Given an integer array nums of even length n.

A cyclic rotation of nums is defined as shifting all elements to the left or right cyclically. A cyclic rotation is considered good if the sum of its first n / $2$ elements is strictly greater than the sum of its last n / $2$ elements.

Return the total number of good cyclic rotations of nums.

Constraints:

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

• $1 \leq$ nums[i] $\leq 10^9$

• n is even.

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.