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 s[11][11];
int k[11];
int p[11];
int on[11];

int main(){

  int n,m,num,ans=0;
  cin>>n>>m;
  
  rep(i,m){
    cin>>k[i];
    rep(j,k[i])cin>>s[i][j];
  }
  
  rep(i,m)cin>>p[i];
  bool ok;

  for(int bit=0;bit<(1<<n);++bit){
    rep(i,n)on[i]=0;
    ok=true;
    
    rep(i,n)if(bit&(1<<i))on[i]=1;//onのスイッチを調べる
    
    rep(i,m){//m個の電球について、ついているか調べる
      num=0;
      rep(j,10)num+=on[s[i][j]];
      if(num%2!=p[i]){ok=false;break;}
    }
    if(ok)ans++;//全てついていたらans++;
  } 
    cout<<ans<<endl;
  
  
}