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 Python (3.4.3) (judge verdict: Wrong Answer)

# https://atcoder.jp/contests/abc128/tasks/abc128_c
from itertools import product
N, M = map(int, input().split())
k = []
s = []
for _ in range(M):
    std_in = list(map(int, input().split()))
    k.append(std_in[0])
    for i in range(std_in[0]):
        std_in[i+1] -= 1
    s.append(std_in[1:])
p = [int(i) for i in input().split()]

switches = [0] * N

# def judge_bulbs(switches):
#     for i in range(M):

#         k_sum = 0
#         for ki in range(k[i]):
#             k_sum += switches[ki]

#         if k_sum % 2 == p[i]:
#             continue
#         else:
#             return False
#     return True

# def solve(idx, switches):
#     if idx == N:
#         if judge_bulbs(switches):
#             return 1
#         else:
#             return 0

#     ans = 0
#     switches = switches.copy()
    
#     ans += solve(idx+1, switches)

#     switches[idx] = 1
#     ans += solve(idx+1, switches)
#     return ans

# print(solve(0, switches))

ans = 0

for x in product([0, 1], repeat=N):
    for i in range(M):
        cnt = 0
        for n in s[i]:
            if x[n] == 1:
                cnt += 1
        if cnt % 2 != 0:
            break
    else:
        ans += 1
print(ans)