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
N, M = map(int, raw_input().split())
ks_list = []
p_list = []
for i in range(M):
    ks_list.append(map(int, raw_input().split()))
p_list.append(map(int, raw_input().split()))

ans_count = 0
for i in range(2**N):
    
    cond = 0
    switch_list = [0]*N
    for j in range(N):
        switch_list[j]=(i>>j)&1

    for m in range(M):
        tmp_count = 0
        for k in range(ks_list[m][0]):
            if switch_list[ks_list[m][1+k]-1] == 1:
                tmp_count = tmp_count + 1

        if p_list[0][m] == (tmp_count % 2):
            cond = 1
        else:
            cond = 0
            break
    if cond == 1:
        ans_count = ans_count + 1
print ans_count
