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
//------------------------------------------
#include <bits/stdc++.h>
using namespace std;

//typedef
//------------------------------------------
typedef long long LL;
typedef vector<LL> VL;
typedef vector<VL> VVL;
typedef vector<string> VS;
typedef pair<LL, LL> PLL;

//container util
//------------------------------------------
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())

//constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI  = acos(-1.0);
const int MOD = 1000000007;

// grid
//--------------------------------------------
VL dx = {0, 1, 0, -1};
VL dy = {1, 0, -1, 0};
VL dx2 = {-1, 0, 1, -1, 1, -1, 0, 1};
VL dy2 = {-1, -1, -1, 0, 0, 1, 1, 1};

//debug
//--------------------------------------------
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;

//IO accelerate
//--------------------------------------------
struct InitIO {
    InitIO() {
        cin.tie(nullptr);
        ios_base::sync_with_stdio(false);
        cout << fixed << setprecision(30);
    }
} init_io;

//template
//--------------------------------------------
template<typename T>
istream& operator >>(istream& is, vector<T>& vec) {
  for(T& x: vec) is >> x;
  return is;
}
template<typename T>
ostream& operator <<(ostream& os, const vector<T>& vec) {
  for(int i=0; i<vec.size(); i++){
    os << vec[i] << ( i+1 == vec.size() ? "" : "\t" );
  }
  return os;
}
template<typename T>
ostream& operator <<(ostream& s, const vector<vector<T>>& vv) {
	for (int i = 0; i < vv.size(); ++i) {
		s << vv[i] << endl;
	}
	return s;
}

// 多重vector
// auto dp=make_v<int>(4,h,w) みたいに使える
template<typename T>
vector<T> make_v(size_t a){return vector<T>(a);}

template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts){
  return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

// 多重vectorのためのfill
// fill_v(dp,0) みたいに使える
template<typename T,typename V>
typename enable_if<is_class<T>::value==0>::type
fill_v(T &t,const V &v){t=v;}

template<typename T,typename V>
typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t,const V &v){
  for(auto &e:t) fill_v(e,v);
}

//main code

int main(int argc, char const* argv[])
{
	int n,m;
	cin >> n >> m;
	VVL dp((1<<n), VL(m+1, INT32_MAX));
	dp[0][0] = 0;
	VL a(m+1), b(m+1,0);
	for (int i = 1; i <= m; i++) {
		int bb;
		cin >> a[i] >> bb;
		for (int j = 0; j < bb; j++) {
			int c;
			cin >> c;
			b[i] += (1<<(c-1));
		}
	}

	for (int i = 1; i <= m; i++) {
		for (int j = 0; j < (1<<n); j++) {
			if (dp[j][i-1] != INT32_MAX) {
				dp[(j | b[i])][i] = min(dp[(j | b[i])][i], dp[j][i-1] + a[i]);
				dp[j][i] = min(dp[j][i], dp[j][i-1]);
			}
		}
	}
	if (dp[(1<<n)-1][m] == INT32_MAX) {
		cout << -1 << endl;
	} else {
		cout << dp[(1<<n)-1][m] << endl;
	}

	return 0;
}