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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {
    long MOD = 1000000007;
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();
        Integer[] l = new Integer[n];
        for (int i=0;i<n;i++)l[i]=sc.nextInt();
        final int[] ans = {Integer.MAX_VALUE};
        BitSearch<Integer,Integer> bs = new BitSearch<>(l,4){
            @Override
            void run(StringBuilder s){
                int sumA=0;
                int sumB=0;
                int sumC=0;
                int MP=0;
                for (int i=0;i<Length;i++){
                    int j = s.charAt(i)-'0';
                    MP++;
                    if (j==0){
                        sumA+=Array[i];
                    } else if (j==1){
                        sumB+=Array[i];
                    } else if (j==2){
                        sumC+=Array[i];
                    }
                    if (j==3)MP--;
                }
                if (sumA!=0&&sumB!=0&&sumC!=0){
                    MP-=3;
                    MP*=10;
                    MP+=Math.abs(a-sumA)+Math.abs(b-sumB)+Math.abs(c-sumC);
                    ans[0] = Math.min(MP, ans[0]);
                }
            }
        };
        bs.start();
        System.out.println(ans[0]);
    }

    public static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            }else{
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }else if(b == -1 || !isPrintableChar(b)){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
    }
    public static class BasicMath {
        private final int MAX = 510000;
        private final int MOD = 1000000007;
        private final long[] fac = new long[MAX];
        private final long[] finv= new long[MAX];
        private final long[] inv = new long[MAX];
        public long factorial(long num){
            if (num<2)return 1;
            else return num*factorial(num-1);
        }
        public int arraySum(int[] array){
            int ans = 0;
            for (int value : array) ans += value;
            return ans;
        }
        public double log(double base,double antilogarithm){
            return Math.log(antilogarithm)/Math.log(base);
        }
        public int gcd(int x,int y){
            if (y==0)return x;
            else return gcd(y,x%y);
        }
        public int lcm(int x,int y){
            return x/gcd(x,y)*y;
        }
        public HashMap<Long,Long> factorization(long num){
            HashMap<Long,Long> hash = new HashMap<>();
            long n = num;
            long count = 2;
            while (n>1){
                while (n%count==0){
                    n/=count;
                    if (hash.containsKey(count))hash.put(count,hash.get(count)+1);
                    else hash.put(count,1L);
                }
                count++;
            }
            return hash;
        }
        public int sum(int[] num){
            int ans = 0;
            for (int i = 0; i < num.length;i++){
                ans += num[i];
            }
            return ans;
        }
        public int[] reduce(int small, int big){
            int ins = 2;
            while (ins<=small){
                if (small%ins==0&&big%ins==0){
                    small/=ins;
                    big/=ins;
                    ins = 2;
                }else {
                    ins++;
                }
            }
            return new int[]{small, big};
        }
        public int reduceCount(int small, int big){
            int ins = 2;
            int ans = 0;
            while (ins<=small){
                if (small%ins==0&&big%ins==0){
                    small/=ins;
                    big/=ins;
                    ins = 2;
                    ans++;
                }else {
                    ins++;
                }
            }
            return ans;
        }
        public int binarySearch(int[] array, int target){
            int pos = -1;
            int left = 0;
            int right = array.length-1;
            int middle;
            while (pos==-1&&left<=right){
                middle = (left+right)/2;
                if (array[middle]==target)pos=middle;
                else if (array[middle]>target)right=middle-1;
                else left=middle+1;
            }
            return pos;
        }
        public long modPow(long a, long n, long mod){
            long res = 1;
            while (n>0){
                if ((n&1)!=0)res = res*a%mod;
                a=a*a%mod;
                n >>= 1;
            }
            return res;
        }
        public long modinv(long a, long mod){return modPow(a,mod-2,mod);}
        public void COMinit(){
            fac[0]=1;
            fac[1]=1;
            finv[0]=1;
            finv[1]=1;
            inv[1]=1;
            for (int i=2;i<MAX;i++){
                fac[i]=fac[i-1]*i%MOD;
                inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
                finv[i]=finv[i-1]*inv[i]%MOD;
            }
        }
        public long COM(int n, int k){
            if (n<k)return 0;
            if (n<0||k<0)return 0;
            return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
        }
        public long HCOM(int n, int k){
            return COM(n+k-1,k);
        }
    }
    public static class Queue<T>{
        private final int max = 1000000;
        private final T[] queue = (T[]) new Object[max];
        private int tail = 0; private int head = 0;
        public void init(){this.head = 0; tail = 0;}
        public boolean isEmpty(){return (head==tail);}
        public boolean isFull(){return (head == (tail+1)%max);}
        public void enqueue(T v){
            if (isFull()){
                System.out.println("error: queue is full.");
                return;
            }
            queue[tail++] = v;
            if (tail == max) tail = 0;
        }
        public T dequeue(){
            if (isEmpty()){
                System.out.println("error: queue is empty");
                return null;
            }
            T res = queue[head];
            ++head;
            if (head == max) head = 0;
            return res;
        }
    }
    public static class Stack<T>{
        private final int max = 100000;
        private final T[] stack =(T[]) new Object[max];
        private int top = 0;
        public boolean isEmpty(){return (top==0);}
        public boolean isFull(){return (top==max);}
        public void init(){top=0;}
        public void push(T v){
            if (isFull()){
                System.out.println("error: stack is full.");
                return;
            }
            stack[top++] = v;
        }
        public T pop(){
            if (isEmpty()){
                System.out.println("error: stack is empty");
                return null;
            }
            return stack[--top];
        }
    }
    public static class Pair<T>{
        private T A;
        private T B;
        Pair(T a,T b){
            A=a;
            B=b;
        }
        public void changeA(T a){A=a;}
        public void changeB(T b){B=b;}
        public void changeAB(T a,T b){A=a;B=b;}
        public static Comparator numberSortWithA = new Comparator() {
            @Override
            public int compare(Object o1, Object o2) {
                Pair p = (Pair)o1;
                Pair q = (Pair)o2;
                if ((int)p.A<(int)q.A)return -1;
                else if ((int)p.A==(int)q.A)return 0;
                else return 1;
            }
        };
        public static Comparator numberSortWithB = new Comparator() {
            @Override
            public int compare(Object o1, Object o2) {
                Pair p = (Pair)o1;
                Pair q = (Pair)o2;
                if ((int)p.B<(int)q.B)return -1;
                else if ((int)p.B==(int)q.B)return 0;
                else return 1;
            }
        };
    }
    public static class Graph{
        private final HashMap<Integer,HashSet<Integer>> graph = new HashMap<>();
        private final int Size;
        private int[] Depth;
        Graph(int size){
            for (int i=0;i<size;i++)graph.put(i,new HashSet<>());
            Size = size;
        }

