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(){
  size_t n,m; cin>>n>>m;
  int ss[11];
  for(int i=0; i<m; ++i){
    ss[i]=0;
  }
  for(int i=0; i<m; ++i){
    int k; cin>>k;
    for(int j=0; j<k; ++j){
      int s; cin>>s;
      ss[i]|=(1<<(s-1));
    }
  }
  int p[11];
  for(int i=0; i<m; ++i){
    cin>>p[i];
  }
  // for(const auto& s:ss){
  //   cout<<s<<'\n';
  // }
  int res=0;
  for(int bits=0; bits<(1<<n); ++bits){
    for(int i=0; i<m; ++i){
      if(__builtin_parity(ss[i]&bits)!=p[i]) goto exit;
    }
    ++res;
    exit:;
  }
  cout<<res<<'\n';
}