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: Runtime Error)

include Math

n = gets.to_i
ary = Array.new(log(n, 2) + 2).map{Array.new}
ary[0] = gets.split.map(&:to_i).sort

ans = []
sum = 0

if n % 2 == 1 && ary[0][n / 2] > 0
  no1 = false
else
  no1 = true
end
  
  while ary[0].size > 1

    x = ary[0].shift
    y = ary[0].pop
    
    if no1 == true
      ans << [y, x]
      ary[1] << y - x
      no1 = false
    else 
      ans << [x, y]
      ary[1] << x - y
    end
  end

  if ary[1].size == 1
    if i == 0
      ary[1].unshift(ary[i].shift)
    else
      ary[1] << ary[i].shift
    end
  end

p ary[0]
while ary[1].size > 2
x = ary[1].shift
y = ary[1].shift
ary[1].unshift(x - y)
p ary[1]
end

puts ary[i]
ans.each do |a|
  puts a.join(" ")
end