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)
am, az, ap = [], [], []
n.times do |i|
  if a[i] < 0
    am << a[i]
  elsif a[i] == 0
    az << a[i]
  else
    ap << a[i]
  end
end
ap.sort!
am.sort!.reverse!
if am != [] && ap != []
  puts ap.inject(:+) + am.inject(:+) * (-1)
  m = am[0]
  (ap.length-1).times do |i|
    puts "#{m} #{ap[i]}"
    m -= ap[i]
  end
  puts "#{ap[-1]} #{m}"
  m = ap[-1] - m
  (am.length-1).times do |i|
    puts "#{m} #{am[i+1]}"
    m -= ap[i+1]
  end
  az.length.times do
    puts "#{m} 0"
  end
elsif am == [] && ap == []
  puts 0
  (az.length-1).times do
    puts "0 0"
  end
elsif am == []
  if az != []
    puts ap.inject(:+)
    m = 0
    (ap.length-1).times do |i|
      puts "#{m} #{ap[i]}"
      m -= ap[i]
    end
    puts "#{ap[-1]} #{m}"
    m = ap[-1] - m
    (az.length-1).times do
      puts "#{m} 0"
    end
  else
    ap.sort!
    puts ap.inject(:+) - ap[0] * 2
    m = ap[0]
    (ap.length-2).times do |i|
      puts "#{m} #{ap[i+1]}"
      m -= ap[i+1]
    end
    puts "#{ap[-1]} #{m}"
  end
else
  if az != []
    puts am.inject(:+) * (-1)
    m = 0
    (am.length).times do |i|
      puts "#{m} #{am[i]}"
      m -= am[i]
    end
    (az.length-1).times do
      puts "#{m} 0"
    end
  else
    am.sort!.reverse!
    puts (am.inject(:+) - am[0] * 2) * (-1)
    m = am[0]
    (am.length-1).times do |i|
      puts "#{m} #{am[i+1]}"
      m -= a[i+1]
    end
  end
end