P6372 [COCI 2006/2007 #6] PROSTOR

Given the positions of $n$ cuboids in three-dimensional space, determine how many pairs of cuboids overlap with each other. (If they intersect at only a single point, it is also counted.)

The first line contains an integer $n$, representing the number of cuboids. The next $n$ lines each contain six integers. The first three numbers are the coordinates of the lower-left-bottom vertex of the cuboid, and the last three numbers are the coordinates of the upper-right-top vertex of the cuboid.

Output one integer on a single line, representing the number of overlapping cuboid pairs.

#### Constraints For $100\%$ of the testdata, it is guaranteed that $1 \le n \le 10^5$. All coordinates are between $1$ and $999$. Each cuboid is guaranteed to be parallel to the coordinate planes. #### Notes **This problem is translated from [COCI2006-2007](https://hsin.hr/coci/archive/2006_2007/) [CONTEST #6](https://hsin.hr/coci/archive/2006_2007/contest6_tasks.pdf) *T6 PROSTOR***。 Translated by ChatGPT 5