Eccoci.

An axis-aligned cuboid, specified by parameters $\{(x_0, y_0, z_0), (dx, dy, dz)\}$, consists of all points $(X,Y,Z)$ such that $x_0 \le X \le x_0 + dx$, $y_0 \le Y \le y_0 + dy$ and $z_0 \le Z \le z_0 + dz$. The volume of the cuboid is the product, $dx \times dy \times dz$. The combined volume of a collection of cuboids is the volume of their union and will be less than the sum of the individual volumes if any cuboids overlap.

Let $C_1, \dots, C_{50000}$ be a collection of $50000$ axis-aligned cuboids such that $C_n$ has parameters

\begin{align} x_0 &= S_{6n - 5} \bmod 10000\\ y_0 &= S_{6n - 4} \bmod 10000\\ z_0 &= S_{6n - 3} \bmod 10000\\ dx &= 1 + (S_{6n - 2} \bmod 399)\\ dy &= 1 + (S_{6n - 1} \bmod 399)\\ dz &= 1 + (S_{6n} \bmod 399) \end{align}

where $S_1,\dots,S_{300000}$ come from the "Lagged Fibonacci Generator":

• For $1 \le k \le 55$, $S_k = [100003 - 200003k + 300007k^3] \pmod{1000000}$.
• For $56 \le k$, $S_k = [S_{k -24} + S_{k - 55}] \pmod{1000000}$.

Thus, $C_1$ has parameters $\{(7,53,183),(94,369,56)\}$, $C_2$ has parameters $\{(2383,3563,5079),(42,212,344)\}$, and so on.

The combined volume of the first $100$ cuboids, $C_1, \dots, C_{100}$, is $723581599$.

What is the combined volume of all $50000$ cuboids, $C_1, \dots, C_{50000}$?