Given an integer array nums of length n, which is a permutation of $[0, 1, \dots, n - 1]$.

For any permutation perm of $[0, 1, \dots, n - 1]$, its score is defined as:

$\text{score}(perm) = \sum_{i = 0}^{n - 1} \left| perm[i] - nums[perm[(i + 1) \bmod n]] \right|$

Return the permutation perm that achieves the minimum score. If multiple permutations achieve the minimum score, return the lexicographically smallest permutation among them.

Constraints:

• $2 \leq n =$ nums.length $\leq 14$

• nums is a permutation of $[0, 1, 2, \dots, n - 1]$.

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.