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 System.Linq;
using static AtCoderProject.Utility;
using BigInteger = System.Numerics.BigInteger;
using BitArray = System.Collections.BitArray;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using TextReader = System.IO.TextReader;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            N = consoleReader.Int;
            var M = consoleReader.Int;
            var keys = consoleReader.Repeat(M).Select(cr => new Key { price = cr.Int, boxes = ToInt(cr.Split.Int0) }).ToArray();

            gyakuhikiPrice = Enumerable.Repeat(int.MaxValue, 1 << N).ToArray();
            gyakuhikiPrice[0] = 0;
            foreach (var key in keys)
            {
                SetPrice(key.price, key.boxes);
            }

            var last = gyakuhikiPrice[gyakuhikiPrice.Length - 1];

            return last == int.MaxValue ? -1 : last;
        }
        int N;
        int[] gyakuhikiPrice;
        void SetPrice(int price, int gyaku)
        {
            if (gyaku == 0) return;
            for (int i = 0; i < gyakuhikiPrice.Length; i++)
            {
                if ((gyaku & i) == gyaku || gyakuhikiPrice[i] == int.MaxValue) continue;
                var next = gyaku | i;
                var nextPrice = price + gyakuhikiPrice[i];
                if (gyakuhikiPrice[next] > nextPrice)
                    gyakuhikiPrice[next] = nextPrice;
            }
        }

        struct Key
        {
            public int price;
            public int boxes;
        }

        static int ToInt(IEnumerable<int> boxes)
        {
            var res = 0;
            foreach (var b in boxes)
                res += 1 << b;
            return res;
        }

        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }

    public class ConsoleReader
    {
        private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries);
        private string[] line = Array.Empty<string>();
        private int linePosition;
        private TextReader textReader;
        public ConsoleReader(TextReader tr) { textReader = tr; }
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string String
        {
            get
            {
                if (linePosition >= line.Length)
                {
                    linePosition = 0;
                    line = ReadLineSplit();
                }
                return line[linePosition++];
            }
        }
        public class SplitLine
        {
            public SplitLine(ConsoleReader cr) { String = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); }
            public int[] Int => String.Select(x => int.Parse(x)).ToArray();
            public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray();
            public long[] Long => String.Select(x => long.Parse(x)).ToArray();
            public double[] Double => String.Select(x => double.Parse(x)).ToArray();
            public string[] String { get; }
        }
        public SplitLine Split => new SplitLine(this);
        public class RepeatReader : IEnumerable<ConsoleReader>
        {
            ConsoleReader cr; int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator();
            System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator();

            public IEnumerable<string> String => this.Select(cr => cr.String);
            public IEnumerable<int> Int => this.Select(cr => cr.Int);
            public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1);
            public IEnumerable<long> Long => this.Select(cr => cr.Long);
            public IEnumerable<double> Double => this.Select(cr => cr.Double);
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);
    }
    public static class Utility
    {
        public static IComparer<T> ReverseComparer<T>() where T : IComparable<T>
            => Comparer<T>.Create((x, y) => y.CompareTo(x));
    }
    #endregion

}