--- Day 24: Never Tell Me The Odds ---

A set of objects have positions and velocities in 3D space, noted as `x, y, z @ Δx, Δy, Δz`, e.g.

19, 13, 30 @ -2,  1, -2
18, 19, 22 @ -1, -1, -2
20, 25, 34 @ -2, -2, -4
12, 31, 28 @ -1, -2, -1
20, 19, 15 @  1, -5, -3

Ignoring the Z axis, which objects will intersect _in future_ within a given bounding box.

For example, with the box 7,7 to 27,27 and the objects above:

Object A: 19, 13, 30 @ -2, 1, -2
Object B: 18, 19, 22 @ -1, -1, -2
Objects' paths will cross inside the test area (at x=14.333, y=15.333).

Object A: 19, 13, 30 @ -2, 1, -2
Object B: 20, 25, 34 @ -2, -2, -4
Objects' paths will cross inside the test area (at x=11.667, y=16.667).

Object A: 19, 13, 30 @ -2, 1, -2
Object B: 12, 31, 28 @ -1, -2, -1
Objects' paths will cross outside the test area (at x=6.2, y=19.4).

Object A: 19, 13, 30 @ -2, 1, -2
Object B: 20, 19, 15 @ 1, -5, -3
Objects' paths crossed in the past for Object A.

Object A: 18, 19, 22 @ -1, -1, -2
Object B: 20, 25, 34 @ -2, -2, -4
Objects' paths are parallel; they never intersect.

Object A: 18, 19, 22 @ -1, -1, -2
Object B: 12, 31, 28 @ -1, -2, -1
Objects' paths will cross outside the test area (at x=-6, y=-5).

Object A: 18, 19, 22 @ -1, -1, -2
Object B: 20, 19, 15 @ 1, -5, -3
Objects' paths crossed in the past for both Objects.

Object A: 20, 25, 34 @ -2, -2, -4
Object B: 12, 31, 28 @ -1, -2, -1
Objects' paths will cross outside the test area (at x=-2, y=3).

Object A: 20, 25, 34 @ -2, -2, -4
Object B: 20, 19, 15 @ 1, -5, -3
Objects' paths crossed in the past for Object B.

Object A: 12, 31, 28 @ -1, -2, -1
Object B: 20, 19, 15 @ 1, -5, -3
Objects' paths crossed in the past for both Objects.



Look for future intersections that happen with an X and Y position each at least 200000000000000 and at most 400000000000000. Disregard the Z axis entirely.

Note: Some objects are moving upwards.