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: Runtime Error)

//Keep working hard :)
#include <bits/stdc++.h>
using namespace std;

#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define ll long long

const int N = 1e1+5;
int a[N];

void fileIO()
{
        #ifndef ONLINE_JUDGE
        freopen("int.txt","r",stdin);
        freopen("out.txt","w",stdout);
        #endif
}
int main()
{
	IOS;
      //  fileIO();
        int n,m;
        cin >> n >> m;
        map<int,vector<int>> mp;
        for(int i = 0; i < m; i++)
        {
                int k;cin >> k;
                while(k--)
                {
                        int dat;cin >> dat;
                        mp[i+1].push_back(dat);
                }
        }
        int tots = 0;
        for(int i = 0; i < m; i++)cin >> a[i];
        for(int i = 0; i < (1 << n); i++)
        {
                bool flag = true;
                int cnt = 0;
                for(int j = 1; j <= m; j++)
                {
                        for(auto x : mp[j])
                        {
                                cnt += a[x];
                        }
                        if(cnt%2 != a[i])flag = false;
                }
                if(flag)tots++;
        }
        cout << tots;
	return 0;
}