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;

typedef long long ll;
typedef pair<int, int> P;
typedef pair<ll, ll> Pl;

const int INT_INF = 2147483646;
const ll LL_INF = 9223372036854775807;

bool SecondCompare(const pair<int,int> &a,const pair<int,int> &b)
{
       return a.second<b.second;
}
 
bool SecondCompareDes(const pair<int,int> &a,const pair<int,int> &b)
{
       return a.second>b.second;
}

ll minll(ll a, ll b){
    if(a >= b)  return b;
    else    return a;
}

ll maxll(ll a, ll b){
    if(a >= b)  return a;
    else    return b;
}

ll n,m;
ll k[100];
ll s[100][100],ss[20][20];
ll p[100];
ll swit[20];
ll ans;
ll ccc;
void solve(int num){
    if(num != n){
    swit[num] = 0;
    solve(num+1);
    swit[num] = 1;
    solve(num+1);
    }
    else{
    ll cou;
    bool f = true;
    for(int i = 0; i < m; i++){
        cou = 0;
        for(int j = 1; j <= n; j++){

            if(ss[i][j] == swit[j-1] && ss[i][j] == 1) ++cou;
        }
        if(p[i] != cou % 2) f = false;
    }
    if(f) ++ans;
    ++ccc;
    }

    return;
}


int main(){
    cin >> n >> m;
    for(int i = 0; i < m; i++){
        cin >> k[i];
        for(int j = 0; j < k[i]; j++){
            cin >> s[i][j];
            ss[i][s[i][j]] = 1;
        }
    }
    for(int i = 0; i < m; i++){
        cin >> p[i];
    }

    solve(0);
    cout << ans << endl;
}