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# (Mono-csc 3.5.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
namespace AtCoder_1
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = Cin();
            long[] a = CinLAr();
            Array.Sort(a);
            Cout(a.Sum() - a[0]);

            Cin();
        } //main

        static readonly int MOD10_9_7 = (1000000000 + 7);
        static Random Rand = new Random();
        static readonly string[] AlphabetTable = new string[] { "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z" };
        static int GetDigits(long num) { return (int)Floor(Log10(num)) + 1; }
        static int GetNumByDigit(long num, int digit)
        {
            return (int)((num / ((int)Pow(10, digit - 1))) % 10);
        }
        static int Loop(int num, int max)
        {
            if (num > max) { return num % max - 1; }
            else if (num < 0) { return max - (-num) % max + 1; }
            else { return num; }
        }
        static long PW10(int n) { return (long)Pow(10, n); }
        static long GCD(long a, long b)
        {
            if (a < b) { return GCD(b, a); }
            if (a % b == 0) { return b; }
            else { return GCD(b, a % b); }
        }
        static long LCM(long a, long b) { return a * b / GCD(a, b); }
        static void Swap<T>(ref T a, ref T b) { T t = a; a = b; b = t; }
        static void SwapArE<T>(T[] a, int i, int j) { T t = a[i]; a[i] = a[j]; a[j] = t; }
        static void SwapLiE<T>(List<T> a, int i, int j) { T t = a[i]; a[i] = a[j]; a[j] = t; }
        static bool IsInt(double d) { return (int)d == d; }
        static string Cin() { return ReadLine(); }
        static string[] CinAr() { var q = Cin().Split(' '); return (q[0] == "") ? new string[0] : q; }
        static int CinT() { return S2i(Cin()); }
        static int[] CinTAr() { return CinAr().Select((x, i) => { return S2i(x); }).ToArray(); }
        static long CinL() { return S2L(Cin()); }
        static long[] CinLAr() { return CinAr().Select((x, i) => { return S2L(x); }).ToArray(); }
        static double CinD() { return S2D(Cin()); }
        static double[] CinDAr() { return CinAr().Select((x, i) => { return S2D(x); }).ToArray(); }
        static int S2i(string s) { return int.Parse(s); }
        static long S2L(string s) { return long.Parse(s); }
        static double S2D(string s) { return double.Parse(s); }
        static void Cout(object s) { WriteLine(s); }
        static string RevStr(string s) { return new string(s.Reverse().ToArray()); }
        static long[] Divisor(long n)
        {
            if (n == 1) { return new long[] { 1 }; }
            List<long> res = new List<long>() { 1, n };
            for (long i = 2; i <= Math.Sqrt(n); i++)
            {
                if (n % i == 0)
                {
                    res.Add(i);
                    long f = n / i;
                    if (f != i) { res.Add(f); }
                }
            }
            return res.ToArray();
        }
        static IEnumerable<decimal> PrimeFactors(decimal n)
        {
            decimal i = 2, tmp = n;
            while (i * i <= n)
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else { i++; }
            }
            if (tmp != 1) { yield return tmp; }
        }
        static bool IsPrime(long num)
        {
            if (num == 1) { return false; }
            for (long i = 2; i <= Sqrt(num) + 1; i++) { if (num % i == 0) { return false; } }
            return true;
        }
        static void CoutAr<Type>(IEnumerable<Type> types) { Cout(string.Join(" ", types)); }
        static long nCr(int n, int r) { return nPr(n, r) / Factorial(r); }
        static long nPr(int n, int r) { return FactorialDivision(n, n - r); }
        static long FactorialDivision(int tf, int df)
        {
            long r = 1;
            for (int i = tf; i > df; i--) { r *= i; }
            return r;
        }
        static long Factorial(int i)
        {
            if (i <= 1) { return 1; }
            return i * Factorial(i - 1);
        }
        static void CoutMemPairAr<Type>(IEnumerable<Pair<Type>> pairs)
        {
            var ar = pairs.ToArray();
            for (int i = 0; i < ar.Length; i++) { Write($"({ar[i].a}, {ar[i].b}, {ar[i].c}), "); }
            Cout("");
        }
    }
    public struct Pair<T>
    {
        public T a, b, c;
        public Pair(T _a, T _b, T _c = default(T)) { a = _a; b = _b; c = _c; }
    }
}