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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

"use strict";

function Main(input) {
  input = input.split("\n");
  var N = parseInt(input[0].split(" ")[0], 10);
  var M = parseInt(input[0].split(" ")[1], 10);
  var k = [];

  for (var index = 1; index <= M; index++) {
    var element = input[index].split(" ").map(function (v) {
      return parseInt(v, 10);
    });
    k.push(element);
  }

  var p = input[M + 1].split(" ").map(function (v) {
    return parseInt(v, 10);
  });
  var init = [];
  var combs = [init];

  for (var _index = 0; _index < N; _index++) {
    combs = comb(combs);
  }

  var result = 0; // each switch cases

  for (var _index2 = 0; _index2 < combs.length; _index2++) {
    var switches = combs[_index2];
    var match = 0; // each lamp        

    for (var m = 0; m < M; m++) {
      var sum = 0; // each connected switch

      for (var s = 1; s <= k[m][0]; s++) {
        sum += switches[k[m][s] - 1];
      } //console.log("sum, p[m]", sum, p[m]);


      if (sum % 2 != p[m]) {
        break;
      }

      match++;
    } //console.log(match);


    if (match == M) {
      result++;
    }
  }

  console.log(result);
}

function comb(combs) {
  var result = [];

  for (var index = 0; index < combs.length; index++) {
    var element = combs[index];
    result.push(element.concat(0));
    result.push(element.concat(1));
  }

  return result;
}