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;
using ll = long long;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

signed main() {
  int n,m; cin >>n >>m;
  vector<vector<int>> s(m);
  rep(i,m) {
    int k; cin >> k;
    s[i].resize(k);
    rep(j, k) cin >> s[i][j];
  }
  vector<int> p(m);
  rep(i,m) cin >> p[i];

  int ans = 0;
  rep(b, 1<<n) {
    bool ok = true;
    rep(i, m) {
      int count = 0;
      for(auto ss : s[i]) if(b & 1<< (ss-1)) count++;
      ok=(count%2 == p[i]);
      if(!ok) break;
    }
    ans += ok;
  }
  cout << ans << endl;

}
