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 Rust (1.15.1) (judge verdict: Accepted)


use std::io;

fn main() {
    let mut s = String::new();
    io::stdin().read_line(&mut s).unwrap();
    let v: Vec<&str> = s.split_whitespace().collect();
    let (n, m) = (v[0].parse::<usize>().unwrap(), v[1].parse::<usize>().unwrap());

    let mut lamps = Vec::new();
    for _i in 0..m {
        let mut buf = String::new();
        io::stdin().read_line(&mut buf).unwrap();
        let s = buf.split_whitespace().skip(1).map(|i| i.parse::<usize>().unwrap() - 1).collect::<Vec<usize>>();
        lamps.push(s);
    }

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    let p = buf.split_whitespace().map(|i| i.parse::<usize>().unwrap()).collect::<Vec<usize>>();

    let mut ans = 0;
    'a: for bit in 0..(1 << n) {
        // スイッチのON/OFFの情報
        let mut swc = vec![false; n];
        for sft in 0..n {
            if (bit >> sft) & 1 == 1 {
                swc[sft] = true;
            }
        }

        for (i, ls) in lamps.iter().enumerate() {
            if !ls.iter().filter(|&l| swc[*l]).count() % 2 == p[i] {
                continue 'a;
            }
        }
        ans += 1;
    }

    println!("{}", ans);
}