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
li = gets.split.map(&:to_i)
p = []
m = []
ansl = []
ans = -1

li.each do |v|
  if v >= 0
    p << v
  else
    m << v
  end
end

p.sort!
m.sort!

if p.size > 0 and m.size == 0
  while p.size > 2
    a = p.shift
    b = p.shift
    p.unshift(a-b)
    ansl << "#{a} #{b}"
  end
  a = p.min
  b = p.max
  ans = b - a
  ansl << "#{b} #{a}"
elsif p.size == 0 and m.size > 0
  while m.size > 1
    a = m.shift
    b = m.shift
    m.unshift(a-b)
    ansl << "#{a} #{b}"
  end
  ans = m.shift
else
  while p.size > 1
    a = m.shift
    b = p.shift
    m.unshift(a-b)
    ansl << "#{a} #{b}"
  end
  while m.size > 1
    a = p.shift
    b = m.shift
    p.unshift(a-b)
    ansl << "#{a} #{b}"
  end
  a = p[0]
  b = m[0]
  ans = a - b
  ansl << "#{a} #{b}"
end

puts ans
ansl.each do |v|
  puts v
end