You are given a $0$ indexed integer array nums of length n.

The average difference at index i is the absolute difference between the average of the first $i + 1$ elements of nums and the average of the last $n - i - 1$ elements of nums. Both averages must be rounded down to the nearest integer.

Return the index with the minimum average difference. If there are multiple indices with the same minimum average difference, return the smallest index.

Note:

• The average of $k$ elements is the sum of the $k$ elements divided by $k$, rounded down to the nearest integer using integer division.

• The average of $0$ elements is considered to be $0$.

Constraints:

• $1 \leq$ 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.