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.

Examples

Input

2 2
2 1 2
1 2
0 1


Output

1


Input

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


Output

0


Input

5 2
3 1 2 5
2 2 3
1 0


Output

8
#include <bits/stdc++.h>
#define rep(i, n) for (ll i = 0; i < n; i++)
using namespace std;
using ll = long long;
using vll = vector<ll>;

int main(){
	//入力
	ll N,M; cin>>N>>M;
	vector<vector<ll>> s(M);
	rep(i,M){
		ll k; cin>>k;
		rep(j,k){
			ll a; cin>>a;a--;
			s[i].push_back(a);
		}
	}
	vll p(M); rep(i,M) cin>>p[i];
	
	ll ans=0;
	for(ll bit=0;bit<(1<<N);bit++){
		bool ok = true;
		rep(i,M){
			ll con=0;
			for (auto v : s[i]) {
                if (bit & (1<<v)) ++con;
            }
			if(con%2!=p[i]) ok=false;
		}
		if(ok)ans++;
	}
	
	//出力
	cout<<ans<<endl;
}
