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: Wrong Answer)

#include <bits/stdc++.h> 
using namespace std; 
 
int main() 
{ 
    int n,m;
    cin>>n>>m;


 

    //データ入力
    vector<int> k(m);
    vector<vector<int>> s(m, vector<int>(n));
    for(int i=0;i<m;i++){
        cin>>k.at(i);
        for(int j=0;j<k.at(i);j++){
            cin>>s.at(i).at(j);
        }
    }

    vector<int> p(m);
    for(int i=0;i<m;i++){
        cin>>p.at(i);
    }

    //2^nを全探索する。
    //i番目のスイッチの点灯状況をチェック　：点灯個数%2==piの時に電球が点灯
    //全ての電球が点灯すればカウントアップ
    int result=0;
    for (int i=0;i<(1<<n);i++) {
        bitset<10> bit_sw(i);
        int light=0;
        for(int j=0;j<m;j++){
            int cnt=0;
            for (int tmp=0;tmp<k.at(j);tmp++) {
                if (bit_sw.test(tmp)==1&&s.at(j).at(tmp)==1)
                    cnt++;
            }
            if(cnt%2==p.at(j))
                light++;
        }
        if(light==m)
            result++;
    }

    cout<<result<<endl;

    return 0; 
}