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 <bits/stdc++.h>
using namespace std;
#define ll long long
#define LLMAX (1ll << 60) - 1
#define INTMAX (1 << 30) - 1
#define MOD 1000000007 
#define NMAX 1000*100+1

#define numberOfSetBits(S) __builtin_popcount(S) // __builtin_popcountl(S) __builtin_popcountll(S)
#define MSET(x,y) memset(x,y,sizeof(x))
#define gcd(a,b) __gcd(a,b)
#define all(x)  x.begin(),x.end()
#define isOn(S, j) (S & (1 << j))
#define endl '\n'
#define setBit(S, j) (S |= (1 << j))
#define clearBit(S, j) (S &= ~(1 << j))
#define toggleBit(S, j) (S ^= (1 << j))
#define print(x)    for(auto it:x) cout<<it<<' '; cout<<endl;
#define printii(x)  for(auto it:x) cout<<it.F<<' '<<it.S<<'\t';  cout<<endl;
#define in(x,n)   for(int e=0;e<n;e++){ll y;cin>>y;x.pb(y);}

#define vi vector<ll>
#define vvi vector<vi>
#define ii pair<ll,ll>
#define pll pair<ll,ll>
#define vii vector<ii>
#define vvii vector<vii>
#define viii vector<pair<ii,ll>>
#define pb push_back
#define F first
#define S second
#define mp make_pair
#define mc(a,b,c) mp(mp(a,b),c)

ll dp[1002][(1<<13)+4];

vi a,b;

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    ll n,x,t,m,y,z;
    cin>>n>>m;
    for(int i=0;i<m;i++){
        cin>>x>>y;
        a.pb(x);
        z = 0;
        for(int j=0;j<y;j++){
            cin>>x;
            x--;
            z+=(1<<x);
        }
        b.pb(z);
    }
    for(int i=0;i<(1<<n);i++){
        dp[m][i] = LLMAX;
    }
    dp[m][(1<<n)-1] = 0;
    
    for(int i=m-1;i>=0;i--){
        for(int j=0;j<(1<<n);j++){
            dp[i][j] = min(dp[i+1][j], dp[i+1][j|b[i]]+a[i]);
        }
    }
    if(dp[0][0]>=LLMAX){
        dp[0][0] = -1;
    }
    cout<<dp[0][0];
    
    

    return 0;
}