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 '.'

The problem can be solved by dividing it into two distinct phases. First, gravity is simulated in the original box by allowing each stone to move as far right as possible within its row until it encounters either an obstacle or another ...