Given two integers left and right, return the total count of numbers in the inclusive range $[$left, right$]$ that have a prime number of set bits in their binary representation.

Recall that the number of set bits is the total count of $1$’s present in the binary representation of an integer.

Constraints:

• $1 \le$ left $\le$ right $\le 10^6$

• $0 \le$ right $-$ left $\le 10^4$

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.