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
#include <bits/stdc++.h>
using namespace std;

int n, m;
vector<int> sw(10);
int x(int bit) {
	int result = 0;
	for (int i = 0; bit > 0; bit >>= 1, i++) {
		if (bit & 1)
			result ^= sw[i];
	}
	return result;
}

int main() {
	cin >> n >> m;
	for (int k, bit = 1 << (m - 1), s; bit > 0; bit >>= 1) {
		cin >> k;
		for (int j = 0; j < k; j++) {
			cin >> s;
			s--;
			sw[s] |= bit;
		}
	}

	int p = 0;
	for (int i = 0, q; i < m; i++) {
		cin >> q;
		p <<= 1;
		p += q;
	}

	int result = 0;
	for (int bit = 0; bit < 1 << n; bit++) {
		if (x(bit) == p)
			result++;
	}
	cout << result << endl;
}
