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
READ = lambda : sys.stdin.readline().strip().split()
READi = lambda : map(int, sys.stdin.readline().strip().split())

N, M = READi()
LINES = []
for i in xrange(M):
  LINES += [READi()]
P = READi()

count = 0
for i in xrange(2**N):
  bits = [(i>>b)&1 for b in xrange(N)]
  ok = True
  for line, p in zip(LINES, P):
    tmp = map(lambda x: bits[x-1], line[1:])
    ok &= (sum(tmp)%2) == p
  count += int(ok)
print count