You are given an integer n. Your goal is to reduce it to $0$ by repeatedly performing either of the following bit operations:

• Flip the rightmost bit (bit at position $0$) of n.

• Flip the bit at position $i$ (for $i > 0$) only if the bit at position $i - 1$ is $1$ and all bits from position $i - 2$ down to $0$ are set to $0$.

Determine and return the minimum number of these operations required to reduce n to $0$.

Constraints:

• $0 \leq$ n $\leq 10^9$

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 on how to solve this problem.

Implement your solution in the following coding playground.