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<iostream>
#include<stdio.h>
#include<bits/stdc++.h>
using namespace std;
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
/*---------------------DEBUGGING--------------------------------------------*/
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
/*-------------------------------------------------------------------------------------*/
//#define mp make_pair
#define pb push_back
#define ll long long
#define pii pair<int,int>
#define pcc pair<char,char>
#define F first
#define S second
#define int long long
#define pi 3.141592653589793238462643383279502
#define M  1000000007
#define rep(i,a,n) for(int i=a;i<n;i++)
#define INF 10000000000000
#define N 200005
#define vi vector<int>
#define all(v) v.begin(),v.end()
//#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
int dp[1<<12];

signed main()
{
   ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
   int n,m;
   cin>>n>>m;
   int a[m];
   int cost[m];
   for(int i=0;i<m;i++)
   {
       cin>>cost[i];
       int k;
       cin>>k;
       int val=0;
       for(int j=0;j<k;j++)
       {
           int x;cin>>x;
           x--;
           val+=(1LL<<x);
       }
       a[i]=val;
   }
   memset(dp,0x3f,sizeof(dp));
   dp[0]=0;
   int full_mask=(1LL<<n)-1;
   for(int mask=0;mask<=full_mask;mask++)
   {
       for(int i=0;i<m;i++)
       {
           dp[a[i]|mask]=min(dp[a[i]|mask],dp[mask]+cost[i]);
       }
   }
   if(dp[full_mask]>1e18)
    cout<<-1<<endl;
   else
   cout<<dp[full_mask]<<endl;



}