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,*as=$<.read.split.map(&:to_i)

as.sort!
ret = []

if 0 < as[0] * as[-1]
  if N == 2
    plus = as[-1]
    minus = as[0]
    as = []
  else
    ret << [as[0], as[-1]]
    if as[0] < 0
      plus = as[0] - as[-1]
      minus = as[1]
    else
      plus = as[1]
      minus = as[0] - as[-1]
    end
    as = as[2..-2]
  end
else
  plus = as[-1]
  minus = as[0]
  as = as[1..-2]
end

as.each do |a|
  if a < 0
    ret << [plus, a]
    plus -= a
  else
    ret << [minus, a]
    minus -= a
  end
end

ret << [plus, minus]

p (plus-minus)
ret.each do|a,b|
  puts "#{a} #{b}"
end