Gleaming the Cubes

As chief engineer of the Starship Interprize, the task of repairing the hyperstellar, cubic, transwarped-out software has fallen on your shoulders. Simply put, you must compute the volume of the intersection of anywhere from 2 to 1000 cubes.

The input data file consists of several sets of cubes for which the volume of their intersections must be computed. The first line of the data file contains a number (from 2 to 1000), which indicates the number of cubes, which follow, one cube per line. Each line, which describes a cube, contains four integers. The first three integers are the x, y, and z coordinates of the corner of a cube, and the fourth integer is the positive distance, which the cube extends in each of the three directions (parallel to the x, y, and z axes) from that corner.

Following the data for the first set of cubes will be a number which indicates how many cubes are in a second set, followed by the cube descriptions for the second set, again one per line. Following this will be a third set, and so on. Your program should continue to process sets of cubes, outputting the volume of their intersections to the output file, one set per line, until a zero is read for the number of cubes.

Note that the data file will always contain at least one set of cubes, and every set will contain at least 2 and at most 1000 cubes. For any given set of cubes, the volume of their intersections will not exceed 1,000,000 units.

Here is a sample input data file:
2
0 0 0 10
9 1 1 5
3
0 0 0 10
9 1 1 5
8 2 2 3
0

This data file should produce the following output file:
25
9