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
#include<stdio.h>
#include<stdlib.h>
#include<stdbool.h>
#include<limits.h>
#include<float.h>

#define NUM 10

int main(){
	int n, m, k[NUM], s[NUM][NUM], p[NUM], ans = 0;
	scanf("%d%d\n", &n, &m);
	for(int i=0; i<m; i++){
		scanf("%d", &k[i]);
		for(int j=0; j<k[i]; j++){
			scanf("%d", &s[i][j]);
		}
	}
	for(int i=0; i<m; i++){
		scanf("%d", &p[i]);
	}
	for(int i=0; i<(1<<n); i++){
		int j;
		for(j=0; j<m; j++){
			int on = 0;
			for(int l=0; l<k[j]; l++){
				if((1 << (s[j][l] - 1)) & i) on++;
			}
			if(on % 2 != p[j]) break;
		}
		if(j == m) ans++;
	}
	printf("%d\n", ans);
	return 0;
}