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: Time Limit Exceeded)


n = gets.to_i
as = gets.split.map {|x| x.to_i}


as.sort!

$str = ""
def set(x,y)
  $str += "#{x} #{y}\n"
  return x - y
end

if as[0] < 0 and as[-1] < 0
  p = as[-1]
  i = n - 2
  while i > 0
    p = set(p, as[i])
    i-=1
  end
  v = set(p, as[0])
  puts v
elsif as[0] > 0 and as[-1] > 0
  m = as[0]
  i = 1
  while i < n - 1
    m = set(m, as[i])
    i+=1
  end
  v = set(as[-1],m)
  puts v
else
  i = 1
  m = as[0]
  p = as[-1]
  while i < n - 1
    if as[i] > 0
      m = set(m,as[i])
    else
      p = set(p,as[i])
    end
    i+=1
  end

  v = set(p,m)
  puts v
end
  

print $str