You are given an array of positive integers maximumHeight, where maximumHeight[i] represents the maximum allowable height for the $i$-th tower.

You need to assign a positive integer height to each tower such that:

• The height assigned to the $i$-th tower is less than or equal to maximumHeight[i].

• All tower heights are unique.

Return the maximum possible total sum of heights across all towers. If it is impossible to assign valid heights to every tower, return $-1$.

Constraints:

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

• $1 \leq$ maximumHeight[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.