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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;

namespace AtCoder.E
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var input = ReadLongs();
            var N = input[0];
            var M = input[1];
            var keys = new List<Key>();
            for (int i = 0; i < M; i++)
            {
                var key = new Key();
                input = ReadLongs();
                key.a = input[0];
                key.b = input[1];
                // インデックス変換
                key.c = ReadLongs().Select(x => x - 1).ToList();
                key.Buyables = string.Join(",", key.c.OrderBy(x => x).ToArray());

                keys.Add(key);
            }

            // 同じ箱を開けられる鍵の中で最もコストが低いものに選別する
            // 高々4096個に絞ることができる
            var dic = new Dictionary<string, Key>();
            foreach (var key in keys)
            {
                if (!dic.ContainsKey(key.Buyables))
                {
                    dic.Add(key.Buyables, key);
                    continue;
                }
                if (dic[key.Buyables].a > key.a)
                {
                    dic[key.Buyables] = key;
                }
            }

            keys = dic.Select(x => x.Value).ToList();
            //keys = keys.GroupBy(x => x.Buyables).Select(x =>
            //      {
            //          var min = long.MaxValue;
            //          var minkey = new Key();
            //          foreach (var item in x)
            //          {
            //              if (min > item.a)
            //              {
            //                  min = item.a;
            //                  minkey = item;
            //              }
            //          }
            //          return minkey;
            //      }).ToList();

            if (!CanOpenAllBox(N, keys))
            {
                return -1;
            }

            var l = 0L;
            var r = keys.Sum(x => x.a);
            while (r - l != 1)
            {
                var mid = (r + l) / 2;
                if (CanOpen(mid, keys, N))
                {
                    r = mid;
                }
                else
                {
                    l = mid;
                }
            }

            return r;
        }

        private static bool CanOpen(long cost, List<Key> keys, long n)
        {
            var max = Math.Pow(2, keys.Count); // 最大値の指定
            for (var i = 0; i < max; i++)
            {
                var bit = Convert.ToString(i, 2).PadLeft(keys.Count, '0'); // Bitの生成
                var selectedKeys = new List<Key>();
                for (int j = 0; j < keys.Count; j++)
                {
                    if (bit[j] == '1')
                    {
                        selectedKeys.Add(keys[j]);
                    }
                }

                // コストの判定
                if (selectedKeys.Sum(x => x.a) > cost) continue;
                // 開けられるかどうかの判定
                if (!CanOpenAllBox(n, selectedKeys)) continue;

                return true;
            }

            return false;
        }

        private static bool CanOpenAllBox(long N, List<Key> keys)
        {
            var hash = new HashSet<long>();
            for (int i = 0; i < keys.Count; i++)
            {
                var key = keys[i];
                for (int j = 0; j < key.b; j++)
                {
                    hash.Add(key.c[j]);
                }
            }
            //foreach (var box in keys.SelectMany(x => x.c))
            //{
            //    hash.Add(box);
            //}

            return N == hash.Count;
        }

        #region Console

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
    [DebuggerDisplay("{a} {b} {Buyables}")]
    class Key
    {
        public long a { get; set; }
        public long b { get; set; }
        public List<long> c { get; set; }
        public string Buyables { get; set; }
    }
}