Count Square Sum Triples

You are given an integer n, and your task is to count all ordered triples (a, b, c) such that:

• a, b, and c are integers within the range 1 to n

• They satisfy the Pythagorean-like condition:

$$a^2 + b^2 = c^2$$

Every valid order counts separately, meaning (a, b, c) and (b, a, c) are treated as different triples if both satisfy the condition.

Return the total number of such triples.