You are given an integer array nums of even length n and an integer k.

In one operation, you can choose any index i satisfying $0 \leq$ i $<$ n and replace nums[i] with any integer in the range $[0, k]$.

Your goal is to choose an integer X such that for all indices i where $0 \leq$ i $<$ n $/ 2$, the condition $|$nums[i] $-$ nums[n - i - 1]$| = X$ holds true.

Return the minimum number of operations required to make the difference equal for all such pairs.

Constraints:

• $2 \leq$ n $==$ nums.length $\leq 10^5$

• n is even.

• $0 \leq$ nums[i] $\leq$ k $\leq 10^5$

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.