P17463 Iridescence / PYTRIP4

This problem is an enhanced version of [SPOJ PYTRIP3](https://www.spoj.com/problems/PYTRIP3/).

Given a positive integer $N$. Find the number of distinct right triangles whose hypotenuse length is at most $N$, and whose three side lengths are all integers.

One line containing one positive integer $N$.

One line containing one non-negative integer, representing the answer.

For all testdata, $1\le N\le 31415926535897\approx 3.14\times 10^{13}$. The time limit is about $1.5$ times the running time of the standard solution on the slowest case. Translated by ChatGPT 5