Problem:
Score : 300 points

Problem Statement

You have N bamboos. The lengths (in centimeters) of these are l_1, l_2, ..., l_N, respectively.

Your objective is to use some of these bamboos (possibly all) to obtain three bamboos of length A, B, C. For that, you can use the following three kinds of magics any number:

Extension Magic: Consumes 1 MP (magic point). Choose one bamboo and increase its length by 1.

Shortening Magic: Consumes 1 MP. Choose one bamboo of length at least 2 and decrease its length by 1.

Composition Magic: Consumes 10 MP. Choose two bamboos and combine them into one bamboo. The length of this new bamboo is equal to the sum of the lengths of the two bamboos combined. (Afterwards, further magics can be used on this bamboo.)

At least how much MP is needed to achieve the objective?

Constraints

3 \leq N \leq 8

1 \leq C < B < A \leq 1000

1 \leq l_i \leq 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B C
l_1
l_2
:
l_N

Output

Print the minimum amount of MP needed to achieve the objective.

Sample Input 1

5 100 90 80
98
40
30
21
80

Sample Output 1

23

We are obtaining three bamboos of lengths 100, 90, 80 from five bamboos 98, 40, 30, 21, 80. We already have a bamboo of length 80, and we can obtain bamboos of lengths 100, 90 by using the magics as follows at the total cost of 23 MP, which is optimal.

Use Extension Magic twice on the bamboo of length 98 to obtain a bamboo of length 100. (MP consumed: 2)

Use Composition Magic on the bamboos of lengths 40, 30 to obtain a bamboo of length 70. (MP consumed: 10)

Use Shortening Magic once on the bamboo of length 21 to obtain a bamboo of length 20. (MP consumed: 1)

Use Composition Magic on the bamboo of length 70 obtained in step 2 and the bamboo of length 20 obtained in step 3 to obtain a bamboo of length 90. (MP consumed: 10)

Sample Input 2

8 100 90 80
100
100
90
90
90
80
80
80

Sample Output 2

0

If we already have all bamboos of the desired lengths, the amount of MP needed is 0. As seen here, we do not necessarily need to use all the bamboos.

Sample Input 3

8 1000 800 100
300
333
400
444
500
555
600
666

Sample Output 3

243

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            //[summary]C - Synthetic Kadomatsu
            var line = ReadLine();
            int n = line[0];

            //作りたい竹の長さを取得
            var goals = new int[] { line[1], line[2], line[3] };

            //最初に与えられた竹
            var firstBamboos = GetFirstBamboos(n);

            //竹のすべての接続パターンを網羅
            var bambooCombis = GetBambooCombis(n, firstBamboos).ToList();
            
            //MPの最小値
            int minMp = int.MaxValue;

            foreach (var bamboos in bambooCombis)
            {
                //いろんな竹から任意の3本を選ぶ
                var threes = AllCombinations(bamboos, 3).ToList();

                foreach (var three in threes)
                {
                    //3本の竹のすべての順列を取得
                    var perms = AllCombinations(three, 3, true).ToList();

                    foreach (var perm in perms)
                    {
                        int mp = CalcMp(goals, perm);

                        if (mp < minMp)
                        {
                            minMp = mp;
                        }
                    }
                }
            }

            Console.WriteLine(minMp);
        }

        static int CalcMp(int[] goals, List<Bamboo> bamboos)
        {
            int mp = 0;

            for(int i = 0; i < 3; i++)
            {
                int diff = bamboos[i].Length - goals[i];
                mp += Math.Abs(diff) + bamboos[i].Mp;
            }

            return mp;
        }

        static List<Bamboo> GetFirstBamboos(int n)
        {
            //最初に与えられた竹の長さ
            var lengths = ReadLines(n);

            var bamboos = new List<Bamboo>();

            foreach(var length in lengths)
            {
                var bamboo = new Bamboo(length, 0);
                bamboos.Add(bamboo);
            }

            return bamboos;
        }

        static List<List<Bamboo>> GetBambooCombis(int n, List<Bamboo> firstBamboos)
        {
            var combis = new List<List<Bamboo>>();
            combis.Add(firstBamboos);

            for (int i = 0; i < n - 3; i++)
            {
                var indexes = GetIndexes(n - i);

                //材料とする竹を選択
                var materials = combis.Where(x => x.Count == n - i).ToList();
                
                //接続魔法でくっつける竹(インデックス)の組み合わせを選択
                //(接続するのは常に2本)
                var joints = AllCombinations<int>(indexes, 2).ToList();

                foreach (var material in materials)
                {
                    foreach (var joint in joints)
                    {
                        var bamboos = new List<Bamboo>();
                        int length = 0;
                        int mp = 0;

                        foreach (var index in indexes)
                        {
                            if (joint.Contains(index))
                            {
                                length += material[index].Length;
                                mp += material[index].Mp;
                            }
                            else
                            {
                                bamboos.Add(material[index]);
                            }
                        }

                        //接続魔法を使ったので、MPに10加算
                        bamboos.Add(new Bamboo(length, mp + 10));
                        combis.Add(bamboos);
                    }
                }
            }

            return combis;
        }

        static List<int> GetIndexes(int n)
        {
            var indexes = new List<int>();

            for (int i = 0; i < n; i++)
            {
                indexes.Add(i);
            }

            return indexes;
        }

        public static IEnumerable<List<T>> AllCombinations<T>(List<T> source, int n,
                                                       bool isAllowDupication = false)
        {
            //[summary]異なる要素から、n個を選ぶ組み合わせを列挙する
            //"isAllowDupication"を"true"にすると、重複を許可する
            //(重複を許可して、nを要素数と同じにすると、順列を列挙する)

            if (n == 1)
            {
                foreach (var s in source)
                {
                    yield return new List<T> { s };
                }

                yield break;
            }
            else
            {
                for (int i = 0; i < source.Count; i++)
                {
                    List<T> clone;

                    if (isAllowDupication)
                    {
                        //重複を許可する場合は、その要素のみを削除
                        clone = new List<T>(source);
                        clone.RemoveAt(i);
                    }
                    else
                    {
                        //重複を許可しない場合は、自分よりも前の要素はすべて削除
                        clone = new List<T>(source.Skip(i + 1));
                    }

                    //再帰処理
                    var items = AllCombinations(clone, n - 1, isAllowDupication);

                    foreach (var item in items)
                    {
                        item.Insert(0, source[i]);
                        yield return item;
                    }
                }
            }
        }

        static List<int> ReadLine()
        {
            var line = Console.ReadLine().TrimEnd();
            var array = line.Split(' ');
            var numbers = new List<int>();

            foreach (var s in array)
            {
                int num = int.Parse(s);
                numbers.Add(num);
            }

            return numbers;
        }

        static List<int> ReadLines(int count = 0)
        {
            //[summary]コンソールの値を読み込む
            var list = new List<int>();

            //読み込む行数が未指定のときは、1行目の値を"count"とみなす
            if (count == 0)
            {
                string s = Console.ReadLine().TrimEnd();
                count = int.Parse(s);
            }

            for (int i = 0; i < count; i++)
            {
                string s = Console.ReadLine().TrimEnd();
                list.Add(int.Parse(s));
            }

            return list;
        }
    }

    class Bamboo
    {
        public int Length { set; get; }
        public int Mp { set; get; }

        public Bamboo(int length, int mp)
        {
            Length = length;
            Mp = mp;
        }
    }
}