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: Accepted)

using System;
using System.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const char White = '.';
    const char Black = '#';
    const long Mod = 1000000007;

    static void Main(string[] args) {
        checked {
#if DEBUG
            MyDebugger.Test(process, "../TextFile1.txt");
            //TestCaseMaker.MakeTestCase1("../TextFile2.txt");
            //MyDebugger.Test(process, "../TextFile2.txt");
#else
            object ret = process(new StreamReader(Console.OpenStandardInput()));
            Console.WriteLine(ret);
#endif
        }
    }

    static object process(TextReader input) {
        var n = int.Parse(input.ReadLine());
        var aa = ToIntArray(input.ReadLine(), n);

        Array.Sort(aa, (x,y) => y-x);

        var queue = new PriorityQueue<Item>(n);
        long sum = 0;

        queue.Push(new Item(aa[0],aa[0]));

        for(int i=1; i<n; i++) {
            var x = aa[i];

            var q = queue.Pop();
            sum += q.happy;

            queue.Push(new Item(q.l, x));
            queue.Push(new Item(x, q.r));
        }

        return sum;
    }

    public class Item : IComparable
    {
        public int l;
        public int r;
        public int happy;

        public Item(int l, int r) {
            this.l = l;
            this.r = r;
            this.happy = Math.Min(l,r);
        }

        public int CompareTo(object obj) {
            var o = obj as Item;
            return o.happy.CompareTo(this.happy);
        }
    }

    //コピペ
    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;
        }
    }

    static int[] ToIntArray(string strs, int n) {
        var ret = new int[n];
        if (n == 0) return ret;
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = int.Parse(spl[i]);
        return ret;
    }
}