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 \textbf{a^n} + \textbf{b^n} = \textbf{c^n} for \textbf{n} > \textbf{2}. Given a positive integer \textbf{N}, you are to write a program that computes two quantities regarding the solution of \textbf{x^2} + \textbf{y^2} = \textbf{z^2}, where \textbf{x}, \textbf{y}, and \textbf{z} are constrained to be positive integers less than or equal to \textbf{N}. You are to compute the number of triples (\textbf{x}, \textbf{y}, \textbf{z}) such that \textbf{x} < \textbf{y} < \textbf{z}, and they are relatively prime, i.e., have no common divisor larger than \textbf{1}. You are also to compute the number of values \textbf{0} < \textbf{p} ≤ \textbf{N} such that \textbf{p} is not part of any triple (not just relatively prime triples). \InputFile 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 \textbf{1000000}. Input is terminated by end-of-file. \OutputFile For each integer \textbf{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 ≤ \textbf{N}). The second number is the number of positive integers ≤ \textbf{N} that are not part of any triple whose components are all ≤ \textbf{N}. There should be one output line for each input line.