You are given two integer arrays lane1 and lane2 of equal length, representing the number of coins available at each mile along a two lane freeway.

Mario drives along a contiguous stretch of the freeway covering at least $1$ mile. He travels according to the following rules:

• He starts driving in lane1.

• He may switch to lane2 at most once.

• After driving in lane2, he may switch back to lane1 at most once.

• He cannot switch back to lane2 again.

In other words, his journey consists of up to three consecutive segments: an initial segment in lane1, a middle segment in lane2, and a final segment in lane1. Any of these segments may be empty, but the total distance driven across all chosen segments must be at least $1$ mile.

Return the maximum total number of coins Mario can collect.

Constraints:

• $1 \leq$ lane1.length $=$ lane2.length $\leq 10^5$

• $-10^9 \leq$ lane1[i], lane2[i] $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.