Given a three-dimensional space of $[1, n] \times [1, n] \times [1, n]$. You're required to place some $1 \times 1 \times 1$ cubes to make this 3D space look $n \times n$ square from above, from left and from front, while the plane $xOy$ stand for the ground and $z$ axis describes the height.
But placing these cubes must follow some restrictions. Obviously, it must obey the gravity laws. It means, when beneath a cube is empty, the height of this cube will drop one, until its height is exactly $1$ (touch the ground) or there is another cube below it.
And besides that, placing cubes has some prices. If a cube is placed at an integer coordinate $(x, y, z)$, the price will be $x \times y^2 \times z$.
Now, satisfying all the requirements above, you're required to calculate the minimum costs and the maximum costs.