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 = gets.to_i
as = gets.split.map(&:to_i)
if N == 2
  puts as[0] > as[1] ? as[0] - as[1] : as[1] - as[0]
  puts as[0] > as[1] ? "#{as[0]} #{as[1]}" : "#{as[1]} #{as[0]}"
  exit(0)
end
as.sort!
ans = []
hu = as.select { |a| a <= 0 }.size.to_i
sei = as.select { |a| a > 0 }.size.to_i
if sei == N
  max = as.pop
  min = as.shift
  ans << [min, max]
  new_n = min - max
  while as.size > 1
    max = as.pop
    ans << [new_n, max]
    new_n -= max
  end
  ans << (as[0] > new_n ? [as[0], new_n] : [new_n, as[0]])
  score = as[0] > new_n ? as[0] - new_n : new_n - as[0]
  p score
  ans.each do |(x, y)|
    puts "#{x} #{y}"
  end
elsif hu == N
  max = as.pop
  min = as.shift
  ans << [max, min]
  new_n = max - min
  while as.size > 1
    max = as.pop
    ans << [new_n, max]
    new_n -= max
  end
  ans << (as[0] > new_n ? [as[0], new_n] : [new_n, as[0]])
  score = as[0] > new_n ? as[0] - new_n : new_n - as[0]
  p score
  ans.each do |(x, y)|
    puts "#{x} #{y}"
  end
else
  min = as.shift
  max = as.pop
  n = max
  as.each do |a|
    if a < 0
      ans << [n, a]
      n -=a
    end
  end
  n = min
  while as.size > 1
    max = as.pop
    ans << [n, max]
    n -= max
  end
  ans << (as[0] > n ? [as[0], n] : [n, as[0]])
  score = as[0] > n ? as[0] - n : n - as[0]
  p score
  ans.each do |(x, y)|
    puts "#{x} #{y}"
  end
end