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
import sys
from collections import deque
import copy
import math
def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline


def bin_count(x, N):
    count = 0
    for i in range(N):
        mask = 0x01 << i
        if (x & mask) != 0:
            count += 1
    return count


def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [N, M] = [int(input_raw[0]), int(input_raw[1])]
    mask_list = []
    for i in range(M):
        input_raw = read_func().strip().split()
        [K] = [int(input_raw[0])]
        mask = 0
        for j in range(K):
            mask += 0x01 << (int(input_raw[j + 1]) - 1)
        mask_list.append(mask)


    input_raw = read_func().strip().split()
    P_list = [int(input_raw[i]) for i in range(M)]

    ans = 0
    for i in range((0x01 << N)):
        is_ok = True
        for j in range(len(mask_list)):
            mask = mask_list[j]
            if (P_list[j] != (bin_count(mask & i, N)%2)):
                is_ok = False
                break
        if is_ok == True:
            ans += 1
    print ans




if __name__ == '__main__':
    main()
