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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.Scanner;

public class Main{
	public static void main(String[] args) {
		Scanner sc =  new Scanner(System.in);
		int s = 1<<(sc.nextInt());
		int e = sc.nextInt();
		Condition[] cons = new Condition[e];
		
		for(int i=0;i<e;i++) {
			int n = sc.nextInt();
			int[] arr = new int[n];
			for(int j=0;j<n;j++) {
				arr[j] = sc.nextInt();
			}
			cons[i] = new Condition(arr);
		}
		
		for(int i=0;i<e;i++) 
			cons[i].OE = sc.nextInt();
		
		sc.close();
		int j;
		int count = 0;
		for(int i=0;i<s;i++) {
			for(j=0;j<e;j++) {
				if(!cons[j].meets(i))
					break;
			}
			if(j==e)
				count++;
		}
		System.out.println(count);
	}
}

class Condition{
	int[] nums;
	int OE;
	
	Condition(int[] nums){
		this.nums = nums;
	}
	
	
	boolean meets(int state) {
		int sum = 0;
		for(int i=0;i<nums.length;i++)
			sum += (state >> (nums[i]-1))&1;
		return OE == (sum&1);
	}
}