public class Solution
extends Object
390 - Elimination Game\.
Medium
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