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
# coding:utf-8
# CCCCCCCCCCCC

import math
import re

def inclement_bi(i):
    return bin(i)

def main(params):
    result = 0
    n,m = params[0]
    ks = params[1:]
    ps = ks.pop(-1).split()
    for i in range(2**n):
        bi = str(inclement_bi(i)).replace('0b','')
        if len(bi) < n:
            bi = '0' * (n-len(bi)) + bi
        cnt = 0
        chk = True
        for j in ks:
            tmp = j.split()
            k = tmp[0]
            s = tmp[1:]
            p = int(ps[cnt])
            total = 0
            for si in s:
                si = int(si) - 1
                if bi[si] == '1':
                    total += 1
            cnt += 1
            if total % 2 != p:
                chk = False
                break
        if chk == True:
            result += 1
    print result

if __name__ == "__main__":
    n,m = [int(i) for i in raw_input().split()]
    cnt = m + 1 # TODO: edit here
    params = [[n,m]]
    for i in range(cnt):
        param = raw_input()
        params.append(param)
    main(params)

