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: Wrong Answer)

package main

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

func main() {
	var N, M int
	fmt.Scanf("%d %d", &N, &M)
	NS := strconv.Itoa(N)
	reader := bufio.NewReader(os.Stdin)
	s := make([][]int, M+1, M+1)
	for i := 1; i <= M; i++ {
		line, _, _ := reader.ReadLine()
		dataS := strings.Split(string(line), " ")
		dataI := make([]int, len(dataS), len(dataS))
		for j := range dataS {
			dataI[j], _ = strconv.Atoi(dataS[j])
		}
		s[i] = dataI[1:]
	}
	line, _, _ := reader.ReadLine()

	_ = strings.Split(string(line), " ")

	ans := 0
	for i := 0; i < int(math.Pow(2, float64(N))); i++ {
		t := strings.Split(fmt.Sprintf("0%0"+NS+"b", i), "")
		ok := true
		for j := 1; j <= M; j++ {
			total := 0
			for k := range s[j] {
				if t[s[j][k]] == "1" {
					total += 1
				}
			}
			if total%2 != 1 {
				ok = false
				break
			}
		}
		if ok {
			ans += 1
		}
	}
	fmt.Println(ans)

}