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) {
        final Scanner scanner = new Scanner(System.in);

        final int n = scanner.nextInt();
        final int m = scanner.nextInt();
        scanner.nextLine();

        final int[][] switchIndices = new int[m][n];
        for (int i = 0; i < m; i++) {
            int k = scanner.nextInt();

            for (int j = 0; j < k; j++) {
                switchIndices[i][scanner.nextInt() - 1] = 1;
            }

            scanner.nextLine();
        }

        final int[] mods = new int[m];
        for (int i = 0; i < m; i++) {
            mods[i] = scanner.nextInt();
        }

        int successCount = 0;

        for (int i = 0; i < Math.pow(2, n); i++) {
            boolean lightAll = true;
            for (int j = 0; j < m; j++) {
                lightAll &= checkLight(switchIndices[j], mods[j], i);
            }

            successCount += lightAll ? 1 : 0;
        }

        System.out.println(successCount);
    }

    private static boolean checkLight(int[] switchIndex, int mod, int switchStatus) {
        int switchCount = 0;
        for (int i = 0; i < switchIndex.length; i++) {
            if (switchIndex[i] == 0) continue;

            if ((switchStatus >> i) % 2 == 1) {
                switchCount++;
            }
        }

        return switchCount % 2 == mod;
    }
}