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 main(void){
  int n,m,i,j,k[10],s[10][10],p[10],t,di,ans=0,d[10]={1,2,4,8,16,32,64,128,256,512};
  bool g;
  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];
  for (t=0;t<d[n-1]*2;t++){
    g=true;
    for (i=0;i<m;i++){
      di=0;
      for (j=0;j<k[i];j++) if (t&d[s[i][j]-1]) di++;
      if (di%2!=p[i]){
        g=false;
        break;
      }
    }
    if (g) ans++;
  }
  cout << ans << endl;
  return 0;
}