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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x)=parse(Int,x)
parseMap(x::Array{SubString{String},1})=map(parseInt,x)
function moveup(x::Array{Int,1},n)
	k = length(x)
	for i in 1:k-1
		if x[k-i+1] > n-1
			x[k-i] += div(x[k-i+1],n)
			x[k-i+1] = x[k-i+1]%n
		end
	end
	if x[1] > n-1
		0
	else
		x
	end
end

function main()
	n,m = readline() |> split |> parseMap
	k = zeros(Int,m)
	a = [Int[] for i in 1:m]
	for i in 1:m
		x = readline() |> split |> parseMap
		k[i] = x[1]
		a[i] = x[2:x[1]+1]
	end
	p = readline() |> split |> parseMap
	on = zeros(Int,n)
	c = 0
	for i in 1:2^n
		flg = 0
		for i in 1:m
			z = 0
			for j in 1:k[i]
				if on[a[i][j]] == 1
					z += 1
				end
			end
			if z%2!=p[i]
				flg = 1
				break
			end
		end
		if flg == 0
			c += 1
		end
		on[n] += 1
		moveup(on,2)
	end
	println(c)
end

main()