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)

N = gets.chomp.to_i
A = gets.chomp.split(' ').map(&:to_i)[0..N].sort
positives, negatives = A.partition{ |v| v > 0 }

min = A.min
max = A.max

puts (if min > 0
  A.reduce(&:+) - min*2
elsif max < 0
  max*2 - A.reduce(&:+)
else
  positives.reduce(&:+) - negatives.reduce(&:+)
end)

(N-1).times do |i|
  a, b = begin
    if positives.size == 2 && negatives.size == 0
      [ positives.pop, positives.shift ]
    elsif positives.size == 0 && negatives.size == 2
      [ negatives.shift, negatives.pop ]
    elsif positives.size > 1
      [ (negatives.empty? ? positives : negatives).shift, positives.shift ]
    else
      [ (positives.empty? ? negatives : positives).pop, negatives.shift ]
    end
  end
  if a > b 
    positives.push(a - b)
  else
    negatives.unshift(a - b)
  end
  puts [a, b].join(" ")
end