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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <string>
#include <sstream>
#include <complex>
#include <vector>
#include <list>
#include <queue>
#include <deque>
#include <stack>
#include <map>
#include <set>
#include <climits>
#include <random>
#include <iomanip>

using namespace std;
typedef long long unsigned int ll;
typedef pair<int, int> P;

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))

#define fillInt(xs, x)        \
  for (int i = 0; i < (x); i++) \
    scanf("%d", &xs[i]);
#define fillLong(xs, x)       \
  for (int i = 0; i < (x); i++) \
    scanf("%ld", &xs[i]);
#define fillString(xs, x)       \
  for (int i = 0; i < (x); i++) \
    cin >> xs[i];
#define sortv(xs) sort(xs.begin(), xs.end())
#define sortvdi(xs) sort(xs.begin(), xs.end(), std::greater<long>())
#define lbv(xs, x) lower_bound(xs.begin(), xs.end(), x) - xs.begin()
#define ubv(xs, x) upper_bound(xs.begin(), xs.end(), x) - xs.begin()
#define bs(xs, x) binary_search(xs.begin(), xs.end(), x)

#define rep(i,n) for(auto i=0; i<(n); i++)
#define isValidPoint(x, y, mx, my) x >= 0 && x  < mx && y >= 0 && y < my

int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};

const int mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x=0):x((x%mod+mod)%mod){}
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod-a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res+=a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res-=a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res*=a;
  }
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t>>1);
    a *= a;
    if (t&1) a *= *this;
    return a;
  }
 
  // for prime mod
  mint inv() const {
    return pow(mod-2);
  }
  mint& operator/=(const mint a) {
    return (*this) *= a.inv();
  }
  mint operator/(const mint a) const {
    mint res(*this);
    return res/=a;
  }
};

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

  int n, m;
  cin >> n >> m;

  int res[4096];
  rep(i, 4096) {
    res[i] = INF;
  }

  rep(i, m) {
    int a, b;
    cin >> a >> b;
    int bit = 0;
    rep(j, b) {
      int c;
      cin >> c;
      bit = bit | (1<<(c-1));
      res[bit] = min(res[bit], a);
    }
  }
  res[0] = 0;

  int resbit = (int)(pow(2, n)) -1;
  rep(k, n) {
    rep(i, resbit) {
      if (res[i] == INF) continue;
      for(int j = i+1; j < resbit; j++) {
        if (res[j] == INF) continue;
        res[i|j] = min(res[i]+res[j], res[i|j]);
      }
    }
  }

  if (res[resbit] == INF) {
    cout << -1 << endl;
  } else {
    cout << res[resbit] << endl;
  }
  
}