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(int i=0;i<(n);++i)
using namespace std;
using ll=long long;
using P =pair<int,int>;

int main(){
int n,m;
cin>>n>>m;
vector<vector<int>>vec(m);
rep(i,m){
int k;cin>>k;
vec[i].resize(k);
rep(j,k){
cin>>vec[i][j];
--vec[i][j];
}
}
vector<int>p(m);
rep(i,m)cin>>p[i];
int ans=0;
for(int i=0;i<(1<<n);++i){
bool ok=true;
rep(j,m){
int c=0;
for(int id:vec[j]){
if((i>>id)&1){++c;}
}
c%=2;
if(c!=p[j]){
ok=false;
}
}
if(ok){++ans;}

}


cout<<ans<<endl;
return 0;
}