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.to_i
a=gets.split.map(&:to_i)
@aa = Array.new(3).map{[]}
a.each do |e|
  @aa[(e<=>0)+1] << e
end
@aa.map!(&:sort)

@r = []
def pp
  if @aa[0].size >= 2
    a = @aa[2].pop
    b = @aa[0].pop
    @aa[2] << a-b
    @r << [a,b]
    return true
  elsif @aa[2].size >= 2
    a = @aa[0].pop
    b = @aa[2].pop
    @aa[0] << a-b
    @r << [a,b]
    return true
  elsif @aa[0].size!=0 && @aa[2].size!=0
    a = @aa[2].pop
    b = @aa[0].pop
    @aa[2] << a-b
    @r << [a,b]
    return false
  else
    if @aa[0].size==1
      @aa[2] << @aa[0].pop*-1
      r = @r.pop
      @r << [r[1], r[0]]
    end
    return false
  end
end

while @aa[1].pop
  if @aa[0].size < @aa[2].size
    @aa[0].unshift(0)
  else
    @aa[2].unshift(0)
  end
end

if @aa[0].size.zero?
  a = @aa[2].shift
  b = @aa[2].shift
  @aa[0] << a-b
  @r << [a,b]
elsif @aa[2].size.zero?
  a = @aa[0].shift
  b = @aa[0].shift
  @aa[2] << b-a
  @r << [b,a]
end


while pp
end

if @aa[2].size!=1 || @aa[0].size!=1
  raise
end

puts @aa[2][0]
puts @r[0...n].map{|m|m.join(' ')}