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(" "))

switch = []
for i in range(0, m):
    s = map(int, raw_input().split(" "))
    switch.append(s[1:])

power = map(int, raw_input().split(" "))

ans = 0
for state_int in range(0, 2 ** n):
    format_str = "{:0" + str(n) + "b}"
    state_bin = format_str.format(state_int)
    # print(state_bin)

    state = [0 for j in range(0, len(state_bin))]
    for i in range(0, len(state)):
        if state_bin[i] == "1":
            state[i] = True
        else:
            state[i] = False

    # print(state)
    on = True
    for s in range(0, m):
        ts = switch[s]
        count = 0

        for j in range(0, len(ts)):
            if state[ts[j] - 1]:
                count += 1

        if power[s] != count % 2:
            on = False
            break

    if on:
        # print(state_bin)
        ans += 1

print(ans)
