Given an array of integers nums, rearrange the elements such that for every index i where $1 \leq$ i $\leq$ nums.length $- 2$, the value at nums[i] is not equal to the average of its immediate neighbors, nums[i - 1] and nums[i + 1].

Return any valid permutation of nums that satisfies this condition.

Note: If multiple valid arrangements exist, return any of them.

Constraints:

• $3 \leq$ nums.length $\leq 10^5$

• $0 \leq$ nums[i] $\leq 10^5$

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.