A spider, S, sits in one corner of a cuboid room, measuring 6 by 5 by 3, and a fly, F, sits in the opposite corner. By travelling on the surfaces of the room the shortest "straight line" distance from S to F is 10 and the path is shown on the diagram.
<imgclass="img-responsive center-block"alt="a diagram of a spider and fly's path from one corner of a cuboid room to the opposite corner"src="https://cdn-media-1.freecodecamp.org/project-euler/cuboid-route.png"style="background-color: white; padding: 10px;">
It can be shown that there are exactly 2060 distinct cuboids, ignoring rotations, with integer dimensions, up to a maximum size of M by M by M, for which the shortest route has integer length when M = 100. This is the least value of M for which the number of solutions first exceeds two thousand; the number of solutions when M = 99 is 1975.