#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <string>
#include <cstring>
#include <queue>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <map>
#include <numeric>
#include <functional>
#include <cmath>
#include <cassert>
#include <string>
#include <iostream>

using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<ll, ll> PL;
const ll mod = 1000000007;
const ll MOD = 1000000007;
const ll INF = 1LL << 60;
#define PI (acos(-1))
#define ALL(c) (c).begin(), (c).end()

ll lcm(ll a, ll b)
{
    return a / __gcd(a, b) * b;
}

vector<ll> divisor(ll n)
{
    vector<ll> ret;
    for (ll i = 1; i * i <= n; i++)
    {
        if (n % i == 0)
        {
            ret.push_back(i);
            if (i * i != n)
                ret.push_back(n / i);
        }
    }
    sort(begin(ret), end(ret));
    return (ret);
}

const ll MAX = 510000;
ll fac[MAX], finv[MAX], inv[MAX];
// テーブルを作る前処理
void COMinit()
{
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (ll i = 2; i < MAX; i++)
    {
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
// 二項係数計算
ll COM(ll n, ll k)
{
    if (n < k)
        return 0;
    if (n < 0 || k < 0)
        return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

struct BIT
{
    int n;
    vector<int> bit;
    BIT()
    {
        init();
    }
    BIT(int n) : n(n)
    {
        init();
    }
    void init()
    {
        bit.clear();
        bit.resize(n + 1, 0);
    }
    int sum(int i)
    {
        int s = 0;
        while (i > 0)
        {
            s += bit[i];
            i -= i & -i;
        }
        return s;
    }
    int sum(int x, int y)
    {
        return sum(y) - sum(x - 1);
    }
    void add(int i, int x)
    {
        while (i <= n)
        {
            bit[i] += x;
            i += i & -i;
        }
    }
    int lower_bound(int w)
    {
        if (w <= 0)
            return 0;
        int x = 0, r = 1;
        while (r < n)
            r <<= 1;
        for (int k = r; k > 0; k >>= 1)
        {
            if (x + k <= n && bit[x + k] < w)
            {
                w -= bit[x + k];
                x += k;
            }
        }
        return x + 1;
    }
};
// 文字列t　->整数　atoi(t.c_str());
// 文字列t　->long long整数　stoll(t); ローカルではつかえない

long long modpow(long long a, long long n, long long mod)
{
    long long res = 1;
    while (n > 0)
    {
        if (n & 1)
            res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}

// a^{-1} mod を計算する
long long modinv(long long a, long long mod)
{
    return modpow(a, mod - 2, mod);
}


struct UnionFind
{
    vector<int> par;

    UnionFind(int n) : par(n, -1) {}
    void init(int n) { par.assign(n, -1); }

    int root(int x)
    {
        if (par[x] < 0)
            return x;
        else
            return par[x] = root(par[x]);
    }

    bool issame(int x, int y)
    {
        return root(x) == root(y);
    }

    bool merge(int x, int y)
    {
        x = root(x);
        y = root(y);
        if (x == y)
            return false;
        if (par[x] > par[y])
            swap(x, y); // merge technique
        par[x] += par[y];
        par[y] = x;
        return true;
    }

    int size(int x)
    {
        return -par[root(x)];
    }
};

struct LazySegmentTree
{
// private:
    ll n;
    vector<ll> node, lazy;

// public:
    LazySegmentTree(vector<ll> v)
    {
        int sz = (int)v.size();
        n = 1;
        while (n < sz)
            n *= 2;
        node.resize(2 * n - 1);
        lazy.resize(2 * n - 1, 0);

        for (int i = 0; i < sz; i++)
            node[i + n - 1] = v[i];
        for (int i = n - 2; i >= 0; i--)
            node[i] = node[i * 2 + 1] + node[i * 2 + 2];
    }

