E. Brainless Brainstorming
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Michael has $$$N$$$ meeting slots numbered $$$1$$$ through $$$N$$$ ($$$1 \leq N \leq 1000$$$) on Brainstorming day. He would like to invite three of his employees, Jim, Dwight, and Kevin into his office to discuss ideas. During each time slot $$$i$$$, each employee will discuss a different number of ideas, denoted $$$a_i, b_i$$$, and $$$c_i$$$ ($$$0 \leq a_i, b_i, c_i \leq 1000$$$).

Michael can only invite at most one employee into his office during each meeting slot. In addition, Michael cannot have meetings during two consecutive meeting slots since he will get a headache. What is the maximum total number of ideas that can be discussed throughout the day?

Input

A single integer $$$N$$$ representing the number of meeting slots ($$$1 \leq N \leq 10^3$$$).

Then, there will be three lines, each with $$$N$$$ integers. These lines represent $$$a_i, b_i$$$, and $$$c_i$$$, respectively.

Output

A single integer representing the maximum total number of ideas that can be discussed.

Example
Input
5
3 0 3 1 2
3 1 4 4 4
1 2 1 4 4
Output
11