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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;

class Program{
  static void Main(){
    string[] input = Console.ReadLine().Split(' ');
    int N = int.Parse(input[0]);
    int M = int.Parse(input[1]);
    
    int W = (int)Math.Pow(2, N);
    int[,] DP = new int[M+1, W+1];
    
    // dp (縦)
    for (int i = 1; i <= M; i++){
      string[] ab = Console.ReadLine().Split(' ');
      int a = int.Parse(ab[0]);
      int b = int.Parse(ab[1]);
      string[] c = Console.ReadLine().Split(' ');
      
      // cを数値に変換
      int c_num = 0;
      for (int k = 0; k < b; k++){
        c_num += (int)Math.Pow(2, int.Parse(c[k]) - 1);
      }
      
      // dp (横)
      for (int j = 0; j < W; j++){
        if(j != 0 && DP[i-1, j] == 0)
          continue;
        
        if(DP[i, j] != 0)
          DP[i, j] = Math.Min(DP[i, j], DP[i-1, j]);
        else
          DP[i, j] = DP[i-1, j];
        
        // d := 状態 j と 鍵 i から得られる状態
        int d = NewStatus(c_num, j);
        int tmp;
        if(DP[i-1, d] != 0)
          tmp = Math.Min(DP[i-1, d], DP[i-1, j] + a);
        else
          tmp = DP[i-1, j] + a;
        
        if(DP[i, d] != 0)
          DP[i, d] = Math.Min(DP[i, d], tmp);
        else
          DP[i, d] = tmp;
      }  
    }
    
    int ans;
    if (DP[M, W-1] == 0)
      ans = -1;
    else
      ans = DP[M, W-1];
    
    Console.WriteLine(ans);
  }
  
  static int NewStatus(int sta1, int sta2){
    if (sta1 > sta2)
      return NewStatus(sta2, sta1);
    else if (sta1 == sta2)
      return sta1;
    
    // 以後、 sta1 < sta2 として行う
    string str1 = Convert.ToString(sta1, 2);
    string str2 = Convert.ToString(sta2, 2);
    string strnew = "";
    
    for (int i = 0; i < str2.Length; i++){
      string str2_i = str2.Substring(str2.Length-i-1, 1);
      if (i >= str1.Length)
        strnew = str2_i +strnew;
      else{
        string str1_i = str1.Substring(str1.Length-i-1, 1);
        if (str1_i == "0" && str2_i == "0")
          strnew = "0" + strnew;
        else
          strnew = "1" + strnew;
      }
    }
    
    return Convert.ToInt32(strnew, 2);
  }
}