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.Text;
using System.Linq;
using System.Numerics;
using System.IO;
using System.Net;
using System.Diagnostics;

namespace Practice
{
    class Program
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();

            Console.Out.Flush();
        }
        private const int MOD = 1000000007;
        private const int MAX = 1000001;
        static long[] fac = new long[MAX];
        static long[] finv = new long[MAX];
        static long[] inv = new long[MAX];
        static Dictionary<long, long> primeDic = new Dictionary<long, long>();

        static int h;
        static int w;
        static int k;
        static bool[] chooseH;
        static bool[] chooseW;
        static void Solve()
        {
            var n = Input.NextInt();
            var a = Input.NextLong(n);
            a.Sort();
            a.Reverse();

            long ans = 0;
            ans = a.Sum() - a[n - 1];
            Console.WriteLine(ans);
        }

        #region よく使う便利関数

        private static void TrialDivision(long m)
        {
            for (long i = 2; i * i <= m; i++)
            {
                long ex = 0;
                while (m % i == 0)
                {
                    ex++;

                    m /= i;
                }

                if (ex >= 1)
                {
                    primeDic.Add(i, ex);
                }
            }
            if (m >= 2)
            {
                primeDic.Add(m, 1);
            }

            // note まぁ1は違うよね
        }

        private static Dictionary<long, int> Factorize(long n)
        {
            var dic = new Dictionary<long, int>();

            for (long i = 2; i * i <= n; ++i)
            {
                while (n % i == 0)
                {
                    if (!dic.ContainsKey(i))
                    {
                        dic.Add(i, 0);
                    }
                    dic[i]++;
                    n /= i;
                }

            }

            if (n != 1)
            {
                dic.Add(n, 1);
            }
            return dic;
        }
        static void COMinit()
        {
            fac[0] = fac[1] = 1;
            finv[0] = 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;
            }
        }

        // 二項係数計算
        static long COM(long n, long k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
        }

        static class Input
        {
            static char[] separator = { ' ' };
            public static bool IsEof { get; set; }
            static Queue<string> q { get; set; }

            static Input()
            {
                IsEof = false;
                q = new Queue<string>();
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="items"></param>
            public static void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="s"></param>
            /// <returns></returns>
            public static bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            /// <returns></returns>
            static bool read()
            {
                var s = Console.ReadLine();
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                if (!q.Any()) return read();

                return true;
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            /// <returns></returns>
            public static string Next()
            {
                if (!q.Any())
                {
                    if (!read())
                    {
                        IsEof = true;
                        return "";
                    }
                }

                return q.Dequeue();
            }

            public static int NextInt() => int.Parse(Next());
            public static long NextLong() => long.Parse(Next());
            public static double NextDouble() => double.Parse(Next());

            public static List<string> Next(int n) => Enumerable.Range(0, n).Select(_ => Next()).ToList();
            public static List<int> NextInt(int n) => Next(n).Select(x => int.Parse(x)).ToList();
            public static List<long> NextLong(int n) => Next(n).Select(x => long.Parse(x)).ToList();
            public static List<double> NextDouble(int n) => Next(n).Select(x => double.Parse(x)).ToList();

            public static List<string> NextLine() => Console.ReadLine().Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries).ToList();
            public static List<int> NextIntLine() => NextLine().Select(x => int.Parse(x)).ToList();
            public static List<long> NextLongLine() => NextLine().Select(x => long.Parse(x)).ToList();
            public static List<double> NextDoubleLine() => NextLine().Select(x => double.Parse(x)).ToList();
        }
        private static bool isPrime(long x)
        {
            if (x == 2) { return true; }
            if (x < 2 || x % 2 == 0) { return false; }
            long i = 3;
            while (i * i <= x)
            {
                if (x % i == 0) { return false; }
                i = i + 2;
            }
            return true;
        }
        private static long lcm(long x, long y)
        {
            return x / gcd(x, y) * y;
        }
        private static long gcd(long x, long y)
        {
            return y > 0 ? gcd(y, x % y) : x;
        }
        private static long pow(long x, long n)
        {
            if (n == 0) { return 1; }
            long res = pow(x * x % MOD, n / 2);
            if (n % 2 == 1)
            {
                res = res * x % MOD;
            }
            return res;
        }
        private static void Swap<T>(ref T x, ref T y)
        {
            T t = x;
            x = y;
            y = t;
        }

        /// <summary>
        /// 指定した値以上の先頭のインデクスを返す
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス [exclusive]</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値以上の先頭のインデクス</returns>
        public static int LowerBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static int LowerBound<T>(IReadOnlyList<T> arr, T value) where T : IComparable
        {
            return LowerBound(arr, 0, arr.Count, value, Comparer<T>.Default);
        }

        /// <summary>
        /// 指定した値より大きい先頭のインデクスを返す
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス [exclusive]</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値より大きい先頭のインデクス</returns>
        public static int UpperBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static int UpperBound<T>(IReadOnlyList<T> arr, T value)
        {
            return UpperBound(arr, 0, arr.Count, value, Comparer<T>.Default);
        }
        #endregion
    }

    public class DisjointSet
    {
        private int[] rank;
        private int[] p;
        private int[] size;
        public DisjointSet(int n)
        {
            rank = new int[n];
            p = new int[n];
            size = new int[n];
            for (int i = 0; i < n; ++i)
            {
                MakeSet(i);
            }
        }
        public void MakeSet(int x)
        {
            p[x] = x;
            rank[x] = 0;
            size[x] = 1;
        }
        public bool IsSame(int x, int y)
        {
            return FindSet(x) == FindSet(y);
        }
        public void Unite(int x, int y)
        {
            Link(FindSet(x), FindSet(y));
        }
        public void Link(int x, int y)
        {
            if (rank[x] > rank[y])
            {
                p[y] = x;
                size[x] += size[y];
                size[y] = 0;
            }
            else
            {
                p[x] = y;
                size[y] += size[x];
                size[x] = 0;
                if (rank[x] == rank[y])
                {
                    rank[y]++;
                }
            }
        }
        public int FindSet(int x)
        {
            if (x != p[x])
            {
                p[x] = FindSet(p[x]);
            }
            return p[x];
        }
        public int Size(int x)
        {
            int root = FindSet(x);
            return size[root];
        }
    }
    public class PriorityQueue<T> where T : IComparable
    {
        private IComparer<T> _comparer = null;
        private int _type = 0;

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

        private int _count = 0;

        /// <summary>
        /// Priority Queue with custom comparer
        /// </summary>
        public PriorityQueue(int maxSize, IComparer<T> comparer)
        {
            _heap = new T[maxSize];
            _comparer = comparer;
        }

        /// <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;
        }

        private int Compare(T x, T y)
        {
            if (_comparer != null) return _comparer.Compare(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;
        }
    }
}