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)

/**
 *      purpose : 
 *      author  : kyomukyomupurin
 *      created : 
**/

// input/output
#include <fstream>
#include <iostream>
#include <sstream>
// container class
#include <array>
#include <deque>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>
// math, algorithm
#include <algorithm>
#include <cmath>
#include <complex>
#include <numeric>
// etc
#include <bitset>
#include <cassert>
#include <cctype>
#include <cstring>
#include <chrono>
#include <ext/random>
#include <ext/rope>
#include <functional>
#include <iomanip>
#include <random>
#include <utility>
// using-directive
using namespace std;
// alias template
using int64 = long long;
using ull = unsigned long long;
using vi = std::vector<int>;
using vl = std::vector<int64>;
using pii = std::pair<int, int>;
using pii = std::pair<int, int>;
using pll = std::pair<int64, int64>;
// text macro replacement
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define all(_) (_).begin(), (_).end()
#define rall(_) (_).rbegin(), (_).rend()
#define print(_) std::cout << (_) << '\n'
#define debug(_) std::cerr << #_ << ": " << (_) << '\n'
// variadic template
template<typename T> inline void chmin(T &a, T b) {if (a > b) a = b; return;}
template<typename T> inline void chmax(T &a, T b) {if (a < b) a = b; return;}
template<typename T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
  os << '{';
  for (size_t i = 0; i < vec.size(); ++i) {
    os << vec[i];
    if (i != vec.size() - 1) os << ',';
  }
  os << '}';
  return os;
}
template<typename T, typename U> std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {
  return os << '{' << p.first << " " << p.second << '}';
}
// constant
const int INF = (1<<30) - 1;  // 1.073741823e9
const int64 INF64 = (1LL<<62) - 1;  // 4.611686018427387903e18
const int MOD = 1000000007;

struct key {
  int64 cost;
  vector<int64> open;
};

int main(){
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);

  int64 n, m; cin >> n >> m;
  vector<key> vec;

  int64 sum = 0;

  rep(i, m) {
    int64 a, b; cin >> a >> b;
    sum += a;
    vector<int64> v;
    rep(j, b) {
      int64 c; cin >> c;
      v.emplace_back(c);
    }
    vec.push_back({a, v});
  }

  sort(all(vec), [](const key& x, const key& y){
    return x.cost > y.cost;
  });

  map<int64, int> mp;
  for (int i = 0; i < m; ++i) {
    for (int j = 0; j < (int) vec[i].open.size(); ++j) {
      ++mp[vec[i].open[j]];
    }
  }

  for (int i = 1; i <= n; ++i) {
    if (mp[i] == 0) {
      cout << -1 << '\n'; return 0;
    }
  }

  for (int i = 0; i < m; ++i) {
    bool flag = true;
    for (int j = 0; j < (int) vec[i].open.size(); ++j) {
      if (mp[vec[i].open[j]] <= 1) {
        flag = false;
        break;
      } 
    }

    if (flag) {
      for (int j = 0; j < (int) vec[i].open.size(); ++j) {
        --mp[vec[i].open[j]];
      }
      sum -= vec[i].cost;
    }
  }

  cout << sum << endl;

  return 0;
}