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: Wrong Answer)

/*
	submission # - User: herp_sy
	https://atcoder.jp/contests/

	coding: utf-8
	lang: C (GCC 5.4.1)
*/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdbool.h>

#define _CRT_SECURE_NO_WARNINGS
#define TLong long long
#define TBMod 1000000007

int main(int argc, char const *argv[])
{
	int n, m;
	int num[12][12] = { 0 };
	int p[12] = { 0 };
	int k, c;
	int bitcnt = 0, ans = 0;
	bool chkflag;

	// input & setup
	scanf("%d%d", &n, &m);
	for (int i = 0; i < 10; ++i){
		for (int j = 0; j < 10; ++j)	num[i][j] = 0;
	}
	for (int i = 0; i < m; ++i){
		scanf("%d", &k);
		for (int j = 0; j < k; ++j){
			scanf("%d", &c);
			num[i][c - 1] = 1;
		}
	}
	for (int i = 0; i < m; ++i)	scanf("%d", &p[i]);

	// countup
	for (int i = 0; i < (1 << n); ++i){
		chkflag = true;
		for (int j = 0; j < m; ++j){
			for (int l = 0; l < n; ++l){
				if (num[j][l] & i >> l)	bitcnt += 1;
			}
			if(bitcnt % 2 != p[j])	chkflag = false;
		}
		if(chkflag) ans += 1;
	}

	printf("%d\n", ans);
	return 0;
}