    void eval(int k, int l, int r)
    {
        if (lazy[k] != 0)
        {
            node[k] += lazy[k];
            if (r - l > 1)
            {
                lazy[2 * k + 1] += lazy[k] / 2;
                lazy[2 * k + 2] += lazy[k] / 2;
            }
            lazy[k] = 0;
        }
    }

    void add(int a, int b, ll x, int k = 0, int l = 0, int r = -1)
    {
        if (r < 0)
            r = n;
        eval(k, l, r);
        if (b <= l || r <= a)
            return;
        if (a <= l && r <= b)
        {
            lazy[k] += (r - l) * x;
            eval(k, l, r);
        }
        else
        {
            add(a, b, x, 2 * k + 1, l, (l + r) / 2);
            add(a, b, x, 2 * k + 2, (l + r) / 2, r);
            node[k] = node[2 * k + 1] + node[2 * k + 2];
        }
    }

    ll getsum(int a, int b, int k = 0, int l = 0, int r = -1)
    {
        if (r < 0)
            r = n;
        eval(k, l, r);
        if (b <= l || r <= a)
            return 0;
        if (a <= l && r <= b)
            return node[k];
        ll vl = getsum(a, b, 2 * k + 1, l, (l + r) / 2);
        ll vr = getsum(a, b, 2 * k + 2, (l + r) / 2, r);
        return vl + vr;
    }
};

ll digit_sum(ll v){
    ll ret = 0;
    while(v){
        ret += (v % 10);
        v /= 10;
    }
    return ret;
}

template <typename T>
struct Kruskal
{

    struct edge
    {
        ll from, to;
        T cost;
        ll used;
        edge() {}
        edge(ll from, ll to, T cost) : from(from), to(to), cost(cost), used(0) {}
        bool operator<(const edge &e) const
        {
            return cost < e.cost;
        }
    };

    ll n;
    vector<ll> p, r;
    vector<edge> edges;

    Kruskal() {}
    Kruskal(ll n) : n(n) {}

    void init(ll n)
    {
        r.assign(n, 1);
        p.resize(n);
        iota(p.begin(), p.end(), 0);
    }

    ll find(ll x)
    {
        return (x == p[x] ? x : p[x] = find(p[x]));
    }

    bool same(ll x, ll y)
    {
        return find(x) == find(y);
    }

    void unite(ll x, ll y)
    {
        x = find(x);
        y = find(y);
        if (x == y)
            return;
        if (r[x] < r[y])
            swap(x, y);
        r[x] += r[y];
        p[y] = x;
    }

    void add_edge(ll u, ll v, T c)
    {
        edges.emplace_back(u, v, c);
    }

    T build()
    {
        sort(edges.begin(), edges.end());
        init(n);
        T res = 0;
        for (auto &e : edges)
        {
            if (!same(e.from, e.to))
            {
                res += e.cost;
                unite(e.from, e.to);
                e.used = 1;
            }
        }
        return res;
    }
};

ll p[11], s[11][13];
ll solve()
{

    ll n, m;
    cin >> n >> m;
    for(int i=0; i < m; i++){
        ll k;
        cin >> k;
        s[i][0] = k;
        for(int j=1; j <= k; j++){
            cin >> s[i][j];
        }
    }
    for(int i=0; i < m; i++){
        cin >> p[i];
    }

    ll ans = 0;
    for(int i=0; i < (1 << n); i++){
        map<ll, ll> c;
        for(int j=0; j < n; j++){
            if(i & ( 1 << j)){
                c[j + 1] = 1;
            }
        }

        bool f = true;
        for(int j=0; j < m; j++){
            ll t = 0;
            for(int k=1; k <=s[j][0] ; k++){
                if(c[s[j][k]]){
                    t++;
                }
            }
            if(t%2 != p[j]){
                f = false;
            }
        }
        if(f){
            ans++;
        }
    }

    cout << ans << endl;

    return 0;
}

int main()
{
    cout.precision(10);
    ios::sync_with_stdio(false);
    cin.tie(0);

    solve();
}


Measured memory_bytes: 256