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 qualified Data.Vector.Unboxed as U
import qualified Data.Vector as V
import qualified Data.ByteString.Char8 as C
import qualified Data.Array.IO as A
import Debug.Trace
import Data.List
import Control.Monad
import Data.Ord

--import qualified Data.IntSet as S
import qualified Data.Sequence as S

r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

rp :: IO (Int,Int)
rp  = toTup . unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

toTup [a,b] = (a,b)

main :: IO ()
main = do
    n <- readLn :: IO Int
    as' <- r' :: IO [Int]
    let as = S.fromList (sort as')
    (res,r) <- solve as []
    print r
    mapM_ printtup (reverse res)

printtup (x,y) = putStrLn $ unwords [show x, show y]

solve :: S.Seq Int -> [(Int,Int)] -> IO ([(Int,Int)],Int)
solve set ac
    | S.length set <= 1  = error "should not happen"
    | S.length set == 2  = let x = S.index set 1 ; y = S.index set 0
                            in return ((x,y):ac, x-y)
    | otherwise = do
        print set
        let (x,rest)    = lastSplit set
        let (y,rest')   = headSplit rest
        let (z,rest'')  = headSplit rest'
        -- y < z < x
        let newset = if z < 0
            then y S.<| (rest'' S.|> (x-z)) -- XZ
            else (y-z) S.<| (x S.<| rest'') -- YZ
        let newpair = if z < 0 then ((x,z):ac) else ((y,z):ac)

        solve newset newpair


headSplit :: S.Seq Int -> (Int, S.Seq Int)
headSplit set = let (hs,ts) = S.splitAt 1 set
                    h  = S.index hs 0
                in  (h,ts)
lastSplit :: S.Seq Int -> (Int, S.Seq Int)
lastSplit set = let (is,ls) = S.splitAt (S.length set - 1) set
                    l  = S.index ls 0
                in  (l,is)