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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n=gets.to_i
abc=[]
n.times do|i|
	abc[i]=gets.chomp.split(" ").map(&:to_i)
end
dp=Array.new(n)
flag=-1
way1=abc[0][0]
way2=abc[0][1]
way3=abc[0][2]
if way1>way2 and way1>way3
	dp[0]=way1
	flag=0
elsif way2>way1 and way2>way3
	dp[0]=way2
	flag=1
else
	dp[0]=way3
	flag=2
end
for i in 1..n-1
	max=0
	tmp_flg=-1
	for j in 0..2
		if j==flag
			next
		end
		result=dp[i-1]+abc[i][j]
		if(max<result)
			max=result
			tmp_flg=j
		end
	end
	flag=tmp_flg
	dp[i]=max
end
p dp[n-1]