You are given two $0$ indexed integer arrays nums and colors, both of length n.

The value nums[i] represents the amount of money at the $i^{ ext{th}}$ house, and colors[i] represents the color of the $i^{ ext{th}}$ house.

You want to rob houses to maximize the total amount of money robbed. You cannot rob two adjacent houses if they have the same color.

Return the maximum amount of money you can rob.

Constraints:

• $1 \leq$ n $==$ nums.length $==$ colors.length $\leq 10^5$

• $1 \leq$ nums[i], colors[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.