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)

N = gets.to_i
A = gets.split.map(&:to_i).sort

if N == 2
  puts A.max - A.min
  puts [A.max, A.min].join(' ')
  exit
end

plus = []
minus = []
query = []

n = N - 1

if A.all? { |x| x >= 0 }
  plus = A
  pl = plus.shift
  mi = plus.pop
  minus << pl - mi
  query << [pl, mi]
  n -= 1
elsif A.all? { |x| x <= 0 }
  minus = A
  pl = minus.pop
  mi = minus.shift
  plus << (minus.pop - minus.shift)
  query << [pl, mi]
  n -= 1
else
  plus = A.select { |x| x >= 0 }
  minus = A.select { |x| x < 0 }
end

n.times do |i|
  pl = plus.pop
  mi = minus.pop

  if i == n - 1
    puts pl - mi
    query << [pl, mi]

    query.each do |x, y|
      puts [x, y].join(' ')
    end
  else
    if plus.size >= minus.size
      minus << mi - pl
      query << [mi, pl]
    else
      plus << pl - mi
      query << [pl, mi]
    end
  end
end