Pythagoras's Revenge
The famous Pythagorean theorem states that a right triangle, having side lengths A and B and hypotenuse length C, satisfies the formula A^2 + B^2 = C^2. It is also well known that there exist some right triangles in which all three side lengths are integral, such as the classic:
Further examples, both having A = 12, are the following:
The question is, given a fixed integer value for A, how many distinct integers B > A exist such that the hypotenuse length C is integral?
Input
Each line contains a single integer A (2 ≤ A < 1048576 = 2^20). The end of the input is designated by a line containing the value 0.
Output
For each value of A, output the number of integers B > A such that a right triangle having side lengths A and B has a hypotenuse with integral length.