These problems are from the atcoder DP contest, and were transferred onto DMOJ. All problem statements were made by several atcoder users. As there is no access to the test data, all data is randomly generated. If there are issues with the statement or data, please contact or on slack.
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 \le i \le 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.
- All values in input are integers.
- ~1 \le N \le 10^5~
- ~1 \le a_i, b_i, c_i \le 10^4~
The first line will contain the integer ~N~.
The next ~N~ lines will each contain 3 space separated integers, ~a_i, b_i, c_i~.
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
Explanation For Sample 1
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
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
Explanation For Sample 3
Taro should do activities in the order C, A, B, A, C, B, A.