You are given an array of positive integers nums.

In a single operation, you can swap any two adjacent elements if they have the same count of set bits in their binary representation. You are allowed to perform this operation any number of times.

Return true if it is possible to sort the array in ascending order, or false otherwise.

Constraints:

• $1 \leq$ nums.length $\leq 100$

• $1 \leq$ nums[i] $\leq 2^8$

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.