2256\. Minimum Average Difference

Medium

You are given a **0-indexed** integer array `nums` of length `n`.

The **average difference** of the 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. Both averages should be **rounded down** to the nearest integer.

Return _the index with the **minimum average difference**_. If there are multiple such indices, return the **smallest** one.

**Note:**

*   The **absolute difference** of two numbers is the absolute value of their difference.
*   The **average** of `n` elements is the **sum** of the `n` elements divided (**integer division**) by `n`.
*   The average of `0` elements is considered to be `0`.

**Example 1:**

**Input:** nums = [2,5,3,9,5,3]

**Output:** 3

**Explanation:** 

- The average difference of index 0 is: |2 / 1 - (5 + 3 + 9 + 5 + 3) / 5| = |2 / 1 - 25 / 5| = |2 - 5| = 3. 

- The average difference of index 1 is: |(2 + 5) / 2 - (3 + 9 + 5 + 3) / 4| = |7 / 2 - 20 / 4| = |3 - 5| = 2. 
 
- The average difference of index 2 is: |(2 + 5 + 3) / 3 - (9 + 5 + 3) / 3| = |10 / 3 - 17 / 3| = |3 - 5| = 2. 
 
- The average difference of index 3 is: |(2 + 5 + 3 + 9) / 4 - (5 + 3) / 2| = |19 / 4 - 8 / 2| = |4 - 4| = 0. 
 
- The average difference of index 4 is: |(2 + 5 + 3 + 9 + 5) / 5 - 3 / 1| = |24 / 5 - 3 / 1| = |4 - 3| = 1. 
 
- The average difference of index 5 is: |(2 + 5 + 3 + 9 + 5 + 3) / 6 - 0| = |27 / 6 - 0| = |4 - 0| = 4. 
 
The average difference of index 3 is the minimum average difference so return 3. 

**Example 2:**

**Input:** nums = [0]

**Output:** 0

**Explanation:** 

The only index is 0 so return 0. 

The average difference of index 0 is: |0 / 1 - 0| = |0 - 0| = 0. 

**Constraints:**

*   <code>1 <= nums.length <= 10<sup>5</sup></code>
*   <code>0 <= nums[i] <= 10<sup>5</sup></code>
