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: Accepted)

--prewritten code: https://github.com/antma/algo
{-# LANGUAGE BangPatterns #-}
{-# Options_GHC -O2 #-}
import Data.ByteString.Builder
import Data.Monoid
import System.IO
import qualified Data.ByteString.Char8 as C
import Data.Char
import Data.Array
import qualified Data.Array.Unboxed as UA
import Data.Int

ru, ri :: C.ByteString -> Int

ru = C.foldl' (\a c -> a * 10 - 48 + ord c) 0
ri s
  | C.head s == '-' = negate $ ru $ C.tail s
  | otherwise = ru s

solve :: [Int] -> Builder
solve (n:z) = (int64Dec $fst $ x ! 0) <> char7 '\n'
  where
    a :: UA.UArray Int Int
    a = UA.listArray (0, n - 1) $ take n z
    f :: Int -> (Int64, Int64)
    f !k = (max (v0 + w) (v1 - w), max (v0 - w) (v1 + w))
      where
        (!v0, !v1) = x ! (succ k)
        !w = fromIntegral $! a UA.! k
    x = listArray (0, n) $ (map f [ 0 .. n - 1]) ++ [(0, div minBound 2)]

main :: IO ()
main = hPutBuilder stdout . solve . map ri . C.words =<< C.getContents