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
def IntToState(X, N):
    ret = []
    bina = bin(X)
    for i in range(2, len(bina)):
        ret.append(int(bina[i]))
    while len(ret) <= N:
        ret.insert(0,0)
    return ret

def solve():
    N, M = [int(_) for _ in raw_input().split()]
    SK = []
    for i in range(M):
        SKi = [int(_) for _ in raw_input().split()]
        SK.append(SKi)
    p = [int(_) for _ in raw_input().split()]
    ans = 0
    MAX_CASE = 1<<N
    for i in range (MAX_CASE):
        state = IntToState(i, N)
        satisfi = True
        for j in range(M):
            tmp_sum = 0
            for k in range(1, SK[j][0] + 1):
                tmp_sum += state[SK[j][k]]
            if tmp_sum % 2 != p[j]:
                satisfi = False
                break
        if satisfi:
            ans += 1
    print ans

if __name__ == '__main__':
    solve()
