Problem:
Score : 500 points

Problem Statement

We have N locked treasure boxes, numbered 1 to N.

A shop sells M keys. The i-th key is sold for a_i yen (the currency of Japan), and it can unlock b_i of the boxes: Box c_{i1}, c_{i2}, ..., c_{i{b_i}}. Each key purchased can be used any number of times.

Find the minimum cost required to unlock all the treasure boxes. If it is impossible to unlock all of them, print -1.

Constraints

All values in input are integers.

1 \leq N \leq 12

1 \leq M \leq 10^3

1 \leq a_i \leq 10^5

1 \leq b_i \leq N

1 \leq c_{i1} < c_{i2} < ... < c_{i{b_i}} \leq N

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
c_{11} c_{12} ... c_{1{b_1}}
:
a_M b_M
c_{M1} c_{M2} ... c_{M{b_M}}

Output

Print the minimum cost required to unlock all the treasure boxes.
If it is impossible to unlock all of them, print -1.

Sample Input 1

2 3
10 1
1
15 1
2
30 2
1 2

Sample Output 1

25

We can unlock all the boxes by purchasing the first and second keys, at the cost of 25 yen, which is the minimum cost required.

Sample Input 2

12 1
100000 1
2

Sample Output 2

-1

We cannot unlock all the boxes.

Sample Input 3

4 6
67786 3
1 3 4
3497 1
2
44908 3
2 3 4
2156 3
2 3 4
26230 1
2
86918 1
3

Sample Output 3

69942

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define rep(i, s, N) for (ll i{s}; i < (N); i++)
#define rem(i, N, s) for (ll i{N}; i > (s); i--)
#define debug(x) cerr << #x << ": " << x << '\n'
#define debugp(i) cerr << "(" << i.first << ", " << i.second << ")\n"
#define debugv(v) cerr << #v << ": ";for(auto&& i : v) cerr << i << " "; cerr << '\n'
#define debugvp(v) cerr << #v << ": ";for(auto&& i : v) cerr << "(" << i.first << ", " << i.second << ") "; cerr << '\n'
const int MOD = (int)1e9 + 7;
const long double pi = 3.141592653589793238462643383279L;
using namespace std;
using ll = long long;
using ld = long double;
using str = string;
using wstr = wstring;
const string rt = "\n", sp = " ";
const wstring wrt = L"\n", wsp = L" ";

/* GCD */
template <typename M, typename N>
constexpr common_type_t<M, N> gcd(M a, N b) { return b != 0 ? gcd(b, a % b) : a; }

/* LCM */
template <typename M, typename N>
constexpr common_type_t<M, N> lcm(M a, N b) { return a * b / gcd(a, b); }

/* UNIONFIND */
template <typename T>
struct UnionFind
{
  vector<T> par;
  UnionFind(T n) : par(n, -1) {}
  void init(T n) { par.assign(n, -1); }
  T root(T x)
  {
    if (par[x] < 0)
      return x;
    else
      return par[x] = root(par[x]);
  }
  bool issame(T x, T y) { return root(x) == root(y); }
  bool merge(T x, T y)
  {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    if (par[x] > par[y])
      swap(x, y);
    par[x] += par[y];
    par[y] = x;
    return true;
  }
  int size(int x) { return -par[root(x)]; }
};

/* COMB */
auto comb(ll N){
  vector<vector<ll>> v(N+1,vector<ll>(N+1));
  for(unsigned int i = 0;i <v.size(); i++){
    v[i][0]=1;
    v[i][i]=1;
  }
  for(unsigned int k = 1;k <v.size();k++){
    for(unsigned int j = 1;j<k;j++){
      v[k][j]=(v[k-1][j-1]+v[k-1][j]);
    }
  }
  return v;
}
auto comb(ll N, ll n){
  vector<vector<ll>> v(max(N+1,n+1),vector<ll>(max(N+1,n+1)));
  for(unsigned int i = 0;i <v.size(); i++){
    v[i][0]=1;
    v[i][i]=1;
  }
  for(unsigned int k = 1;k <v.size();k++){
    for(unsigned int j = 1;j<k;j++){
      v[k][j]=(v[k-1][j-1]+v[k-1][j]);
    }
  }
  return v[N][n];
}

/* COMB % MOD */
template <typename T>
ll combpm(T N_, T C_)
{
  const int NUM_ = 400001;
  static ll fact[NUM_ + 1], factr[NUM_ + 1], inv[NUM_ + 1];
  if (fact[0] == 0)
  {
    inv[1] = fact[0] = factr[0] = 1;
    for (int i = 2; i <= NUM_; ++i)
      inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;
    for (int i = 1; i <= NUM_; ++i)
      fact[i] = fact[i - 1] * i % MOD, factr[i] = factr[i - 1] * inv[i] % MOD;
  }
  if (C_ < 0 || C_ > N_)
    return 0;
  return factr[C_] * fact[N_] % MOD * factr[N_ - C_] % MOD;
}

/* MAKE VECTOR */
template <class T>
constexpr vector<T> make_vector(size_t a) { return vector<T>(a); }
template <class T, class... Ts>
auto make_vector(size_t a, Ts... ts) { return vector<decltype(make_vector<T>(ts...))>(a, make_vector<T>(ts...)); }

