Problem:
Score: 400 points

Problem Statement

Quickly after finishing the tutorial of the online game ATChat, you have decided to visit a particular place with N-1 players who happen to be there. These N players, including you, are numbered 1 through N, and the friendliness of Player i is A_i.

The N players will arrive at the place one by one in some order. To make sure nobody gets lost, you have set the following rule: players who have already arrived there should form a circle, and a player who has just arrived there should cut into the circle somewhere.

When each player, except the first one to arrive, arrives at the place, the player gets comfort equal to the smaller of the friendliness of the clockwise adjacent player and that of the counter-clockwise adjacent player. The first player to arrive there gets the comfort of 0.

What is the maximum total comfort the N players can get by optimally choosing the order of arrivals and the positions in the circle to cut into?

Constraints

All values in input are integers.

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

Print the maximum total comfort the N players can get.

Sample Input 1

4
2 2 1 3

Sample Output 1

7

By arriving at the place in the order Player 4, 2, 1, 3, and cutting into the circle as shown in the figure, they can get the total comfort of 7.

They cannot get the total comfort greater than 7, so the answer is 7.

Sample Input 2

7
1 1 1 1 1 1 1

Sample Output 2

6

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.Tracing;
using System.Linq;
using System.Net.NetworkInformation;
using System.Runtime.CompilerServices;
using System.Security.Cryptography;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading;
using Extensions;
using DSA;
using static System.Math;
using static Extensions.MathExtension;
using static Extensions.ConsoleInputExtension;
using static Extensions.ConsoleOutputExtension;

class Solver
{
    public void Solve()
    {
        //Solve Code Here
        int n = Cin;
        var a = new long[n];
        for (int i = 0; i < n; i++) a[i] = Cin;
        a = a.OrderByDescending(val => val).ToArray();
        if (n == 1)
        {
            Coutln(0);
            return;
        }

        if (n == 2)
        {
            Coutln(a[0]);
            return;
        }

        if (n == 3)
        {
            Coutln(a[0] + a[1]);
            return;
        }

        long sum = a[0] + a[1];
        for (int i = 3; i < n; i++) sum += a[i - 2];
        Coutln(sum);
    }
}

//Other Classes Here

#if !DEBUG
class EntryPoint
{
    static void Main(string[] args)
    {
        new Solver().Solve();
        Flush();
    }
}
#endif

namespace DSA
{
    public class PriorityQueue<T>
    {
        private readonly List<Tuple<int, T>> _list = new List<Tuple<int, T>>();

        public int Count => _list.Count;

        public PriorityQueue()
        {
        }

        public void Push(T item, int priority)
        {
            _list.Add(Tuple.Create(priority, item));

            int itemIndex = Count - 1, parentIndex;
            while ((parentIndex = GetParentIndex(itemIndex)) != -1 &&
                   priority > _list[parentIndex].Item1)
            {
                Swap(itemIndex, parentIndex);
                itemIndex = parentIndex;
            }
        }

        private int GetParentIndex(int index)
        {
            if (index == 0) return -1;
            return ((index + 1) >> 1) - 1;
        }

        private Tuple<int, int> GetChildrenIndex(int index)
        {
            var item2 = (index + 1) << 1;
            var item1 = item2 - 1;
            return Tuple.Create(item1, item2);
        }

        public T Pop()
        {
            if (Count <= 0) throw new IndexOutOfRangeException();
            var item = _list[0].Item2;
            _list[0] = _list[Count - 1];
            _list.RemoveAt(Count - 1);

            int index = 0;
            Tuple<int, int> childrenIndex = GetChildrenIndex(index);
            while (childrenIndex.Item1 < Count || childrenIndex.Item2 < Count)
            {
                if (childrenIndex.Item2 >= Count || _list[childrenIndex.Item1].Item1 > _list[childrenIndex.Item2].Item1)
                {
                    if (_list[childrenIndex.Item1].Item1 <= _list[index].Item1) return item;

                    Swap(index, childrenIndex.Item1);
                    index = childrenIndex.Item1;
                }
                else
                {
                    if (_list[childrenIndex.Item2].Item1 <= _list[index].Item1) return item;
                    Swap(index, childrenIndex.Item2);
                    index = childrenIndex.Item2;
                }

                childrenIndex = GetChildrenIndex(index);
            }

            return item;
        }

        public T Peek()
        {
            return _list[0].Item2;
        }

        private void Swap(int index1, int index2)
        {
            var tmp = _list[index1];
            _list[index1] = _list[index2];
            _list[index2] = tmp;
        }
    }

    public class UnionFind
    {
        private readonly int[] _array;

        public UnionFind(int size)
        {
            _array = new int[size];
            for (int i = 0; i < size; i++)
            {
                _array[i] = i;
            }
        }

        public int GetRootNode(int n)
        {
            if (_array[n] == n) return n;
            return _array[n] = GetRootNode(_array[n]);
        }

        public void UnionGroup(int a, int b)
        {
            var rootA = GetRootNode(a);
            var rootB = GetRootNode(b);
            if (rootA == rootB) return;
            _array[rootA] = rootB;
        }

        public bool IsSameGroup(int a, int b) => GetRootNode(a) == GetRootNode(b);

        public bool IsRoot(int n) => _array[n] == n;
    }

    public delegate T SegTreeCombiner<T>(T item1, T item2);

    public class SegTree<T>
    {
        private readonly T _defaultItem;
        private readonly SegTreeCombiner<T> _func;
        private T[] List;
        private int size;

