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)

posc = as.count { |a| a >= 0 }
negc = as.count { |a| a <= 0 }

ans = []
if n == posc
  as.sort!
  while as.count > 1 do
    x = as.shift
    y = as.shift
    as << x-y
    ans << "#{x} #{y}"
  end
elsif n == negc
  as.sort!.reverse!
  while as.count > 1 do
    x = as.shift
    y = as.shift
    as.unshift(x-y)
    ans << "#{x} #{y}"
  end
else
  if as.max.abs > as.min.abs
    as.sort!
    while as.count > 1 do
      x = as.shift
      y = as.shift
      as << x-y
      ans << "#{x} #{y}"
    end
  else
    as.sort!.reverse!
    while as.count > 1 do
      x = as.shift
      y = as.shift
      as.unshift(x-y)
      ans << "#{x} #{y}"
    end
  end
end
puts as.first
puts ans