You are given an integer array books indexed from $0$, where books[i] denotes the number of books available on the $i^{ {th}}$ shelf.

You want to collect books from a contiguous segment of shelves from index l to index r, where $0 \leq l \leq r <$ books.length. For each shelf i in the range from l to r, you can take $c[i]$ books such that:

• $1 \leq c[i] \leq$ books[i] for all $l \leq i \leq r$

• $c[i] < c[i + 1]$ for all $l \leq i < r$

Return the maximum total number of books you can collect.

Constraints:

• $1 \leq$ books.length $\leq 10^5$

• $0 \leq$ books[i] $\leq 10^5$

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.