You have a list `arr` of all integers in the range `[1, n]` sorted in a strictly increasing order. Apply the following algorithm on `arr`:

- Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.
- Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.
- Keep repeating the steps again, alternating left to right and right to left, until a single number remains.

Given the integer `n`, return the last number that remains in `arr`.

Example 1:

    Input: n = 9
    Output: 6
    Explanation:
    arr = [1, 2, 3, 4, 5, 6, 7, 8, 9]
    arr = [2, 4, 6, 8]
    arr = [2, 6]
    arr = [6]

Example 2:

    Input: n = 1
    Output: 1

Constraints:

- `1 <= n <= 109`