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;
int main(){
  int N,M; cin>>N>>M;
  vector<int>K(M);
  vector<vector<int>>S(M,vector<int>(N));
  vector<int>p(M);
  for(int i=0;i<M;i++){
    cin>>K[i];
    for(int j=0;j<K[i];j++)cin>>S[i][j];
  }
  for(int i=0;i<M;i++)cin>>p[i];
  long long ans=0;
  for(int bit=0;bit<(1<<N);bit++){
    vector<bool>C(N,false);
    for(int i=0;i<N;i++)if(bit&(1<<i))C[i]=true;
    for(int i=0;i<M;i++){
      long long count=0;
      for(int j=0;j<K[i];j++)if(C[S[i][j]-1])count++;
      if(count%2!=p[i])break;
      if(i==M-1)ans++;
    }
  }
  cout<<ans<<endl;
}