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 ford(i,a,b) for(int i=(a);i>=b;i--)
#define rep(i,a,b) for(int i=(a);(i)<(b);(i)++)
#define ll long long
#define re return
#define mp map<int,int>
using namespace std;
int main() {
	int n,m;
	cin>>n>>m;
	int k[m],s[m][n],p[m];
	ll ans=0;
	rep(i,0,m){
		cin>>k[i];
		rep(j,0,k[i]) cin>>s[i][j];
	}
	rep(i,0,m) cin>>p[i];
	rep(i,0,(1<<n)){
		int cnt=0;
		rep(j,0,m){
			int sum=0;
			rep(q,0,n){
				if(i&(1<<q))
                    rep(l,0,k[j])
						if(s[j][l]-1==q)sum++;
			}
			if(sum%2==p[j])cnt++;
		}
		if(cnt==m)ans++;
	}
	cout<<ans;
	re 0;
}
