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<iostream>
#include<vector>
#include<algorithm>

using namespace std;

int main(){
  int N,M; cin >> N >> M;
  vector<int> switches(N,0);
  for(int i = 0; i < M; i++){
    int k; cin >> k;
    for(int j = 0; j < k; j++){
      int s; cin >> s; s--; switches[s] |= 1 << i;}}
  
  int cnt = 0; int p = 0;
  for(int i = 0; i < M; i++){ int q; cin >> q; p |= q << i;}
  
  for(int i = 0; i < ( 1 << N ); i++){
    int key = 0;
    for( int j = 0; j < N; j++){
      if( ( i >> j ) & 1){ key ^= switches[j];}}
    
    if( key == p){ cnt++;}}
  
  cout << cnt << endl; return 0;}