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>
using namespace std;
int N_MAX = 10;
int main()
{
  int n,nn,m,i,j,kk,t,res=0;
  int k[N_MAX],s[N_MAX][N_MAX],p[N_MAX],ss[N_MAX];
  cin >> n >> m;
  for(i=0;i<m;i++){
    cin >> k[i];
    for(j=0;j<k[i];j++)
      cin >> s[i][j];
  }
  for(i=0;i<m;i++)
    cin >> p[i];
  nn=1<<n;
  for(i=0;i<nn;i++){
    for(j=0;j<n;j++)
      ss[j]=(i>>j)%2;
    for(j=0;j<m;j++){
      t=0;
      for(kk=0;kk<k[j];kk++)
        if(ss[s[j][kk]-1]==1) t++;
      if(t%2!=p[j]) break;
    }
    if(j==m) res++;
  }
  cout << res << endl;
  return 0;
}