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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static ABC119.Util;
using static System.Console;

#if DEBUG
using System.Diagnostics;
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif

namespace ABC119
{
    class Program
    {
        static void Main(string[] args)
        {
#if DEBUG
            while (true)
            {
#endif
                // StillTBD(); // 3m
                // DigitalGifts(); // 12m
                // SyntheticKadomatsu(); // 60m wakaran
                //LazyFaith(); // 4h47m

                SyntheticKadomatsu();
#if DEBUG
            }
#endif
        }

        static void LazyFaith()
        {
            int[] tmp = ReadIntArray();
            int A = tmp[0];
            int B = tmp[1];
            int Q = tmp[2];

            long[] s = new long[A];
            long[] t = new long[B];
            long[] q = new long[Q];

            for (int i = 0; i < A; i++) s[i] = ReadLong();
            for (int i = 0; i < B; i++) t[i] = ReadLong();
            for (int i = 0; i < Q; i++) q[i] = ReadLong();

            Sort(s);
            Sort(t);

            long[] s2 = AddHeadAndTail(s);
            long[] t2 = AddHeadAndTail(t);

            s2[0] = t2[0] = -INF;
            s2[s2.Length-1] = t2[t2.Length-1] = INF;

            long[] ansArray = new long[Q];
            for(int i = 0; i < Q; i++)
            {
                long n = q[i];
                int si = BinarySearch(s2, n);
                int ti = BinarySearch(t2, n);

                long ans = long.MaxValue;

                foreach (var S in new long[] { s2[si - 1], s2[si] })
                {
                    foreach (var T in new long[] { t2[ti - 1], t2[ti] })
                    {
                        long d1 = Math.Abs(S - n) + Math.Abs(T - S);
                        long d2 = Math.Abs(T - n) + Math.Abs(T - S);

                        ans = Math.Min(ans, Math.Min(d1, d2));
                    }
                }

                ansArray[i] = ans;
            }

            DontAutoFlush();
            foreach(var _a in ansArray)
            {
                WriteLine(_a);
            }
            Flush();
        }

        static void SyntheticKadomatsu()
        {
            int[] tmp = ReadIntArray();
            int N = tmp[0];
            int A = tmp[1];
            int B = tmp[2];
            int C = tmp[3];
            int[] take = new int[N];
            for (int i = 0; i < N; i++)
            {
                take[i] = ReadInt();
            }

            Func<int, int, int, int, int> dfs = null;
            dfs = (int cur,int a,int b,int c) => {
                if (cur == N)
                {
                    if (Math.Min(a,Math.Min(b,c)) > 0)
                    {
                        return Math.Abs(a - A) + Math.Abs(b - B) + Math.Abs(c - C) - 30;
                    }
                    else
                    {
                        return INFi;
                    }
                }
                else
                {
                    return new List<int> {
                        dfs(cur + 1, a, b, c),
                        (dfs(cur + 1, a + take[cur], b, c) + 10),
                        (dfs(cur + 1, a, b + take[cur], c) + 10),
                        (dfs(cur + 1, a, b, c + take[cur]) + 10)
                    }.Min();
                }
            };

            WriteLine(dfs(0, 0, 0, 0));
        }

        static void DigitalGifts()
        {
            double BTC = 380000.0D;
            int N = ReadInt();
            double[] X = new double[N];
            string[] U = new string[N];

            for (int i = 0; i < N; i++)
            {
                string[] tmp = ReadString().Split(' ');

                X[i] = double.Parse(tmp[0]);
                U[i] = tmp[1];
            }

            double ans = 0;
            for (int i = 0; i < N; i++)
            {
                if (U[i] == "JPY")
                {
                    ans += X[i];
                }
                else
                {
                    ans += BTC * X[i];
                }
            }

            WriteLine(ans);
        }

        static void StillTBD()
        {
            string input = ReadString();
            int[] nums = input.Split('/').Select(int.Parse).ToArray();

            if (nums[0] <= 2019 && nums[1] <= 4 && nums[2] <= 30)
            {
                WriteLine("Heisei");
            }
            else
            {
                WriteLine("TBD");
            }
        }
    }

#if DEBUG
    [TestClass]
    public class Test
    {
        public static StreamReader StringToStreamReader(string s)
        {
            byte[] byteArray = Encoding.ASCII.GetBytes(s);
            MemoryStream stream = new MemoryStream(byteArray);
            StreamReader reader = new StreamReader(stream);
            return reader;
        }

        [TestMethod]
        public void Test1()
        {
            string input = "Testing 1-2-3";
            System.Console.SetIn(StringToStreamReader(input));
        }
    }

#endif

    #region ToolBox

    /// <summary>
    /// ユーティリティー
    /// </summary>
    public static class Util
    {
        public static readonly int INFi = 200000000;
        public static readonly long INF = 20000000000;

        public static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }

        public static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        public static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        public static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }

        public static string ReadString()
        {
            return Console.ReadLine();
        }

        /// <summary>
        /// "00101001010"という様な入力をintの配列にして返す
        /// </summary>
        /// <returns></returns>
        public static int[] ReadIntArrayFromBinaryString()
        {
            return Console.ReadLine().Select(c => int.Parse(c.ToString())).ToArray();
        }

