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
def multy(a,b):
	c = 0
	for i in range(len(a)):
		c += a[i]*b[i]
	return c
N,M = map(int, raw_input().split())
ks = []
for i in range(M):
	ks2 = map(int, raw_input().split())
	ks.append(ks2)
pm = map(int, raw_input().split())
plist = []
for i in ks:
	t = [0]*N
	ini = 1
	for j in i:
		if(ini == 1):
			ini = 0
			continue
		else:
			t[j-1] = 1
	plist.append(t)
slist = []
for i in range(2**N):
	t = []
	for j in range(N):
		t.append(i%2)
		i = i/2
	slist.append(t)
r = 0
for p in plist:
	s2 = []
	for s in slist:
		if(multy(p,s)%2 == pm[r]):
			s2.append(s)
	r = r+1
	slist = s2
print(len(slist))