Dima and Hares

题意翻译

N个物品排成一排,按照一定顺序将所有物品都拿走，如果拿走某个物品时相邻两个物品都没有被拿过，那么得到的价值为ai；如果相邻的两个物品有一个被拿过（左右无所谓），那么得到的价值为bi；如果相邻的两个物品都被拿走了，那么对应价值为ci。问能够获得的最高价值为多少。

题目描述

Dima liked the present he got from Inna very much. He liked the present he got from Seryozha even more. Dima felt so grateful to Inna about the present that he decided to buy her $ n $ hares. Inna was very happy. She lined up the hares in a row, numbered them from 1 to $ n $ from left to right and started feeding them with carrots. Inna was determined to feed each hare exactly once. But in what order should she feed them? Inna noticed that each hare radiates joy when she feeds it. And the joy of the specific hare depends on whether Inna fed its adjacent hares before feeding it. Inna knows how much joy a hare radiates if it eats when either both of his adjacent hares are hungry, or one of the adjacent hares is full (that is, has been fed), or both of the adjacent hares are full. Please note that hares number 1 and $ n $ don't have a left and a right-adjacent hare correspondingly, so they can never have two full adjacent hares. Help Inna maximize the total joy the hares radiate. :)

输入输出格式

输入格式

The first line of the input contains integer $ n $ $ (1<=n<=3000) $ — the number of hares. Then three lines follow, each line has $ n $ integers. The first line contains integers $ a_{1} $ $ a_{2} $ $ ... $ $ a_{n} $ . The second line contains $ b_{1},b_{2},...,b_{n} $ . The third line contains $ c_{1},c_{2},...,c_{n} $ . The following limits are fulfilled: $ 0<=a_{i},b_{i},c_{i}<=10^{5} $ . Number $ a_{i} $ in the first line shows the joy that hare number $ i $ gets if his adjacent hares are both hungry. Number $ b_{i} $ in the second line shows the joy that hare number $ i $ radiates if he has exactly one full adjacent hare. Number $ с_{i} $ in the third line shows the joy that hare number $ i $ radiates if both his adjacent hares are full.

输出格式

In a single line, print the maximum possible total joy of the hares Inna can get by feeding them.

输入输出样例

输入样例 #1

4
1 2 3 4
4 3 2 1
0 1 1 0

输出样例 #1

13

输入样例 #2

7
8 5 7 6 1 8 9
2 7 9 5 4 3 1
2 3 3 4 1 1 3

输出样例 #2

44

输入样例 #3

3
1 1 1
1 2 1
1 1 1

输出样例 #3

4