/* MAKE DEQUE */
template <class T>
constexpr deque<T> make_deque(size_t a) { return deque<T>(a); }
template <class T, class... Ts>
auto make_deque(size_t a, Ts... ts) { return deque<decltype(make_deque<T>(ts...))>(a, make_deque<T>(ts...)); }

/* TEST */
void test(ll n) { cout << "test" << n << endl; }

/* PRECISION */
void fixsp(ll n) { cout << fixed << setprecision(n); }
void defsp(ll n) { cout << defaultfloat << setprecision(n); }

/* WEIGHTENED UNIONFIND */
struct WUnionFind
{
  vector<int> par;
  vector<int> rank;
  WUnionFind(int n = 1) { init(n); }
  void init(int n = 1)
  {
    par.resize(n);
    rank.resize(n);
    for (int i = 0; i < n; ++i)
      par[i] = i, rank[i] = 0;
  }
  int root(int x)
  {
    if (par[x] == x)
    {
      return x;
    }
    else
    {
      int r = root(par[x]);
      return par[x] = r;
    }
  }
  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 (rank[x] < rank[y])
      swap(x, y);
    if (rank[x] == rank[y])
      ++rank[x];
    par[y] = x;
    return true;
  }
};

/* DIVISOR */
deque<ll> divisor(ll n)
{
  deque<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);
}

/* MODE */
template <typename T>
auto mode(T data)
{
  if (data.size() == 1)
    return *begin(data);
  sort(begin(data), end(data));
  typename decltype(data)::value_type mode{};
  size_t n{}, count{1};
  for (auto iter = adjacent_find(begin(data), end(data)), last = end(data), next = end(data); iter != last;)
  {
    next = upper_bound(iter, last, *iter);
    count = distance(iter, next);
    if (n < count)
      n = count, mode = *iter;
    iter = adjacent_find(next, last);
  }
  return mode;
}

/* MEDIAN */
template <typename T>
auto median(T data)
{
  sort(begin(data), end(data));
  size_t median_index = data.size() / 2;
  return (data.size() % 2 == 0 ? static_cast<double>(data[median_index] + data[median_index - 1]) / 2 : data[median_index]);
}

/* INT POW */
template <typename T>
T multi(T a, ll b)
{
  T ans{1};
  for (int i{}; i < b; i++)
    ans *= a;
  return ans;
}

/* INF */
template <typename T>
constexpr T inf() { return numeric_limits<T>::max(); } 

/* FASTER IO */
void fastio(ll a)
{
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cerr.tie(nullptr);
  if(a) fixsp(a);
}

/* MIN COST FLOW */
template <typename flow_t, typename cost_t>
struct PrimalDual
{
  const cost_t INF;
  struct edge
  {
    int to;
    flow_t cap;
    cost_t cost;
    int rev;
    bool isrev;
  };
  vector<vector<edge>> graph;
  vector<cost_t> potential, min_cost;
  vector<int> prevv, preve;
  PrimalDual(int V) : graph(V), INF(numeric_limits<cost_t>::max()) {}
  void add_edge(int from, int to, flow_t cap, cost_t cost)
  {
    graph[from].emplace_back((edge){to, cap, cost, (int)graph[to].size(), false});
    graph[to].emplace_back((edge){from, 0, -cost, (int)graph[from].size() - 1, true});
  }
  cost_t min_cost_flow(int s, int t, flow_t f)
  {
    int V = (int)graph.size();
    cost_t ret = 0;
    using Pi = pair<cost_t, int>;
    priority_queue<Pi, vector<Pi>, greater<Pi>> que;
    potential.assign(V, 0);
    preve.assign(V, -1);
    prevv.assign(V, -1);
    while (f > 0)
    {
      min_cost.assign(V, INF);
      que.emplace(0, s);
      min_cost[s] = 0;
      while (!que.empty())
      {
        Pi p = que.top();
        que.pop();
        if (min_cost[p.second] < p.first)
          continue;
        for (int i = 0; i < graph[p.second].size(); i++)
        {
          edge &e = graph[p.second][i];
          cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] - potential[e.to];
          if (e.cap > 0 && min_cost[e.to] > nextCost)
          {
            min_cost[e.to] = nextCost;
            prevv[e.to] = p.second, preve[e.to] = i;
            que.emplace(min_cost[e.to], e.to);
          }
        }
      }
      if (min_cost[t] == INF)
        return -1;
      for (int v = 0; v < V; v++)
        potential[v] += min_cost[v];
      flow_t addflow = f;
      for (int v = t; v != s; v = prevv[v])
      {
        addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
      }
      f -= addflow;
      ret += addflow * potential[t];
      for (int v = t; v != s; v = prevv[v])
      {
        edge &e = graph[prevv[v]][preve[v]];
        e.cap -= addflow;
        graph[v][e.rev].cap += addflow;
      }
    }
    return ret;
  }
  void output()
  {
    for (int i = 0; i < graph.size(); i++)
    {
      for (auto &e : graph[i])
      {
        if (e.isrev)
          continue;
        auto &rev_e = graph[e.to][e.rev];
        cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << rev_e.cap + e.cap << ")" << endl;
      }
    }
  }
};

