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;
const int maxn = 300001;
int n, m, s[11][11], slen[11], p[11], ans;
int ok(int light){
	for(int i = 0;i < m;++i){
		int cnt = 0;
		for(int j = 0;j < slen[i];++j){
			cnt += (bool)(light & (1 << s[i][j]));
		}
		if(p[i] != (cnt & 1))return false;
	}
	return true;
}
int main(){
	cin >> n >> m;
	for(int i = 0;i < m;++i){
		cin >> slen[i];
		for(int j = 0;j < slen[i];++j){
			cin >> s[i][j];
			--s[i][j];
		}
	}
	for(int i = 0;i < m;++i)cin >> p[i];
	for(int light = 0;light < (1 << n);++light){
		ans += ok(light);
	}
	cout << ans << '\n';
}
