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.CodeAnalysis;
using System.IO;
using System.Linq;
using System.Numerics;

namespace CompetitionPrograming2
{
    public sealed class Program : BaseProgram
    {
        public static void Main(string[] _) { using (new SetConsole()) { Solve(); } }
        public static void Solve()
        {
            var n = GetNumber<int>();
            var array = GetArray<long>();
            var q = new PriorityQueue<long>(Priority.Larger);
            var score = 0L;
            var f = array.OrderByDescending(x => x).ToArray();
            q.Enqueue(f[0]);
            var index = 1;
            foreach (var item in f.Skip(1))
            {
                score += q.Dequeue();
                index++;
                if (index % 2 == 0)
                {
                    q.Enqueue(item);
                    q.Enqueue(item);
                }
                else
                {
                    q.Enqueue(item);
                }
            }
            
            Write(score);
        }

        public class PriorityQueue<T> : IEnumerable<T>, IReadOnlyCollection<T> where T : IComparable<T>
        {
            private readonly Priority priority;
            private List<T> heap = new List<T> { default };

            private PriorityQueue() { }
            public PriorityQueue(Priority p)
            {
                priority = p;
            }
            public int Count => heap.Count - 1;
            public T Peek()
            {
                if (Count <= 0) { throw new Exception("要素が空です"); }
                return heap[1];
            }
            public T Dequeue()
            {
                if (Count <= 0) { throw new Exception("要素が空です"); }

                var max = heap[1];
                heap[1] = heap[^1];
                heap.RemoveAt(heap.Count - 1);
                MaxHeapify(1);
                return max;
            }
            public void Enqueue(T key)
            {
                HeapIncreaseKey(key);
            }
            public void EnqueueRange(IEnumerable<T> keys)
            {
                foreach (var key in keys) { HeapIncreaseKey(key); }
            }
            public void Clear()
            {
                heap = new List<T>() { default };
            }
            private void MaxHeapify(int i)
            {
                int largest;
                int l = Left(i);
                int r = Right(i);

                if (l <= heap.Count - 1 && Compare(heap[i], heap[l]) < 0)
                {
                    largest = l;
                }
                else
                {
                    largest = i;
                }

                if (r <= heap.Count - 1 && Compare(heap[r], heap[largest]) > 0)
                {
                    largest = r;
                }

                if (largest == i) { return; }

                var temp = heap[i];
                heap[i] = heap[largest];
                heap[largest] = temp;
                MaxHeapify(largest);
            }
            private void HeapIncreaseKey(T key)
            {
                heap.Add(key);
                int lastIndex = heap.Count - 1;
                while (lastIndex > 1 && Compare(heap[Parent(lastIndex)], heap[lastIndex]) < 0)
                {
                    var temp = heap[lastIndex];
                    heap[lastIndex] = heap[Parent(lastIndex)];
                    heap[Parent(lastIndex)] = temp;
                    lastIndex = Parent(lastIndex);
                }
            }
            private static int Parent(int i) => i / 2;
            private static int Left(int i) => i * 2;
            private static int Right(int i) => i * 2 + 1;
            private int Compare(T x, T y)
            {
                var isLarger = priority == Priority.Larger;
                if (typeof(string) == typeof(T))
                {
                    return isLarger ? StringComparer.Ordinal.Compare(x, y) : StringComparer.Ordinal.Compare(y, x);
                }

                return isLarger ? x.CompareTo(y) : y.CompareTo(x);
            }
            IEnumerator<T> IEnumerable<T>.GetEnumerator() => heap.Skip(1).GetEnumerator();
            public System.Collections.IEnumerator GetEnumerator()
            {
                return heap.Skip(0).GetEnumerator();
            }
        }
    }


