An $n$ bit Gray code sequence is a sequence of $2^n$ integers where:

• The first integer is $0$.

• Every integer appears at most once in the sequence.

• The binary representation of every pair of adjacent integers differs by exactly one bit.

• The binary representation of the first and last integers differs by exactly one bit.

Given an integer n, return any valid $n$ bit Gray code sequence.

Constraints:

• $1 \leq$ n $\leq 16$

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.