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: Accepted)

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

namespace AtCoder
{
    class Program
    {
        static int[] goals;

        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
            goals = new int[] { line[1], line[2], line[3] };

            //最初に与えられた竹
            var materials = ReadLines(n);

            //最初に与えられた竹を A,B,Cの材料,使わない のいずれかに当てはめたパターンを列挙
            var numStrs = GetBase4NumberStrings(n).ToList();

            int minMp = int.MaxValue;

            foreach(var numStr in numStrs)
            {
                //空のListを作成
                var bambooCombis = new List<List<int>>();

                for(int i = 0; i < 3; i++)
                {
                    bambooCombis.Add(new List<int>());
                }

                for(int i = 0; i < n; i++)
                {
                    if (numStr[i] != '3')
                    {
                        int index = GetIndex(numStr[i]);

                        bambooCombis[index].Add(materials[i]);
                    }
                }

                int mp = CalcMp(bambooCombis);

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

            Console.WriteLine(minMp);
        }

        static int CalcMp(List<List<int>> bambooCombis)
        {
            int sum = 0;
            int i = 0;

            foreach(var bamboos in bambooCombis)
            {
                if (bamboos.Count == 0)
                {
                    return int.MaxValue;
                }
                else
                {
                    int length = bamboos.Sum();
                    int mp = (bamboos.Count - 1) * 10;

                    mp += Math.Abs(goals[i] - length);
                    sum += mp;
                }

                i++;
            }

            return sum;
        }

        static int GetIndex(char numChar)
        {
            string s = numChar.ToString();
            return int.Parse(s);
        }

        static IEnumerable<string> GetBase4NumberStrings(int n)
        {
            //[summary]最初に与えられた竹を A,B,Cの材料,使わない のいずれかに当てはめる

            int count = (int)Math.Pow(4, n);

            string s = ConvertBaseNumber(count - 1, 4);
            int digit = s.Length;

            for(int i = 0; i < count; i++)
            {
                s = ConvertBaseNumber(i, 4);
                yield return s.PadLeft(digit, '0');
            }
        }

        static string ConvertBaseNumber(int sourceNum, int n)
        {
            //[summary]10進数の数字をN進数に変換
            //変換方法については、以下リンクの最下部を参照
            //http://manabi.matiralab.com/binary/

            var mods = new List<int>();
            int num = sourceNum;

            //元の数字が"n"で割れなくなるまで繰り返し
            while (num != 0 && num != 1)
            {
                mods.Add(num % n);
                num /= n;
            }

            //最後の商も入れる
            mods.Add(num);

            //記憶した数字の順番を入れ替える
            mods.Reverse();

            //連結した文字列の最初がゼロになることもあるので、削除
            mods = mods.SkipWhile(x => x == 0).ToList();

            //Listの値を結合
            return string.Join("", mods);
        }

        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;
        }
    }
}