You are given $n$ boxes labeled from $0$ to $n - 1$. You are provided with the following arrays:

• status: An integer array of length $n$, where status[i] is $1$ if the $i^{ {th}}$ box is open, and $0$ if it is closed.

• candies: An integer array of length $n$, where candies[i] represents the number of candies inside the $i^{ {th}}$ box.

• keys: A $2$D integer array, where keys[i] contains the labels of boxes for which keys can be found inside the $i^{ {th}}$ box.

• containedBoxes: A $2$D integer array, where containedBoxes[i] contains the labels of other boxes located inside the $i^{ {th}}$ box.

• initialBoxes: An integer array containing the labels of the boxes you start with.

You can open a box if you possess it and it is either already open or you have obtained its corresponding key. When you open a box, you collect all the candies inside it, obtain all the keys contained within it, and discover all the new boxes inside it.

Return the maximum number of candies you can collect by opening the available boxes according to these rules.

Constraints:

• n == status.length == candies.length == keys.length == containedBoxes.length

• $1 \leq n \leq 1000$

• status[i] is either $0$ or $1$.

• $1 \leq$ candies[i] $\leq 1000$

• $0 \leq$ keys[i].length $\leq n$

• $0 \leq$ keys[i][j] $< n$

• All values of keys[i] are unique.

• $0 \leq$ containedBoxes[i].length $\leq n$

• $0 \leq$ containedBoxes[i][j] $< n$

• All values of containedBoxes[i] are unique.

• Each box is contained in at most one box.

• $0 \leq$ initialBoxes.length $\leq n$

• $0 \leq$ initialBoxes[i] $< n$

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.