Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

2 2
2 1 2
1 2
0 1

Sample Output 1

1

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

There are four possible combinations of states of (Switch 1, Switch 2): (on, on), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all the bulbs, so we should print 1.

Sample Input 2

2 3
2 1 2
1 1
1 2
0 0 1

Sample Output 2

0

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an even number of switches that are "on" among the following: Switch 1.

Bulb 3 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

Switch 1 has to be "off" to light Bulb 2 and Switch 2 has to be "on" to light Bulb 3, but then Bulb 1 will not be lighted. Thus, there are no combinations of states of the switches that light all the bulbs, so we should print 0.

Sample Input 3

5 2
3 1 2 5
2 2 3
1 0

Sample Output 3

8

Solution in Python (3.4.3) (judge verdict: Accepted)

list=input().split(" ")
n=int(list[0])
m=int(list[1])

denkyu=[]

for i in range(m):
    info=input().split(" ")
    for j in range(len(info)):
        info[j]=int(info[j])
    list=[]
    for i in range(n):
        list.append(0)
    
    #print(info)
    for j in range(len(info)-1):
        list[info[j+1]-1]=1
    denkyu.append(list)

#print(denkyu)

shogo=[]

for x in range(2**n):
    shinsu=[]
    for y in range(n):
        if x%2==1:
            shinsu.append(1)
            x=int((x-1)/2)
        else:
            shinsu.append(0)
            x=int((x)/2)
    shogo.append(shinsu)

#print(shogo)

plist=input().split(" ")
for j in range(len(plist)):
    plist[j]=int(plist[j])

#print(plist)

#print("")
kosu=0
for s in shogo:
    switch=1
    now=0
    complete=0
    while switch==1:
        match=0
        for i in range(n):
            if s[i]==denkyu[now][i] and s[i]==1:
                #print("X", s[i], denkyu[now][i], s, denkyu[now])
                match+=1
        if match%2==plist[now]:
            now+=1
        else:
            switch=0
        if now==(m):
            if switch==1:
                complete=1
                switch=0
                #print(s)
    if complete==1:
        kosu+=1
        #print("y", s)
print(kosu)