Given an integer array nums, consider every non empty contiguous subarray of nums. For each such subarray, define its range as the difference between its maximum element and its minimum element.

Return the sum of these ranges over all non empty contiguous subarrays of nums.

Note: A follow up asks whether you can solve this in $O(n)$ time.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $-10^9 \leq$ nums[i] $\leq 10^9$

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.