elimination-game

Elimination Game

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

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

Given the integer <code>n</code>, return the last number that remains in <code>arr</code>.

&nbsp;
Example 1:

<pre>
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]
</pre>

Example 2:

<pre>
Input: n = 1
Output: 1
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 109</code></li>
</ul>

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