\clearpage
\section{Problem: Fermat v. Pythagoras}

\subsection*{Background}
Computer generated and assisted proofs and verification occupy a small
niche in the realm of Computer Science.  The first proof of the
four-color problem was completed with the assistance of a computer
program and current efforts in verification have succeeded in verifying
the translation of high-level code down to the chip level.

This problem deals with computing quantities relating to part of
Fermat's Last Theorem: that there are no integer solutions of $a^n + b^n
= c^n$ for $n > 2$. 


\subsection*{The Problem}
Given a positive integer $N$, you are to write a program that computes two
quantities regarding the solution of
\begin{displaymath}
x^2 + y^2 = z^2
\end{displaymath}
where $x$, $y$, and $z$ are constrained to be positive integers
less than or equal to $N$.   You
are to compute the number of triples $(x,y,z)$ such that $x$, $y$,
and $z$ are relatively prime, i.e., have no common divisor larger than
1.  You are also to compute the number of values $0 < p \leq N$ such that
$p$ is not part of any triple (not just relatively prime triples).

\subsection*{The Input}
The input consists of a sequence of positive 
integers one per line.  Each integer
in the input file will be less than or equal to 1,000.  Input is
terminated by end-of-file.


\subsection*{The Output}
For each integer $N$ in the input file print two integers separated by a
space.  The first integer is the number of relatively prime triples
(such that each component of the triple is $\leq N$).  The second number
is the number of postive 
integers $\leq N$ that are not part of any triple whose
components are all $\leq N$.  There should be one output line for each
input line.

\subsection*{Sample Input}
\begin{verbatim}
10
25
100
\end{verbatim}


\subsection*{Sample Output}
\begin{verbatim}
1 4
4 9
16 27
\end{verbatim}