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>
#include<vector>

using namespace std;

#define rep(i,n) for(int i=0;i<n;++i)

int main(){
  int N, M;
  cin >> N >> M;
  vector<vector<int>> S(M);
  rep(i,M) {
    int k;
    cin >> k;
    S[i].resize(k);
    rep(j,k){
      cin >> S[i][j];
      --S[i][j];
    }
  }
  
  vector<int> P(M);
  rep(i,M) cin >> P[i];
  int ans = 0;
  rep(i, 1<<N){
    bool ok = true;
    rep(j,M){
      int x = 0;
      rep(k,S[j].size()) if ((i >> S[j][k] & 1)) ++x;
      x %= 2;
      if (x != P[j]) ok = false;
    }
    if (ok) ++ans;
  }
  cout << ans << endl;          
}