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 8.8.3) (judge verdict: Wrong Answer)

{-# LANGUAGE BangPatterns        #-}
{-# LANGUAGE FlexibleContexts    #-}
{-# LANGUAGE MultiWayIf          #-}
{-# LANGUAGE RankNTypes          #-}
{-# LANGUAGE ScopedTypeVariables #-}
import           Control.Monad.State
import qualified Data.ByteString.Char8 as BS
import           Data.Char
import qualified Data.Vector.Unboxed   as VU

main :: IO ()
main = do
  n <- readLn :: IO Int
  abcs <- readLnAsUVecWith3Tuple unconsInt n

  print $ solve n abcs


solve :: Int -> VU.Vector (Int,Int,Int) -> Int
solve n abcs = go 1 $ abcs VU.! 0
  where go :: Int -> (Int,Int,Int) -> Int
        go m (a,b,c)
          | m == n = maximum [a,b,c]
          | otherwise = let (a',b',c') = abcs VU.! m
                        in go (m+1) ((a + max b' c'),(b + max c' a'),(c + max a' b'))


unconsInt :: StateT BS.ByteString Maybe Int
unconsInt = StateT $ BS.readInt . BS.dropWhile isSpace

-- for unboxed vector
readLnAsUVecWith :: VU.Unbox a => StateT BS.ByteString Maybe a -> Int -> IO (VU.Vector a)
readLnAsUVecWith !st !n = VU.unfoldrN n (runStateT st) <$> BS.getLine

-- example: 1D tuple vector
readLnAsUVecWith3Tuple :: VU.Unbox a => StateT BS.ByteString Maybe a -> Int -> IO (VU.Vector (a,a,a))
readLnAsUVecWith3Tuple !st !n = VU.replicateM n $ (\vec -> (vec VU.! 0, vec VU.! 1, vec VU.! 2)) <$> readLnAsUVecWith st 3