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 (2.7.1) (judge verdict: Wrong Answer)

n = gets.to_i
nums = gets.split.map(&:to_i)
plus_nums = nums.select { |num| num >= 0 }.sort
minus_nums = nums.select { |num| num < 0 }.sort.reverse
changes = []

if plus_nums.empty?
  a = minus_nums.shift
  b = minus_nums.shift
  plus_nums << (b.abs - a.abs)
  changes << [a, b]
end

if minus_nums.empty?
  a = plus_nums.shift
  b = plus_nums.shift
  minus_nums << b - a
  changes << [a, b]
end

until plus_nums.empty? || minus_nums.empty?
  a = minus_nums.shift
  b = plus_nums.shift
  changes << [a, b]
  if plus_nums.empty?
    plus_nums << (a.abs + b.abs)
  else
    minus_nums << -(a.abs + b.abs)
  end
end

puts plus_nums.first
changes.each { |a, b| puts "#{a} #{b}"}