1718 - Construct the Lexicographically Largest Valid Sequence\.

Medium

Given an integer n, find a sequence that satisfies all of the following:

• The integer 1 occurs once in the sequence.

• Each integer between 2 and n occurs twice in the sequence.

• For every integer i between 2 and n, the distance between the two occurrences of i is exactly i.

The distance between two numbers on the sequence, a[i] and a[j], is the absolute difference of their indices, |j - i|.

Return the lexicographically largest sequence_. It is guaranteed that under the given constraints, there is always a solution._

A sequence a is lexicographically larger than a sequence b (of the same length) if in the first position where a and b differ, sequence a has a number greater than the corresponding number in b. For example, [0,1,9,0] is lexicographically larger than [0,1,5,6] because the first position they differ is at the third number, and 9 is greater than 5.

Example 1:

Input: n = 3

Output: 3,1,2,3,2

Explanation: 2,3,2,1,3 is also a valid sequence, but 3,1,2,3,2 is the lexicographically largest valid sequence.

Example 2:

Input: n = 5

Output: 5,3,1,4,3,5,2,4,2

Constraints:

• 1 <= n <= 20