## Diophantine reciprocals II

### Problem 110

In the following equation `x`, `y`, and `n` are positive integers.

1 x |
+ | 1 y |
= | 1 n |

It can be verified that when `n` = 1260 there are 113 distinct solutions and this is the least value of `n` for which the total number of distinct solutions exceeds one hundred.

What is the least value of `n` for which the number of distinct solutions exceeds four million?

NOTE: This problem is a much more difficult version of Problem 108 and as it is well beyond the limitations of a brute force approach it requires a clever implementation.