/* BELLMANFORD */

vector<long long> BellmanFord(int s, int V, vector<tuple<long long,long long,long long>> &G)
{
  vector<long long> d(V, inf<long long>());
  vector<bool> neg(V);
  d[s] = 0;
  for (int i = 0; i < V - 1; ++i)
  {
    for (auto &&e : G)
    {
      if (d[get<0>(e)] == inf<long long>())
        continue;
      d[get<1>(e)] = min(d[get<1>(e)], d[get<0>(e)] + get<2>(e));
    }
  }
  for (int i = 0; i < V; ++i)
  {
    for (auto &&e : G)
    {
      if (d[get<0>(e)] == inf<long long>())
        continue;
      if (d[get<1>(e)] > d[get<0>(e)] + get<2>(e))
      {
        d[get<1>(e)] = d[get<0>(e)] + get<2>(e);
        neg[get<1>(e)] = 1;
      }
      if (neg[get<0>(e)])
        neg[get<1>(e)] = 1;
    }
  }
  for (int i = 0; i < V; i++)
  {
    if (neg[i])
      d[i] = -inf<long long>();
  }
  return d;
}

/* DIJKSTRA */

vector<long long> Dijkstra(int s, int V, vector<tuple<long long,long long,long long>> &G){
  vector<vector<pair<long long,long long>>> uv(V);
  for(auto&& i : G) uv[get<0>(i)].emplace_back(get<1>(i), get<2>(i));
  vector<long long> d(V, inf<long long>()/2);
  vector<long long> prev(V, -1);
  d[s] = 0;
  priority_queue<pair<long long,long long>,vector<pair<long long,long long>>,greater<pair<long long,long long>>> Q;
  rep(i,0,V) Q.emplace(d[i], i);
  while(!Q.empty()){
    long long u = Q.top().second;
    Q.pop();
    for(auto&& v : uv[u]){
      long long alt = d[u] + v.second;
      if(d[v.first] > alt){
        d[v.first] = alt;
        if(d[v.first] > inf<long long>()/4) d[v.first] = inf<long long>()/2;
        else if(d[v.first] < -inf<long long>()/4) d[v.first] = -inf<long long>()/2;
        prev[v.first] = u;
        Q.emplace(alt, v.first);
      }
    }
  }
  for(auto&& i : d){
    if(abs(i)>inf<long long>()/4) (i*=2)++;
  }
  return d;
}

/* BFS */

vector<long long> BFS(long long s, long long V, vector<pair<long long,long long>> &G){
  queue<long long> Q;
  vector<vector<long long>> uv(V);
  for(auto&& i : G) uv[i.first].emplace_back(i.second);
  vector<long long> d(V,inf<long long>());
  d[s] = 0;
  Q.emplace(s);
  while(!Q.empty()){
    long long v = Q.front();
    Q.pop();
    for(auto&& i : uv[v]){
      if(d[i] == inf<long long>()){
        d[i] = d[v]+1;
        Q.emplace(i);
      }
    }
  }
  return d;
}

/* WARSHALLFLOYD */
vector<vector<long long>> WarshallFloyd(int V, vector<tuple<long long,long long,long long>> &G){
  vector<vector<long long>> d(V, vector<long long>(V, inf<long long>()));
  for(auto&& i : G){
    d[get<0>(i)][get<1>(i)] = get<2>(i);
  }
  rep(k,0,V) rep(i,0,V) rep(j,0,V){
    if(d[i][k] != inf<ll>() && d[k][j] != inf<ll>())
    d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
  }
  rep(i,0,V){
    d[i][i] = 0;
  }
  return d;
}

/* KYOTO UNIVERSITY */

/* LAST EDITED ON 9.5.2019 */

/* CODE STARTS FROM HERE */

int main(){
  fastio(0);
  ll N, M;
  cin >> N >> M;
  auto key = make_deque<pair<ll,deque<ll>>>(M);
  rep(i,0,M){
    ll a, b;
    cin >> a >> b;
    key[i].first = a;
    rep(j,0,b){
      ll c;
      cin >> c;
      key[i].second.emplace_back(c-1);
    }
  }
  unordered_map<ll,unordered_map<ll,ll>> DP;
  DP[-1][0] = 0;
  rep(i,0,M){
    for(auto&& j : DP[i-1]){
      ll stat = j.first;
      ll cost = j.second;
      if(DP[i].count(stat)) DP[i][stat] = min(DP[i][stat], cost);
      else DP[i][stat] = cost;
      for(auto&& k : key[i].second){
        if((stat >> k)%2 == 0){
          stat += multi(2,k);
        }
      }
      if(DP[i].count(stat)) DP[i][stat] = min(DP[i][stat], cost + key[i].first);
      else DP[i][stat] = cost + key[i].first;
    }
  }
  if(DP[M-1].count(multi(2,N)-1) == 0){
    cout << -1;
    return 0;
  }
  cout << DP[M-1][multi(2,N)-1];
}