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;
 cin>>N>>M;
  int ans=0;
  vector<int>a(N);
  for(int i=0;i<M;i++){
  int K;
    cin>>K;
   for(int j=0;j<K;j++){
   		int s;
        cin>>s;
      	s--;
      a.at(s) |= 1<<i;
	  }
  }
  int P=0;
  for(int i=0;i<M;i++){
    int x;
    cin>>x;
    P |=x<<i;
  }
  for(int s=0;s< (1<<N);s++){
  int t=0;
    for(int i=0;i<N;i++){
    if(s>>i &  1){
    	t ^=a.at(i);
      }
    }
    if(t==P){
    ans++;
    }
  }
  cout<<ans<<endl;
}