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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Control.Monad
import Data.List

pm_list2 :: [Int] -> ([Int], [Int])
pm_list2 ls =
  let n = length ls
   in splitAt (div n 2) $ sort ls

max_val2 :: ([Int], [Int]) -> Int
max_val2 (m, p) = (sum p) - (sum m)

construct_op2 :: Bool -> ([Int], [Int]) -> [(Int, Int)]
construct_op2 is_even (m, p) =
  if is_even
    then let rev = reverse $ concat [[pp, mm] | (pp, mm) <- (zip p m)]
          in eater (head rev) (tail rev)
    else let rev =
               reverse $
               ((head p) : (concat [[mm, pp] | (pp, mm) <- (zip (tail p) m)]))
          in eater (head rev) (tail rev)

eater :: Int -> [Int] -> [(Int, Int)]
eater now [] = []
eater now (x:xs) = (x, now) : (eater (x - now) xs)

solver :: [Int] -> (Int, [(Int, Int)])
solver ls =
  let (m, p) = pm_list2 ls
   in (max_val2 (m, p), construct_op2 (even $ length ls) (m, p))

main :: IO ()
main = do
  _ <- getLine
  dat <- (map read . words) <$> getLine
  let (v, ls) = solver dat
  print v
  forM_ ls (\(x, y) -> putStrLn $ show x ++ " " ++ show y)