        /// <summary>
        /// "00101001010"という様な入力をboolの配列にして返す
        /// </summary>
        /// <returns></returns>
        public static bool[] ReadBoolArrayFromBinaryString()
        {
            return Console.ReadLine().Select(c => c == '1').ToArray();
        }

        /// <summary>
        /// ソートをして結果を返します。
        /// 破壊的関数です。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] Sort<T>(T[] array)
        {
            Array.Sort<T>(array);
            return array;
        }

        /// <summary>
        /// 逆順ソートをして結果を返します。
        /// 破壊的関数です。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] ReverseSort<T>(T[] array)
        {
            Array.Sort<T>(array);
            Array.Reverse(array);
            return array;
        }

        /// <summary>
        /// Rubyにあるようなやつ
        /// ex) 5.Times(i => Console.WriteLine(i));
        /// </summary>
        /// <param name="times"></param>
        /// <param name="action"></param>
        public static void Times(this int times, Action<int> action)
        {
            for (int i = 0; i < times; i++)
            {
                action(i);
            }
        }

        /// <summary>
        /// 引数aと引数bの値を入れ替えます
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="a"></param>
        /// <param name="b"></param>
        public static void Swap<T>(ref T a, ref T b)
        {
            T _a = a;
            a = b;
            b = _a;
        }

        /// <summary>
        /// Console.WriteLineの自動フラッシュをしないようにする
        /// </summary>
        public static void DontAutoFlush()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
        }

        public static void Flush()
        {
            Console.Out.Flush();
        }

        /// <summary>
        /// 先頭と末尾に要素を増やした新しい配列を返します。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] AddHeadAndTail<T>(T[] array)
        {
            int len = array.Length;
            T[] res = new T[len + 2];
            Array.Copy(array, 0, res, 1, len);
            return res;
        }

        /// <summary>
        /// 昇順ソート済みの配列を2分探索します。
        /// 要素が見つからなかった場合はnより大きい数値の中で最小の数値のインデックスを返す。
        /// </summary>
        /// <param name="array"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public static int BinarySearch(long[] array, long n)
        {
            int left = 0;
            int right = array.Length;

            while(left <= right)
            {
                int mid = (right - left) / 2 + left;

                if (array[mid] == n)
                {
                    return mid;
                }
                else if (n < array[mid])
                {
                    right = mid - 1;
                }
                else
                {
                    left = mid + 1;
                }
            }

            return left;
        }

#if DEBUG
        static void SampleGenerator()
        {
            int A = 1000;
            int B = 1000;
            int Q = 1000;

            Random r = new Random();
            StringBuilder sb = new StringBuilder();
            sb.AppendLine(string.Format("{0} {1} {2}", A, B, Q));
            A.Times(a => sb.AppendLine(((long)r.Next() * r.Next()).ToString()));
            B.Times(b => sb.AppendLine(((long)r.Next() * r.Next()).ToString()));
            Q.Times(q => sb.AppendLine(((long)r.Next() * r.Next()).ToString()));

            Debug.WriteLine(sb.ToString());
        }
#endif

    }

    /// <summary>
    /// HashSetにTupleを入れた時の、等値性判定方法の指定に使います。
    /// HashSetのコンストラクタに渡して使います。
    /// EqualsとGetHashCodeを提供します。
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class EqualityComparer<T> : IEqualityComparer<T>
    {
        private Func<T, T, bool> _equals;
        private Func<T, int> _getHashCode;

        public EqualityComparer(Func<T, T, bool> equals, Func<T, int> getHashCode)
        {
            _equals = equals;
            _getHashCode = getHashCode;
        }

        public bool Equals(T x, T y)
        {
            return _equals(x, y);
        }

        public int GetHashCode(T obj)
        {
            return _getHashCode(obj);
        }
    }

    /// <summary>
    /// UnionFindTree
    /// </summary>
    public class UnionFindTree
    {
        int[] Node;

        public UnionFindTree(int N)
        {
            Node = new int[N];
            for (int i = 0; i < N; i++)
            {
                Node[i] = -1;
            }
        }

        public bool IsSameGroup(int x, int y)
        {
            return GetRoot(x) == GetRoot(y);
        }

        public bool Merge(int x, int y)
        {
            int xr = GetRoot(x);
            int yr = GetRoot(y);

            if (xr == yr)
                return false;

            // xが、大きなグループを示すようにSwapする（値が小さい方が大きなグループ）
            if (Node[xr] > Node[yr])
                Swap(ref xr, ref yr);

            // グループの数を合算する
            Node[xr] += Node[yr];

            // 根を張り替える
            Node[yr] = xr;
            return true;
        }

        public int Size(int x)
        {
            return -Node[GetRoot(x)];
        }

        public int GetRoot(int n)
        {
            if (Node[n] < 0)
            {
                return n;
            }
            else
            {
                // 根を張りなおす。
                Node[n] = GetRoot(Node[n]);
                return Node[n];
            }
        }
    }

    /// <summary>
    /// PriorityQueue
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class PriorityQueue<T> where T : IComparable
    {
        private Comparison<T> _comparison = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        public PriorityQueue(int maxSize, Comparison<T> comparison)
        {
            _heap = new T[maxSize];
            _comparison = comparison;
        }

        private int Compare(T x, T y)
        {
            if (_comparison != null) return _comparison(x, y);
            return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }
    }

    #endregion
}