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;
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
 
int main(){
 int N,M,i,j;
 cin >> N >> M;
 
 vector<vector<int>> s(M);
 vector<int> p(M);
 
 rep(j,M){
  int k; cin >> k;
  s[j].resize(k);
  rep(i,k){
   cin >>s[j][i];
   --s[j][i];
  }
 }
 rep(j,M){
 cin >> p[j];
 }
 
int c=0;
int ans=0;
 
rep(i,(1<<N)){
 bool ok = true;
 rep(j,M){
 c=0;
  for(int id : s[j]){
   if((i>>id) & 1) c++;
  }
  c=c%2;
  if(c != p[j]) ok=false;
 }
if(ok) ++ans;
}
 
cout << ans << endl;
 
return 0;
}