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<vector<int> >a(m);
  for(int i=0;i<m;i++)
  {
    int s;
    cin>>s;
    a[i].resize(s);
    for(int j=0;j<s;j++)cin>>a[i][j];
  }
  vector<int>p(m);
  vector<int>s(n);
  for(int i=0;i<m;i++)cin>>p[i];
  
  int ans=0;
  for(int i=0;i<=pow(2,n)-1;i++)
  {
    int k=0; 
    for(int j=0;j<m;j++)
    {
      int so=0;
      for(auto u:a[j])
      {
        so+=(i&(1<<(u-1)))? 1:0;
      }
      if((so%2)!=p[j])
      {
        k=1;
        break;
      }
    }
    if(!k)ans++;
  }
  cout<<ans<<endl;
  return 0;
}