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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mab = math.abs
local n = io.read("*n")
local a = {}
local sum = 0
local abssum = 0
for i = 1, n do
  a[i] = io.read("*n")
  sum = sum + a[i]
  abssum = abssum + mab(a[i])
end
table.sort(a)
local allplus = 0 <= a[1]
local allminus = a[n] < 0

if n == 2 then
  if a[1] < a[2] then
    print(a[2] - a[1])
    print(a[2] .. " " .. a[1])
  else
    print(a[1] - a[2])
    print(a[1] .. " " .. a[2])
  end
else
  if allplus then
    print(sum - a[1] * 2)
    local cur = a[1]
    for i = 2, n - 1 do
      print(cur .. " " .. a[i])
      cur = cur - a[i]
    end
    print(a[n] .. " " .. cur)
  elseif allminus then
    print(a[n] * 2 - sum)
    local cur = a[n]
    for i = 1, n - 1 do
      print(cur .. " " .. a[i])
      cur = cur - a[i]
    end
  else
    print(abssum)
    local minlast = 1
    for i = 1, n do
      if a[i] < 0 then
        minlast = i
      else
        break
      end
    end
    local cur = a[minlast]
    for i = minlast + 1, n - 1 do
      print(cur .. " " .. a[i])
      cur = cur - a[i]
    end
    print(a[n] .. " " .. cur)
    cur = a[n] - cur
    for i = 1, minlast - 1 do
      print(cur .. " " .. a[i])
      cur = cur - a[i]
    end
  end
end