Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

2 2
2 1 2
1 2
0 1

Sample Output 1

1

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

There are four possible combinations of states of (Switch 1, Switch 2): (on, on), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all the bulbs, so we should print 1.

Sample Input 2

2 3
2 1 2
1 1
1 2
0 0 1

Sample Output 2

0

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an even number of switches that are "on" among the following: Switch 1.

Bulb 3 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

Switch 1 has to be "off" to light Bulb 2 and Switch 2 has to be "on" to light Bulb 3, but then Bulb 1 will not be lighted. Thus, there are no combinations of states of the switches that light all the bulbs, so we should print 0.

Sample Input 3

5 2
3 1 2 5
2 2 3
1 0

Sample Output 3

8

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
int main()
{
	int n, m;
	scanf("%d %d", &n, &m);
	int i, j;
	int k[11], s[11][11];
	for (i = 0; i < m; i++)
	{
		scanf("%d", &k[i]);
		for (j = 0; j < k[i]; j++)
			scanf("%d", &s[i][j]);
	}
	int p[11];
	for (i = 0; i <m; i++)
		scanf("%d", &p[i]);
	int ans = 0;
	int q, max = 1;
	q = n;
	while (q > 0)
	{
		q--;
		max *= 2;
	}
	int w[11], r;
	for (i = 0; i < 11; i++)
		w[i] = 0;
	int count, x;
	for (q = 0; q < max; q++)
	{
		r = q;
		for (i = 0; i < n; i++)
		{
			w[i] = r % 2;
			r /= 2;
		}
		x = 0;
		for (i = 0; i < m; i++)
		{
			count = 0;
			for (j = 0; j < k[i]; j++)
				if (w[s[i][j] - 1] == 1)
					count++;
			count %= 2;
			if (p[i] != count)
			{
				x++;
				break;
			}
		}
		if (x == 0)
			ans++;
	}
	printf("%d\n", ans);
	return 0;
}