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: Accepted)

package main

import (
	"bufio"
	"bytes"
	"fmt"
	"io"
	"os"
	"strconv"
	"sort"
       "math"
)

// -----------------------------------------------------------------------------

// IO helper functions

// Returns next token from input.  It must be initialized by SetInput()
// before the first call.
var nextToken func() ([]byte, error)
var nextLine func() ([]byte, error)

// Holds a buffer for output.  It must be initialized by SetOutput().
// All IO fucntions (read*() and [e]print*()) should write to OutputWriter
// instead of this.
var OutputBuffer *bufio.Writer

// Holds an io.Writer.  It must be initialized by SetOutput()
var OutputWriter io.Writer

// Set IO functions for interactive input/output.
func SetInteractive(w io.Writer, r io.Reader) {
	SetUnbefferedInput(r)
	OutputBuffer = nil
	OutputWriter = w
}

// Setup OutputBuffer and OutputWriter.
func SetOutput(w io.Writer) {
	OutputBuffer = bufio.NewWriter(w)
	OutputWriter = OutputBuffer
}

// Flushes OutputBuffer
func Flush() {
	if OutputBuffer != nil {
		OutputBuffer.Flush()
	}
}

// Returns true if c is a white space
func IsSpace(c byte) bool {
	switch c {
	case '\t', '\n', '\v', '\f', '\r', ' ':
		return true
	}
	return false
}

func IsNewLine(c byte) bool {
	switch c {
	case '\n', '\r':
		return true
	}
	return false
}

// Setup nextToken with input buffer.
func SetInput(r io.Reader) {
	buf := new(bytes.Buffer)
	var b []byte

	var i int
	rest := func() ([]byte, error) {
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		return b[j:i], nil
	}
	initial := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextToken = rest
		return rest()
	}
	nextToken = initial

	restLn := func() ([]byte, error) {
		for i < len(b) && IsNewLine(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsNewLine(b[i]) {
			i++
		}
		return b[j:i], nil
	}

	initialLn := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextLine = restLn
		return restLn()
	}
	nextLine = initialLn
}

// Setup nextToken without input buffer.
func SetUnbefferedInput(r io.Reader) {
	buf := bufio.NewReader(r)
	var b []byte

	var i int
	nextToken = func() ([]byte, error) {
		var err error
		if i == len(b) {
			b, err = buf.ReadBytes('\n')
			if err != nil {
				return nil, err
			}
			i = 0
			j := len(b) - 1
			for 0 <= j && IsSpace(b[j]) {
				j--
			}
			b = b[0 : j+1]
		}
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		if i == j {
			return nil, io.ErrUnexpectedEOF
		}
		return b[j:i], nil
	}
}

// -----------------------------------------------------------------------------

// IO functions

// Reads next token and return it as []byte
func readb() []byte {
	b, err := nextToken()
	if err != nil {
		panic(err)
	}
	return b
}

// Reads next token and return it as string
func reads() string {
	return string(readb())
}

// Read next line as []byte
func readbln() []byte {
	b, err := nextLine()
	if err != nil {
		panic(err)
	}
	return b
}

// Read next line as string
func readsln() string {
	return string(readbln())
}

// Reads next token and return it as int64
func readll() int64 {
	i, err := strconv.ParseInt(reads(), 10, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// Reads next token and return it as int
func readi() int {
	return int(readll())
}

// Reads next token and return it as float64
func readf() float64 {
	f, err := strconv.ParseFloat(reads(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// ReadIntSlice returns an integer slice that has n integers.
func readislice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = readi()
	}
	return b
}

// ReadInt64Slice returns as int64 slice that has n integers.
func readllslice(n int) []int64 {
	b := make([]int64, n)
	for i := 0; i < n; i++ {
		b[i] = readll()
	}
	return b
}

// Write args to OutputWriter with the format f
func printf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(OutputWriter, f, args...)
}

// Write args to OutputWriter without format
func println(args ...interface{}) (int, error) {
	return fmt.Fprintln(OutputWriter, args...)
}

// Write args to stderr with the format f
func eprintf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(os.Stderr, f, args...)
}

// Write args to stderr without format
func eprintln(args ...interface{}) (int, error) {
	return fmt.Fprintln(os.Stderr, args...)
}

// -----------------------------------------------------------------------------

// Simple math functions

const (
	// big prime
	MOD = 1000000007
	INF = math.MaxInt64
)

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func minll(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a < b {
		return b
	}
	return a
}

func maxll(a, b int64) int64 {
	if a < b {
		return b
	}
	return a
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func absll(a int64) int64 {
	if a < 0 {
		return -a
	}
	return a
}

func pow(p, q int) int {
    return int(math.Pow(float64(p), float64(q)))
}

// egcd(a, b) returns d, x, y:
//   d is gcd(a,b)
//   x, y are  integers that satisfy ax + by = d
func egcd(a, b int) (int, int, int) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcd(b, a%b)
	return d, y, x - a/b*y
}

func egcdll(a, b int64) (int64, int64, int64) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcdll(b, a%b)
	return d, y, x - a/b*y
}

func gcd(a, b int) int {
	d, _, _ := egcd(a, b)
	return d
}

func gcdll(a, b int64) int64 {
	d, _, _ := egcdll(a, b)
	return d
}

func lcm(a,b int) int{
  return a * b / gcd(a, b)
}

func isInteger(x float64) bool {
    return math.Floor(x) == x
}

// lower_bound
func bisectLeft(a []int, x int) int {
    return sort.SearchInts(a, x)
}

// upper_bound
func bisectRight(a []int, x int) int {
    return sort.Search(len(a), func(i int) bool { return a[i] > x })
}

// set up IO functions
func init() {
	// for non-interactive
	SetInput(os.Stdin)
	SetOutput(os.Stdout)

	// Enable below when interactive.  Its ok to leave above intact.
	// SetInteractive(os.Stdout, os.Stdin)
}

func main() {
  	defer Flush()

	N, M := readi(), readi()
	K := make([]int, M)
	S := make([][]int, M)

	for i := range K{
		K[i] = readi()
		S[i] = readislice(K[i])
	}

	P := readislice(M)

	cnt := 0

	for bits := 0; bits<(1<<uint64(N)); bits++ {
		on_lights_cnt := 0

		for i := 0; i < M; i++ {
			on_switches_cnt := 0

			for _, s := range S[i] {
				if (bits>>uint64(s-1)) & 1 == 1 {
					on_switches_cnt++
				}
			}

			if on_switches_cnt % 2 == P[i] {
				on_lights_cnt++
			}
		}

		if on_lights_cnt == M {
			cnt++
		}
	}

  	println(cnt)
}