You are given an integer array prices where prices[i] is the price of a given stock on the $i^{ ext{th}}$ day, an integer array costs of the same length $n$, and an integer cooldown.

You want to maximize your profit by trading the stock according to the following rules:

• You may complete as many transactions as you like, but you cannot hold more than $1$ share of stock at any time (you must sell before you can buy again).

• If you buy the stock on day $i$ and sell it on day $j$ (where $i < j$), the holding duration is $j - i$ days, which incurs a fee of costs[j - i]. The profit obtained from this transaction is prices[j] $-$ prices[i] $-$ costs[j - i].

• After selling the stock on day $j$, a cooldown period of cooldown days is required. This means the next purchase can only be made on or after day $j +$ cooldown $+ 1$.

Return the maximum profit you can achieve.

Constraints:

• $1 \leq n ==$ prices.length $\leq 1500$

• costs.length $== n$

• $1 \leq$ prices[i] $\leq 10^5$

• $0 \leq$ cooldown $\leq n - 1$

• $0 \leq$ costs[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.