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)

-- https://github.com/minoki/my-atcoder-solutions
{-# LANGUAGE BangPatterns #-}
import Data.Char (isSpace)
import Data.List (unfoldr)
import Control.Monad (forM_)
import qualified Data.Vector.Unboxed as U
import qualified Data.ByteString.Char8 as BS

main = do
  n <- readLn
  xs <- U.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let ys = U.scanl' (\(!m,!n) x -> (maximum [x - m, x - n, m - x, n - x], minimum [x - m, x - n, m - x, n - x])) (U.head xs, U.head xs) (U.tail xs)
      (r, _) = U.last ys
  print r
  let loop 0 acc !y = acc
      loop i acc y
        | y == x - m = loop (i - 1) ((x, m) : acc) m
        | y == m - x = loop (i - 1) ((m, x) : acc) m
        | y == x - n = loop (i - 1) ((x, n) : acc) n
        | y == n - x = loop (i - 1) ((n, x) : acc) n
        | otherwise = error $ "invalid input " ++ show (y,x,m,n)
        where x = xs U.! i
              (m,n) = ys U.! (i - 1)
  forM_ (loop (n - 1) [] r) $ \(x,y) -> do
    putStrLn $ concat [show x, " ", show y]