You are given an integer array heights of length n.

A configuration of towers is defined as beautiful if it can be represented by an array result of length n that satisfies the following conditions:

• $1 \leq$ result[i] $\leq$ heights[i] for all $0 \leq i < n$.

• result forms a mountain shape, meaning there exists a peak index $p$ where $0 \leq p < n$ such that:

  • result[i] $\leq$ result[i + 1] for all $0 \leq i < p$

  • result[i] $\geq$ result[i + 1] for all $p \leq i < n - 1$

Return the maximum possible sum of heights among all beautiful tower configurations.

Constraints:

• $1 \leq$ n $==$ heights.length $\leq 10^3$

• $1 \leq$ heights[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.