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-----
2 2
2 1 2
1 2
0 1

-----Sample Output-----
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.

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