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>
#define REP(i, n) for (int i = 0; i < (n); i++)
using namespace std;

int main() {
	int n, m; cin >> n >> m;
	vector<vector<int> > s(m);
	REP(i, m) {
		int k; cin >> k;
		s[i].resize(k);
		REP(j, k) {
			cin >> s[i][j];
			s[i][j]--;
		}
	}
	vector<int> p(m);
	REP(i, m) cin >> p[i];

	int res = 0;
	REP(bit, (1 << n)) {
		bool ok = true;
		REP(j, m) {
			int cnt = 0;
			for (int id : s[j])
				if ((bit >> id) & 1)
					cnt++;
			cnt %= 2;
			if (cnt != p[j])
				ok = false;
		}
		if (ok) res++;
	}
	cout << res << '\n';
	return 0;
}
