You are given a $2$D integer array buildings where buildings[i] $= [$start_i, end_i, height_i$]$ denotes that the $i^{ {th}}$ building exists along the half open interval $[$start_i, end_i$)$ with a height of height_i.

The average height of a segment is defined as the total sum of heights of all buildings present in that segment divided by the total number of buildings in that segment, rounded down to the nearest integer.

Return a sorted list of non overlapping segments $[$start, end, avg_height$]$ sorted by start in ascending order such that:

• Every point within $[$start, end$)$ is covered by at least $1$ building.

• The average height avg_height is identical for all points within $[$start, end$)$.

• There are no two adjacent segments with the same average height that share a boundary point (adjacent segments with the same average height must be merged into a single segment).

• Intervals with no buildings are omitted from the output.

Constraints:

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

• buildings[i].length $= 3$

• $0 \leq$ start_i $<$ end_i $\leq 10^8$

• $1 \leq$ height_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.