Given an integer n, construct a sequence of length $2 imes$ n $- 1$ that satisfies the following conditions:

• The integer $1$ appears exactly once in the sequence.

• Every integer i from $2$ to n appears exactly twice in the sequence.

• For each integer i between $2$ and n, the distance between the two occurrences of i is exactly i. That is, if the first occurrence is at index j, the second occurrence is at index j + i.

Return the lexicographically largest valid sequence. It is guaranteed that a valid sequence always exists for the given constraints.

A sequence a is lexicographically larger than a sequence b of the same length if, at the first index where a and b differ, the element in a is greater than the element in b.

Constraints:

• $1 \leq$ n $\leq 20$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.