You are given three integers x, y, and z.

You have:

• x strings equal to "AA"

• y strings equal to "BB"

• z strings equal to "AB"

You want to concatenate a subset of these strings to create the longest possible string such that it does not contain "AAA" or "BBB" as a substring.

Return the maximum possible length of the resulting string.

Constraints:

• $1 \leq$ x, y, z $\leq 50$

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.