Problem:
Score : 100 points

Problem Statement

Taro's summer vacation starts tomorrow, and he has decided to make plans for it now.

The vacation consists of N days.
For each i (1 \leq i \leq N), Taro will choose one of the following activities and do it on the i-th day:

A: Swim in the sea. Gain a_i points of happiness.

B: Catch bugs in the mountains. Gain b_i points of happiness.

C: Do homework at home. Gain c_i points of happiness.

As Taro gets bored easily, he cannot do the same activities for two or more consecutive days.

Find the maximum possible total points of happiness that Taro gains.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq a_i, b_i, c_i \leq 10^4

Input

Input is given from Standard Input in the following format:

N
a_1 b_1 c_1
a_2 b_2 c_2
:
a_N b_N c_N

Output

Print the maximum possible total points of happiness that Taro gains.

Sample Input 1

3
10 40 70
20 50 80
30 60 90

Sample Output 1

210

If Taro does activities in the order C, B, C, he will gain 70 + 50 + 90 = 210 points of happiness.

Sample Input 2

1
100 10 1

Sample Output 2

100

Sample Input 3

7
6 7 8
8 8 3
2 5 2
7 8 6
4 6 8
2 3 4
7 5 1

Sample Output 3

46

Taro should do activities in the order C, A, B, A, C, B, A.

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

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE TypeSynonymInstances #-}
{-# LANGUAGE FlexibleInstances #-}
module Main where

import Data.Char (isSpace)
import Data.List (unfoldr)
import qualified Data.Vector.Unboxed as U
import qualified Data.ByteString.Char8 as C
import qualified Data.ByteString.Unsafe as B

type Parser a = C.ByteString -> Maybe (a, C.ByteString)

parseInt :: Parser Int
parseInt = C.readInt . C.dropWhile isSpace

getInts :: IO [Int]
getInts = unfoldr parseInt <$> C.getLine

getIntVec :: Int -> IO (U.Vector Int)
getIntVec n = U.unfoldrN n parseInt <$> C.getLine

----------------------------
pair (f, g) x = (f x, g x)
cross (f, g) (x, y) = (f x, g y)

newtype Fix f = In { out :: f (Fix f) }

newtype Cofree f a = Cf { unCf :: (a, f (Cofree f a)) }
extract :: Cofree f t -> t
extract = fst . unCf
sub :: Functor f => Cofree f a -> f (Cofree f a)
sub = snd . unCf

newtype Free f a = Fr { unFr :: Either a (f (Free f a)) }
inject :: a -> Free f a
inject = Fr . Left

-- catamorphism
cata :: Functor f => (f a -> a) -> Fix f -> a
cata phi = phi . fmap (cata phi) . out
-- anamorphism
ana :: Functor f => (a -> f a) -> a -> Fix f
ana psi = In . fmap (ana psi) . psi
-- hylomorphism
hylo :: Functor f => (f b -> b) -> (a -> f a) -> a -> b
hylo phi psi = cata phi . ana psi -- phi . fmap (hylo phi psi) . psi
-- metamorphism
meta :: Functor f => (f a -> a) -> (a -> f a) -> Fix f -> Fix f
meta phi psi = ana psi . cata phi -- In . fmap (meta phi psi) . out
-- paramorphism
para :: Functor f => (f (Fix f, t) -> t) -> Fix f -> t
para phi = phi . fmap (pair (id, para phi)) . out
-- apomorphism
apo :: Functor f => (t -> f (Either (Fix f) t)) -> t -> Fix f
apo psi = In . fmap (uncurry either (id, apo psi)) . psi
-- histomorphism
histo :: Functor f => (f (Cofree f t) -> t) -> Fix f -> t
histo phi = extract . cata (Cf . pair (phi, id))
-- futumorphism
futu :: Functor f => (t -> f (Free f t)) -> t -> Fix f
futu psi = ana (uncurry either (psi, id) . unFr) . inject
-- chronomorphism
chrono :: Functor f => (f (Cofree f b) -> b) -> (a -> f (Free f a)) -> a -> b
chrono phi psi = histo phi . futu psi
-- cochronomorphism
cochrono :: Functor f => (f (Cofree f t) -> t) -> (t -> f (Free f t)) -> Fix f -> Fix f
cochrono phi psi = futu psi . histo phi
-- zygomorphism
zygo :: Functor f => (f a -> a) -> (f (a, b) -> b) -> Fix f -> b
zygo f phi = snd . cata (pair (f . fmap fst, phi))
-- cozygomorphism
cozygo :: Functor f => (a -> f a) -> (b -> f (Either a b)) -> b -> Fix f
cozygo f psi = ana (uncurry either (fmap Left . f, psi)) . Right
-- dynamorphism
dyna :: Functor f => (f (Cofree f b) -> b) -> (a -> f a) -> a -> b
dyna f g = chrono f (fmap inject . g) -- histo f . ana g
-- codynamorphism
codyna :: Functor f => (f b -> b) -> (a -> f (Free f a)) -> a -> b
codyna f g = chrono (f . fmap extract) g
-- mutumorphism
mutu :: Functor f => (a -> b) -> (f a -> a) -> Fix f -> b
mutu proj phi = proj . cata phi
-- comutumorphism
comutu :: Functor f => (b -> a) -> (a -> f a) -> b -> Fix f
comutu proj psi = ana psi . proj


foldn (c, f) 0 = c
foldn (c, f) n = f (foldn (c, f) (n-1))

paran (c, f) 0 = c
paran (c, f) n = f n (paran (c, f) (n-1))

---------------------------------------------------------

getTriple = do
  (x:y:z:_) <- getInts
  return (x, y, z)

main :: IO ()
main = do
  n <- readLn :: IO Int
  xs <- U.replicateM n getTriple
  print $ solve xs (n-1)

type ABC = (Int, Int, Int)

data NonEmptyListF a = NonEmptyListF ABC (Maybe a) deriving (Show, Functor)
type NonEmptyList = Fix NonEmptyListF
instance Show NonEmptyList where
  show (In (NonEmptyListF h Nothing)) = show h ++ ":[]"
  show (In (NonEmptyListF h (Just t))) = show h ++ ":" ++ show t

type Point = Int
type Score = (Point, Point, Point)

max3 (x,y,z) = max x (max y z)

solve vec = max3 . dyna phi psi
  where
    psi 0 = NonEmptyListF (vec U.! 0) Nothing
    psi i = NonEmptyListF (vec U.! i) (Just (i-1))

    phi :: NonEmptyListF (Cofree NonEmptyListF Score) -> Score
    phi (NonEmptyListF abc Nothing) = abc
    phi (NonEmptyListF (a, b, c) (Just t)) =
      let (a', b', c') = extract t
      in (max (a+b') (a+c'), max (b+a') (b+c'), max (c+a') (c+b'))