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
l = raw_input().split()
N = int(l[0])
M = int(l[1])

K = []
S = []
P = []

for i in range(M):
    l = raw_input().split()
    t = [int(x) for x in l]
    K.append(t[0])
    S.append(t[1:])

l = raw_input().split()
P = [int(x) for x in l]

# print(N, M, K, S, P)

def numBits(n):
    count = 0
    while n > 0:
        if n % 2 == 1:
            count += 1
        n /= 2
    return count

def solve(n, S, p):
    # print('nsp', n, S, p)
    count = 0
    for s in S:
        # print(s, n, n >> (s - 1))
        count += (n >> (s - 1)) & 1
    # print('count={}'.format(count))
    return p == (count  & 1)

ans = 0
for j in range(2**N):
    # print(j)
    ret = True
    for i in range(len(S)):
        s = S[i]
        p = P[i]
        # print(i, s, p)
        if not solve(j, s, p):
            ret = False
            break
    if ret:
        ans += 1
print(ans)
