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>
#define r(i,n) for(long long i = 0; i<n; i++)
typedef long long ll;
using namespace std;

int main() {
  int n,m,ans=0;
  cin >> n >> m;
  vector<vector<int>> v(m,vector<int>(n+2,0));
  r(i,m){
    cin >> v[i][1];
    r(j,v[i][1])cin>>v[i][2+j];
  }
  r(i,m)cin>>v[i][0];
  for(int bit=0; bit < (1<<n);bit++){
    r(i,m+1){
      if(i==m)ans++;
      else{
        int bit2=0;
        r(j,v[i][1])bit2=bit2^bitset<10>(bit)[v[i][2+j]-1];
        if(bit2!=v[i][0])break;
      }
    }
  }
  cout<<ans<<endl;
}