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.to_i
a = gets.split.map(&:to_i)
a.sort!.reverse!
# p a
# puts "---------------"

ans = 0
anss = []
if a.size.even?
  aa = a[-1]
  a.pop
  (a.size).times do |i|
    if i.even?
      anss << [a[0], aa]
      if a.size == 1
        ans = (a[0] - aa)
        break
      end
      aa = a[0] - aa
      a.shift
    else
      anss << [a[-1], aa]
      aa = a[-1] - aa
      a.pop
    end
    # p a
    # puts '----'
  end
else
  aa = a[-1]
  a.pop
  (a.size).times do |i|
    if i.even?
      anss << [aa, a[0]]
      aa = aa - a[0]
      a.shift
    else
      anss << [a[0], aa]
      if a.size == 1
        ans = (a[0] - aa)
        break
      end
      aa = a[0] - aa
      a.pop
    end
    # p a
    # puts '----'
  end
end

p ans
puts anss.map{|x|x.join(' ')}.join("\n")