HZNUOJ

Fermat vs. Pythagoras

Tags:
Time Limit:  1 s      Memory Limit:   128 MB
Submission:10     AC:8     Score:99.54

Description

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 tex2html_wrap_inline29 for n > 2.

Given a positive integer N, you are to write a program that computes two quantities regarding the solution of

displaymath22

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< z, and they are relatively prime, i.e., have no common divisor larger than 1. You are also to compute the number of values tex2html_wrap_inline51 such that p is not part of any triple (not just relatively prime triples).

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 1,000,000. Input is terminated by end-of-file.

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 tex2html_wrap_inline57 ). The second number is the number of positive integers tex2html_wrap_inline57 that are not part of any triple whose components are all tex2html_wrap_inline57 . There should be one output line for each input line.

Samples

input
10 25 100
output
1 4 4 9 16 27