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<iostream>
#include<vector>
using namespace std;
int main(){
   int N,M;
  cin>>N>>M;
  vector<vector<int>>s(M);
  for(int i=0;i<M;++i){
    int k;
    cin>>k;
    for(int j=0;j<k;++j){
      int a;
      cin>>a;
      --a;
      s[i].push_back(a);
    }
  }
  vector<int>p(M);
  for(int i=0;i<M;++i){
    cin>>p[i];
  }
  long long res=0;
  for(int bit=0;bit<(1<<N);bit++){
    bool ok=true;
    for(int i=0;i<M;i++){
      int con=0;
      for(auto v:s[i]){
         if(bit&(1<<v)) con++;
      }
      if(con%2!=p[i]) ok=false;
    }
    if(ok) res++;
  }
  cout<<res<<endl;
}
    
