Problem:
Score : 500 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on a blackboard.

We will repeat the following operation N-1 times so that we have only one integer on the blackboard.

Choose two integers x and y on the blackboard and erase these two integers. Then, write a new integer x-y.

Find the maximum possible value of the final integer on the blackboard and a sequence of operations that maximizes the final integer.

Constraints

2 \leq N \leq 10^5

-10^4 \leq A_i \leq 10^4

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value M of the final integer on the blackboard, and a sequence of operations x_i, y_i that maximizes the final integer, in the format below.

Here x_i and y_i represent the integers x and y chosen in the i-th operation, respectively.

If there are multiple sequences of operations that maximize the final integer, any of them will be accepted.

M
x_1 y_1
:
x_{N-1} y_{N-1}

Sample Input 1

3
1 -1 2

Sample Output 1

4
-1 1
2 -2

If we choose x = -1 and y = 1 in the first operation, the set of integers written on the blackboard becomes (-2, 2).

Then, if we choose x = 2 and y = -2 in the second operation, the set of integers written on the blackboard becomes (4).

In this case, we have 4 as the final integer. We cannot end with a greater integer, so the answer is 4.

Sample Input 2

3
1 1 1

Sample Output 2

1
1 1
1 0

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

require 'pry'
def main
  n = gets.chomp.to_i
  numbers = gets.chomp.split(' ').map(&:to_i).sort
  
  combi = []

  (n-2).times do |_i|
    x = numbers.shift
    y = numbers.pop
    c = if (x - y).abs > (y - x).abs
          [x, y]
        elsif (x - y).abs < (y - x).abs
          [y, x]
        elsif (x - y).abs == (y - x).abs
          if numbers[-1] <= -1 
            x-y >= y-x ? [x, y] : [y, x]
          else
            [x, y]
          end
        end
    
    diff =  c[0] - c[1]
    combi << [c[0],c[1]]
    if numbers[-1] <= diff
      numbers.push(diff)
    else
      numbers.unshift(diff)
    end
  end

  combi << [numbers[1], numbers[0]]
  numbers = numbers[1] - numbers[0]
  
  puts numbers
  combi.each {|x,y| puts"#{x} #{y}" }
end


main