There are several square blocks dropped onto the horizontal axis in a sequence. You are given a $2\text{D}$ integer array positions where each positions[i] = [left_i, sideLength_i] represents the $i^{th}$ square with a side length of sideLength_i falling such that its bottom left corner lands at the coordinate left_i.

Each block falls from an infinite height down to the ground or onto the top of previously dropped blocks. A square lands on top of another square if their horizontal intervals overlap across a non-zero length. If two squares only touch at their boundary edges, they do not stack on each other.

After dropping each block, determine the maximum height among all dropped squares.

Return an array of integers representing the maximum height observed after each respective square is dropped.

Constraints:

• $1 \leq$ positions.length $\leq 1000$

• $1 \leq$ left_i $\leq 10^8$

• $1 \leq$ sideLength_i $\leq 10^6$

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.