# 0390. Elimination Game

<https://leetcode.com/problems/elimination-game>

## Description

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`

## ac

```java
```