Problem:
Score : 400 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, arranged in a row in this order.

You can perform the following operation on this integer sequence any number of times:

Operation: Choose an integer i satisfying 1 \leq i \leq N-1. Multiply both A_i and A_{i+1} by -1.

Let B_1, B_2, ..., B_N be the integer sequence after your operations.

Find the maximum possible value of B_1 + B_2 + ... + B_N.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

-10^9 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value of B_1 + B_2 + ... + B_N.

Sample Input 1

3
-10 5 -4

Sample Output 1

19

If we perform the operation as follows:

Choose 1 as i, which changes the sequence to 10, -5, -4.

Choose 2 as i, which changes the sequence to 10, 5, 4.

we have B_1 = 10, B_2 = 5, B_3 = 4. The sum here, B_1 + B_2 + B_3 = 10 + 5 + 4 = 19, is the maximum possible result.

Sample Input 2

5
10 -4 -8 -11 3

Sample Output 2

30

Sample Input 3

11
-1000000000 1000000000 -1000000000 1000000000 -1000000000 0 1000000000 -1000000000 1000000000 -1000000000 1000000000

Sample Output 3

10000000000

The output may not fit into a 32-bit integer type.

Solution in Haskell (GHC 7.10.3) (judge verdict: Runtime Error)

import Control.Monad
import Control.Applicative
import Data.List
import qualified Data.Map as M
--import qualified Data.Vector as V
--import qualified Data.Vector.Mutable as VM

getBysplit = map read . words <$> getLine

main :: IO()
main = do
  n <- readLn :: IO Int
  l <- getBysplit :: IO [Int]
  print $ solve l


solve :: [Int] -> Int
solve lst = let
              ls = (sort . filter (<0)) lst
              bs = (sort . filter (>=0)) lst
              ans = if even $ length ls
                    then sum bs - sum ls
                    else let
                          temp1 = sum $ init ls
                          temp2 = sum $ tail bs
                          temp3 = if - last ls > head bs
                                  then - last ls - head bs
                                  else last ls + head bs
                          in - temp1 + temp2 + temp3
              in ans