#include <bits/stdc++.h>

#pragma GCC optimize("O3")
#pragma GCC target("tune=native")
#pragma GCC target("avx")
// #pragma GCC target("avx2")
#pragma GCC optimize("unroll-loops")

using namespace std;

using i64 = int64_t;

const i64 MOD = 1e9+7;

const i64 INF = i64(1e18)+MOD;

template <typename T = i64>
struct Range{
    struct iterator{
        T value;
        const T step, last;
        const T& operator*(){return value;}
        iterator(T value, T step, T last) :
            value(step < static_cast<T>(0) ? max(last, value) : min(last, value)),
            step(step),
            last(last)
        {
        }
        iterator operator++(){value = step < static_cast<T>(0) ? max(value + step, last) : min(value + step, last); return *this;}
        bool operator!=(const iterator& x){return value != x.value;}
    };
    const T start, last, step;

    Range(const T start, const T last, const T step = static_cast<T>(1)) :
        start(start),
        last(last),
        step(step)
    {
    }

    Range(const T last) :
        start(0),
        last(last),
        step(1)
    {
    }

    iterator begin(){return iterator(start, step, last);}
    iterator end(){return iterator(last, step, last);}
};

template <typename F>
struct FixPoint{
    const F _f;
    FixPoint(F&& f) : _f(forward<F>(f)){}

    template<typename... Types>
    decltype(auto) operator()(Types&&... args) const{
        return _f(*this, forward<Types>(args)...);
    }
};

template <typename F>
static decltype(auto) makeRec(F&& f){
    return FixPoint<F>(forward<F>(f));
}

template <typename T, T Value = T()>
vector<T> makeVector(size_t x){
    return vector<T>(x, T(Value));
}

template <typename T, T Value = T(), typename... Types>
auto makeVector(size_t x, Types... args){
    return vector<decltype(makeVector<T, Value>(args...))>(x, makeVector<T, Value>(args...));
}

template <typename T = i64>
bool chmax(T& a, T b){
    if(a < b){
        a = b;
        return true;
    }
    return false;
}

template <typename T = i64>
bool chmin(T& a, T b){
    if(a > b){
        a = b;
        return true;
    }
    return false;
}

#define dump(x) fprintf(stderr, "line =%4d, name =%7s , ", __LINE__, #x); clog << "value = " << x << endl;

#define vecdump(x) fprintf(stderr, "line =%4d, name =%7s\n", __LINE__, #x); _dump_macro(x);

void _dump(int, string& x){
    clog << x << endl;
}

template <typename T>
void _dump(bool, T& x){
    clog << x << " ";
}

template <typename T, typename U = typename T::iterator>
void _dump(int, T& x){

    for(auto& elm : x)
        _dump(0, elm);

    clog << endl;
}

template <typename T>
void _dump_macro(T& x){
    _dump(0, x);
}

void _input(int, string& x){
    cin >> x;
}

template <typename T>
void _input(bool, T& x){
    cin >> x;
}

template <typename T, typename U = typename T::iterator>
void _input(int, T& x){

    for(auto& elm : x)
        _input(0, elm);
}

template <typename T>
void input_single(T& x){
    _input(0, x);
}

auto input(){}

template <typename T, typename... Types>
void input(T& value, Types&&... args){
    input_single(value);
    input(forward<Types>(args)...);
};

void _pararell_input(size_t){}

template <typename T, typename... Types>
void _pararell_input(size_t index, T& value, Types&&... args){
    input(value[index]);
    _pararell_input(index, forward<Types>(args)...);
}

template <typename... Types>
void pararell_input(size_t count, Types&&... args){
    for(const auto& i : Range<>(count))
        _pararell_input(i, forward<Types>(args)...);
}

template<typename T>
struct Compression{
    vector<T> compvec;
    Compression(vector<T>& inp){//圧縮する
        compvec = inp;
        sort(compvec.begin(), compvec.end());
        compvec.erase(unique(compvec.begin(), compvec.end()), compvec.end());
    }
    int Index(T val){//圧縮を元に対応するインデックスを返す
        auto it = lower_bound(compvec.begin(), compvec.end(), val);
        return distance(compvec.begin(), it);
    }
    vector<T>& operator*(){
        return compvec;
    }
};

template<typename T, typename U>
struct Segtree{
    int n;
    T op_t;
    U op_u;
    vector<T> elm;
    vector<U> lazy;
    vector<int> length;
    function<T(T, T)> f;
    function<T(T, U, int)> g;
    function<U(U, U)> h;

