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: Accepted)

using System;
using System.Collections.Generic;
using static Assistant.Input;
using System.Linq;
using Assistant;

namespace Temp20200521
{
    class Program
    {
        static void Main(string[] args)
        {
            N = ReadInt;
            M = ReadInt;

            a = new int[M];
            b = new int[M];
            c = new int[M][];
            for (int i = 0; i < M; i++)
            {
                a[i] = ReadInt;
                b[i] = ReadInt;
                c[i] = ReadInts.Select(x => x - 1).ToArray();
            }

            //bitDP
            dp = new int[1 << N];//頂点、鍵
            for (int i = 0; i < 1 << N; i++)
            {
                    dp[i] = int.MaxValue / 2;
            }
            dp[(1 << N) - 1] = 0;

            for (int i = (1 << N) - 1; i >= 0; i--)
            {
                for (int j = 0; j < M - 1; j++)
                {
                    int next = i;
                    for (int k = 0; k < c[j].Length; k++)
                    {
                        next = next | (1 << c[j][k]);
                    }

                    dp[i] = Math.Min(dp[i], dp[next] + a[j]);
                }
            }

            int ans = dp[0];
            //int ans = DP(0, 0);
            if (ans == int.MaxValue / 2) ans = -1;
            Console.WriteLine(ans);

            //DrawMapforDebug(dp, 1);
        }

        static int N, M;
        static int[] a, b;
        static int[][] c;
        static int[] dp;
        //再帰バージョンを書いてみる
        //static int DP(int S, int v)
        //{
        //    if (S == (1 << N) - 1)
        //    {
        //        return 0;
        //    }
        //    if (dp[S, v] != int.MaxValue / 2) return dp[S, v];

        //    int next = S;
        //    for (int k = 0; k < c[v].Length; k++)
        //    {
        //        next = next | (1 << c[v][k]);
        //    }

        //    dp[S, v] = Math.Min(dp[S, v], DP(next, v - 1) + a[v]);

        //    return dp[S, v];
        //}

        /// <summary>
        /// 二次元配列の可視化メソッド
        /// </summary>
        /// <param name="map"></param>
        static void DrawMapforDebug(int[,] map, int mode = 0)
        {
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            int[,] map2 = new int[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0;
                    else if (i == 0) map2[i, j] = j - 1;
                    else if (j == 0) map2[i, j] = i - 1;
                    else map2[i, j] = map[i - 1, j - 1];
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j] % 10);
                    else Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
        }
    }


}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String ReadNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int ReadInt => int.Parse(ReadNext());
        public static long ReadLong => long.Parse(ReadNext());
        public static int[] ReadInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] NextLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
    }
}