--description--

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 $x_0 ≤ X ≤ x_0 + dx$, $y_0 ≤ Y ≤ y_0 + dy$ and $z_0 ≤ Z ≤ z_0 + dz$. The volume of the cuboid is the product, $dx × dy × dz$. 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 $C_1, \ldots, C_{50000}$ be a collection of 50000 axis-aligned cuboids such that $C_n$ has parameters

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

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

For $1 ≤ k ≤ 55$, $S_k = [100003 - 200003k + 300007k^3] \; (modulo \; 1000000)$

For $56 ≤ k$, $S_k = [S_{k - 24} + S_{k - 55}] \; (modulo \; 1000000)$

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, $C_1, \ldots, C_{100}$, is 723581599.

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

--hints--

combinedValueOfCuboids() should return 328968937309.

assert.strictEqual(combinedValueOfCuboids(), 328968937309);

--seed--

--seed-contents--

function combinedValueOfCuboids() {

  return true;
}

combinedValueOfCuboids();

--solutions--

// solution required