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 Go (1.6) (judge verdict: Runtime Error)

package main

import "fmt"

func main() {
	var n, m uint
	fmt.Scan(&n, &m)

	lightBulbs := make([][]int, m)
	var k int
	for i := range lightBulbs {
		fmt.Scan(&k)
		lightBulbs[i] = make([]int, k)
		for j := range lightBulbs[i] {
			fmt.Scan(&lightBulbs[i][j])
		}
	}

	ps := make([]int, m)
	for i := range ps {
		fmt.Scan(&ps[i])
	}

	var (
		match int
		flag  bool
		onOff string
		ans   int
	)
	for i := 0; i < (1 << n); i++ {
		flag = true
		onOff = fmt.Sprintf("%08b", i)
		for j, l := range lightBulbs {
			match = 0
			for k := range l {
				if onOff[len(onOff)-l[k]] == '1' {
					match++
				}
			}
			if match%2 == ps[j] {
				continue
			} else {
				flag = false
				break
			}
		}
		if flag == false {
			continue
		} else {
			ans++
		}
	}

	fmt.Println(ans)
}