You are given an integer array prices where prices[i] represents the price of the $(i + 1)^{ ext{th}}$ fruit.

Fruits are presented in order from the $1^{ ext{st}}$ fruit to the $n^{ ext{th}}$ fruit, where $n$ is the length of prices.

When acquiring fruits, you can follow these rules:

• If you purchase the $i^{ ext{th}}$ fruit (where $1 \leq i \leq n$) for prices[i - 1] coins, you are eligible to claim the next $i$ fruits for free, which includes all fruits from index $i + 1$ up to index $i + i$.

• You may still decide to purchase a fruit even if you are allowed to claim it for free.

Return the minimum total number of coins required to collect all the fruits.

Constraints:

• $1 \leq$ prices.length $\leq 10^5$

• $1 \leq$ prices[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.