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: Wrong Answer)

n = gets.chomp.to_i
a_arr = gets.chomp.split(" ").map(&:to_i).sort

puts_arr = []

(n-1).times do
  min = a_arr[0]
  max = a_arr[-1]
  if a_arr.length == 2 then
    puts_arr << "#{max} #{min}"
    puts max - min
    break
  end

  if max.abs >= min.abs then
    x = a_arr[0]
    y = a_arr[-2]
    a_arr.delete_at(0)
    a_arr.delete_at(-2)
  else
    x = a_arr[-1]
    y = a_arr[1]
    a_arr.delete_at(-1)
    a_arr.delete_at(1)
  end
  puts_arr << "#{x} #{y}"
  diff = x - y
  flag = false
  if diff <= a_arr[0] then
    a_arr.unshift(diff)
  elsif diff >= a_arr[-1]
    a_arr.push(diff)
  else
    a_arr.each_with_index do |a, i|
      if diff >= a then
        a_arr.insert(i+1, diff)
        break
      end
    end
  end
end

puts_arr.each do |str|
  puts str
end