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:

• <code>1 <= n <= 10⁹</code>