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)

input = readlines()
total = input.shift.chomp.to_i
list = input.shift.chomp.split("\s").map{|x| x.to_i}

total_score = 0

positions = []
total_max = nil
current_maxmin = nil
list.sort.reverse.each_with_index do |score, i|
  if i == 0
    total_max = score
    next
  end
  if i == 1
    total_score += total_max
    positions.push([total_max, score])
    positions.push([total_max, score])
    current_maxmin = [total_max, score].min
    next
  end

  tmp_max = nil
  tmp_index = nil
  positions.each_with_index do |pair, pair_idx|
    if tmp_max.nil? || pair.min > tmp_max['score']
      tmp_max = {'score' => pair.min, 'total' => pair[0] + pair[1]}
      tmp_index = pair_idx
      next
    end
    if pair.min == tmp_max['score'] && pair[0] + pair[1] < tmp_max['total']
      tmp_max = {'score' => pair.min, 'total' => pair[0] + pair[1]}
      tmp_index = pair_idx
      next
    end
  end

  total_score += positions[tmp_index].min

  new_positions = []
  positions.each_with_index do |pair, pair_idx|
    if pair_idx != tmp_index
      new_positions.push(pair) if pair.min > current_maxmin #???
      next
    end
    pair.each do |member|
      new_positions.push([member, score])
    end
  end
  positions = new_positions
end

puts total_score