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;
vector<tuple<string, int, int> > S;
int N, M;
int a[11];
int main()
{
  scanf("%d%d", &N, &M);
  for(int i=0; i<M; ++i)
  {
    int t; scanf("%d", &t);
    for(int j=0; j<t; ++j)
    {
      int x; scanf("%d", &x);
      a[x-1] += 1<<i;
    }
  }
  int p = 0;
  for(int i=0; i<M; ++i)
  {
    int t; scanf("%d", &t);
    p += t<<i;
  }
  int cnt= 0;
  for(int i=0; i<(1<<N); ++i)
  {
    int f = p;
    for(int j=0; j<N; ++j)
    {
      if(i&(1<<j))
        f^= a[j];
    }
    if(!f) ++cnt;
  }
  printf("%d\n", cnt);
}