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)

function Main(input) {
    input = input.trim().split("\n").map(function(x) { return x.split(" ")});
    var NM = [ ];
    var vec_p = [ ];
    var vec_s = [ ];
    var ary_ks = [];
    var ans = 0;
    var tmpAry, j, tmpNum, tmpSum;
    NM = input[0].map(e => parseInt(e, 10)); 
    vec_p = input[NM[1]+1].map(e => parseInt(e, 10)); 
    for (var ki = 1; ki <= NM[1]; ki++){
    	ary_ks.push(input[ki].map(e => parseInt(e, 10))); 
    }
  var x=0; 
    for (var i = Math.pow(2, NM[0]); i <  Math.pow(2, NM[0]) * 2; i++){
      x++;
    	tmpAry = i.toString(2).substr(1);
    	tmpSum = 0;
    	tmpAry_loop:
    	for (var ki = 1; ki <= NM[1]; ki++){
			for (var sij = 1; sij <=  ary_ks[ki-1][0]; sij++){
				tmpNum = parseInt(tmpAry[ary_ks[ki-1][sij]-1], 10);
 				tmpSum +=  tmpNum;
			}
			if (ki == NM[1])  {
              //console.log("tmpNum %d", tmpNum);
            }
		
			if (tmpSum % 2 != vec_p [ki-1]) break tmpAry_loop;
			if (ki == NM[1]) {
                           //console.log(tmpAry); 
              	//			console.log(tmpSum);
				//console.log(tmpSum % 2);
              
              ans ++;
            }
		}
    }
    console.log(ans);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));