You are given an integer array flowers of size $n$, where flowers[i] represents the beauty of the $i$-th flower.

A garden is considered valid if:

• It contains at least $2$ flowers.

• The first flower and the last flower in the garden have the same beauty value.

You want to produce a valid garden by removing zero or more flowers from the original array flowers while maintaining the relative order of the remaining flowers.

The beauty of a garden is the sum of the beauty values of all its flowers.

Return the maximum possible beauty of a valid garden.

Constraints:

• $2 \leq$ flowers.length $\leq 10^5$

• $-10^4 \leq$ flowers[i] $\leq 10^4$

• It is possible to create a valid garden by removing some (possibly none) flowers.

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.