Given that the positive integers, x, y, and z, are consecutive terms of an arithmetic progression, the least value of the positive integer n, such that the equation x^2 - y^2 - z^2 = n has exactly two solutions, is n = 27:

34^2 - 27^2 - 20^2 = 12^2 - 9^2 - 6^2 = 27

It turns out that n = 1155 is the least value which has exactly ten solutions.

How many values of n less than one million have exactly ten distinct solutions?

The Number Theory Library (NTL) may be useful for mapping out a brute-force solution; however, your final solution should be a bit more elegant, as a brute-force approach would be highly inefficient.

(This problem came from Project Euler).