Given an integer n, you start with a list of integers from $1$ to n sorted in ascending order from left to right.

You repeatedly apply the following elimination operations until only one integer remains:

• Starting from the left, remove every second integer beginning with the second element from the left.

• Starting from the right, remove every second integer beginning with the second element from the right.

• Keep alternating between left to right and right to left passes until a single number is left.

Return the last remaining integer.

Constraints:

• $1 \leq$ n $\leq 10^{15}$

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.