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 (
    "fmt"
)

func main() {
    var n, m int
    fmt.Scan(&n, &m)
    ls := make([]int, m)
    for i := 0; i < m; i++ {
        var k int
        fmt.Scan(&k)
        var sb int
        for j := 0; j < k; j++ {
            var s uint
            fmt.Scan(&s)
            s--
            sb |= 1 << s
        }
        ls[i] = sb
    }
    ps := make([]int, m)
    for i := 0; i < m; i++ {
        var p int
        fmt.Scan(&p)
        ps[i] = p
    }
    var sc int
    for i := 0; i < 1<<uint(n); i++ {
        var ng bool
        for j := 0; j < m; j++ {
            so := ls[j] & i
            var cnt int
            for l := 0; l < n; l++ {
                if so&(1<<uint(l)) > 0 {
                    cnt++
                }
            }
            if cnt%2 != ps[j] {
                ng = true
            }
        }
        if !ng {
            sc++
        }
    }
    fmt.Println(sc)
}