You are given a $0$ indexed integer array usageLimits.

There are usageLimits.length distinct elements labeled from $0$ to usageLimits.length $- 1$. You are allowed to use each element i at most usageLimits[i] times in total across all created groups.

Your goal is to form the maximum number of groups such that:

• Each group contains only distinct elements.

• Each group has a size strictly greater than the size of the previous group.

Return the maximum number of groups that can be constructed under these conditions.

Constraints:

• $1 \leq$ usageLimits.length $\leq 10^5$

• $1 \leq$ usageLimits[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.