Problem:
Score : 300 points

Problem Statement

There are N sightseeing spots on the x-axis, numbered 1, 2, ..., N.
Spot i is at the point with coordinate A_i.
It costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis.

You planned a trip along the axis.
In this plan, you first depart from the point with coordinate 0, then visit the N spots in the order they are numbered, and finally return to the point with coordinate 0.

However, something came up just before the trip, and you no longer have enough time to visit all the N spots, so you decided to choose some i and cancel the visit to Spot i.
You will visit the remaining spots as planned in the order they are numbered.
You will also depart from and return to the point with coordinate 0 at the beginning and the end, as planned.

For each i = 1, 2, ..., N, find the total cost of travel during the trip when the visit to Spot i is canceled.

Constraints

2 \leq N \leq 10^5

-5000 \leq A_i \leq 5000 (1 \leq i \leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print N lines.
In the i-th line, print the total cost of travel during the trip when the visit to Spot i is canceled.

Sample Input 1

3
3 5 -1

Sample Output 1

12
8
10

Spot 1, 2 and 3 are at the points with coordinates 3, 5 and -1, respectively.
For each i, the course of the trip and the total cost of travel when the visit to Spot i is canceled, are as follows:

For i = 1, the course of the trip is 0 \rightarrow 5 \rightarrow -1 \rightarrow 0 and the total cost of travel is 5 + 6 + 1 = 12 yen.

For i = 2, the course of the trip is 0 \rightarrow 3 \rightarrow -1 \rightarrow 0 and the total cost of travel is 3 + 4 + 1 = 8 yen.

For i = 3, the course of the trip is 0 \rightarrow 3 \rightarrow 5 \rightarrow 0 and the total cost of travel is 3 + 2 + 5 = 10 yen.

Sample Input 2

5
1 1 1 2 0

Sample Output 2

4
4
4
2
4

Sample Input 3

6
-679 -2409 -3258 3095 -3291 -4462

Sample Output 3

21630
21630
19932
8924
21630
19288

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Applicative
import Control.Monad
import Control.Monad.ST
-- import qualified Data.ByteString as BS
import Data.Functor
import Data.Function
import Data.Monoid
import Data.Maybe
import Data.List
import qualified Data.Foldable as Foldable
--import qualified Data.Set as Set
--import qualified Data.Sequence as Sequence
import Data.List.Split
import Data.Bits
import Data.Char
import Data.Ix
import Data.Ratio
import Data.Ord
import Data.Fixed
import Data.Tuple
--import Data.Array
--import Data.Array.Unboxed
import Data.Array.IArray
import Data.Array.MArray
import Data.Array.IO
import Data.Array.ST
import Data.IORef
import Data.STRef
import Text.Printf
import System.IO
-- import System.IO.Unsafe
 
-- templete
readInt = read :: String -> Int
readInteger = read :: String -> Integer
readDouble = read :: String -> Double
getInt = readLn :: IO Int
getInts = map readInt . words <$> getLine
getInteger = readLn :: IO Integer
getIntegers = map readInteger . words <$> getLine
getDouble = readLn :: IO Double
getDoubles = map readDouble . words <$> getLine
sjoin :: (Show a) => [a] -> String
sjoin = unwords . map show
tjoin :: (Show a, Show b) => (a, b) -> String
tjoin (x, y) = show x ++ (' ' : show y)
cond :: a -> a -> Bool -> a
cond t f c = if c then t else f
apply2 :: (a -> a -> b) -> [a] -> b
apply2 f [x,y] = f x y
apply3 :: (a -> a -> a -> b) -> [a] -> b
apply3 f [x,y,z] = f x y z
apply4 :: (a -> a -> a -> a -> b) -> [a] -> b
apply4 f [x,y,z,w] = f x y z w
fnTuple :: (a -> b, a -> c) -> a -> (b, c)
fnTuple (f,g) a = (f a, g a)
replace :: (Eq a) => a -> a -> [a] -> [a]
replace x y = map (\z -> if z==x then y else z)
binMap :: (a -> a -> b) -> [a] -> [b]
binMap f (x:xs@(y:_)) = f x y : binMap f xs
binMap _ _ = []
splitRec :: Int -> [a] -> [[a]]
splitRec _ [] = []
splitRec n xs = let (y,ys) = splitAt n xs in y : splitRec n ys
infixl 7 `divCeil`
divCeil :: Integral a => a -> a -> a
x `divCeil` y = (x+y-1) `div` y
coverC :: Ord a => (a, a) -> a -> Bool
coverC (l,r) x = l<=x && x<=r
coverH :: Ord a => (a, a) -> a -> Bool
coverH (l,r) x = l<=x && x<r
ibsearch :: (Int -> Bool) -> (Int,Int) -> Int
ibsearch f (ok,ng) = if abs (ok-ng) <= 1 then ok else let mid = (ok + ng) `div` 2 in ibsearch f (if f mid then (mid,ng) else (ok,mid))
whenM :: Monad m => m Bool -> m () -> m ()
whenM c a = c >>= flip when a
unconsU :: [a] -> (a, [a])
unconsU (x:xs) = (x, xs)
-- templete

triMap f (x:xs@(y:z:_)) = f x y z : triMap f xs
triMap _ _ = []

main = do
    n <- getInt
    a <- (0:) . (++[0]) <$> getInts
    let def_cost = sum . binMap (\x y -> abs (x-y)) $ a
    let ress = map (+def_cost) . triMap (\x y z -> abs (x-z) - abs (x-y) - abs (y-z)) $ a
    mapM_ print ress