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
// C - Switches
#include <bits/stdc++.h>

using namespace std;

int main(int argc, char *argv[])
{
	int n, m;
	cin >> n >> m;
	vector<int> s(n);
	for (int i = 0; i < m; i++) {
		int k, j;
		cin >> k;
		while (k--) {
			cin >> j;
			s[j - 1] |= (1 << i);
		}
	}
	int t, z = 0;
	for (int i = 0; i < m; i++) cin >> t, z += (t << i);

	int ans = 0;
	for (int i = 0; i < (1 << n); i++) {
		int y = 0;
		for (int j = 0; j < n; j++)
			if (i & (1 << j)) y ^= s[j];
			if (y == z) ans++;
	}

	cout << ans << endl;

	return 0;
}
