# Problem 212: Combined Volume of Cuboids
An axis-aligned cuboid, specified by parameters { (x0,y0,z0), (dx,dy,dz)
}, consists of all points (X,Y,Z) such that x0 ≤ X ≤ x0+dx, y0 ≤ Y ≤
y0+dy and z0 ≤ Z ≤ z0+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 C1,...,C50000 be a collection of 50000
axis-aligned cuboids such that Cn has parameters x0 = S6n-5 modulo
10000y0 = S6n-4 modulo 10000z0 = S6n-3 modulo 10000dx = 1 + (S6n-2
modulo 399)dy = 1 + (S6n-1 modulo 399)dz = 1 + (S6n modulo 399) where
S1,...,S300000 come from the "Lagged Fibonacci Generator": For 1 ≤ k ≤
55, Sk = \[100003 - 200003k + 300007k3\]   (modulo 1000000)For 56 ≤ k,
Sk = \[Sk-24 + Sk-55\]   (modulo 1000000) Thus, C1 has parameters
{(7,53,183),(94,369,56)}, C2 has parameters
{(2383,3563,5079),(42,212,344)}, and so on. The combined volume of the
first 100 cuboids, C1,...,C100, is 723581599. What is the combined
volume of all 50000 cuboids, C1,...,C50000 ?