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)
A.sort!
plus, minus = A.partition { |i| i >= 0 }
if minus.size == 0
  puts plus.inject(:+) - plus[0] * 2
  temp = plus.shift
  while plus.size > 1
    a = plus.shift
    puts "#{temp} #{a}"
    temp -= a
  end
  a = plus.pop
  puts "#{a} #{temp}"
  temp = a - temp
elsif plus.size == 0
  puts -minus.inject(:+) + minus[-1] * 2
  temp = minus.pop
  while minus.size > 0
    a = minus.shift
    puts "#{temp} #{a}"
    temp -= a
  end
else
  puts plus.inject(:+) - minus.inject(:+)
  temp = minus.pop
  while plus.size > 1
    a = plus.pop
    puts "#{temp} #{a}"
    temp -= a
  end
  a = plus.pop
  puts "#{a} #{temp}"
  temp = a - temp
  while minus.size > 0
    a = minus.shift
    puts "#{temp} #{a}"
    temp -= a
  end
end