    public abstract class BaseProgram
    {
        protected readonly static long divisor = 1000000007;
        protected static Action<object> Write => Console.WriteLine;
        protected static string GetString()
        {
            var str = Console.ReadLine();
            if (str is null) { throw new NullReferenceException("標準入力がnullです Solveメソッド内の解答コードが間違っています"); }
            return str;
        }
        protected static T GetNumber<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>, IFormattable
        {
            var str = GetString();
            return Activator.CreateInstance<T>() switch
            {
                int _ => (T)(object)str.ToInt(),
                long _ => (T)(object)str.ToLong(),
                double _ => (T)(object)str.ToDouble(),
                decimal _ => (T)(object)str.ToDecimal(),
                BigInteger _ => (T)(object)str.ToBigInteger(),
                _ => throw new NotSupportedException(),
            };
        }
        protected static T[] GetArray<T>() where T : IComparable, IComparable<T>, IEquatable<T> => ToArray<T>(GetString());
        protected static List<T> GetList<T>() where T : IComparable, IComparable<T>, IEquatable<T> => ToList<T>(GetString());
        protected static void Swap<T>(ref T item1, ref T item2) => (item2, item1) = (item1, item2);
        protected static IEnumerable<char> AtoZ()
        {
            for (char i = 'a'; i <= 'z'; i++)
            {
                yield return i;
            }
        }
        private static T[] ToArray<T>(string str) where T : IComparable, IComparable<T>, IEquatable<T>
        {
            return ConvertEnumerator<T>(str).ToArray();
        }
        private static List<T> ToList<T>(string str) where T : IComparable, IComparable<T>, IEquatable<T>
        {
            return ConvertEnumerator<T>(str).ToList();
        }
        private static IEnumerable<T> ConvertEnumerator<T>(string str) where T : IComparable, IComparable<T>, IEquatable<T>
        {
            return Activator.CreateInstance<T>() switch
            {
                byte _ => str.Split().Select(byte.Parse).Cast<T>(),
                int _ => str.Split().Select(int.Parse).Cast<T>(),
                long _ => str.Split().Select(long.Parse).Cast<T>(),
                double _ => str.Split().Select(double.Parse).Cast<T>(),
                decimal _ => str.Split().Select(decimal.Parse).Cast<T>(),
                BigInteger _ => str.Split().Select(BigInteger.Parse).Cast<T>(),
                _ => throw new NotSupportedException()
            };
        }
        protected sealed class SetConsole : IDisposable
        {
            readonly StreamWriter sw = new StreamWriter(Console.OpenStandardOutput());
            public SetConsole()
            {
                sw.AutoFlush = false;
                Console.SetOut(sw);
            }
            public void Dispose()
            {
                Console.Out.Flush();
                sw.AutoFlush = true;
                Console.SetOut(sw);
            }
        }
    }
    public static class ExtentionsLibrary
    {
        public static long Choose(this int n, int a, long divisor = 1000000007)
        {
            long numerator = 1, denominator = 1;
            for (int i = 0; i < a; i++)
            {
                numerator *= n - i;
                numerator %= divisor;
                denominator *= i + 1;
                denominator %= divisor;
            }
            return numerator / denominator;
        }
        /// <summary>
        /// 階乗を求める
        /// </summary>
        /// <param name="num"></param>
        /// <returns></returns>
        public static long Factorial(this long num)
        {
            var result = 1L;
            for (int i = 1; i <= num; i++)
            {
                result *= i;
            }
            return result;
        }
        private static T[] NextPermutation<T>(this IEnumerable<T> collection, IComparer<T> cmp) where T : IComparable
        {
            var array = collection.ToArray();
            int? exchangingNumIndex = null;
            for (int i = 1; i < array.Length; i++)
            {
                if (cmp.Compare(array[i - 1], array[i]) >= 0) { continue; }

                exchangingNumIndex = i - 1;
            }

            if (exchangingNumIndex is null) { return null; }

            for (int j = array.Length - 1; j >= 0; j--)
            {
                if (cmp.Compare(array[(int)exchangingNumIndex], array[j]) >= 0) { continue; }

                var tmp = array[j];
                array[j] = array[(int)exchangingNumIndex];
                array[(int)exchangingNumIndex] = tmp;
                array = array.Take((int)exchangingNumIndex + 1).Concat(array.Skip((int)exchangingNumIndex + 1).Reverse()).ToArray();
                break;
            }
            return array;
        }
        public static string[] NextPermutation(this IEnumerable<string> collection)
        {
            return NextPermutation(collection, StringComparer.Ordinal);
        }
        public static T[] NextPermutation<T>(this IEnumerable<T> collection) where T : IComparable
        {
            return NextPermutation(collection, Comparer<T>.Default);
        }
        public static IEnumerable<T[]> Permutations<T>(this IEnumerable<T> collection) where T : IComparable
        {
            var next = collection.NextPermutation();

            while (next != null)
            {
                yield return next;

                next = next.NextPermutation();
            }
        }
        public static long Gcd(this long a, long b)
        {
            if (a < b) { return Gcd(b, a); }
            long tmp;
            do
            {
                tmp = a % b;
                a = b;
                b = tmp;
            } while (tmp != 0);
            return a;
        }
        public static long Lcm(this long a, long b) => a * b / Gcd(a, b);
        /// <summary>
        /// 素因数分解を行う
        /// </summary>
        /// <param name="num"></param>
        /// <returns></returns>
        public static IEnumerable<(long num, int count)> Factorize(this long n)
        {
            yield return (1, 1);
            var rootN = Math.Sqrt(n);
            for (long i = 2; i <= rootN; i++)
            {
                if (n % i != 0) { continue; }

