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
//Bit full search.
#include<iostream>
#include<vector>
#define REP(i,n) for(int i=0;i<(n);++i)
using namespace std;
typedef vector<int>   vi;
typedef vector<vi >   vvi;

int main(){
	int n,m;
	cin>>n>>m;
	
	vvi v(m);
	REP(i,m){
		int k;
		cin>>k;
		v[i].resize(k);
		REP(j,k){
			cin>>v[i][j];
			v[i][j]--;
		}
	}
	
	vi p(m);
	REP(i,m) cin>>p[i];
	
	int ans=0;
	REP(i,(1<<n)){//スイッチの付き方を全探索.
		bool jud=true;
		REP(j,m){//全ての電球を試す.
			int cnt=0;
			for(auto &elem:v[j]){
				if((i>>elem)&1) cnt++;
			}
			if(cnt%2!=p[j]){
				jud=false;
				break;
			}
		}
		if(jud) ans++;
	}
	
	cout<<ans<<endl;
}
