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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program EDPCC
    implicit none
    integer(8)::N,i,j,flg,flg_next,calced
    integer(8),allocatable,dimension(:,:)::H
    integer(8),allocatable,dimension(:)::dp
    read(5,*)N
    allocate(H(3,N))
    allocate(dp(N))
    do i=1,N
        read(5,*)(H(j,i),j=1,3)
    end do

    flg=0
    do i=1,N
        calced=0
        do j=1,3
            if(j/=flg)then
                if(calced==0)then
                    if(i==1)then
                        dp(i)=H(j,i)
                        flg_next=j
                    else
                        dp(i)=dp(i-1)+H(j,i)
                        flg_next=j
                    end if
                    calced=1
                else
                    if(i==1)then
                        if(H(j,i)>dp(i))then
                            dp(i)=H(j,i)
                            flg_next=j
                        end if
                    else if(dp(i-1)+H(j,i)>dp(i))then
                        dp(i)=dp(i-1)+H(j,i)
                        flg_next=j
                    end if
                end if
            end if
        end do
        flg=flg_next
    end do

    print'(i0)',dp(N)
end program EDPCC