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)

# util functions

# debug
$debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if $debugFlag

def pd(str)
  p str if $debugFlag
end

def printd(str)
  print str if $debugFlag
end

# input
inputs = []
lc = 0
nn = 0
while l = $stdin.gets do
  if lc == 0
    nn = l.chomp.to_i
  else
    inputs = l.chomp.split(" ").map(&:to_i)
  end
  lc += 1
end

# body
if $debugFlag
  p nn
  p inputs
end

inputs.sort!

neg_exists = (inputs[0] < 0)
pos_exists = (inputs[-1] > 0)

pd inputs

ans = 0
ansseq = []
if neg_exists
  if pos_exists
    inputs.reverse!
    ans = inputs[-1]
    for i in 0..inputs.length-2 do
      if inputs[i] >= 0
        if inputs[i+1] < 0
          ansseq << "#{inputs[i]} #{ans}"
          ans = inputs[i] - ans
        else
          ansseq << "#{ans} #{inputs[i]}"
          ans -= inputs[i]
        end
      else
        ansseq << "#{ans} #{inputs[i]}"
        ans -= inputs[i]
      end
    end
  else
    inputs.reverse!
    ans = inputs[0]
    for i in 1..inputs.length-1 do
      if i == inputs.length-1
        ans -= inputs[i]
        ansseq << "#{ans} #{inputs[i]}"
      else
        ans -= inputs[i]
        ansseq << "#{ans} #{inputs[i]}"
      end
    end
  end
else
  if pos_exists
    ans = inputs[0]
    for i in 1..inputs.length-1 do
      if i == inputs.length-1      
        ans = inputs[i] - ans
        ansseq << "#{inputs[i]} #{ans}"
      else
        ans -= inputs[i]
        ansseq << "#{ans} #{inputs[i]}"
      end
    end
  else
    ans = 0
  end
end
    
puts ans
ansseq.each do |a_i|
  puts a_i
end