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<int> a(n);
  vector<int> count(m, 0);
  int ans = 0;
  rep(i,m) {
    int k;
    cin >> k;
    rep(j,k) {
      int s;
      cin >> s;
      s--;
      a[s] |= (1<<i);
    }
  }
  int p = 0;
  rep(i,m) {
    int x;
    cin >> x;
    p |= (x<<i);
  }
  rep(i,1<<n) {
    int t = 0;
    rep(j,n) if(i>>j&1) t ^= a[j];
    if(t==p) ans++;
  }
  cout << ans << endl;
  return 0;
}