    Segtree(int n, T init, function<T(T, T)> f, function<T(T, U, int)> g, function<U(U, U)> h, T op_t = T(), U op_u = U()) :
        n(n),
        op_t(op_t),
        op_u(op_u),
        elm(2 * n, init),
        lazy(2 * n, op_u),
        length(2 * n, 0),
        f(f),
        g(g),
        h(h)
    {
        for(int i = n - 1; i > 0; --i){
            elm[i] = f(elm[2 * i], elm[2 * i + 1]);
            length[i] = length[2 * i] + 1;
        }
    }

    Segtree(int n, vector<T> init, function<T(T, T)> f, function<T(T, U, int)> g, function<U(U, U)> h, T op_t = T(), U op_u = U()) :
        n(n),
        op_t(op_t),
        op_u(op_u),
        elm(2 * n),
        lazy(2 * n, op_u),
        length(2 * n, 0),
        f(f),
        g(g),
        h(h)
    {
        for(int i = 0; i < n; ++i)
            elm[i + n] = init[i];

        for(int i = n - 1; i > 0; --i){
            elm[i] = f(elm[2 * i], elm[2 * i + 1]);
            length[i] = length[2 * i] + 1;
        }
    }

    vector<int> get_list(int x, int y){

        vector<int> ret_list;
        for(x += n, y += n - 1; x; x >>= 1, y >>= 1){
            ret_list.emplace_back(x);
            if(x != y)
                ret_list.emplace_back(y);
        }

        return ret_list;
    }

    void eval(int x){

        elm[x] = g(elm[x], lazy[x], 1 << length[x]);
        if(x < n){
            lazy[2 * x] = h(lazy[2 * x], lazy[x]);
            lazy[2 * x + 1] = h(lazy[2 * x + 1], lazy[x]);
        }
        lazy[x] = op_u;
    }

    void update(int x, int y, U val){

        vector<int> index_list = get_list(x, y);
        for(int i = index_list.size() - 1; i >= 0; --i)
            eval(index_list[i]);

        for(x += n, y += n - 1; x <= y; x >>= 1, y >>= 1){
            if(x & 1){
                lazy[x] = h(lazy[x], val);
                eval(x++);
            }
            if(!(y & 1)){
                lazy[y] = h(lazy[y], val);
                eval(y--);
            }
        }

        for(auto index : index_list){
            if(index < n){
                eval(2 * index);
                eval(2 * index + 1);
                elm[index] = f(elm[2 * index], elm[2 * index + 1]);
            }
        }
    }

    T get(int x, int y){

        vector<int> index_list = get_list(x, y);
        for(int i = index_list.size() - 1; i >= 0; --i)
            eval(index_list[i]);

        T l = op_t, r = op_t;
        for(x += n, y += n - 1; x <= y; x >>= 1, y >>= 1){
            if(x & 1){
                eval(x);
                l = f(l, elm[x++]);
            }
            if(!(y & 1)){
                eval(y);
                r = f(elm[y--], r);
            }
        }
        return f(l, r);
    }
};

void solve(){
    int n, m;
    input(n, m);
    vector<int> k(m);
    vector<vector<int>> s(m);
    vector<vector<int>> edges(n);
    for(int i = 0; i < m; ++i){
        input(k[i]);
        s[i].assign(k[i], 0);
        input(s[i]);
        for(auto& x : s[i]){
            edges[x - 1].emplace_back(i);
        }
    }
    vector<int> p(m);
    input(p);
    int cnt = 0;
    for(int i = 0; i < (1 << n); ++i){
        vector<int> c(m, 0);
        for(int j = 0; j < n; ++j)
            if(i & (1 << j))
                for(auto& x : edges[j])
                    ++c[x];
        bool fl = true;
        for(int j = 0; j < m; ++j)
            fl &= (c[j] % 2 == p[j]);
        cnt += fl;
    }
    cout << cnt << endl;
}

signed main(){

    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);

    solve();
}



Measured memory_bytes: 256