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.*;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.run();
	}

	public void run() {
		Scanner sc = new Scanner(System.in);
		int N=sc.nextInt();
		int M=sc.nextInt();

		ArrayList<Integer> a = new ArrayList<>(); //スイッチと繋がっている電球の集合
		for(int i=0; i<N; i++) {
			a.add(0);
		}

		for(int i=0; i<M; i++) {
			int k=sc.nextInt();
			for(int j=0; j<k; j++) {
				int s = sc.nextInt();
				s--;
				a.set(s, a.get(s) | (1<<i));
			}
		}

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

		//押すスイッチの全集合を試す
		int ans = 0;
		for(int s = 0; s < (1<<N); s++) {
			int t=0;//スイッチ押した後の電球の状態
			for(int i=0; i<N; i++) {
				if(((s>>i)&1)==1) {
					//スイッチiを押すと対応する電球が変化する
					t ^= a.get(i);
				}
			}
			if(p==t) {
				ans++;
			}
		}
		System.out.println(ans);
		sc.close();
	}


}
