Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

2 2
2 1 2
1 2
0 1

Sample Output 1

1

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

There are four possible combinations of states of (Switch 1, Switch 2): (on, on), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all the bulbs, so we should print 1.

Sample Input 2

2 3
2 1 2
1 1
1 2
0 0 1

Sample Output 2

0

Bulb 1 is lighted when there is an even number of switches that are "on" among the following: Switch 1 and 2.

Bulb 2 is lighted when there is an even number of switches that are "on" among the following: Switch 1.

Bulb 3 is lighted when there is an odd number of switches that are "on" among the following: Switch 2.

Switch 1 has to be "off" to light Bulb 2 and Switch 2 has to be "on" to light Bulb 3, but then Bulb 1 will not be lighted. Thus, there are no combinations of states of the switches that light all the bulbs, so we should print 0.

Sample Input 3

5 2
3 1 2 5
2 2 3
1 0

Sample Output 3

8

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define ll          long long int
#define pb          push_back
#define pll         pair<ll,ll>
#define speed_up    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define mod         1000000007
#define inf         1000000000000000000LL
#define vl          vector<ll>
#define F           first
#define S           second
#define ld          long double
#define sz(x)       (ll)x.size()
#define fix(n)      cout<<fixed<<setprecision(n)
#define rep(i,a,b)  for(ll i=a;i<b;i++)
#define all(x)      x.begin(),x.end()
#define pi          3.14159265358979323



void solve()
{
      ll n, m;
      cin>>n>>m;
      ll k[m+1], p[m+1];
      ll s[15][15];
      memset(s, 0, sizeof s);
      rep(i,1,m+1)
      {
             cin>>k[i];
             rep(j,1,k[i]+1)
                     cin>>s[i][j];
      }
      rep(i,1,m+1) cin>>p[i];
      ll lim = (1 << n);
      ll ans=0;
      for(ll mask=0; mask < lim; mask++)
      {
             bool ok=1;
             ll cnt=0;
             for(ll i=1; i<=m; i++)
             {
                    cnt=0;
                    ll sws = k[i];
                    for(ll j=1; j<=sws; j++)
                    {
                           ll cur = s[i][j];
                           cur--;
                           if((mask >> cur) & 1) cnt++;
                    }
                    if(cnt%2 != p[i]) ok=0;
             }
             if(ok) ans++;
      }
      cout<<ans<<endl;

}

int main()
{
       speed_up;
       //pre();
       ll T=1;
       //cin>>T;
       while(T--) solve();
	return 0;
}