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;
using ll = long long;
#define rep(i,n) for(ll i=0;i<(n);++i)

int main(){

  ll n,m;
  cin>>n>>m;
  vector<ll> k(m),p(m);
  vector<set<ll>> s(m);
  rep(i,m){
    cin>>k[i];
    rep(j,k[i]){
      ll x;
      cin>>x;
      x--;
      s[i].insert(x);
    }
  }
  rep(i,m)cin>>p[i];

  ll ans=0;
  for(ll b=0;b<(1LL<<n);++b){
    bitset<16> bit(b);
    vector<ll> a(m);
    rep(k,12){
      if(bit[k]){
        rep(i,m){
          if(s[i].find(k)!=s[i].end())a[i]++;
        }
      }
    }
    rep(i,m)a[i]%=2;
    if(p==a)ans++;
  }
  cout<<(ans)<<endl;

}