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.ArrayList;
import java.util.Scanner;
class Main{

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力



		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] k = new int[m];
		ArrayList<ArrayList<Integer>> list = new ArrayList<ArrayList<Integer>>();
		int[] p = new int[m];

		for(int i = 0;i < m;i++){
			k[i] = sc.nextInt();
			ArrayList<Integer> sub = new ArrayList<Integer>();
			for(int j = 0;j < k[i];j++){
				sub.add(sc.nextInt()-1);
			}
			list.add(sub);
		}
		for(int i = 0;i < m;i++){
			p[i] = sc.nextInt();
		}
		
		

		int bit = 0;
		int ans = 0;
		for(;bit < 1<<n;bit++){
			if(checkswitch(bit,k,list,p,m)){
				ans++;
			}
		}
		System.out.print(ans);




	}


	static boolean checkswitch(int bit,int[] k,ArrayList<ArrayList<Integer>> list,int[] p,int m){
		
//		System.out.println("bit " + bit);
			
		for(int i = 0;i < m;i++){
			
			ArrayList<Integer> sub = list.get(i);
			int onnum = 0;						//onの数
			for(int j = 0;j < sub.size();j++){
//				System.out.println("sub "+ sub.get(j));
				if((bit & (1 << sub.get(j))) != 0){				//目的のスイッチがついているか
					onnum++;
//					System.out.println("on  ");
				}
				
			}
			if(onnum % 2 != p[i]){				//一個でも電球がつかなかったらout
				return false;
			}
			
		}
		

		return true;

	}

	static int gcd(int a,int b){				//最大公約数を返す
		if(b == 0){
			return a;
		}else{
			return gcd(b, a%b);
		}
	}





}



class Pair implements Comparable{
	int from;
	int end;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return  otherpair.end - end;
	}
}