                var count = 1;
                n /= i;
                while (n % i == 0)
                {
                    n /= i;
                    count++;
                }
                yield return (i, count);
            }
            if (n != 1) { yield return (n, 1); }
        }
        public static int ToInt(this string str) => int.Parse(str);
        public static int ToInt(this char chr) => int.Parse(chr.ToString());
        public static long ToLong(this string str) => long.Parse(str);
        public static double ToDouble(this string str) => double.Parse(str);
        public static decimal ToDecimal(this string str) => decimal.Parse(str);
        public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
        public static DateTime ToDateTime(this string str) => DateTime.Parse(str);
        public static string StringJoin<T>(this IEnumerable<T> collection, string separator = "") => string.Join(separator, collection.Select(c => c.ToString()));
        public static string StringConcat(this IEnumerable<char> collection) => string.Concat(collection);
        public static int LowerBound<T>(this IReadOnlyList<T> a, T v) => LowerBound(a, v, Comparer<T>.Default);
        public static int LowerBound(this IReadOnlyList<string> str, string v) => LowerBound(str, v, StringComparer.Ordinal);
        public static int LowerBound<T>(this IReadOnlyList<T> a, T v, IComparer<T> cmp)
        {
            var l = 0;
            var r = a.Count - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var result = cmp.Compare(a[mid], v);
                if (result == -1)
                {
                    l = mid + 1;
                }
                else
                {
                    r = mid - 1;
                }
            }
            return l;
        }
        public static int UpperBound(this IReadOnlyList<string> str, string v) => UpperBound(str, v, StringComparer.Ordinal);
        public static int UpperBound<T>(this IReadOnlyList<T> a, T v) => UpperBound(a, v, Comparer<T>.Default);
        public static int UpperBound<T>(this IReadOnlyList<T> a, T v, IComparer<T> cmp)
        {
            var l = 0;
            var r = a.Count - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var res = cmp.Compare(a[mid], v);
                if (res <= 0) l = mid + 1;
                else r = mid - 1;
            }
            return l;
        }
        public static IOrderedEnumerable<TSource> OrderBy<TSource>(this IEnumerable<TSource> source, Func<TSource, string> keySelector)
        {
            return source.OrderBy(keySelector, StringComparer.Ordinal);
        }
        public static IOrderedEnumerable<TSource> OrderByDescending<TSource>(this IEnumerable<TSource> source, Func<TSource, string> keySelector)
        {
            return source.OrderByDescending(keySelector, StringComparer.Ordinal);
        }
        public static void Deconstruct<T>
        (
            this IList<T> self,
            out T first
        )
        {
            first = self[0];
        }

        public static void Deconstruct<T>
        (
            this IList<T> self,
            out T first,
            out T second
        )
        {
            first = self[0];
            second = self[1];
        }

        public static void Deconstruct<T>
        (
            this IList<T> self,
            out T first,
            out T second,
            out T third
        )
        {
            first = self[0];
            second = self[1];
            third = self[2];
        }

        public static void Deconstruct<T>
        (
            this IList<T> self,
            out T first,
            out T second,
            out T third,
            out T forth
        )
        {
            first = self[0];
            second = self[1];
            third = self[2];
            forth = self[3];
        }
        public static void Deconstruct<T>
        (
            this IList<T> self,
            out T first,
            out T second,
            out T third,
            out T forth,
            out T fifth
        )
        {
            first = self[0];
            second = self[1];
            third = self[2];
            forth = self[3];
            fifth = self[4];
        }
    }

    public struct Mint
    {
        private static readonly long MOD = (long)1e9 + 7;

        /// <summary>
        /// 0以上MOD未満の整数
        /// </summary>
        public long Value;

        public Mint(long val)
        {
            Value = val % MOD;
            if (Value < 0) Value += MOD;
        }

        private static Mint Ctor(long val) => new Mint() { Value = val };
        public static Mint operator +(Mint a, Mint b)
        {
            long res = a.Value + b.Value;
            if (res > MOD) res -= MOD;
            return Ctor(res);
        }
        public static Mint operator -(Mint a, Mint b)
        {
            long res = a.Value - b.Value;
            if (res < 0) res += MOD;
            return Ctor(res);
        }
        public static Mint operator *(Mint a, Mint b)
        {
            long res = a.Value * b.Value;
            if (res > MOD) res %= MOD;
            return Ctor(res);
        }
        public static Mint operator /(Mint a, Mint b) => a * Inv(b);
        public static Mint Pow(Mint a, long n)
        {
            if (n == 0) return new Mint(1);
            Mint b = Pow(a, n >> 1);
            b *= b;
            if ((n & 1) == 1) b *= a;
            return b;
        }
        public static Mint Inv(Mint n)
        {
            long a = n.Value;
            long b = MOD;

            long x = 1;
            long u = 0;
            while (b != 0)
            {
                long k = a / b;
                long _x = u;
                u = x - k * u;
                x = _x;

                long _a = a;
                a = b;
                b = _a - (k * b);
            }

            return new Mint(x);
        }
        public override string ToString() => Value.ToString();
        public static implicit operator Mint(long a) => new Mint(a);
        public static explicit operator long(Mint a) => a.Value;
        public static Mint Choose(long n, long k)
        {
            Mint numerator = 1, denominator = 1;
            for (int i = 0; i < k; i++)
            {
                numerator *= n - i;
                denominator *= i + 1;
            }
            return numerator / denominator;
        }
    }
    public enum Priority : byte
    {
        Smaller = 0,
        Larger = 1
    }
}