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Elimination Game

You have a list arr of all integers in the range [1, n] sorted in a strictly increasing order.

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:

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 <= 10^9

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