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>
using namespace std; 

int main(){
    

int N,M;
cin>>N>>M;
int s[100][100];
int p[100];
for(int i=0; i<M; i++){
    int k;
    cin>>k;
    for(int j=0; j<k; j++){
        int r;
    cin>>r;
    s[i][j]=r;
    }
}
for(int i=0; i<M; i++){
    cin>>p[i];
}

int res=0;

for(int bit=0; bit<(1<<N); bit++){
    


bool t=true;

for(int i=0; i<M; i++){
    
    int counter=0;
    
    for(int j:s[i]){

if (bit & (1<<j)) counter++;

}

if (counter%2==p[i]) t=true;
else {t=false; break;}
}

if(t) res++;

}

cout<<res<<endl;
}