# Pythagoras's Revenge

# 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`

. It is also well known that there exist some right triangles in which all three side lengths are integral, such as the classic:^{2}

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`

). The end of the input is designated by a line containing the value ^{20}**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.

3 12 2 1048574 1048575 0

1 2 0 1 175