#include <iostream>
#include <vector>
#include <set>

using namespace std;

set<int> v;

int dfs(int i, int m, int **s, int *p, int n, int *k) {
    if (i == m) {
        bool flag = true;
        for (int j = 0; j < n; j++) {
            int cnt = 0;
            for (int l = 0; l < k[j]; l++) {
                if (v.find(s[j][l]) != v.end())
                    cnt++;
            }
            if (cnt % 2 != p[j])
                flag = false;
        }
        if (flag)
            return 1;
        else 
            return 0;
    }

    int ans = 0;
    v.insert(i);
    ans += dfs(i+1, m, s, p, n, k);
    v.erase(i);
    ans += dfs(i+1, m, s, n, p, k);
    return ans;
}

int main() {
    int n, m;   cin >> n >> m;
    int *k = new int[n], **s = new int*[n], *p = new int[m];
    for (int i = 0; i < n; i++) {
        cin >> k[i];
        s[i] = new int[k[i]];

        for (int j = 0; j < k[i]; j++)
            cin >> s[i][j];
    }

    for (int i = 0; i < m; i++)
        cin >> p[i];

    cout << dfs(0, m, s, p, n, k) << endl;

    return 0;
}