++ ) {
				s[j] = in.nextInt();
			}
			switches[i] = s;
		}
		for ( int i = 0; i < m; i++ ) {
			p[i] = in.nextInt();
		}

		// スイッチのパターンを上限まで列挙
		for ( int ptr = 0; ptr < Allptr; ptr++ ) {
			// 電球ごとのスイッチパターンと照らし合わせる
			for ( int d = 0; d < m; d++ ) {
				int temp = 0;
				for ( int i : switches[d] ) {
					// System.out.println("switch:" + i);
					int mask = 1 << (i - 1);
					temp += ((ptr & mask) >> (i - 1));
				}
				// System.out.println("temp:" + temp);
				if ( temp % 2 != p[d] ) {
					light[ptr] = false;
					break;
				}
				// if(d == m-1)System.out.println("ptr:" + Integer.toBinaryString(ptr) + " is OK");
			}
		}

		int cnt = 0;
		for ( int i = 0; i < Allptr; i++) {
			if ( light[i] ) {
				// System.out.println(Integer.toBinaryString(i));
				cnt++;
			}
		}

		System.out.println(cnt);

		// 確認用
//		for ( int i = 0; i < m; i++ ) {
//			System.out.print("電球 " + i + "     p: " + p[i] + "    s: ");
//			for ( int j : switches[i] ) {
//				System.out.print(j + " ");
//			}
//			//System.out.print(" p:" + p[i]);			
//			System.out.println();
//		}
		in.close();
	}
}
