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 Lua (5.3.2) (judge verdict: Wrong Answer)

local n = io.read("*n")
local p, m = {}, {}
for i = 1, n do
  local a = io.read("*n")
  if 0 <= a then
    table.insert(p, a)
  else
    table.insert(m, a)
  end
end
local v = 0
local r1, r2 = {}, {}
if #m == 0 then
  v = p[1]
  for i = 3, #p do
    table.insert(r1, v)
    table.insert(r2, p[i])
    v = v - p[i]
  end
  table.insert(r1, p[2])
  table.insert(r2, v)
  v = p[2] - v
elseif #p == 0 then
  v = m[1]
  for i = 2, #m do
    table.insert(r1, v)
    table.insert(r2, m[i])
    v = v - m[i]
  end
else
  v = m[1]
  for i = 2, #p do
    table.insert(r1, v)
    table.insert(r2, p[i])
    v = v - p[i]
  end
  table.insert(r1, p[1])
  table.insert(r2, v)
  v = p[1] - v
  for i = 2, #m do
    table.insert(r1, v)
    table.insert(r2, m[i])
    v = v - m[i]
  end
end
print(v)
for i = 1, n - 1 do
  print(r1[i] .. " " ..r2[i])
end