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())
check=[]
for i in  xrange(m):
    s=map(int,raw_input().split())
    s.pop(0)
    check.append(s)
ans=0
p=map(int,raw_input().split())
for i in xrange(0,pow(2,n)):
    switch=[0 for j in xrange(n)]
    j=0
    k=i
    while j < n:
        switch[j]=k%2
        k=k/2
        j += 1
    #print switch
    flag=0
    ###########
    ###########
    odd=0
    even=0
    for j in switch:
        if j ==0:
            even += 1
        else:
            odd += 1
    kk=0
    for j in check:
        onn=0
        off=0
        for k in j:
            if switch[k-1]==0:
                off += 1
            else:
                onn += 1
        if p[kk]%2==0:
            if onn%2==1:
                flag=-1
        else:
            if onn%2==0:
                flag=-1
        kk += 1
    if flag == -1:
        ans += 0
    else:
        ans += 1
print ans
        