A professional robber plans to rob some houses along a street. These houses are arranged in a circle, which means that the first and the last house are neighbors. The robber cannot rob adjacent houses because they have security alarms installed.

Following the constraints mentioned above and given an integer array money representing the amount of money in each house, return the maximum amount the robber can steal without alerting the police.

Constraints:

• $1\leq$ money.length $\leq 10^3$
• $0\leq$ money[i] $\leq 10^3$

So far, you’ve probably brainstormed some approaches and have an idea of how to solve this problem. Let’s explore some of these approaches and figure out which to follow based on considerations such as time complexity and implementation constraints.

The rule to decide about robbing a particular house is to either rob the current house and skip the adjacent house or skip the current house and rob the adjacent house. The house containing the greater amount will get selected from these two options. For the given set of houses, we must accumulate the robbed amount for all houses according to the rule mentioned above. This requires exhaustive testing of all possible combinations and selecting a combination that gives the maximum robbery amount.

We will have repeated subcombinations to traverse in multiple computations. Also, while robbing, we cannot allow the first and last houses to be robbed in a single combination because they are neighbors. So, we will divide the houses into two sets, ranging from $1$ ...