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.

Examples

Input

2 2
2 1 2
1 2
0 1


Output

1


Input

2 3
2 1 2
1 1
1 2
0 0 1


Output

0


Input

5 2
3 1 2 5
2 2 3
1 0


Output

8
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;

		// 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++ ) {
				// パターン作成
				int sptr = 0;
				for ( int i : switchPatterns[d] ) {
					sptr += 1 << i - 1;	// 順序：四則演算 → ビットシフト → 論理演算 → 代入
				}
				if ( Integer.bitCount(ptr & sptr) % 2 != p[d] ) {
					cnt--;
					break;
				}
			}
		}
		System.out.println(cnt);
		in.close();
	}
}