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.

![img](/data/images/blog/p085.gif)

However, there are up to three "shortest" path candidates for any given cuboid and 
the shortest route doesn't always have integer length.

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`.

Find the least value of M such that the number of solutions first exceeds one million.