Given an integer array nums, you may perform the following operation any number of times: choose an index i and increase nums[i] by $1$.

Return the minimum number of operations required to make every value in nums distinct.

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.