        public void addEdge(int node1,int node2){
            if (graph.containsKey(node1)&&graph.containsKey(node2)){
                graph.get(node1).add(node2);
                graph.get(node2).add(node1);
            }
        }
        public void addDirectEdge(int from,int to){
            if (graph.containsKey(from)&&graph.containsKey(to)){
                graph.get(from).add(to);
            }
        }
        public int[] Depth(int root){
            Queue<Integer> q = new Queue<>();
            q.enqueue(root);
            boolean[] seen = new boolean[Size];
            Arrays.fill(seen, false);
            seen[root]=true;
            int[] depth = new int[Size];
            depth[root]=0;
            while (!q.isEmpty()){
                int v = q.dequeue();
                for (int u : graph.get(v)){
                    if (!seen[u]){
                        seen[u]=true;
                        q.enqueue(u);
                        depth[u]=depth[v]+1;
                    }
                }
            }
            Depth = depth.clone();
            return depth;
        }
    }
    public static class UnionFindTree{
        int[] parent;
        int[] rank;
        int[] Size;
        public UnionFindTree(int size){
            this.parent = new int[size];
            this.rank = new int[size];
            this.Size = new int[size];
            for (int i=0;i<size;i++){
                makeSet(i);
            }
        }
        public void makeSet(int i){
            parent[i]=i;
            rank[i]=0;
            Size[i]=1;
        }
        public void union(int x, int y){
            int xRoot = find(x);
            int yRoot = find(y);
            if (rank[xRoot]>rank[yRoot]){
                parent[yRoot] = xRoot;
                Size[xRoot]+=Size[yRoot];
            }else if (rank[xRoot]<rank[yRoot]){
                parent[xRoot] = yRoot;
                Size[yRoot]+=Size[xRoot];
            }else if (xRoot!=yRoot){
                parent[yRoot] = xRoot;
                rank[xRoot]++;
                Size[xRoot]+=Size[yRoot];
            }
        }
        public int find(int i){
            if (i!= parent[i]){
                parent[i]=find(parent[i]);
            }
            return parent[i];
        }
        public boolean same(int x, int y){
            return find(x) == find(y);
        }
        public int getSize(int i){return Size[find(i)];}
    }
    public static class BitSearch<K,V>{
        K[] Array;
        int Width;
        int Length;
        BitSearch(K[] t, int width){
            Array = t;
            Width = width;
            Length = Array.length;
        }
        void start(){
            long max = (long)Math.pow(Width,Length);
            for (long i=0;i<max;i++){
                StringBuilder s = new StringBuilder(Long.toString(i, Width));
                while (s.length()<Length) s.insert(0, "0");
                run(s);
            }
        }
        void run(StringBuilder s){

        }
    }
}