You are given an $m \times n$ matrix of characters boxGrid representing a side-view of a box. Each cell in the box contains one of the following:

• A stone '#'

• A stationary obstacle '*'

• An empty space '.'

The box is rotated $90$ degrees clockwise, causing stones to fall due to gravity. Each stone falls downward until it lands on an obstacle, another stone, or the bottom of the box. Gravity does not affect obstacle positions, and the rotation’s inertia does not affect stones’ horizontal positions.

It is guaranteed that every stone in boxGrid initially rests on an obstacle, another stone, or the bottom of the box.

Return an $n \times m$ matrix representing the box after the rotation described above.

Note: Gravity acts after the rotation, so stones fall in the direction of the new bottom (i.e., toward the last column of the original orientation).

Constraints:

• m == boxGrid.length

• n == boxGrid[i].length

• $1 \leq$ m, n $\leq 500$

• boxGrid[i][j] is either '#', '*', or '.'

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.