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: Accepted)

N = gets.to_i
a = gets.split.map(&:to_i)
pl = []
mi = []
a.each do |v|
  if v > 0
    pl << v
  else
    mi << v
  end
end
opr = []
if pl.length > 0 && mi.length > 0
  mi.sort!
  if mi.length > 1
    (mi.length-1).times do |i|
      opr << [pl[0],mi[i+1]]
      pl[0] -= mi[i+1]
    end
  end
  if pl.length > 1
    (pl.length-1).times do |i|
      opr << [mi[0],pl[i+1]]
      mi[0] -= pl[i+1]
    end
  end
  opr << [pl[0],mi[0]]
  ans = pl[0]-mi[0]
elsif pl.length == 0
  mi.sort!
  (mi.length-1).times do |i|
    opr << [mi[-1],mi[i]]
    mi[-1] -= mi[i]
  end
  ans = mi[-1]
elsif pl.length >= 3
  pl.sort!
  (pl.length-2).times do |i|
    opr << [pl[0],pl[i+1]]
    pl[0] -= pl[i+1]
  end
  opr << [pl[-1],pl[0]]
  ans = pl[-1] - pl[0]
else
  pl.sort!
  opr << [pl[1],pl[0]]
  ans = pl[1]-pl[0]
end
puts ans
opr.each do |x,y|
  puts "#{x} #{y}"
end