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)

// int n = 5;
// // {0, 1, ..., n-1} の部分集合の全探索
// for (int bit = 0; bit < (1<<n); ++bit)
// {
//     /* bit で表される集合の処理を書く */
//     // bit の表す集合を求める
//     for (int i = 0; i < n; ++i) {
//         if (bit & (1<<i)) { // i が bit に入るかどうか
//             cout << i << endl ;
//         }
//     }
// }

#include <bits/stdc++.h>
typedef long long ll;
#define _GLIBCXX_DEBUG
#define int long long
using namespace std;
#define REP(i, n) for (ll i = 0; i < (ll)(n); i++)
#define REPR(i, n) for (ll i = (ll)(n)-1; i >= 0; i--)
#define FOR(i, a, b) for (ll i = a; i <= (ll)(b); i++)
#define FORD(i, a, b) for (ll i = a; i >= (ll)(b); i--)
#define ALL(x) (x).begin(), (x).end()
#define SIZE(x) ((ll)(x).size())
#define MAX(x) *max_element(ALL(x))
#define MIN(x) *min_element(ALL(x))
#define INF 1000000000000
#define MOD 10000007
#define MAXR 100000
#define PI 3.14159265358979323846
using namespace std;
void debugVV(vector<vector<int> >& deV) {
    for (int i = 0; i < deV.size(); i++) {
        cout << i << " ";
        for (int j = 0; j < deV[i].size(); j++) {
            cout << "[" << j << "]= " << deV[i][j] << ",";
        }
        cout << endl;
    }
}
void debugV(vector<int>& deV) {
    for (int i = 0; i < deV.size(); i++) {
        cout << "[" << i << "]= " << deV[i] << ",";
    }
    cout << endl;
}

signed main() {
    int n, m;
    cin >> n >> m;
    vector<int> k(m);
    vector<vector<int> > s;
    REP(i, m) {
        cin >> k[i];
        s.push_back(vector<int>());
        REP(j, k[i]) {
            int a;
            cin >> a;
            s[i].push_back(a);
        }
    }
    vector<int> p(m);
    REP(i, m) { cin >> p[i]; }
    int ans = 0;

    // int n = 5;
    // {0, 1, ..., n-1} の部分集合の全探索
    for (int bit = 0; bit < (1 << n); ++bit) {
        /* bit で表される集合の処理を書く */
        // bit の表す集合を求める
        vector<int> S;
        for (int i = 0; i < n; ++i) {
            if (bit & (1 << i)) {  // i が bit に入るかどうか
                S.push_back(i);
            }
        }

    //    cout << "DEGUG S" << endl;
    //    debugV(S);

        REP(i, m) {  // 各電球ごと
            int ONcnt = 0;
            REP(jj, k[i]) {          //各電球のすいっち
                REP(kk, S.size()) {  // ONの個数
                    if (S[kk] == s[i][jj]-1){
                        ONcnt++;
             //           cout << kk<<"'s on" <<endl ;
                    }
                        
                }
            }
         //   cout << i << ",on=" << ONcnt << endl;
            if (ONcnt % 2 != p[i])
                break;
            if (i == m - 1) {
                ans++;
            //    cout << "itisOK" << endl;
            }
        }
    }

    cout << ans << endl;

    // debugVV(s);

    return 0;
}