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)

int main() {
  int n, m;
  cin >> n >> m;
  vector<int> a(n);
  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;
  }

  int ans = 0;
  rep(s, 1 << n) {
    int t = 0;
    rep(i, n) {
      if (s >> i & 1) {
        t ^= a[i];
      }
    }
    if (t == p) ++ans;
  }
  cout << ans << endl;
  return 0;
}
