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>
using namespace std;

int main()
{
    int n, m; cin>>n>>m;
    vector<vector<int>> s(m);
    for(int i=0; i<m; ++i) {
        int k; cin>>k;
        vector<int> t(k);
        for(auto& e: t) cin>>e;
        s[i]=t;
    }
    vector<int> p(m);
    for(auto& e: p) cin>>e;

    int res=0;
    for(int i=0; i<(1<<n); ++i) {
        int cnt=0;
        for(int j=0; j<m; ++j) {
            int x=0;
            for(int k: s[j]) if ((i>>(k-1))&1) x++;
            if (x%2==p[j]) ++cnt;
        }
        if (cnt==m) ++res;
    }
    cout<<res<<endl;
}
