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 (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func main() {
	scanInit()

	n := nextInt()
	m := nextInt()
	kl := make([]int, m)
	s := make([][]int, m)
	for i := 0; i < m; i++ {
		kl[i] = nextInt()
		tmp := make([]int, kl[i])
		for j := 0; j < kl[i]; j++ {
			tmp[j] = nextInt()
		}
		s[i] = tmp
	}

	pl := make([]int, m)
	for i := 0; i < m; i++ {
		pl[i] = nextInt()
	}

	cnt := 0
	for bit := 0; bit < (1 << n); bit++ {

		var setlist []int
		for j := 0; j < n; j++ {
			if bit&(1<<j) != 0 { // 今回ヒットした場合
				setlist = append(setlist, j+1)
			}
		}

		// 表示
		//fmt.Println(setlist)

		// 電球mごとに全て点灯したかをカウント
		allLightFlag := true
		for i := 0; i < m; i++ {

			// 電球mにつながっているスイッチのうちONの個数をカウント
			cntmon := 0
			for j := 0; j < kl[i]; j++ {
				tmp := s[i]
				f, _ := hasX(tmp[j], setlist)
				if f == true { // ON
					cntmon++
				}
			}
			if cntmon%2 != pl[i] {
				allLightFlag = false //少なくとも１つ消えている
				break
			}
		}
		if allLightFlag == true {
			cnt++
		}
	}

	fmt.Println(cnt)
}
func hasX(x int, plist []int) (bool, int) {
	for i, p := range plist {
		if x == p {
			return true, i
		}
	}
	return false, -1
}

// ---- readfunc
func scanInit() {
	const cap = 200 * 1024 // Default=64
	var buf = make([]byte, cap)
	sc.Buffer(buf, cap)
	sc.Split(bufio.ScanWords)
	return
}
func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}
func nextStr() string {
	sc.Scan()
	return sc.Text()
}