You are given two integers red and blue, representing the count of red and blue balls available.

You want to build a triangle of balls to achieve the maximum possible height subject to the following conditions:

• The $1^{ ext{st}}$ row has $1$ ball, the $2^{ ext{nd}}$ row has $2$ balls, the $3^{ ext{rd}}$ row has $3$ balls, and in general, the $i^{ ext{th}}$ row has $i$ balls.

• Every ball in a single row must share the same color.

• Consecutive rows must alternate in color.

Return the maximum height of a triangle that can be constructed.

Constraints:

• $1 \leq$ red, blue $\leq 100$

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.