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,k,s;
  cin >> n >> m;
  vector<vector<int>> light(m);
  vector<int> p(n);
  for(int i=0;i<m;i++){
    cin >> k;
    light[i] = vector<int>(k);
    for(int j=0;j<k;j++)
      cin >> light[i][j];
  }
  for(int i=0;i<m;i++) cin >> p[i];

  int cnt = 0;
  for(int r = 0; r < (1 << n); r++){
    bitset<10> pt(r);
    for(int i=0;i<m;i++){
      int sm = 0;
      for(int j:light[i]){
        sm ^= pt[--j];
      }
      if(p[i] != sm){
        cnt --;
        break;
      }
    }
    cnt++;
  }
  cout << cnt << endl;
}