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: Wrong Answer)

#include "bits/stdc++.h"
using namespace std;

/*
vector.push_back()
vector<int> hoge(3,-1); {-1,-1,-1}
vector<vector<int>> hogehoge(2,vector<int>(2,-1)); {{-1,-1},{-1,-1}} 
cin >>temp;
scanf("%d %d %d",&A,&B,&Q);
sort(a.begin(),a.end());
a.push_back(4000000000000);
a.insert(a.begin(),-1000000000000);
upper_bound(a.begin(),a.end(),x); // list[i] > x のイテレータ取得. *itrで数値化 
    std::priority_queue<
      int,
      std::vector<int>,
      decltype(compare) // 比較関数オブジェクトを指定
    > que(comp);
*/
template <typename T> void debug(T arr);
template <typename T> void debug (T arr, int dim);

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;
      }
    }
  }
};

int main(void){
    int n,m;
      int a,b,c;
      cin >> n >> m;
      PrimalDual<int,int> g(n+m+2);
      for (int i = 0; i < n; ++i){
          g.add_edge(0,i+1,1,0);
      }
      for (int i = 0; i < m; ++i){
          cin >> a >> b;
          for (int j = 0; j < b; ++ j){
              cin >> c;
              g.add_edge(c,i+n+1,1000000,0);
          }
          g.add_edge(i+n+1,n+m+1,1000000,a);
      }
      auto cost = g.min_cost_flow(0,n+m+1,n);
      cout << cost << endl;
};


template <typename T> void debug(T arr){
    for (auto col:arr){
        cout << col << " ";
    }
    cout <<endl;
};

template <typename T> void debug (T arr, int dim){
    for (auto raw:arr){
        for(auto col:raw){
            cout << col << " ";
        }
        cout << endl;
    }
};