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 Ruby (2.7.1) (judge verdict: Wrong Answer)

class PriorityQueue
  def initialize(array = [])
    @data = []
    array.each{|a| add(a)}
  end

  def add(element)
    @data.push(element)
    bottom_up
  end

  def peek
    @data[0]
  end

  def poll
    if size == 0
      return nil
    elsif size == 1
      return @data.pop
    else
      min = @data[0]
      @data[0] = @data.pop
      top_down
      return min
    end
  end

  def size
    @data.size
  end

  private

  def swap(i, j)
    @data[i], @data[j] = @data[j], @data[i]
  end

  def bottom_up
    idx = size - 1
    while(has_parent?(idx))
      parent_idx = parent_idx(idx)
      if @data[parent_idx][:key] > @data[idx][:key]
        swap(parent_idx, idx)
        idx = parent_idx
      else
        return
      end
    end
  end

  def top_down
    idx = 0
    while (has_child?(idx))
      a = left_child_idx(idx)
      b = right_child_idx(idx)
      if @data[b].nil?
        c = a
      else
        c = @data[a][:key] <= @data[b][:key] ? a : b
      end
      if @data[idx][:key] > @data[c][:key]
        swap(idx, c)
        idx = c
      else
        return
      end
    end
  end

  def parent_idx(idx)
    (idx - (idx.even? ? 2 : 1)) / 2
  end

  def left_child_idx(idx)
    (idx * 2) + 1
  end

  def right_child_idx(idx)
    (idx * 2) + 2
  end

  def has_child?(idx)
    ((idx * 2) + 1) < @data.size
  end

  def has_parent?(idx)
    idx > 0
  end
end

N = gets.to_i
A = gets.split.map(&:to_i)

sorted = A.sort_by{ |v| -v }
comb = PriorityQueue.new([{ key: sorted[1], value: [sorted[0],sorted[1]]}] * 2)

ans = sorted[0]
sorted[2..-1].each do |v|
  tmp = comb.poll
  ans += tmp[:key]
  comb.add({ key: v, value: [v, tmp[0]] })
  comb.add({ key: v, value: [v, tmp[1]] })
end

puts ans