        public SegTree(T[] list, T defaultItem, SegTreeCombiner<T> func)
        {
            _defaultItem = defaultItem;
            _func = func;
            size = 1;
            while (size < list.Length) size <<= 1;
            List = new T[2 * size - 1];
            for (int i = 0; i < list.Length; i++) List[i + size - 1] = list[i];
            for (int i = list.Length; i < size; i++) List[i + size - 1] = defaultItem;
            for (int i = size - 1 - 1; i >= 0; i--)
            {
                List[i] = _func(List[2 * i + 1], List[2 * i + 2]);
            }
        }

        public void Update(int index, T value)
        {
            index += size - 1;
            List[index] = value;
            while (index > 0)
            {
                index = (index - 1) >> 1;
                List[index] = _func(List[2 * index + 1], List[2 * index + 2]);
            }
        }

        public T Query(int a, int b)
        {
            return Query(a, b, 0, 0, size);
        }

        private T Query(int a, int b, int k, int l, int r)
        {
            if (r <= a || b <= l) return _defaultItem;
            if (a <= l && r <= b) return List[k];
            return _func(Query(a, b, k * 2 + 1, l, (l + r) >> 1), Query(a, b, k * 2 + 2, (l + r) >> 1, r));
        }
    }

    public static class BinarySearch
    {
        public delegate bool Terms<T>(T i);

        public static int UpperBound(int initLeft, int initRight, Terms<int> term)
        {
            int left = initLeft - 1, right = initRight;
            while (right - left > 1)
            {
                int mid = (left + right) >> 1;
                if (mid != initLeft - 1 && term(mid)) left = mid;
                else right = mid;
            }

            return left;
        }

        public static long UpperBound(long initLeft, long initRight, Terms<long> term)
        {
            long left = initLeft - 1, right = initRight;
            while (right - left > 1)
            {
                long mid = (left + right) >> 1;
                if (mid != initLeft - 1 && term(mid)) left = mid;
                else right = mid;
            }

            return left;
        }

        public static int LowerBound(int initLeft, int initRight, Terms<int> term)
        {
            int left = initLeft - 1, right = initRight;
            while (right - left > 1)
            {
                int mid = (left + right) >> 1;
                if (mid != initRight && term(mid)) right = mid;
                else left = mid;
            }

            return right;
        }

        public static long LowerBound(long initLeft, long initRight, Terms<long> term)
        {
            long left = initLeft - 1, right = initRight;
            while (right - left > 1)
            {
                long mid = (left + right) >> 1;
                if (term(mid)) right = mid;
                else left = mid;
            }

            return right;
        }
    }
}


struct ModInt
{
    public long Value { get; }
    public static long Mod { get; set; } = 1000000000L + 7;

    public ModInt(long l)
    {
        long value = l % Mod;
        while (value < 0) value += Mod;
        Value = value % Mod;
    }

    public static implicit operator long(ModInt m)
    {
        return m.Value;
    }

    public static implicit operator ModInt(long l)
    {
        return new ModInt(l);
    }

    public static ModInt operator +(ModInt a, ModInt b)
    {
        return new ModInt(a.Value + b.Value);
    }

    public static ModInt operator -(ModInt a, ModInt b)
    {
        return new ModInt(a.Value - b.Value);
    }

    public static ModInt operator *(ModInt a, ModInt b)
    {
        return new ModInt(a.Value * b.Value);
    }

    public static ModInt operator /(ModInt a, ModInt b)
    {
        return new ModInt(a * b.Inverse());
    }

    public override string ToString()
    {
        return Value.ToString();
    }
}

static class ModIntMath
{
    public static ModInt Pow(this ModInt a, ModInt b)
    {
        var pow = b.Value;
        var m = a;
        ModInt ans = new ModInt(1);
        while (pow != 0)
        {
            if ((pow & 1) == 1)
            {
                ans *= m;
            }

            pow >>= 1;
            m *= m;
        }

        return ans;
    }

    public static ModInt Inverse(this ModInt m)
    {
        return m.Pow((ModInt) (ModInt.Mod - 2));
    }
}


namespace Extensions
{
    public class ConsoleInputExtension
    {
        private static readonly ConsoleInputExtension _cin = new ConsoleInputExtension();

        public static ConsoleInputExtension Cin => _cin;

        private static readonly Queue<string> _inputQueue = new Queue<string>();

        private ConsoleInputExtension()
        {
        }

        public static implicit operator string(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return _inputQueue.Dequeue();
        }

        public static implicit operator int(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return int.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator long(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return long.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator float(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return float.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator double(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0)
                Console.ReadLine().Split(' ')
                    .ForEach(val => _inputQueue.Enqueue(val));
            return double.Parse(_inputQueue.Dequeue());
        }
    }

    public static class ConsoleOutputExtension
    {
        private static StringBuilder _builder = new StringBuilder();

        public static void Cout(object o)
        {
            _builder.Append(o);
        }


        public static void CoutF(object o)
        {
            _builder.Append(o);
            Flush();
        }

        public static void Coutln(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
        }

        public static void Coutln()
        {
            _builder.Append('\n');
        }

        public static void CoutlnF(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
            Flush();
        }

        public static void Flush()
        {
            Console.Write(_builder.ToString());
            _builder.Clear();
        }
    }

    public static class MathExtension
    {
        //最小公倍数
        public static int LCM(int num1, int num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        public static long LCM(long num1, long num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        //最大公約数
        public static int GCD(int num1, int num2)
        {
            int a = Math.Max(num1, num2);
            int b = Math.Min(num1, num2);
            if (b == 0) return a;
            int mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }

        public static long GCD(long num1, long num2)
        {
            long a = Math.Max(num1, num2);
            long b = Math.Min(num1, num2);
            if (b == 0) return a;
            long mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }
    }

    public static class EnumerableExtension
    {
        public delegate void Function<in T>(T val);

        public static void ForEach<T>(this IEnumerable<T> enumerable, Function<T> function)
        {
            foreach (var x in enumerable)
            {
                function(x);
            }
        }
    }
}