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 in = new Scanner(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		int[][] switchPatterns = new int[m][];
		int[] p = new int[m];
		for ( int i = 0; i < m; i++ ) {
			int k = in.nextInt();
			int[] s = new int[k];
			for ( int j = 0; j < k; j++ ) {
				s[j] = in.nextInt();
			}
			switchPatterns[i] = s;
		}
		for ( int i = 0; i < m; i++ ) {
			p[i] = in.nextInt();
		}

		int Allpatterns = 2 << (n - 1); // 2のn乗
		int cnt = Allpatterns;
//		boolean[] light = new boolean[Allpatterns];
//		Arrays.fill(light, true);

		// スイッチのパターンを上限まで列挙
		for ( int ptr = 0; ptr < Allpatterns; ptr++ ) {
			// 電球ごとのスイッチパターンと照らし合わせる
			for ( int d = 0; d < m; d++ ) {
				int temp = 0;
				for ( int i : switchPatterns[d] ) {
					// System.out.println("switch:" + i);
					//					int mask = 1 << (i - 1);
					//					temp += ((ptr & mask) >> (i - 1));

					temp += ptr >> i - 1 & 1; // 順序：四則演算 → ビットシフト → 論理演算 → 代入
				}
				// System.out.println("temp:" + temp);
				if ( temp % 2 != p[d] ) {
					//light[ptr] = false;
					cnt--;
					break;
				}
				// if(d == m-1)System.out.println("ptr:" + Integer.toBinaryString(ptr) + " is OK");
			}
		}

//		int cnt = 0;
//		for ( int i = 0; i < Allpatterns; i++ ) {
//			if ( light[i] ) {
//				// System.out.println(Integer.toBinaryString(i));
//				cnt++;
//			}
//		}

		System.out.println(cnt);

		// 確認用
		//		for ( int i = 0; i < m; i++ ) {
		//			System.out.print("電球 " + i + "     p: " + p[i] + "    s: ");
		//			for ( int j : switches[i] ) {
		//				System.out.print(j + " ");
		//			}
		//			//System.out.print(" p:" + p[i]);			
		//			System.out.println();
		//		}
		in.close();
	}
}