Given an integer array nums and two integers lower and upper, count how many index pairs (i, j) satisfy all of the following:
the indices are distinct with i < j, and the sum nums[i] + nums[j] lies within the inclusive range from lower to upper.

Return the total number of such pairs.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• nums.length $==$ n

• $-10^9 \leq$ nums[i] $\leq 10^9$

• $-10^9 \leq$ lower $\leq$ upper $\leq 10^9$

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.