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(){
  long N,M;cin>>N>>M;
  vector<vector<bool>>S(M,vector<bool>(N));
  for(long i=0;i<M;i++){
    long k;cin>>k;for(long j=0;j<k;j++){
      long s;cin>>s;
      S[i][s-1]=1;
    }
  }
  vector<long>P(M);for(long i=0;i<M;i++)cin>>P[i];
  long ans=0;
  for(long i=0;i<(1<<N);i++){
    long b=i;
    vector<long>B(M,0);
    for(long j=0;j<N;j++){
      for(long k=0;k<M;k++)if(b%2&&S[k][j])B[k]++;
      b/=2;
    }
    bool ok=1;
    for(long j=0;j<M;j++)if(P[j]!=B[j]%2)ok=0;
    if(ok)ans++;
  }
  cout<<ans<<endl;
  
}

/*




*/